Energy Geotechnics 978-1-315-31524-9

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COPYRIGHT © 2016 TAYLOR and FRANCIS GROUP, LONDON, UK

CRC PRESS / BALKEMA - PROCEEDINGS AND MONOGRAPHS IN ENGINEERING, WATER AND EARTH SCIENCES WWW.CRCPRESS.COM, WWW.TAYLORANDFRANCIS.COM

ISBN 978-1-138-03299-6

Energy Geotechnics Editors: Frank Wuttke, Sebastian Bauer and Marcelo Sánchez

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Committees

INTERNATIONAL ADVISORY BOARD Tony Amis (UK) Malek Bouazza (Australia) Leonardo Cabral (Brazil) Gye-Chun Cho (Korea) Yu-Jun Cui (France-China) Pierre Delage (France) Antonio Gens (Spain) Leonardo Guimaraes (Brazil) Jacco Haasnoot (Netherlands) Tomasz Hueckel (US) Lyesse Laloui (Switzerland) M. R. Lakshmikantha (Spain) John McCartney (US) Guillermo Narsilio (Australia) Duncan Nicholson (UK) Guney Olgun (US)

Fernando Pardo (Spain) Jean-Michel Pereira (France) Enrique Romero (Spain) Marcelo Sánchez (US) Tom Schanz (Germany) Kenichi Soga (UK) J. Carlos Santamarina (US) Anh Minh Tang (France) Hywel Thomas (UK) Ivan Verdugo (Colombia) Thomas Vienken (Germany) Peter Bourne-Webb (Portugal) Frank Wuttke (Germany) Tae Sup Yun (Korea) Dietmar Adam (Austria)

NATIONAL TECHNICAL PROGRAM COMMITTEE Frank Wuttke, Kiel University, Germany Sebastian Bauer, Kiel University, Germany Andreas Dahmke, Kiel University, Germany Tom Schanz, RU Bochum, Germany Rolf Katzenbach, TU Darmstadt, Germany Ernst Huenges, GFZ Potsdam, Germany Olaf Kolditz, UFZ Leipzig, Germany Stavros Savidis, TU Berlin, Germany Dietmar Adam, TU Wien, Austria MINISYMPOSIA ORGANIZERS Dietmar Adam (TU Wien, Austria) and Malek Bouazza (Monash University, Australia) – Minisymposium thermo-active foundations, tunnels and earth-coupled structures Marcelo Sánchez (Texas A & M University, USA) and Christian Deusner (GEOMAR, Germany) – Minisymposium geomechanical characterization and modeling of hydrate bearing sediments David M.J. Smeulders (Eindhoven University of Technology, The Netherlands) and Sebastian Bauer & Frank Wuttke (Kiel University, Germany) – Minisymposium trends and challenges in energy geotechnical storage systems and materials Robert Charlier (Université de Liège, Belgium) and Bertrand François (Université Libre de Bruxelles, Belgium) – Minisymposium shallow geothermal systems Pierre Duffaut (French Committee on Rock Mechanics) – Minisymposium geotechnics risk and items for underground nuclear power plants Enrique Romero (Universitat Politècnica de Catalunya UPC, Spain), Xiangling Li (European Underground Research Infrastructure for Disposal of Nuclear Waste In Clay Environment EIG EURIDICE, Belgium) and Paul Marschall (Nationale Genossenschaft für die Lagerung Radioaktiver Abfälle NAGRA, Switzerland) – Minisymposium geotechnics for nuclear waste disposal

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CONFERENCE ORGANIZATION AND TECHNICAL ENQUIRIES Henok Hailemariam, Hem Motra and Frank Wuttke Geomechanics and Geotechnics Kiel University, Germany

LIST OF REVIEWERS Malek Bouazza Dietmar Adam Christian Deusner Marcelo Sánchez Sebastian Bauer Frank Wuttke Robert Charlier Bertrand François David M.J. Smeulders

Enrique Romero Pierre Duffaut Paul Marschall Xiangling Li Henok Hailemariam Zarghaam H. Rizvi Dinesh Shrestha Amir S. Sattari

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Preface

The 1st International Conference on Energy Geotechnics (ICEGT 2016) was held from 29th to 31st August 2016, at the University of Kiel, Kiel, Germany. This was the first conference under the guidance of the International Society for Soil Mechanics and Geotechnical Engineering (ISSMGE) TC308 on Energy Geotechnics. With the increasing energy demand and climate change implications, the development of sustainable energy systems based on integrated schemes of energy production, transport, and transfer as well as energy storage is of the utmost importance. This issue is of increasing interest to the research field of geotechnical engineering. The focus of this relatively new research area is new developments and solutions for civil, environmental, and industrial applications. The behaviour of geomaterials (i.e. soils and rocks) when subjected to thermo-hydro-mechanical and chemical solicitations is generally very complex. Their response is also strongly influenced by, shape, size and mineralogy of the aggregates, as well as, by the type of loading and porosity. The ability of these materials to store and dissipate energy is of great importance to energy transportation and storage systems. Beside the understanding of the material behaviour, the study and development of energy geo-structure as well the multiphysics interaction behaviour becomes of highest importance too. The aim of the conference was to provide a wide platform for the interaction among colleagues from different countries working in different subjects, and playing different roles in the energy sector. The discussions focused on past, present and future investigations & practices in the area of energy geotechnics, covering from experimental up to numerical and fundamental studies. This proceedings consists of 97 peer reviewed papers from engineers and researchers, investigations and reporting from their findings. The editors wish that this proceedings acts as a stack of knowledge for the frontier of Energy Geotechnics. Frank Wuttke Chairman of the ICEGT 2016 Head of Geomechanics and Geotechnics Kiel University

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Sponsors

ORGANIZING INSTITUTION Kiel University, Germany

ORGANIZING ASSOCIATION ISSMGE TC 308 on Energy Geotechnics

SPONSORS Fugro Consult GmbH, Germany (Platin-Sponsor)

APS Antriebs-, Prüf- und Steuertechnik GmbH, Germany (Gold-Sponsor)

SUPPORTING AUTHORITIES Business Development and Technology Transfer Corporation of SchleswigHolstein, Germany

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Acknowledgements

We would like to thank GEOMAR Helmholtz Centre for Ocean Research (Kiel, Germany), Andre Lindhorst (Pur.pur, Kiel, Germany), Dietmar Adam (TU Wien, Austria) and Stiftung OFFSHORE-WINDENERGIE (Berlin, Germany) for providing us with the photos used on the conference webpage as well as on the front book cover. We would also like to thank Henok Hailemariam (Kiel University, Kiel, Germany) for his outstanding organizational work in the ICEGT 2016.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Potential of district-scale geothermal energy in urban cities K. Soga, Y. Zhang & R. Choudhary University of Cambridge, Cambridge, UK

ABSTRACT: Ground source heat pumps (GSHPs) is a shallow geothermal system of pumping heat from or to the ground to supply low carbon heating or cooling to buildings. The underground becomes a heart storage and combination of heating and cooling can be beneficial to system efficiency improvement and temperature balance underground. In this study, a GIS based simulation tool was developed to quantify how many GSHPs could be installed at a district or a city scale without losing control of ground thermal capacity, and to identify its contribution to both heating and cooling demands of buildings. The City of Westminster, London was selected as a case study. Results show that many buildings (more than 50%) can install enough boreholes to support their own heating and cooling demands. For high-rise buildings and the high people density infrastructures, the limited space for geothermal energy extraction is a concern for geothermal applications. As domestic buildings have more space to install boreholes and thus to obtain more energy from underground, residential houses can share their surplus geothermal energy with commercial buildings and urban infrastructure at city scale. Parametric analysis was carried out to investigate the influence of district size for sharing a GSHP network at city scale.

1

INTRODUCTION

utilise the heat convection mechanism of groundwater flow by extracting heated or cooled water. Vertical GSHPs are normally constructed by placing two smalldiameter polyethylene tubes in a vertical borehole (typically 150 m deep), which horizontal GSHPs are placed in narrow trenches and this design requires greater amount of ground area. The vertical GSHPs are commonly chosen for urban areas because they need relatively small plots of space; contact with the soil that varies little in temperature and thermal properties; consume the smallest amount of pipe and pumping energy; and can yield the most efficient performance. For the existing buildings in urban areas, closed vertical loops are used due to space limitations and their system efficiency. Additional requirement for heat network is better to provide cooling as well. Cooling is playing an increasing part in comfort satisfactory in buildings, especially in the offices and other commercial buildings. The cooling demand is projected to grow further. The combination of heating and cooling can make district energy more economically attractive in the areas with a mix of land use buildings (DECC, 2012; DECC, 2013a). GSHP systems can match with this requirement. Not only is cooling supply a basic function for the GSHP system, but combination of heating and cooling can be also greatly beneficial to system efficiency improvement and temperature balance underground. The underground essentially becomes a heart storage. The benefits of GSHP systems also include low running cost, minimal maintenance cost and long life expectancy. Heat pump can be expected to use for

In the UK, £32 billion is spent on heating every year and the heat consumption accounts for approximately a third of total greenhouse gas emissions. As space heating accounts for about 66% of the domestic energy bills (DECC, 2013a) and delivers approximate 74% of the carbon dioxide emissions, the majority of heat related activities are from fossil fuel consumption in the domestic sector (DECC, 2012). Many countries which have similar situation encourage the adaptation of renewable energy technologies. As part of 2009 EUwide action to increase the use of renewable energy, the UK government has committed to set 15% renewable energy target by 2020. This is a significant rise compared with approximate 2% in 2008. It is traditionally considered that heat is generated on-site in individual buildings and the most common sources are electric heaters, gas boilers, and oil boilers. Ground source heat pumps (GSHPs) is a shallow geothermal system of pumping heat from or to the ground to supply low carbon heating or cooling to buildings. Shallow geothermal systems require no specific geological condition or high temperature gradient, so they are increasingly popular worldwide as an environmental friendly alternative to traditional technologies such as gas fired boilers (Haehnlein et al., 2010). GSHPs can be mainly grouped into two types, closed loops and open loops. In closed GSHP, borehole system achieves heat exchange through the circulation of fluid in a closed U-loop embedded within an infill medium. In contrast, open loop GSHP systems

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20–25 years and the borehole can be used as long as 100 years (Kensa Heat Pumps, 2014). In order to encourage the growth of this technology in the UK, Renewable Heat Incentive (RHI) classified the GSHP district heating into non-domestic tariff stream. The system is eligible to receive 8.7 pence per kWh heating consumption for as long as 20 years (DECC, 2013c). Although GSHP has been available for long time, their applications are generally limited to a small scale. If such ground source energy systems are employed at a larger scale to provide low carbon heating solutions to buildings and infrastructures, a low carbon city would be developed. According to the UK Environment Agency (2009), the total number of installed GSHP systems in the UK at the time of year 2009 was 8000, of which, there were only 300 open loops (3.75%) and the rest are closed loops (96.75%). There has only a very few works on evaluating the potential capacity and sustainability of shallow geothermal energy at a large scale. In this study, a GIS based simulation tool was developed to quantify the number of GSHPs that can be installed at a district or a city scale without losing control of ground thermal capacity, and to identify its contribution to both heating and cooling demands of buildings. Previously Zhang et al. (2014; 2015) used this model to the city of Westminster, London. Results show that more than 50% of the buildings can install enough boreholes to support their own heating and cooling demands. Although such large scale GSHP installations can approach long-term heating cost saving of up to 70% (Committee on Climate Change, 2013), it still requires more than 20 years for a general domestic home to get full cost-recovery. Hence more proactive effort to increase the adoption rate of GSHP is required from both commercial and regulatory sides. A small scale district heating/cooling system is an attractive solution to implement the low carbon energy utilization. For high-rise buildings and the high people density infrastructures, the limited space for geothermal energy extraction is a concern for geothermal applications. As domestic buildings have more space to install boreholes and thus to obtain more energy from underground, residential houses can share their surplus geothermal energy with commercial buildings and urban infrastructure at city scale. This paper extends the work of the authors (Zhang et al., 2014; 2015) by considering the potential of a shallow geothermal technology for district scale heating. 2

peak and an office building with day-time peaks, so that the heating load can be allowed to get balanced. According to the heat strategy of the UK government, provided they can be used to district heat from low carbon sources, heat networks can be the core and have great potential to play a key role in achieving targeted low carbon heat supply by 2050 (DECC, 2012). Although district heating has started since the 1950’s, the market penetration is still quite low. The typical district heating are university campuses, new inner city commercial buildings and urban infrastructures (DECC, 2013b). It is estimated that networks currently provide less than 2% of UK heat demand, including 1600 networks (DECC, 2013b) serving around 210,000 dwellings and 1700 commercial and public buildings across the UK (The Association for Decentralised Energy, 2015). This percentage is much lower than the average value of 10% in Europe. In some other parts of Europe, the district heating applications are much wider spread. In Denmark, Finland and Sweden, for example, the market shares are high to around 70%, 49% and 50%, respectively (DECC, 2012). In some countries, although the district heating contributes a low percentage at the nation scale, it makes a major supply in large cities. For example, district heating provides only 18% of total heat in Austria, but the percentage is doubled to be 36% for Vienna (Poyry, 2009). The potential estimated by DECC is to supply 14% of all homes in the UK by 2050 (DECC, 2012). There are currently many types of heat sources available. However, in order to achieve the Carbon Plan by 2050, low carbon intensive ways over long term are required by the government to heat the buildings relying on coal, oil, and even the natural gas (HM Government, 2011). In addition, DECC have also given further support to heat networks in the Renewable Heat Incentive Policy (DECC, 2013c). Moreover, Energy Company Obligation (ECO), a subsidy from energy suppliers, works alongside the Green Deal to provide energy-saving improvement for vulnerable households. The district heating has been considered as a primary measure (DECC, 2015). The Office of Gas and Electricity Markets (Ofgem) has recently confirmed the lifetime of GSHP district heating connections are 40 years under ECO (DECC, 2014). Unlike the single system, the heat pump used in the district system can be either a centralised system with a larger heat pump or a de-centralised system with multiples of smaller controlled heat pumps (DECC, 2012). In both of cases, the heat pumps should be connected to a communal ground array including one or more borehole heat exchangers (BHE) to collect energy from ground. In the design process of BHE, the coverage of the targeted area that receives energy supply should be firstly confirmed. The next step is to investigate all the geological site information and the building load information for design. With all these prepared work, the total required borehole length can be finally calculated. After determining the total required BHE length, the most important task before installation is

DISTRICT SCALE HEATING AND COOLING

A district heating network is either two or more distinct buildings connected to a single heat source or on building in which there are more than ten individual customers connected to a single heat source (DECC, 2013b). Heat networks are to transport heat to consumers through a network of insulated pipes. They are able to deliver heat to the areas with a mix of sources of demand such as a residential house with night-time

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to consider a borehole array for the reasonable district sharing. The array arrangement will decide what is the proportion of the total required length can be satisfied. Therefore, the borehole array and the size of the targeted district are the two key parameters to influence the capacity of a GSHP district system. 3 3.1

is the building design heating block load (W), qlc is the building design cooling block load (W), Rga is the effective thermal resistance of the ground in annual pulse (mK/W), Rgd is the effective thermal resistance of the ground in daily pulse (mK/W), Rgm is the effective thermal resistance of the ground in monthly pulse (mK/W), Rb is the thermal resistance of borehole (mK/W), tg is the undisturbed ground temperature (K), tp is the temperature penalty for interference of adjacent boreholes (K), twi is the liquid temperature at heat pump inlet (K), two is the liquid temperature at heat pump outlet (K), Wh is the power input at design heating load (W), and Wc is the power input at design cooling load (W). The GIS tool gives the output of the total required borehole length of GHE per building, which is the larger one of the results from Equations (1) and (2).The individual borehole length is set typically as 150 m, which is the common-used value in practice for vertical closed loop GSHP installations. The number of boreholes per building is then calculated based on these two length values. The land area may not be enough for the required number of boreholes for some buildings. In such cases, the maximum possible borehole length (the maximum borehole number × 150 m) for a land area is provided as input into the model. The model inversely calculates the maximum heating and cooling demands that can be provided by a GSHP system for that building. In this study, the GSHP capacity of a building is defined as the ratio of capacity to demand (C/D), and calculated by dividing the maximum possible number of boreholes within the building’s land area by the required borehole number. If the C/D ratio of a building is equal to or greater than 100%, both heating and cooling demands of this building could be satisfied by its own GSHP system.

CITY-SCALE GSHP SIMULATOR Background

The efficiency of a vertical GSHP system is highly dependent on correctly sizing the ground heat exchangers according to energy demand (Shonder and Hughes, 1998). In order to estimate the numbers of GSHPs that can be installed in specific areas of cities or districts, and the numbers that are required to satisfy heating demands, it is necessary to quantify the geothermal capacity using high-resolution information about land-use, underground conditions and heating/cooling demand. Zhang et al. (2014; 2015) developed a simulation tool that integrates, within a geographic information system (GIS), high-resolution land use datasets, heating/cooling demands of buildings, ground properties, and the ground heat exchanger (GHE) design calculations. A PYTHON code that estimates the size of GSHP required for a given heat demand of a building was developed and embedded into ArcGIS software, which is a widely used platform for spatial design and analysis. This integrated simulation tool has been used to quantify the exact geothermal capacity of specific areas. A brief overview of the tool is given in this section, but further details can be found in Zhang et al. (2014; 2015). Most current GHE design software packages refer to the Cylinder and Line Source Method, which has been found to be the most accurate model through comparisons with calibrated data from actual installations (Shonder and Hughes, 1998). The tool utilises the following heat transfer equation that determines the required vertical borehole length Lh for heating (Kavanaugh and Rafferty, 1997).

3.2

Case Study: The city of Westminster, London

The influence of switching the single system to the district network system on the GSHP satisfactory capacity at the city scale was investigated for the city of Westminster, London. The site specific or spatial inputs in the design calculation were firstly prepared for the case study, which were heating demand per building, cooling demand per building, thermal conductivity, thermal diffusivity, and ground temperature. In addition to the spatial data, related conditions and assumptions for the GSHP and the borehole are listed in Table 1. For the calculation of heating and cooling demands, UKMap, a GIS database, was used to obtain spatial information about buildings within the City of Westminster including building type, floor area and height. According to this database (see Figure 1), there are 95,817 buildings within this district. 83% of the floor area is made up of residences, offices, and retail. The remaining 17% includes hotels, schools, hospitals and leisure facilities (Choudhary, 2012). The intensity of heating and cooling demand per building type

The required vertical borehole length Lc for cooling is found using the following equation.

where Fsc is the short-circuit heat loss factor, PLF m is the part-load factor during design month, qa is the net annual average heat transfer to the ground (W), qlh

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Table 1. Conditions and assumptions in bhe design for planning parametric study. Parameter

Unit

Value

Justification

Coefficient of Performance (COP) Energy Efficiency Ratio (EER) Short-circuit Heat Loss Factor (Fsc ) Liquid Temperature at heat pump inlet for Heating (twi ) Liquid Temperature at heat pump outlet for Heating (two ) Liquid Temperature at heat pump inlet for Cooling (twi ) Liquid Temperature at heat pump outlet for Cooling (two ) Minimum Borehole Spacing Borehole Diameter

/

3.3

/

4.2

/

1.04

K

278.5

Kavanaugh and Rafferty, 1997 Kavanaugh and Rafferty, 1997 Kavanaugh and Rafferty, 1997 Chosen Design value

K

275.0

K

300.0

K

308.0

mm

52

/

25% Mono MIS (DECC, Ethylene 2008)a Gylcol

Pipe Diameter Thermal Conductivity of Pipe Pipe Centre-Pipe Centre Shank Spacing Thermal Transfer Fluid

Estimate based on typical temperature drop Chosen Design value

Figure 1. Land use type distributions of buildings in westminster.

Estimate based on typical temperature drop m 6 MIS (DECC, 2008)a mm 130 MIS (DECC, 2008)a mm 32 mm OD MIS (DECC, SDR-11 2008)a W/m.K 0.420 MIS (DECC, (PE 100) 2008)a

in east-west and north-south directions and 1 m in the vertical direction. In the case study, the average thermal property value within the depth of 150 m of each grid was estimated to develop the thermal conductivity and the thermal diffusivity maps of Westminster. For the ground temperature, the ground temperature of London was used. Headon et al. (2009) gave the underground temperature information of London city based on the well data as 12.3◦ C at 60 m depth, 12.8◦ C at 80 m depth and 13.1◦ C at 100 m depth. Accordingly, the ground temperature in the design was set to be 12.8◦ C, which was considered as the average ground temperature value within the depth of 150 m. Sizing Heat pump is a key intermediate step in the GHE design calculation. A database of heat pumps within capacity range of 5–75 kW is therefore also included within the model. If the required capacity is outside of this range, a combination of two or more heat pumps is used. In the design calculation, the temperature penalty tp is used as a parameter to consider thermal interference of adjacent boreholes with reasonable borehole arrangements. Hence, within the run time, there is temperature decrease surrounding the borehole, and the temperature reduction decreases with time as transient state. It is assumed that no heat is diffused out of a square cylinder with sides equal to the borehole separation distance (Kavanaugh and Rafferty, 1997).

MIS (DECC, 2008)a

a. MIS (Microgeneration Installation Standard), DECC (Department of Energy and Climate Change, UK) (2008).

(in kWh/m2 per year) was gathered from DECC certificates (compiled and released by the UK Centre for Sustainable Energy), Chartered Institution of Building Services Engineers Guide F and TM 46 (CIBSE, 2004, 2008) and 2011 energy distribution charts (EDCs).The design heating block load per building (qlh in kW) was estimated by multiplying the heating demand per building type in kWh/m2 per year with the floor area of a building and dividing by the number of heating hours in a year (2160 h in this case, assuming 12 h of heating per day for half the year). Cooling estimation is performed in the same way. The thermal conductivity and thermal diffusivity maps were developed based on the geological map and the thermal property look-up table. The soil distribution map of the City of Westminster was obtained from the British Geological Survey (BGS) geological map of London. For each type of soil, its thermal conductivity and thermal diffusivity were assigned according to the logs from site investigation work by BGS. A thermal conductivity map and a thermal diffusivity map were then developed with grids of size 50 m × 50 m

3.3 Borehole location scenarios In this case study, the required number of boreholes for each building was allocated at a spatial position. Two scenarios were considered: (a) under building (Figure 2a) – within the land-area of the existing building, and (b) around the building (Figure 2b) – on the buffer area with the building boundary as the midline. The shaped polygons and the points stand for the buildings and the installed boreholes, respectively. In order to avoid thermal interference, the spacing between any two boreholes was fixed at 6 metres, as per the MIS (DECC, 2008). This means that no heat is diffused

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Figure 3. Map of ratio of capacity to demand of westminster for heating and cooling (Scenario 1: Under buildings).

Figure 2. Borehole allocation map.

out of a square cylinder with sides equal to 6 metres with a reasonable temperature penalty. Outside this square cylinder, the ground temperature is assumed to be undisturbed. Scenario 1 is more suitable for new and refurbished buildings, but scenario 2 is more practical for existing buildings and can be achieved by using directional drilling at a shallow depth to the target borehole location followed by drilling vertically downwards. In these two cases, the permitted areas for locating the boreholes are different, and thus the maximum number of boreholes that can be installed for each building also varies. In scenario 2, boreholes are installed in a buffer area that is within 3 meters of the edges of a building, both away from and under it. The installation area can be changed in the model to correspond to more restrictions, such as pavements and parking areas. The ratio of capacity to demand (C/D) is calculated by dividing the maximum possible number of boreholes within the building’s land area by the required borehole number for the heating and cooling demand. Figure 3 shows the map of the C/D ratio for Scenario 1, whereas Figure 4 shows the map for Scenario 2. Green colour represents the buildings that have a large enough land area to support their own heating and cooling demands. Red represents buildings that can support less than 50% heating demand due to their small land area. The rest buildings with ratio in the range from 50% to 100% are indicated by the yellow colour. In Scenario 1, 51% of buildings can meet their own heating and cooling requirements. Such buildings are generally found at the edges of built-up areas. In Scenario 2, 67% of the buildings have enough land area for a GSHP system to cover their heating and cooling demands. Buildings that can support less than 50% of their heating demand are concentrated in the centre of Westminster. The main reason that such a

Figure 4. Map of ratio of capacity to demand of westminster for heating and cooling (Scenario 2: Around buildings).

high proportion of buildings are capable of meeting their own demands is that, for the total 95,817 buildings in Westminster, 77,355 buildings have 5 floors or fewer (80.7%), 17,638 buildings have 6–10 floors (18.4%) and only 824 buildings have more than 10 floors (0.87%). Most of the low rise (5 floors or fewer) buildings can meet their own heating demands by GSHP only since the typical heating demand for these buildings is only around 40 W/m2 . The difference between the two scenarios is mainly the result of the presence of many long, narrow buildings in Westminster. For these buildings, more land area is available for borehole installation around them than underneath them. In contrast, buildings in the central area cover larger areas, and so they could have more boreholes installed under the buildings. The detailed discussion of this particular result can be found in Zhang et al. (2014; 2015). Under both scenarios, not all the buildings have GSHP capacity greater than 100%. However, if boreholes can be shared with neighbours who have surplus geothermal capacity, then such district scale GSHP system has the potential to meet the heating and cooling demands of all buildings within this area, which is the main objective of the study presented in this paper.

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4 4.1

DISTRICT SCALE NETWORK Background

A district heating network is either two or more distinct buildings connected to a single heat source or on building in which there are more than ten individual customers connected to a single heat source. The network size is also defined on the basis of the number of domestic and non-domestic customers connected to the heat source. These are large networks (500 or more residential properties and/or more than 10 non-domestic users); Medium networks (between 100 and 500 residential properties and/or between 3 and 10 non-domestic users; and Small networks (less than 100 residential properties and/or less than 3 non-domestic users). Currently in the UK, the small size networks take the predominant position, occupying 75% of the total 1765 individual district heating networks. The average number of the dwellings per network is 35.The medium and the large sizes share the rest proportions, which are 20% and 5%, respectively (DECC, 2013b). For the GSHP district heating, the size can range from micro to macro scale. With this linking together, the capital cost can be reduced due to smaller number of deeper boreholes and the borehole location can be more flexible. Moreover, residential houses can share their surplus geothermal energy with commercial buildings and urban infrastructure at a large scale to achieve a low carbon city. In addition, for the residential houses, more tariff benefits from switching to a district network can be received because the eligible incentive scheme can change from the domestic to the non-domestic. The domestic scheme offers 19.1 pence per kWh renewable energy consumption for 7 years (DECC, 2013d) and the non-domestic one provides 8.84 pence per kWh energy consumption for 20 years (DECC, 2013c). According to the results of investigating the GSHP capacity at city-scale for Westminster, the C/D ratios are not evenly distributed. If district planning can be introduced to play a role, the buildings with high C/D ratios will achieve to share their surplus capacities with neighbours, so that more heating and cooling demands in this area will be satisfied. An analysis needs here to prove if district sharing can truly increase the proportion of high C/D ratios and also to investigate what is the influence of district size on the GSHP capacity at city scale. 4.2

Figure 5. Grids for dividing westminster into districts.

Figure 6. C/D ratio frequency distribution with various district sizes for scenario 1.

one district by itself. For all the cases, it was assumed that, no matter how large the district was, the network was able to achieve the perfect energy sharing and supplying. The C/D ratio of one district (or one grid) was calculated by dividing the total maximum borehole number allowed by the whole available installation space by the total required borehole number satisfying all the heating and cooling demands within this district. The C/D ratio frequency distributions for all the cases with various district sizes were estimated and compared for the parametric analysis. 4.3 Results Figure 6 shows the C/D ratio frequency distributions with various district sizes under Scenario 1 (Borehole under Buildings). The values on the horizontal axis demonstrate the district size. For example, GS50 means grid size of 50 m × 50 m. Figure 7 shows spatial distributions of C/D ratio with district size of 50 m under Scenario 1. In Figures 6 and 7, green colour indicates the ratio of 100% or more, which means the heating and cooling demand can be fully satisfied by its own capacity. Yellow colour and red colour stand for 50%–100% and 0%–50%, respectively. In the case of GS0, the largest proportion of around 50% is taken by the green colour and the smallest percentage of approximately 15% is yellow. In the case of Whole, the C/D ratio value representing the GSHP capacity of the one whole Westminster district network is in the yellow colour. It can be seen that C/D ratio distribution changes gradually from GS0 to Whole. The most significant difference in the C/D ratio distribution occurs at the beginning, where the grid size is

Parametric study on district network scale

In this analysis, the whole Westminster was divided into grids, which were uniform in the size (see Figure 5). Each grid was considered to be one district. There were 13 cases with various grid sizes for comparison analysis. The grid sizes were set to be 0 m, 50 m, 100 m, 200 m, 300 m, 400 m, 500 m, 600 m, 700 m, 1000 m, 1500 m, 2000 m and a Whole. Among these, ‘0 m’ stood for that there was no district sharing, and ‘a Whole’stood for an extreme case that Westminster was

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Figure 7. Spatial distributions of C/D ratio with district size of 50 m for scenario 1.

Figure 9. Spatial distributions of C/D ratio with district size of 50 m for scenario 2.

red colour proportion, which stands for the C/D ratio less than 50%, is slowly reduced. Therefore, GS50 is considered to be an optimal network size for enhancing GSHP capacity at the city scale for Westminster. The GSHP district network of this size, 50 m × 50 m, can greatly improve the C/D ratio distribution and also practical to achieve with considerations of the construction feasibility and the capital cost. Around 20% of buildings in Westminster are highrise with more than five floors and it is highly difficult to satisfy them with GSHP. With building district networks, more and more low-rise buildings can share their capacities with high-rise ones. However, for the gathering place of high-rise buildings, no surplus energy from surrounding low-rise buildings can be provided any more. Therefore, within a certain range of district size, enlarging the size has quite slight effect on the C/D ratio distribution. This can be an issue for the megacities, for example, the city of Westminster in this study. Compared with continuing increasing the district size, keeping the district size of GS50 and introducing supplementary energy sources are considered to be more cost-effective.

Figure 8. C/D ratio frequency distribution with various district sizes for scenario 2.

enlarged from GS0 to GS50. After this, the C/D ratio distribution changes more gently. Figure 8 shows the C/D ratio frequency distributions with various district sizes under Scenario 2 (Borehole around Buildings). In the case of GS0, green, yellow and red take account for 67%, 15% and 14%, respectively. Followed by a gradual change, all the 98% turns to green in the case of Whole.Among the changing procedure, the most significant step is at the very beginning, where the size increases from GS0 to GS50. According to Figure 9, which shows spatial distributions of C/D ratio with district size of 50 m under Scenario 2, very small percentages of grids are in the red colour and most of the districts can be fully satisfied as they have enough space to install the required boreholes. In addition, the change from GS2000 to Whole is also great as the green proportion increases from around 75% to 98%. However, the improvement from GS50 to GS2000 is very gentle and every time of size growth can only lead to a slight change. For the city of Westminster, it can be found that C/D ratio distributions under Scenarios 1 and 2 have similar variation trends with the grid size. Both of them change gradually from the distribution in the condition of no district sharing (GS0) to the C/D ratio in the condition that Westminster is one large district network (Whole). However, the influence of district size variation is greater under Scenario 1 than Scenario 2 because the difference between GS0 and Whole is larger under Scenario 1. In addition, under both scenarios, the most significant change due to increasing the grid size occurs from GS0 to GS50.After GS50, the

5

CONCLUSIONS

Vertical closed loop GSHP system can be an environmental friendly application for supplying heating and cooling in the urban areas. In this paper, a cityscale simulation tool developed by Zhang et al. (2014; 2015) was used to identify how many GSHPs could be installed in a district without overusing geothermal energy and to calculate the ratio of its contribution to the heating and cooling demands of buildings.The City of Westminster was selected as a case study. Two scenarios for borehole installations (‘under buildings’and ‘around buildings’) were examined and the borehole allocation maps and C/D ratio distribution maps were generated. Results show that many buildings (51% for Scenario 1 and 67% for Scenario 2) can install enough boreholes to support their own heating and cooling demands. There is a high proportion of C/D ratios (the

9

ratio of capacity to demand) over 100%, which means a great number of houses and buildings have enough space to install GSHP and thus to fully satisfy their own heating demands. However, the C/D ratios are not evenly distributed due to various heating demands and available spaces. If district heating can be introduced to play a role, the buildings with high C/D ratios will achieve to share their surplus capacities with neighbours, so that more heating demands in this area will be satisfied. Following the work of Zhang et al. (2014; 2105), parametric analysis was carried out to investigate the influence of planning parameters on the application of GSHP systems for heating and cooling at city scale for a case study of Westminster, London. The district network is encouraged by the government for improving energy utilization and reducing carbon emissions. The influence of district size for sharing a GSHP network on the C/D ratio distribution at city scale was investigated. It was found that C/D ratio distributions under Scenarios 1 and 2 have similar variation trends with the grid size. Both of them change gradually from the distribution in the condition of no district sharing (GS0) to the C/D ratio in the condition that Westminster is one large district network (Whole). Under both of scenarios, the most significant change due to increasing the grid size occurs from GS0 to GS50 (50 m × 50 m grid). After GS50, the red colour proportion is slowly reduced. GS50 is considered to be an optimal network size for enhancing GSHP capacity at the city scale for Westminster. Compared with continuing increasing the district size, taking the district size of GS50 and using supplementary energy sources for the unsatisfied districts are considered to be more costeffective.

Department of Energy and Climate Change (DECC). 2013b. Summary evidence on District Heating Networks in the UK. London, UK. Department of Energy and Climate Change (DECC). 2013c. Renewable Heat Incentive: Non-Domestic Scheme Early Tariff Review. London, UK. Department of Energy and Climate Change (DECC). 2013d. Domestic Renewable Heat Incentive: the first step towards transforming the way we heat our homes. London, UK. Department of Energy and Climate Change (DECC). 2012. The Future of Heating: A strategic framework for low carbon heat in the UK. London, UK. Department of Energy and Climate Change (DECC). 2008. Microgeneration Installation Standard:MIS 3005 Issue 3.0. London,UK. Environment Agency. 2009. Ground Source heating and cooling pumps-state of play and future trends. Bristol, UK. Haehnlein, S., Bayer, P. & Blum, P. 2010. International legal status of the use of shallow geothermal energy. Renewable and Sustainable Energy Reviews. 14(9), 2611–2625. Headon J., Banks D., Waters A. & Robinson V.K. 2009. Regional distribution of ground temperature in the Chalk aquifer of London, UK. Quarterly Journal of Engineering Geology and Hydrogeology, 42, 313–323. HM Government. 2011.The Carbon Plan: Delivering our low carbon future. Presented to Parliament pursuant to Section 12 and 14 of the Climate Change Act 2008. London, UK. Kavanaugh S.P. & Rafferty K. 1997. Ground-Source Heat Pumps Design of Geothermal Systems for Commercial and Industrial Buildings. 1997 American Society of Heating. USA. Puttagunta S., Aldrich R.A., Owens D. & Mantha P. 2010. Residential Ground-Source Heat Pumps: In-Field System Performance and Energy Modeling. GRC Transaction, 34, 941–948. Kensa Heat Pumps. 2014. Ground Source District Heating. www.kensaengineering.com. The Association for Decentralised Energy. 2015. District heating sector: A step ahead on protecting heat customers. http://www.theade.co.uk/district-heating-sector– a-step-ahead-on-protecting-heat-customers_3016.html POURY. 2009. The potential and costs of district heating networks, A report to the Department of Energy and Climate Change. Schwencke A.B. 2013.Analysis and modelling of deep energy wells. Master’s thesis. Norwegian University of Science and Technology. Department of Energy and Process Engineering. Svendson P. 2008. A heat exchange module, in particular for a ground source heat pump. EP. WO2008009289A1. 24/01/2008. Synergy boreholes and systems Ltd. 2015. Geothermal Boreholes. http://www.synergyboreholes.co.uk/geothermal_ boreholes/ Shonder, J.A. & Hughes, P.J. 1998. Increasing confidence in geothermal heat pump design methods. In: Stiles L, editors. 2nd Stocjton Geothermal Conference, pp. 41–57. The GeoInformation Group Ltd. 2010. UK Map USER GUIDE Version 4.0 February 2010.UK. ZhangY., Soga K. & Choudhary R. 2014. Shallow geothermal energy application with GSHPs at city scale: study on the City of Westminster. Geotechnique Letters, 4, 125–131. Zhang, Y., Choudhary, R. and Soga, K. (2015) “Influence of GSHP System Design Parameters on the Geothermal Application Capacity and Electricity Consumption at City Scale for Westminster, London,” Energy and Buildings, 106, 3–12.

REFERENCES Banks D. 2012. An Introduction to Thermogeology, 2nd ed., Wiley-Blackwell. British Geological Survey. 2011. Temperature and Thermal Properties (Detailed). GeoReports. London, UK. CIBSE. 2008. Energy benchmarks: Technical memorandum 46, Technical Report, 2008. CIBSE. 2004. Cibse guide F: Energy efficiency in buildings, Technical Report, CIBSE; 2004. Choudhary, R. 2012. Energy analysis of the non-domestic building stock of Greater London. Building and Environment, 51, 243–254. Committee on Climate Change. 2013. Fourth Carbon Budget Review-technical report. Chapter 3: Reducing emissions from buildings. London, UK Department of Energy and Climate Change (DECC). 2015. Policy paper 2010 to 2015 government policy: household energy. London, UK. Department of Energy and Climate Change (DECC). 2014. The Future of the Energy Company Obligation. London, UK. Department of Energy and Climate Change (DECC). 2013a. The Future of Heating: Meeting the challenge. London, UK.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Multiphysical phenomena and mechanisms involved with energy piles Lyesse Laloui & Alessandro F. Rotta Loria Swiss Federal Institute of Technology in Lausanne, EPFL, Laboratory of Soil Mechanics, LMS, Lausanne, Switzerland

ABSTRACT: This study proposes an analysis of the multiphysical phenomena and mechanisms governing the thermo-mechanical behaviour of energy piles. The analysis is based on the results of a series of full-scale in-situ tests, laboratory experiments and numerical analyses. First, the thermo-mechanical behaviour of energy piles is considered. Attention is given to both single and groups of energy piles. Next, the response of soils and concrete-soil interfaces subjected to temperature changes is reviewed. The behaviours of clayey soils in different overconsolidation states as well as of both concrete-sand and concrete-clay interfaces are analysed. Finally, aspects considered of paramount importance for the analysis and design (e.g., geotechnical, structural and energy) of energy piles are presented. Both floating and end-bearing energy piles are investigated. The goal of this paper is to increase the confidence of civil engineers on the performance of energy piles.

1

INTRODUCTION

obtained through laboratory experiments dealing with oedometric tests (Di Donna and Laloui, 2015) and concrete-soil interface shear tests (Di Donna et al., 2015) under non-isothermal cyclic conditions are proposed for this aim. Finally, aspects considered of paramount importance for the analysis and design of energy piles are presented. Results of finite element analyses devoted to analyse the geotechnical and structural performance of single (Rotta Loria et al., 2015) and groups (Rotta Loria and Laloui, 2016) of energy piles as well as to investigate the energy performance (Batini et al., 2015) of these foundations are presented for this purpose.

Geothermal heat exchanger piles, often referred to as energy piles, are foundations equipped with absorber pipes with a heat carried fluid circulating into them that exchange heat with the surrounding ground. The temperature variations associated to the geothermal operations of these foundations bring new challenges to geotechnical and structural engineers. Thermal expansions and contractions of these elements and the surrounding soil, with associated variations of the stress and displacement fields in these media, are examples of such challenges. These phenomena must be kept within acceptable limits to ensure an adequate serviceability performance (e.g., mechanical) of the energy piles. This paper proposes insights into the analysis of the various challenges associated to the geothermal and structural support operations of energy piles. In particular, it proposes an analysis of the multiphysical phenomena and mechanisms governing the thermomechanical behaviour of these foundations. The analysis is based on the results of a series of full-scale in-situ tests, laboratory experiments and numerical analyses performed at the Swiss Federal Institute of Technology in Lausanne (EPFL), Switzerland. The goal of this paper is to increase the confidence of civil engineers on the performance of energy piles, looking at their increasing worldwide diffusion. First, the thermo-mechanical behaviour of energy piles is considered. The results of in-situ tests carried out on single (Laloui et al., 2003) and groups (Rotta Loria and Laloui, 2016) of real-scale energy piles are summarised for the considered purpose. Next, the response of soils and concrete-soil interfaces subjected to temperature changes is reviewed. Data

2 THERMO-MECHANICAL BEHAVIOUR OF ENERGY PILES 2.1

Single energy piles

A full-scale in-situ test was performed by Laloui et al. (2003) to investigate the thermo-mechanical behaviour of single energy piles. 2.1.1 The foundation and site A four-storey building under construction at the EPFL was chosen for this in-situ test. The structure (cf., Figure 1) was founded on piles approximately 25 m long. The tested pile was 0.88 m in diameter and 25.8 m long and was drilled in soil whose stratigraphic profile is presented in Figure 2. The groundwater table in this zone is located at the ground surface. Polyethylene tubes were attached vertically (U-shaped configuration) to the reinforcing cage of the pile to allow for the heating and cooling of this element for experimental purposes. The instrumentation chosen for the

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Figure 1. The single energy pile test at the EPFL. Figure 3. Evolution of temperature in the energy pile during heating.

Figure 4. Evolution of vertical strains in the energy pile during heating.

Figure 2. Stratigraphic profile and instrumentation of the tested single energy pile.

Notable temperature changes can develop in energy piles. In one of the considered tests, starting with initial values of temperature that ranged from 13 to 14◦ C along the energy pile length, it was reached an average maximum value of 35◦ C (cf., Figure 3). The thermal loads that are applied to energy piles generate expansive strains upon heating and contractive strains upon cooling. These strains are generally not uniform and develop primarily depending on the friction characterising the pile-soil interface. In one of the considered tests, average expansive vertical strain variations caused by the temperature change in the energy pile up to
εv = −200 µε were measured (cf., Figure 4). These strains showed a reversible, i.e., thermo-elastic, character (cf., Figure 5). The radial strain measurements also showed a reversible thermo-elastic character. Because a proportion of the strain that is induced by the thermal loads that are applied to energy piles is generally prevented by the friction with the surrounding soil, the presence of the superstructure at the pile head and the end-bearing at the pile toe, thermal stresses develop in energy piles. Thermally-induced compressive stresses comparable to those induced by the applied superstructure mechanical loads were observed in this study.

measurement of strain, temperature and load in this test was made up of 58 gauges placed as indicated in Figure 2. More detailed information on the site and foundation investigated as well as on instrumentation used can be found in Laloui et al. (2003). 2.1.2 Features of the experimental test The tested energy pile was subjected to two types of loading: mechanical and thermal. The mechanical load was applied through the dead weight of the building under construction. The thermal load was applied through a heat pump. The solicitations were alternated in order to show the thermo-mechanical coupling clearly. At the end of the construction of each storey, a thermal loading cycle was applied to the pile. Nine different tests were performed. 2.1.3 Observed behaviour The result of this study demonstrated that the behaviour of single energy piles is significantly characterised by the applied thermal loads associated to the geothermal operation of these foundations.

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Figure 7. (a) The EPFL Swiss Tech Convention Centre (http://www.tstcc.ch/, author: Frédéric Rauss); (b) plan view of the foundation; (c) schematic of the soil stratigraphy.

Figure 5. Evolution of vertical strains in the energy pile during heating and cooling at a depth of z = −6.5 m.

piles (labelled P1-16 in Figure 7 (b)) below a heavily reinforced 0.9 m-thick slab. The energy piles are 28 m long and 0.9 m in diameter. All of the piles were bored, cast onsite and are made of reinforced concrete. Vertical loads of 0, 800, 2200 and 2100 kN are applied to energy piles EP1, 2, 3 and 4, respectively. The energy piles were equipped with four 24-m-long high-density polyethylene U-loops that are connected in series. These loops were thermally insulated at the inflow and outflow for 4 m to limit the affection of the heat exchange process characterising the energy piles by the surface thermal conditions. All of the energy piles were instrumented with strain gauges, optical fibres and thermocouples along their lengths as well as with pressure cells at their toes. Piezometers and thermistors were installed in two boreholes in the soil. The soil stratigraphy of the site (cf., Figure 7 (c)) was extrapolated based on information that was obtained during the construction of the foundation and data from Laloui et al. (2003; 2006) collected for the single energy pile test described above. More detailed information on the site and foundation investigated as well as on instrumentation used can be found in Rotta Loria and Laloui (2016).

Figure 6. Evolution of vertical pile head displacements throughout the considered test.

Head heaves occur in energy piles upon heating whereas head settlements occur upon cooling as a consequence of the thermal deformation. An example of the head heaves (negative displacement values) that characterised the energy pile in one of the considered tests is presented in Figure 6. 2.2

Energy pile groups

A number of in-situ tests were recently performed by Mimouni and Laloui (2015) and Rotta Loria and Laloui (2016) to investigate the thermally-induced group effects and interactions characterising closely spaced energy pile groups. A short series of results of the in-situ test performed by Rotta Loria and Laloui (2016), which involved the analysis of closely spaced energy piles that partially operate as geothermal heat exchangers over a time-scale that is typical of practical applications, will be considered in the following.

2.2.2 Features of the experimental test The experimental test involved the application of a heating-passive cooling cycle to energy pile EP1 (for approximately 5 and 10 months, respectively), which was the only energy pile of the group that operated as a geothermal heat exchanger (cf., Figure 7 (b)). Throughout the test, the mechanisms and phenomena occurring in the operating energy pile EP1, in the three surrounding non-operating energy piles EP2, 3 and 4, and in the soil were recorded.

2.2.1 The foundation and site The pile foundation that was considered for the experimental test is located under the recently built Swiss Tech Convention Centre, Lausanne, Switzerland (cf., Figure 7 (a)). The foundation supports a 9 × 25 m2 water retention tank and comprises a group of four endbearing energy piles (labelled EP1, EP2, EP3 and EP4 in Figure 7 (b)) and sixteen semi-floating conventional

2.2.3 Observed behaviour The result of this study demonstrated that the behaviour of groups of closely spaced energy piles that operate partially as geothermal heat exchangers over time-scales that are typical of practical applications is characterised by significant thermally-induced group effects. These group effects are evidenced through

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Figure 9. Experimental setup: (a) global view and (b) detail (1: tubes with circulating water at the desired temperature, 2: LVDTs, 3: thermocouples, 4: water supplier, 5: insulation, 6: acquisition system, 7: heaters).

than the expansion that this pile would have undergone under free thermal expansion conditions. As a proportion of the thermally-induced deformation of the energy piles was restrained due to the presence of the soil and slab, vertical stress variations were observed in such elements. At the end of the heating phase of the test, the operating energy pile EP1 was subjected to a maximum compressive vertical stress variation of
σv = 5500 kPa. The non-operating energy pile EP2 was characterised in its upper and lower portions by maximum vertical stress variations of
σv =1370 kPa (compressive) and −1419 kPa (tensile), respectively. Particular attention was devoted to the analysis of these interactions by Rotta Loria and Laloui (2016) because they were demonstrated to play an important role in the geotechnical, structural and energy performance (e.g., serviceability) of energy piles.

Figure 8. Temperature and vertical strain variations in operating and non-operating energy piles in a group.

thermal and thermally-induced mechanical interactions between the operating and non-operating energy piles. Thermal interactions between operating and nonoperating energy piles occur during successive stages of geothermal operations. In this case study, thermal interactions between a single operating energy pile and the surrounding non-operating energy piles (3 m away; i.e., centre-to-centre spacing of approximately 3·D) occurred after 10 days of geothermal operation (constant thermal power of 3 kW) over 156 days. At the end of the heating phase of the test (t = 156 days of testing), the uninsulated portion of the operating energy pile EP1 was subjected to an average temperature change of
T = 20◦ C (cf. Figure 8). Because of the aforementioned thermal interactions, the region of the non-operating energy pile EP2 in correspondence with the considered setting was subjected to an average temperature change of
T = 5.3◦ C (heat diffused in the soil with time). Thermally-induced mechanical interactions are always present throughout geothermal operations. These interactions are governed by the interplay between the responses of the piles, slab and soil to temperature changes. Heating the operating energy pile EP1 resulted in an expansion (negative strain variation) of its thermally active portion and a compression (positive strain variation) of its thermally inactive top portion because of the entrapment with the slab. The aforementioned interactions eventually induced an expansion of the non-operating energy pile EP2 that was comparable in its lower portion to the expansion of EP1. This deformation was also greater

3

3.1

RESPONSE OF SOILS AND CONCRETE-SOIL INTERFACES SUBJECTED TO TEMPERATURE CHANGES Response of soils subjected to monotonic and cyclic temperature changes

The response of soils subjected to monotonic and cyclic temperature changes was recently investigated by Di Donna and Laloui (2015). 3.1.1 Experimental setup, material and methods The devices that were employed for the experiments are four oedometric cells that were adapted to include the control of temperature (cf., Figure 9). Four natural silty-clay samples were collected near Geneva, Switzerland. The in-situ soil conditions were normally consolidated (NC). The experimental program was divided into two parts, one devoted to characterise the material from a thermal point of view and the other to study the effects of thermal cyclic loading. This corresponded to two different stress-temperature paths: (i) oedometric tests at different constant temperatures (20, 40 and 60◦ C) and (ii) thermal cycles under constant vertical effective stress.

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Figure 10. Soil response at different temperature changes. Figure 11. Soil response during thermal cycles.

More detailed information on the experimental setup, materials and methods can be found in Di Donna and Laloui (2015). 3.1.2 Observed behaviour: monotonic temperature changes In accordance to data available in the literature, it was shown that clayey soils are characterised by thermal softening when subjected to increasing temperature changes (cf., Figure 10). The results also confirmed the known effects of temperature on the primary consolidation coefficient and the hydraulic conductivity: they increase with temperature leading to a faster consolidation. This is mainly linked to the effects of temperature on water viscosity.

Figure 12. Development of the shear box for soil-concrete investigation at different temperatures: (a) electrical heating tissue, (b) installation of the tissue in the lower part of the shear box, (c) support for the concrete specimen, (d) position of the concrete specimen, (e) initial position of the upper part of the box containing the soil and (f) electrical power supplier and insulation system.

3.1.3 Observed behaviour: cyclic temperature changes The results confirmed that clayey soils show thermoelastic response if overconsolidated (OC) and thermoelastic thermo-plastic response if normally consolidated (NC) (cf., Figure 11). In the latter case, it was shown that these materials undergo most of the thermal plastic deformation during the first heating-cooling cycle, followed by an accommodative behaviour during the subsequent ones. Increments of irreversible deformation are observed in the thermal cycles successive to the first one, which become smaller and smaller cycle after cycle until stabilisation. In the end, the material’s stress state tends to remain inside the elastic domain showing a thermo-elastic expansion and contraction during heating and cooling, respectively. 3.2

3.2.1 Experimental setup, material and methods The device that was employed for the experiments is a direct shear box produced by GDS Instruments™. This apparatus was modified for reproducing the in-situ behaviour of the energy pile-soil interface conditions at the laboratory scale (cf., Figure 12). The experimental campaign included tests on sandconcrete and clay-concrete interfaces at different temperatures, as well as tests on soil-soil specimens. For both types of interfaces, different degrees of concrete roughness were tested as well as monotonic and cyclic stress paths under constant normal loads (CNL) and constant normal stiffness (CNS) conditions. More detailed information on the experimental setup, materials and methods can be found in Di Donna et al. (2015).

Response of concrete-soil interfaces subjected to temperature changes

The response of soils subjected to monotonic and cyclic temperature changes was recently investigated by Di Donna et al. (2015).

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the most significant thermal effect resulted from an increase in the adhesion between the two tested materials. This result was related to the thermal consolidation of the clay, which results in an increase of the contact surface between the two materials. The same effect was shown for the high and medium rough interface, with the second interface having lower adhesion at ambient and high temperatures due to its smaller asperities. In addition, the same response obtained at high temperature was also qualitatively shown at ambient temperature under the same testing conditions but applied to the soil sample over a consolidated state. 4 ANALYSIS AND DESIGN OF ENERGY PILES 4.1

Geotechnical and structural performance

Several numerical analyses were recently performed for investigating the geotechnical and structural performance of energy piles at both short- and longterm periods. Those include finite difference and finite element analyses. The former technique was applied to consider the mechanical response of single energy piles when subjected to the mechanical and thermal loads associated to their structural support and geothermal operations (Knellwolf et al., 2011; Mimouni and Laloui, 2014). The latter technique was applied for the same purpose to single energy piles (Laloui et al., 2006; Rotta Loria et al., 2015) but has shown a remarkable potential for the analysis of energy pile groups (Di Donna et al., 2016; Rotta Loria and Laloui, 2016). Different mathematical formulations and extents of coupling between the variables governing the considered problem were used. The choice of these tools was primarily based on both the goals of the study and the aspects that wanted to be considered in the investigation. Rotta Loria et al. (2015) remarked that the mechanical behaviour of energy piles can be crucially affected by significant magnitudes of thermal and mechanical loads. Plastic strain can occur in these conditions at the pile-soil interface, involving a redistribution and/or variation of forces in this setting that causes a shift of the null point, i.e., the setting where zero thermallyinduced displacements occur in the energy pile when this element is subjected to a temperature change (cf., Figure 15). The location of null point is key for the mechanical analysis of energy pile-related problems because allows the end-restraint conditions and the displacement and stress fields of the pile-soil system to be analysed in detail. In most cases of practical interest, the mechanical behaviour of energy piles subjected to the serviceability mechanical and thermal loads appears however to be well captured by linear thermo-elasticity theory. This theory, in particular, is considered a sufficiently accurate and expedient tool for both research- and engineering-oriented analyses of energy pile-related problems. The successfulness of numerical analyses exploiting linear thermo-elasticity has been recently

Figure 13. Sand-concrete interface (high roughness): comparison between results at 20 and 50◦ C.

Figure 14. Clay-concrete interface (medium roughness): comparison between results at 20 and 50◦ C.

3.2.2 Observed behaviour The sand-concrete interface behaviour did not appear to be affected by temperature changes based on both monotonic and cyclic (cf., Figure 13) interface shear tests results. This result was expected because sandy soils are known to behave thermo-elastically, without showing any particular relationship between their strength and temperature. Conversely, the response of the clay-concrete interface changed at different temperatures, indicating an increase in strength with increasing temperature based on both monotonic and cyclic (cf., Figure 14) interface shear test results. Interestingly, the interface friction angle slightly decreased at higher temperatures and

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Figure 16. Thermal power extracted from the ground for different pipe configurations.

from the configuration of the pipes. However, a lengthening or shortening of the energy pile resulted in markedly diverse responses of the foundation to the thermo-mechanical loads, depending on the impact that the different mechanical and thermal properties of the surrounding soil layers may have had on the bearing response of the pile. The mass flow rate of the fluid circulating in the pipes remarkably influenced only the energy performance of the foundation. Usual mixtures of a water-antifreeze liquid circulating in the pipes did not markedly affect both the energy and the geotechnical performance of the pile.

Figure 15. Null point movements in a semi-floating energy pile subjected to different combinations and magnitudes of thermal and mechanical loads.

demonstrated for energy pile groups by Rotta Loria and Laloui (2016). 4.2

Energy performance

The energy performance of energy piles was recently analysed by Batini et al. (2015) in a coupled thermomechanical study that also considered the geotechnical performance of these foundations. The investigation was based on finite element sensitivity analyses that were performed with reference to a base-case design configuration characterising one of the energy piles of the EPFL. This study outlined the impacts of different design solutions such as the (i) pipe configurations, (ii) foundation aspect ratios, (iii) mass flow rates of the fluid circulating in the pipes and (iv) fluid mixture compositions on the energy and geotechnical behaviour of the energy piles. It was observed that the pipe configuration strongly influenced both the energy (cf., Figure 16) and the geotechnical performance of the energy piles. It was noted that the W-shaped pipe configuration resulted in an increase of up to 54% in the heat transfer rate compared with the single U-shaped configuration at the same flow rate. The double U-shaped pipe configuration, which possessed a double flow rate with respect to the other configurations, resulted in the highest cooling of the concrete with the greatest related stress and displacement distributions. Therefore, it was considered to be a less advantageous solution with respect to the W-shaped pipe configuration both from a thermo-hydraulic and a geotechnical point of view. The foundation aspect ratio also played an important role in this context. The increase of the foundation aspect ratio resulted in an approximately linear increase of the exchanged heat that was independent

5

CONCLUDING REMARKS

This paper proposed a number of insights on the multyphisical phenomena and mechanisms involved with energy piles. Some aspects of the thermo-mechanical behaviour of both single and groups of energy piles were presented and discussed. Comments on the response of soils and concrete-soil interfaces subjected to temperature changes were also proposed. Insights on some concepts that appear key for the analysis and design of energy piles were finally presented. This work highlighted the significant impact that the thermal and mechanical loads associated to the geothermal and structural support operations of energy pile foundations have on the performance of these ground structures. REFERENCES Batini, N., Rotta Loria, A. F., Conti, P., Testi, D., Grassi, W. & Laloui, L. (2015) Energy and geotechnical behaviour of energy piles for different design solutions. Computers and Geotechnics, 86, 199–213. Di Donna, A., Ferrari, A. & Laloui, L. (2015) Experimental investigations of the soil-concrete interface: physical mechanisms, cyclic mobilisation and behaviour at different temperatures. Canadian Geotechnical Journal, 10.1139/cgj-2015-0294.

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exchanger pile. International Journal for Numerical and Analytical Methods in Geomechanics, 30, 763–781. Mimouni, T. & Laloui, L. (2014) Towards a secure basis for the design of geothermal piles. Acta Geotechnica, 9, 355–366. Mimouni, T. & Laloui, L. (2015) Behaviour of a group of energy piles. Canadian Geotechnical Journal, 52, 1913– 1929. Rotta Loria, A. F., Gunawan, A., Shi, C., Laloui, L. & Ng, C. W. (2015) Numerical modelling of energy piles in saturated sand subjected to thermo-mechanical loads. Geomechanics for Energy and the Environment, 1, 1–15. Rotta Loria, A. F. & Laloui, L. (2016) Thermallyinduced group effects among energy piles. Géotechnique, Submitted.

Di Donna, A. & Laloui, L. (2015) Response of soil subjected to thermal cyclic loading: experimental and constitutive study. Engineering Geology, 190, 65-76. Di Donna, A., Rotta Loria, A. F. & Laloui, L. (2016) Numerical study on the response of a group of energy piles under different combinations of thermo-mechanical loads. Computers and Geotechnics, 72, 126–142. Knellwolf, C., Peron, H. & Laloui, L. (2011) Geotechnical analysis of heat exchanger piles. Journal of Geotechnical and Geoenvironmental Engineering, 137, 890–902. Laloui, L., Moreni, M. & Vulliet, L. (2003) Comportement d’un pieu bi-fonction, fondation et échangeur de chaleur. Canadian Geotechnical Journal, 40, 388–402. Laloui, L., Nuth, M. & Vulliet, L. (2006) Experimental and numerical investigations of the behaviour of a heat

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Geomechanical and numerical modeling of gas hydrate sediments M. Sánchez & X. Gai Texas A&M University, College Station, Texas, USA

ABSTRACT: Gas hydrates sediments are generally found in sub-marine sediments and in permafrost regions. They are recognized as a huge potential energy resource. Methane hydrate deposits can lead to large-scale submarine slope failures, blowouts, platform foundation failures, and borehole instability. Hydrate formation, dissociation and methane production from hydrate bearing sediments are coupled Thermo-Hydro-Chemical and Mechanical (THCM) processes that involve, amongst other, exothermic formation and endothermic dissociation of hydrate and ice phases, mixed fluid flow and large changes in fluid pressure. The behavior of Hydrate Bearing Sediments (HBS) is very complex and the mechanical modeling poses great challenges. The presence of hydrates has a huge impact on the mechanical behavior of soils, affecting stiffenss, strength and dilatancy.A comprehensive THM formulation for HBS is briefly presented in this paper. Special attention is paid to the mechanical behavior of HBS. The model performance was very satisfactory in all the cases studied. It managed to capture very well the main features of HBS behavior and it also assisted to interpret the behavior of this type of sediment under different loading and hydrate conditions.

1 1.1

INTRODUCTION

and geomechanical properties of hydrate sediments. Depressurization, thermal injection and chemical stimulation are the three basic mechanisms that trigger hydrate dissociation. Current methods accepted as feasible for extracting methane gas from hydrate bearing sediments are based on these three processes mainly. A proper modelling of this challenging problem will assist to study optimal methane production strategies and also to prevent the multiple hazards associated with uncontrolled hydrate dissociation and gas release from hydrate sediments. Considering the complex multiphysics phenomena involved in gas hydrate formation/dissociation a fully coupled Thermo-Hydro-Chemical and Mechanical formulation is an indispensable component to conduct realistic engineering problems involving HBS. The mechanical modeling of gas hydrate sediments is particularly challenging. In this paper an elastoplastic model based on the strain partition concept (Pinyol et al. 2007) and the HIerarchical Single Surface (HISS) framework (e.g. Desai 1996) was adopted in an effort to provide a more general and versatile constitutive model for HBS. The model is very well suited to simulate problems involving hydrate dissociation. The proposed framework was widely validated against recently published experiments involving both, synthetic and natural hydrate soils, as well as different sediments conditions (i.e., different Sh , and different hydrates morphologies) and confinements. A brief description of the THM formulation adopted in this work is presented in the next section. Code validation are reported elsewhere (e.g. Sanchez et al. 2015). Then the mechanical model is briefly presented.

Background

Hydrate bearing sediments (HBS) are natural soil deposits that contain ice like methane hydrates in its pore space. Methane hydrates are solid compounds made of water molecules clustered around low molecular weight methane molecules. The stability of methane depends on pressure (P) and temperature (T) conditions. Methane hydrates forms are common in sub-permafrost layers and in deep marine sediments, this is because of the necessary conditions of low temperature and high pressure required for hydrate stability (e.g. Collett 2002). If changes in temperature and/or pressure are such that the methane hydrate shift from the ‘P-T’ stability zone, it will dissociate producing methane and water. Hydrate dissociation will induce in turn profound changes in the sediment structure and physical properties. According to the U.S. Geological Survey, the estimated global natural gas hydrate reserves are in the range from 100,000 to about 300,000,000 trillion cubic feet (Mahajan et al. 2007). Given the sheer magnitude of this resource, sediments with (a relatively) high concentration of methane hydrate in the pore space are considered to be a significant energy resource for future exploitation. However, hydrates dissociation is associated with engineering problems, such as: blowouts; platform foundation failures; pipeline related issues; large submarine landslides; and borehole instability. Hydrate dissociation is a complex phenomenon involving changes in fluid pressure, effective stresses,

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where, the gas constant R = 8.314 J/(molo K) and the molecular mass of methane Mm = 16.042 g/mol (example: ρg = 86 g/m3 at T = 280◦ K and Pg = 10 MPa). The hydrate phase is made of water and methane. The mass fraction of water in hydrate α = mw /mh depends on the hydration number ξ for methane hydrates. The ice transformation may take place during fast depressurization. The densities of the hydrate, the ice and the mineral phases are assumed constant. 2.3 Main equations

Figure 1. a) HBS schematic representation; b) HBS phase diagram.

2 2.1

The total volume is the sum of the partial volume of each β-phase Vβ , where the subscript β is related to the solid ‘s’, liquid ‘ℓ’, gas ‘g’, hydrate ‘h’ and ice ‘I ’ phases. Assuming that the solid mineral is a nonreactive phase, the total porosity (φ) is defined as the ratio of the volume of voids to the total volume

COUPLED THCM FORMULATION Basics

The THM phenomena that take place in hydratebearing sediments include the main following phenomena: i) heat transport through conduction, liquid and gas phase advection; ii) heat of formation-dissociation; iii) water flux as liquid phase; iv) methaneflux in gas phase and as dissolved methane(diffusion in liquid phase); v) heat of ice formation/thaw; vi) fluid transport of chemical species; vii) mechanical behavior depending on effective stress and hydrate concentration/morphology. Those phenomena have been implemented in the finite element program CODE-BRIGHT (Olivella et al. 1996). Some components of the coupled formulation are presented in the subsequent sections. 2.2

The following relationship can be written:

where Sℓ , Sg , Sh and Si are the liquid, gas, hydrate and ice saturations, respectively. The mathematical formulation is composed of three main types of equations: i) balance equations (i.e. mass balance of species, internal energy balance and momentum balance equations); ii) constitutive equations; and iii) equilibrium restrictions. As an example of the mass balance equations the mass balance of water is presented below:

Phases and Species

The pores in the granular skeleton of HBS are filled with gas, hydrate, water or ice (Fig. 1a). The three main species mineral, water, and methane are found in five phases: solid mineral particles, liquid, gas, hydrates and ice as shown in the phase diagram in Figure 1b. The liquid phase is made of water and dissolved gas. The density of the liquid ρℓ depends on temperature T [◦ K] and pressure Pℓ [MPa]. The asymptotic solution for small volumetric changes is:

where ρh is the density of the hydrates, and qg is flux of methane. Constitutive equations and equilibrium restrictions relate the main unknowns (i.e. u, Pl ; Pg , Ph T ) with the dependent variables (i.e. stresses; Sl ; Sg ; Sh fluxes). For example, the retention curve dictates the relationship between the interfacial tension sustained by the difference in liquid and gas pressures. Because of space limitations the full set of equations are not presented here, more details can be found elsewhere (e.g. Sanchez et al. 2015, 2016).

where, ρℓo = 0.9998 g/m3 is the mass density of water at atmospheric pressure T is temperature in ◦ K and Bℓ = 2000 MPa is the maximum bulk stiffness of water (at 277◦ K), and βT ℓ = 0.0002◦ K−1 is the thermal expansion coefficient. The mass density of the gas phase is pressure Pg [MPa] and temperature T [◦ K] dependent and it can be estimated using the ideal gas law modified for methane gas.

3

MECHNICAL BEHAVIOR OF HBS

3.1 Overview The presence of hydrates strongly affects key mechanical properties of soils. The samples containing hydrates exhibit, higher shear strength, more dilation under shearing, and they also soften more after

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Figure 3. a) Schematic representation of the hydrate damaged during shearing; b) rearrangement of the HBS structure upon dissociation.

Figure 2. Main types of hydrate morphology: a) cementation; b) pore filling; and c) supporting matrix.

components of the proposed geomechanical model is briefly introduced below.

yielding when compared against the free hydrate samples (Masui et al. 2008, Miyazaki et al. 2011). Identical sediments but with different hydrate saturations, generally shown an increases in HBS stiffness, pre-consolidation pressure, and sediment strength with the increase of Sh . A degradation of the tangent stiffness of hydrate-bearing soils during shearing has also been reported (e.g. Masui et al. 2005; Hyodo et al. 2013). Hydrates morphology also impacts on HBS behavior. Hydrates can be present in soils in three main types of pore habits, namely (e.g. Waite et al. 2009): a) cementation (Fig. 2a); b) pore-filling (Fig. 2b); and c) supporting matrix (Fig. 2c). In the cementation mode the hydrates act as a bonding material at mainly on sediment grain boundaries and grow freely into the pore space without bridging two or more particles together. The hydrates present in this morphology assists to the mechanical stability of the granular skeleton contributing to the load-bearing framework of the sediment.The presence of hydrates in this case can strongly affects the sediment permeability and water storage capacity. The behavior of HBS upon dissociation is very complex because their response not only depend on the amount of hydrate, but also on the type of pore habit, and the stress level at which hydrate dissociation is induced. For example, when hydrate dissociation takes place at a low deviatoric stress (i.e. lower than the strength of the pure sediment), the tendency of the sediment after dissociation is to harden. An opposite behavior was observed when dissociation occurs at a higher deviatoric stress. Significant volumetric compression deformations are observed when hydrate dissociation is induced under constant effective stresses (Santamaria et al. 2015). It was also suggested that hydrate bonding effects can be damaged during shearing (Uchida et al. 2012). The progressive stiffness degradation in tests involving HBS is generally very evident. Figure 3a illustrates the phenomenon of hydrate damage during shearing. Hydrate dissociation is also accompanied by profound changes in the sediment structure. Figure 3b shows schematically the expected changes in the soil structure that lead to the collapse compression deformations observed during dissociation under normally consolidated conditions (as discussed later on, Fig. 6b). In summary, the mechanical response of HBS is highly non-linear and complex, controlled by multiple inelastic phenomena that depends on hydrate saturation, sediment structure, and stress level. The main

3.2 Constitutive model The elasto-plastic framework contemplates the presence of two basics components: sediment skeleton and hydrates. The strain-partition concept proposed by Pinyol et al. (2007) was adapted for the case of HBS. Through this concept it is possible to account for the role of these two different structures on the global response of HBS under different loading and hydrate saturation conditions, particularly during hydrate dissociation. Specific constitutive equations for these two basic structural components can be proposed. For the sediment skeleton, a model based on critical state soil mechanics was adopted. The particular constitutive equation adopted was based on a modification of the HISS elasto-plastic model (Desai 1986). The proposed framework also incorporates sub-loading and dilation enhancement concepts. As for the hydrates, a damage model that considers the material degradation due to loading and dissociation was suggested. Only some basics components of the model are introduced below, a detailed description can be found elsewhere (e.g. Sanchez et al., 2015, 2016, and Gai & Sanchez, 2016). The total volumetric strain (εv ) accounting for both, sediment skeleton and hydrate deformations (i.e. subscript ss and h, respectively) can be calculated as:

where Ch is the volumetric concentration of methane hydrate; which in turns is equal to the porosity times the hydrate saturation (i.e., Ch = φSh ). The relationships that link hydrates and soil skeleton strains are proposed following an approach similar to Pinyol et al. (2007):

where χ is the strain partition variable that evolves during loading. As for the hydrates, previous studies suggested that hydrate effects can be damaged during shearing (Uchida et al. 2012). It is assumed that loading degradation occurs when the stress state arrives to a predefined threshold value ‘r0 ’. When the stresses are below a pre-established threshold, a linear elastic response of the material is assumed via the following relationships:

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where σh corresponds to the stresses taken by the hydrate and Dh0 is the methane hydrate elastic constitutive matrix of the intact material. Loading damage takes place when the changes in the stress state is such that the secant elastic energy reaches r0 . In this case the damage variable L (i.e. +∞ > L ≥ 0) increases and the stiffness reduces. The damage evolution is determined by means of the function below (Carol et al. 2001):

Figure 4. Yield surfaces considered in the model.

where r1 controls the damage rate. The evolution law for the partition variable is defined by:

Table 1. Soil parameters adopted in the modeling of HBS Test Test Test Test Properties Sh = 0 Sh = 24.2% Sh = 35.1% Sh = 53.1% M λ κ pc (MPa) n a γ Ch α β r1 r0 η χ0 Kh (MPa) Gh (MPa)

where χ0 is an initial reference value assumed for the partition variable. As for the sediment skeleton, a critical state constitutive model based on a modified HISS framework was adopted. The model incorporates sub-loading concepts, as well as hardening and dilation enhancement mechanisms associated with the presence of hydrates in the sediments. The modified HISS model involves a single and continuous yield surface that can adopt different shapes depending on the selected parameters (Desai 1986). The HISS yield surface (F) is given by:

where a and γ are model constants; n is the parameter related to the transition from compressive to dilative behavior; p′ss and qss are the mean effective and deviatoric stresses, respectively, both associated with the sediment skeleton; M is the slope of critical line in the qss −p′ss space; and pc is the effective pre-consolidation pressure. The Modified Cam-Clay yield surface corresponds to a particular case of this model. The yield function incorporating the strength enhancement (pd ) associated with the presence of methane hydrate can be expressed as

1.30 .16 .004 10. 3 1 −1/9 0 − − − − 42 − − −

1.30 .16 .004 10 3 1 −1/9 .096 32 1.0 4.1 1e–5 42 1 9600 4300

1.30 .16 0.004 10 3 1 −1/9 .138 32 1.0 4.1 1e–5 42 1 9600 4300

1.30 16 0.004 10 3 1 −1/9 .213 32 1.0 4.1 1e–5 42 1 9600 4300

3.3 Model applications The tests reported by Hyodo et al. (2013) were selected to study the effect of hydrate saturation on the behavior of HBS. A series of triaxial compression tests on synthetic methane hydrate soils were conducted at different (constant) hydrate saturations, namely: Sh = 0; Sh = 24.2%; Sh = 35.1%; and Sh = 53.1%. All the samples were prepared at a similar porosity (i.e. φ ∼ 40%). The effective confining pressure for all the tests was 5 MPa. The samples where isotropically consolidated first and then subjected to shearing. The model parameters were determined using back-analysis based on two tests, the one involving sediments without hydrates (i.e., Sh = 0) and the test related to the highest hydrate saturation (i.e., Sh = 53.1%). Then, this model (without modifying the parameters adopted before) was used to predict the behavior of the samples with Sh = 24.2 and Sh = 35.1%. Table 1 presents the parameters adopted in the analyses. Figures 5a & b show the comparisons between experimental and model results for the different hydrate saturations in terms of deviatoric stress and volumetric strain versus axial strains. The compression behavior was dominant in all the samples, but the one with Sh = 53.1% showed a dilatant response

Sub-loading concepts are incorporated in the formulation to account for any irrecoverable strain that may occur in HBS when stresses are inside the yield surface, and also for having a smooth transition between elastic and plastic states. The three yield surfaces considered in this model are presented schematically in Figure 4. The principle of virtual work was advocated to obtain the final expressions relating the external effective stress σ′ with the total strain increment. (Sanchez et al., 2015, 2016).

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Figure 5. Comparisons between model and experimental results for synthetic samples of HBS prepared at different Sh : a) stress-strain behavior; and b) volumetric responses (experimental data from (Hyodo et al. 2013).

Figure 6. Behavior during dissociation of natural HBS specimens under oedometric conditions: a) core 8P; and b) core 10P, (experimental data from Santamarina et al. 2015).

structure is huge during dissociation. The main reasons behind this different behavior can be related to: i) hydrate saturation is much smaller in core-8P than core-10P (i.e., Sh = 18% for core-8P, and Sh = 74% for core-10P); ii) the vertical stress at which hydrates are dissociated is lower and the dissociation took place under over-consolidated conditions, therefore the effect of confinement on the re-accommodation of the sediments particles is less significant; and iii) this sample was previously loaded up to a very high effective vertical stress (i.e. σv′ = 6 MPa) that degraded the bonding effect of the hydrate and induced important changes in the sediment structure previous to dissociation.

with a slight stress-softening behavior. The relatively high confining pressure at which the tests were performed (i.e. σc′ = 5 MPa) could be one reason for the predominant hardening behavior with positive volumetric strains observed in these tests. In all the tests the initial stiffness and shear strength increase with Sh . The model was able to match very well the stress-strain curves for all the experiments under study. Quite good agreements were also observed in terms of volumetric behavior (Fig. 4b). The ability of the model to simulate tests involving different hydrate morphology was also checked using the triaxial experiments conducted by Masui et al. (2008), more details can be found elsewhere (Gai & Sanchez, 2016; Sanchez et al., 2016). The tests conducted by Santamarina et al. (2015) were selected to study the effect of hydrate dissociation under loading conditions. Two natural core samples were extracted from the Nankai Trough using Pressure Core Characterization Tools (Santamarina et al. 2012) and tested under oedometric conditions. Figure 6a shows the comparison between experimental and modeling results for the sample coded as ‘core 8P’ with Sh = 18%. Prior to hydrate dissociation the specimen was loaded up to a vertical stress σv′ = 6 MPa and then unloaded back to σv′ = 3 MPa to study the stress-volume response of HBS. Under this over-consolidated conditions, hydrate dissociation was induced. Once the hydrate fully dissociated, the sample was subjected to loading-unloading cycles with a maximum σv′ = 9 MPa. Figure 6b presents the results related to specimen coded as ‘core 10P’, initial Sh = 74%. This sample was loaded until σv′ = 3 MPa, at this normally-consolidated conditions, the effective stress was hold constant and hydrate dissociation was induced. After hydrate dissociation, the sample was loaded up to σv′ = 9 MPa and then unloaded. The model managed to capture very satisfactorily the main trends observed in both tests. The yield stress and unloading-reloading behavior are quite well modeled in both specimens. It is worth to highlight the model ability to reproduce the difference in volumetric strains observed during dissociation at constant stress in these two tests. In the case of core-8P, the collapsecompression behavior is significantly less marked than in core-10P, where the rearrangement of the HBS

4

CONCLUSIONS

The interest for gas hydrates have increased in the last few years. They represent huge opportunities in terms of energy resource and they are also associated with some drawbacks because of the metastable character of the HBS structure and its impact on sediment stability. A coupled THCM formulation for HBS was briefly presented in this paper. A key component of the proposed approach is the geomechanical model. An advanced constitutive model for HBS was also presented and applied to reproduce the mechanical behavior observed in recent experiments involving both synthetic and natural HBS specimens. The model was able to reproduce quite satisfactorily the main features of soil behavior observed in these tests as, for example: the enhancement in stiffness and strength induced by the presence of the hydrate, stiffenss degradation during shearing, soil dilatancy, and the volumetric soil collapse compression observed during hydrate dissociation at constant stresses.

ACKNOWLEDGEMENTS The authors would like to acknowledge the financial support from NETL (National Energy Technology Laboratory), DOE (Department of Energy, US) through Award No.: DE-FE0013889. The authors would also like to acknowledge the other researcher

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involved in this project, amongst others: J. Carlos Santamarina; Ajay Shastri and Mehdi Teymouri.

artificial gas hydrate bearing sediments. Proceedings 6th International Conference on Gas Hydrates ICGH 2008, Vancouver, British Columbia, Canada Miyazaki, K., Masui, A., Sakamoto,Y., Aoki, K., Tenma, N. & Yamaguchi, T. 2011. Triaxial compressive properties of artificial methane-hydrate-bearing sediment. Journal of Geophysical Research: Solid Earth 1978–2012 116(B6). Olivella, S., Gens, A., Carrera, J. & Alonso E.E. 1996. Numerical formulation for a simulator (CODE-BRIGHT) for the coupled analysis of saline media. Engineering Computations, 13(7): 87–112. Pinyol, N., Vaunat, J. & Alonso, E.E. 2007. A constitutive model for soft clayey rocks that includes weathering effects. Géotechnique; 57(2): 137–151. Sánchez, M., Santamarina, J.C., Gai X. & Sun Z. 2015. Quarterly Research Performance Progress Report (Period ending 03/31/2015) Sánchez, M., Santamarina, J.C. & Shastri, A. (2016). “Coupled THM Analysis of Gas Hydrate Bearing Sediments” under review. Santamarina, J.C., Dai, S., Terzariol, M., Jang, J., Waite, W.F., Winters, W.J., Nagao, J., Yoneda, J., Konno, Y., Fujii, T. & Suzuki, K. 2015. Hydro-bio-geomechanical properties of hydrate-bearing sediments from Nankai Trough. Marine and Petroleum Geology. Uchida, S., Soga, K. &Yamamoto, K. 2012. Critical state soil constitutive model for methane hydrate soil. Journal of Geophysical Research: Solid Earth 1978–2012, 117(B3). Waite, W.F., Santamarina, J.C., Cortes, D.D., Dugan, B., Espinoza, D.N., Germaine, J., Jang, J., Jung, J.W., Kneafsey, T.J., Shin, H. & Soga, K. 2009. Physical properties of hydrate-bearing sediments. Reviews of Geophysics 1 47(4).

REFERENCES Carol, I., Rizzi, E. & Willam, K. 2001On the formulation of anisotropic elastic degradation. I. Theory based on a pseudo-logarithmic damage tensor rate. International Journal of Solids and Structures 38(4): 491–518 Collett, T.S. 2002. Energy resource potential of natural gas hydrates. AAPG bulletin 86(11):1971–92. Desai, C.S., Somasundaram, S. & Frantziskonis, G. 1986. A hierarchical approach for constitutive modelling of geologic materials. International Journal for Numerical and Analytical Methods in Geomechanics 10(3): 225–57. Gai, X. & Sánchez, M. 2016. Mechanical Modeling of Gas Hydrate Bearing Sediments Using an Elasto-Plastic Framework. Environmental Geotechnics (accepted). Hyodo, M., Yoneda, J., Yoshimoto, N. & Nakata, Y. 2013. Mechanical and dissociation properties of methane hydrate-bearing sand in deep seabed. Soils and foundations. 53(2): 299–314. Mahajan, D., Taylor, C.E. & Mansoori, G.A. 2007. An introduction to natural gas hydrate/clathrate: The major organic carbon reserve of the Earth. Journal of Petroleum Science and Engineering 56(1): 1–8. Masui, A., Haneda, H., Ogata, Y. & Aoki, K. 2005. Effects of methane hydrate formation on shear strength of synthetic methane hydrate sediments. 15th International Offshore and Polar Engineering Conference. Masui, A., Miyazaki, K., Haneda, H., Ogata, Y. & Aoki, K. 2008. Mechanical characteristics of natural and

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Coupled chemo-mechanics: A comprehensive process modeling for Energy Geotechnics T. Hueckel Duke University, Durham, NC, USA

L.B. Hu University of Toledo, Toledo, OH, USA

M.M. Hu University of Sydney, Sydney, Australia

ABSTRACT: Geo-chemistry and geo-mechanics have had a fruitful period of independent development over last 50 years, and are now conceptually matured having produced useful and sophisticated modeling tools used in the energy industry. As the understanding of the processes becomes more in-depth, interdependence of chemical and mechanical phenomena in geo-materials are more and more appreciated. The primary variables/properties that are involved in the interdependence are mineral, ion and proton mass transfer between porous medium phases and mechanical stiffness and deformation, and soil permeability. The paper outlines the efforts in modeling of coupling of geochemical reaction laws and laws of deformation and fluid flow. It identifies changes of mass of ion concentration, electrical charge, or individual solid minerals as primary chemical variables affecting the constitutive mechanical laws of behavior of rocks and soils, as well as of the fluid or species transport in the porous media. Examples of chemo-plasticity and chemo-elasticity are discussed. A particular case of chemical softening or hardening as a function of mineral mass removed or added is focused on. Additional chemo-mechanical coupling comes via micro-fracturation, which generates an extra specific surface area of fluid/solid interface, at which an enhanced dissolution, and/or precipitation takes place. Formulations of permeability evolution due to chemo-plastic process are also reviewed. Experimental data and simulation results are discussed for processes exemplified by reservoir sediment aging/pressure solution and compaction, acidization enhanced subcritical crack propagation in hydraulic fracturing, or due to CO2 injection. Importance of multi-scale considerations (both for time and space scales), as well as of innovation in chemo-mechanical experimentation are emphasized.

1

INTRODUCTION

three decades of experience in thermo-mechanics mainly in the context of nuclear waste disposal and geothermal energy, there is virtually nothing in terms of chemo-mechanics as applied to energy geotechnics. Geo-chemistry and geo-mechanics have had a fruitful period of independent development over last 50 years, in which they both conceptually matured and produced useful and sophisticated modeling tools of prediction of reservoir compaction or diagenesis in petroleum engineering, contaminant isolation in nuclear waste disposal design, landfill settlement prediction, clay swelling, coastal landform stability or CO2 mineralization, to mention a few areas of relevance. However, as the understanding of the processes became more in-depth, it was realized that the interdependence of chemical and mechanical phenomena in geo-materials is often of the first order, both in nature and in engineering and goes beyond a p-V -T framework (Bayly, 1992). The primary variables/properties that are involved in the interdependence are chemically

Simultaneous emergence of several new energy technologies that are related to energy extraction either as fluids or minerals from the earth, or long- or short-term storing or retrieving energy resources or by-products in or from the ground, gave a very strong impetus to development in geotechnics, including some basic areas. Most of the new technologies require rigorous production predictions, as well as need to meet demanding safety requirements, together with longterm performance assessment. All of the above vastly rely on experiments based numerical simulations. However, basic science and often knowledge data base is by far insufficient to provide confident products. Traditional geotechnics only sporadically dealt with problems resulting from energy production issues, which pose problems related to heating/cooling of soil/rock and may involve chemical changes affecting soil/rock mechanical properties. While there is nearly

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3

affected mineral, ion and proton mass transfer between porous medium phases and mechanical stiffness and deformation, as well as rock/soil permeability. The lecture outlines the efforts in modeling of coupling of geochemical reactions and processes and laws of deformation and fluid flow. It identifies changes of mass of ion concentration, electrical charge, or individual solid minerals as primary chemical variables affecting the constitutive mechanical laws of behavior of rocks and soils, as well as of the fluid or species transport in the porous media. Reference to thermodynamic principles is made. Examples of chemo-plasticity and chemo-elasticity are discussed. A particular case of chemical softening or hardening as a function of mineral mass removed or added is focused on. Additional chemo-mechanical coupling comes via micro-fracturation, which generates an extra specific surface area of fluid/solid interface, at which an enhanced dissolution, and/or precipitation takes place. Formulations of permeability evolution due to chemo-plastic process are also reviewed. Experimental data and simulation results are discussed for processes exemplified by aging/pressure solution in reservoir sediment subsidence, acidization enhanced subcritical crack propagation in hydraulic fracturing, or due to CO2 injection. The importance of multi-scale considerations (both for time and space scales), as well as of innovation in chemo-mechanical experimentation.

2

CONSTITUTIVE EQUATIONS

To account for the role of chemical changes in mechanical material response one needs to formulate a set of constitutive hypotheses on how to couple the mechanics of the soil solids to their chemistry, and in particular to the evolution and possibly transport of chemical species. To start with let us note that to describe total free energy (isothermal process) in two-phase, multispecies reactive porous medium, the work by total stress during deformation process must be supplemented by the work of chemical potential µkK (mass based, [J/g]) during addition of mass of species of both phases, (k are indices for the fluid species, K are for the solid species)

Species may be entities of any kind, pore water, adsorbed water, other fluid species, minerals, ions, even entire rock. Mass of species added to or removed from the system and energy associated with the addiK + tion/removal (i.e. chemical potential δµkK = δp ρkK RT δ(lnx ) are the only variables related to the chemkK (M ) mk

ical processes. In this definition, R = 8.31451 J/molK is the universal gas constant, T [K] the absolute tem(M ) perature and mk is the molar mass of the species (M ) k, e.g. for free pore water mw = 18 g, pK is pressure or mean stress in phase K, assumed as equal in all the species of the given phase, whereas xkW are molar fractions of the species k in phase W , which is actually the mass variable. We will use both the changes in mass and or chemical potentials in reaction equations, as well as to quantify the effect that reactions make on the mechanical properties of soil/rock. To derive constitutive properties of the solid phase, inclusive of the adsorbed water, we shall adopt a strategy proposed originally by Heidug and Wong (1996). The free energy of the solid phase is represented by the difference between the total energy of the whole system of porous medium and that of free pore water, the latter classically defined per unit volume of the fluid phase as

PHENOMENOLOGICAL AND ENGINEERING BACKGROUND

There are innumerous chemical processes and reactions that affect the mechanical properties of geomaterials. Chief among them are removal or accretion of mass of minerals within the pore space. This may occur through dissolution of precipitation. The result of such mass loss/gain for the mechanical properties is a strength increase or decrease, direct chemical strain, usually volumetric expansion or compaction. Also other properties of relevance may be affected, such as thermal conductivity. There may be a change in ionic content of pore fluid that is in contact with the materials solids. In materials that are electrically charged, as clays, it produces swelling or shrinkage, resulting often in a change in strength and compressibility, as well as in hydraulic conductivity. The causes for the mentioned processes are diverse. They may result directly from the technology, as injection of water or vapor, as in fracking, or in geothermal technologies, injection of CO2 in technologies related to its geological sequestration, or specific chemicals, for instance acids, as in fracking. Some processes that are of interest are natural processes as a part of diagenesis, like pressure solution. Similar processes are involved in subsidence due to oil or gas extraction, such as resulting compaction.

and re-scaled with respect to unit volume of REV to yield

where pW and vW are pressure and volume content, respectively, of the fluid phase. Gibbs-Duhem relationship for fluid was used in the above derivation, which restricts changes of all intensive variables, and for isothermal processes of pressure and chemical potential of species being exchanged in reactions. Recalling

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point of view of material failure and factor of safety it may be of critical importance. Considering the plastic part of dissipation, with a chemical component to it, and assuming for independent reasons that diffusional dissipation, chemical reaction dissipation and thermal dissipation, if any, are independently each non-negative, its inevitable to conclude that

the Heidug –Wong strategy, the free energy of the reactive solid phase reads

The elastic part of the free energy

requires that a reversible part of mass change, µel kK is identified, so that

which to ensure positiveness of eq. 10 may require the positivesess of each term separately, which implies a sort of generalized normality rule,

Or through a Legendre transform one can employ mixed form energy as a function of effective stress and mass changes

If we assume that the yield locus evolution includes a chemical softening, when mineral mass is removed, or hardening when it is added (but with no compensation rule for accretion).

As a result the chemo-elasticity equations can be expressed alternatively via energy gradients where q = 1/2 ∼s : ∼s , is an invariant of stress deviator, while p′c is an apparent preconsolidation pressure, which is a value of the maximum past isotropic effective stress, but amplified or de-amplified by possible chemical processes. M critical state parameter related to the internal friction angle, possibly also dependent on the chemical processes (Hueckel, 1997). Hence,

The modeling practice is to identify experimentally main features of the chemo-elastic behavior and then propose a corresponding expression consistent with the equations (7) and (8). A typical chemo-elastic law would contain two particular features: a chemically induced (mass or concentration dependent) volumetric strain (e.g. osmotic swelling) and again, mass or concentration change dependent elasticity modulus. An example of such a law for swelling clays was given by Loret et al. (2002) or Gajo et al. (2002) in the form as follows:

In both p′c and M the chemical process is represented by an accumulated change of mass of a chemical pl species, mkS . However, this variable is highly process specific, as will be discussed in the next paragraphs. 4

CHEMICALLY INDUCED SEDIMENT COMPACTION

In this section we shall discuss modeling of chemically induced compaction of sediment enhanced by inundation with water and leading to mineral dissolution and possibly decrease of permeability by precipitating mineral in the open pore space. Such a process is a component of diagenesis, in the from of pressure solution, as well as as that of reservoir compaction during extraction of oil or gas, when the emptied pores are filed with water, either in a natural process or during water injection. The natural process of normal consolidation of sediments is believed to be a superposition of several coupled processes regarding the sediment solid matrix and pore fluids. The processes involved are: deformation of sediment grains, including plastic deformation,

Notably, the chemical potential evolution rule is needed to complement the description of the coupled chemo-elastic process. Chemo-plasticity formulation is needed to properly describe the effect of all dissipative processes and in particular a number of chemical changes in the material on its mechanical processes. Physically, the most important factor is that of chemical softening, as it may in many instances to be the most important factor. It describes the weakening of the material in terms of its strength and all its derivatives as a result of mass removal and other concentration changes. From the

27

Figure 2. Schematic of a rigid grain indentation into a adjacent rigid-plastic grain.

solid grain mineral. Stress and strain are microstress and microstrain at the scale of a fraction of the grain, positive in compression. The material of individual grain is taken as rigid plastic. To describe mathematically a near contact failure one needs to identify a micro-stress (σij ) yield locus, f (δij ) ≤ 0, within which no strain (εij ) occurs, whereas at yielding, the strain rate is entirely irreversible

Figure 1. Scenario of multiple processes involved in chemically induced compaction after Hueckel & Hu, 2009.

especially near contact between grain asperities and corresponding locally smooth surface of another grain; dilatant damage induced by the plastic yielding; infiltration of the dilatant zone by pore water; activation of damage (microcracking) related internal interfaces between pore liquid and solid; dissolution of minerals at these interfaces; diffusion within the grain of the dissolved species away from the reaction sites; interpore diffusion of the dissolved minerals in the pore water and precipitation of those on the free surface of adjacent or remote grains with the consequent reduction of pore space and permeability. The above sequence of processes is common to other phenomena such as aging (see Mitchell & Solymar, (1984), Hueckel et al. (2001), Hueckel et al. (2005)), or pressure solution in petroleum reservoir modeling (Rutter (1976), Lehner (1995). Hu & Hueckel (2007) have developed a sequence of threescale models to simulate aging, and identified leading feedbacks and feedforwards of intersacale coupling to evaluate the evolution of meso-scale stiffness and permeability (Hueckel & Hu, 2009). A summary of the feedbacks and feedforwards involved in the process are redrawn in Figure 1. As can be seen in the schematic the whole phenomenon of compaction consists of a number of coupled processes that are either parallel or sequential in time. They can be arranged to form alternative scenarios, which can be modeled, to select the most reasonable one. One such three-scale scenario for chemo-plasticdiffusional processes is described in detail by Hu and Hueckel 2007). In what follows only the main concepts are presented. The models at the micro-scale include stress-strain relationship, dissolution law, and intra-grain diffusion. At the meso-scale the models include intergranular diffusion with precipitation and the resulting increase of material stiffness. The macroscale is not shown in figure 1. The micro-scale the medium is a porous material of the solid grain minerals. Its porosity is the internal grain porosity, and the mechanical properties of the material are those of the

whereas

The superimposed dot over a symbol denotes a time rate. Dilatancy damage at the sub-grain scale is a critical variable for this concept as a vehicle of the chemo-mechanical coupling. It is linked to microcracking, which first, provides a connected network across the damaged part of the grain that becomes instantly permeated with water as a result of suction induced by dilatancy. Second, micro-crack walls form new solid-fluid interface, which constitute a source of dissolution of mineral species, that is solid mass removal. Third, irreversible micro-slips occur across micro-cracks. As a result of micro-slips and mass removal, the yielding behavior of the material is affected by two competing plastic - hardening mechanisms: deviatoric strain-hardening and mass removal softening. Hence, pc which is the apparent preconsoliation stress, i.e. isotropic size characteristics of the yield locus, depends on two hardening parameters, which pl are mechanical (εq ) or chemical (ξ) in nature (Hueckel 2002).

Chemical softening parameter ξ ≤ 1 is an accumulated relative mass removal of a single mineral species that dominates the material strength, computed with respect to the original total mass of that particular species. The relationship between change in the apparent preconsolidation stress pc and a reaction progress

28

variable is established empirically. A mineral in the example, dominating the strength of quartz sand is silica. Dissolution reaction of silica in water may be measured through a change in activity of its product, which is silicic acid H4 SiO4 formed in the aqueous solution. The rate of silica dissolution is determined by Rimstidt and Barnes (1981) formula as proportional to the specific surface area of the solid-fluid interface A, normalized with respect to 1 m2 to yield a non-dimensional quantity Ã

pl f˙ (δij , εq ξ) = 0 (see e.g. Hueckel (2002) therefore it is a function of rates of stress and reaction progress

In particular, at constant stress, an irreversible strain rate is generated proportional to the reaction rate. The yield locus in the form of a set of linear functions for single principal stress components has the advantage of a very simple kinematics, yet capturing the essence of straining,

where ai are activities, and γ i ,activity coefficients, of i-th species, while k+ and k− are rate constants of respectively forward and backward reactions. Ã is a dimensionless specific interfacial surface area, as above, per unit mass of pore fluid. For details see Hu and Hueckel, 2007). ξ is a reaction progress variable constrained by the inequalities: 0 ≤ ξ ≤ 1; when ξ = 1, the reaction is completed, that is all silica is removed from the material. In the current context the damage occurs within a single grain and consists in opening of micro-cracks. A new scalar variable, ã, represents the amount of the added interface surface area per unit volume of the grain medium. It is linked to the relative reaction area, Ã,

where α and β are constants, σ3 remains undetermined. As discussed earlier, ξ is the relative mass removal, as its rate is described by eq. (20). At this point the precipitation term is ignored, as it would lead to a constitutive non-linearity, making it impossible to solve the equation system semi-analytically. The intra-grain diffusion of silicic acid is limited to the damaged zone (in radial coordinates with axial symmetry here), as shown in Fig. 3a. It is described by a linear reactive diffusive transport law combined with a mass balance law, with a reaction term (last term of the RHS), which through its link couples it to deformation via eq. (21):

where ρ0 = 1 kg/m3 , ρw is the density of water, ng is porosity of the grain solid. The new internal interface surface area generated by the micro-cracking per unit volume is proposed to be proportional to the volumetric strain. Hence,

where XH4 SiO4 is molar fraction of aqueous silica in the fluid phase within the grain. Assuming the pore fluid to be a dilute solution, the molar fraction of any of its species k, has mass content mkF = MkF /V0 , linked to molar fraction, XkF through V0 is the reference volume of the entire grain medium. D is the solute diffusion coefficient. The above system of constitutive equations is to be supplemented by equilibrium equations and kinematics expression to yield displacements. Hu & Hueckel (2007) provided a solution to the coupled chemomechanical deformation-diffusion through what is known as Johnson’ (1985) approximation for the contact problem, by assuming it is axisymmetric. Experiments with compressed pure silica grains in contact with water provide evidence of formation of the solid coating of silica polymer links, growing in density and strength in time as short as 14–21 days (Guo & Hueckel, 2013, 2015).

where φ is a constant, whereas φc represents the specific surface area of pre-existing voids. For εv > 0; φ = 0 which aims at excluding the compressive strain for which there are no micro-cracks and hence no change in dissolution surface area. Therefore

Notably, precipitation at the dissolution site is neglected. The irreversible strain rate mode is determined by the associated flow rule, whereas its magnitude by the plastic multiplier λ˙ results from the extended Prager’s consistency condition,

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Figure 3. (a) A cartoon showing intra-grain diffusion of the dissolved species; (b) inter-grain pore with the flux of the dissolved silica; (c) pore fluid flow through a dissolution/precipitation altered meso-scale inter-grain pore system.

Figure 4. (a) Inter-grain porosity change (n), as originated from deformation of the grain (n1 ) and from precipitation induce grain coating; (b) Flux of dissolved silica from a grain as a function of intra-grain mass transfer coefficient M = k+ a2 /Dx0 , where x0 is the initial concentration of silicic acid within the grain.

5

CHEMO-MECHANICALLY INDUCED EVOLUTION OF PERMEABILITY

its variable part of ua as a function of time depending on the dissolution rate constant k+ . The rate of the formation of coating can be calculated as a change in the coating thickness, d˙ c over an area, dS of the free surface, as certain number of moles of silica are precipitated in the water volume, dV,

In a similar way to the evolution of stiffness, the evolution of permeability is evaluated at the meso-scale, at which we consider as a REV a quadruplet of 1/4th grains, with equal radii, R, as shown in Fig. 3b. There are two processes that affect the inter-grain pore system as shown in Fig. 3b: the increase of the contact size between two stressed grains due to chemoplastic deformation of the grain and the precipitation of the solute within the pore. In terms porosity variation, the effect of contact area increase is more significant, as seen in Fig. 4a. However, it is an open question if the same is true for the permeability evolution. The most important from the present perspective is the result concerning the flux of dissolved mineral, Fig. 4b. As is seen it heavily depends on the reaction rate coefficient and the diffusion coefficient. The current radius of contact may be approximated as a = a0 + ua where a0 is the initial radius of the contact, while ua is the vertical indentation advancment. Fig. 5a shows the evolution of the radius a in terms of

where ̟p = Vvoid /Sfree = (2/π − 1/2)R, while υSiO2 and υHO2 are the molar mass of SiO2 and H2 O, respectively. XH4 SiO4 (θ, t) is the distribution of precipitating aqueous silica determined from a steady state solution of diffusion-precipitation transport eqution, where θ, −π/4 < θ < π/4 is an angular coordinate along the grain surface, with a grain mineral mass flux ± fp (t) = Ja πa/4̟p , as a boundary conditions at the contact points, while Ja (t) the mass flux across the inner boundary of the grain, r = a (see Hu and Hueckel, (2007) for details).

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Figure 5. (a) Increment of the contact area (also grain penetration) as function of time and rate constant; (b) relative coating rate of the walls of inter-grain pore (also of free surfaces of grains) for different values of constant inter-grain pressure. Normalized with respect to grain size, R (calculated for k+ = 1 × 10−12 s−1 ).

Table 1. Characteristics dimensions of the flow conduit. Name

Symbol

Value

grain size estimated damage zone radius size of the indent radius asperity size = contact slit initial (nominal) pore opening

R b a0 = b/10 δc δp0

1 mm 0.7 mm 0.07 mm 0.05 mm 0.86 mm

As a result of linearization of eq. (x), the coating rate becomes uniformly distributed, i.e. independent of θ.

The two variables shown in Fig. 5 control the overall change in permeability of the pore system as visualized in Fig. 4c: the mechanical displacement of the inner radius of the pore (Fig. 5a) and the relative coating rate d˙ c /R/R plotted against time in Fig. 5b. Notably their dependence with time is different. The change in the contact area appears to accelerate with time, whereas the coating rate increases nearly linearly, after an initial period. To evaluate the effect of the two factors, a simple formula based on Poisseuille flow through two connected in series planar tubes of different thickness, is is employed (after Hueckel et al., 1997) in examining the meso-scale structural changes. Given that gravity plays an essential role in the stress pattern, in which horizontal contacts are usually acted upon by twice as big grain force than vertical contact, we shall limit our consideration to conduit denoted as F1 . The explicit data needed to calculate the permeability evolution are listed in Table 1. The flow is envisioned as occurring through a 2D flat vessel composed of the intergranular slit

Figure 6. Schematic of an idealized flow conduit F1 across the inter-grain pore space.

communicating with the adjacent inter-grain pore, as shown in Fig. 6. The intergrain slit has a very limited opening, equivalent to a size of an asperity, or a piece of mineral debris locked in the contact space. As such it will be assumed not to change during the process of deformation, nor affecting the contact extent. Clearly the vessel is a very simplistic representation of the conduit. Especially the shape of the portion representing the inner-grain pore, with its initial size taken as an average between the pore entrance and its maximum, is a major simplification. However, as our goal is to capture main features of the evolution of the flow, following the earlier experience with such models (Hueckel et al. 1997) these simplifications seem acceptable. The specific discharge of the two conduits connected in series, per unit area over which the vessel

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is the only conduit, in this case 2Rx1, is obtained from the rules of a series connection, which are

where p, pc and pp are total, contact and pore fluid pressure difference between the exit and entrance to the respective segment of the conduit, where the flow velocities in the contact portion and pore portion, and the one with respect to the entire cross section area, are respectively equal to

Figure 7. Evolution of permeability: K t (t)-intrinsic permeability factor (left scale); ratio of the thickness of contact slit to the pore size, δc /δp (right scale); integrated precipitation pore coating dc /R.

where µ is dynamic viscosity of the pore fluid, and K s is a resultant intrinsic permeability of the medium. Combining (26) and (27) one arrives at the expression for evolution of the specific discharge of the medium expressed in terms of a variable resultant intrinsic permeability,

Hence,

Figure 8. Stress–strain curve from Uniaxial Compression Test on Gravina di Puglia calcarenite, dry (d1&2), wet with water (w1&2), and with acid solution (w-d1&w-d2) (from Ciantia et al., 2015).

the increase of stiffness is concerned (Hu and Hueckel, 2007), while it is not felt in terms of permeability until it reaches a critical moment when porosity drastically drops in a short time. A practical conclusion from the simulation concerns the critical time to clogging that may be easily estimated from the mass dissolution rate needed to produce a solute to fill almost completely the pore.

where K t is a coefficient describing the evolution of the intrinsic permeability due to chemo-mechanical coupling in the medium, υi denote the molar mass of species “i”. As may be easily anticipated from the form of the expression for K t , the evolution of the permeability will be not much sensitive to the effect of pore coating, until well into an advanced stage when the size of the pore approaches the size of the contact slit, as seen in Fig. 7. The intrinsic permeability factor (time dependent) is seen to decline slightly (30%) in the first 1200 hours mainly due to the increase of the contact area, whereas it seems to be unaffected by the pore wall coating by precipitating mineral. This abruptly changes in a short time, when the pore is practically clogged by the precipitate, and hence its size becomes of the order, and then even smaller than the intergranular contact slit. So, within a few days the permeability drops over one order of magnitude, and more. It is therefore concluded that precipitation is felt very quickly as far as

6

CHEMICALLY ENHANCED CRACK PROPAGATION

Subcritical crack propagation resulting from a spontaneous or engineered change in the rock chemical environment is of relevance in several energy technologies, among which are unconventional oil and gas recovery, and enhanced geothermal systems. The enhancement consists of a combination of fluid pressure and injection of acids. Acid chemically softens the material, which occurs relatively quickly, especially in carbonate rocks. The main question is to correlate

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Figure 9. Circumferential stress distribution near the crack tip, for a chemo-elastic behavior with coupled chemical shrinkage coefficient, dependent on the shear strain invariant for a) a chemically swelling rock (silicate) and b) a chemically shrinking rock (carbonate).

the chemical flux to the rate of crack propagation. Hu and Hueckel (2013, 2014) addressed the effect of mineral mass removal on the material strength, via coupled chemo-plasticity approach. The chemical part of the processes being explicitly rate-dependent, requires plasticity to be treated incrementally and iteratively. Simplified calculations with Extended Johnson approximation (all fields are axially symmetric around the crack tip point) makes it possible to follow the stress evolution as minerals are dissolved. The approach is analogous to that used in the problem of indentation discussed in the previous paragraphs, and will not be elaborated here. To investigate the effect of coupling of chemicals on elasticity in the vicinity of a crack subject to acidizing requires quite different tools (Hu and Hueckel, 2016). The release of mineral mass in a reaction into liquid phase affects solute diffusion, while the rate of mass release is dependent on local acidity. As embodied through equation (9) there are two main mechanical responses to the mass removal. There is an additionally induced (stress independent) strain, often seen to be proportional to the mass removal, with the proportionality (chemical deformation) coefficient, likely dependent on the material damage. A good example here is osmotic swelling in shale, or swelling of silica in contact with water. In contrast in carbonates water induces shrinkage of rock (Ciantia and Hueckel, 2013. The second effect results from the change in elastic stiffness modulus (shear or/and isotropic). Figure 8 shows a decrease in elasticity modulus, between a material that is dry, wet and wetted with acid water (Ciantia et al. (2015)). In what follows only the first aspect is discussed. A particular form of the chemical shrinkage coefficient is chosen, as linearly dependent on deviatoric strain invariant to simulate the effect of microcracking (Hu & Hueckel, 2016). Such dependence was found to

be physically most justified and acceptable under the assumption of elasticity (if limitation to monotonic process is imposed). The key step is introduction of the Airy stress function φ (Airy, 1863) defined as

Substituting the stress-strain relationship into the usual strain compatibility equation, with the use of equilibrium equations, we can eventually obtain fourth order equation for the single variable of the Airy function φ.

where chemical shrinkage coefficient is a linear function of deviatoric strain invariant.

The solution of the set of equation follows the one used for thermo-elasticity (Saad, 2005) and can be found in Hu and Hueckel, 2016. The most significant finding concerns a substantial difference in the effect of acidized water on the subcritical crack propagation in sandstone and carbonate, the former one elastically swelling and the latter one shrinking in response to acidized water injection. Comparing the symptomatic distribution of circumferential stress in front of the crack tip, one finds that the stress is much higher for the shrinking rock than for chemically swelling rock, Figure 9a and b. Hence, silicate rocks require much higher base pressure or acid

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concentration than carbonates to activate subcritical propagation. 7

Hu M.M. and T. Hueckel, 2013, Environmentally Enhanced Crack Propagation in a Chemically Degrading Isotropic Shale, Geotechnique, SIP 2013, 63, 4, 313–321. Hu M.M. and T. Hueckel, 2016, A chemo-elasticity coupling in an acid enhancement modeling of pressurized crack propagation, Geomechanics for Energy and the Environment, v. 7, 48–57. Hueckel, T. 1997, Chemo-plasticity of Clays Subjected to Flow of a Single Contaminant and Stress, International Journal for Numerical and Analytical Methods in Geomechanics, 21, 1, 43–72. Hueckel, T., M. Kaczmarek and P. Caramuscio, 1997, Theoretical Assessment of Fabric and Permeability Changes in Clays Affected by Organic Contaminants, Canadian Geotechnical Journal, 34, 4, 588–603. Hueckel, T., G. Cassiani, Fan Tao, A. Pellegrino and V. Fioravante, 2001, Effect of aging on compressibility of oil/gas bearing sediments and their subsidence, J. of Geotechnical and Geoenv. Eng, ASCE, 127, 11, pp. 926–938. Hueckel T., 2002, Reactive plasticity for clays during dehydration and rehydration. Part I: Concepts and options, Int J Plasticity; 18: 281–312. Hueckel, T., Cassiani G., Prévost J.H. and Walters D.A. 2005, Field Derived Compressibility Of Deep Sediments of Northern Adriatic, Proceedings Seventh International Symposium on Land Subsidence (Sisols 2005), Shanghai, China, October 2005, Spec. Vol., F.B.J. Barends et al., eds., 35–50. Hueckel, T. and Hu, L.B. 2009, “Feedback mechanisms in chemo-mechanical multi-scale modeling of soil and sediment compaction”, Computers and Geotechnics, 36, 934–943. Johnson K.L., 1985, “Contact Mechanics”. Cambridge: Cambridge University Press. Lehner F.K. 1995, “A model for intergranular pressure solution in open systems” Tectonophys, 245:153–70. Loret, B., T. Hueckel, A. Gajo, 2002, Chemo-mechanical coupling in saturated porous media: elasto-plastic behaviour of homoionic expansive clays, International Journal of Solids and Structures, 39, 2773–2806. Mitchell, J.K. and Solymar, Z.V. 1984, Time-dependent strength gain in freshly deposited or densified sand. J. Geotech. Engrg., ASCE, 110(11), 1559–1576. Rutter E.H., 1976, The kinetics of rock deformation by pressure solution, Phil. Trans R Soc A, 283:203–19. Rimstidt J.D., Barnes D.L., 1980, The kinetics of silica water reaction” Geochim Cosmoch. Acta; 44, 1683–99.

CONCLUSIONS

Chemo-mechanical coupling is widely engineered, or when naturally occurring it needs to be dealt with in the energy industry to enhance the recovery and productivity. However, the engineering practice is widely based on costly experience and errors often leading to disasters. The attempts were presented to show a potential for developing predictive tools, allowing for an optimalization of engineering solutions with environmental constraints in mind. It is clear that such predictable power can only be achieved if an appropriate, and appropriately designed experiments are available. This work should help to design the experiment. REFERENCES Airy, G. B. 1863, “On the Strains in the Interior of Beams”. Philosophical Transactions of the Royal Society 153: 49–80. Bayly, B. 1992. Chemical Change in Deforming Materials Oxford UP, New York. Ciantia, M.O., Castellanza R., Crosta, G.B. and T. Hueckel, 2015, Effects of mineral suspension and dissolution on strength and compressibility of soft carbonate rocks, Engineering Geology, 184, 1–18. Gajo, A., B. Loret, and T. Hueckel, 2002, Electrochemo-mechanical coupling in saturated porous media: elasto-plastic behaviour of heteroionic expansive clays, International Journal of Solids and Structures, 39, 4327– 4362. Guo R. and T. Hueckel, 2015, Silica polymer bonding of stressed silica grains: an early growth of intergranular tensile strength, Geomechanics for Energy and the Environment, v. 1, 1, 48–59. Guo R. and T. Hueckel, 2013, Growth of Silica Polymer Micro-Structures within Stressed Intergranular Contacts in Sands: A Chemo-Mechanical Coupling, Geotechnique SIP 2013, 63, 4, 322–330. Heidug W.K. and Wong, S. W., 1996, Hydration swelling of water absorbing rocks: a constitutive model, Int. Jnl. Num. and Anal. Meth. in Geomech., 20, 402–430. Hu L.B. and Hueckel T. 2007, Coupled chemo-mechanics of intergranular contact: toward a three-scale model, Comput. Geotech, 34(4):306–327.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Thermomechanical properties of a new small-scale reinforced concrete thermo-active pile for centrifuge testing A. Minto, A.K. Leung, D. Vitali & J.A. Knappett University of Dundee, Dundee, Scotland, UK

ABSTRACT: The use of thermo-active geo-structures has been recognised to be a sustainable engineering solution that can reduce carbon emissions from civil infrastructure. Physical modelling in a geotechnical centrifuge has been increasingly used to study the behaviour of this kind of geo-structures and their interaction with the surrounding soil under cyclic heating/cooling loads. Previous studies have been limited by the choice of materials used to model thermo-active geo-structures (such as aluminium and conventional concrete), due to inaccurate scaling of the thermal properties and the inability to capture the quasi-brittleness and strength properties of reinforced concrete (RC) due to improper scaling of aggregate sizes. The paper aims to develop a new thermally-enhanced plaster-based model concrete which can realistically reproduce both the thermal and mechanical properties that are representative of concrete at prototype scale. The new model concrete, combined with steel wire reinforcement (i.e. geometrically scaled reinforcing bars and stirrups), was then used to create 1:20 scaled RC thermo-active piles. Effects of temperature on their thermomechanical behaviour, including the coefficient of thermal expansion, moment capacity and flexural stiffness, were investigated. The suitability of using the newly-developed RC thermo-active piles for future centrifuge testing is discussed. 1

INTRODUCTION

internal diameter, and hence the second moment of area, of the model pile. In terms of thermal properties, aluminium has a coefficient of thermal expansion (CTE) of 22.2 µε/◦ C (where µ is micron; and ε is thermally-induced axial strain). In their aluminium piles, an epoxy resin with a thickness of 1.5 mm had to be applied on the pile shaft to protect the strain gauges. As the CTE of epoxy is 85 µε/◦ C (Rotta Loria et al., 2015), the CTE of the overall instrumented aluminium pile should be higher than 22.2 µε/◦ C, which is thus at least 30% higher than the CTE of unrestrained RC (15–16 µε/◦ C; Goode III et al., 2015). This makes it difficult for this kind of aluminium pile to realistically capture the soil-structure interaction of thermo-active piles that are made of RC in the prototype. Numerical studies (Yavari et al., 2014) have shown that the coefficient of thermal expansion of a thermo-active pile plays a significant role in affecting the mobilisation and distribution of pile axial loads under a combination of mechanical and thermal loadings. Moreover, this type of elastic aluminium pile is not able to mimic the nonlinear quasi-brittleness feature of RC under tensile and bending stresses such as when subject to lateral loading conditions (Karihaloo and Huang, 1991). Stewart and McCartney (2014) modelled a thermoactive pile using RC with scaled steel reinforcement and scaled aggregates in their centrifuge tests. Although the thermal properties of prototype RC might be properly scaled using RC as a model pile, the use of gravel with a maximum diameter of 6 mm (in model scale) to model coarse aggregates could pose a scaling problem of the mechanical properties. At 24g

Thermo-active geo-structures such as pile foundations and diaphragm walls have been used to exploit shallow geothermal energy to provide heating and cooling to buildings (Brandl, 2006). A number of field tests (Laloui et al., 2006, Bourne-Webb et al., 2009, Murphy and McCartney, 2015) have been conducted to investigate the thermomechanical behaviour of these types of structures and their interaction with the surrounding soil. It was demonstrated that cyclic heating/cooling processes introduced additional stresses and strains to the thermo-active geo-structures. In order to improve understanding of the soil-structure interaction in more detail, small-scale physical model tests in a geotechnical centrifuge have been conducted (Stewart and McCartney, 2014, Ng et al., 2015). By elevating the acceleration of a physical model by N times Earth’s gravity (i.e., N -g), the stress levels experienced by the soil in a small-scale physical model are similar to that in a full scale prototype, enabling the stress dependency of the soil behaviour to be correctly captured. A major challenge of testing a thermoactive geo-structure in the centrifuge is the selection of appropriate model materials that model both the mechanical and thermal properties realistically and simultaneously. In the centrifuge tests performed by Ng et al., (2015), aluminium alloy was used to model a thermoactive pile. Scaling of the mechanical properties such as the axial or flexural rigidity of the aluminium pile can be achieved through careful selection of the

37

which Stewart and McCartney (2014) adopted in their centrifuge tests, the prototype diameter of the gravel was 144 mm, which was 7 times larger than the diameter of coarse aggregates in prototype concrete. This size effect would potentially lead to an over-strength of RC (Litle and Paparoni, 1966, Belgin and Sener, 2008). This modelling method is thus limited to relatively low scaling factors (or g-level) to minimise any over-strength of RC. In order to more realistically capture the nonlinear quasi-brittleness feature and failure mechanisms of concrete in centrifuge at higher scaling factors, Knappett et al. (2011) developed model concretes using plaster-based mortars. In the mortar mix, fine silica sand was used to geometrically scale the aggregate found in concrete. Such model concrete was shown to have representative mechanical strengths, in terms of unconfined compressive strength and modulus of rupture. The model concrete has been successfully used for modelling various engineering structures such as piles (Al-Defae and Knappett, 2014) and bridge piers (Loli et al., 2014) in the centrifuge where simultaneous modelling of stiffness and strength are crucial. For modelling thermo-active RC geo-structures, this type of model concrete requires further modification to ensure correct scaling of the thermomechanical properties. This study aims to develop a new type of model concrete that can realistically scale the mechanical and thermal properties of real concrete for future centrifuge testing of concrete energy geo-structures for larger scaling factors. An application of the new model concrete to produce RC thermo-active piles is presented. Temperature effects on thermomechanical properties, including the coefficient of thermal expansion, moment capacity and flexural stiffness, of a model pile were tested. By comparing the model and prototype properties, the suitability of testing this type of new RC model pile in centrifuge is discussed. 2 2.1

Figure 1. Particle-size distribution of silica sand and copper powder.

distribution of the silica sand and copper powder were measured using a laser diffraction analyser. The results are compared in Fig. 1. It can be seen that both the sand and copper powder were uniformly graded, and that the size of copper powder was finer than that of the sand. 2.2 Thermomechanical properties of the new model concrete In order to investigate the effects of the copper powder content on the thermal conductivity of the model concrete, a series of laboratory testing was carried out using a hot-box apparatus developed by Jones et al. (2007). It is an apparatus that can create a temperature gradient across a slab-shaped specimen (45 mm width, 150 mm long and 150 mm height) and also can measure the corresponding heat flux. At the steady state, the thermal conductivity of the specimen can be determined by dividing the heat flux by the temperature gradient, according to Fourier’s law. Model concrete mixed with five different percentages of copper powder (by volume), 0%, 1.5%, 3%, 6% and 12% were tested. The test results depicted in Fig. 2 show that the thermal conductivity of the model concrete originally designed by Knappett et al. (2011) was 0.4 W/(m·K), which was lower than the typical range of concrete (i.e., 0.9 to 1.1 W/(m·K); Kanbur et al. (2013)). When copper powder was added, there was almost a linear increase in the thermal conductivity with the amount of copper added. This shows that the addition of copper powder was effective to enhance the thermal properties of the model concrete. In particular, 6% and 12% copper powder contents appeared to match the prototype range reasonably well. Although adding copper powder could significantly improve the thermal properties of the new model concrete, one concern is any detrimental effects of such addition on the mechanical properties. For this purpose, a series of four-point bending (FPB) tests were conducted to measure the modulus of rupture (fr ) of prismatic specimens (25 × 25 × 250 mm) when different percentages of copper powder were added to the model concrete. The testing procedures outlined by Knappett et al. (2011) were adopted.

NEW MODEL CONCRETE Constituents of the model concrete

The new model concrete developed in this study is based on the design previously proposed by Knappett et al. (2011). The original design consisted of a mixture of β-form surgical plaster (manufactured by Saint Gobain), water and fine silica sand (Congleton HST95). The sand was used to geometrically scale and approximate the size of aggregates found in concrete. Knappett et al. (2011) suggested that a water/plaster (W/P) ratio of 0.9:1 and a sand/plaster (S/P) ratio of 1:1 would result in a model concrete that can realistically mimic the mechanical properties of concrete in prototype. In order to properly scale and mimic the thermal properties of prototype concrete, a new constituent, copper powder (manufactured by Phoenix Scientific), was added to the design mix to enhance the thermal conductivity of the model concrete. The particle-size

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due to the rapid evolution of the pore structure during the hydration process (Song et al., 2009). Fig. 4(c) shows the model concrete mix at × 300 where both the sand and copper particles are visible. There was a gap between the irregular-shaped sand particles and plaster, hence creating some weakened interfaces. However, such gapping was not found for the copper particles. It must be pointed out that no chemical bonding was formed along the plaster, sand and copper particles after the hydration process. These constituents were bonded physically through weak inter-particle van der Waal force. Such physical bond is an important feature of the model concrete to realistically mimic the non-linear quasi-brittleness nature of concrete in prototype, which cannot be captured by existing elastic model piles made of aluminium, and which avoids the potential over-strength of using cement as the binder.

Figure 2. Effects of copper powder content on thermal conductivity of model concrete. Error bars represent standard errors (n = 3).

3

NEW MODEL RC THERMO-ACTIVE PILE

3.1 Structural analysis and design Before producing a RC thermo-active pile, a detailed structural analysis and design was carried out. In future centrifuge tests, model thermo-active piles with a square cross-section will be used to stabilise a silty slope in a 1:20 scale model tested at 20 g. Preliminary analysis and a literature review of previous studies using piles to reinforce soil slopes (Al-Defae and Knappett, 2014, Hayward et al., 2000) suggests that a moment capacity of 250 kNm would be sufficient for the piles to maintain the slope stability for representative soil properties and slope angles. Based on the targeted moment capacity, the pile reinforcement was designed according to the design procedures outlined in Eurocode 2: Design of Concrete Structures (BSI, 2004). Hence, at model scale, the thermo-active pile will have a square cross section with the side of 25 mm and a length of 250 mm. In the following discussion, all dimensions are expressed in model scale, unless stated otherwise. The arrangement of the reinforcement is detailed in Fig. 5. It was a doubly-reinforced concrete pile, since to allow bending in either or both horizontal directions in future centrifuge testing. All the longitudinal reinforcement bars chosen were 1.25 mm in diameter, while the diameter of shear reinforcement (aka stirrups) was 0.6 mm. The thickness of concrete cover was 2 mm. The total area of steel reinforcements (As ) was 12.93 mm2 for a cross-sectional area of 625 mm2 of the model pile. This means that the reinforcement ratio, As /bd (where b and d is the breath and the depth of the model pile, respectively), is 2.1%, which falls within a typical range found in high-strength doubly reinforced concrete beams under flexural loads (Rashid and Mansur, 2005). The model reinforcement used in this study was a stainless steel (Grade 316), which was manufactured by Ormiston Wire Ltd. It has a yield strength

Figure 3. Effects of copper powder content on fr of the new model concrete. Error bars represent standard errors (n = 6).

Fig. 3 shows the variations of copper powder content with normalised fr (by the values obtained from 0% copper powder content, fr0 ). It is clear that the addition of copper powder up to 12% did not cause significant changes in the mechanical properties. The addition of copper powder could thus enhance the thermal conductivity of the model concrete, while simultaneously maintaining its ability to mimic the mechanical properties of concrete. 2.3

Micro-structure of the new model concrete

In order to have a better understanding of the interaction between the plaster, sand grains and copper powder as well as the uniformity of these constituents within the mixture, the micro-structure of the new model concrete was imaged by a scanning electron microscope (SEM). Fig. 4(a) shows an SEM image at a magnification of × 55. The image depicts some silica sand physically interlocked with the flake-shaped plastic matrix. The distribution of the sand appears uniform. At a higher magnification of ×500 (Fig. 4(b)), the fine copper particles can be viewed. They were spherical in shape and physically embedded into the fibre-like irregular structures of the plaster. This kind of micro-structure is a key feature of the β-form plaster

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Figure 5. Cross-section and reinforcement details of a 1:20 model RC thermo-active pile.

Figure 6. Overview of the formwork used to cast two model piles.

reinforcement bars and stirrups were coated with epoxy resin and then immersed in a pool of HST95 silica sand for 24 hours to ensure an intimate mechanical frictional contact between the reinforcements and the sand, preventing the reinforcements from slipping inside the model concrete. In order to allow water to be circulated inside the new model concrete, two pairs of closed-loop U-shaped silicon pipes were attached to the internal surface of the stirrups (Fig. 5), which is a typical arrangement for a thermo-active pile prototype (Loveridge and Powrie, 2013). Placing the pipes closer to the pile perimeter aimed to minimise their thermal interaction and the heat loss to the concrete material, hence achieving a more uniform distribution of pile temperature. Cecinato and Loveridge (2015) showed that circulation pipes spaced too closely can reduce the heat transfer efficiency to the surrounding soil. The diameter of the silicon pipe was 3 mm, which was the minimum internal size of the pipe required to minimise the thrust force caused by the change in water flow direction at the U-turn of the pipe (see Fig. 6). Three thermocouples were attached to both ends and the centre of the reinforcement bar for monitoring the temperature distribution along the pile. When the reinforcements, silicon pipe and thermocouples were fixed in position, the mix of model concrete (including plaster, water, silica sand and copper powder) was poured into the formwork. The mix

Figure 4. SEM images of at (a) ×55; (b) ×500; and (c) ×300 magnification.

of 460 MPa (Knappett et al. 2011) and a coefficient of thermal expansion of 18.5 µε/◦ C (Lee et al., 2007). 3.2

Model preparation

Formwork with a dimension identical to the model pile (25 mm × 25 mm × 250 mm; Fig. 6) was constructed to cast the model piles. Before casting, all

40

was allowed to cure for 28 days in a room maintained at an ambient temperature of around 20◦ C. In order to heat and cool the model pile, a heating system (Julabo Ltd; Model F12) that can control and maintain constant water temperature between 1 and 99◦ C was connected to the silicon pipes. Change in pile temperature was monitored by the three thermocouples embedded in the model pile. 4 TESTING OF THE MODEL PILE 4.1 Test plan Figure 7. Typical setup of a FPB test for model pile.

Laboratory testing was undertaken to determine the thermo-mechanical properties of the small-scale RC thermo-active pile made by the new model concrete. The primary aim was to ensure the design of the model pile was mechanically and thermally representative of the prototype RC thermo-active pile. An important thermal property that needed to be characterised was the coefficient of thermal expansion (CTE). Upon pile temperature changes, the pile expansion (upon heating) and contraction (upon cooling) would have direct effect on the soil-pile contact, hence affecting the soil-pile interaction and the mobilisation of pile axial load (Yavari et al., 2014). Another test series aimed to determine any temperature dependency on the flexural properties, which is a key thermo-mechanical property that governs the pile behaviour when the piles are subjected to lateral loading in slope stabilization applications. In both types of tests, effects of the percentage of copper powder addition were studied. This aimed to determine any optimum amount of copper powder that could realistically scale both the mechanical and thermal properties of the model pile simultaneously.

The CTE tests were started by submerging each model pile in a water bath with a controlled temperature of 50◦ C for at least two hours. When a uniform distribution of pile temperature of about 50◦ C was reached at the steady state (as indicated by the three thermocouples), each model pile was removed from the water bath and any change in pile length between the two reference points was measured immediately using a calliper with an accuracy of 0.01 mm. The measurements were taken as quickly as possible to minimise heat loss from each model pile. For the measurements of the pile moment capacity, the four-point bending (FPB) testing method was adopted (Balendran et al., 2002). Two pile temperatures were considered: circulating water at ambient temperature (20◦ C) and an elevated level of 50◦ C. At each pile temperature, model piles cast with three different amount of copper powder (0%, 6% and 12% by volume) were tested. 17 FPB tests were carried out (7 tests at 0%, 4 tests at 6% and 6 tests at 12%). A typical set up for a FBD test is shown in Fig. 7. The model pile was roller-supported, having a span (L) of 210 mm. Vertical loading was applied symmetrically at two locations, both of which were 35 mm away from the centre of the pile to ensure that the loads and reactions were spaced at L/3 as per typical FPB testing procedures (Huurman and Pronk, 2009). By using the heating system, water was controlled at a constant temperature of 20 or 50◦ C and was circulated to the model pile. When all thermocouples showed a temperature matching the targeted value set on the heating system, test began by loading the model pile at a rate of 0.6 mm/min. The test was complete when the pile section exhibited large deformation and formed prominent cracking.

4.2 Test procedures The testing method of CTE followed a modification of the procedures outlined in AASHTO TP 60. CTE was calculated by the change in the length of a model pile when there is an increase in pile temperature. After casting the model piles, they were coated with a silicon conformal coating spray to ensure a waterproof condition, as would be required in future centrifuge tests. Then, two reference points were defined in each model pile to determine their initial pile length. The two reference points were fixed along the axis of the two different longitudinal sides, which are orthogonal with respect to each other. From Fig. 5, ‘side 1’ refers to the four longitudinal reinforcement bars laid in parallel, while ‘side 2’ refers to the adjacent side, where no longitudinal reinforcement bars were added. By comparing the test results obtained from sides 1 and 2, any effects of heat-induced elongation of the reinforcement bars on the overall length of the model pile may be quantified. In total, three tests were conducted, one with no copper powder added (Pile A), and two replications with 6% copper powder content (Piles B and C).

5

RESULTS AND DISCUSSION

5.1 Coefficient of thermal expansion Table 1 summarises the measured values of CTE for the Piles A to C. It is found that the CTE of the model pile without copper powder (i.e., Pile A) was 15.7 µε/◦ C, which was close to the values ( Tel,grenz ).

CWRL (Equations 10 and 11):

where lel,grenz = length of the rod along which u(x) ≤ wel and lpl = length of the rod along which u(x) > wel . The solutions to Equation 5 and 3 are as follows for the plastic region of the CWRL (Equations 12 and 13):

Furthermore, Equations 10 and 13 show that the change in temperature from the current state T is the movement and normal force provoking cause. If T = 0 there are no resulting displacements or normal forces as wel and terms including wel only become relevant if T > Tel,grenz which would be contradictory to the precondition T = 0. In contrast to piles no external loads are required to provoke movement, displacements and normal forces. 8

lel,grenz is a fixed value and decribes the “elastic” length of the rod along which the displacement u(x), which also represents the soil spring deflexion, is smaller or equal to wel . lel,grenz can be determined using Equations 14 and 15.

where Tel,grenz = change in temperature for which the displacement u at the free to move end of the rod will exactly be wel . This means that once Tel,grenz is exceeded the “elastic” length of the rod is “frozen” and simply slips to the left as the “plastic” length increases with increasing T . The additional constant thermal strain along the “elastic” length resulting from T > Tel,grenz is compensated by the normal force generated in the

COMPARATIVE EXAMPLE OF CALCULATION

Comparative calculations using sand respectively a TFSB (Table 1) as backfill material have been done for a rectilinear DHP made up of a plastic jacket compound pipe DN 40/125 representing the rod. The plastic jacket compound pipe is the most common DHP in Germany (Espig 2012). The outer diameter of the plastic jacket is 125 mm and 48.3 mm for the steel medium pipe with a wall thickness of 2.6 mm. The space between the medium pipe and the plastic jacket is filled with polyurethane resin mainly for the purpose of heat insulation. The stiffness (E and A) of the pipe is dominated by the medium pipe. Shear strains between the different components of the plastic jacket compound pipe are usually neglected. The laying depth has been assumed to be 2.6 m equaling a vertical overburden stress of approximately 50 kN m−2 . The CWRLS for the backfill materials are shown in Figure 9 (standardized with sand values) and have been determined for sand by the relevant rules and standards (AGFW 2007, DIN e.V. 2010) respectively by TFSB Re-SIST tests, assuming the first warm-up stage is taking place 28 d after backfilling.

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Figure 9. Calculation example: CWRLs for TFSB (simplified) and sand; standardized with sand values.

Figure 11. Normal forces along DHP (= rod) for TFSB and sand, T = 130K > Tel,grenz .

Figure 10. Displacements along DHP (= rod) for TFSB and sand, T = 130K > Tel,grenz .

The CWRL for the TFSB includes necessary adjustments in regard to the strains of the testing rod (see paragraphs 3 and 4) by means of a developed appropriate algorithm. The CWRL for the TFSB has in addition been simplified neglecting the softening region as already indicated in paragraph 7. To make up for this neglect and in regard to findings of additional large-scale test, the plastic value of τ has been raised. Starting from a stress and strain-free state and the same system temperature the required pipe lengths, the displacements and the normal forces along the pipe for T = 130 K have been calculated. Practical questions like limitations of steel stresses are not considered within the example. Figures 10 (displacements) and 11 (normal forces) show the calculation results. In the subsequent discussion of results the term “elastic” specifies that shear stresses from the elastic region of the CWRLS are relevant and the term “plastic” that the shear stresses from the plastic region of the CWRLs are relevant.

As theoretically discussed in paragraph 7 the calculations show that a significantly smaller length of the DHP shows displacements when the backfill material is TFSB. The DHP is sooner at rest. The displacements are furthermore smaller compared to those when sand is used, but the generated normal forces are equal (as the condition of the equilibrium is full compensation of thermal elongation). The elastic length for TFSB is noticeably smaller but the normal force generated along the elastic length is higher. This is due to the fact that although compared to the CWRL for sand the elastic displacement wel to reach the higher maximum elastic shear stress τel is smaller higher mechanical strains εm are generated within the elastic length. This illustrates the higher elastic work potential of TFSB compared to sand, resulting in a higher Tel,grenz . Therefore and due to the higher plastic shear stress, the required plastic length is smaller compared to sand. The overall view clearly shows that the new backfill material TFSB enhances axial bedding of district heating pipes. This is done by reducing the pipe length showing displacements and by reducing these displacements. This reduces the need for additional technical measures like expansion joints. 9

CONCLUSIONS

The main focus of District heating engineering is axial bedding to reduce and compensate thermal induced elongations. For cost reducing Temporary Flowable, Self-compacting Backfill material (TFSB) the corresponding state of knowledge is small. A possible way to calculate displacements and normal forces of axially bedded district heating pipes (DHP) for the first warm-up stage is an axial non-linear spring-based calculation method based on a differential equation. The soil spring represents the interface behaviour between the DHP and the backfill material

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and is described by the contact-resistance-workingline (CRWL). The CRWL has to be investigated by interface tests. For several reasons and boundary conditions standard common interface tests are less suitable for TFSB. A new Rod-Shear-Test-based testing device Re-SIST (Regensburger Stab-I nterfaceScher-T est) allows the investigation and identification of the trilinear (linear, softening, plastic) CWRL for TFSB. Based on the CWRL the solution to the differential equation can be determined using appropriate Dirichlet- and Neumann-boundary conditions. Comparative calculations show that the new backfill material TFSB enhances axial bedding of district heating pipes due to its different CWRL compared to sand as the standard backfill material. The CWRL shows a significantly additional work potential. The main effects are the reduction of the pipe length showing displacements and the reduction of these displacements, whereas the same normal forces are generated. ACKNOWLEDGEMENTS This research was funded by the Federal Ministry for Economic Affairs and Technology, support codes FKZ 03ET1063B and FKZ 03T1063D, whose support is greatly appreciated. REFERENCES AGFW (ed.) 2007. Arbeitsblatt FW 401 – Verlegung und Statik von Kunststoffmantelrohren (KMR) für Fernwärmenetze. Frankfurt: AGFW.

Alpan, I. 1978. Das Last-Setzungsverhalten des Einzelpfahls. Bauingenieur 53: 293–298. Beilke, O. 1993. Interaktion des Bauwerks “Fernwärmeleitung – Bettungsmaterial”. Hannover: n.p. Deutscher Beton und Bautechnik-Verein e.V. (ed.) 2004. DBV-Sachstandsbericht. Betonoberfläche – Betonrandzone – Fassung November 1996, redaktionell überarbeitet 2004. Berlin: n.p. DIN e.V. (ed.) 2010. DIN EN 13941. Auslegung und Installation von werkmäßig gedämmten Verbundmantelrohren für die Fernwärme; Deutsche und Englische Fassung EN13941;2009+A1:2010. Berlin: Beuth. Espig, F. 2012. Schadensstatistik KMR 2010 des AGFW. Euroheat & Power 41 (5): 32–35. Geisenhanslüke, C. 2008. Einfluss der Granulometrie von Feinstoffen auf die Rheologie von Feinstoffleimen. Kassel: kassel university press. Mooney, D.T. 1998. Experimental and numerical study of the Rod Shear Test for determining steel-sand interface behavior. Arizona: University of Arizona. Musharaf, Z. & Arumugam, A. 1995. Soil-Structure Interface: Experimental Aspects. In A.P.S. Selvadurai, & M.J. Boulon, (eds), Studies in Applied Mechanics 42: Mechanics of Geomaterial Interfaces: 127–145. Amsterdam: Elsevier. Wagner, B. et al. 2013. Einsatz fließfähiger Verfüllbaustoffe zur KMR-Verlegung. Euroheat & Power 42 (9): 54–56. Wagner, B. in prep. Ein Beitrag zur axialen Bettung von warmgehenden Leitungen, speziell Kunststoffverbundmantelrohren des Fernwärmeleitungsbaus, in Zeitweise fließfähigen, selbstverdichtendenVerfüllbaustoffen (working title). Weidlich, I. 2008. Untersuchungen zur Reibung an zyklisch axial verschobenen erdverlegten Rohren. Hannover: IGBE.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Assessment of geothermal snow-melting system used in cold region area I.-Hsuan Ho & Mark Dickson Harold Hamm School of Geology and Geological Engineering, University of North Dakota, ND, USA

ABSTRACT: The improvement of pavement heating system has a great impact on transportation in cold regions, such as highway and airport pavements. In the USA, Federal Aviation Administration (FAA) invested money in developing new technologies in pavement heating system for runways and taxiways. Geothermal can be one of the efficient energy resource for these engineering needs. The observed advantages of geothermal heating system include: (1) Energy is renewable and reliable; (2) avoid using the chemical treatment; (3) increase the snow removal safety; and (4) lower the CO2 emission. Moreover, by providing a sustainable temperature higher than 32◦ F, the maintenance cost can be reduced massively due to the frozen-thawed cycles. A few applications have been demonstrated in some countries such as USA, Japan, Switzerland and Poland. However, the effectiveness and limitations of the snow melting system depends on climatic conditions, properties of geomaterials and the heat transfer mechanisms between the heat source and the pavement surface. In the state of North Dakota, the annual snowfall ranges from 26 to 38 inches and the temperatures can be below −20◦ F for several months. If the limitations can be overcome to increase the effectiveness of snow melting system using geothermal energy, the technique can also be adopted in these areas with the similar climatic conditions. In this paper, three cases of snowmelting design for pavements were reviewed, the snow melting equations using geothermal energy were revisited and the limitations on snow melting system design in ND are discussed. The strategy to increase the effectiveness of a snow melting system using geothermal energy is also addressed. Keywords: Pavement heating system, geothermal energy, CO2 emission, heat transfer mechanisms, snow melting system

1

INTRODUCTION

The least thing people in cold region would do is to drive on the highways. The presence of snow and ice on the roads is more than just a nuisance, but a genuine safety concern. There are over 200,000 car accidents every year caused by snow and sleet every year in the United States. This is not only costly, but causes hundreds of deaths every year. In order to compensate for the dangerous weather conditions, drivers must reduce their speed, which can cause traffic congestion and millions of dollars in reduced productivity. Snow buildup on airport runways can make an airport inoperable, creating hazardous landing conditions and costly delays. This is why so many public and private organizations invest in snow removal and snow melting systems. These systems remove snow and ice buildup by chemical treatment, ploughing, or application of heat. Unfortunately, many of these systems can be expensive, inefficient, harmful to the environment, or too slow to respond to the snow in an appropriate amount of time. Moreover, the frozenthawed cycle to the pavement materials increase the cost for maintenance.

The snow-melting methods have been very attractive to researchers. Several types of heating or snowremoval methods have been used and developed in the past decades, such as vehicle removal, chemical removal, electric snow removal, hydronic heating system water spray and geothermal heating system. Using salt and other chemical treatments to prevent ice buildup requires the recurring costs of the chemicals, as well as maintaining the trucks that distribute the chemicals. Salts such as NaCl, MgCl2 , and various glycols are often used (Ekolist, 2001). The frequent use of these chemicals can weaken and damage asphalt and concrete over time, decreasing the longevity of roads and pavement (Melcher, 2001). After the snow melts, the chemical treatment runoff can cause local environmental damage, harming plant life and polluting local water systems. Expensive electric coils or water boiler heating systems can also be used to heat the concrete and melt snow. These systems can respond fairly quickly to snow fall, but are expensive to install, have high recurring energy expenses, can be very inefficient in colder climates, and consume large amounts of either electricity/fuel which create additional CO2 emissions.

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Global climate change (NOAA, 2006) is an increasing concern, so companies and individuals are increasingly turning towards renewable energy such as geothermal. In comparison to electric or boiler based systems, geothermal systems use about 2–10% of the energy. (3) The Kyoto Protocol target CO2 reduction is 4.2% (Olivier et al., 2011) over the next 5 years, so this system more than exceeds that requirement. Meanwhile, some geothermal applications have been conducted in Japan (Nagai et al. 2013), Poland (Zwarycz, 2002) and Switzerland…etc. In the state of North Dakota, the average temperature is 19◦ F for four months data (Nov. to Feb.) during winter. The available fluid temperature circulated to melt the snow was estimated to be 45◦ F (Gosnold, 2012). The energy required to melt the snow is 25% compared to Alaska (Rees et al., 2002; Ho and Dickson, 2015). The weather conditions are unique compared among other states in the U.S. Also, North Dakota’s shallow depth geothermal resources are abundant, especially in the western region of North Dakota. Several studies have focused on geothermal snow melting systems, however, very little research on snow-melting systems conducted in this area, with its unique climate and geological environments, particularly using low-temperature heating fluids. In order to overcome the limitations of using geothermal energy directly or through heat pumps to melt snow and balance the high heat requirement, a detailed parametric study is needed prior to a further pilot experimental study. 2

several limitations. However, it still can provide the good estimation of heat requirement. The limitations can be overcome when a finite element analysis is introduced. 2.1 Transient weather conditions Most snowfall events happen over the course of several hours, and during that time precipitation rates, ambient air temperature, humidity, wind speed, and solar radiation can change enough to affect a systems performance. An ideal system would melt snow and ice as soon as it forms on the surface, using the least amount of energy as possible. Some systems use moisture and temperature sensors to automatically activate in response to freezing conditions and precipitation, while others systems are on a timer or are manually activated. When a snowfall event begins, the rate of snowfall usually increases until the peak snowfall rate is reached.A system can be designed so that it melts snow as it falls by heating the pavement to prevent snow from forming on the surface. Preventing snow from falling has several advantages; it insures that driving conditions will be safer throughout the snowfall event, and it prevents the snow from creating an insulating layer that interferes with the melting process. Heavier rates of snowfall, lower temperatures, and several other factors affect the amount of energy to most effectively keep the surface snow and ice free. The water content of the snow also affects the efficiency of the system, as not all inches of snowfall require equivalent amounts of thermal energy to melt them.

PARAMETRIC STUDY

In order to design a geothermal snow melting system, several conditions must be considered. Previous studies on snow melting systems have been performed, many of which propose designs based on steady state conditions. Variables such as the snowfall rate, ambient air temperature, and wind speed, are often derived from weather data compiled over several years, and usually these values represent a typical or upper value one would expect during a snow fall event. The equation below by Chapman and Katunich (1956) assumes steady state conditions and is used to calculate the amount of heat needed per square foot to adequately melt snow. Chapman and Katunich Equation is derived in the following form:

where qo = total heat flux per unit area of the surface, Btu/h · ft2 (W/m2 ); qs = total sensible heat flux, Btu/h · ft2 (W/m2 ); qm = melting load, Btu/h · ft2 (W/m2 ); Ar = snow-free area ratio; qh = sum of the convection and radiation losses, Btu/h ·ft2 (W/m2 ); and qe = evaporative losses, Btu/h · ft2 (W/m2 ). This equation can be useful for roughly approximating the heat load required to melt snow, but has

3

CLIMATIC CONDITIONS OF NORTH DAKOTA

The climatic conditions are the most important influential factor when designing a snow melting system. The air temperature, rate of snow fall and frequency of snow fall, moisture content of snow, wind speed, and amount of sunlight all control the rate at which snow will be melted. The Data for the climatic conditions in North Dakota used for snow melting system design is from the National Oceanic and Atmospheric Administration. The data used was averaged over the last 15 years from 1999 to 2014. The snow melting system needs an insight of climatic conditions over the months of November to February the next year. These winter months typically have the greatest snowfall and lowest temperatures over the year, where the snow is likely to stick to pavement and affect transportation safety. Most of the data was collected from the National Oceanic and Atmospheric Administration and the World Data Center for Meteorology. Figure 1 presents the averaged fifteen-year of air temperatures in cold months from 1999 to 2014. The coldest month in a year is in January and the snow usually starts from November. The snow melting design should take account of various climatic conditions to optimize the use of available geothermal energy.

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Figure 1. Average temperature during cold months in North Dakota, USA.

Apparently, the worst climatic conditions should not be the first priority in the snow-melting system design. However, the principles of a design should consider a system which can provide the most convenient period in a year. The other significant climatic factors such as wind speed, snowfalls rate, humidity and moisture content also need to be considered properly in a design. As for the magnitude used, a guideline should be proposed and it’s basically depends on the significance of the infrastructure. 4

Figure 2. Subsurface temperature distribution.

GEOTHERMAL RESOURCE

The subsurface temperature data shown in Figure 2 was collected from a well near Grand Forks area in North Dakota, USA, where temperature data was gathered from November 1st 2011 to February 13th 2012. Although heat measurements have been taken from several different wells throughout North Dakota, However, the data is very limited, the data gathered throughout the year, allowing for a seasonal comparison of underground temperatures. According to the data, the ground temperature stabilizes at about 7 degrees C at a depth of 5–7 meters, or 16–23 feet. Although there is a slight drop in ground temperature during the coldest months, the overall the temperature is still much more stable than atmospheric weather conditions. This means that the shallow underground temperature could be used as a heat source for pavement heating during cold season. The amount of energy that can be extracted out of the earth is limited by the temperature difference between the underground and the surface. Another important thing to note about shallow geothermal energy is that it is a renewable resource; not an unlimited one. If a greater amount of energy is pulled out of the ground by the system than can be replaced, the reservoir can be depleted. This is why supplementing the system with a heat pump or

Figure 3. Geothermal resource distribution in the US (Refer to DOE, USA).

seasonal energy storage system is recommended to optimize the use of shallow geothermal resource. In the United States, over 2000 wells of heat flow data have been released. The thermal energy distribution based on milliwatts per square meter is shown on Figure 3. In the US, the abundant geothermal resources are mainly concentrated in the Western United States. On the contrary, the available geothermal resource can be used is relatively low in the rest of area, especially in cold regions. The available shallow geothermal resources become significant if a snow melting system for the pavement has to be designed. 5

SNOW MELTING SYSTEM DESIGN

Based on the climatic conditions, the available geothermal resource and the subsurface temperature in the state of North Dakota, USA. The examples of snow-melting system are presented. The design

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considers the climatic conditions such as air temperature, wind speed, snowfall rate, humidity and moisture content in heat requirement calculations and then balanced by the available geothermal heat resource. Chapman’s equation (1952, 1956) was used in calculating the energy requirements based on climatic data in North Dakota. Outlined below are the designs for the numerical model of a geothermal snow melting system. It shows the weather conditions and heat requirements according to the Chapman and Katunich Equation 1952. This equation can be used to estimate the overall heat needed in terms of Btu/h-ft2 . per second in order to melt snow at a specified snowfall rate. 5.1

Pipe design for hydronic/geothermal snow melting system

The pipe designs described below were modeled using spreadsheet calculations in Excel. The equation is the one-dimensional heat flow equation derived by Chapman (1957). The obvious advantage of having a denser pipe spacing is more heat per square foot will be supplied, but it increases installation costs and pulls more water and heat out of the geothermal reservoir. On the other hand, having fewer pipes requires warmer water, meaning the heat pump must apply additional heat to compensate, making the system less energy efficient. Based on 1-in diameter of pipes, the spacings between pipes were assumed to be 6, 4 and 2 inches, respectively. Water temperature used in the calculations is 40◦ C, as that is what most low temperature systems utilize. The low temperature is 0 ◦ C or 33 ◦ F as that is the required temperature to melt snow. The embedment of pipes is 3.25 inches below the surface; some systems embedded pipes as shallow as 2 inches but that runs the risk of damaging the pipes. The thermal conductivity was assumed to be 0.84 w/m-k which converts to 5.26 Btu/hr-ft-F. A thermal conductivity for asphalt and concrete often falls within these values. The heat requirement calculations are based on Chapman’s equation (1952, 1956) and the class III system recommended by American Society of Heating and Air-Conditioning Engineers (ASHRAE). 5.2

Heat requirements

The heat requirement for the air temperature, 0◦ F; wind speed, 15 m/s; free area ratio of snow, and rate of snowfall, in/hr, is 309 BTU/hr-ft2 . This estimated heat requirement is based on Class III recommended by ASHRAE for the worst scenario. The usual target heat requirement is mainly between 200 to 250 BTU/hr-ft2 in North Dakota. 5.3

Shallow geothermal resource

The heat flow transfer mechanism includes three governing factors: conduction, convection, and radiation. The heat flow rate based on the following equation:

where q is the heat flow rate; k is the thermal conductivity; A is the cross-sectional area; d is the thickness of the material; T1 is subsurface temperature; and T2 is the surface temperature. The pipe designs below were modeled in Excel using the one-dimensional heat flow equation described above. Three scenarios are estimated by assuming the ratio of spacing (S) to diameter of pipes (D) equal to 2, 4 and 6, respectively. When assuming heat flow rate per pipe is 115.27 BTU/hr-ft2 , thermal conductivity is 5.26 BTU/hr-ft2 , cross-sectional area, 0.1667 ft2 , subsurface temperature, T1 is 40◦ C and surface temperature, T2 is 0◦ C, the heat requirements for pipe designs, S/D equal to 2, 3 and 6 are 230, 345 and 690 BTU/hr-ft2 , respectively.

6

DISCUSSION

After calculating the heat requirements based on available weather data, the system must be capable of supplying at least 309 BTU per hour, per square foot during peak snow fall times, and be able to efficiently supply 200–250 BTU per hour, per square foot during the regular snowfall events. The lower the water temperature that can be used, the greater the energy efficiency of the system. At 40 degrees Celsius, the geothermal system is supplying approximately 30% of the systems thermal energy. This thermal energy supply increases to approximately 45-60% during lighter and more typical snowfall events. The spacing design of S/D=2.0 could compromise the structural strength of the pavement and is most likely not realistic, and supplies far more heat than is necessary. On the contrary, the design of S/D=6 cannot make the snow-melting system meet the heat requirements and work efficiently, unless a higher temperature of water (> 40◦ C) is available. This would mean the heat pump is supplying such a large percentage of the overall heat energy that it would not be practical to utilize a geothermal heat resource. The ratio, S/D=4 is most likely can supply the heat against the worst scenario by using 40◦ C of water in this area. This design also can work efficiently to melt the snow under the normal snowfall condition in winter season which required the heat ranging between 200– 250 BTU per hour, per square foot most often.

7

SUMMARY AND CONCLUSIONS

The shallow geothermal energy is a form of sustainable and renewable energy. The heat can help the cold regions to melt the snow for pavements in winter. Hence, a proper design is needed to optimize the use of this renewable energy. Several conclusions can be made as follows: (1) When designing a snow-melting system, a proper design to consider the heat requirement can melt the most events in winter is more practical.

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(2) The geothermal heat should work with heat pump to optimize the pipes design under the pavement. However, the more direct contribution from the geothermal resource is the optimal design. (3) The geothermal heating system for the pavement not only can increase the safety for road users but can extend the life for the roads and reduce the maintenance cost in cold regions. ACKNOWLEDGMENT This research is supported by NSF ND EPSCoR project. REFERENCES Chapman, W. P., (1952). “Design of Snow Melting Systems, Heating and Ventilating (April): 95 and (November): 88”. Chapman, W.P., and S. Katunich. (1956). Heat requirements of snow melting systems. ASHAE Transactions 62: 359–372. Ekolist, FHWA Report (2011): How do Weather Events Impact Roads, Federal Highway Administration. Gosnold, W. (2012): Geothermal Well Data Grand Forks North Dakota. Ho, I. H. and Dickson, M. (2015). “Assessment of Pavement Snow-Melting System Using Geothermal Energy in Cold

Region.” 1st International Conference for Geo-Energy and Geo-Environmental, GeGe 2015, Hongkong. Lund, J. W. (2000). Pavement snow melting. Geo-Heat Center Quarterly Bulletin, 21(2), 12–19. Melcher, K. (2001): Winter road maintenance spreadings in the Czech Republic and in EU countries. Nagai, N., Miyamoto, S., Osawa, Y., Igarashi, S., Shibata, K., & Takeuchi, M. (2013). Numerical simulation of snow melting using geothermal energy assisted by heat storage during seasons. Heat Transfer-Asian Research, 42(8), 724–744. NOAA (2006): NCRFC Climate and Topography, National Oceanic and Atmospheric Administration Olivier, J. G. J. et. al. (2011), Long-term trend in global CO2 emissions; 2011 report (PDF), The Hague, Netherlands: PBL Netherlands Environmental Assessment Agency; Institute for Environment and Sustainability (IES) of the European Commission’s Joint Research Centre (JRC), ISBN 978-90-78645-68-9 PBL publication number 500253004. JRC Technical Note number JRC65918.Rees, S. J., Spitler, J. D., & Xia, X. (2002). Transient analysis of snow-melting system performance. ASHRAE Transactions, 108, 406. Zarling, John P. “High Capacity Intersection Thaw System “School of Engineering University of Alaska Fairbanks, Fairbanks, Alaska 99775. Zwarycz, K. (2002). “Snow melting and heating systems based on geothermal heat pumps at Goleniow Airport” Poland Transportation.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Difficult behavior of young continental “loess – like” clayey soil deposits of mud-volcanogenetic heritage in Azerbaijan E.E. Vicente Consultant, A-Mehr, California, USA

A.M. Krumb & F. Ulbricht Fugro Consult GmbH, Berlin, Germany

ABSTRACT: These soil deposits, while in their native unsaturated condition are relatively stiff to very stiff in consistency, reflected in their relatively low compressibility and moderate shear strength. These soils, however, also exhibit “collapsible” behavior upon wetting, a sudden drastic loss of their bearing capacity, namely, softening and losing much or most of their initial “dry” shear and compressive strength. In some cases, these soils collapse even under its own weight, i.e., without any increase of external or surface loads. These soils may lose a significant fraction of their original (unsaturated) undrained shear strength, in some cases more than 50% and even up to 95%, with potentially serious consequences on the bearing capacity and settlement of shallow foundations. These soils also contain sufficient amount of active clay minerals to be considered potentially “expansive” upon wetting (subject to a low to medium degree of heave or “swelling”) which may seem an apparent contradiction. Since those phenomena are both triggered by the addition of water they would occur simultaneously, and it may be difficult to identify and quantify contributions of each of them. Further, clay components of these soils are also considered slightly to moderately “dispersive” (i.e., exhibiting deflocculating tendencies) in a Sodium environment (rather than flocculating as in a Calcium environment). Dispersive clay (as opposed to “ordinary” clays) particles can easily and rapidly dislodge in the presence of flowing water, which added to the presence of a large fraction silt-size particles, make these clayey soils “erodible” (quite susceptible to soil particle detachment and migration) in presence of flowing water. An exploratory drilling and CPT sounding program, combined with a variety of in-situ and geotechnical, chemical laboratory tests and geologic analyses were conducted to characterize the behavior of this material of difficult behavior, along coastal Caspian Sea areas (CSA) of Azerbaijan.

1 1.1

INTRODUCTION Genesis

Relatively young soils deposits (recent, ongoing soil forming processes) of mud-volcanogenic heritage deposited within an alluvial sedimentological environment that can be described as weathering products of volcanic muds with components of daciticandesitic origin, covering extended areas of southeast Azerbaijan. 1.2

to the effects of one or more of the above listed characteristics. A history of earthwork-related problems includes excessive settlement and bearing capacity failure of shallow foundations (collapse upon wetting), failure of road pavements and scour erosion requiring significant maintenance efforts and resources. Specifically, this type of soils has caused significant damage to existing roadways and foundations of energy infrastructure facilities in and around the main study area of roughly 10 km2 along coastal Caspian Sea areas about 40 kilometers south of Baku, Azerbaijan.

Problematic soils

These surficial unsaturated “loess-like” soil deposits soils are known to be very sensitive to, and adversely affected by, the presence of water in its porous spaces and to the flow of water. These fine-grained soils are known to have caused serious difficulties, upon wetting, to civil projects during and after construction, with costly unintended or premature repairs, due

1.3 Objective of this study Consequently, this study has focused on: a) understanding soil behavior; b) evaluating cost-effective earthwork requirements by performing compaction trials and cost-effective earthwork utilizing these locally abundant soils, both freshly-excavated (FE) as well as re-excavated spoil heap (SH) stockpiled

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soils; c) assessing deep and shallow foundation requirements for their adequate long-term and costeffective performance. 1.4

Investigated site conditions

The main study site is underlain by a thickness of typically 2 to 12 meters of this type of “loess-like” soil deposits of mud volcano-genetic origins. Field exploration of this site primarily included performing 119 Cone Penetration Test (CPT) soundings to maximum depths of 25 meters, and 70 boreholes to maximum depths of 60 meters, 40 test pits, downhole as well as surface geophysical surveys (shear wave propagation velocities, and electrical and thermal resistivity), constructing “test embankments” (compaction trials), in addition to conducting an extensive geotechnical laboratory test program. Where groundwater is deep, for instance deeper than 10 meters, soils are mostly unsaturated (herein called “dry” or “unsoaked” for simplicity). However, due to poor surface water drainage conditions, swampy areas also existed the study site which resulted in wet and softened soils (and very difficult to access to exploration locations). These soft and swampy areas were also explored using CPT soundings and/or dynamic penetration probing light (DPL). 1.5

Geotechnical characterization

At a large study site, these materials are mostly fine grained, and generally consist of lean clay (CL) to silty clay (CL-ML), and occasionally fat clay (CH) with variable amounts of sand. In their natural unsaturated (“dry”) condition, these soils generally exhibit a stiff to hard consistency, namely, SPT-N ≈ 20 to 70 blows/per 0.3 m; and CPT-qc ≈ 2.5 to 18 MPa. In-situ measurements of shear wave velocity, from downhole velocity logging at 10 exploratory borings typically were, Vs ≈ 250 to 360 m/s. Typical ranges (excluding highly infrequent or extreme values) of particle size fractions are: median grain size, D50 , commonly ranges from 0.002 to 0.034 millimeters, with clay-size fraction (minus 2 micra), or CF ≈ 15 to 45%, plasticity index, PI ≈ 10 to 30, and clay “activity” index CAI=PI/CF ≈ 0.4 to 0.9. A summary of Soil Classification and Index Properties is provided in Table 1a; a summary of their Geotechnical Engineering Properties for both natural unsaturated condition and after wetting is provided in Table 1b. Tables 1a and 1b provide “maximum” measured ranges of the soil properties or parameters of natural soils; however “typical” ranges were also provided in the following paragraphs, which exclude what were deemed as outliers, namely, highly infrequent or extreme values of these properties. 1.6 Mineralogy and geologic characterization X-Ray diffraction (XRD) analysis performed (at T.U. Freiberg, Germany) on two specimens to identify the

mineralogical content of these soils indicate quartz ≈ 30%, chlorites ≈ 7%, muscovite/illite ≈ 26%, smectite mixed-layer ≈ 8 to 14%, plagioclase ≈ 13%, calcite ≈ 10%, gypsum ≈ 1 to 2% and Anatas ≤1%. Concentrations of Chlorides and Sulphates range below oceanic seawater, approximately meet the value of the Caspian Sea; no crystalline salts and only 1 to 2 percent gypsum were identified; hence the material could be classified as “non-saline” soil. Chemical analyses show a calcium carbonate content of about 10 percent and total dissolved salts (TDS) between 5 and 20%. Measured pH-values range from neutral to slightly alkaline which reflects an environment ideal for the formation of chlorites and smectitic clay minerals. Smectite mixed-layer minerals were identified in a volume mass of 10 to 15 mass percent; and the high sodium absorption ratio (SAR > 8%) and exchange sodium percentage (ESP ≈ 9 to 24%) leads to the conclusion of that clay minerals are dominated by Sodium type. Clays rich in sodium smectite are well known as bentonite.

2

NATURAL SOIL BEHAVIOR, INDEX AND ENGINEERING PROPERTIES

Geotechnical Properties for the “loess-like” CSA soil deposits are summarized in Table 1b, including properties in their unsaturated (“dry”) as well as “wet” conditions. Their natural or in-situ properties have been studied using a variety of field exploration, insitu and laboratory testing methods in their initially “Dry” (Unsaturated, or unsoaked) and “Wet” (soaked or nearly fully saturated) soil conditions, as described in the following paragraphs. A sudden drop in their original (unsaturated) strength and bearing capacity was measured and documented in the field by performing cone penetration test (CPT) soundings, with correlated undrained shear strength after wetting on the order of 2 to 15% of the unsaturated value. A similarly drastic drop in resistance was observed using various other geotechnical laboratory testing techniques. For example, the resistance of pavement’s native subgrade soils was measured in the laboratory by performing CBR (California Bearing Ratio) tests, as well as triaxial unconsolidated-undrained compression (Tx-UU) tests. Often, “postwetting” strength and stiffness values were as low as 2 to 10% of those for unsaturated soils. Similarly, a significant drop on effective shear strength parameters (roughly 65% and 15% of their initial unsaturated values, respectively, for friction angle and cohesion intercept) were measured by performing direct shear (DS) tests. Furthermore, drastic changes in compressibility parameters (stiffness) were measured in laboratory by performing double (1-D) oedometer tests on specimens of initially “dry” (unsaturated or “unsoaked”) as well as initially “wet” (nearly saturated or “soaked”) soils, and also combined cases (initially “dry” then “soaked”) at different 1-D compression loads.

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Table 1a. Soil classification and index properties. Unsaturated (“Dry”) soils Natural soils Parameter, Property Particle size distribution Clay-Size Fraction [6%; and “excessive” Sodium conditions exist when ESP > 15%, or SAR >10 meq/L. Average ESP value was approximately 35%, and average SAR ≈ 12 meq/L for the 10 Km2 study area. 3 3.1

COMPACTED FILL SOIL BEHAVIOR AND PROPERTIES Compaction trials

An initial pair of test embankments were performed to collect in-situ and laboratory test data on field-compacted specimens using Modified Proctor

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Table 2a. Soil classification and index properties of field compacted material. Compaction trials Engineered fill parameter, property

Number of tests

Field Consistency (Compaction Trials) CPT-qc – Resistance 8 soundings (MPa) [No. of passes] CPT-Rf – Friction Ratio 8 soundings (%)[No. of passes] Unit Weight and Phase Relationships Total Unit Weight (kN/m3 ) 222 Dry Unit Weight (kN/m3 ) 222 Moisture Content (%) 344 53 Specific Gravity, Gs Void Ratio, e 222 Porosity, n 222 Saturation Degree, S (%) 216 Moisture-Density Relationships of Compacted (Fill) Soils Maximum Dry Unit Weight 57 (kN/m3 ) – Modified Proctor Maximum Dry Unit Weight 17 (kN/m3 ) – Standard Proctor Optimum Moisture Content 57 (%) – Modified Proctor Optimum Moisture Content 17 (%) – Standard Proctor

compaction efforts; a second pair of test embankments used the Standard Proctor compaction efforts. Relatively undisturbed field-compacted specimens were collected for: 1) freshly-excavated (FE) and compacted; as well as 2) re-excavated from available spoil heap (SH) stockpiles and re-compacted soils. These two options (compacted FE and SH fill soils) were considered to address concerns by local engineers inclined not to use of this type of “bad” soils. These soils had a long history of cases of excessive settlement and bearing capacity failure of shallow foundations, and excessive repairs to roadways and pipeline utilities. Therefore, both compacted FE and SH fill soils were tested after 3, 5 and 7 passes of a 14-ton vibratory sheep-foot roller per 0.25-meter-thick of each compacted soil layer, for a total thickness of each test embankment of approximately 2.5 meters, to compare their geotechnical properties as described in subsequent paragraphs and summarized in Table 2a. A relative compaction (or degree of compaction) of RC ≈ 95% and near-optimum molding moisture content had initially been targeted (namely, −1% to +3%) per Modified Proctor (MP) compaction test. That range of moisture content was intended to simulate generally desired earthwork specifications during construction. These soils were, however, usually field-compacted slightly on the dry side of the optimum moisture content because of great difficulties in soil-water mixing of this soil type in the field without a special soil-water mixing equipment or plant. This is about 10 to 15 percent moisture content per MP test. Using layer or sublayer thickness of 0.10 m had

Measured range 5 to 13 [3 pass.] 6 to 16 [7 pass.] 3 to 4

13.5 to 22.5 12.5 to 20.5 4.5 to 20 2.61 to 2.85 0.30 to 0.99 0.24 to 0.72 13 to 82 18.5 to 20 16.7 to 18 10 to 15 14 to 19

the advantage of allowing a more uniform distribution of moisture content throughout the compaction layer. A second set of embankment tests was conducted to further test different combinations of compacted layer thickness (0.25 m, 0.20 m, 0.15 m and 0.10 m, number of passes of vibratory sheep foot roller (VSFR), vibratory smooth roller (VSM), and comparing Modified versus Standard Proctor compaction energy, as well as the VSFR speed (about 2 km/hour). Note: the use of Standard Proctor test was also considered and suggested to provide a practical balance between expansive and collapsible tendencies in the soil upon wetting. With higher compaction moisture contents and lower dry densities, the result is a lower expansion potential, possibly at the expense of a slightly higher soil collapse potential. A description of geotechnical properties of compacted soils is presented in the following paragraphs for both unsaturated conditions and upon wetting. 3.2 Compressibility Laboratory oedometer (1D consolidation) tests were performed on field-compacted and laboratorycompacted (reconstituted) fill soil specimens. Compacted fill soil properties, summarized in Table 2b, for three tested moisture conditions, were: a) At near-optimum moisture content, compacted soils are very stiff, with compression index, Cc ≈ 0.02 to 0.12 and rebound index, Cr ≈ 0.002 to 0.011, respectively; b) At near-saturation conditions, when inundated at the initial seating load of about 5 or 12 kPa, their

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Table 2b. Summary of geotechnical engineering properties for compacted fill soils. Compaction trials (Drive-cylinder laboratory-tested specimens field compacted at near-optimum moisture content and RC ≈ 95%)

Engineered fill parameter, property

Near-optimum moisture

Near-saturation moisture

Number of tests

Measured range

Number of tests

Measured range

0.020 to 0.158 0.002 to 0.020 9.8

20 29 29

0.04 to 0.12 0.003 to 0.032 4.8

– –

4 10

1.4 to 3.8 1.1 to 6.9

100 to 680 –

9

φ ≈ 19± 1 degrees; c ≈ 5± 3 kPa

9

φ′ ≈ 30 ± 2 degrees; c′ ≈ 6 ± 3 kPa (Post-hydrocompression)

Compressibility (Oedometer tests) Compression Index, Cc 39 Recompression Index, Cr 38 Average Cc /Cr Ratio 38 Volumetric Changes Upon Wetting Collapse Index at 100–800 kPa, Ic (%) – Free Swell [at 1 to 12 kPa], FS (%) – Undrained Shear Strength Parameters – Peak Values From Tx-UU Tests, Su (kPa) 49 From Tx-CIU Tests, Su (kPa) – Correlated CTP- Su (kPa) Drained Shear Strength - Peak Values From Laboratory DS Tests

9

300 to 750 [3, 7 passes]

16

φ′ ≈ 31 ± 2 degrees; c′ ≈ 50± 15 kPa

From Laboratory Tx-CIU Tests

Saturated Hydraulic Conductivity (Permeability) Field-Compacted, K (m/s) – – 13 1.9 × 10−10 − 1.4 × 10−9 Laboratory-Compacted, K (m/s) – – 8 6.5 × 10−11 − 1.6 × 10−9 Pavement Subgrade Static Resistance (California Bearing Ratio, CBR) In-Situ CBR (%) - Field 41 18 to 93 Laboratory CBR (%) – Laboratory 17 22 to 48 10 1.4 to 2.6 Plate Load Test (PLT) – After 3, 5 and 7 passes of 14-ton sheepfoot roller Deformation Modulus, Loading 93 10 to 29 Phase, Ev1 (kN/m2 ), 20 to 42 29 to 55 Deformation Modulus, Re-Loading Phase, 93 32 to 73 Ev2 (kN/m2 ) 58 to 88 67 to 110 Moisture-Density Relationships of Compacted (Fill) Soils – Modified and Standard Proctor (MP & SP) Tests Maximum Dry Unit Weight (kN/m3 ) 57 18.6 to 20 [MP] Maximum Dry Unit Weight (kN/m3 ) 17 16.7 to 18 [SP] Optimum Moisture Content (%) 57 10 to 15 [MP] Optimum Moisture Content (%) 17 14 to 19 [SP]

compression indices increase significantly to Cc ≈ 0.04 to 0.10, with rebound, Cr ≈ 0.007 to 0.025, respectively; c) When inundated at loads between 100 and 400 kPa, their compressibility curves prior to and after wetting also tend to be somewhat similar (nearparallel) to those of “dry” and “wet” soils, respectively. Even though these soils had been previously compacted to RC ≈ 95%, a residual collapse generally about 1.5 percent was never-the-less still observed at an inundation load of 200 kPa, (down from an average of 3.5 percent for natural soils). At inundation loads between 100 and 800 kPa, for samples from another compaction trials area, collapse potential values measured in the laboratory were generally less than 4 percent.

3.3

Swell potential upon wetting

Laboratory-compacted clayey FE and SH soils also showed some swelling potential when wetted at relatively low confining pressures. At seating loads of about 10 to 12 kPa, free swell averaged approximately 3.3 to 4 percent, respectively. Ranges of free swell for compacted FE and SH soils were about 1 to 7 percent and 2 to 5 percent, respectively. Overall, no significant difference was found between FE and SH soils. 3.4

Undrained shear strength

Undrained shear strength data were collected from field-compacted FE and SH fill soils during compaction trials, using Cone Penetration Test (CPT)

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soundings in the field, and triaxial tests on relatively undisturbed soil specimens in the laboratory. CPT soundings provided undrained shear strength data at four locations through the 2- and 3-meterthick test embankments, plus about 3.5 to 4 meters of their underlying natural soils to a total depth of approximately 5.5 to 6 meters. Compacted FE fill soils exhibited undrained shear strength of, Su ≈ 500 ± 100 kPa and ≈650 ± 150 kPa, for 3 and 7 passes of the 14-ton vibratory sheepfoot roller (per 0.25-meter-thick compacted soil layer), respectively. Median strength, Su(50) ≈ 500 and 650 kPa were obtained for 3 and 7 passes of the 14-ton vibratory sheepfoot roller, with typical ranges of Su(50) ≈ 350 to 650 kPa and 400 to 900 kPa, respectively. Similarly, for compacted SH fill soils, four CPT soundings were conducted through the 2-meter-thick test embankment, plus about 3.5 to 4 meters of their underlying soils to a total depth of approximately 5.5 to 6 meters. The undrained shear strength of compacted SH soils for 3 passes ranged from less than 300 to over 850 kPa, with occasional localized peaks in excess of 1,000 kPa. For 7 passes, the undrained shear strength ranges typically from about 400 to 900 kPa. Statistical (cumulative frequency distribution) analyses indicate a median strength, Su(50) ≈ 530 and 560 kPa, suggesting also that no significant densification of soils takes place after 7 passes. This seems to be the case for both compacted FE and SH fill soils. Tx-UU Tests: Undrained shear strength from undisturbed specimens of field-compacted FE and SH fill soils was directly measured from Tx-UU compression tests in the laboratory. Field-compacted specimens of FE and SH fill soils were tested at confining pressures of 50 and 400 kPa, respectively. Undrained shear strength results ranged from about 130 to 230 kPa and from 500 to 590 kPa, respectively, at those confining stresses. Similarly, undrained shear strength results for compacted SH soils tested ranged from about 130 to 380 kPa and from 490 to 680 kPa, for confining pressures of 50 and 400 kPa respectively. This appears to suggest that compacted SH soils are not significantly stronger and are slightly more variable than FE compacted soils. 3.5 Effective and total shear strength parameters Triaxial CIU Laboratory Tests were performed on field-compacted FE soil specimens during compaction trials to help evaluate the stress-strain-strength behavior of engineered fill soils. Field-compacted soil specimens were initially saturated in the laboratory, achieving Skempton’s B-value of 0.95 or greater, to measure pore pressures during testing and to provide both undrained and drained sets of shear strength parameters. Effective internal friction angle φ′ ≈ 30 degrees and an effective cohesion intercept c′ ≈ 6 kPa, were derived from a data set of 8 tests (2 test series).

Total strength parameters were: friction angle φ ≈ 19 degrees and cohesion intercept, c ≈ 5 kPa. Direct Shear (DS) tests were performed on undisturbed field-compacted (unsaturated) samples of CSA soils. The specimens were moisture-conditioned in the field to about 8 to 11 percent, which is 2 to 5 percent less than the optimum moisture content, based on the Modified Proctor (MP) compaction tests. The tested specimens were not initially inundated in the laboratory prior to shearing, and they remained unsaturated throughout DS testing. For this testing condition, the derived shear strength parameters were: effective friction angle, φ′ ≈ 31 degrees an effective cohesion, c′ ≈ 50 kPa. For comparison purposes, the internal friction angle is about 4 degrees higher than what was derived from Tx-CIU tests for natural soils initially saturated in the laboratory. It is anticipated that for the inundated (or “wet”) condition, DS-derived shear strength parameters will be significantly lower. 3.6

Saturated hydraulic conductivity (permeability)

Field-Compacted Soils: The permeability coefficient measured in the laboratory for FE and SH fieldcompacted soils ranged from about 1.9 × 10−10 to 1.4 × 10−9 m/s, with an average of about 8.9 × 10−10 m/s from 13 laboratory tests, with a standard deviation of 3.64 × 10−10 m/s and a coefficient of variation of nearly 0.5. It should be noted that the moisture contents of the field-compacted specimens collected from compaction trials were often 1 to 5% below the optimum moisture content (based on MP test) because of significant difficulties in soil-water mixing in the field. Laboratory-Compacted Soils: The permeability of laboratory-compacted specimens of engineered fill soils remolded to near-optimum moisture content and 95 percent relative compaction (MP), ranged from about 6.5 × 10−11 to 1.6 × 10−9 m/s, with an average of about 4.2 × 10−10 m/s from 8 laboratory tests, and a standard deviation of 5.6 × 10−10 m/s. 3.7 Subgrade resistance and deformation modulus Subgrade resistance for pavements and deformation modulus of engineered fill soils were evaluated during compaction trials by performing a series of: a) California Bearing Ratio (CBR) tests both in the field and in the laboratory, as well as b) field plate load tests (PLT) on FE and SH field-compacted soils. Pavement Subgrade Resistance from CBR tests: The typical range of “unsoaked” field CBR values on compacted FE fill, performed at near-optimum moisture content, was 39 to 61%, with a maximum range of 18 to 93. Both unsaturated or “unsoaked” and “soaked” CBR tests were performed in the laboratory. Optimum moisture content values were actually achieved in the

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laboratory. The typical range for “unsoaked” laboratory CBR values was 22 to 48. Since soaking duration time is also known to have an effect on measured CBR, compacted soils were “soaked” in the laboratory for two different soaking periods: 4 days and 20 days. Measured laboratory “soaked” CBR values ranged from 4 to as little as 0.5, namely, drastically lower than (or roughly 2 to 10 percent of) the “unsoaked” laboratory CBR values, for specimens remolded at near-optimum moisture content and a relative compaction (RC) ≥ 95 % (per MP tests). Deformation Modulus from field plate load tests: were measured for both field-compacted FE and SH soils, including the initial loading (Ev1 ) and reloading (Ev2 ) phases. For field-compacted FE fill: The median moduli for 3, 5, and 7 passes of a 14-ton vibratory sheepfoot roller were: Ev1 ≈ 26, 32 and 40 kN/m2 , and Ev2 ≈ 68, 72 and 80 kN/m2 , respectively. Furthermore, the stiffening rate of compacted FE soils, was measured by the ratio of the reloading and initial loading modulus of deformation, Ev2 /Ev1 ≈ 2.7, 2.2 and 2.0 for 3, 5, and 7 passes of compaction equipment, respectively. For field-compacted SH fill: The median moduli were: Ev1 ≈ 24, 30 and 35 kN/m2 , and Ev2 ≈ 67, 74 and 80 kN/m2 , respectively. The stiffening rate of compacted SH soils, as measures by the modulus of deformation ratio, was Ev2 /Ev1 ≈ 2.8, 2.5 and 2.3 for 3, 5, and 7 passes of compaction equipment, respectively. In general, compaction trials therefore suggested fairly similar results of deformation modulus for both field-compacted FE and SH fill soils.

4

MITIGATION MEASURES – SITE PREPARATION, EARTHWORK AND FOUNDATIONS

When avoidance of these soils for earthwork and shallow foundations is not feasible, it is considered especially important to mitigate these conditions and anticipated consequences. This may include, for instance, cases of: structures straddling on shallow foundation supported by or into these soil deposits, therefore subject to high potential for differential settlements or loss of bearing capacity resulting from soil wetting. Active pipelines that may be particularly vulnerable to differential settlements at roadway crossings and that would require protection against these settlements. Site Preparation and Earthwork Measures: Implementation of design and construction provisions are advised, which may generally include: a) adequate surface and subsurface water drainage control measures (and impermeabilization or water barrier); b) a fairly thorough soil-water mixing (moisture-conditioning) procedure for engineered fill soils, which may include the use of an effective and advanced soil-water mixing plant (for compaction of fill soils at a large site); c) soil compaction in the field slightly wet of optimum

moisture content (≈ +1% to +3%); and d) full-time continuous program geotechnical engineering monitoring of earthwork during construction including in-situ and laboratory testing for conformance to project construction quality assurance specifications throughout the engineered (compacted) fill area. Foundation Support: use of deep foundations for critical heavy and settlement-sensitive structures, or any structures that have connections to other structures with low-movement tolerances. Consideration may be given to, for instance, drilled and cast-in-place reinforced concrete piles (with diameters ranging from 0.45 to 0.9 meters, depending on the load). The use of driven precast concrete or steel piles in very stiff to hard unsaturated soils may not have significant advantages and result in potential installation difficulties or higher cost. Small, lightly-loaded structures that can tolerate some settlements could be supported on shallow foundations or mats resting on engineered fill. “Loess-like” CSA soil deposits at the Azerbaijan study area primarily consist of lean clay (CL) to silty clay (CL-ML) and occasional fat clay (CH) with variable amounts of sand. This soil unit in its native unsaturated (“dry”) condition is generally stiff to very stiff in consistency, with carbonate bonding. The results of the index tests in the region indicate that these soils are generally “collapsible” and soften considerably upon wetting. These soils are considered potentially “expansive” and subject to volumetric changes upon moisture changes (namely, heave or “swelling/shrinkage”), and also slightly to moderately “dispersive” in nature and therefore may cause difficulties during and after construction. The degree of collapse potential within the study area ranged between slight to moderate. Expansion potential was generally estimated as low to medium. Since those phenomena are both triggered by the addition of water, they will likely occur simultaneously, and it may be very hard to identify contributions from each of the processes. Nonetheless, with a good understanding of the degree of severity of each process, a balanced approach may be adopted for treating this type of soil deposits within a specific area. The following discussions are general guidelines (namely, not meant to be site-specific or projectspecific recommendations, but) to try to assist in initial planning and preliminary design activities for site preparation, earthwork and foundations construction in similar CSA “loess-like” soil deposits, and to minimize associated risks as much as possible. 4.1 Expansive soils Based on the results of the Atterberg Limits tests and the available volume change data, these native “loesslike” soils above the groundwater level are judged to be somewhat expansive with a low to medium degree of shrink/swell potential, which would generally be a primary consideration for grading and foundation design. With seasonal weather and associated soil moisture

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content changes, and longer-term periods of drying and rewetting, soil shrink and swell could occur. Those soil volume changes can damage slabs, pavements, and shallow foundations. The general approaches that can be used individually or in combination in order to deal with expansive soils and reduce the risk of structural damage and cracking are described in Section 4.3. 4.2

Collapsible soils

Based on the results of the Atterberg Limits tests and the available volume change data, the CSA native unsaturated “loess-like” soils (above the groundwater level) are judged to have a slight to moderate degree of collapse potential upon wetting. Note– Rodgers (1995) proposed the following definition of this type of soils: “…a collapsible soil which constituting parts have an open packing and which forms a metastable state that can collapse to form a closer-packed more stable structured of significantly reduced volume. In most collapsible soils the structural units will be primary mineral particles rather than clay minerals. The collapse process that occurs in these soils gives them a geotechnical significance.” The collapse potential of these soils is another primary consideration to be accounted for grading and foundation design. Soil collapse or additional settlement could occur with seasonal moisture content changes and infiltration of surface water due to rainfall or onsite activities. Soil volume changes can damage slabs-on-grade, pavements, and shallow foundations. The following are the general approaches that can be used individually or in combination in order to deal with collapsible soils and reduce the risk of structural damage and cracking: 4.3

General approach to reduce effects of collapsible and expansive soils

Both effects Collapse (or hydrocompression) and Swelling are triggered by an increase of moisture within the sensitive soil. Therefore, the general approach is to separate water and soil or to strengthen or design the structure to deal with soil movements. Removal and Replacement. In this method, the collapsible or expansive soils are removed to a specified depth and replaced with engineered (moistureconditioned and compacted) fill consisting of import materials or materials excavated onsite. For best results, soil within the full depth of the “active” zone (seasonal moisture fluctuation zone), which could range up to about 4 to 8 meters, would need to be replaced. However, a more practical approach may be to limit the depth of removal and replacement to a lesser depth and accept some level of risk, if at all feasible. Non-expansive fill may be selected so that it does not cause accumulation of subsurface water. Therefore, native “loess-like” soils are prevented from being in contact with water. Special Foundation Systems. The slabs and foundations may be designed stiff enough to span over

the localized depressions caused by collapses or resist expansion forces and the resulting differential movement without causing cracks and distress to the superstructure. Reinforced concrete slabs with a system of underlying rigid cross-beam grids or post-tensioned slabs-on-grade have been used successfully on collapsible and expansive soils. In general, shallow spread footings are not used for critical structures in a collapsible and expansive soil environment. For collapse: Where they are used, however, techniques such as deepening and widening the footings and increasing the reinforcement around the perimeter and into the floor slab to stiffen the foundations, are usually applied to decrease the bearing pressure and strengthen the foundations, therefore minimizing the potential for distress. For expansion: Where they are used, however, techniques such as deepening and narrowing the width of the footings, and increasing the reinforcement around the perimeter and into the floor slab to stiffen the foundations are usually applied to increase the bearing pressure and strengthen the foundations to minimize the shrink/swell potential. Deep Foundations. Deepened foundation and piles may be used to transfer the structural loads to lower strata and bearing zones where the potential expansion and collapse is not an issue and adequate foundation support can be provided. The piles may either be designed as structural elements and directly support the structures or they may be used to strengthen and stabilize the collapsible soil zone with the structures supported on a shallow and mat system of foundation. The deepened foundation and pile option may be considered to be the most risk-free system; however, it may not be the most economical option. Control of Potential Water Sources. Since the source of the settlement and collapse or expansion is derived from an increase in the moisture content of the subject soil, one method for controlling the collapse or expansion would be to control fluctuations in moisture content. It is nearly impossible to fully prevent moisture fluctuation of the subsurface soils. However, it is possible to control the rate of change and seasonal fluctuations. The most commonly used technique is to place horizontal and vertical moisture-barriers under and around the foundations to some depth. The barriers are not fully effective, but are quite helpful in reducing the edge effect and differential movements. These barriers may consist of low-permeability earth or geosynthetic (geomembrane) liners, and combined “geomembranes” and compacted lowpermeability earth liners, as well as associated filters and subdrain systems (such as geosynthetic drains wrapped in filter fabric or geotextile). However, permeable erosion protection measures (or “geotextiles”) should only be installed where collapse settlement of CSA “loess-like” soils will not cause a problem for foundations or underground utilities, unless a tailored design (with specialty engineered details) is provided. Other Miscellaneous Options. Other options that are also used to deal with collapsible soils are ground

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modification or improvement methods, such as deep dynamic compaction, stabilization with additives, and areal water ponding and pre-saturation of the site, inducing collapse prior to foundation construction, if feasible. 4.4

Erodible soils

In general, erosion is defined as the natural process by which wind, moving water, ice, and gravitational forces displace the solid and particulate materials of the land. Determination of soil erodibility is a complex process that requires consideration of soil type and texture, among several other factors. The most vulnerable soils are non-plastic soils with a particle diameter roughly on the order of 100 microns (µ), such as fine sands and sandy silt. The erodibility of soils generally decreases for smaller (clay-size) and larger (sand- and gravel-size) particles, respectively. These CSA “loess-like” mud-volcano-genetic soils deposits within the study area have been found to have silt-size particle fraction on the order of 40 to 70%, and other particle-size fractions as shown in Table 1a. At the investigated location, soils are typically classified as clays in accordance with the plasticity charts. In general, “ordinary” clay and clayey soil types are cohesive (and plastic), and therefore would not normally be expected to degrade (erode) rapidly. However, “dispersive” clays tend to deflocculate in the presence of water even without the aid of mechanical agitation or chemical deffloculants. At the study site, clays generally exhibited a low to moderate degree of dispersivity and are considered erodible soils therefore requiring erosion protection measures. The following are general approaches or measures that appear applicable mitigate this problem, and can be used individually or in combination in order to minimize and control soil erosion on sloping or level ground: •

•

• • • • •

Soil grading measures to provide effective surface water drainage, e.g., low slope gradients, slope benches, diversion ditches, etc. Gravel or sand-filled cellular confinement system, such as Geocell™or Geowe™placed on the surface or in multilayer horizontal pattern forming the slope face, Riprap or rock fill underlain by filter fabric, Concrete aprons or facings, Roller-compacted concrete, Retaining structures such as gabions, crib walls, or reinforced earth, and Soil-cement slurry or controlled low strength materials (CLSM).

alternative to compacted fill” (ACI, 2005). Several other names have been used to describe this material, such as flowable fill, unshrinkable fill, controlled density fill, flowable mortar, plastic soil-cement, soilcement slurry, and cement-sand slurry grout. Where future excavation of these materials will not be required, CLSM would generally have an unconfined compressive strength of less than 8.3 MPa. Where future excavation of CLSM is anticipated, a compressive strength of less than 2.1 MPa may be used. Where low unit-weight materials are needed, a low-density LD-CLSM material may be used. In general, surface water penetration into underlying soils must be minimized in areas where possible collapse settlement could cause a problem. Therefore, erosion protection measures must be carefully selected in order prevent or minimize surface water penetration in areas where collapse settlement is a potential issue.

ACKNOWLEDGEMENTS Our deepest thanks are extended to all contributors of test data and advise that assisted the authors in the preparation of this article, including Ines Rommel, Roberto Quaas, Dr. Jens Krumb, Jens-Peter Ertel, Kemal Guerel, Farhad Boniadi, Massimo Deiana, Shuai Wang and many others.

REFERENCES American Society for Testing and Materials (2011), Annual Book of ASTM Standards, Section 4 Construction, Volume 04.08, Soil and Rock. American Concrete Institute, ACI (2005), Controlled Low Strength Materials; Report 229R-99. Atkins (2010), Geologic and Geomorphological Mapping of Coastal Strip (Azerbaijan). BSI British Standard Institution (1990), “British Standard Methods of Test for Soils for Civil Engineering Purposes,” BS 1377:1990 (Parts 1–9, with Amendments). DIN 4023, 18125-1, 18134: Geotechnical Investigations and Testing, Laboratory Tests, and Plate Load Testing. EN ISO 22475-1, 22476-1, -2 and-3 (2005): Geotechnical Investigation and Testing. GOST 23161-78 (19768), Laboratory Method for Determination of Subsiding Characteristics. Rogers, CDF (1995), Genesis and properties of collapsible soils. Springer SNIP 2.02.01-83, National Codes & Standards of Russia.

A CLSM material is a “self-compacted, cementitious material used primarily as a backfill as an

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Wind farm development and the use of geogrid-stabilised unbound platforms and floating access roads on soft ground M.A. Horton, T.L.H. Oliver & J. Cook Tensar International Ltd, Blackburn, UK

ABSTRACT: Onshore wind farms in Northern Europe are frequently located on land that is marginal in terms of accessibility by conventional plant. They are frequently located in upland areas on soils of with little recognisable shear strength at formation. These factors, coupled with increasingly onerous bearing capacity and deformation demands for access track and working platforms for delivery and erection of turbines plus a claims-conscious industry, make for challenging designs to deliver economical and safe construction. This paper considers track and platform specifications and requirements, and examines the risks that these contain in terms of safe and economical design and construction in upland areas. The paper examines design methods incorporating the use of stiff hexagonal polymeric geogrids to stabilise access tracks and platforms. The paper also discusses the advantages, limitations and problems involved with ‘floating’ working platforms to create stiff platforms to limit movement on heavily loaded but very soft ground. 1 1.1

INTRODUCTION Development in upland areas

Wind farm development in upland areas in the United Kingdom has been conducted since the mid-1980s, initially with small-scale developments but more recently with much larger scale developments incorporating many tens of turbines. In northern Europe, upland windfarm construction occurs on low-value land with relatively low productivity, commonly represented by moorland. Soils in such areas consist of peats and clays with very low stiffness interspersed with rock, the latter frequently providing the source of the stone that is used to construct the wind farm infrastructure. Construction of wind turbines in such areas can permit dual land use, for example combined with forestry or sheep and deer farming and recreational activities. There is advice available in previously published documents that outline good practice with respect to construction in these environments (SNH 2010, Scottish Renewables et al 2010). 1.2

Ground conditions

Upland areas in Northern Europe are typified by generally wet ground conditions and soils with poor bearing capacity. Soils frequently demonstrate shear strengths typically of 24 kN/m2 (approximately 1% CBR) and less and typically comprise varying depths of peat and weathered glacial till clays. The latter can show a marked tendency to lose shear strength when wetted and subjected to compaction loads, such that their shear strengths can fall to less than 50% of that which might be obtained from a static soil test. It is therefore important that ground investigation techniques are

appropriate to this environment and able to detect any sensitivity that natural site materials might possess. Investigations should be directed and interpreted by appropriately experienced staff to ensure that design data passed to access roads and platform designers is reasonably accurate and reliable. One of the issues with this type of land is that access can be poor. During ground investigations, the use of low ground pressure plant may be the only means of accessing much of the site to conduct activities as drilling and trial pitting; safe foot and plant access might not be feasible on extremely poor ground. For access roads, this is not always such an issue as relatively shallow investigation ( 1.7, power of the order of 35 W/m2 can be exchanged. These values are greater than those recommended by Brandl (2006) that are 30 W/m2 . The variation of the total allowable thermal power exchanged by conduction Pc and by advection Pv is presented in Figure 7. It can be noted that the

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Figure 6. Variation of Ptotal as a function of Péclet number.

Figure 4. Variation of the allowable thermal exchanged power along x direction for the right and left wall.

Figure 5. Variation of the total allowable thermal exchanged power during the heating season (case 1, kh = 10−5 m/s).

thermal power exchanged by conduction is approximately constant and tends to decrease slightly as Pe increases, also the effect of conduction becomes more important as Pe decreases (for low hydraulic conductivity, kh = 10−6 m/s). On the other hand, the power exchanged by advection Pv increases linearly with Pe . 4.3

Influence of the active length of the wall

The effect of the total length of the wall is analyzed through the comparison of two different

Figure 7. Influence of conduction and advection on the exchanged powers Pc and Pv .

configurations: the wall totally equipped (W1) and the wall with only the embedment part being equipped (W2) with the heat exchanger elements. Figure 8 shows the difference in the exchanged power between these two configurations. The equipment of the whole wall induces an enhancement in the allowable exchanged power which appears to be more important for high water flow. For a water velocity of 334 × 10−6 m/s the power exchanged increases by 32 %, and this increase only reaches 10 % for lower water velocities of the order 8.34 × 10−7 m/s.

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Figure 8. Ratio of the total thermal power between the configurations W1 and W2 (kh = 10−5 m/s).

4.4

Effect of soil thermal properties on the heat exchange phenomena

The thermal properties as the thermal conductivity and specific heat capacity may have an impact on the heat exchange between the soil and the energy foundation. The thermal conductivity of the soil is increased to 3 W/m/K and the specific heat capacity to 1500 J/kg/K. It was noticed that for the same hydraulic conditions imposed before (kh = 10−5 m/s), the heat exchange increases slightly as these parameters increase. From Figure 9, it is clear that the increase in the exchanged heat is more evident for case 3 with the smallest water velocity than the other two cases. This may be related to the relative effect of the conductive and advective terms. As the conductive term presented by the thermal conductivity becomes more important, the effect of the advective term presented by the water velocity becomes less significant. This result is in accordance with Di Donna & Barla (2016). 5

EFFECT OF CYCLIC LOADING ON THE ALLOWABLE EXCHANGED THERMAL POWER

The temperature variation near an energy diaphragm wall affected by heating-cooling cycles is presented in Figure 10. In this figure, the temperature variation is measured from the edge of the right wall and for three heating-cooling cycles where each cycle consists of a heating period followed by a cooling period (Hi and Ci are the heating and cooling periods of cycle i respectively for i varying from 1 to 3). Along the horizontal distance, as the distance from the edge of the wall increases, the temperature increases during the heating period and decreases during the cooling period till reaching a constant value for both periods equal to the initial ground temperature at a distance 6 m away from the edge of the wall. Katzenbach et al.(2008) obtained similar results for the variation of temperature near a bored pile wall for a section parallel to the water flow direction. Concerning the allowable power exchange during the thermal cycles, for the first loading cycle, the power exchanged between the soil and the wall varies

Figure 9. Variation of the total allowable thermal power with the thermal conductivity of the soil.

with time during each period. Figure 11 presents the variation of the exchanged power for the three heatingcooling cycles in the zone near the structure which is being affected by the heat exchange. Starting with the heating period, the exchanged power is approximately constant for small water flow velocities, and then it decreases slightly at the end of this period. This can be interpreted by the fact that the temperature in the soil surrounding the wall starts to decrease along this period due to continuous heat extraction from the soil. Then for the cooling period, negative values indicate that heat is being injected into the soil, thus increasing the soil temperature near the foundation. The allowable exchanged power decreases during the loading period. This slight decrease of the exchanged power in the heating or in the cooling period is obvious for important water flow conditions, whereas for small water flow, the variation has a constant profile for each period. The power exchanged is greater in the cooling period than in the heating one, this is due to the fact that at the beginning of the cooling period, the ground temperature is the lowest and thus the difference in temperature between the soil and the wall is the greatest, leading to the greatest exchanged power. Then the soil temperature rises up causing a decrease in the heat exchange. During the second thermal loading cycle, the heat transferred between the soil and the wall increases significantly in both periods, since the heat is stored during the cooling period in the soil surrounding the wall, thus increasing the efficiency of the heat exchange. During the third heating-cooling cycle, the exchanged power during the two periods drops down compared to the second cycle; this is due to the fact that part of the heat stored in the soil near the wall in cycle 2 disseminates to points far away from the wall edge, this lowers the geothermal potential of the ground around the wall and thus decreases the total power. In addition, with time the efficiency of the system starts decreasing. According to our results, the power exchange is greater in the cooling period than in the heating period. This may be related to the thermal properties of the soil

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Figure 10. Variation of temperature during the loading cycles.

with heat exchanger tubes compared to wall equipped with the tubes only along its embedment length. On the other hand, this enhancement is considered to be negligible for small groundwater velocities. Soil thermal properties are also proved to have an influence on the allowable power exchanged between the soil and the wall, where this influence appears to be significant for low water flow velocities. The variation of the allowable exchanged power affected by thermal cyclic loading was evaluated through considering the loading cycle as a heating period followed by a cooling period. It is obtained that thermal cyclic loading leads to the depletion of the power transferred by the soil volume. Finally, adequate understanding of the local geology and groundwater flow is of great importance to estimate the impact of groundwater flow, soil thermal properties, the active length of the wall, and the cyclic thermal loading on the performance of energy diaphragm walls, and to adopt the best solution from an economical and thermal point of view. Further study should be carried regarding the behavior of energy diaphragm walls under coupled thermo-mechanical loading.

REFERENCES

Figure 11. Variation of the exchanged power under cyclic loading (kh = 10−5 m/s).

that seems to exhibit a higher potential to gain heat in the cooling period than to lose heat in heating period. These results are consistent with those obtained by Hassani Nezhad Gashti et al. (2015). 6

CONCLUSION

Numerical analyses conducted in this paper aim to focus on the impact of the presence of water flow on the transfer phenomena between energy diaphragm walls and soil. Significantly, for high groundwater flow presented by high hydraulic conductivity and Darcy velocity, the allowable exchanged thermal power increases, due to the effect of coupled conductive and advective phenomena. For this, the presence of water flow should be taken into account for the evaluation of the performance of the system. It is found that the heat transfer process is a function of the active length, thus it should be carefully considered for the dimensioning of energy walls. In the presence of high groundwater flow, the transfer is enhanced in the case of a wall totally equipped

Adam, D. & Markiewicz, R. 2009. Energy from earth-coupled structures, foundation, tunnels and sewers. Géotechnique 59(3): 229–236. Amis, T., Robinson, C.A., & Wong, S. 2009. Integrating geothermal loops into the diaphragm walls of the Knightbridge palace hotel project. Bouazza, A., Laong, B., & Sigh, R. 2013. Soil effective thermal conductivity from energy pile thermal tests. Coupled phenomena in environmental geotechnics. London: CRC Press. Brandl, H. 2006. Energy foundations and other thermo-active ground structures. Géotechnique 56(2): 81–122. Cecinato, F. & Loveridge, F.A. 2015. Influences on thermal efficiency of energy piles. Energy 82: 1021–1033. Cervera, C.P. 2013. Ground thermal modeling and analysis of energy pile foundations. Di Donna, A. & Barla, M. 2016. The role of ground conditions on energy tunnels’ heat exchange. Environmental geotechnics. Fromentin, A. & Pahud, D. 1997. Recommendations pour la réalisation d’installation avec pieux échangeurs. Laussane: 247 pages. Gao, J., Zhang, X., Liu, J., Shan, Li K., & Yang, J. 2008. Thermal performance and ground temperature of vertical pile foundation heat exchangers: A case study. Applied thermal engineering 28: 2295–2304. Hassani Nezhad Gashti, E., Malaska, M., & Kujala, K. 2015. Analysis of thermo-active pile structures and their performance under groundwater flow conditions. Energy and Buildings 105: 1–8. ITASCA. 2005. FLAC3D Version 3.0 Theory and Background. Itasca consulting group, Inc. Minnesota, USA. Katzenbach, R., Clauss, F., Waberseck, T., & Wagner, I. 2008. Coupled numerical simulation of geothermal energy systems. International association for computer methods and advances in geomechanics; Proc. intern. conf., Goa, 1–6 October 2008. India: Curran associates, Inc.

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Kersten, M. 1949. Thermal properties of soils. Minnesota, LII(21): 233 pages. Link, K., Rybach, L., Inhasly, S., & Wyss, R. 2015. Geothermal energy in Switzerland. World geothermal congress; Proc. intern. conf., Melbourne, 19–25 April. Australia. Lund, J.W., Freeston, D.H., & Boyd, T.L. 2010. Direct utilization of geothermal energy 2010 worldwide review. World geothermal congress; Proc. intern. conf., Bali, 25–29 April. Indonesia. Ma, X. & Grabe, J. 2010. Efficiency increase of soil heat exchangers due to groundwater flow and air injection wells. World geothermal congress; Proc. intern. conf., Bali, 25–29 April. Indonesia. SIA. 2005. Utilisation de la chaleur du sol par des ouvrages de fondation et de soutènement en bèton, guide pour la conception, la réalisation et la maintenance. Documentation D0190-Swiss society of engineers and architects, Geneva, 100 pages.

Sigfusson, B. & Uihlein, A. 2015. 2014 JRC Geothermal energy status report: 64 pages. Sterpi, D., Angelotti, A., Corti, D., & Ramus, M. 2014. Numerical analysis of heat transfer in thermo-active diaphragm walls. Numerical methods in geotechnical engineering. Suryatriyastuti, M. 2013. Numerical study of the thermoactive piles behavior in cohesionless soils, Lille: 143 pages. Weber, J., Ganz, B., Schellschmidt, R., Sanner, B., & Schulz, R. 2015. Geothermal energy use in Germany. World geothermal congress; Proc. intern. conf., Melbourne, 19–25 April. Australia. Xia, C., Sun, M., Zhang, G., Xiao, S., & Zou, Y. 2012. Experimental study on geothermal heat exchangers buried in diaphragm walls. Energy and buildings 52: 50–55.

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Analysis of thermally induced mechanical interactions in energy pile groups Alessandro F. Rotta Loria & Lyesse Laloui Swiss Federal Institute of Technology in Lausanne, Laboratory of Soil Mechanics, Lausanne, Switzerland

ABSTRACT: This study investigates the thermally induced mechanical interactions among closely spaced energy piles that partially operate as geothermal heat exchangers over a time-scale that is typical of practical applications. The analysis is based on the results of a full-scale in-situ test of a group of energy piles and a coupled 3-D thermo-mechanical finite element analysis. The work highlights two types of thermally induced mechanical interactions in energy pile groups, i.e., first- and second-kind interactions. The former interactions develop during early stages of geothermal operations of energy piles. The latter interactions develop during successive stages of geothermal operations of energy piles. The impact of these interactions on the variation of the mechanical behaviour of energy pile groups varies with time. Attention must be devoted to these interactions throughout the design process (e.g., geotechnical and structural) of energy piles because they play an important role in the serviceability performance of these foundations.

1

INTRODUCTION

Over the last decade, energy piles have shown potential to couple the structural support role of conventional pile foundations with the role of geothermal heat exchangers to satisfy the energy needs of the building environment. Because of this twofold operation, energy piles are subjected to multi-source actions: thermal and mechanical loads. The thermal loads that are applied to energy piles represent an innovative challenge for geotechnical and structural engineers because they induce unprecedented thermally induced effects on the mechanical response of these foundations. For over ten years, a large amount of research has investigated the impact of thermally induced effects on the thermo-mechanical behaviour of single isolated energy piles. Because it has been proved that the impact of thermally induced effects on the stress and displacement variations in single energy piles can be comparable to the impact of the superstructure mechanical loads that are applied to these foundations, increasing efforts are devoted to propose codes of practice and standards for an optimal design of these ground structures. In recent years, an increasing amount of research is also being devoted to investigate the impact of thermally induced effects on the thermo-mechanical behaviour of energy pile groups (Salciarini et al., 2013; Jeong et al., 2014; Di Donna & Laloui, 2014; Mimouni & Laloui, 2015; Suryatriyastuti et al., 2015; Di Donna et al., 2016). Extensive amounts of research (e.g., Poulos & Davis, 1980; Fleming et al., 2008) have proved that when piles in a group are located far enough from each

other (e.g., widely spaced pile groups), their individual responses can be considered independent and comparable to the case of an isolated pile. However, when piles in a group are close enough to each other (e.g., closely spaced pile groups), their individual responses are influenced by the neighbouring piles and differ from that of an isolated pile. In the latter case, the influences between the individual pile responses of the group represent interactions (e.g., mechanical). These interactions occur between the piles, the connecting slab and the surrounding soil. They have been shown to manifest through so-called group effects, to control the response of pile groups to loading and to deserve to be considered for an optimal design of pile foundations. To date, despite the increasing research on energy pile groups, knowledge of the development and impact of thermally induced group effects and interactions among closely spaced energy piles on their thermomechanical behaviour has been preliminary due to the lack of field data about the exploitation of energy piles that either partially or entirely operate as geothermal heat exchangers for time-scales that are typical of practical applications. To address this challenge, Rotta Loria & Laloui (2016) recently carried out a full-scale in-situ test of a group of closely spaced energy piles that partially operate as geothermal heat exchangers over a time-scale that is typical of practical applications, and performed a coupled 3-D thermo-mechanical finite element analysis. This paper expands on the analyses and results of the aforementioned experimental and numerical study and proposes an analysis of the thermally induced mechanical interactions among closely spaced energy piles.

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Figure 1. (a) The EPFL Swiss Tech Convention Centre (http://www.tstcc.ch/, author: Frédéric Rauss); (b) plan view of the foundation including the four energy piles; (c) schematic of the soil stratigraphy.

2

EXPERIMENTAL TESTING

2.1 The foundation and site The pile foundation that was considered for the experimental test is located under the recently built Swiss Tech Convention Centre, Lausanne, Switzerland (cf., Fig. 1 (a)). The foundation supports a 9 × 25 m2 water retention tank and comprises a group of four endbearing energy piles (labelled EP1, EP2, EP3 and EP4 in Fig. 1 (b)) and sixteen semi-floating conventional piles (labelled P1-16 in Fig. 1 (b)) below a heavily reinforced 0.9 m-thick slab. In plain view, the energy piles form a triangle within a 4.21 m square in which the central pile is located 3 m from the others. The energy piles are 28 m long and 0.9 m in diameter, and the conventional piles are 16 m long and 0.6 m in diameter. All of the piles were bored, cast onsite and are made of reinforced concrete. Vertical loads of 0, 800, 2200 and 2100 kN are applied to energy piles EP1, 2, 3 and 4, respectively. Vertical loads of 300 kN are applied to

each of the conventional piles. The energy piles were equipped with four 24-m-long high-density polyethylene U-loops that are connected in series. The inlets and outlets of the absorber pipes were thermally insulated. The top of the U-loops were installed 4 m below the pile heads to limit the influence of the climatic conditions on the heat exchange process. All of the energy piles were instrumented with strain gauges, optical fibres and thermocouples along their lengths as well as with pressure cells at their toes. Piezometers and thermistors were installed in two boreholes in the soil. More detailed information on these instruments, which allow the thermo-hydromechanical response of the foundation to be monitored during the simulation of different operations of the energy piles via the use of a dedicated heating module, are reported by Mimouni & Laloui (2015), and Rotta Loria & Laloui (2016). The soil stratigraphy of the site (cf., Fig. 1 (c)) was extrapolated based on information that was obtained

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Figure 2. Geometry and boundary conditions of the finite element model of the entire foundation.

during the construction of the foundation and data from Laloui et al. (2003; 2006) for another experimental site that is located 200 m away. During the construction of the piles, the groundwater table was located at the top of the deposit, which is estimated to be in an overconsolidated state condition (overconsolidation ratio of OCR ≈3–4). Layers of alluvial soil and sandy-gravelly moraine were encountered at shallow depths. The upper soil profile of the alluvial soil was inferred to reach a depth from the uppermost surface of the successively built slab of z = −8.6 m. The lower sandy-gravelly moraine layer was located between depths of z = −8.6 and −16.6 m (Laloui et al., 2003; 2006). A thin layer of bottom moraine was present below the sandy-gravelly moraine layer between depths of z = −16.6 and −20.1 m and laid on a molasse layer. The energy piles were socketed 8.8 m into this bottom molasse layer. 2.2

Features of the experimental test

The experimental test involved the application of a heating-passive cooling cycle to energy pile EP1 (for approximately 5 and 10 months, respectively), which was the only energy pile of the group that operated as a geothermal heat exchanger (cf., Fig. 1 (b)). This paper devotes particular attention to the heating phase of the test. Throughout the test, the mechanisms and phenomena occurring in the operating energy pile EP1, in the three surrounding non-operating energy piles EP2, 3 and 4, and in the soil were recorded. 3

piles through linear entities in which a heat carrier fluid is assumed to flow, which allows the problem of the heat exchange that occurs in the pipes-pile-soil system to be considered. 3.2

Modelling choices

The numerical analysis of the response of the reinforced concrete foundation in the soil under mechanical and thermal loads is based on the following assumptions: (i) the displacements and deformations of all of the materials can be representatively described through a linear kinematic approach under quasi-static conditions (i.e., negligible inertial effects); (ii) the materials that constitute the pile foundation are considered to be isotropic with pores that are fully filled by air and are assumed to be purely conductive domains with equivalent thermo-physical properties that are given by the fluid and the solid phases; (iii) the materials that make up the soil layers are assumed to be isotropic, fully saturated by water and purely conductive domains with equivalent thermo-physical properties that are given by the fluid and the solid phases; (iv) the loads that are associated with this problem have a negligible impact on the variation of the hydraulic field in the soil; and (v) the materials that compose the foundation and surrounding soil are considered to be representatively described by linear thermo-elastic behaviours. Under these conditions, a thermo-mechanical mathematical formulation is employed. Interested readers can find more detailed information about the mathematical formulation exploited for the numerical analysis in the work of Batini et al. (2015).

NUMERICAL MODELLING 3.3 Boundary and initial conditions

3.1

Finite element model

A 3-D finite element model of the site was developed using the software COMSOL Multiphysics (COMSOL, 2014) (cf., Fig. 2). The model reproduces the foundation supporting the water retention tank. It also accounts for the presence of the pipes in the energy

Restrictions are applied to both the vertical and horizontal displacements on the base of the model (i.e., pinned boundary) and to the horizontal displacements on the sides (i.e., roller boundaries). The initial stress state due to gravity in the foundation and the soil is considered to be geostatic and assumes a coefficient

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of Earth pressure at rest of K0 = 1. No residual stresses from the installation of the piles are considered in these elements and in the adjacent region of soil. This hypothesis may not be completely representative of reality but can be applied successfully in almost all methods of pile groups deformation analysis by choosing appropriate values of the soil moduli (Poulos & Davis, 1980). The temperature is fixed on each of the external boundaries of the model (T = 13.3◦ C). The initial temperatures in the pipes, energy and conventional piles, slab and soil are set to T0 = 13.3◦ C, which is the average temperature that was recorded at the beginning of the experimental test between depths of z = −4.9 and −28.9 m from the surface of the site (this temperature corresponds to the portions of the energy piles that are not thermally insulated). The fluid that circulates inside the pipes is water. The inner diameter of the pipes is φ = 26.2 mm (the outer diameter is 32 mm, and the wall thickness is 2.9 mm). A thermal conductivity of λp = 0 W/(m K) is imposed in the shallowest 4 meters of the inlet and outlet of the pipes to simulate the thermal insulation near the ground surface. The trends of the inlet temperature and velocity of the fluid in the pipes that were experimentally recorded throughout the test are considered as input parameters for the numerical simulation. 3.4

Classification of the numerical simulation and material properties

The numerical analysis that is described in this paper is considered a Class C1 prediction (Lambe, 1973) because it was carried out after the modelled in-situ test was performed and the associated results were available. The material properties that were used for the numerical analysis (Rotta Loria & Laloui, 2016) are those that were recently proposed by Di Donna et al. (2016) for the characterisation of the site with two main changes. These changes were made to accurately represent the thermo-mechanical behaviour of the foundation during the late stages of geothermal operation and included the linear thermal expansion coefficient of layers B, C and D, as well as the thermal conductivity of the solid particles of all of the soil layers. The variation of the former parameter was based on the ranges of variability that typically characterise the thermal expansion coefficient of moraine and molasse deposits in the geographical area of Lausanne. The modification of the latter parameter was based on the determination (without accounting for capacitive effects) of an effective thermal conductivity for the soil deposit of λeff = 2.78 W/(m K) based on the experimental data. 4

COMPARISON BETWEEN EXPERIMENTAL AND NUMERICAL RESULTS

This section presents a comparison between the experimental and numerical results.

The experimental and numerical data include variations of the parameters from the beginning of the test over time. Therefore, they reflect the impact of the geothermal operation of energy pile EP1 on the thermo-mechanical behaviour of the foundation. 4.1 Temperature variations along the energy piles Figure 3 presents the temperature variations that were observed experimentally and numerically along the lengths of the operating energy pile EP1 and of the non-operating energy piles EP2, 3 and 4. The geothermal operation of energy pile EP1 involved average temperature changes along its uninsulated portion of T = 5, 10, 15 and 20◦ C after t = 2, 8, 35, and 156 days, respectively. These changes were observed in both the experimental and numerical results (cf., Fig. 3 (a)). After t = 2 and 8 days (i.e., during the early stages of the heating phase of energy pile EP1), the corresponding portions of the non-operating energy piles EP2, 3 and 4 were characterised by no changes in temperature. However, temperature changes were observed over time because heat diffused through the soil from EP1 and indirectly heated them. After t = 35 and 156 days (i.e., during the late stages of the heating phase of EP1), heat diffusion resulted in average experimental temperature variations of T = 1.6, 0.7 and 1.1◦ C and T = 5.3, 3.6 and 4.5◦ C, respectively. The numerical results showed slightly higher average temperature changes than the experimental results (cf., Fig. 3(b-d)). This difference was attributed to differences between the actual and modelled heat diffusion processes. The differences between the actual and modelled heat diffusion processes in the foundation were inferred to be caused by (i) potential inhomogeneity (spatial and of material properties) of the soil layers of the site that were not accounted for in the numerical model and (ii) different positions of the pipes inside EP1 than those that were considered in the simulation. In addition to the observed temperature changes with time that corresponded to the uninsulated portion of energy pile EP1, temperature variations also occurred in the shallowest 4 m of EP2, 3 and 4 even though the pipes of EP1 were thermally insulated at these depths. This behaviour was observed in both the experimental and numerical results and was attributed to the impact of the heat exchange operation of energy pile EP1 on the shallower portions of the other piles. The experimental results further indicated changes in temperature at the surface of the foundation, which were attributed to the variation of the surface thermal conditions during the experimental test. The numerical results showed slightly smaller temperature variations in the shallowest 4 m of all of the piles than the experimental results. They also indicated that no changes in temperature occurred at the surface of the foundation. These results were consistent with the fixed temperature boundary condition that was imposed on the top surface of the numerical model.

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Figure 3. Comparison between the experimental and numerical temperature variations observed along (a) the operating energy pile EP1 and (b-d) the non-operating energy piles EP2, 3, and 4, after t = 2, 8, 35 and 156 days of testing.

4.2 Vertical strain variations along the energy piles Figure 4 shows the variations in vertical strain that were observed experimentally and numerically along energy piles EP1, 2, 3 and 4. The heating due to the geothermal operation of energy pile EP1 during the first phase of the test resulted in an expansion of the portion of EP1 in which the pipes were not thermally insulated and a compression of the thermally insulated portion because of the entrapment with the slab (cf., Fig. 4 (a)). Maximum negative (expansive) vertical strains of εν = −22, −56, −109 and −167 µ ε were recorded along the uninsulated portion of energy pile EP1 during the experiment when it was subjected to temperature changes of T = 5, 10, 15 and 20◦ C, respectively

(i.e., after t = 2, 8, 35, and 156 days, respectively). Maximum positive (contractive) vertical strains variations of εν = 31, 56, 68 and 79 µε were recorded along the insulated portion during the same stages of the test. Marked negative vertical strains were observed with time in the bottom portion of this pile. Similar results were obtained by the numerical analysis. The heating of the operating energy pile EP1 also induced an expansion of the surrounding nonoperating energy piles EP2, 3 and 4 (cf., Fig. 4 (b–d)). After t = 2 and 8 days (i.e., during the early stages of the heating phase of EP1), the expansions of EP2, 3 and 4 were caused by (i) the negative strain of pile EP1 as a result of its direct heating and (ii) the associated upward deformation of the slab. This deformation

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Figure 4. Comparison between the experimental and numerical variations in vertical strain observed along (a) the operating energy pile EP1 and (b–d) the non-operating energy piles EP2, 3, and 4, after t = 2, 8, 35 and 156 days of testing.

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was thus purely mechanical. However, the evolution of deformation along the piles (decreasing from top to bottom) indicates that the deformation was comparable to that caused by an upward force applied at their heads. After t = 35 and 156 days (i.e., during the late stages of the heating phase of EP1), the expansions of piles EP2, 3 and 4 were caused by (i) the negative strain of EP1 as a result of its direct heating, (ii) the associated upward deformation of the slab, (iii) the negative strains of these elements as a result of their indirect heating and (iv) the negative strain in the soil as a result of its heating. In contrast to the deformation of the non-operating energy piles EP2, 3 and 4 during the early stages of the geothermal operation of energy pile EP1, this deformation was characterised by both mechanical and thermal contributions. Marked negative vertical strains of up to εν = −106 µε were observed during these stages in the lower portions of EP2, 3 and 4 in both the experimental and numerical results. These negative strains were significantly greater than those that developed in the top portions of these elements (i.e., between εν = −10 and −30 µε). They were also greater than those under free thermal expansion conditions, which can be calculated according to a one-dimensional scheme as

where αEP is the linear thermal expansion coefficient of the energy pile and T is the observed temperature variation. The marked expansive vertical strains that were observed in the bottom portions of all of the piles during the late stages of the heating phase of EP1 occurred because as heat diffused through the system, the mechanical response of the foundation was governed by the thermally induced deformation of the molasse layer. These strain variations were caused not only by the interplay between the thermally induced deformations (direct and indirect) of the piles and the slab but also and primarily by the thermally induced deformation of the soil mass (e.g., molasse layer) surrounding the piles. The value of the thermal expansion coefficient of the molasse layer, which was found to be greater than that of the piles based on the results of the numerical analysis, was the key factor of this phenomenon. Heating the very stiff molasse layer over time caused a marked expansion of this layer.This field was superimposed on the expansion field of the bottom portions of the piles. Remarkably high expansive vertical strains therefore developed in these settings. 5

are evidenced through thermal and thermally induced mechanical interactions between the operating and non-operating energy piles. The thermal interactions between the piles appear during successive stages of geothermal operations. The thermally induced mechanical interactions between the piles are always present throughout the geothermal operations.Two types of thermally induced mechanical interactions can be distinguished: firstand second-kind interactions. First-kind interactions develop during early stages of geothermal operations of energy piles and are primarily caused by the direct heating and associated thermally induced deformation of the operating energy piles. Second-kind interactions develop during successive stages of geothermal operations of energy piles and are caused by (i) the direct heating and related thermally induced deformation of the operating energy piles, and (ii) the indirect heating and related thermally induced deformation of the soil surrounding the operating energy piles as well as of the non-operating energy piles. The presence of the slab is key for the development of all of these interactions. The rate of the heat exchange process characterising energy pile groups also appears to be crucial for the development and magnitude of these interactions. The soil-pile thermal expansion coefficient ratio, the pile-soil stiffness ratio and the slab-soil stiffness ratio (Rotta Loria & Laloui, 2016) further appear to be very important characteristics. The soil-pile thermal expansion coefficient ratio has the greatest influence on the thermally induced mechanical behaviour of the piles during successive stages of geothermal operation. The experimental and numerical results expand upon the key role of the soil-pile thermal expansion coefficient ratio that was recently described by Bourne-Webb et al. (2015) for single isolated energy piles.

6

CONCLUDING REMARKS

This study investigated the development, magnitude and impact of the thermally induced mechanical interactions that develop in energy pile groups as a consequence of the partial or entire operation of the piles as geothermal heat exchangers on the thermo-mechanical behaviour of such foundations. The main conclusions that can be drawn from this work are:

DISCUSSION

The results that were described in the previous sections demonstrate that the behaviour of groups of closely spaced energy piles that operate partially as geothermal heat exchangers over time-scales that are typical of practical applications is characterised by significant thermally induced group effects. These group effects

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Thermally induced mechanical interactions among energy piles are always present throughout geothermal operations of these foundations. • Two types of thermally induced mechanical interactions can be distinguished: first- and second-kind interactions. First-kind interactions develop during early stages of geothermal operations of energy piles and are primarily caused by the direct heating and associated thermally induced deformation of the operating energy piles. Second-kind interactions develop during successive stages of geothermal operations of energy piles and are caused by (i) the direct heating and related thermally induced •

deformation of the operating energy piles, and (ii) the indirect heating and related thermally induced deformation of the soil surrounding the operating energy piles as well as of the non-operating energy piles. The magnitude and development of these interactions are governed by the interplay between the thermally induced responses of the operating and non-operating energy piles and soil to temperature changes. The presence of the slab represents a key contribution for the development of all of the aforementioned interactions. • The soil-pile thermal expansion coefficient ratio, the pile-soil stiffness ratio and the slab-soil stiffness ratio appear to be crucial characteristics for the development and magnitude of all of these interactions. The former characteristic was shown to have the most influence on the thermally induced mechanical behaviour of both the operating and non-operating energy piles during successive stages of geothermal operation. Significant attention must be paid to this parameter because it characterises the analysis and design (e.g., geotechnical and structural) of energy pile groups. • The rate of the heat exchange process that characterises energy pile groups controls the development and magnitude of all of the thermally induced interactions in these foundations.

ACKNOWLEDGEMENTS The financial support of N. 160117 (Division IIII) from the Swiss National Science Foundation is acknowledged.

REFERENCES Batini, N., Rotta Loria, A. F., Conti, P., Testi, D., Grassi, W. & Laloui, L. (2015) Energy and geotechnical behaviour of

energy piles for different design solutions. Computers and Geotechnics, 86, 199–213. Bourne-Webb, P., Bodas Freitas, T. & Freitas Assunção, R. (2015) Soil–pile thermal interactions in energy foundations. Géotechnique, 1–5. Di Donna, A. & Laloui, L. (2014) Numerical analysis of the geotechnical behaviour of energy piles. International Journal for Numerical and Analytical Methods in Geomechanics, 39, 861–888. Di Donna, A., Rotta Loria, A. F. & Laloui, L. (2016) Numerical study on the response of a group of energy piles under different combinations of thermo-mechanical loads. Computers and Geotechnics, 72, 126–142. Fleming, K., Weltman, A., Randolph, M. & Elson, K. (2008) Piling engineering, CRC press. Jeong, S., Min, H. & Lee, J. K. (2014) Thermally induced mechanical response of energy piles in axially loaded pile groups. Applied Thermal Engineering, 71, 608–615. Laloui, L., Moreni, M. & Vulliet, L. (2003) Comportement d’un pieu bi-fonction, fondation et échangeur de chaleur. Canadian Geotechnical Journal, 40, 388–402. Laloui, L., Nuth, M. & Vulliet, L. (2006) Experimental and numerical investigations of the behaviour of a heat exchanger pile. International Journal for Numerical and Analytical Methods in Geomechanics, 30, 763–781. Lambe, T. (1973) Predictions in soil engineering. Géotechnique, 23, 151–202. Mimouni, T. & Laloui, L. (2015) Behaviour of a group of energy piles. Canadian Geotechnical Journal, 52, 1913–1929. Poulos, H. G. & Davis, E. H. (1980) Pile foundation analysis and design, New York, Wiley. Rotta Loria, A. F. & Laloui, L. (2016) Thermally induced group effects among energy piles. Géotechnique, Submitted. Salciarini, D., Ronchi, F., Cattoni, E. & Tamagnini, C. (2013) Some remarks on the thermomechanical effects induced by energy piles operation in a small piled raft. International Journal of Geomechanics, 10.1061/ (ASCE)GM.1943-5622.0000375. Suryatriyastuti, M., Burlon, S. & Mroueh, H. (2015) On the understanding of cyclic interaction mechanisms in an energy pile group. International Journal for Numerical and Analytical Methods in Geomechanics, 10.1002/nag.2382.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Ground thermal response to borehole ground heat exchangers O. Mikhaylova, I.W. Johnston & G.A. Narsilio The University of Melbourne, Melbourne, Australia

ABSTRACT: Ground heat exchangers (GHEs) are the elements of ground source heat pump (GSHP) systems that provide thermal interactions with the ground. Closed-loop borehole GHEs are commonly used for GSHP systems in urban areas where land availability can be limited. The installation costs of borehole GHEs are usually the largest component of the capital costs of GSHP systems. More research, including experimental studies, into GHEs can improve GHE design and reduce their costs. This paper presents the first findings of a full-scale experimental study of the ground thermal response to a 120 kW commercial GSHP system in Melbourne, Australia. The system uses twenty-eight 50 m deep borehole GHEs to interact with the ground. Several temperature monitoring boreholes were installed close to some of the GHEs to monitor their thermal impact on the ground. The first sets of ground monitoring data are summarised to show trends of ground thermal disturbance by real-life thermal loads.

1

INTRODUCTION

Ground heat exchangers (GHEs) are the key elements of ground source heat pump (GSHP) systems which provide thermal interactions between the ground and the fluid circulating within the systems. The installation costs of GSHP systems largely depend on the costs of GHEs, so an optimum design of GHEs is important for financial feasibility of such systems. More research, including experimental studies, should be undertaken into GHE-ground thermal interactions, so that more informative design decisions can be made in sizing of GHEs. Yavuzturk & Spitler (2001) summarised criteria for the experimental data sets for GHE model validations. Such observations should be continuously collected from the beginning of the system operation and include, at least, measurements of inlet and outlet circulation fluid temperatures and fluid flow rates over time. Also, such data sets should provide accurate information about the geometrical parameters of the GHEs and thermal properties of the ground, grout and circulating fluid. If obtained, such data sets can be used to extend understanding of thermal processes during GHE-ground interactions and to validate GHE analytical and numerical models. Even though quite a few experimental studies into GSHP systems have been published, quality monitoring data sets involving relatively long-term performance of GHEs under real-life building loads are rare. In addition, there have been only a few experimental studies of the thermal response of the ground around GHEs. Recently, Cullin et al. (2015) commented that the observational data of the quality that is suitable for the validation of GHE design methodologies is difficult to obtain.

The Elizabeth Blackburn School of Sciences (EBSS) full-scale shallow geothermal installation in Melbourne, Australia was designed to study ground thermal reactions to borehole GHEs. The GSHP system is heavily instrumented to monitor power and energy input and output, GHE fluid temperatures throughout the system, ground temperatures around GHEs at different depths, undisturbed ground temperatures, building thermal loads and on-site weather. The system was commissioned in March, 2014 and has been in continuous operation since. This paper presents some of the first observations of the EBSS instrumental installation. Based on this data, a number of performance characteristics have been observed. It is suggested that these characteristics should be taken into account when developing more comprehensive design methodologies.

2

EXPERIMENTAL SET-UP

The 1,500 m2 two-storey school building (Fig.1) was fitted with a 120 kW GSHP system which provides heating and cooling energy. The heat pumps are coupled with twenty-eight 50 m deep double U-loop borehole GHEs (Fig. 2). Sixteen of the twenty-eight GHEs are located under the thermally insulated concrete floor slab of the building and the remaining twelve GHEs are located outside the building footprint. A view of a GHE being installed at the site is shown in Figure 3. This paper focuses on the observations of grout and ground temperatures around a single GHE located under the building as indicated in Figure 2. Two ground temperature monitoring boreholes were installed to

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Figure 1. The Elizabeth Blackburn School of Sciences.

Figure 3. A GHE being installed.

Figure 2. Location of GHEs and monitoring boreholes.

record ground temperatures around this GHE at R = 1.3 m and R = 3.2 m from its centre. A plan view section of this GHE and nearby temperature monitoring boreholes is shown in Figure 4. The vertical location of the temperature sensors attached to the external wall of the downward (or inlet) U-loop leg of the GHE and installed in the two monitoring boreholes is shown in Figure 5. The GHE has eleven temperature sensors installed along its downward U-loop leg. The monitoring boreholes are fitted with eleven and ten temperature sensors installed along their lengths. In addition to the grout and ground temperature sensors, inlet and outlet in-water temperature ports as well as a water flow meter were fitted into the header pipes leading to the GHE to record thermal loads applied to it. Continuous core samples were collected from the site to study the thermal conductivity of the ground. The ground at the site from around 1.5 m and down to 50 m is Silurian mudstone (Johnston 1992). In addition, several samples of the grout were collected during the grouting of the GHEs. The thermal conductivities

Figure 4. A plan view section of the GHE under consideration showing location of temperature sensors (not to scale).

of the ground and grout were measured in the laboratory using a TCi scanner (www.ctherm.com). The average thermal conductivity of the ground and grout materials are around 2.7 W/(m · K) and 2.2 W/(m · K) respectively. The ground water level measured in the open borehole on the site is about 18 m below the ground surface.

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Figure 5. A vertical location of the temperature sensors attached to the outside wall of the downward U-loop leg of the GHE and installed in two monitoring boreholes. Dots indicate sensors.

Figure 7. Farfield ground temperatures at selected dates over a year to a depth of about 50 m.

are shown in Figure 7. The ground temperatures at depths of up to 5 m were subjected to ambient temperature fluctuations whereas the temperatures below 5 m were almost constant through the year. The undisturbed ground temperature below about 5 m at the site is around 19.4◦ C. 3.2 Thermal loads

Figure 6. Annual ambient air temperatures recorded on site.

3

EXPERIMENTAL OBSERVATIONS

3.1 Air and farfield ground temperatures Figure 6 presents the outside shade air temperatures recorded on the roof of the building during a one year period starting August 2014. The maximum temperature recorded during this period was 38.6◦ C in January, 2015 and the minimum temperature was 2.4◦ C in July, 2015. The average air temperature during this period was 15.8◦ C. The ground temperatures at around 8 m from the installed GHEs (Fig. 2) were monitored to observe the values of the temperatures not affected by the installation or the farfield ground temperatures. Some of these observations at selected dates to a depth of about 50 m

The thermal loads applied to GHEs were determined by the building heating and cooling demands. Typical thermal power applied to the single monitored GHE in winter (heating) and summer (cooling) is shown in Figure 8. As seen in the figure, the GSHP system is scheduled to work from 7 am until 6 pm during weekdays and typically switched off for the rest of the time. The heating power from the GHE normally reached around 3 kW whereas the applied cooling power to the GHE was typically a little more. The cumulative geothermal energy to the GHE from the start of the system operation is shown in Figure 9. As observed, from approximately April to November (including a winter in Melbourne), the system mainly works in heating. From approximately November to April (including a summer in Melbourne) the system predominantly works in cooling. When the system started operation in March, 2014, the cumulative ground energy was zero. By March, 2015, after a full year of operation, this one GHE extracted 1,336 kWh of geothermal energy for heating and injected 1,732 kWh for cooling. In total, the GHE supplied around 3,070 kWh of geothermal energy for air-conditioning the building. In March, 2015, the cumulative heating applied to the GHE reached 397 kWh (cooling). This demonstrates that the overall

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Figure 10. Annual observations of the temperatures of the outside wall of the downward U-loop leg of the GHE at a) 0.5 m and 30 m and b) 0.5 m and 50 m below the underside of the building slab.

Figure 8. Typical geothermal power to the GHE during a) heating in winter and b) cooling in summer.

Figure 9. Cumulative ground load applied through the GHE.

annual load applied to the ground throughout the first year of operation (from March, 2014 to March, 2015) was cooling dominant with a net injection of thermal load to the ground of nearly 400 kWh per GHE. The overall maximum cumulative heating energy extracted from the GHE reached around −800 kWh. The overall maximum cumulative cooling energy applied to the GHE was slightly more than 600 kWh.

3.3 Grout and ground thermal reactions to GHE Grout and ground thermal properties, including thermal conductivity, diffusivity and temperatures, determine the performance of GHEs. Temperatures around GHEs might substantially change during operation of a system and can, therefore, affect its performance, especially in the long-term. It is important to anticipate this aspect of system operation and consider it in the design of GHEs. In the EBSS facility, grout and ground thermal reactions to GHEs have been being studied in detail. Some observations on the grout and ground temperatures at different stages of the system operation are presented in this section of the paper. 3.3.1 Grout and ground temperatures along and around GHE To demonstrate grout thermal response along the GHE, the observations of three sensors – at 0.5 m, 30 m and 50 m below the underside of the building slab – were selected for presentation and discussion. These sensors are attached to the outside wall of the downward U-loop leg of the GHE. The annual temperatures recorded by these sensors are shown in Figure 10. Generally, as shown in the figure, the 0.5 m sensor recorded lower temperature peaks in heating and higher temperature peaks in cooling compared to the 30 m and 50 m sensors. Also, the observed temperature peaks at the depth of 30 m are lower in heating and higher in cooling than at a depth of 50 m. As an example, the minimum temperatures in heating at these sensors were observed on 13 August, 2014

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Figure 11. Annual observations of the temperatures of the ground at a) 0.5 m and b) 30 m below the underside of the building slab at the outside wall of the downward U-loop leg of the GHE at R = 1.3 m and R = 3.2 m radially from the GHE.

with 12.1◦ C recorded at 0.5 m, 13.1◦ C – at 30 m and 14.2◦ C – at 50 m. A similar trend is observed in cooling where the maximum temperatures at these sensors were on 11 February, 2015 with 30.5◦ C recorded at 0.5 m, 29.7◦ C – at 30 m and 27.8◦ C – at 50 m. These observations demonstrate that the grout is affected by heat extraction or injection unevenly along the length of the GHE. In particular, the grout thermal disturbances (or its temperature deviations from the undisturbed ground temperature of 19.4◦ C) in both heating and cooling were higher at the top part of the GHE and decrease with the depth of the GHE. In addition, these thermal disturbances are nonlinear along the length of the GHE. Such thermal reactions can be explained by higher heat exchange rates between the grout and circulating fluid in the top section of the GHE. Such disturbed grout temperature profile determines the pattern of the temperatures of the ground adjacent to the GHE. To consider ground thermal disturbance around the GHE, Figure 11 shows annual changes in temperatures at 0.5 m and 30 m below the building floor slab at three radial distances from the GHE: at the downward Uloop wall, at R = 1.3 m and at R = 3.2 m. These plots demonstrate that, at both depths, for heating and cooling, the thermal disturbance is significantly higher at the U-loop wall compared to the thermal disturbance at 1.3 m and 3.2 m distances. Indeed, over the monitoring period, at the depth of 0.5 m, the maximum

Figure 12. Minimum and maximum average temperatures along the length of the GHE for the grout and the ground at R = 1.3 m and R = 3.2 m radially from the GHE.

temperature at the U-loop wall was 30.5◦ C whereas at 1.3 m and 3.2 m, the maximum temperatures were 21.8◦ C and 21.3◦ C respectively. At the depth of 30 m, the maximum temperature at the U-loop wall was 29.7◦ C whereas at 1.3 m and 3.2 m, the maximum temperatures were 20.5◦ C and 19.8◦ C respectively. A similar trend is observed in heating. Overall, the ground temperatures follow a similar trend as the grout temperatures with higher cooling and lower heating peaks recorded at the 0.5 m depth compared to the 30 m depth at the same radial distances. Figure 12 presents a vertical profile of the ground temperatures at and around the GHE at depths of up to 50 m from the underside of the building slab for the same radial locations as considered previously. For this plot, the temperatures at U-loop walls were considered at the end of night recovery (just before the GSHP system switched on at 7 am each day, see Figures 8). This excludes immediate temperature rises and drops at the U-loop wall due to the temperature of the water circulating inside the GHE. Also, after a night recovery, the temperatures at the sensors attached to the downward and upward U-legs at the same depths normally equalise. Hence, the grout temperatures at these times show general temperature trends of the grout. At different depths, the grout and ground temperatures reached peaks at different times (see, for example, Fig. 11). For Figure 12, for each radial location, the times were found when the maximum and minimum temperatures, averaged along the length of the GHE, occurred. Grout or ground temperatures have been plotted at these times to show their most thermally

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disturbed states at heating and cooling. The dates of these times are shown in the figure. From the figure, the first 5 m of the grout and ground were considerably more thermally influenced by the GHE, both in heating and cooling. The temperature changes due to energy extractions and injections are nonlinear along the depth. Since the GHE is located under the insulated floor slab, there is only little temperature exchange with the surface. Such boundary conditions might contribute to the observed temperature profiles. In general, the deviation of the grout and ground temperature from the undisturbed ground temperature of 19.4◦ C is larger in cooling compared to heating. This follows from the fact that the annual cumulative thermal load applied to the ground was cooling dominant (Fig. 9). Figure 12 also illustrates the propagation of thermal disturbance through the ground over time. The maximum average temperature along the depth of the GHE was recorded on 21 February at the U-loop wall, on 21 March at 1.3 m and at 5 April at 3.2 m from the GHE centre. Hence, the maximum thermal disturbance in cooling occurred 28 days later at 1.3 m and 43 days later at 3.2 m from the GHE compared to the grout thermal disturbance at the U-loop wall. Similarly, the minimum values of the average temperatures were observed at 15 August, 20 September and 28 October at the U-loop wall, 1.3 m and 3.2 m from the GHE respectively. Two points can be made based on the monitoring data presented in this section. Firstly, current analytical models of GHEs assume different grout and ground thermal reactions to those observed to be operating in the EBSS installation. For example, infinite and cylindrical line source models ignore both top and bottom boundary conditions of a GHE. This results in constant ground temperatures along the length of the GHE at any radial distance from it and at any particular point of time of GHE operation (Marcotte et al. 2010). Another popular analytical solution, the finite line source model, assumes that the surface is at a constant temperature equal to the undisturbed ground temperature at the site (Marcotte et al. 2010). Such an assumption leads to the ground vertical disturbed temperature profile different from the observed in the EBSS installation. A further study should be performed to understand how observed disturbed ground temperature patterns might affect GHE performance in a long-term. Also, further research is required to evaluate the accuracy of the GHE performance predictions made by current GHE analytical models. Secondly, even though the GHE delivered a significant amount of geothermal energy (3,070 kWh during the first year, see Section 3.2), the resultant thermal disturbance of the ground around the GHE is not significant. Indeed, at R = 3.2 m, the maximum average ground temperature along the 50-m monitoring borehole was recorded on 5 April (Fig. 12). However, by this time, the ground temperatures just slightly exceeded the undisturbed ground temperature of 19.4◦ C at depths below 5 m at that radial distance.

Figure 13. Typical grout temperatures at the outside wall of the downward U-loop leg of the GHE over a week of heating at a) 0.5 m and b) 30 m depths.

At these depths, the difference between the disturbed and undisturbed temperatures was no more than about 0.5◦ C. Although measurements cover only 1 year of the design period, this small difference may be desirable in an efficient design. In addition, the balancing of ground cooling with ground heating loads and ground thermal recovery appear to contribute to such a low thermal disturbance. Further observations and analysis should be undertaken to evaluate the ground thermal disturbance trends in the long-term. 3.3.2 Grout thermal recovery during nights and weekends Since the building heating and cooling schedule includes significant periods when the GSHP system is turned off (Fig. 8), the EBSS facility provides an opportunity to observe grout thermal recovery during standby periods of the system. Figures 13 and 14 show typical temperatures of the grout at the outside wall of the downward U-loop leg of the GHE over a typical week of heating and a typical week of cooling respectively. The grout temperatures are presented for three depths, 0.5 m, 30 m and 50 m below the underside of the building slab. As shown, the temperatures followed the building operation schedule, so the grout was being thermally disturbed due to the applied thermal loads at 7 am to 6 pm during weekdays and recovering during weeknights and weekends.

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can influence the design of GHEs, and particularly the required lengths of GHEs. Hence, anticipated breaks in building thermal loads, which might help to keep ground and grout temperatures within targeted operational values, should be considered in the design of GHEs.

4

Figure 14. Typical grout temperatures at the outside wall of the downward U-loop leg of the GHE over a week of cooling at a) 0.5 m and b) 50 m depths.

During the week of heating (Fig. 13), the U-loop wall temperatures decreased each weekday starting from 7 am due to heat extraction from the ground. At nights between weekday operations, the temperatures increased because of the ground thermal recovery when the GHSP system was switched off. However, the recovery over weeknights was not complete and the Uloop wall temperatures were lower at 6 pm on Friday compared to the beginning of the week, at 7 am on Monday. During the weekend, the system was not in operation, so the grout recovery continued. The weekend recovery was significant and the wall temperatures at 7 am on Monday after the weekend were almost the same as at 7 am of the previous Monday. A similar thermal recovery trend can be observed in Figure 14 where the U-loop wall temperatures during a week of cooling are presented. Also, Figures 13 and 14 illustrate the same point made before that the grout and ground around the GHE were more thermally influenced at the top sections, closer to the slab, and the thermal disturbance decreases with depth. This can be observed by comparing the grout temperatures at three different depths plotted. The observed trends suggest that, when the GSHP system is switched off, grout recovery occurs. The recovery over nights and especially over weekends was significant, so it can considerably influence the grout temperature around GHEs. Since the grout and ground temperatures around GHEs determine the performance of GSHP systems, grout thermal recovery

CONCLUSIONS

The paper presents an overview of the first observations of the Elizabeth Blackburn School of Sciences (EBSS) full-scale shallow geothermal installation in Melbourne, Australia. The GSHP system is heavily instrumented to monitor power and energy input and output, GHE fluid temperatures throughout the system, ground temperatures around GHEs at different depths, undisturbed ground temperatures, building thermal loads and on-site weather. The average annual ambient temperature at the site over the monitoring period was 15.8◦ C. The farfield ground temperatures over the top 5 m fluctuated following the seasonal fluctuations of the ambient air temperature. The undisturbed ground temperatures at depths of 5 to 50 m were nearly constant at 19.4◦ C. During the first year of operation, a single GHE provided around 3,070 kWh of geothermal energy to heat and cool the building. Over this time, the building cooling demand was higher than its heating demand, so the annual thermal energy applied to the ground was cooling dominant with about 400 kWh more energy injected into the ground than extracted for this one GHE. The experimental results suggest that the grout and ground thermal disturbance is nonlinear along the length of a GHE in both heating and cooling. Over the upper 5 m of the GHE, the grout and ground temperatures around the GHE were significantly lower during heating and significantly higher during cooling of the building compared to the sections below. In general, the grout and ground thermal disturbance around the GHE decreases with its depth. Existing analytical models of GHEs do not consider such disturbed ground temperature profiles around GHEs. Further investigations are required to evaluate whether such a disturbed ground temperature pattern can significantly influence the performance of GHEs, especially in the long term, and should be considered in sizing GHEs. When the GSHP system was in a standby mode, the grout showed significant thermal recovery. Such recovery periods seem to significantly reduce ground thermal disturbances. Hence, scheduled pauses in the building thermal loads should be anticipated and considered in the sizing of GHEs. Potentially, this can reduce design lengths of GHEs. Further research should be undertaken to investigate whether the existing GHE modelling methodologies accurately simulate ground thermal recovery when GSHP systems are switched off.

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ACKNOWLEDGEMENT The authors would like to acknowledge the support provided by the Sustainable Energy Pilot Demonstration (SEPD) Program funded by the Department of Economic Development, Jobs, Transport and Resources of the Government of Victoria. REFERENCES Cullin JR, Spitler JD, Montagud C, Ruiz-Calvo F, Rees SJ, Naicker SS, Koneèný P and Southard LE (2015)

Validation of vertical ground heat exchanger design methodologies. Science and Technology for the Built Environment, Taylor & Francis, 21(2), 137–149. Johnston IW (1992) Silurian and Lower Devonian engineering properties. Engineering Geology of Melbourne, Peck, W.A. et al (Eds), Balkema, Rotterdam. Marcotte D, Pasquier P, Sheriff F and Bernier M (2010) The importance of axial effects for borehole design of geothermal heat-pump systems. Renewable Energy, 35(4), 763–770. Yavuzturk C and Spitler JD (2001) Field Validation of a Short Time Step Model for Vertical Ground-Loop Heat Exchangers. ASHRAE Transactions, 107(1), 1–9.

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Effect of moisture migration on the thermal conductivity of a geothermal well seal C. Walton-Macaulay & J.C. Evans Department of Civil and Environmental Engineering, Bucknell University, Lewisburg, PA, USA

L. Daher Geotechnical Specialist, Gannett Fleming, Camp Hill, PA, USA

ABSTRACT: Bentonite is typically used as the seal between the fluid circulating pipes and the adjacent soil/rock formation for geothermal well systems. Over the design life of a geothermal well, the seal is subjected to many cycles of heating and cooling. After many cycles of heating and cooling throughout the design life of the geothermal system, the bentonite is expected to still function as a competent seal, by maintaining contact with the fluid circulating pipes and the adjacent soil/rock formation surrounding the circulating pipes. Moisture migration can occur from the adjacent soil/rock formation to the seal or from the seal to the adjacent soil/rock formation. If moisture migration out of the bentonite seal is excessive, defects in the seal such as separation of the seal from either the soil formation or the circulating pipes can occur. Such defects could therefore potentially affect the thermal conductivity. This research presents the results of a study of the effect of moisture migration on thermal conductivity. A model well, seal and sand formation were created in the laboratory and the system was subjected to 30 cycles of heating and cooling. The average thermal conductivity for the heating cycles was 0.69 W/k.m and that for the cooling cycles was 0.49 W/k.m. In previous tests using a closed system without allowing moisture migration, the average thermal conductivity for the heating cycles was at 0.79 W/k.m, and for the cooling cycles was 0.19 W/k.m. The study results are encouraging in that after thirty cycles of heating and cooling with the bentonite seal in an open system free to gain or lose moisture, no degradation in thermal conductivity was observed. However, moisture content analysis of bentonite seal samples from the model showed moisture migration had indeed occurred illustrating the need for a long-term field study of the performance of bentonite geothermal well seals.

1

INTRODUCTION

1.1

The use of geothermal (ground source) heat pumps in both residential and commercial construction is increasing. Geothermal heat pumps are installed in the earth with heating/cooling loops that circulate fluids over the system design life. This includes one or more pre-drilled boreholes in which the circulating pipes are placed, and the surrounding space around the pipes filled with a thermal conductive material. Geothermal heat pumps have the potential to recycle energy from the earth and reduce primary energy consumption and emissions of greenhouse gases. The U.S. Environmental Protection Agency estimated that geothermal heat pumps could reduce energy consumption by as much as 44% when compared to air-source heat pumps, and reductions in energy consumption can be as high as 72% when compared to conventional electrical heating and air conditioning (USGAO, 1994).

How does the geothermal system work?

The circulating pipes (typically HDPE plastic pipes) placed in the borehole are connected to a heat pump unit above ground.A seal material (typically bentonite) used around the pipes allows for efficient heat transfer between the pipes and the earth. In an active heating system, a fluid (typically a mixture of water and antifreeze) is circulated in the plastic pipes (loops) underground to allow heat transfer from the earth to the fluid. The fluid absorbs the heat and with circulation, the heat is returned to the heat pump. The heat pump extracts the heat, and re-circulates the cooler fluid for another cycle of heat transfer. The heat pump distributes the extracted heat as warm air. In an active cooling system, the roles are reversed and the heat pump extracts heat from the surrounding hot air and distributes the cool air as air-conditioning. The extracted heat is transferred into the pipe loops with the fluids and circulated underground to allow heat transfer from the fluids to the earth.

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Figure 1. Section of geothermal borehole with gap formations (Allan and Philappacopoulus, 1998).

1.2 Why a bentonite seal? Bentonite is typically used as the grouting material to seal the geothermal well. It is placed in slurry form consisting of bentonite (sodium montmorillonite) a viscosifying polymer, and water with a solids concentration of not less than 20%. Bentonite grout is employed due to its 1) good thermal conductivity, which is critical for heat transfer, 2) its low permeability which is essential to protect the groundwater, and 3) its relatively low viscosity allows for its placement with no voids, which is critical for efficient heat transfer, and groundwater protection. However, the bentonite grout slurry has a very high water content and there is a risk of free water migrating within the slurry, and between the slurry and the surrounding formations. It has be postulated that excessive moisture migration could cause shrinking and cracking, or desiccation of the well seal, which would compromise its integrity (Evans & Sicwebu, 2014). A compromised seal manifests itself as the formation of gaps between the grout and piping, and/or the grout and surrounding soil interfaces, and result in a loss of efficiency in thermal conductivity. Figure 1 shows the types of gap formation that compromises the grout seal. 1.3

Research objective

The research reported in this paper extends the closed system studies of the thermal and hydraulic properties of geothermal well seals (Evans & Sicwebu 2014). Using an open system, that allows for moisture migration (not used in Evans & Sicwebu, 2014), this research studies the thermal conductivity over numerous cycles of heating and cooling and how moisture migrates within the bentonite seal and between the seal and formation. 2

MATERIALS AND METHODS

To study the effects of moisture migration on thermal conductivity on the geothermal well bentonite grout seals, the grout material was selected based on the

Figure 2. Side view of geothermal well model.

performance requirements necessary for an efficient function of the well system. An efficiently functioning system includes the control of ground water migration vertically between formation strata and the conduction of heat horizontally through the grout from the circulating pipes or from the surrounding formation material. BENSEAL® and EZ-MUD® , used in a closed system study by Evans & Sicwebu, (2014), was also used for this experimental study. BENSEAL® and EZMUD® are manufactured/sold by Baroid Industrial Drilling Products. BENSEAL® is a bluish/gray granular natural Wyoming sodium bentonite. EZ-MUD® is a liquid polymer emulsion and is used to stabilize the BENSEAL® from excessive swelling and sloughing during the slurry preparation. The EZ-MUD® makes the slurry more viscous at a given bentonite content, thereby increasing the workability of the grout. Figure 2 shows a photograph of the laboratory geothermal well model used to contain the BENSEAL® /EZ-MUD® grout. The apparatus (cell) used for grout placement was constructed of a 152 mm inside diameter polyvinyl chloride (PVC) pipe, which is a similar radial dimension to that of an actual geothermal system. The height of the apparatus is 30 cm, representing only a portion of the vertical height of a typical geothermal system. The cell had an inner High Density Polyethylene (HDPE) pipe of 25 mm diameter to circulate the heating and cooling fluid. The piping material used is a material that is used in field geothermal well systems. In a field installed geothermal well system, moisture migration can occur into or from the formation. Moisture migration depends on the water retention

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Figure 3. Cross-sectional view of the open system geothermal well model.

capacities of the bentonite slurry and of the formation. Though surface water tensions may effect water retention capacities, it is the mechanisms related to the materials physico-chemical interactions at microscopic levels, in particular, the transfer of interlayer water to the macropores (that can be triggered by temperature increases) that has the greater effect on its water-retention (Villar and Gomez-Espina, 2008). In this experimental system, the cell piping material was pre-drilled with holes of 3.175 mm diameter spaced 30.48 cm on center vertically and horizontally to allow for moisture migration between the bentonite slurry and the formation. Figure 3 shows a schematic diagram of a slice through the geothermal well model. A non-woven geotextile fabric was placed on the inside of the outer cell wall, and then the cell was placed in a larger system of approximately 50 cm in diameter and 40 cm deep. Fine sand was placed within the larger system and around the cell, which acted as the formation soil around the geothermal system. The fine sand is well graded with a maximum particle size of 4.75 mm with just over two percent larger than the 0.075 mm size. To maintain moisture equilibrium within the sand formation, bowls of water were placed on top of the sand and the entire surface of the larger system was covered with a plastic cling wrap. This approach effectively maintained 100% humidity in the air above the top of the sand. The geothermal system setup is shown in Figure 4. To measure the thermal conductivity of the bentonite slurry seal, an instrumentation setup identical to that of Evans & Sicwebu, (2014) was used, and therefore only a summary is presented here. A total of sixteen thermocouples were used in this study. Fourteen thermocouples were placed within the annulus of the cell as shown in Figure 5, and used to calculate the system’s thermal conductivity using Fourier’s law for heat flux density in soils. Two thermocouples were used to measure the inflow and outflow temperatures of the circulating fluids Knowing the temperature difference and flow rate allowed for a calculation of heat loss/gain as the fluid circulated.

Figure 4. Open system geothermal cell test setup model.

Figure 5. Thermocouple placement in the geothermal system model.

The geothermal test system included a flow system as shown in Figure 6. The flow system included a peristaltic pump for a continuous flow through the system’s continuous loop for heating and cooling fluids. The flow rate of the pump was 0.1 mL/hr. Based on Fourier’s law and the geothermal system test setup, the thermal conductivity, kt of the grout slurry is determined from the heat flux q (Equation 1) and by the formulated Equation 2:

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Figure 6. Schematic of thermal and hydraulic conductivity testing apparatus (Evans & Sicwebu, 2014).

In Equation 1 and 2, m ˙ is the mass flow rate, cp is the specific heat capacity of water (1 g/◦ C),
T is the change in temperature of the grout, R1 is the inside radius of the cylindrical cell, R2 is the outer radius, and x is the height of the geothermal model.

3

Figure 7. Schematic of bentonite slurry sampling locations water content determination.

Table 1. Final moisture content results of 18 bentonite sample after being subjected to heating and cooling cycles.

RESULTS

3.1 Moisture Migration A series of gravimetric water content tests were performed at the end of the heating and cooling cycles in the open system geothermal well model, to determine the moisture content migration trends within the grout mixture. Figure 7 presents a visual aid of the location of grout samples used to determine the moisture contents. A total of eighteen water content samples were chosen at the locations shown in Figure 7 to establish a diametric and vertical patterns along which moisture migration, if any, can be determined. The diametric pattern consists of sampling from three depths with each depth having six diametric sampling locations. For each depth, the samples were obtained in series starting from an outside edge of the specimen going towards the center core (e.g. 1, 2, 3) and continued from the other side of the center core towards the diametrically opposing outer edge (e.g. 4, 5, 6). Similarly the vertical patterns consist of six vertical lines of sampling, with each line of sampling having three samples at varying depths (e.g. 1, 7, 13). The gravimetric water content data of all the eighteen samples obtained from the bentonite grout are shown in Table 1. The mean water content for the grout samples is 429 percent. There appears to be a large variation in the water content data. The table shows the range of water content from a minimum of 327

Sample #

Water content (%)

Relative water content (%)

1 2 3 4 5 6 7 8 9

327 260 281 352 384 430 331 465 469

−34.6 −47.9 −43.9 −29.6 −23.3 −14.0 −33.8 −7.0 −6.2

Sample #

Water content (%)

Relative water content (%)

10 11 12 13 14 15 16 17 18

441 490 451 498 527 567 336 569 550

−11.8 −2.1 −9.8 −0.5 +5.5 +13.4 −32.8 13.7 10.0

percent (Sample #1) to the maximum of 569 percent (Sample #17). 3.1.1 Lateral migrations To determine the relative water contents shown in Table 1, the difference in the measured water content from the initial water content of 500 percent of the bentonite grout at the start of testing were compared to the initial water content. Given the following variables: w (measured water content); wini (initial water content), the relative water content, Rw is determined by

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Figure 8. Water content test results with respect to distance from center of the geothermal system.

Equation 3. Rw can also be expressed as a percentage by multiplying Rw by 100.

The relative water content data in Table 1 is plotted in Figure 8 with respect to the distance sampled from the center of the test setup. This provides a visual representation of relative water contents diametrically across the bentonite grout. Samples 1 through 6 were taken at approximately the same elevation across the grout and within the top section, with Samples 7 through 12 taken within the center section, and Samples 13 through 18 within the bottom section. An anomaly of relative water content reduction is noted for Samples 13 through 18 that were sampled diametrically within the top section of the grout. The noted drop from Samples 15 to 16, then the immediate increase in Sample 17, does not appear to be consistent with the general trends noted. In general, there appears to be a slight decrease in water content diametrically across the grout (from right to left) at each sampling elevation. The average relative water content at the top, center, and bottom sampling elevations are −32.2, −11.8, and 8.4 percent respectively. A negative relative water content implies a loss of moisture from the initial condition, and a positive change implies a gain of moisture from the initial condition. The average diametric relative water content for the grout is 11.9 percent. Decreases in water content diametrically across the grout may be due to the idea that moisture can migrate from areas with high temperature towards cooler areas (Chen, 1988). This process of moisture migration due to thermal gradients is called thermo-osmosis. Thermal gradients can occur from non-heterogeneity within the grout such as variations in consolidation. Differences in the water contents across the grout system may also be due to the effects of boundary conditions created by the off-centered placement of the grout system within the surrounding soil (see Figure 4). Though a relative change in water content is

Figure 9. Water content test results for a closed geothermal system. (Evans & Sicwebu, 2014).

shown from one end to the other (diametrically), it is noted that moisture loss (relative to the initial water content of 500 percent) occurred at all test locations for the top and center portions of the grout (Samples 1–6, 7–12), but with a higher rate of loss at the top portion. However, moisture increases occurred at most test locations for the bottom portion of the grout (Samples 13–18). The changes in moisture content at each of these top, center and bottom sections of the grout indicates a trend of high moisture loss at the top, moderate moisture loss at the center and moisture increase at the bottom, which indicates a moisture migration with depth. Evans & Sicwebu, (2014) performed a series of gravimetric water content tests using a closed system, whereby net moisture migration from the grout mixture was not possible. A closed polyvinyl chloride (PVC) pipe was used to contain the bentonite seal. Figure 9 shows the relative water contents of samples from the closed system at distances from the center. Though net moisture migration was prohibited out of the grout mixture, moisture migration redistribution within the grout mixture occurred. Figure 9 indicates a general consistent moisture contents radially but with loss of moisture content only at the top section of the grout mixture, and very close to the center (Samples 1–6). Due to the increased variation of relative water contents in the open system geothermal well model used in this study, than that of the closed system used by Evans & Sicwebu, (2014), it appears that the open system did allow for moisture migration. 3.1.2 Vertical migrations The water content data from Table 1 for the open system is also shown in Figure 10, but with respect to sampling locations relative to depth. This aids as a visual representation of water contents vertically through the bentonite grout. For example, Samples 1, 7, 3 represent a vertical layout of samples at different depths that were obtained for water content tests, and were the furthest on the left side from the centerline of the grout system (see Figure 7 for complete

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Figure 11. Water content test results for a closed geothermal system. (Evans & Sicwebu, 2014).

Figure 10. Water content test results with depth.

layout). Showing the water content for Sample 16 as an anomaly, as previously discussed in the diametric distribution of water contents, Figure 10 shows in general, increases in the relative water content with depth. Relative water contents were much lower at the top (approximate depth of 7.5 cm), slightly higher at the center section (approximate depth of 15 cm), and about or above the initial water content at the bottom section (approximate depth of 22.5 cm). The average vertical relative percent change in water content with depth were determined at each vertical location. The average relative water content with depth for all vertical locations vary from −23.0 percent (Samples 1, 7, 13) to 0.1 percent (Samples 6, 12, 18), with an average of −12.7 percent for all vertical locations. The increases of relative water content of the bentonite grout with depth are most likely due to gravitational migration. Similarly, the relative water content data from the closed system by Evans & Sicwebu, (2014) were analyzed with respect to depth at each vertical layout and graphically shown in Figure 11. The figure shows very minimal variation of water content with depth from the initial water grout slurry water content of 500 percent for the closed system. The exception is noted in only one of the vertical layouts (Samples 4, 10, 16), where the relative water content vary by as much as −27 percent (Sample 4) and only at the top section of the grout, and closest to the center of the grout with the pipes circulating heating and cooling fluids. To assess moisture migration through the grout slurry, into and from the formation, a series of water content were performed on the formation material (natural fine sand) around the geothermal well annulus and presented in Figure 12. Due to the apparent relative increases in some of the water contents at the top section (e.g. Samples 2, 8, 14) above that of the center section, it appears that lateral moisture migration may have occurred. However, the apparent relative increases in water content at depths, indicate that moisture migration with depth is more pronounced than lateral moisture migration.

Figure 12. Water content test results of the natural sand soil formation around the geothermal well.

3.2 Steady state thermal conductivity A steady state thermal conductivity value was computed for each heating and each cooling cycles from the data obtained from the thermocouples. The computed steady state thermal conductivity values for 30 cycles of heating and cooling cycles are presented in Figure 13 as a function of cycle number. The first noted observation from Figure 13 is that the thermal conductivity for cycles of heating is higher (average value 0.688 W/m-K) than that of the cycles of cooling (average of 0.491 W/m-K). These findings are consistent with Evans & Sicwebu, (2014) for higher thermal conductivity values for the heating cycles than those of the cooling cycles. Thermal conductivity changes with temperature because heat conduction in non-metallic solids is mainly due to lattice vibrations (phonons) (Evans & Sicwebu, 2014). As atoms vibrate more energetically at one part of a solid due to high temperatures, heat is transferred to less energetic neighboring atoms.

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Figure 13. Thermal conductivity test results for open system.

Due to the material temperature increase, the internal particle velocity increases as well, thereby increasing the thermal conductivity. The increased velocity transfers heat with less resistance (Ziman, 1967). The grout manufacturer specifies the thermal conductivity of the grout to be 0.74 Watts/m. ◦ C. This specified value of 0.74 Watts/m. ◦ C is similar to the average value for cycles of heating of 0.688 Watts/m. ◦ C. Figure 13 shows that there was no significant degradation in either heating or cooling thermal conductivity values for 30 cycles. Furthermore, the thermal conductivity for the 30 cycles for both heating and cooling, appear consistent throughout the cycles with some anomalies. A noted anomaly was of two separate reductions in thermal conductivity during the cooling cycles, but with subsequent increases in the cycles immediately following. Another anomaly was an increase in the thermal conductivity for the heating cycles closer to the end of the cycles, but also with subsequent decrease of thermal conductivity thereafter, that approaches the more consistent values. Though there were no change in thermal conductivity within the 30 cycles for the open system, a change in the constant thermal conductivity between the open and closed systems for the cooling cycle occurred as shown in Figure 14. No change was noted in the thermal conductivity between the open and closed systems for the heating cycles.

4

CONCLUSIONS AND LIMITATIONS

The integrity and performance of a geothermal well system is dependent on several components of the system that includes the formation soil and bentonite grout conditions, and the thermal conductivity of the bentonite grout seal.An improved understanding of the impact of cyclic heating and cooling would include the study of an open system that would permit moisture

Figure 14. Thermal conductivity for cooling cycles of open and closed systems.

Figure 15. Depiction of moisture migration in the grout seal.

migration in and out of the system as moisture can substantially affect thermal conductivity (Salomone et al. 1984; Salomone and Kovacs 1984; Salomone and Marlowe 1989). A bentonite grout condition of moisture migration was a limitation in the study by Evans & Sicwebu, (2014). The testing apparatus in this study allowed for moisture migration within and between the grout and soil formations. Moisture migration occurred laterally as a result of a drying thermal gradient, and vertically (downwards) within the grout seal as a result of a wetting gravity gradient. The lateral migration of moisture indicates that moisture migration between the soil formation and the grout seal occurred. Figure 15 shows the direction of moisture migration and also shows the results of moisture migration as a negative change at the top of the grout and a positive change at the bottom for a net negative change in the relative water content of the grout seal. Though moisture migration occurred, moisture migration did not have an effect on the thermal conductivity of the grout seal, as the seal maintained its initial thermal conductivity of heating and that of cooling in 30 cycles. However, a change in the thermal conductivity between the open and closed systems for

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the cooling cycle occurred. These results illustrate the need for a long-term field study of the performance of bentonite geothermal well seals.

ACKNOWLEDGEMENTS The authors acknowledges the financial support provided by the Bucknell University Program for Undergraduate Research, the Chiloro Fund of the Department of Civil and Environmental Engineering, and the Michael and Laureen Costa endowment of the Jeffrey C. Evans Geotechnical Engineering Laboratory. The idea of moisture migrations in geothermal systems were in part based on discussions with Mr. William Reichart, President of the Pennsylvania Ground Water Association (www. pwgwa.org) and President of William W. Reichart, Inc. a geothermal system installation company.

REFERENCES Allan, M.L., Philippacopoulos, A.J. (1998). Thermally Conductive Cementitious Grouts for Geothermal Heat Pumps. FY 1998 Progress Report, BNL 66103, Brookhaven National Laboratory

Armitage, D.M., Bacon, D.J., Massey-Norton, J.T., and Miller J.D. (1980). Ground-water Heat Pumps: an Examination of Hydrogeologic, Environmental, Legal, and Economic Factors Affecting Their Use. U.S. Department of Energy. Washington, D.C. DOE/CS/20060-5120(V.1). Chen, F.H. (1988). Foundations on Expansive Soils, Development in Geotechnical Engineering, Vol. 54. Elsevier Science Publishing Company, New York. Evans, J. and Sicwebu, A. (2014). Geothermal Well Seals Subjected to Cyclic Heating and Cooling. New Frontiers in Geotechnical Engineering: pp. 88–97. Salomone, L. and Kovacs, W. (1984). Thermal Resistivity of Soils. Journal of Geotechnical Engineering. 110(3), pp. 375–389 Salomone, L. and Kovacs, W, and Kusuda, T. (1984). Thermal Performance of Fined-Grained Soils. Journal of Geotechnical Engineering. 110(3), pg 359–374. Salomone, L. and Marlowe, J. (1989). Soil and Rock Classification According to Thermal Conductivity: Design of Ground-Coupled Heat Pump Systems. Report to Electric Power Research Inistitute, Report No. EPRI CU-6482. Chantilly, VA. USGAO, (1994). Geothermal energy: outlook limited for some uses but promising for geothermal heat pumps, U.S. General Accounting Office RECD-94-84 Villar, M.V., Gomez-Espina, R. (2008). Effect of temperature on the water retention capacity of FEBEX and MX-80 bentonites, Unsaturated Soils: Advances in Geo-Engineering, London, UK Ziman, J. (1967). The thermal properties of materials. In Materials (pp. 111–126). WH Freeman

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Heat content in soil-borehole thermal energy systems in the vadose zone T. Ba¸ser Department of Structural Engineering, University of California San Diego, Gilman Dr. La Jolla, CA, USA

Y. Dong Colorado School of Mines, Golden, CO, USA

J.S. McCartney Department of Structural Engineering, University of California San Diego, Gilman Dr. La Jolla, CA, USA

ABSTRACT: This study focuses on understanding the heat content within soil-borehole thermal energy storage (SBTES) systems installed in different types of soils in the vadose zone. Temperature fluctuations in the atmosphere can create a variety of heat flux conditions resulting in different temperature gradients in the subsurface, even when a surficial insulation layer is incorporated. A three-dimensional (3D), transient finite element model was built in COMSOL to consider the representative field conditions as well as coupled heat transfer and water flow processes in the unsaturated soil within the SBTES system. The heat content is used to quantify the heat gain above the temperature profile expected above the ambient ground temperature fluctuations. The heat content changes with different type of soils as the hydraulic and thermal properties are specific to soil types. Results indicate that presence of an insulation layer leads to a significant heat gain in the shallow subsurface in all types of soils.

1

INTRODUCTION

Soil-Borehole Thermal Energy Storage (SBTES) systems are used to store heat collected from renewable sources so that it can be used later for heating of buildings (Sibbitt et al. 2012; Zhang et al. 2012, McCartney et al. 2013, Ba¸ser & McCartney 2015). They function in a similar way to conventional geothermal heat exchange (GHE) systems, where heat is transferred from a source to a sink via circulation of fluid through a series of closed-loop heat exchangers. However, they differ from GHE systems in that the heat is injected or extracted continuously over the course of a season into the borehole heat exchanger array. Further, the borehole array in a SBTES system is overlain by a hydraulic barrier to retain pore water within the subsurface and a thermal insulation layer to minimize heat losses to the atmosphere (Ba¸ser et al. 2015a, 2015b, 2016). In the shallow subsurface, below the soilatmosphere interface, heat transport plays a critical role in determining the energy fluxes between the soil surface and the atmosphere. Atmospheric conditions may be very complex due to the climatic changes and can create a variety of heat flux conditions at the soil surface. In arid and semiarid regions, temperature gradients in the shallow subsurface can be very large and may have a significant effect on temporal temperature distributions. The main goal of this paper is to understand the impact of the insulation layer on spatial and temporal

temperature distributions in heat exchanger arrays installed in different types of soils in unsaturated conditions, considering coupled heat flow and thermally induced water flow. Thus a series of numerical analyses were performed on unsaturated silt and clay soils to evaluate the role of the surficial insulation layer along with the atmospheric boundary conditions. These are compared with preliminary data from a field SBTES site in San Diego, CA. 2

BACKGROUND AND FIELD STUDY

Several field and numerical studies have established that SBTES are proven to be efficient at storing heat in the subsurface (Sibbitt et al. 2012, Zhang et al. 2012, Ba¸ser et al. 2015b). However, a better understanding of the heat transfer processes in these systems is required as the temperature increase in the SBTES arrays is highly dependent on the thermal properties of the soils and these properties change with the type of soil and the degree of saturation of the soil. To prevent heat loss from the upper surface of an SBTES system, layers of expanded polystyrene (EPS) are placed atop the array beneath a vegetative soil layer. There have only been a few studies justifying the role of the insulation layer. Ba¸ser et al. (2016) performed a numerical study on this topic, but only considered 2D flow processes and did not evaluate the change in temperature above ambient ground temperature fluctuations.

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Figure 1. UCSD SBTES system: (a) Plan; (b) Elevation.

Recently a full-scale SBTES system was installed at the Englekirk Research Center on the University of California San Diego Campus. The SBTES system consists of a vertical borehole array and two horizontal arrays. Borehole array includes 15 m deep 15 borehole heat exchangers in a hexagonal array with a spacing of 1.5 m, as shown in Figure 1. The heat exchangers consist of high density polyethylene tubing with a “U”shape coupling at the base. Three additional boreholes were installed that included thermistor strings, which have six thermistors along the length of a single cable. Their purpose is to measure the temperature distribution with depth to infer heat transfer processes within the array. One of these thermistor strings was installed in an isolated borehole to observe undisturbed ground temperature fluctuations during operation, which is a useful variable to assess the heat storage in an SBTES array. After drilling the boreholes, the soil excavated to a depth of 1 m around the array. After placing a layer of site soil to cover the heat exchangers, a 30 milthick hydraulic barrier was placed on the soil surface. A layer of expanded polystyrene (EPS) insulation was then placed on top of the hydraulic barrier, and the site soil was then backfilled up to grade. Before operation of the system, the initial ground temperature fluctuations are being collected to determine the effect of the

Figure 2. Initial temperatures of UCSD site with and without insulation layer (a) Time series for different depths; (b) Temperature profiles on February 15, 2016; (c) Ambient air temperature.

ambient air temperature fluctuations on the temperature penetration into the soil under the array and in the undisturbed ground. The ground temperature data collected inside of the array where the array is covered with an insulation layer and outside of the array from September 13, 2015 to February 15, 2016 are plotted in Figure 2. Placing an insulation layer decreases the effect of the ambient temperature fluctuation on the soil temperature.

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3 3.1

NUMERICAL MODEL Model formulation

A transient three-dimensional finite element model was built in COMSOL to predict temperature distributions inside and outside of the thermal heat exchanger arrays. The model was developed considering both heat transfer and water flow since when the unsaturated soils is heated water flows due to the decrease in density. The other driving mechanism for water flow is the alteration of surface tension with temperature. Thermally-induced vapor flow is not considered in this study. Water flow in unsaturated soils can be expressed by Richards’ equation assuming that air pressure in the pores equal to atmospheric pressure. Thus mass balance in unsaturated soils is expressed as follows (Bear 1972):

where n = porosity of the soil; Sw = wetting (water) degree of saturation (dim.); ρw = density of water (kg/m3 ); µw = dynamic viscosity of water (Pa · s); Pc = capillary pressure (Pc = Pnw − Pw ) (kPa); t = time (s); kint = intrinsic permeability of soil (m2 ); krw = relative permeability of water (dim.); g = gravitational acceleration (m2 /s); and Qm = mass source (kg/(m3 s)). Since phase change between liquid water and water vapor was neglected in this study, Qm was assumed to be to zero. Heat transfer in unsaturated soils is governed by the combined Fourier’s and Newton’s law. The governing equation for heat transfer is porous media can be expressed as follows:

where ρ = total density of the soil (kg/m3 ); Cp = specific heat capacity of the soil at constant pressure (J/(kgK)); uw = Darcy velocity; T = absolute temperature (K); λ = apparent thermal conductivity of the soil (W/(mK)); and Q = heat source (W/m3 ).

3.2 Model geometry and boundary conditions The model geometry consists of an array of 15 m-deep vertical borehole geothermal heat exchangers installed in a deep homogeneous soil layer in an array having a width of 30 m and a depth of 30 m. A 0.1 m-thick insulation layer was placed on top of the heat exchangers, which was covered by a layer of site soil. The details of the model geometry is given in Figure 3. Symmetry was used in configuring the model geometry, with one of the geothermal heat exchangers at the corner of the array, and the other two are spaced at a distance of 2.5 m from the center in orthogonal directions.

Figure 3. Model geometry.

For heat transfer, a constant heat flux of 30 W/m was applied at the borehole boundaries for a period of 90 days. A sinusoidal temperature function was applied at the top assuming that maximum and minimum daily air temperatures are 25◦ C and 10◦ C. The bottom temperature was fixed to 12◦ C because of the groundwater. For water flow, zero flux was assumed for all boundaries except the bottom boundary, where a constant total head of 14 m was applied. The initial temperature of the domain was assumed to be uniform and equal to 12◦ C. This is equal to the mean annual air temperature in San Diego, CA, and represents the transition profile between the hot and cold seasons of the year. The water table was assumed to be at a depth of 16 m, coinciding with the bottom of the heat exchangers. The initial conditions for the profiles of degree of saturation and suction with depth correspond to hydrostatic conditions. The entire domain is assumed to be a uniform and isotropic soil layer. The properties of two soil types were considered for the soil layer, those of Hopi silt and Denver claystone. The thermal and hydraulic properties needed for coupled heat transfer and water flow analyses of these soil are given in Figures 4(a) to 4(d) (Lu and Dong 2015).These properties differ for the different type of soils as they are dependent on the grain size, pore size distribution, and degree of saturation of the soil. Saturated thermal conductivity of Hopi silt and Denver claystone are 5.3 × 10−7 and 2.2 × 10−7 (m/s), respectively. After the implementation of the initial and boundary conditions, the system of partial differential equations (1) and (2) in three-dimensional domain was simultaneously solved using the COMSOL Multiphysics software that is based on the finite element method. The simulated domain has a volume about 10 times that of the heat exchanger domain in order to minimize boundary effects. Also initial simulations verified that there was no boundary effects.

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determined. In heat transfer modeling efforts surface temperature boundary conditions are important as the ambient air temperatures have an effect up to depth of 10 m from the surface (Brandl 2006). The first analysis was performed to observe the penetration of surface temperature without any heat input into the soil layer. Then, heat input is initiated until the last time step reaches 90 days for two cases; without the insulation layer and with the insulation layer. Temperature profiles inside of the array for Hopi silt were plotted for different time steps at x = 1.25 m, y = 1.25 m, and are given in Figures 5(a), 5(b), and 5(c). Ambient temperature fluctuations has an effect on the soil temperature distribution in the subsurface. However, the amplitudes decrease depth with due to the thermal inertia of the soil (Brandl 2006). The penetration depth from the field data is 7 m while it is 11 m from the numerical results. This is mainly because of the different thermal properties of the soils. The baseline temperature distribution trend from numerical analysis is compatible with those of measured in the field as shown in Figure 5a. Also insulation layer in the numerical analysis led to a relatively lower temperature values inside of the array. A maximum temperature of 43◦ C without the insulation layer is observed at 7.5 m at the end of the heating while the temperature reaches a value of 44◦ C at a depth of 6 m in the analysis with the insulation as shown in Figures 5b and 5c. Yesiller et al. (2005) defined a new parameter for evaluating exothermic reactions in municipal solid waste landfills called the “heat content”. This parameter can be used to account for the amount of heat in the landfill above that expected for seasonal ground temperature fluctuations at a given depth. In a similar way heat content, HC (◦ C × day/day) of the heat exchanger array was determined by first calculating the area between the time series curves for the temperature increase by the constant heat input and the baseline temperatures. Then it was divided by the duration of the analysis period to normalize HC with respect to time. HC can be expressed by the following equation:

Figure 4. Hydraulic and thermal properties of soils used in the analyses (a) SWRC; (b) HCF; (c) TCF; (d) Cp vs VWC.

4 ANALYSIS Spatial and temporal distributions of the temperatures inside and outside of the heat exchanger array were

To calculate the area, first the temperature time series at different locations are plotted in Figures 6(a) to 6(c). The maximum temperature inside of the array where is very close to the center borehole was 55◦ C while it decreased a value of 23◦ C outside of the array. The insulation layer had a negligible effect on temperature at a depth of 6 m. This effect is the same inside and outside of the array. Heat contents for two different depths was calculated and plotted at the different locations (inside and outside of the array) for Hopi silt as shown in Figures 7(a) and 7(b). It was observed that the insulation layer has a greater effect on the heat content of the soil closer to the surface.

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Figure 5. Temperature profiles inside of the heat exchanger array for Hopi silt (a) Baseline; (b) Heat input without insulation; (c) Heat input with insulation.

The heat content must be dependent of soil type as the thermal and hydraulic properties change with different soils. To understand the effect of soil type on the heat content a series of analyses were performed for Denver claystone applying the same boundary conditions. Although not given here, the temperature in the middle of the array reached a temperature value of 51.7◦ C at the depth of 6.2 m due to the relatively low thermal conductivity. As the insulation layer has its greater effect very close to surface heat contents for

Figure 6. Temperature time series at a depth of z = 6.0 m: (a) 0.5 m from the center; (b) 1.25 m from the center; (c) 3.5 m from the center.

Denver claystone are plotted in Figure 8(a) at 1.5 m. The maximum heat content value of 32 (◦ C × day/day) was observed at 1.5 m. This value is 31% greater than the value of 24.4 which was observed for Hopi silt in Figure 8(b). The contribution of the insulation layer on heat content was also an interesting subject to investigate. Thus, heat contents were determined for the temperature gain by the insulation layer having different thicknesses (h = 0.1 m and h = 0.2 m). This time the area for the temperature increase with insulation layer and

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Figure 7. Heat content changing with distance from the center of the array (a) at a depth of 1.5 m; (b) at a depth of 6.0 m.

Figure 8. Heat content versus distance from the center for Denver claystone (a) Denver claystone; (b) Comparison of different soil types.

the temperature increase without the insulation layer were calculated for different soil types. The contribution of the insulation layer ranges between 60–70% for Hopi sit while this value is 24% for Denver claystone inside of the array. It was also observed that when the thickness of the insulation layer is doubled, the heat content increases in the array while it slightly decreases outside of the array at very close to the surface. This is because with the thicker insulation layer more heat can be preserved inside the array resulting in a lower temperature increase outside of the heat exchanger array. This increase also differs with different type of soils as shown in Figures 9(a) to 9(d). The heat content increase with increasing insulation layer is quantitatively greater in soils having higher thermal conductivity than in soils with a comparatively lower thermal conductivity. There was no significant increase in heat content at a depth of 6 m due to the effect of the insulation layer. This is because the heat at this depth is not affected greatly by the surface temperature fluctuations. Thermally-induced water flow has been studied by many researchers as the thermal properties of soils change with degree of saturation (Philip & deVries 1957, Smits et al. 2012, Ba¸ser et al. 2014). The study

by Lu and Dong (2015) has shown that there is a significant increase in thermal conductivity as well as specific heat capacity with increasing degree of saturation from dry to unsaturated conditions. Thus in the modeling efforts thermally induced water flow is considered as the water in the pores decrease in density and moves away from heat source to cold regions. This movement is mainly dependent on the hydraulic conductivity of the different soils (Catolico et al. 2016) and the temperature gradients. To understand the unsaturated water flow in the heat exchanger arrays due to the temperature gradients the initial and final volumetric water content profiles were plotted for Hopi silt in Figure 10. It was seen that even though this movement is small, its contribution to the specific heat capacity is not negligible. The biggest increase in volumetric water content was observed very close to the heat source due to the higher temperature increase while the thermally induced water flux magnitude decreases with increasing distance from the center. It should be noted that this analysis does not consider thermally-induced vapor flow, which may have an additional effect on the thermally induced water flow. However, this analysis is quite complex and

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Figure 10. Volumetric water content profiles inside and outside of the array.

5

CONCLUSIONS

This study focuses on numerical simulations of the spatial and temporal temperature distributions in soilborehole thermal energy storage (SBTES) systems with and without a surficial insulation layer. A 3D transient finite element model was built to consider representative field conditions in an unsaturated soil layer in and around the SBTES system. Experimental and numerical results indicate that installing an insulation layer on top of the heat exchanger array leads an increase in the temperature in the shallow subsurface by reducing the heat exchange between the subsurface and the thermal storage array. The “heat content” of a thermal heat exchanger array defined as the area between the time series curves for the temperature increase by the constant heat input and the baseline temperatures normalized by the time was used to quantify the heat storage in the array. The magnitude of heat content (HC) was observed to increase in the array with increasing depth. Soils having a higher thermal conductivity has a lower HC values as the heat can dissipate faster under high temperature gradients. Increase in temperature with an insulation layer is also quantified with the increase in HC. This increase is bigger in the soils having a relatively higher thermal conductivities. When the insulation layer is doubled the preserved amount of heat in the array increases. This increase is significant right below the surface while there is no significant increase with increasing depth. ACKNOWLEDGEMENTS Figure 9. The effect of insulation layer on the heat content (a) Hopi silt h = 0.1 m; (b) Hopi silt h = 0.2 m; (c) Denver claystone h = 0.1 m; (d) Denver claystone h = 0.2 m.

will be left for a future study. The conclusions regarding the role of the insulation layer are still expected to be valid regardless of not considering this additional coupled flow process.

Funding from National Science Foundation (NSF 1230237) is much appreciated. The opinions are those of the authors alone and do not reflect those of the sponsor. REFERENCES Ba¸ser, T., Linkowski, D. & McCartney, J.S. 2014. Charging and discharging of soil-borehole thermal energy

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storage systems in the vadose zone. In: Bouazza, Abdulmalek (Editor); Yuen, Samuel T S (Editor); Brown, Bruce (Editor). 7th International Congress on Environmental Geotechnics: ICEG2014: Engineers Australia, 2014: 362–369. Ba¸ser, T. & McCartney, J.S. 2015a. Development of a fullscale soil-borehole thermal energy storage system. Proc. Int. Foundations Conference and Equipment Exposition (IFCEE 2015). ASCE. pp. 1608–1617. Ba¸ser, T., Lu, N., & McCartney, J.S. 2015b. “Operational response of a soil-borehole thermal energy storage system.” ASCE Journal of Geotechnical and Geoenvironmental Engineering. 04015097-1-12. 10.1061/(ASCE) GT.1943-5606.0001432. Ba¸ser, T., McCartney, J.S., Moradi, A., Smits, K., and Lu, N. 2016. “Effect of a thermo-hydraulic insulating layer on the long-term response of soil-borehole thermal energy storage systems.” GeoChicago 2016: Sustainability, Energy and the Geoenvironment. Chicago. Aug. 14–18. pp. 1–10. Bear, J. 1972. Dynamics of Fluids in Porous Media. Dover, Mineola, N. Y., 764 p. Brandl, H., 2006. Energy foundations and other thermoactive ground structures. Géotechnique 56(2): 81–122. Catolico, N., Ge, S., & McCartney, J.S. 2016. Numerical modeling of a soilborehole thermal energy storage system. Vadose Zone Hydrology. 1–17. doi:10.2136/ vzj2015.05.0078.

Lu, N. & Dong, Y. 2015. A closed form equation for thermal conductivity of unsaturated soils at room temperature. Journal of Geotechnical and Geoenvironmental Eng. 141(6), 04015016. Philip, J.R. & de Vries, D.A. 1957. Moisture movement in porous materials under temperature gradients. Trans. Amer. Geophys. Union 38:222–232. Sibbitt, B., McClenahan, D., Djebbara, R., Thornton, J., Wong, B., Carriere, J., & Kokko, J. 2012. The performance of a high solar fraction seasonal storage district heating system – Five years of operation. Energy Procedia, 30: 856–865. Smits, K.M., Sakaki, S.T., Howington, S.E., Peters, J.F., & Illangasekare, T.H. 2013. Temperature dependence of thermal properties of sands across a wide range of temperatures (30–70◦ C). VadoseZone Journal, doi:10.2136/vzj2012.0033. Zhang, R., Lu, N. & Wu,Y. 2012. Efficiency of a communityscale borehole thermal energy storage technique for solar thermal energy. Proc. GeoCongress 2012. ASCE. 4386– 4395. Yesiller, N., Hanson, J.L. & Liu, W-L. 2005. Heat Generation in Municipal Solid Waste Landfills. Journal of Geotechnical and Geoenvironmental Eng. 131(11), 1330–1344.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Advanced shallow geothermal systems: Temperature induced cracking of backfill materials and system hydraulic conductivity H. Anbergen APS Antriebs-, Prüf- und Steuertechnik GmbH, Rosdorf, Germany

W. Rühaak & I. Sass Technische Universität Darmstadt, Darmstadt, Germany

J. Frank Frank GeoConsult GmbH, Hamburg, Germany

ABSTRACT: Shallow geothermal systems are one of the key technologies for a renewable and sustainable energy supply. The most common system is the borehole heat exchanger (BHE). These systems are capable to provide both, heating and cooling. A significant reduction of fossil thermal and electrical energy consumption can be achieved by using this kind of renewable geothermal energy. Furthermore the underground can be used as a thermal storage (UTES). For an efficient use of these advanced systems, fast thermal loading cycles are needed. However, legal constraints for the groundwater protection must be fulfilled as well. The fast heat extraction from the underground requires materials that are resistant to rapid temperature changes. These temperature changes might include temperatures below zero degrees Celsius and consequently a potential freezing of the pore water of the surrounding grouting material. The frost resistance of grouting materials is discussed controversy over the past decades. Recently a testing procedure was developed that quantifies the influences of freeze-thaw-cycles on the hydraulic conductivity of the system BHE. The main component is a testing device that simulates the in-situ geomechanical boundary conditions and quantifies the sealing capability of the grout. Due to the consideration of the in-situ direction of the freezing process, the results differ substantially from earlier investigations on frost resistance. With this procedure standardized and repeatable evaluations become feasible. This paper presents the testing device itself including numerical and experimental proofs of concept. Besides the numerical simulation of the phase change processes inside a grout specimen, results from calibration and round robin test will be discussed. The thermo-hydraulic influences and implications on the modelling of the heat flow in BHEs are analysed. The experimental results enable a comparison of the frost resistance of commercial grouts used (e.g. in central Europe). Finally the options and needs for further investigations and the implementation for the construction and operation of advanced geothermal systems are discussed.

1 1.1

INTRODUCTION Borehole heat exchanger

The use of geothermal energy is still one of the most promising technologies for achieving the goals of carbon dioxide reduction. The most popular and installed type of shallow geothermal systems is the borehole heat exchanger (BHE). A heat pump is connected to a polyethylene (PE) probe that is mounted into a borehole. The space between probe and borehole wall is filled with a backfill material that ensures a permanent embedment of the probe in the underground. Figure 1 shows a schematic of a double-U-pipe BHE. 1.2

is potentially a region of increased hydraulic conductivity. In order to prevent an increased water transport through the borehole, the sealing of the borehole is mandatory in several countries, such as Germany. The BHE needs to be back filled as soon as the probe is installed. Besides the permanent embedment, the backfill needs to meet two main features. On the one hand it needs to have adequate sealing properties, which ensure the hydraulic integrity of the aquicludes. On the other hand the temperature conductivity needs to be high enough in order to provide sufficient thermal exchange with the surrounding soil. The requirements must be fulfilled at any time during any states of operation. 1.3

Requirements on the backfill material

In central Europe it is likely that layered aquifers and aquicludes are penetrated. The drilled borehole

Freeze-thaw-cycles

The most critical states of operation for a BHE are large amplitudes of the temperature of the carrier

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Figure 1. Schematic of a borehole heat exchanger and its components (DGG & DGGT 2014).

Figure 3. Schematic of the developed FTC testing cell and its infrastructure for measurement of hydraulic conductivity and for tempering the specimen.

focusses on the described frost induced cracking and the effects on the hydraulic sealing. 2 TEST PROCEDURE 2.1 Testing setup and procedure The test procedure aims to assess the frost resistance of geothermal grouts with a strong focus on the in-situ boundary conditions. In order to ensure reliable results with a direct link to the in-situ system, the following requirements to the testing procedure were formulated (Anbergen et al. 2011). 1) The crucial parameter for an assessment of backfill materials for BHEs is the hydraulic conductivity (of the system). 2) For an evaluation of the frost resistance it is necessary to measure the hydraulic conductivity (of the system) before and after a FTC-simulation. 3) The specimen must remain in the test cell during the whole test procedure and tree-dimensional mechanical boundary conditions (ε1,2,3 and/or o’1,2,3 ) must be applied. 4) The freezing direction of the test procedure must follow the in-situ freezing direction from inside to the outside.

Figure 2. Temperature profile of a BHE system in northern Germany during winter time.

fluid. Depending on the type of operation, temperatures above 70◦ C (UTES) or below 0◦ C (extensive heat extraction) need to be taken into account. Figure 2 shows monitored operation temperatures of a BHE system in northern Germany during periods of extensive heat extraction. It is obvious that the flow temperature decreases to a level below 0◦ C. At this temperature phase change events from pore water to ice become possible. This phenomenon is commonly referred to as freeze-thawcycles (FTC). The ice lens growth with its ice pressure can induce cracking. It was uncertain how this affects the hydraulic sealing of the system. This paper

Based on these requirements a testing device (Figure 3) was developed that allows an independent assessment of the hydraulic properties of grouting material under cyclic freeze-thaw-events. 2.2

Specimen preparation

In order to fulfill the forth requirement a special specimen design is needed. The specimens are a simplified

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Figure 4. Specimen composed of an axial pipe and grout for combined tests of the system’s hydraulic conductivity and the frost resistance of the grout.

model of the system BHE. An axial PE pipe is surrounded by grouting material (Figure 4). Hence the pipe can be tempered by a fluid and operation cycles of a BHE can be simulated. For specimen preparation special casting systems were built, as the pipe must be perfectly centered in the grout body. The grout suspension was mixed and filled into the casting system, embedding the pipe. The specimen cures under in-situ temperature (10◦ C) and humidity conditions (evaporation prevented) for 28 or 56 days. For the test the specimen is demolded and trimmed to defined axial dimensions with planar surfaces. 2.3 Hydraulic conductivity of the system For the assessment of potential hydraulic processes in the underground it is necessary to have information about the hydraulic conductivity. In many cases the hydraulic conductivity of the observed material has no dependency on the direction of flow. However, in the case of BHEs the hydraulic conductivity strongly depends on direction. Due to the contact surface of the PE pipe and the backfill material there is a gap that is a preferred water connection area. The hydraulic conductivity in direction of the BHE pipe is higher than the hydraulic conductivity of the bulk backfill material or bulk PE. For groundwater flow analysis the higher hydraulic conductivity needs to be taken into account. Consequently, it is necessary to assess the system BHE (or an accurate model) instead of the bulk material for reliable observation of the groundwater flow. 2.4 Freeze-thaw tests and change in hydraulic conductivity The formation of ice lenses during the freezing process of the backfill material likely induces cracking. The cracks are of a concentric shape and are preferred water path ways for vertical water flow. The number and size of frost induced cracks depends on the material tested. Hence, a general assessment whether the backfill material is prone to cracking or not is feasible. In order to provide a unified test conditions, all tests are executed with the same pore-pressure, freezing and thawing temperatures and durations. For freezing the fluid temperature was set to −10◦ C for a minimum of 20 hours, for thawing to +8◦ C. Before and after each FTC the hydraulic conductivity was determined

Figure 5. Quartz flour as a standard material for round robin tests.

according to ASTM D-5084 (2010) and DIN 18130-1 (1998). 3

PROOF OF CONCEPT

3.1 Round robin tests One critical issue about geotechnical testing is to ensure the reproducibility of a testing procedure and its results. In order to test whether the results are independent from the laboratory where the tests are performed or not, the testing equipment was built up in three laboratories.As a standard test material quartz flour (Figure 5) of a defined grain size distribution was chosen. The industrial production ensures a comparable quality and availability. The results of the three laboratories with its test differ only within a small range, as shown in Figure 6. With this basis it is proven, that the testing set up can be installed independently and produce comparable results. 3.2 Visual observations All backfill specimen tested were observed visually regarding the cracking schemes. The schemes are of a concentric shape. With increasing distance from PE pipe, which is the frost entrance point, the number of cracks increases. This is in agreement with the theory of cryostatic suction processes (Konrad & Lemieux 2005, Unold 2006). 3.3 Tracer tests Several specimens were tested with a tracer fluid in order to visualize the preferred flow paths through the system. It can be observed that most water transport occurs between the PE pipe and the backfill material (Figure 7).This is in good agreement with observations of grouted wells (Baumann et al. 2003). Besides the dominant water flow along the PE pipe, there is fluid transport through the matrix. Especially

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Figure 8. Relative increase in hydraulic conductivity. Comparison of bulk material and system specimens. Figure 6. Comparison of the measured hydraulic conductivities of the standard material in three different laboratories.

model was set up in order to verify whether the specimen freezes axisymmetric or not. The model was implemented using the software code FEFLOW (Diersch 2014). FEFLOW is a common code for thermos-hydraulic coupled groundwater modelling and is frequently applied for geothermal simulation. In order to simulate the phase change of the freezing process a plug-in was developed that manipulated the thermo-hydraulic parameters of the fluid. It includes an apparent heat capacity approach that respects the latent heat effects during crystallization of water to ice and vice versa (Mottaghy & Rath 2006, McKenzie et al. 2007). The numerical simulations prove the primary radial freezing process inside the testing cells as well that the chosen testing times are sufficient for a complete phase-change of the pore water (Anbergen 2015b).

4

RESULTS

4.1 System hydraulic conductivity

Figure 7. Inner surface of a specimen, split up after tracer test.

the concentric, frost induced cracks are a preferred water path. Again the total amount of water streaming through the cracks depends on the material and its frost resistance. 3.4

The hydraulic conductivity of the system is significantly higher than the hydraulic conductivity of the bulk backfill material. Due to the PE pipe and its preferred flow path the axially directed water flow increases about two orders of magnitude (Anbergen 2015). Figure 8 shows the relative increase in hydraulic conductivity.

Numerical model

As the testing procedure follows the in-situ freezing direction radially from inside out, a numerical

With kMat the hydraulic conductivity of the bulk material, kSys the hydraulic conductivity of the system.

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Figure 9. Relative increase in hydraulic conductivity of the system caused by 6 (or more) FTC.

4.2

Frost resistance

In dependence on the number of FTC, there is an increase of the system hydraulic conductivity. The first FTCs have the gravest effect on the conductivity. Most materials tested show no further increase after 6 FTC, which is in agreement with observations on clay-liners of landfill-covers (ASTM D-6035 2008).

With kFTC the hydraulic conductivity of the system after 6 (or more) FTC. The increase of the system hydraulic conductivity caused by FTC depends on the properties of the grouting material. There is a significant difference between materials with or without swelling (clay) components. Backfill materials with a certain percentage of swelling components have a higher frost resistance than pure cement based backfills. Figure 9 shows the relative increase in hydraulic conductivity due to FTC (a minimum of 6 FTC were executed). 5

DISCUSSION

5.1 Comparison to large testing setups While the described laboratory testing setup was established, a large scale test was carried out by Kuckelkorn & Reuß (2013). Specimens of an axial length of 2.75 m and a diameter of 150 mm were installed in a hydraulic conductivity apparatus. The specimens were composed of a real size HDPE-probe and different backfill materials. The system’s axial hydraulic conductivity was determined as well as the change of conductivity

Figure 10. Comparison of the absolute range of increase in hydraulic conductivity. Comparison of bulk material and system specimens.

due to cyclic freeze-thaw-simulations. A comparison of the obtained results of the laboratory and the large scale tests is shown in Figure 10. It is obvious that results are alike and the measured system hydraulic conductivities have a similar order of magnitude. This proofs the equality of the testing setups. Besides the general systems hydraulic conductivity the increase due to FTCs is comparable as well, as jointly published (Anbergen et al. 2015b).

5.2

Practicability of the test procedure

The practicability of the test procedure was tested of the past years. About 80 percent of the geothermal backfill materials available in Germany were tested. There is a broad acceptance of the procedure. The latest guidelines for shallow geothermal systems suggest a quality control according to the described testing routine (e.g. DGG & DGGT 2014, VDI 4640-2 Draft 2015). With the procedure an independent and unified assessment of the frost-restistance of geothermal backfill materials becomes feasible. 6

OUTLOOK

Based on the findings, there is a further development of the testing cell. Due to its construction there are several further fields of research such as the heat transport of buried power cables, in which the cell can be applied.

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Therefore the cell will be equipped with further sensors and a thermal conductivity measuring system. The FTC-behavior of geothermal backfill was analyzed by several further researchers (e.g. Erol & François 2014). There thermos-mechanic models were developed in order to predict the cracking schemes. The mechanical approaches will be combined with the thermo-hydraulic phase change plug-in (Anbergen et al. 2015a). The performance of the plug-in is assessed in an international benchmark for phasechange codes, called INTERFROST (Grenier et al. 2016). Besides the ongoing benchmark, there are further numerical investigations based on the developed FEFLOW code (Dalla Santa et al. 2016) in order to increase the reliability of the prediction of thermal plumes of BHEs. REFERENCES Anbergen, H., Frank, J., Albrecht, I. & Dittrich, H. (2011). Prüfzelle zur Bestimmung des Frost-Tau-WechselWiderstands von Verpressmaterial für EWS, bbr – Fachmagazin für Brunnen- und Leitungsbau, 2011/10: 38–43. Anbergen, H., Frank, J., Müller, L. & Sass, I. (2014). FreezeThaw-Cycles on Borehole Heat Exchanger Grouts: Impact on the Hydraulic Properties, Geotechnical Testing Journal, 37 (4): 639–651. Anbergen, H., Rühaak, W., Frank, J. & Sass, I. (2015a). Numerical simulation of a freeze–thaw testing procedure forborehole heat exchanger grouts. Canadian Geotechnical Journal 52(8): 1005–1022 Anbergen, H., Frank, J., Reuß, M., Kuckelkorn, J., Müller, L. & Sass, I. (2015b). Hydraulische Integrität des Systems Erdwärmesonde. bbr – Fachmagazin für Brunnen- und Leitungsbau, 2015/02: 34–41 ASTM Standard D-5084 (2010). Standard test methods for measurement of hydraulic conductivity of saturated porous materials using a flexible wall permeameter. Annual book of ASTM Standards, ASTM International, West Conshohocken, Pa., USA Baumann, K., Niehues, B., Tholen, M. & Treskatis, C. (2003). Untersuchungen zur Bestimmung von Qualitätskriterien für Abdichtungsmaterialien im Brunnenbau, Abschlussbericht, Deutsche Vereinigung des Gas- und Wasserfaches e.V. – DVGW, Bonn

Dalla Santa, G., Galgaro, A., Tateo, F. & Cola, S. (2016). Modified compressibility of cohesive sediments induced by thermal anomalies due to a borehole heat exchanger. Engineering Geology 202: 143–152 Diersch, H.-J.G. (2014). FEFLOW – Finite Element Modeling of Flow, mass and heat transport in porous and fractured media. Springer, Berlin, Germany DIN 18130-1 (1998). Baugrund – Untersuchung von Bodenproben; Bestimmung des Wasserdurchlässigkeitsbeiwertes – Teil 1: Laborversuche. Deutsches Institut für Normung e. V. (ed.), Beuth Verlag, Berlin. DGG & DGGT.(2013). Empfehlungen des Arbeitskreises Geothermie – Oberflächennahe Geothermie – Planung, Bau, Betrieb, Qualitätssicherung, Version der Offenlegung, Deutsche Gesellschaft für Geowissenschaft e.V. (DGG) und Deutsche Gesellschaft für Geotechnik e.V. (DGGT) (ed), Ernst & Sohn, Berlin Erol, S. & François, B. (2014). Efficiency of various grouting materials for borehole heat exchangers. Applied Thermal Engineering 70: 788–799 Grenier, C., Rühaak, W. & The Interfrost Team (2016). The InterFrost benchmark of Thermo-Hydraulic codes for cold regions hydrology – first inter-comparison phase results. EGU General Assembly 2016, Vienna Konrad, J.-M. & Lemieux, N. (2005). Influence of fines on frost heave characteristics of a well-graded base-course material. Canadian Geotechnical Journal 42(2): 515–527 Kuckelkorn, J. M. & Reuß, M. (2013). Hydraulische Systemdichtheit und Frostbeständigkeit von Erdwärmesonden, bbr – Fachmagazin für Brunnen- und Leitungsbau, Sonderheft Geothermie, (2013): 6–13 McKenzie, J.M., Voss, C.I., & Siegel, D.I. (2007). Groundwater flow with energy transport and water-ice phase change: Numerical simulations, benchmarks, and application to freezing in peat bogs. Advances in Water Resources, 30: 966–983 Mottaghy, D., & Rath, V. (2006). Latent heat effects in subsurface heat transport modelling and their impact on palaeotemperature reconstructions. Geophysical Journal International, 164: 236–245 Unold, F. (2006). Der Gefriersog bei der Bodenfrostung und das Kompressionsverhalten des wieder aufgetauten Bodens. Ph.D. thesis, Universität der Bundeswehr München, München, Germany VDI 4640-2 Draft (2015) Thermische Nutzung des Untergrundes – Erdgekoppelte Wärmepumpenanlagen. Verein Deutscher Ingenieure (ed), Beuth Verlag, Berlin

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Studying cryogenic fracturing process using transparent specimens M. Cha Texas A&M University, College Station, Texas, USA

N.B. Alqahtani King Abdulaziz City for Science and Technology (KACST), Riyadh, Saudi Arabia

B. Yao, L. Wang, X. Yin & Y.S. Wu Colorado School of Mines, Golden, Colorado, USA

T.J. Kneafsey Lawrence Berkeley National Laboratory, Berkeley, California, USA

ABSTRACT: Cryogenic fracturing exploits thermal gradient and resulting local tensile stress to initiate fractures on a surface exposed to cryogenic fluids. This study investigates the development and morphology of cracks generated from cryogenic thermal shock in a borehole geometry under no external confining stress. A borehole was drilled through transparent acrylic specimens. Liquid nitrogen was injected into the wellbore, and the fractures were initiated by the thermal shock. The initiated fractures allowed further penetration of the cryogen, which helped to propagate fractures throughout the specimen. Fracture growth was characterized by abrupt starts and stops, which suggest that the tensile stress inside the borehole must reach a certain threshold for fracture initiation and growth. Two distinctive patterns in crack development were observed: horizontal-planarradial pattern created by longitudinal thermal contraction, and vertical cracks by circumferential contraction. The horizontal cracks appeared to be spaced by a certain length, known as the exclusion distance.

1

INTRODUCTION

Hydraulic fracturing has been demonstrated as one of the most effective technologies and are widely applied in combination with horizontal drilling for developing shale reservoirs (Steward, 2013). Due to the general availability and low cost of water, fracturing fluids of hydraulic fracturing are mostly water-based, containing proppants and some chemical additives (Sharma et al., 2004, Shaefer, 2005). Several major shortcomings accompany the application of water-based fracturing fluids. First, water can cause significant formation damage to shale formation in the sense that clay-rich shale tends to absorb water and swell, narrowing the conductive fractures and pores. Also, capillary retention of water would partially or completely block the flowpath of hydrocarbon from matrix to fracture networks (Mazza, 1997). Secondly, water usage in large quantities is concerning, placing demands upon local water supply and environments, especially in areas where water supply is at shortage. For instance, during the period of 2009-6/2011 in Texas, the median water usage in hydraulic fracturing for each horizontal well in Barnett, Eagle Ford, and Haynesville were 10,600, 16,100, and 21,500 m3 , respectively (Nicot and Scanlon, 2012). The lower volume, 10,600 m3 can fill more

than two Olympic swimming pools or supply water for 65 families for one year. Finally, high pressure downhole injection of fracturing fluids containing chemical additives has led to a contentious community and political climate over underground water contamination. In contrast to hydraulic fracturing, cryogenic fracturing using liquid nitrogen (LN) offers potentially greater fracturing capabilities without any of the issues associated with water-based fracturing fluids. Cryogenic fracturing is a relatively new stimulation technology that looks to expand and improve the traditional hydraulic fracturing technology. Cryogenic fracturing rests on the idea that a sharp thermal gradient caused by contacting with and vaporization of a cryogen, can induce fractures when brought into contact with a much warmer rock under downhole conditions. Cryogen exists in the gaseous phase at standard conditions but takes a liquid form at low temperatures, such as liquid nitrogen and liquid carbon dioxide. Specifically, when liquid nitrogen is injected into a borehole, heat from the rock near the borehole will quickly transfer to the liquid nitrogen at boiling point (−195.8◦ C or −320.4◦ F at atmospheric pressure), resulting in rapid cooling of the near-borehole area, which will cause the surface of the rock or borehole wall to contract. Once the tension due to contraction is sufficiently increased, fractures orthogonal

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to the interface of cryogen and rock can be initiated. These newly induced fractures can be further extended by high pressure gas from LN vaporization. Note that nitrogen has a liquid-to-gas expansion ratio of 1:694 at 20◦ C (68◦ F) and atmospheric pressure. Although cryogenic fracturing has not been widely deployed for developing unconventional reservoirs, it was tested in a few field cases during the 1980s and 1990s. Instead of water, Lillies and King (Lillies and King, 1982, King, 1983) pumped gelled liquid carbon dioxide at −28.9◦ C to −40◦ C (−20◦ F to −40◦ F) to stimulate tight gas sand formations using standard tubing and casing configurations. On average, 3–4 days after the fracturing treatments, oil and gas wells were cleaned up with complete flowback of vaporized liquid carbon dioxide, without producing any formation damage. In these cases, the gelled carbon dioxide was capable of carrying proppants due to its higher viscosity than liquid CO2 , hence the fractures were able to stay open. Accordingly, all the wells for which they published results experienced increased production rates (Lillies and King, 1982, King, 1983). McDaniel et al. (1997) conducted simple laboratory studies in which coal samples were immersed in LN for observation of their fracturing process. The coal samples experienced significant shrinkage and broke into smaller cubic units, creating microfractures orthogonal to the surface exposed to the liquid nitrogen. The researchers found that repeated exposure cycles to the cryogen caused the coal to break into smaller pieces, or become rubblized. After three cycles of submersion into liquid nitrogen and warm-up to ambient temperatures, the coal sample was reduced to grain-size particles. McDaniel et al. (1997) then continued field tests with liquid nitrogen, and published before-andafter production rates for five wells. The results were mixed: three CBM wells showed increased production, one CBM well showed equivalent production, and one low permeability sandstone well initially completed with slick water fracturing showed decreased production. By injecting liquid nitrogen, Grundmann et al. (1998) treated a Devonian shale well and observed an initial production rate 8% higher than the rate in a

Figure 1. Setup for cryogenic stimulation experiments.

nearby offset well that had undergone traditional fracturing with nitrogen gas. Although the increased initial production rate in this research suggests the efficacy of cryogenic fracturing, there could be a number of reasons why an offset well in a shale formation might produce differently, including anisotropic stress conditions and heterogeneous reservoir conditions over short distances. Although several field cases have been implemented, during the past 15 years, no further studies were continued for better understanding and application of this fracturing technology. The fracturing processes, mechanisms, and controlling factors of cryogenic fracturing are still poorly understood. We conducted preliminary cryogenic tests to understand the cryogen and material behaviors by performing submersion tests and applying cryogen to boreholes in unconfined concrete specimens (Cha et al., 2014). In this study, we investigate the development and morphology of fractures generated from cryogenic thermal shock in a borehole geometry in the laboratory. Liquid nitrogen is injected into the center of a transparent acrylic block to visualize fracture initiation. It is to understand the cryogenic fracturing mechanisms and toward developing and improving the process for field applications.

2

EXPERIMENTAL SETUP

2.1 Devices and procedure We consider fracturing cryogenic thermal shock, which depends on pure thermal gradient and resulting thermal tensile fracturing and subsequent cryogen transportation into fractures. In the test setup, we are mainly concerned about cooling the borehole as rapidly as possible to maximize thermal gradient. This is done by flowing LN2 continuously through the borehole. In this lab-scale experiment, LN2 was pumped from the Dewar by pressure difference using a liquid nitrogen withdrawal device (Figure 1). Liquid nitrogen was transported by a vacuum-jacketed hose to the specimen, and injected into the borehole and then directed to an outlet. A pressure transducer was attached to monitor the borehole pressure. In this thermal shock setup, pressure inside the borehole was basically the same as the pressure inside the Dewar. Cryogenic fracturing was done purely by thermal gradient; little pressure existed inside the boreholes (less than 70 kPa) throughout the thermal shock. Pressure inside the borehole, LN2 consumption, and temperature were monitored and logged. A pressure transducer was located at the top of 20 cm-long stainless steel extension tube (3.2 mm OD), which create vapor cushion and dissipate low temperature to limit heat transfer (temperature above 0◦ C (32◦ F) observed at the top of the tubing throughout testings). Thermocouples are used to measure cryogenic temperature, and their thin wires allow prompt response to temperature changes. Having data for both

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temperature and pressure provide reliability about data interpretation. More complete information about the setup can be found in (Cha et al., 2014). Taking advantage of the specimen being transparent, we observed the flow characteristics inside the borehole. Upon the start of the experiment, nitrogen inside the borehole was flown initially as a gas (for about 1 ∼ 2 minutes), and then flown as a gas mixed

with droplets of liquid, and finally flown in a more continuous phase of liquid with still a significant amount of gas phase intermixed. 2.2 Specimen preparation: transparent acrylic specimens Two acrylic specimens are used as transparent specimens. Acrylic specimens are chosen because they are transparent, and relatively brittle, which is one of the important characteristics of rocks. The dimensions of the acrylic specimen 1 are illustrated in Figure 2a. The acrylic cylinder is 10 cm in diameter and 23 cm in height and the borehole is drilled from top, and 18 cm in depth and 1.3 cm in diameter. A 1.3 cm O.D. stainless steel tube was inserted and attached to the borehole wall using epoxy to the depth of 6.4 cm. An LN2 inlet tubing was inserted to 5.7 cm beyond the casing end. The sample dimensions of Specimen 2 are the same as those of the Specimen 1. However, unlike Specimen 1, both the steel casing and the inlet point were 3.8 cm in depth (Figure 2b). The injection point was purposely placed higher than Specimen 1 to study the effect of the injection point location. 3

RESULTS

3.1 Temperature, pressure, and LN2 consumption

Figure 2. Acrylic specimens tested – Dimensions and locations of the stainless steel (SS) casing and the inlet tube.

Temperature of the specimen dropped rapidly with the introduction of LN2 , and reached LN2 boiling point within five minutes in this laboratory setups. The temperature distribution at the surface was also dependent on the proximity to the cracks due to transportation of LN2 through cracks. Temperatures dropped by nonnegligible amount shortly after the end of the test (e.g. TC #2 of Specimen 1 and TC #2, TC #4, and TC #5 of Specimen 2 in Figure 3), which probably caused by the pressure drop at the borehole.

Figure 3. Locations of thermocouple tips and temperature evolutions during the cryogenic thermal shock experiments.

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Although a lot of LN2 (20 kg) was flown in the experiment 1, most of the fractures occurred at an early stage (within 15 minutes). The Dewar lever was opened fully during releasing LN2 without intermediate closure. The experiment for Specimen 2 was terminated by depletion of the LN2 tank. The duration of the experiment 2 was 11 minutes and the amount of nitrogen consumption was 7.6 kg. Pressure measured at the borehole was in the range of 20–35 kPa, which was exerted by the Dewar tank. 3.2

Crack development

Images of specimens were captured throughout the testings using a digital camera. 3.2.1 Specimen 1 Images of specimens were captured in a video throughout the experiment (Figure 5). It was observed that fracture growth was not continuous, but rather jumpy,

Figure 4. Borehole pressure and LN2 released during the test – Specimen 1.

characterized by abrupt starts and stops. This suggests that the tensile stress generated inside the borehole must reach a certain threshold for fracture initiation and growth. The increased material’s brittleness at low temperature may have also contributed to this behavior. During the experiment, clear audible sounds were emitted, when the fractures were observed to grow. The magnitude/amount of instantaneous growth between starts and stops tends to decrease as the fracture grew larger. Most of the cracks occurred within 20 minutes. Two distinctive patterns in crack development were observed: horizontal, planar, radial fractures, and vertical cracks joining the horizontal fractures. The horizontal, planar, radial fractures form the dominant pattern of crack morphology. This can be explained by the fact that the specimen is cylindrical with a borehole height greater than the diameter, which makes thermal contractions more pronounced in the longitudinal direction. The horizontal fractures were clearly spaced by a certain length, which can be considered as an “exclusion distance”. An exclusion distance exists because a set of crack cannot be created closer than a certain length due to a limited amount of thermal contraction (Figure 6). The behavior of exclusion distance also exist in other phenomena, such as

Figure 6. Crack morphology and driving thermal tensile stresses – Specimen 1.

Figure 5. Crack development. The steps do not represent all the crack growth steps – Specimen 1.

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mud crack, frost heaving area, and dissolution pipes etc. (Buijse, 2000, Toramaru and Matsumoto, 2004, Jenkins, 2005). Fractures were generated in the vertical direction in a less magnitude compared to the horizontal fractures, caused by the circumferential thermal contraction. The vertical tensile fractures tend to initiate from or form between the horizontal fractures and bridge them. It is energy-efficient to start from one pre-existing defect (i.e., a horizontal fracture) and propagate toward another pre-existing defect (Figure 5 – Figure 6).At the end of the experiment, the specimen showed a complex fracture morphology created by the interplay between longitudinal and circumferential thermal contractions (Figure 5). 3.2.2 Specimen 2 Two horizontal fractures were observed: one in the steel cased part of the acrylic sample and another right next to the inlet port (Figure 7). Following the initiation and propagation of the horizontal fractures, vertical cracks were created and they bridged the horizontal fractures. Similar to the Specimen 1 test, the fracture in the uncased part was located close to the inlet port. In this test, however, one big radial wing was created (compared to three in the previous test), which means that there was not enough driving longitudinal contraction to generate more horizontal fractures. The lack of thermal driving and multiple horizontal fractures could be due to the shorter stimulation time – 11 min vs. 36 min in Specimen 1 test, thus lower amount of LN2 applied – 7.6 kg vs. 20 kg in Specimen 1 test, by the early depletion of the LN2 tank. 3.3

Effect of presence of fracture on temperature distribution

Temperature distribution at the surface and inside the acrylic samples was dynamically coupled to the initiation and growth of fractures. During the experiments, it was observed that liquid nitrogen moved into and flowed through created fractures, which helped fractures to further propagate. This, in turn, accelerated the temperature propagation. Figure 5 and 7 show that some cracks approached the surface at the later stage

of the experiment, and the temperature on surface near the crack was readily affected by the proximity to the cracks. 3.4 Effect of casing/inlet location For both Specimen 1 and Specimen 2 tests, one major horizontal fractures were initiated from early stage at the steel cased parts of the acrylic cylinders (Figure 5 and Figure 7) although they are far from inlet ports. This is perhaps due to the efficient heat transfer of the casings, which has a high heat conductivity. The steel casing will also have shorter period during which it is under Leidenfrost effect. These fractures, however, did not propagate as far as those in the borehole. This, perhaps, is due to the steel casing blocking the flow of LN2 into these fractures; this may be also due to the steel casing, epoxied to the acrylic cylinder, changing the stress condition and preventing further growth of the fracture. Clearly, the steel casing and the epoxy have influenced heat transfer, flow of LN2 , stress distribution and eventually affected the fracture distribution. We notice that the distribution of cryogenic temperature inside the borehole was affected by the location of the injection point (Figure 2). Fractures were mainly generated near the injection point, which suggests colder temperatures near the injection point. 4

CONCLUSIONS

Experiments were performed to study the development and morphology of fractures generated by a cryogenic thermal shock in a borehole geometry. We designed our experimental apparatus and procedures specifically for thermal stimulation using liquid nitrogen. Direct observations of fracture formation were made possible by the use of transparent acrylic specimens. The study provides key observations on fracture initiation and propagation when sufficient thermal contraction/tensile stress is achieved in a borehole. Cryogenic fracture growth was observed to be abrupt due to the brittleness of the material at the cryogenic temperature and the accumulation-release of tensile stress coupled with fracture propagation

Figure 7. Crack development – Specimen 2.

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and heat transfer. The area of fracture created at each growth event tends to decrease as the fractures become larger. Two distinctive patterns in the fracture development were observed: one is horizontal, planar, and radial propagation created by longitudinal thermal contraction, and another is vertical fractures created by circumferential contraction. The horizontal fractures were initiated first and were more dominant than the vertical fractures. This is perhaps because the borehole height is much greater than the borehole diameter, which makes thermal contractions more pronounced in the longitudinal direction. The horizontal fractures tend to be spaced by a certain length (exclusion distance), which exists because a set of fractures cannot be created closer than a certain length due to limited amount of thermal contraction. The vertical fractures tend to initiate from or form between the horizontal fractures and bridge them. We expect that the sequence of initiation and patterns will also depend on the stress condition of the specimen and this will be examined in future experiments. ACKNOWLEDGEMENTS Support for this research was provided by Research Partnership to Secure Energy for America (RPSEA) (Grant no. 10122-20). REFERENCES Buijse, M. A. (2000) Understanding wormholing mechanisms can improve acid treatments in carbonate formations. SPE Production & Facilities, 15, 168–175. Cha, M., Yin, X., Kneafsey, T., Johanson, B., Alqahtani, N., Miskimins, J., Patterson, T. & Wu, Y.-S. (2014) Cryogenic fracturing for reservoir stimulation – Laboratory studies.

Journal of Petroleum Science and Engineering, 124, 436– 450. Grundmann, S. R., Rodvelt, G. D., Dials, G. A. & Allen, R. E. (1998) Cryogenic Nitrogen as a Hydraulic Fracturing Fluid in the Devonian Shale. SPE-51067-MS. SPE Eastern Regional Meeting. Pittsburgh, Pennsylvania, Society of Petroleum Engineers. Jenkins, D. R. (2005) Optimal spacing and penetration of cracks in a shrinking slab. Physical Review E, 71. King, S. R. (1983) Liquid CO2 for the Stimulation of LowPermeability Reservoirs. SPE-11616-MS. SPE/DOE Low Permeability Gas Reservoirs Symposium. Lillies, A. T. & King, S. R. (1982) Sand Fracturing With Liquid Carbon Dioxide. SPE Production Technology Symposium, 8-9 November, Hobbs, New Mexico. Society of Petroleum Engineers. Mazza, R. L. (1997) Liquid CO2 improves Fracturing. Hart’s Oil and Gas World, 22. Mcdaniel, B., Grundmann, S., Kendrick, W., Wilson, D. & Jordan, S. (1997) Field applications of cryogenic nitrogen as a hydraulic fracturing fluid. SPE Annual Technical Conference and Exhibition. Nicot, J.-P. & SCANLON, B. R. (2012) Water Use for ShaleGas Production in Texas, U.S. Environmental Science & Technology, 46, 3580–3586. Shaefer, M. T. (2005) Are Slick Water-Fracturing Applications Effective in the J-Sand Formation? SPEAnnualTechnical Conference and Exhibition, 9–12 October, Dallas, Texas. Society of Petroleum Engineers. Sharma, M. M., Gadde, P. B., Sullivan, R., Sigal, R., Fielder, R., Copeland, D., Griffin, L. & Weijers, L. (2004) Slick Water and Hybrid Fracs in the Bossier: Some Lessons Learnt. SPE Annual Technical Conference and Exhibition, 26–29 September, Houston, Texas. Society of Petroleum Engineers. Steward, D. B. (2013) George P. Mitchell And The Barnett Shale. Journal of Petroleum Technology, 65, 58–68. Toramaru, A. & Matsumoto, T. (2004) Columnar joint morphology and cooling rate: A starch-water mixture experiment. Journal of Geophysical Research: Solid Earth, 109, B02205.

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Interactions between hydraulic fracture and interfaces in layered formations S.M. Ham & Tae-Hyuk Kwon KAIST, Daejeon, Republic of Korea

Y.J. Sim Korea Land and Housing Corporation, Gyeongsangnam-do, Republic of Korea

ABSTRACT: Hydraulic fracturing is widely used to enhance hydrocarbon productivity or to enhance heat recovery. Predicting fracture propagation and geometry is an important but daunting task because of complexities in natural geologic rock conditions. This study explores the interactions between hydraulic fracture and interfaces in layered formations.A series of laboratory experiments were performed, in which hydraulic fracture propagation behavior in 2D gelatin plates were monitored. It was found that the fracture propagation was heavily affected by the stiffness of bounding layers. When the stiffness of the bounding layer was lower than that with the fracture, it appeared that the fracture passed through the interface. Whereas, fracture propagation was confined when the bounding layer had the same or higher stiffness. This study presents the simple but unique experiment data on the interactions between hydraulic fracture and interfaces, and can be further used to develop models for geometry prediction of hydraulic fracture.

1

INTRODUCTION

Hydraulic fracturing is now an important technique for the oil and gas industry. It is a process where viscous fluid is pumped into a borehole at a high injection rate to generate a permeable fracture. The design of hydraulic fracture requires the geometry prediction of the induced fractures. Many researchers have suggested models that predict the fracture geometry in homogeneous rocks. For example, KGD (Khristianovic & Zheltov, 1955, Geertsma & Klerk, 1969) and PKN (Perkins & Kern, 1961, Nordgren, 1972) are representative models widely used in oil industry. However, natural rock has several discontinuities, such as joints, flaws, and faults, and this draws a significant attention for considering the interactions between hydraulic fractures and natural discontinuities to obtain a better design. Accordingly, Simonson et al. (1978) have found that when the shear modulus of the barrier formation is less than that of the payzone, hydraulic fracture can propagate through the interface easily. Teufel & Clark (1984) have presentedthat the large normal stress is required to make fracture cross the rougher discontinuity. Further, Warlinski (2011) stated that large permeability terminated the growth of fracture. However, there are only few studies that observed hydraulic fracture propagation because it occurs within a second in the core-scale experiments (Frash, 2007, Bohloli & De Pater, 2006). Thus, this study presents high-quality images of hydraulic fracture propagation at difference shear

modulus of bounding layers. Laboratory experiments were performed, in which hydraulic fracture propagation behaviors in 2D gelatin plates were monitored. Stiffness of bounding layers was controlled by adjusting the concentration of gelatin, and three different bounding layer formations were tested. During fracture propagation, the images were recorded at a high speed to obtain the fracture geometry and the pressure curves were measured.

2 2.1

EXPERIMENTAL PROCEDURE Gelatin plate

Gelatin was used as an analogue to a homogeneous, isotropic, and elastic rock medium. It stays as a viscous liquid form at high temperatures and as a solid gel form at low temperatures. The most important characteristic of gelatin is its transparent property. This allows us to visualize fracture propagation during experiments. The stiffness of the gelatin was controlled by gelatin weight percent: 7.41 wt% (low stiffness, L), 12.28 wt% (medium stiffness, M), and 16.67 wt% (high stiffness, H). Each gelatin solution was made by mixing the dry gelatin powder with distilled water at 50◦ C. This solution was then poured in an acryl mold having a dimension of 200 mm × 200 mm × 10 mm, as shown in Figure 1a. The mold was kept in a refrigerator at 4◦ C for 24 h to cure the gelatin. For homogeneous samples with no discontinuity, the gelatin was poured in the mold at once. For samples with discontinuity,

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Figure 1. (a) The acryl mold used in the experiment and (b) the composition of galatin sample with interfaces (M2H case). Figure 2. Experiment setup.

the gelatin plate was prepared to have three layers with two interfaces, as shown in Figure 1b. Each layer was made 2 h after pouring the previous layer to allow hardening of the previous layer. The first and third layers were 50 mm thick while the middle layer was 100 mm thick (Figure 1b). The stiffness of the bounding layer was controlled in this study. Six samples of different stiffnesses were used to examine fracture propagation. Three homogeneous samples were prepared with different stiffnesses of gelatin: low stiffness (L-gelatin), medium stiffness (M-gelatin), and high stiffness (H-gelatin). Three layered samples were prepared to have different bounding layers: medium to low stiffness (M2L), medium to medium stiffness (M2M), and medium to high stiffness (M2H).

2.4 Experiment procedure When the curing of gelatin was completed, at the borehole two initial cracks having lengths of ∼5 mm, aligned perpendicular to the layer interfaces, were created by scratching the gelatin using a thin wire (thickness 100,000 t) are compared. The results show that the sandstone reservoir rock, at in-situ stress and pore-pressures, is likely to suffer failure, which changes the effective flow properties affecting the plume migration dynamics. The results improve the understanding of the implications of industrial scale GSC. Keywords: geological carbon dioxide storage (GCS), deep saline aquifers, discrete element method, microfracturing, permeability change

1

INTRODUCTION

Carbon capture and storage (CCS) in geological formations, or geological carbon storage (GCS), represents a viable solution for reducing the increasing carbon dioxide (CO2) levels in the atmosphere (Bachu, 2015; Celia et al., 2015; Cook et al., 2014; IPCC, 2005). Sandstone rock represents the lithology of approximately 50% of the small-scale GCS injection projects (less than 100,000 tonnes of injected CO2), respectively, 75% of the large scale injection projects (Cook et al., 2014). The CO2 injection rates must be selected appropriately in order to satisfy the economic and operational considerations. However, the rate of injection should not affect the stability of the system (Eshiet and Sheng, 2013). Large masses of injected CO2 can induce insitu stresses and deformations in the reservoir and the cap rock, which can cause changes of the hydraulic properties (Hu et al., 2010). Cooling down of the storage formation leads to temperature induced stresses

(e.g., Luo and Bryant, 2014), while the mechanical stresses are caused by increased reservoir pressure (Hou et al., 2012; Rutqvist et al., 2008). As a result, irreversible mechanical changes can create new fractures or reactivate old ones, which constitute leakage pathways for the CO2. The elastic and strength properties of the reservoir rock and induced micro-cracks define the hydromechanical behaviour of the reservoir. Brittle and/or weakly consolidated sandstone reservoir rocks tend to fail under the tensile-shear failure mechanism induced by CO2 injection. Real-time crack coalescence process in sandstone rock has been investigated in several experimental studies, e.g., (Yang et al., 2015a) and numerically using a two-dimensional particle flow code (PFC2D) (Yang et al., 2015b). Permeability changes during rock damage and cracking have been investigated through a number of laboratory experiments (Hu et al., 2010) and studies (Homand-Etienne et al., 1998; Levasseur et al., 2013; Shao et al., 2005). Yang et al., (2015a) define a relationship between

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permeability and deformation, identifying five phases. A recent review of advancement of permeability evolution models for fractured porous media is given in (Ma, 2015). Fluid permeability of sedimentary rocks in a complete stress-strain process is discussed in (Wang and Park, 2002). Standard macroscopic multiphase multi-component models usually do not take into account the changes in hydraulic parameters (e.g., permeability) occurring during the injection of fluid (Class et al., 2009, 2002; Nordbotten et al., 2012; Tatomir et al., 2011). Nevertheless, there are several coupled numerical models to account for thermos-hydro-mechanical processes under multi-phase conditions (e.g., Hou et al., 2012; Rutqvist et al., 2008, 2002; Rutqvist and Tsang, 2002). The literature review has shown that the rock permeability evolution is directly related to the distribution, opening and coalescence of induced microcracks. Furthermore, the determination of hydraulic and poroelastic properties with the evolution of rock damage is a challenging research topic. Numerical and theoretical work has been performed to study damage of the basement rock and caprock during a CO2 injection by several researchers. Rutqvist and Tsang (2005) used coupled TOUGH2-FLAC3D computer codes to study hydromechanical changes in a caprock during CO2 disposal in brine formations. They obtained a general reduction in the effective mean stress in the lower part of the caprock, indicating a possible rock failure. Shear reactivation seems to be more likely than the probability of fracturing and shear under poro-elastic stresses induced by slow increase in pressure during the injection period (Rutqvist, Wu, Tsang, & Bodvarsson, 2002). Cerasi and Walle (2016) conducted tests on weak sandstone outcrop samples, in order to assess whether sequences of injection of a pore fluid and shut-in could have a destabilizing effect on the borehole wall of the hollow cylinder specimen. The tests showed no signs of fatigue weakening under cycling injection, for low injection pressure and high confinement of the sample (Cerasi and Walle, 2016). Large CO2 injection over 10 000 years’ period was modeled by Liu et al. (2010). However, the emphasis is given to hydro mechanical and chemical processes

over years (Liu et al., 2011). Rathnaweera et al. (2016) found that the significant rock mass mineralogical structure alterations enhance the permeability of the aquifer by the long term CO2 reaction. The pore structure changes caused by the CO2 reaction also affect the effective stress response of the aquifer rock mass (Rathnaweera et al., 2016). In this study two numerical simulators are used to solve the CO2 -injection processes at micro- and fieldscale. The PFC2d simulator based on the Discrete Element Method (DEM) is used to model microscale stress induced damage, while the two-phase two-component (2p2c) model within the numerical toolbox DuMux is used to simulate the field-scale multiphase/multi-component (CO2 -brine) flow and transport in the (fractured) porous system. The objective of this paper is to investigate the capability of the linked approaches with DuMux -DEM for one case study on the injection of supercritical CO2 at a pilot site located at Heletz, Israel. First, a parameter sensitivity study on the CO2 injection pressure on the damage of the reservoir sandstone and caprock is performed. Further, the hydro-mechanical effects of current pilot scale (10,000 t) CO2 injection and those of an industrial scale (>100,000 t) are compared. 2

2.1 Simulation environment The two codes are coupled sequentially; the output of one code being used by the other. DuMux two-phase two-component model simulates the reservoir-scale supercritical CO2-brine flow and uses an input function obtained from the DEM model, which relates local porosity and permeability to the fluid pressure and the degree of damage. The general simulation procedure is illustrated in Figure 1. A relationship between permeability change and stress is determined with the PFC2D model to be used by the large(field)-scale 2p2c-Dumux simulator. However, PFC2D model uses as first input the pressure ranges attained in the reservoir due to CO2 injection, calculated with no hydro-mechanical effects by the 2p2c model. 2.2

Figure 1. Schematic representation of the modelling workflow DuMux – PFC2D .

METHODOLOGY

Discrete element method (DEM)

The DEM defines a system of particles that are represented by finite spherical or discs particles and walls in PFC2D . The calculation cycle in PFC2D (Cundall and Strack, 1979; Itasca, 2004) is a time-stepping algorithm that consists of the repeated application of the Law of Motion to each particle, a Force-displacement Law to each contact, and a constant updating of wall positions.The motions of particles and walls are solved using the explicit finite difference scheme. The Bonded-particle model (BPM) for rock is introduced in PFC2D with the pre-scribed procedures that are used to determine the mechanical parameters of the synthetic rock mass (Potyondy, 2007; Potyondy

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and Cundall, 2004). The parallel bond is a component within the particle contact and can be pictured as a cementitious material at the particles contact that is able to transfer forces and moments from one particle to another. Such a bond can be envisioned as a set of elastic springs with constant normal and shear stiffness uniformly distributed over either a circular or rectangular cross-section lying on the contact plane and centered at the contact point. After the parallel bond has been created between neighboring particles, the relative motion at the contact causes normal and shear stresses to develop within the bonded material, as a result of the parallel-bond stiffness. If either of these stresses exceeds its corresponding maximum strength, the parallel bond breaks. The parameters required to model the parallel bond are normal and shear strength and stiffness. Mechanical parameters of the resulting solid comprised of the bonded particles are modeled indirectly by implementing an iterative procedure for obtaining the parallel bond parameters. For rock mass modeling, usually the Direct tension test, the Brazilian test, the unconfined compression tests (UCS) and the triaxial tests are used. A fracture can propagate within the bonded particles assembly by breaking the bonds between particles. For low porosity solids the flow pathways may be assumed to consist of parallel-plate channels at contacts accompanied with artificial fluid reservoirs scheme for calculation (Figure 2). The aperture of such a channel is proportional to the normal displacement at corresponding contacts. In the case of bonded material, the channel opening will not increase from its initial value unless the bond is broken, and the adjacent particles distance increases. Pressures stored in fluid reservoirs are updated during the fluid calculation, and act on the surrounding particles as equivalent forces. Each channel is a link between two adjacent fluid reservoirs. As far as the fluid is concerned, the channel is equivalent to a parallel-plate channel, with the length L, the aperture a, and the unit depth in the out-of-plane dimension.

processes in porous media build as a modular toolbox. The partial differential equations for multiphase flow and transport are for solved with grid-based methods such as the vertex-centered finite volume scheme (box method, Helmig, 1997; Huber and Helmig, 2000). The implicit Euler method is applied for the temporal discretization. The 2p2c model was benchmarked in several studies, e.g. (Class et al., 2009; Nordbotten et al., 2012). The mathematical model on which 2p2c is constructed comprise the mass balance equations for each phase and each component. The starting assumption is that the medium is a continuum where the extended Darcy’s law (Bear, 1972; Helmig, 1997) is valid. The resulting set of equations are closed with the constitutive relationships for capillary pressure and knowing the sum of saturations is 1. A description of the basic mathematical model for 2p2c is given in for instance in (Flemisch et al., 2011), or in (Tatomir et al., 2015) an extension of 2p2c to include reactive tracer transport. The 2p2c standard model as provided in the free open-source repository (www.dumux.org) is further developed to account for the permeability changes induced by the pressure effects of CO2 injection. 2.4 Heletz sandstone reservoir Heletz, Israel (Niemi et al., 2016; Tatomir et al., 2016) is the location for an onshore deep saline CO2 storage pilot site. ‘Heletz sandstone’ is the building unit of the deep saline CO2 storage pilot site. The physical and geomechanical properties of Heletz sandstone are given in (Edlmann et al., 2016; Elhami et al., 2016; Niemi et al., 2016; Tatomir et al., 2016). A series of destructive and non-destructive tests have been performed on core sample material showing that the reservoir sandstone is extremely weak with respect to its depth of deposition (>1600 m) (Elhami et al., 2016). The sandstone is poorly cemented and little consolidated as shown by SEM images in Figure 3. Small micro-cracks (1–5 mm long) are present acting as preferential flow paths and influencing the hydraulic behaviour.

2.3 Two phase two component (2p2c) simulator (DuMux ) The two phase two component simulator isothermal (2p2c) model is developed in the DuMux (www.dumux.org) numerical toolbox (Flemisch et al., 2011). DuMux is a simulator for flow and transport

Figure 2. The BPM scheme with fluid channels and reservoirs for hydraulic fracturing.

Figure 3. Heletz sandstone core sample analysis from CO2 Pilot Site. Thin section and SEM images showing the mineral conglomerate of quartz grains interconnected by clayey and carbonatic cement. Right hand side: µCT image revealing a micro-crack (after Tatomir et al., 2016).

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From permeameter tests on the sandstone sample tested under triaxial compression it was found that the permeability is not a constant, but changes with the stress and strain in the rock. (Yang et al., 2015a) came to similar observations. However, is varying between 50 and 700 mD. An accepted value obtained from pumping tests is 400 mD which is going to be used in this study. The porosity is 23.2%. The Brooks-Corey (BC) parameters for capillary pressuresaturation relationship are λ = 0,762 and entry pressure Pe = 3861,2 Pa. These parameters are obtained from core experiments and showed high variability (Niemi et al., 2016).

3 3.1

Viscous fluid flows into the specimen at a constant flow rate on the left boundary, and the pressure differences across the model are recorded at prescribed times during the test. The final pressure difference is recorded following the test convergence, as shown in Figure 6. The numerical relationship between the initial average synthetic rock permeability and the model Table 1. Micro-mechanical properties of BPM, Rmin = minimum particle radius; Rmax = maximum particle radius; fi = particle friction coefficient; Pb_kn = parallel bond normal stiffness; Pb_ks = parallel bond shear stiffness; Pb_sstr = parallel bond shear strength; Pb_nstr = parallel bond normal strength.

RESULTS DEM sandstone model calibration

Text PFC2D synthetic sandstone mechanical properties are matched with the available data from the laboratory tests performed on the Heletz sandstone and for weakly bonded sandstones (Tatomir et al., 2016. In press; (Elhami et al., 2016; Haimson and Lee, 2004; Lin et al., 2009). The obtained micro and macro parameters are shown in Tables 1 and 2. The boundary and initial conditions, as well as, the CO2 parameters are shown in Tables 3 and 4. Figure 4 shows the initial and boundary conditions. The permeability of the synthetic sandstone depends on the particle size and the initial aperture of the fluid channels. Therefore, it is not possible to directly set the initial permeability. Modeling permeability laboratory tests permits obtaining an average DEM model permeability. Simulation of permeability tests in PFC2D uses the constant flow technique, which is suitable for testing low permeability geo-materials (Nakajima, Takeda, & Zhang, 2007; Olsen, 1966). The Darcy flow equation is used for determining the average permeability of the tested rock sample with the prescribed initial width of fluid flow channels. During cycling, the bond-breakage is disabled by setting the bond strengths unrealistically high. The no bondbreakage model enables use of high flow rates and low fluid dynamic viscosities, which aids in computational time saving. The tested rock sample has dimensions 0.015 × 0.015 m (Figure 5).

Parameter

Value

Rmin (mm) Rmax /Rmin (−) fi (−) γ (kg/m3 ) Pb_kn (GPa) Pb_ks (GPa) Pb_sstr (MPa) Pb_nstr (MPa)

0.00025 1.66 0.5 2670.0 10.0 3.5 44.0 ± 15 10.0 ± 3.5

Table 2. Macro-mechanical properties of BPM compared to the average granite and sandstone (Elhami, Ask, & Mattsson, 2016; Haimson & Lee, 2004; Lin, Fakhimi, Haggerty, & Labuz, 2009; Tatomir et al., 2016. In press). Setting

PFC2D Sandstone Heletz

Tensile Strength σt (MPa)

Young’s Modulus E (GPa)

Fracture Toughness KIC √ (MPa m)

Poisson’s Ratio ν (−)

3.1

31.9

0.24

0.23

1.8–4.4

24.0–32.0

0.28

0.22

Table 3. Boundary conditions of the model, where x is horizontal axes and y is vertical axes in the model (representation of two dimensional field conditions, x is in the direction of the fluid flow and horizontal, y is vertical). Parameter

Magnitude

σmin (MPa) σmax (MPa) pp (MPa)

16.4 1.66 15.7

Table 4. Fluid injection properties (single-phase flow).

Figure 4. Initial, boundary conditions and the DEM model size for lightly cemented sandstone.

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Parameter

Magnitude

µ (Pa·s) ρ (kg/m3 ) E (MPa)

52.64·10−6 662.08 32.26

Figure 5. Initial and final DEM model snapshot for permeability measurement.

Figure 8. Gas flow into the saturated sample, where the left hand boundary pressure is a) Pg = 17,0 MPa, b) Pg = 20,0 MPa, c) Pg = 25,0, MPa, d) Pg = 30,0 MPa and reservoir initial pore pressure is Pp = 15,6 MPa.

Figure 6. Initial permeability testing example of the synthetic sandstone without bond breakage.

Figure 9. Pressure profiles across the 50 cm wide sample at early times (t1 = 1377 s, t2 = 2760 s) for the left-hand fixed pressures Pg = 17.0 MPa, Pg = 20.0 MPa, Pg = 25.0 MPa and Pg = 30.0 MPa.

Figure 7. The numerical relationship between the initial average synthetic rock permeability and the initial fluid channel aperture in the model.

parameter of initial fluid flow channel is established and shown in Figure 7. Initial synthetic rock permeability is calibrated for published values of average grain size and measured permeability (k = 3.95 · 10−13 m2 = 400 mD) of the Heletz sandstone (Tatomir et al., 2016. In Press; Elhami et al., 2016).

3.2 Sandstone permeability and gas pressure relationship DEM modeling The DEM synthetic sandstone model was used to investigate effects of gas pressurization on micromechanical damage and permeability evolution. Figure 8a-d shows the vertical two dimensional section of the sandstone near the wellbore, with dimensions 50 × 50 cm. Boundary far-field total stress field in imposed to the model are the same as specified in

Figure 4 (maximum compressive stress is in the vertical direction σv,max = 42.7 MPa, minimum horizontal compressive stress σv,min = 15.7 MPa). The horizontal in-situ total stress is estimated based on the earth pressure at rest K0 = 1 − sin φ, with the internal sandstone friction angle of φ = 38◦ . The in-situ stresses are calculated based on the total unit weight of the sandstone material at the depth of h = 1600 m. The initial pore pressure is obtained using the unit weight of the water and depth h = 1600 m, and is Pp = 15.6 MPa. The wellbore is assumed to be on the left side of the model. Green colored area represents the saturated sandstone, while blue lines are broken parallel bonds between DEM particles. The broken bonds denote the micro-cracks and damage caused by infiltration of pressurized gas into rock. The simulations were established for a small time, in order to observe the effect of pressure to rock damage. Figure 9 accompanies the Figure 8, where the actual pressure profiles are plotted across the width of the model at times 22.95 and 45.9 min after beginning of injection. It can be observed that differences in the pressure profiles are indeed recognizable. The area where micro cracks occurred due to gas pressurization is isolated for permeability measurements. First, a set of new significantly smaller

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Figure 10. Figure 7. Micro cracks developed in the biaxially compressed sample with initial dimensions 15 × 15 cm, where σv,max = 42.7 MPa and σh,min = 15,7 MPa, for gas pore pressures a) Pg = 17.0 MPa, b) Pg = 20.0 MPa and c) Pg = 25.0 MPa.

Figure 12. a) CO2 pressure spatial distribution after 10 hour of injection; b) CO2 Saturation spatial distribution after 40 days of injection.

Figure 11. Horizontal permeability change in the biaxially confined sample, where σv,max = 42.7 MPa and σh,min = 15.7 MPa, for gas pore pressures Pg = 17.0–25.0 MPa (kin = 3.95 · 10−13 m2 = 400 mD).

synthetic sandstone models are subjected to the same initial and boundary conditions. Second, the pore pressure is increased thorough the entire model which is cycled for some time to reach equilibrium. The development of micro cracks is evident for even small pore pressure increase, indicating breakage of bonds between DEM particles or sandstone grains. Figure 10 shows micro cracks (blue lines) in the pressurized models. It can be also observed that the higher pore pressure in Figure 10c causes larger deformation of the model in the horizontal direction with the minimum far-field confinement. After obtaining the equilibrium of the model, the permeability is measured in the horizontal direction. The obtained relationship between the gas pressure and the new average model horizontal permeability is shown in Figure 11. 3.3

Field scale CO2 migration

Following the DEM micro-scale models, the forward simulation of CO2 injection at the field-scale. Due to its symmetry the domain size of the modeled reservoir is reduced to a 400 m by 400 m (with 15 m thickness), which only one quarter of the entire domain. The first (static) field-scale CO2 saturation and pressure profiles resulted from 2p2c model with a constant injection rate of 10 t/h are shown in Figure 12a) and b) and the corresponding breakthrough curves (non-wetting saturation – Sn and pressure – pn) in Figure 14. The influence of the hydro-mechanical effects on the reservoir performance is identified by comparing a numerical model using the permeability

Figure 13. Comparison between static and dynamic – hydro-mechanical (HM) models expressed as parameter variation with time at location x = 50 m, y = 50 m from the injection well on top of the reservoir (z = 15 m): a) CO2 saturation; b) CO2 pressure; c) change in permeability.

function (hydro-mechanical model) and another one with no permeability change (static model).The results are depicted in Figure 13. It can be observed that the CO2 front does suffer almost no change. However, the changes in non-wetting phase permeability are visible even though they are quite small (16.15 MPa in the HM model and 16.05 in the static model). Permeability changes are plotted in Figure 13c. As expected the static model has no change due to pressure whereas the HM model increases from 4e-13 to 5e-13 m2 .

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Figure 14. Breakthrough curves of CO2 and pressure in the location of the injection well.

Figure 15. Comparison between CO2 plume profile at 10,000 t (top) and 100,000 t (bottom) injected.

4

CONCLUSIONS

In spite of the fact that lot of research has been done on chemical damage of sandstone formations during CO2 injections, relatively little effort has been dedicated to better understanding of the mechanical damage in weak sandstones due to high gas pressure during injection. This paper shows results of DEM modeling of Heletz sandstone samples which are subjected to different pore pressure increases due to CO2 injection. It was found that increased pore pressures cause mechanical damage in forms of breaking bonds between sandstone and causing increase in formation permeability. Significant micro cracking was accompanied with deformation of the samples in the direction of minimum in-situ stress at high pressures.

ACKNOWLEDGEMENTS This research has received funding from the European Community’s 7th Framework Programme through the TRUST (Grant agreement no. 309067) project. REFERENCES Bachu, S., 2015. Review of CO2 storage efficiency in deep saline aquifers. International Journal of Greenhouse Gas Control, Special Issue commemorating the 10th year anniversary of the publication of the Intergovernmental Panel on Climate Change Special Report on CO2 Capture and Storage 40, 188–202. doi:10.1016/j.ijggc.2015.01.007

Bear, J., 1972. Dynamics of fluids in porous media. American Elsevier, New York. London and Amsterdam. Celia, M.A., Bachu, S., Nordbotten, J.M., Bandilla, K.W., 2015. Status of CO2 storage in deep saline aquifers with emphasis on modeling approaches and practical simulations – Celia – 2015 – Water Resources Research – Wiley Online Library. Water Resources Research 51. doi:10.1002/ 2015WR017609 Cerasi, P., Walle, L.E., 2016. Investigation of Potential Loss of Injectivity and Formation Integrity Due to Pressure Cycling. Energy Procedia, The 8th Trondheim Conference on CO2 Capture, Transport and Storage 86, 420–431. doi:10.1016/j.egypro.2016.01.043 Class, H., Ebigbo, A., Helmig, R., Dahle, H.K., Nordbotten, J.M., Celia, M.A., Audigane, P., Darcis, M., Ennis-King, J., Fan, Y., Flemisch, B., Gasda, S.E., Jin, M., Krug, S., Labregere, D., Naderi Beni, A., Pawar, R.J., Sbai, A., Thomas, S.G., Trenty, L., Wei, L., 2009. A benchmark study on problems related to CO2 storage in geologic formations?: Summary and discussion of the results (Original paper). Computational geosciences 13, 409–434. Class, H., Helmig, R., Bastian, P., 2002. Numerical simulation of non-isothermal multiphase multicomponent processes in porous media.: 1. An efficient solution technique. Advances in Water Resources 25, 533–550. doi:10.1016/S0309-1708(02)00014-3 Cook, P., Causebrook, R., Gale, J., Michel, K., Watson, M., 2014. What Have We Learned from Small-scale Injection Projects? Energy Procedia, 12th International Conference on Greenhouse Gas Control Technologies, GHGT-12 63, 6129–6140. doi:10.1016/j.egypro.2014.11.645 Cundall, P.A., Strack, O.D.L., 1979. A discrete numerical model for granular assemblies. Géotechnique 29, 47–65. doi:10.1680/geot.1979.29.1.47 Edlmann, K., Niemi, A., Bensabat, J., Haszeldine, R.S., McDermott, C.I., 2016. Mineralogical properties of the caprock and reservoir sandstone of the Heletz field scale experimental CO2 injection site, Israel; and their initial sensitivity to CO2 injection. International Journal of Greenhouse Gas Control. doi:10.1016/j.ijggc.2016.01.003 Elhami, E., Ask, M., Mattsson, H., 2016. Physicaland geomechanical properties of a drill core sample from 1.6 km depth at the Heletz site in Israel: Some implications for reservoir rock and CO2 storage. International Journal of Greenhouse Gas Control. doi:10.1016/j.ijggc.2016.01.006 Eshiet, K.I.-I., Sheng, Y., 2013. Carbon dioxide injection and associated hydraulic fracturing of reservoir formations. Environ Earth Sci 72, 1011–1024. doi:10.1007/s12665013-3018-3 Flemisch, B., Darcis, M., Erbertseder, K., Faigle, B., Lauser, A., Mosthaf, K., Müthing, S., Nuske, P., Tatomir, A., Wolff, M., Helmig, R., 2011. DuMux: DUNE for multi{phase, component, scale, physics, …} flow and transport in porous media. Advances in Water Resources 34, 1102–1112. doi:10.1016/j.advwatres.2011.03.007 Haimson, B., Lee, H., 2004. Borehole breakouts and compaction bands in two high-porosity sandstones. International Journal of Rock Mechanics and Mining Sciences 41, 287–301. doi:10.1016/j.ijrmms.2003.09.001 Helmig, R., 1997. Multiphase Flow and Transport Processes in the Subsurface: A Contribution to the Modeling of Hydrosystems, 1st ed. Springer. Hingerl, F.F., Yang, F., Pini, R., Xiao, X., Toney, M.F., Liu, Y., Benson, S.M., 2016. Characterization of heterogeneity in the Heletz sandstone from core to pore scale and quantification of its impact on multi-phase

229

flow. International Journal of Greenhouse Gas Control. doi:10.1016/j.ijggc.2015.12.037 Homand-Etienne, F., Hoxha, D., Shao, J.F., 1998. A continuum damage constitutive law for brittle rocks. Computers and Geotechnics 22, 135–151. doi:10.1016/ S0266-352X(98)00003-2 Hou, Z., Gou, Y., Taron, J., Gorke, U.J., Kolditz, O., 2012. Thermo-hydro-mechanical modeling of carbon dioxide injection for enhanced gas-recovery (CO2-EGR): a benchmarking study for code comparison. Environ Earth Sci 67, 549–561. doi:10.1007/s12665-012-1703-2 Huber, R., Helmig, R., 2000. Node-centered finite volume discretizations for the numerical simulation of multiphase flow in heterogeneous porous media. Computational Geosciences 4, 141–164. doi:10.1023/A:1011559916309 Hu, D.W., Zhou, H., Zhang, F., Shao, J.F., 2010. Evolution of poroelastic properties and permeability in damaged sandstone. International Journal of Rock Mechanics and Mining Sciences 47, 962–973. doi:10.1016/j.ijrmms.2010.06.007 IPCC, 2005. IPCC special report on carbon dioxide capture and storage. Metz, B., Davidson, O., de Coninck, H.C., Loos, M., Meyer, L.A. (Editors): Prepared by Working Group III of the Intergovernmental Panel on Climate Change. Cambridge University Press. Itasca, 2004. PFC user manual: Minneapolis: Itasca Consulting Group Inc. Levasseur, S., Collin, F., Charlier, R., Kondo, D., 2013. A micro–macro approach of permeability evolution in rocks excavation damaged zones. Computers and Geotechnics 49, 245–252. doi:10.1016/j.compgeo.2012.12.001 Lin, Q., Fakhimi, A., Haggerty, M., Labuz, J.F., 2009. Initiation of tensile and mixed-mode fracture in sandstone. International Journal of Rock Mechanics and Mining Sciences 46, 489–497. doi:10.1016/j.ijrmms.2008. 10.008 Liu, F., Lu, P., Zhu, C., Xiao, Y., 2011. Coupled reactive flow and transport modeling of CO2 sequestration in the Mt. Simon sandstone formation, Midwest U.S.A. International Journal of Greenhouse Gas Control 5, 294–307. doi:10.1016/j.ijggc.2010.08.008 Luo, Z., Bryant, S., 2014. Impacts of Injection Induced Fractures Propagation in CO2 Geological Sequestration – Is Fracturing Good or Bad for CO2 Sequestration. Energy Procedia, 12th International Conference on Greenhouse Gas Control Technologies, GHGT-12 63, 5394–5407. doi:10.1016/j.egypro.2014.11.570 Ma, J., 2015. Review of permeability evolution model for fractured porous media. Journal of Rock Mechanics and Geotechnical Engineering 7, 351–357. doi:10.1016/ j.jrmge.2014.12.003 Niemi, A., Bensabat, J., Shtivelman, V., Edlmann, K., Gouze, P., Luquot, L., Hingerl, F., Benson, S.M., Pezard, P.A., Rasmusson, K., Liang, T., Fagerlund, F., Gendler, M., Goldberg, I., Tatomir, A., Lange, T., Sauter, M., Freifeld, B., 2016. Heletz experimental site overview, characterization and data analysis for CO2 injection and geological storage. International Journal of Greenhouse Gas Control. doi:10.1016/j.ijggc.2015.12.030 Nordbotten, J.M., Flemisch, B., Gasda, S.E., Nilsen, H.M., Fan, Y., Pickup, G.E., Wiese, B., Celia, M.A., Dahle, H.K., Eigestad, G.T., Pruess, K., 2012. Uncertainties in practical simulation of CO2 storage. International Journal of Greenhouse Gas Control 9, 234–242. doi:10.1016/j.ijggc.2012.03.007 Potyondy, D.O., 2007. Simulating stress corrosion with a bonded-particle model for rock. International Journal

of Rock Mechanics and Mining Sciences 44, 677–691. doi:10.1016/j.ijrmms.2006.10.002 Potyondy, D.O., Cundall, P.A., 2004. A bonded-particle model for rock. International Journal of Rock Mechanics and Mining Sciences, Rock Mechanics Results from the Underground Research Laboratory, Canada 41, 1329– 1364. doi:10.1016/j.ijrmms.2004.09.011 Rathnaweera, T.D., Ranjith, P.G., Perera, M.S.A., 2016. Experimental investigation of geochemical and mineralogical effects of CO2 sequestration on flow characteristics of reservoir rock in deep saline aquifers. Sci Rep 6, 19362. doi:10.1038/srep19362 Rutqvist, J., Birkholzer, J.T., Tsang, C.-F., 2008. Coupled reservoir–geomechanical analysis of the potential for tensile and shear failure associated with CO2 injection in multilayered reservoir–caprock systems. International Journal of Rock Mechanics and Mining Sciences 45, 132–143. doi:10.1016/j.ijrmms.2007.04.006 Rutqvist, J., Tsang, C.-F., 2002. A study of caprock hydromechanical changes associated with CO2-injection into a brine formation. Env Geol 42, 296–305. doi:10.1007/s00254-001-0499-2 Rutqvist, J., Wu, Y.-S., Tsang, C.-F., Bodvarsson, G., 2002. A modeling approach for analysis of coupled multiphase fluid flow, heat transfer, and deformation in fractured porous rock. International Journal of Rock Mechanics and Mining Sciences, Numerical Methods in Rock Mechanics 39, 429–442. doi:10.1016/S1365-1609(02)00022-9 Shao, J.F., Zhou, H., Chau, K.T., 2005. Coupling between anisotropic damage and permeability variation in brittle rocks. Int. J. Numer. Anal. Meth. Geomech. 29, 1231– 1247. doi:10.1002/nag.457 Tatomir, A.B.A., Halisch, M., Duschl, F., Peche, A., Wiegand, B., Schaffer, M., Licha, T., Niemi, A., Bensabat, J., Sauter, M., 2016. An integrated core-based analysis for the characterization of flow, transport and mineralogical parameters of the Heletz pilot CO2 storage site reservoir. International Journal of Greenhouse Gas Control. doi:10.1016/j.ijggc.2016.01.030 Tatomir, A.B., Schaffer, M., Kissinger, A., Hommel, J., Nuske, P., Licha, T., Helmig, R., Sauter, M., 2015. Novel approach for modeling kinetic interface-sensitive (KIS) tracers with respect to time-dependent interfacial area change for the optimization of supercritical carbon dioxide injection into deep saline aquifers. International Journal of Greenhouse Gas Control 33, 145–153. doi:10.1016/j.ijggc.2014.11.020 Tatomir, A.B., Szymkiewicz, A., Class, H., Helmig, R., 2011. Modeling two phase flow in large scale fractured porous media with an extended multiple interacting continua method. CMES - Computer Modeling in Engineering and Sciences 77, 81–111. Wang, J.-A., Park, H.D., 2002. Fluid permeability of sedimentary rocks in a complete stress–strain process. Engineering Geology 63, 291–300. doi:10.1016/S00137952(01)00088-6 Yang, S.-Q., Huang, Y.-H., Jiao, Y.-Y., Zeng, W., Yu, Q.-L., 2015a. An experimental study on seepage behavior of sandstone material with different gas pressures. Acta Mech. Sin. 31, 837–844. doi:10.1007/s10409-015-0432-7 Yang, S.-Q., Huang, Y.-H., Ranjith, P.G., Jiao, Y.-Y., Ji, J., 2015b. Discrete element modeling on the crack evolution behavior of brittle sandstone containing three fissures under uniaxial compression.Acta Mech. Sin. 31, 871–889. doi:10.1007/s10409-015-0444-3

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Experimental study of proppant particle-particle interaction micromechanics during flow and transport in the fracture Ingrid Tomac & Lan Luo University of California, San Diego, San Diego, USA

ABSTRACT: This paper presents analysis experimental study of the proppant behavior during settling in a narrow smooth fracture. The objective of this study is to better understand particle interactions in a dense phase slurry. The study focuses on identifying and observing proppant agglomerations in narrow fracture like slot in the laboratory. The Geo Particle Image Velocimetry (GeoPIV) method was used for analyzing the movements of proppants during settling on a particle scale. The proppant settling velocity depends on the relationship between settlement, particle concentration and occurrence of particle agglomeration. In this study, the settling of single particles was compared to the Stokes’ Law, as well as agglomerated particles. Due to the very small ratio of the average proppant particle size and the slot aperture, deviations from the Stoke’s law increases significantly for the case when particles agglomerate. However, the power law relationship between the settling and Stokes’ law ratio and particle or agglomerate size was found to be valid. The significance of the visually observed agglomerates in the slurry and their larger settling velocities indicate that the proppant initial volumetric concentration might not be a good parameter for predicting the final slurry settling when significant agglomeration occurs.

1

INTRODUCTION

Selection of both proppants and fracturing fluid affects the process and results of hydraulic fracturing. Proppant is small granular material which keeps fractures open after fluid injection. A better understanding of micro-mechanics of proppant flow and transport into hydraulic fracture has impact on both industrial and environmental applications. Many researchers have studied proppant flow and transport in fractures, but relatively little work has been done on micro-mechanical understanding of particle-particle interactions effects on the overall behavior of proppant. Deng et al. (2014) studied the effects of proppant size,Young’s moduli and pressure levels on the size the crack aperture. Hammond (1995) did numerical analysis on the gravity-driven vertical motion of proppant in a hydraulic fracture. Hammond (1995) concluded that proppant settling processes significant contributed to the proppant rearrangement on the time scale and the rearrangement was also severe at lower proppant concentrations in homogeneous flows. Dontsov & Peirce (2014) analyzed the gravitational settling of spherical particles in steady flow. They introduced an approximate solution to reduce the complexity of problem of boundary conditions. Furthermore, Dontsov & Peirce (2015) extended to observe the tip screen- out effects for proppant transport in hydraulic fractures while the ratio of facture width to diameter of sand particle is small, the effect of the wall cannot be neglected.

Joseph (1994) focused on different particle interactions or particle-wall interactions between Newtonian and viscoelastic fluids. Joseph (1994) found the attraction behavior of two particles in viscoelastic fluid but the repulsion behavior in Newtonian fluid while the gap between the two particles is really small. Joseph (1994) also concluded that particles will be attracted by the wall in viscoelastic liquid but will be repelled in Newtonian liquid as they are close to a vertical wall at the beginning. Malhotra & Sharma (2012) conducted an experimental study to qualify the wall factor for shear thinning viscoelastic fluids. Malhotra & Sharma (2012) kept the ratio of particle diameter to wall spacing constant to find the retardation effect of confining walls due to the increasing of shearing thinning behavior of fluid. As for low proppant concentrations in flow through horizontal or near horizontal pipes, Stevenson et al. (2001) obtained a correlation for sand velocity while there is no sand movement by the intermittent flow. Patankar et al. (2002) conducted both numerical and experimental studies on the sediment flow and transport in pressure driven channel and obtained the power law correlations, which can be used as a basis for sediment transport models. Furthermore, to enhance the design process of hydraulic fracturing, the migration process and the volumetric concentration of proppant were also investigated by Zhao et al. (2008) by using numerical simulation. McClure et al. (2015, 2016) also contributed to the implementing proppant flow and transport in the numerical model to describe

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propagation of hydraulic fractures and opening and shear stimulation of natural fractures. They used nonlinear empirical equations are used to relate normal stress, fracture opening, and fracture sliding to fracture aperture and transmissivity. Eskin & Miller (2008) presented governing equations which are composed of boundary conditions and constitutive relations for the proppant flow and transport model which takes the micro-level particle dynamics into account. Eskin & Miller (2008) concluded that the slurry dynamics is governed by particle fluctuation in a high-shear-rate flow and that slurry flow in a fracture is characterized by non-uniform solids concentration across the fracture width. Roy et al. (2015) conducted both experimental and numerical analysis on the proppant transport. The particles were separated as transparent and opaque groups for easier tracking and finding out different displacement behavior. They concluded that the initially consolidated pack of soils at the top of the cell tend to serve as a source of particles and it will increase the duration and concentration of the settling particle phase. In addition, in experiments with the lowest particle concentration particles ultimately had lowest settling velocity. The objectives of the study presented in this paper is better understanding of the single particle and particle agglomeration settling rates in a 2 mm narrow slot. Particularly, the agglomeration processes and agglomerate settling is compared to a single particle settling rate. An experimental setup was built at a small scale in 20 × 40 cm slot between two parallel acrylic plates. The proppants were stored up at one end of the closed frame first and then the experiment was turned by 180◦ to let the proppants move downward. For recording the movements of proppants, a 60 frame/s camera was placed in front of the transparent side of the frame. In this paper, the GeoPIV method was used to transfer the digital figures to manageable data and particle displacement analysis. 2

EXPERIMENTAL SETUP

The components of the experiment for this test are the 2 mm wide slot made of acrylic plates, water and glycerol mixture, and 20/40 mesh sand as proppant. The 20 × 40 cm frame was used to hold two transparent plastic plates with 2 mm spacing between them, as

Figure 1. Experiments of narrow slot with proppants.

shown in Figure 1. The plastic was clear enough to see through in order to let the proppants be recorded by digital camera. One of the plastic plates which locates on the back side had dark blue background in order to enhance the color contrast. Two different tests with different viscosity fluids were conducted, one with 75% and other with 50% volumetric water-glycerol mixture.

3

EXPERIMENTAL METHODOLOGY AND ANALYSIS

The GeoPIV software was used for analysis of individual particle movements in time. The GeoPIV uses the principles of the Particle Image Velocimetry (PIV) method for obtaining the particle displacement data from couple of digital images. Images can be extracted from camera directly when the time interval is sufficient, otherwise it should be extracted from videos if time interval is too small. Adrian (1991) first introduced the particle-imaging technique measure the motion of small, marked regions of a fluid by observing the locations of the images of the markers at two or more times. Willert & Gharib (1991) further developed PIV method to make it easier and faster to handling of the whole series of operations. White (2001) used digital photography and PIV image processing to measure displacements of partially obscured soils in area of high strain gradient. White (2002) presented a new system for deformation measuring in geotechnical tests based on PIV method with improved the accuracy and precision, adding the displacement array. In this study, the digital image is first divided into a mesh as shown in Figure 2. The GeoPIV software is used for analyzing subsequent pictures of the frames obtained from the recorded video. Particle position comparisons between two subsequent frames permits obtaining displacement and particle velocities. Figure 3 shows displacement arrays of tracked particles in a predefined mesh in Figure 2. The GeoPIV method is chosen because it obtains the particle movement arrays and clearly shows the movement directions. The displacement data can be converted to velocity, knowing the speed of the camera recording, which is 60 frames per second.

Figure 2. Meshes of digital images.

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Figure 3. Displacement arrays of tracked meshes.

Figure 6. Average velocity in y direction.

Figure 4. Particle group settling at low concentrations.

Figure 7. Average velocity in x direction.

Figure 5. Movement vectors for particle at low concentrations.

4 ANALYSIS OF PARTICLES SETTLING 4.1

Particle settling 75% glycerol-water mixture

Particle settling was analyzed in a 75% glycerol water mixture, with the fluid dynamic viscosity is µ = 0.0355 Pa · s (Glycerine Producers’ Association, 1963). However, the movement of proppants is not stable during the entire test. Thus it is necessarily to find out the particle movements for the whole period of settlement to find out the stable period. The average velocities of the four patches are analyzed with locations shown in Figure 4. For analysis, the movement vectors are extracted for every time interval between two subsequent frames. Figure 5 shows one example of the movement vectors for the first time interval.

In Figures 6 and 7 the average values of particle settling velocities for each patch in Figure 4 are plotted against time. Figure 6 shows the vertical particle velocities in the direction y, and Figure 7 shows the horizontal particle velocities in the direction x. As shown in both Figure 6 and Figure 7, both of the velocities of group of particles in x direction and in y direction were larger at the beginning of the settling which indicates that the movement at the beginning is random and circular. After about 2 seconds, the velocity in x direction almost disappears, which means that the movement can be treated as settling and the steady settling velocity is established. At that time, the movement of sand particles can be treated as settlement. 4.1.1 Velocity of a single particle During the process, there are both single particle and agglomerated particles settling in the fluid. Figure 8 shows the analyzed single particle with different diameters. The settling velocity against size can be extracted during the stable settling period as shown in Figure 9.

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Figure 8. Different sizes of one single particle.

Figure 10. Different sizes of agglomerated particles.

Figure 9. Velocities of one single particle in y direction vs. particle size.

Figure 11. Velocities of agglomerated particles in y direction vs. particle size, compared with the Stoke’s law prediction of sphere settling in unbounded fluid.

The expression of Stokes’ law which can determine the terminal velocity of sphere falling in fluid is:

where Vt is the flow settling velocity (m/s), g is the gravitational acceleration (m/s2 ), ρp is the particle mass density (kg/m3 ), ρf is the fluid mass density (kg/m3 ) and µ is the fluid dynamic viscosity (Pa · s). The proppant is medium 20/40 mesh sand with approximate density of 2.65 kg/m3 . When the percentage of glycerol is 75 %, the density of fluid is 1198.45 kg/m3 and the dynamic viscosity is 0.0355 Pa · s. By using the Stokes’ law, the settling velocity of ideal spherical particle with respect of particle sizes was presented in Figure 9. It can be seen that the velocity extracted from the test is consistent with the results from Stokes’law, but with the increasing of the particle size, the velocity from tests did not change as much as the Stokes’ law would have predicted. If the wall effect is considered, one of the conclusion is that when the ratio of particle diameter with slot aperture is as small as 0.2 or smaller, the results in tests can be consistent with the prediction by Stokes’ law, otherwise the wall effect cannot be ignored. 4.1.2 Velocities of agglomerated particles In viscoelastic fluid, agglomerated groups of particles are observed during settling besides single particles. Figure 10 shows particle agglomerates with different approximate diameters. The diameter approximation is obtained for easier comparison of the agglomerate settling velocity with the Stoke’s law. However, the

agglomerates are observed with different shapes and irregular sizes in fluid. As shown in Figure 11, different sizes of agglomerated particles have different average velocities and with larger diameter, the velocity becomes higher. Comparing the data from the lab test with those from Stokes’ law, the difference becomes significant while the particle size increases. Similar like for the single particle, the wall effect plays a role in retarding the particle settling velocities.

4.2 Particle settling 50% glycerol-water mixture Conducting the same analysis as for the 75% glycerolwater solution, it is visible from the recorded video that the movements of proppants in 50% glycerol-water fluid are even faster than that in 75% glycerol-water fluid. As shown in Figures 12 and 13, the velocities in both x direction and y direction are large, after around 3 seconds the velocities becomes stable. Figure 14 shows particle vector arrays extracted from the beginning of the test at 6 different times. It is reasonable that at the very first part of the test, the horizontal movement cannot be ignored to treat it as settlement. Figure 15 shows the displacement vectors at the end part of the test. It shows that the vectors are approximate to be vertical. Thus after periods of time, the movement of sands can be treated as settlement. 4.2.1 Velocity of a single particle Similar with the settling in fluid with higer viscosity, there are still both single particle and agglomerated

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Figure 12. Average velocities in x direction.

Figure 15. Displacement vectors of particles.

Figure 13. Average velocities in y direction.

Figure 16. Different sizes of one single particle.

Figure 17. Velocities of one single particle in x direction vs. particle size.

Figure 14. Displacement vectors of particles.

particle exsisting. Figure 14 shows pictures for analized single particles with different sizes, taken from the camera. The velocity of x direction shown in Figure 17 is relatively small compared with the velocities of y direction in Figure 18, thus it is reasonable to treat the movement of particles as settlement. It is obvious that the velocity of settling varies with different sizes of particles.

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Figure 18. Velocities of one single particle in y direction vs. particle size.

Figure 20. Velocities of one agglomerated particles in y direction vs. particle size.

Figure 19. Different sizes of agglomerated particles.

The density of the 50% glycerol solution is 1126.30 kg/m3 and the dynamic viscosity is 0.006 Pa · s. Compared the test data with the prediction by Stokes’ law, it is also the same rule as in 75% glycerol. The prediction only works when the particle size is small compared to the slot size. 4.2.2 Velocities of agglomerated particles Although in the 50% glycerol-water solution the viscosity is lower than that in 75% glycerol-water solution, there are still agglomerated particles. Figure 19 shows three selected agglomerates of particles in fluid. The approximate diameter of the agglomerates was estimated and shown in Figure 19, in order to obtain the Stoke’s law settling velocity prediction. The settling velocity increases as the agglomerate size increases as shown in Figure 20. Comparing the test results with predictions from Stokes’law, it is obvious that with the increasing of the particle size, the difference between practical results and the predictions is also becoming larger, indicating the importance of the wall effect. Comparing Figure 20 with Figure 18, it shows that the general velocity is faster if the particles agglomerate with each other. Figure 21 summarizes the analyzed single and agglomerated particle settling velocities normalized with the Stoke’s law. The particle diameter and slot aperture ratio is plotted on the horizontal axis. It can be seen that the single particle settling velocities follow power law relationship in both glycerol solutions. However, the agglomerates settling velocities deviate more from the idealized power law relationship presented with the fit line in Figure 21. As the particle or agglomerate diameter increases, the wall effect becomes more significant and the ratio of the settling velocity and Stokes’ law decreases.

Figure 21. Ratio of settling velocity and Stokes’ law.

5

CONCLUSION

This paper shows analysis of experimental data of proppant settling in a narrow slot with smooth walls. The objective of the study was to better understand occurrence and settling of single and agglomerated particles in two glycerol-water solutions, with 75% and 50% volume concentrations. Settling velocities of particles were analyzed during predominantly vertical settling, in spite of the fact that observed motions were also circular and erratic. The interruption at the beginning of the movements of proppants could not be ingnored. The main issue was that the average velocities in x direction was almost the same as those in y direction, indicating that the proppant motion was not simple settling. After the proppants started to move as simple settling which means the velocities in x direction can be ignored, the effects of particle size compared to the slot diameter were found significant in both solutions. Consequently, it was observed that particle settling velocities are similar to the Stokes’law prediction only when the ratio of particle diameter and slot aperture is as small as 0.1–0.2. The observed settling velocity of agglomerated particles was larger than single particles, where the deviation from the Stokes’

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law was also bigger. However, it was possible to obtain a power-law relationship when plotting the ratio of both single particle or different sizes of agglomerates and Stokes’ law versus the particle size. The experimental results identify the occurrence of agglomerated particles and prove that the settling rates of agglomerated particles are larger than single particles. In the performend experiments, it was visually observed that the agglomerates form significant portion of the slurry. Future work will be focused on establishing the understanding of how agglomerated particles influence the average settling of the slurry and if the volumetric concentration of proppant, along with the fluid properties and the particle-fracture size ratio solely can or cannot predict the slurry settling. REFERENCES Adrian, R.J. 1991. Particle-imaging techniques for experimental fluid mechanics. Annual Reviews of Fluid Mechanics. 23: 26304. Deng, S., Li, H., Ma, G., Huang, H. & Li, X. 2014. Simulation of shale–proppant interaction in hydraulic fracturing by the discrete element method. International Journal of Rock Mechanics & Mining Sciences. 70: 219–228. Dontsov, E.V. & Peirce, A.P. 2014. Slurry flow, gravitational settling and a proppant transport model for hydraulic fractures. Journal of Fluid Mechanic. 760: 567–590. Dontsov, E.V. & Peirce, A.P. 2015. Proppant transport in hydraulic fracturing: Crack tip screen-out in KGD and P3D models. International Journal of Solids and Structures. 63: 206–218. Eskin, D. & Miller, M.J. 2008. A model of non-Newtonian slurry flow in a fracture. Powder Technology. 182: 313–322.

Hammond, P.S. 1995. Settling and slumping in a Newtonian slurry, and implications for proppant placement during hydraulic fracturing of gas wells. Chemical Engineering Science. 50: 3247–3260. Joseph, D.D. 1994. Aggregation and dispersion of spheres falling in viscoelastic liquids. Journal of Non-Newtonian Fluid Mech. 54: 45–86. Malhotra, S. & Sharma, M.M. 2012. Settling of spherical in unbounded and confined surfactant-based shear thinning viscoelastic fluids: An experimental study. Chemical Engineering Science. 84: 645–655. Patankar, N.A., Joseph, D.D., Wang, J., Barree, R.D., Conway, M. & Asadi, M. 2002. Power law correlations for sediment transport in pressure driven channel flows. International Journal of Multiphase Flow. 28: 1269–1292. Roy, P., Wyatt, L. & Stuart, D. 2015. Proppant transport at the fracture scale: simulation and experiment. American Rock Mechanics Association Conference. San Francisco, 28 June–1 July 2015. Stevenson, P., Thorpe, R.B., Kennedy, J.E. & McDermott, C. 2001. The transport of particles at low loading in near-horizontal pipes by intermittent flow. Chemical Engineering Science. 56: 2149–2159. White, D.J., Take, W.A., Bolton, M.D. & Munachen, S.E. 2002. A deformation measurement system for geotechnical testing based on digital imaging, close-range photogrammetry, and PIV image analysis. 15th International Conference on Soil Mechanics and Geotechnical Engineering. Pp: 539–542. Balkema, Rotterdam. White, D.J., Take, W.A. & Bolton, M.D. 2003. Soil deformation measurement using particle image velocimetry (PIV) and photogrammetry. Géotechnique. 53: 619–631. Willert, C.E. & Gharib, M. 1991. Digital particle image velocimetry. Experimental Fluids. 10: 181–193 Zhao, Z., Cui, B.,Yue,Y., Wang, L. & Wu,Y. 2008. Numerical simulation of horizontal migration of proppant. Journal of Hydrodynamics. 20: 74–80.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Modeling of discrete intersecting discontinuities in rock mass using XFEM/level set approach Kamal C. Das, Sandeep S. Sandha, Eduardo Rodrigues & U. Mello IBM Research

Ignacio Carol ETSECCPB (School of Civil Engineering), UPC (Technical University of Catalonia), Barcelona, Spain

Pablo E. Vargas, Nubia A. González, J.M. SeguraSerra & M.R. Lakshmikantha REPSOL CTR, Madrid, Spain

ABSTRACT: Modeling of discontinuities is of major importance to assess the geomechanical behavior of oil and gas reservoirs. Traditionally, discrete discontinuities have been introduced in the numerical analysis using continuum with modified constitutive laws (e.g. multi-laminate model (ML) or zero-thickness interface elements (IE’s)). More recently, there have been several attempts to use extended finite element method (XFEM). The development of an XFEM tool could lead to improved predictions for porosity/permeability changes in coupled geomechanical reservoirs. Multiple intersecting faults are often the case in complex Reservoir and has been explored less in the literature. In this work, we have presented a novel methodology based on XFEM to analyze the behavior of multiple intersecting faults. Detailed mathematical framework has been derived by using the concept of level-set and is implemented using distributed computing to solve complex geo-mechanical problems. For validation purpose, we analyze the different examples and comparison them with standard finite element method using zero-thickness IE’s (IE-FEM).

1

INTRODUCTION

Mechanical discontinuities (fractures, faults, cracks etc) affect the strength and deformability of the rock mass and may play a crucial role in the geomechanical behaviour of reservoirs. Depending on the procedure used to represent discontinuities, numerical techniques can be classified into two different categories in the finite element literature. In the first, discontinuities are represented in a smeared fashion, by using constitutive equation for the continuum which incorporates also the additional deformations due to opening/slip. In the second one, discontinuities are represented explicitly. This in turn may be done in various ways, the more classical one is via zero-thickness (or sometimes thin layer) elements inserted in-between element faces/edges while all nodal variables maintain the traditional meaning as regular displacements (Goodman et al., 1968; Gens et al., 1988). In a second, more recent approach, we do implicit representation of the discontinuities using level set functions. The discontinuity can cut the elements in arbitrary ways, which is captured using zero values of level set function. This approach gives the flexibility to define the discontinuities with complex geometries. An appropriate enrichment function is introduced near the discontinuity to capture the jump in the displacement field. Enrichment techniques

(for implicit representation methods), include: (a) Extended finite element (XFEM) method (Belytschko et al., 2001; Fries and Belytschko, 2010; Das, 2013) and, (b) Assumed enhanced strain (AES) method, which are reviewed and compared in (Borja, 2008; Das et al., 2015). ‘Enrichment’ signifies the additional problem specific functions for displacement approximation. For example, for rock faults modeling, ‘Heaviside function’is used to enrich nodes (Watanabe et al., 2012). In Geomechanics, multiple discontinuities often arise in rock medium. Many of these discontinuities are arbitrary and can be intersecting each other in the actual reservoir. To the authors’ knowledge, there are only a few studies that have applied the XFEM to multiple discrete geomechanical discontinuities in 2D (Watanabe et al., 2012; Deb et al., 2015) and 3D (Das et al., 2015). This paper develops the concept of XFEM by incorporating arbitrary multiple intersecting rock faults in 3D. A standard weak formulation method is used for developing the discrete equations. A finite element can be defined as regular, partially, singly or doubly enriched depending upon the number of discontinuities intersecting the element. Based on enrichment, we have derived the element stiffness matrices. The proposed procedure has been validated by solving different examples and their comparison with standard FEM using zero-thickness IE’s

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(Goodman, 1968). The examples show that the developed method produces results which are in strong agreement with reference solutions.

2.1

Discrete variational formulation

The finite element setting is briefly summarized here. First, the displacement field is obtained as the sum of a regular and discontinuous parts, such that, the variational formulation for the problem then reads: Find u ∈ V such that

Consider a finite element interserted by two faults Ŵ1d and Ŵ2d of
as shown in Figure 1(a) for 2D quadrilateral element. For representation, Ŵ1d and Ŵ2d are assumed to be made up of triangles or quadrilaterals in 2D, and tetrahedra or hexahedra in 3D. The total number of elements in the partition will be denoted by ne and the total number of vertices by np . The discrete form of problem (1) proceeds by considering a discrete space Vh ⊂ V for the displacement field. In this work, chosen displacement field belong to the following space

∀ v ∈ V , where V = [H 1 (
)]d is the space of vector square integrable functions whose gradients are also square integrable. To capture the discontinuous behavior of the displacement field in the presence of two intersecting discontinuities, Ŵ1d , Ŵ2d , we start by considering the following form for u.

The space Vdi (TŴi ) is not other than P1 (TŴi ) for the case d d of triangular/tetrahedral meshes or Q1 (TŴi ) for the d case of quadrangular/hexahedral meshes. In this for j mulation, we have: Vdi (AŴi ) = { j∈J bj Md }, where d J is the set of vertices shared by elements in AŴi

2

MATHEMATICAL AND NUMERICAL SETTING

where ur is continuous and u1d , u2d , and u12 d are discontinuous across Ŵ1d , Ŵ2d . For convenience we write the discontinuous part as follows

j

d

and Md are appropriate nodal enrichment functions. Before detailing the enrichment functions, we present the discrete variational formulation: Find (ur , u1d , u2d , u12 d ) ∈ Uh such that

where MŴi = [HŴi (x) − HŴi (xi )] and HŴi (x) is the d d d d Heavyside function (HŴi (x) = 1 if x ∈
+ , HŴi d d (x) = 0 if x ∈
− ), whose distributional gradient is ∇HŴi (x) = δŴi n, ˘ with δŴi the Dirac function and d

d

d

HŴi (xi ) is heaviside function value at xi . In (3), u˜ id d

is continuous across Ŵi and
ui (x)
= u˜ i (x), x ∈ Ŵi , d

d

d

d

where · denotes the jump of any quantity at Ŵid . Now, we choose as weighting function

whose distributional symmetric gradient is given by

As for the traction law tŴi , a constitutive behavd ior needs to be assumed for tŴi = DŴi · uid if uid · n ≤ 0 d d for ∀ i = 1,2,12. In the next subsection, we describe constitutive laws which are used in this work 2.2

Enrichment functions

The displacement field on the standard elements is written as

The variational formulation can be obtained by considering independent variations of vr , v1d , v2d and v12 d in the usual way. For the sake of brevity we ommit the details here and focus on the discrete variational problem.

Denoting by Njr , j = 1, . . . , d + 1 the standard P1 /Q1 basis functions for an element, we define as usual

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2.3 XFEM element equations For the sake of simplicity we restrict here the attention to the linear case. The element stiffness matrix is written as

where the index r refers to the standard degree of freedoms (DOFs) and the index d 1 , d 2 , and d 12 are the enriched DOFs for Ŵ1d , Ŵ2d and Ŵ12 d respectively. Computation of matrices Kα,β proceeds as usual:

Each matrix block reads Figure 1. A quadrilateral element (a) intersect by two faults, and (b)–(c) are sum of the nodal enrichment functions cut by the faults Ŵ1d and Ŵ2d respectively.

eki

k

where {e } is the canonical basis, = δik , i, k = 1, . . . , d. As for the elements cut by two faults (Figure 1) the displacement field is written as a linear combination of (8) plus a linear combination of n enrichment functions for fault-1, fault-2 and their interaction:

where npe is the number of nodes per element (4 for tetrahedra and 8 for hexahedra), α refers either to r (regular) or d 1 , d 2 , and d 12 (enrichment) functions, and the matrices Bi , i = 1, . . . , npe are computed as usual with the spatial derivatives of the shape functions. α,β Computation of surface integrals KS in Equation 14 explained in Das et al., 2015. 3

In this work, we adopted a shifted-type enrichment scheme in order to avoid additional computation in the partially enriched elements (Das et al., 2015) as follows:

IMPLEMENTATION DETAILS

In the follwing subsections, we have explained implementation of XFEM for 3D intersecting fault. 3.1 Fault representation using level set function

i.e., we use the product of the shifted Heavyside function and the standard shape functions. As an illustration, in Figure 1(b)–(c), we plot the sum of the enrichment functions for the case of a quadrilateral element in 2D. Similary, sum of the interaction enrichj ment function (MŴ12 (x)) is defined as the product of d

enrichment functions of fault (Ŵ1d ) and fault (Ŵ2d ) as shown in equation

The level set parameterization which is also adopted in some commercial software is used to represent the faults. The idea consists of defining a scalar function φj :
→ R, such that

where Nf is the number of faults presents in the domain. A practical choice is to define the level set function as a signed distance function to the fault linearly interpolated on TŴi . In this case the fault has d

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a simple planar representation on each element and conformity across interelement faces is in principle ensured (Dompierre et al., 1999). The level set representation adds flexibility and ellegance to the mathematical/computational formulation even in the case of static faults. For those faults that end inside the domain, an auxiliary level set function is introduced so as to define the boundary of Th . This is illustrated with an example in Figure 2. We consider the computational domain
= [0, 1]3 and two level set functions with a given hierarchy among them

Figure 2. Example to define a fault whose boundary lies inside the computational domain
by means of two different level sets.

The first level set has the highest hierarchy, while the second, that is used to define the boundary of the first one, has lowest hierarchy. The discrete interface Th and its boundary ∂Th are drawn in the right part of Figure 2. In order to represent multiple intersecting faults, different level-sets are used for each fault. Figure 3. Elemental/nodal enrichment scheme in 2D.

3.2 Classification of element and nodes Elements and nodes close to the fault need to be identified so as to perform the necessary local operations related to the enrichment terms computation define in integral from in Equation 14. This is done only once during the preprocessing stage of the computation and the enrichment type is stored. For example, a finite element intersected by single/double faults is considered as a “singly” or “doubly” enriched element. Similarly, an element sharing a node of an enriched element is termed as “partially” enriched. If an element is not in any of the above situations then it is termed as regular element. However, the enrichment functions are identically zero at the nodes (Figure 1-(b)-(c)). Therefore, we do not need to compute additional stiffness matrices for partially enriched elements. The enrichement scheme for multiple discontinuities is illustrateded in Figure 3 for quadrilateral elements in 2D by considing three faults in the domain. In Figure 3, faults are shown with red lines. Singly enriched elements are shown in yellow color which are enriched by any of the fault. Doubly enriched elements are shown in green color which are enriched by any two faults. It is noted that, regular and partially enriched elements are shown with white color. Similarly, regular, singly and doubly enriched nodes are shown with white, yellow and red color respectively. 3.3 Element subdivision Subdivision of elements that are cut by faults is a necessary step to redefine the quadrature rules in order to integrate the submatrices defined in Equation 14. There are several ways in which quadrilateral elements can be cut by faults as shown in Figure 3. The idea is to

Figure 4. Eight possible cases for the smallest vertex in the left bottom corner.

subdivide enriched element into a number of triangular subdivisions in 2D and tetrahedral subdivisions in 3D. In order to explain this more clearly, we will elaborate one of the most complex cases of hexahedron subdivision. Firstly, a hexahedron is subdivided into 5 or 6 tetrahedrons in several ways. An important question when dealing with hexahedral meshes is to ensure conformity of the fault across inter-element faces after subdivision. Since in our case the fault is represented by a level set function defined as nodal values, and the interface is reconstructed by linear interpolation of this level set along the element edges, care must be taken to ensure that subdivision of a given face shared by two hexahedrons is made through the same diagonal. This is done by making a remapping of the element incidencies so as to end up with the smallest incidence id at the left bottom corner as indicated in Figure 4 (Dompierre et al., 1999). There are 8 cases, depending on the smallest id of a indices in given element that are summarize in Table 1. Once the remapping is performed, subtetrahedra are defined. Then fault plane is introduced and

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Table 1. Remapping of incidences for an hexahedral element to avoid nonconformity across interelement faces.

each of these subtetrahedra’s are further subdivided as shown in Figure 5(a). Similar, steps are followed for doubly enriched elements in which we introdue the second fault after subdivision is done by the first fault. The different cases which might arise due to the introduction of second fault are shown in Figure 5(b)–(d). In this manner we introduce different faults through the element one after another, which reuse the subdivision algorithms recursively. The implemented subdivision scheme is general and can handle various intersecting/non-intersecting faults (X and T shape), and their all the different possible configurations in 3D.

3.4

Figure 5. Elemental subdivisions scheme of a hexahedron cut by (a) single fault, (b) two non-intersecting faults, (c) two intersecting faults (X-shaped) and (d) T-shaped faults.

a) Surface is not intersected by any faults: In this case, dirichelet boundary conditions are imposed similar as in the standard finite element method (FEM). b) Surface is intersected by single fault: In this case, dirichelet boundary conditions are imposed as reported author’s earlier work (Das et al., 2015). c) Surface is intersected by two faults: Dirichlet boundary conditions (DBC) are imposed on regular as well as additional (enriched by individual faults and their interaction) DOFs. Imposition of DBC on regular DOFs is idential to the case (a). Imposition of DBC on enriched DOFs for individual faults is identical to case (b). However, on interaction DOFs we might impose or leave free depending upon the physical meaning of the DBC. For example, if a surface has uniform DBC, then the solution of interaction DOF is constrained to have zero value. However, for non-uniform DBC, multiple sub cases arises which are individually handled.

Gauss point generation

Subdivision of singly and doubly enriched elements is performed in order to generate Gauss points which facilitates different integrations to be performed at element level. Each subdivision can have a number of Gauss points depending on the integration rule (linear/quadratic). For example, each of the subtetrahedra can either have a single Gauss point in the linear case or three Gauss points in the quadratic case. The Gauss point coordinates and their corrsponding weights are generated in physical space using the physical shape function of the subdivided tetrahedrals. Similar computations can also be performed in the master space and then corresponding transformation to physical space using isoparametric mapping. However, we have avoided the mapping step by performing direct computations in the physical space. The concept of Gauss quadrature scheme in the physical space using mapping has been explained in Das et al., 2015.

4 3.5

Boundary conditions on the fault

Neumann boundary conditions are imposed by computing enriched force vectors (Fid ∀i = 1, 2, 12) which are surface integrals defined in Equation 14. Details about the imposition of Dirichlet and Neumann boundary conditions on the enriched element has been reported in the authors’ earlier work (Das et al., 2015). Here, we have extended similar concept for doubly enriched element. Dirichlet boundary conditions applied on the surface of a doubly enriched element are handled depending upon number of faults intersecting the surface. There can be three different cases:

NUMERICAL EXAMPLES: RESULTS AND DISCUSSIONS

We have developed in-house XFEM code which runs over distributed environment and can handle very large models. The code is conceived to solve complex geomechanical problems with different loading conditions and in order to simulate the behavior of reservoir rock mass with faults. The first verification example considered is a column (Figure 6) with two orthogonal intersecting fault planes. Body is subjected to different displacement boundary conditions on the lateral surfaces (Table 2), in order to create different displacement mechanisms and evaluate the influence of faults

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Figure 7. (a) Horizontal and (b) vertical displacement profile for case-A.

Figure 6. Example definition and dimensions. Table 2. Boundary conditions on lateral surfaces. δx

δy

Surface

1

2

3

4

5

6

7

8

Case-A Case-B Case-C Case-D

0 0 0 0

0 δ δ δ

−δ −δ −δ −δ

−δ 0 0 0

0 0 0 0

0 δ 0 0.5δ

−δ −δ 0 −δ

−δ 0 0 0

Figure 8. (a) XFEM and (b) IE-FEM normal stress on fault planes for Case-A.

on stresses field. For further validation purpose, a second example considers arbitrary inclined faults in a column (Figure 15) with Triaxial 3D loading conditions. In both the examples, results are compared with existing analytical solutions and with standard FEM using zero-thickness IE’s code results. 4.1

Orthogonal fault planes

In this example, a three-dimensional column 10 m × 10 m × 20 m is cut by two orthogonal intersecting fault planes as shown in Figure 6. In this subsection, all test cases assume following mechanical properties of rock mass and faults stiffness parameters: Young modulus (E) 10 GPa, Poisson ratio (ν) is 0.0, fault normal and shear stiffness are kn = 10000 GPa/m, and kt1 = kt2 = 1 GPa/m respectively. In all the cases, lateral displacement profiles along with deformed bodies are shown with 10 times magnification. The normal stress on the fault plane is also plotted. Case-A: Uniform displacement of amount (δ) has been applied in the horizontal (on the faces 3-4) and vertical (on the faces 7-8) directions respectively, whereas no-slip boundary conditions are imposed on opposite faces in the horizontal (on the faces 1-2) as well in the vertical directions (on the faces 5-6). Therefore, uniform displacement profile as shown in Figure 7 is observed in both the directions (horizontal and vertical) as expected. In other words, constant normal jump has occurred on each face of fault planes and uniform normal stress of 50 MPa is observed as shown

Figure 9. (a) Horizontal and (b) vertical displacement profile for case-B.

Figure 10. (a) Horizontal and (b) vertical displacement profile for case-C.

in Figure 8(a). It noted that, computed normal stress is in good agreement with the IE-FEM results shown in Figure 8(b). Case-B: Rigid DBC are imposed on surfaces 1, 4, 5, 8 whereas uniform displacement (δ) is applied on surfaces 2, 3, 6, 7 in order to form direct shear state

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Figure 11. Displacement along the line ABC (Figure 9) (inset showing zoomed view of displacement jump on fault).

Figure 12. Normal stress on fault planes for Case-B and Case-C respectively.

of movement with respect to both the faults planes as specified in Table 2. Displacement profiles in the lateral directions are shown in Figure 9(a) and (b) which are evidence of successful creation of the direct shear kind of movement as imposed through DBC. In these conditions, each face of the fault plane has uniform normal displacement and hence, uniform normal stress (∼50 MPa) is observed as shown in Figure 12(a). Case-C: Simplified version of Case-B is considered here by restricting no-slip boundary in vertical direction. This case represents direct shear movement with respect to the fault plane x = 5. The computed displacement profiles are shown in Figure 10. Horizontal displacement along the line ABC which crosses the fault plane x = 5 at point B is shown in Figure 11 along with the theoretical result (Das, 2013). In the inset of the Figure 11 the jump is plotted in the horizontal displacement. Excellent agreement is observed with the theoretical solution (XFEM: 0.000049, analytical: 0.00005). Uniform normal stress of 50 MPa occurs on fault plane x = 5 whereas negligible normal stress occurs on fault plane y = 5 as shown in Figure 12(b). This is as expected due to the nature of applied DBC as uniform jump occurs in the normal direction of one fault plane (x = 5) whereas negligible jump occurs on the other. Case-D: This case is similar to the Case-B except for the applied DBC on surface 6. On Surface 6 displacement of 0.5 × δ is applied in the vertical direction which creates asymmetric movement w.r.t fault planes. Due to non-uniform DBC, interaction DOFs plays active role. Distribution of lateral displacement profiles are plotted in the Figure 13 which replicates the applied DBC mentioned in Table 2. It is noted that, the surface y = 0 experience 0.5 × δ amount of jump along

Figure 13. (a) Horizontal and (b) vertical displacement profile for case-D.

Figure 14. (a) XFEM and (b) IF-FEM normal stress on fault planes for Case-D.

the fault plane x = 5 whereas δ amount of jump has occurred in all other lateral surfaces. Due to different movement of lateral surfaces, normal stress distribution on the fault planes is non-uniform as shown in Figure 14(a). Normal stress of ∼25 MPa is observed on the face of fault plane located in the middle of surfaces 6 and 8 and all other faces on faults plane experienced uniform normal stress of ∼50 MPa. These results are in close agreement with the interface element results shown in Figure 14(b). 4.2 Column with inclined intersecting faults In this subsection, we studied column example with two intersecting faults plane at an angle β1 = 46.94◦ and β2 = −60◦ with horizontal axis as shown in Figure 15. A total of 2000 hexahedral elements are considered for this column example. The width, length and height of the column are 10 m × 10 m × 20 m respectively. Mechanical properties of rock mass and faults stiffness parameters are assumed as: Young modulus (E) 10 GPa, Poisson ratio (ν) is 0.25, fault normal stiffness (kn ) is 100 GPa/m and shear stiffness (kt1 = kt2 ) are 10 GPa/m respectively. No-slip boundary conditions are applied on the bottom surface and uniform pressure (σ1 ) 30 MPa is applied on top surface in zdirection. Confining pressure of (σ2 = σ3 ) 20 MPa is applied on lateral surfaces. Normal and shear stresses on inclined fault planes are shown in Figure 15 and 16 respectively. In static condition, analytical solution for stress on faults (Jaeger, 1960) is also applicable for multiple fault planes. The traction profile on inclined fault planes matches the theoretical results and has less than 1% error which is reported in Table 3.

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In XFEM, FE mesh suffices and the faults can arbitrarily cut the elements. This advantage of the XFEM has been leveraged for many applications in fracture mechanics, and in this paper we have shown that it is equally advantageous for modeling intersecting faults. Three-dimensional benchmark cases are presented to validate the accuracy of the approach, and the potential benefits in applications. The present study shows that interaction DOFs and their associated surface stiffness matrices plays a significant role in accurate modeling of cohesive faults via XFEM. REFERENCES

Figure 15. Normal stress on fault with two inclined faults (46.94 deg and 60 deg respectively).

Figure 16. Resultant shear stress on fault with two inclined faults (46.94 deg and 60 deg respectively). Table 3. Comparison of stresses on faults plane: theoretical solution vs. XFEM results. Inclination (β) (Deg)

46.54

−60

Theoretical Normal stress (MPa) Shear stress (MPa) XFEM Normal stress (MPa) Min Max Shear stress (MPa) Min Max Average Normal stress error (%) Shear stress

24.660 4.988 24.611 24.704 4.988 4.989 0.378 0.020

22.500 4.330 22.490 22.500 4.330 4.330 0.044 0.004

5

CONCLUSIONS

In this paper, we have introduced a novel formulation of XFEM which can handle arbitrary multiple intersecting cohesive faults in 3D. Due to different possible intersections of multiple faults within elements, several types of enrichments are defined and handled with “Shifted Heaviside function”. A generalized subdivision scheme has been described to capture the complex geometries of multiple faults using Level set function.

Belytschko, T., Moës, N., Usui, S., & Parimi, C. (2001). Arbitrary discontinuities in finite elements. International Journal for Numerical Methods in Engineering, 50(3), 993–1013. Borja, R. I. (2008). Assumed enhanced strain and the extended finite element methods: A unification of concepts. Computer Methods in Applied Mechanics and Engineering, 197(33), 2789–2803. Das, K.C. (2013), Enriched Finite Element Method and Applications to Reinforced Jointed Rock Mass, PhD Thesis, Indian Institute of Technology Kharagpur, India. Das, K. C.,Ausas, R. F., Serra, J. M. S., Narang,A., Rodrigues, E. R., Carol, I., & Mello, U. T. , EFEM vs. XFEM: A comparative study for modeling strong discontinuity in geomechanics. 13th International ISRM Congress, Montreal, May 10–13, 2015. Das, K.C., R. Ausas, I., Carol, E. Rodrigues, S.S. Sandha, P.E. Vargas, N. A. González, J. M. Segura, M.R. Lakshmikantha & U.T. Mello, “Discrete Modeling of Multiple Discontinuities in Rock Mass using XFEM.” 49th US Rock Mechanics/Geomechanics Symposium, American Rock Mechanics Association (ARMA), San Francisco, 28 Jun–1 July, 2015. Deb., D., Pramanik, R., Das, K.C., A generalized XFEM procedure for analyzing intersecting joints in rock masses with excavation. Engineering Computations 2015; 32(3): 806–833 Dompierre, J., Labbé, P., Vallet, M. G., & Camarero, R. (1999, October). How to Subdivide Pyramids, Prisms, and Hexahedra into Tetrahedra. In IMR (195–204). Jaeger, J.C. (1960). Shear fracture of anisotropic rocks, Geological Magazine 97: 65–72. Fries,T. P., & Belytschko,T. (2010).The extended/generalized finite element method: an overview of the method and its applications. International Journal for Numerical Methods in Engineering, 84(3), 253–304. Gens, A., Carol, I., and Alonso, E.E., 1988. An interface element formulation for the analysis of soil-reinforcement interaction. Computers and Geotechnics, 7:133–151. Goodman, R. E., Taylor, R. L., & Brekke, T. L. (1968). A model for the mechanics of jointed rock. Journal of Soil Mechanics & Foundations Div., 94 (SM3): 637–659, 1968. Watanabe, N., Wang, W., Taron, J., Gorke, U.J., Kolditz, O. (2012). Lower dimensional interface elements with local enrichment: application to coupled hydro-mechanical problems in discretely fractured porous media. International Journal for Numerical Methods in Engineering, 90(8), 1010–1034.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

DEM modeling of hydraulic fracturing in fractured shale formation: Effect of inherent anisotropy and induced anisotropy K. Duan & C.Y. Kwok State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, China Department of Civil Engineering, the University of Hong Kong, Hong Kong

ABSTRACT: Hydraulic fracturing has been widely used in the oil and gas industry to increase the recovery of hydrocarbons from low permeability formations. The hydraulic fracturing process can be very complex in naturally fractured reservoirs due to the anisotropy of material properties and existing of natural fractures. The aim of this study is to better understanding the mechanics of hydraulic fracturing in fractured reservoirs by performing numerical simulations in a two-dimensional discrete-element particle flow code (PFC2D). In the numerical model, rock matrix is represented by bonded-particle model (BPM). The intrinsic anisotropy is explicitly represented by imposing smooth-joint models. Any pre-existing horizontal or vertical natural joints are added by superimposing continuous smooth joint contacts onto the BPM to form a Synthetic Rock Mass (SRM) in which fluid injection and rock fracturing can be modeled in a fully coupled manner. The models are first calibrated to reproduce the mechanical behaviors of the isotropic and anisotropic rock in field. Effects of inherent anisotropy, joints orientation, and joint apertures on the hydraulic fracturing growth are investigated by conducting a series of comparative simulations. Results of these simulations show that the formation’s anisotropy plays an important role in the orientation of hydraulic fractures and it promotes horizontal fracture growth. Joints properties (orientation and aperture) could have a major impact on the behavior of rock mass during hydraulic fracturing operations.

1

INTRODUCTION

Hydraulic fracturing has been widely used in the industry of oil and gas production to increase the recovery of hydrocarbons from low permeability formations. The objective of hydraulic fracturing is to increase the permeability of the surrounding rock mass. In naturally fractured reservoirs, due to the heterogeneity and anisotropy of material properties and existing of naturally fractures, hydraulic fracturing processes are highly complex (Germanovich et al., 1997, Maxwell et al., 2002). Understanding the mechanics of propagation of hydraulic fracturing in fractured reservoirs is important to the design and operation of hydraulic fracturing. In the laboratory, a number of small-scale hydraulic fracturing experiments have been conducted on either natural rock samples (Matsunaga et al., 1993, Falls et al., 1992) or artificial materials (Groenenboom and van Dam, 2000, Zhou et al., 2008). Various interaction types (cross, dilate and arrest) between induced fractures with pre-fracture have been observed (Zhou et al., 2008), controlled by the differential horizontal stress, angle of approach and shear strength of prefracture. In the field, microsecimic monitoring was often used to provide information about the extent and

nature of hydraulic fracturing. Field studies (Britt et al., 1994, Rodgerson, 2000, Azeemuddin et al., 2002) conducted in naturally fractured formations reveal that the effects of natural fractures on hydraulic fracture propagation are enhanced fluid leak-off, premature screen-out, arrest of the fracture propagation, formation of multiple fractures, fracture offsets, and high net pressure. Various numerical approaches have been developed to estimate the development of hydraulic fractures, e.g., the Khristianovic-Geertsma-deKlerk (KGD) model (Geertsma and De Klerk, 1969), the Perkins-Kern-Nordgern (PKN) model (Perkins and Kern, 1961, Nordgren, 1972), pseudo-3D models (P3D)(Mack and Warpinski, 2000) and planar 3D models (PL3D) (Advani et al., 1990). However, all of these continuous methods are based on several assumptions such as isotropic and homogeneous material, linear elastic deformation, and assumption of linear elastic fracture mechanics (LEFM) for fracture growth. In fact, most rock mass formations in field are inhomogeneous with abundant bedding planes and natural fractures which will significantly affect the hydraulic fracturing trajectory (Damjanac et al., 2013). The discrete nature of Discrete Element Method (DEM) allows for explicitly modeling of out-of-plane

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Figure 1. Schematic diagram of smooth-joint contact (after Ivars et al., 2011).

fracture propagation, fracture branching and reorientation, and shearing of natural fractures ahead of the hydraulic fracture front. In this study, the propagation of hydraulic fracturing in fractured shale formation is investigated by DEM modeling. 2

NUMERICAL METHODOLOGIES

DEM simulations in this study are performed in twodimensional Particle Flow Code (PFC2D). In the numerical model, intact rock is represented as an assembly of rigid disks bonded at their contact points (Bonded Particle Model). Any pre-existing horizontal bedding and vertical joints are added by superimposing smooth joint contacts onto the BPM to form the synthetic rock mass (SRM). A brief introduction to the smooth joint model and the fluid flow model-ing algorithm in PFC2D are provided in this section. 2.1

and that these channels connect up small reservoirs that store fluid at some pressure, as illustrated in Figure 2. Each pipe is assumed to be a set of parallel plates with some aperture. The flow rate in a pipe is given by:

where µ is fluid viscosity, (P1 − P2 ) is the pressure difference between the two adjacent domains. L and a represent the length and aperture of pipe, respectively. Each pipe has an aperture with it which is defined by:

Smooth joint mode

The smooth-joint contact model was first proposed by Cundall et al. (1996) to represent fractures. The smooth-joint contact model allows particles at the joint surface experience relative slip on the specified joint surface rather than sliding along the particle surface as depicted in Figure 1. The behavior of joints can be modeled by assigning smooth-joint models to all contacts between particles that lie on opposite side of the joint. Most recently, the authors have adopted the individual smooth joint model to represent the intact anisotropic rock with great success (Duan and Kwok, 2015, Duan et al., 2015). In this study, the inherent anisotropy of intact rock is simulated by imposing individual smooth joint models onto the bonded particle model. The induced anisotropy originated from joints is modeled by assigning continuous smooth-joint models to all contacts that lie on the opposite sides of the joints. 2.2

Figure 2. PFC model used in the hydraulic fracture simulation. Reservoirs (black dots), flow paths (black lines) and bonds (while lines) in compacted bonded assembly of particles (after Itasca, 2010).

where a0 is the residual aperture when the two particles are just in contact, σ is the normal stress at the contact and σ0 is the normal force at which the aperture decrease to a0 /2 Each domain receives flows from the surrounding pipes: q. In one time step, t, the increase in fluid pressure P is given by:

where Kf is the fluid bulk modulus and Vd is the apparent volume of the domain. The change in fluid pressure will exerts forces on enclosing particles causing deformation and subsequent particle movement alters the contact forces, which affects the fluid flow by altering the channel aperture. 3

Fluid flow modelling in PFC

Fluid flow is simulated in PFC2D (Itasca, 2010) by assuming that each particle contact is a flow channel

SETUP OF NUMERICAL MODEL

The DEM model is constructed to simulate a 2D slice of the Haynesville shale reservoir approximately

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Table 1. Micromechanical parameters for the intact isotropic model. Particle parameters E0 kn /ks µ Rmax /Rmin ρ

Parallel bond parameters

28 GPa 2.5 0.5 1.66 3169 kg/m3

E¯ c k¯n /k¯s σ¯ c τ¯c λ¯

28 GPa 2.5 56 ± 11.2 MPa 56 ± 11.2 MPa 1

Table 2. Mechanical properties for the anisotropic model. Modelled formations Numerical model Property

H/V

UCS, MPa 0.96 Young’s 1.6 Modulus, GPa

Vert.

Reduction Horiz. H/V factor

74.19 70.89 20.98 33.53

0.96 2.5 1.60 3.0 Figure 3. Setup of numerical model for the simulation of hydraulic fracturing in anisotropic m odel with open joints in vertical direction.

3,739 m subsurface. A model size of 50 × 50 m with particle diameter of 0.5 m is used. Particles in this model do not represent single mineral grains in the rock. They are simply a way to discretize the medium. The micro parameters used in the DEM model are calibrated to match the mechanical responses of the intact rock under uniaxial compression test (uniaxial compression strength 73.53 MPa, Young’s modulus 32.9 GPa, and Poission’s ratio 0.27). The size of sample used for calibration is 10 × 20 m with particle diameter of 0.5 m. Corresponding micro-parameters obtained from calibration are illustrated in Table 1. The anisotropic model is generated by removing any sub-horizontal parallel bonds (those dipping less than 20◦ ) and replacing them with horizontal smooth joint contacts. The properties of the smooth joint contacts, except for dip angle which is zero in this case, are inherited from the propertied of the deleted parallel bond contact and the two contacting particles. Theses smooth joints used to represent the bedding planes have an initial aperture of 0.5 mm. The values of stiffness and bond strength for the smooth joints are lowered with different reduction factors by trial-and-error to achieve the desired anisotropy (ratio between properties obtained from horizontal and vertical direction, H/V listed in Table 2) Virtual uniaxial compression tests are carried out in vertical (perpendicular to beddings) and horizontal (parallel with beddings) direction of the anisotropic model in order to obtain the reduction factor for Young’s Modulus and parallel bond strength of bedding plane contacts. The obtained macroscopic mechanical properties and related reduction factors for the anisotropic model are shown in Table 2. After the anisotropic model is calibrated, natural fractures including vertical or horizontal joints are added to the assembly to create different models that mimic the individual lithology in field. In this study,

four different cases are considered: intact isotropic model, intact anisotropic model, anisotropic model with open vertical joints, and anisotropic model with open horizontal joints. Open vertical and horizontal joints are represented in the model by unbounded continuous smooth joints. The spacing between each joint is 2.5 m, which is 5 particles apart. Three different initial apertures, 0.1 mm, 0.7 mm and 1.0 mm, are assigned to the open joints to test the sensitivity of these parameters. As illustrated in Figure 3, the vertical in-situ stress Sv = 93 MPa and the horizontal maximum principal stress SH max = 80 MPa. The pore pressure is 75 MPa. These initial conditions are applied to the DEM models prior to fluid injection. In all simulations, the location of the injection point is at the bottom of the simulated domain, assuming the model is symmetric along the boundary. The outside model boundary is fixed and impermeable. The average operational parameters used in the simulation are: the injection fluid viscosity 0.001Pa.s; average injection rate 6.3588 m3 /min. Figure 3 illustrates an example of the anisotropic model with vertical joints before injection. 4

SIMULATION RESULTS

Results of the simulations are presented in this section. For each case, two sets of plots are included: (1) Injection pressure history; (2) The results of fluid injection showing induced fractures, pore pressures and smooth joint slip at the last stage of modeling 4.1

Hydraulic fracturing in isotropic model

In the isotropic rock mass without beddings and fractures, the hydraulically induced fracture propagates

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difference can be found by comparing the fluid pressure in Figure 5(b): in the case of anisotropic rock, the induced fracture shows less pressure differential along its length than the fracture in the isotropic rock which means that the average aperture in the former case is larger, leading to better hydraulic communication along the fracture. Boundary effects can be observed from the anisotropic model at the beginning of the injection process as shown in Figure 5 (b) (horizontal part of the fracture near the injection point). However, later in the injection process, the fracture propagates within the model, and become inclined as it is affected by both the in-situ stress and the inherent horizontal bedding. It is clear that in this case, vertical fracture growth is hindered by the modeled bedding. For this anisotropic model, the final fracture height achieves after fluid injection is less than 1/3 of the fracture height achieved in the case of isotropic model as shown in Figure 4(b) (with injection time being about 600 sec in both cases). 4.3

Figure 4. Simulation results of hydraulic fracturing in isotropic model. (a) Injection pressure history. (b) Induced cracks and induced pore pressure. The radii of the blue circles are proportional to the magnitude of induced fluid pressure.

nearly vertically upward as dictated only by the initial stress state (Figure 4(b)). The radii of the blue circles are proportional to the induced fluid pressure magnitude, thus, the pressure differential between the injection point and fracture tip is large. From the injection pressure history (Figure 4(a)), there is a steady increase of injection pressure after the initial breakdown. This can be explained by the fact that as the fracture propagates farther away from the injection point, more energy is necessary to propagate the crack. 4.2

Hydraulic fracturing in anisotropic model

Simulation results of hydraulic fracturing in anisotropic model are illustrated in Figure 5. The history of injection pressure (Figure 5(a)) reveals a similar behavior to the one found in the case of isotropic model (see Figure 4(a)): a breakdown peak, followed by a continuous linear pressure increase over time. In this case, however, the slope of such increase is higher; in other words, the amount of energy needed for sustaining fracture propagation is higher than that of isotropic rock. Another

Hydraulic fracturing in anisotropic model with open vertical joints

The presence of open vertical joints is modeled in this part and the effect of the changes in the aperture of such joints on fracture propagation is evaluated. Three different apertures are tested: 0.1 mm, 0.7 mm and 1.0 mm. The injection pressure histories for the three apertures are presented in Figure 6(a). The models run long enough to see fluid pressure breakthrough into the upper edge of the model. Very similar shape and magnitude in their pressure response can be observed between the cases with different apertures, which mean that comparable amounts of energy were necessary in each case in order to sustain fracture propagation. In this series of tests, and despite the fact that the simulation for aperture 0.1 mm fails (Figure 6(b)), modeling shows that the hydraulic fracture tends to propagate along the open vertical joints once they are contacted (see Figure 6(c) and (d)). The time it takes to reach upper boundary is, in general, proportional to the apertures assigned to the vertical joints. For 0.7 mm aperture, it takes 56.5 sec to reach the upper model boundary, while it takes 46.18 sec for the case with aperture equals to 1.0 mm. 4.4

Hydraulic fracturing in anisotropic model with open horizontal joints

The presence of open horizontal joints is modeled in this part. The effect of changes in the apertures on fracture propagation is evaluated. Same with that of vertical joints in Section 4.3, three magnitudes of joint aperture are tested: 0.1 mm, 0.7 mm and 1.0 mm. As illustrated in Figure 7(a), the injection pressure histories of the simulations for the three apertures show the same behavior at the beginning of the injection (about the first 130 sec of injection), probably showing rock failure between the injection point and the

250

Figure 5. Simulation results of hydraulic fracturing in anisotropic model. (a) Injection pressure history. (b) Induced cracks and induced pore pressure. The radii of the blue circles are proportional to the magnitude of induced fluid pressure.

first open horizontal bedding plane. But after such plane is contacted, the amount of energy needed for fracture propagation becomes a direct function of the assigned joint aperture. Larger joint aperture in general demands less injection pressure to sustain the same injection rate. The case with joints apertures equal to 0.1 and 0.7 mm are run for about 600 sec of injection time. However, for the case with the largest aperture, the simulation is stopped when the fracture extends horizontally to reach the model lateral edge, which occurs about 519 sec of injection. In all these tests, it is observed that the injected fluid tends to follow the horizontal joint planes once they are contacted; thus, severely impending fracture vertical growth. It appears, at least for these aperture magnitudes, that the effect of applied stress on fracture propagation is overcome by the presence of the horizontal open joints.

Figure 6. Simulation results of hydraulic fracturing in anisotropic formation with vertical open joints. (a) Injection pressure history. Induced cracks and induced pore pressure when the aperture of joints equals to (b) 0.1 mm, (c) 0.7 mm and (d) 1.0 mm. The radii of the blue circles are proportional to the induced fluid pressure.

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5

CONCLUSIONS

The effects of inherent anisotropy (beddings) and induced anisotropy (pre-existing joints) on the propagation of hydraulic fracturing in fractured shale formation are investigated in this study. In the DEM model, rock matrix is represented by bonded particle model. The existing of inherently anisotropy is represented by imposing individual smooth-joint contacts horizontally. Any pre-existing horizontal or vertical joints are added by superimposing continuous smooth joint contacts onto the sample. A series of comparative studies are conducted based on different combinations of open horizontal and vertical joints. Simulation results show that the formation’s anisotropy plays an important role in the orientation of hydraulic fractures and it promotes horizontal fracture growth. Likewise, the presence of open vertical fractures in the rock creates the distinct possibility for uncontrolled height growth. This is a function of vertical joints aperture: larger apertures allow for easier flow transmission within the joints and consequently, make fracture propagation in the vertical direction easier. The joints properties (orientation and aperture) could have a major impact on the behavior of rock mass during hydraulic fracturing operations. Thus, the need for a comprehensive characterization of the fractures in the rock is not only apparent but critical. The numerical method presented in this study has shown the flexibility to explicitly model the presence of such fractures and also the effects that they could have on the fracturing operation.

ACKNOWLEDGEMENT This study is supported by the National Natural Science Foundation of China (NSFC) (Grant no. 51428902) and Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Grant NO. Z014004. REFERENCES

Figure 7. Simulation results of hydraulic fracturing in anisotropic formation with open joints in horizontal direction. (a) Injection pressure history. Induced cracks and induced pore pressure when the aperture of joints equals to (b) 0.1 mm, (c) 0.7 mm and (d) 1.0 mm. The radii of the blue circles are proportional to the induced fluid pressure.

Advani, S., Lee, T. & Lee, J. 1990. Three-dimensional modeling of hydraulic fractures in layered media. I, Finite element formulations. Journal of energy resources technology, 112, 1–9. Azeemuddin, M., Ghori, S., Saner, S. & Khan, M. Injectioninduced hydraulic fracturing in a naturally fractured carbonate reservoir: a case study from Saudi Arabia. International Symposium and Exhibition on Formation Damage Control, 2002. Britt, L., Hager, C. & Thompson, J. Hydraulic fracturing in a naturally fractured reservoir. International Petroleum Conference and Exhibition of Mexico, 1994. Cundall, P., Potyondy, D. & Lee, C. Micromechanics-based models for fracture and breakout around the mine-by tunnel. Proceedings, International Conference on Deep Geological Disposal of Radioactive Waste, Winnipeg.

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Edited by JB Martino and CD Martin. Canadian Nuclear Society, Toronto, 1996. 113–122. Damjanac, B., Detournay, C., Cundall, P. A. & Varun 2013. Three-Dimensional Numerical Model of Hydraulic Fracturing in Fractured Rock Masses. Duan, K. & Kwok, C. Y. 2015. Discrete element modeling of anisotropic rock under Brazilian test conditions. International Journal of Rock Mechanics and Mining Sciences, 78, 46–56. Duan, K., Kwok, C. Y. & Pierce, M. 2015. Discrete element method modeling of inherently anisotropic rocks under uniaxial compression loading. International Journal for Numerical and Analytical Methods in Geomechanics n/a–n/a. Falls, S., Young, R., Carlson, S. & Chow, T. 1992. Ultrasonic tomography and acoustic emission in hydraulically fractured Lac du Bonnet grey granite. Journal of Geophysical Research: Solid Earth (1978–2012), 97, 6867–6884. Geertsma, J. & De Klerk, F. 1969. A rapid method of predicting width and extent of hydraulically induced fractures. Journal of Petroleum Technology, 21, 1571–1581. Germanovich, L. N., Astakhov, D. K., Mayerhofer, M. J., Shlyapobersky, J. & Ring, L. M. 1997. Hydraulic fracture with multiple segments I. Observations and model formulation. International Journal of Rock Mechanics and Mining Sciences, 34, 97.e1-97.e19. Groenenboom, J. & van Dam, D. B. 2000. Monitoring hydraulic fracture growth: Laboratory experiments. Geophysics, 65, 603–611.

Itasca 2010. PFC2D Particle Flow Code in 2 Dimensions. 4.0 ed. Minneapolis. Ivars D M, Pierce M E, Darcel C, et al. 2011. The synthetic rock mass approach for jointed rock mass modelling. International Journal of Rock Mechanics and Mining Sciences, 48, 219–244. Mack, M. G. & Warpinski, N. 2000. Mechanics of hydraulic fracturing. Reservoir Stimulation 6–1. Matsunaga, I., Kobayashi, H., Sasaki, S., et al Studying hydraulic fracturing mechanism by laboratory experiments with acoustic emission monitoring. International journal of rock mechanics and mining sciences & geomechanics abstracts, 1993. Pergamon, 909–912. Maxwell, S.C., Urbancic, T.I., Steinsberger, N., et al. Microseismic imaging of hydraulic fracture complexity in the Barnett shale. SPE Annual Technical Conference and Exhibition, 2002. Nordgren, R. 1972. Propagation of a vertical hydraulic fracture. Old SPE Journal, 12, 306–314. Perkins, T. & Kern, L. 1961. Widths of hydraulic fractures. Journal of Petroleum Technology, 13, 937–949. Rodgerson, J. Impact of natural fractures in hydraulic fracturing of tight gas sands. SPE Permian Basin Oil and Gas Recovery Conference, 2000. Zhou, J., Chen, M., Jin, Y. & Zhang, G.-Q. 2008. Analysis of fracture propagation behavior and fracture geometry using a tri-axial fracturing system in naturally fractured reservoirs. International Journal of Rock Mechanics and Mining Sciences, 45, 1143–1152.

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Comparison of discrete and equivalent continuum approaches to simulate the mechanical behavior of jointed rock masses N.A. González & P.E. Vargas REPSOL Technology Center, Mostoles, Madrid, Spain

I. Carol ETSECCPB (School of Civil Engineering), UPC (Technical University of Catalonia), Barcelona, Spain

K.C. Das, S.S. Sandha, E. Rodrigues & U. Mello IBM Research

J.M. Segura & M.R. Lakshmikantha REPSOL Technology Hub, The Woodlands, Houston, Texas, USA

ABSTRACT: Modeling of rock masses is of major importance to assess the Geomechanical behaviour of oil & gas reservoirs, especially for fractured tight reservoirs. The presence of discontinuities will significantly influence the general behavior of the rock masses, in particular introducing strength reduction, enhanced/reduction permeability, anisotropic behavior and a non-linear response. In the present study, Discrete and Equivalent continuum approaches have been used to simulate the mechanical behavior of jointed rock masses. Discrete approach uses the eXtended Finite Element Method (XFEM) and the Zero-thickness interface elements, while the Equivalent continuum approaches uses an elastic-viscoplastic constitutive model of the multilaminate type to represent the rock mass behavior. Advantages and limitations of each approach are identified and some hints for their practical use are given. Although the discrete approach is sometimes preferred for being based on a mature theory, the equivalent continuum analysis seems to be more often applicable for usual geomechanical analyses from engineering practice.

1

INTRODUCTION

Modeling of rock masses is of major importance to assess the Geomechanical behaviour of mining/civil tunnel, oil & gas reservoirs, etc. Rock masses are in most cases composed of an assembly of rock blocks separated by sets of discontinuities such as joints, bedding planes, fractures and faults that will condition the behavior of the system. Global behavior of the rock mass depends on the relative importance of both components (matrix and discontinuities), the number, nature and characteristics of discontinuities and the scale of the analysis. The presence of discontinuities will significantly influence the general behavior of the rock masses, in particular introducing strength reduction, enhanced/reduction permeability, anisotropic behavior and a non-linear response. In the Oil & Gas industry, an accurate description of the discontinuities behavior is a fundamental aspect during reservoir development and production including well planning, completion operations such as hydraulic fracturing interaction with pre-existing natural fractures/faults, and production/injection operations that might reduce/ maintain

the permeability depending on the deformation of the rock mass. Finite Element Method (FEM)-based models for the analysis of the mechanical behavior of rock masses can be split into two main groups: those that explicitly discretize each discontinuity using special joint/interface/enriched finite elements, and those based on a continuum-type representation of the medium. In the present study, discrete and equivalent continuum approaches based on FEM have been implemented in a Parallel in-house-Finite element code. Discrete representation of discontinuities can be done using both explicit and implicit ways. The more classical explicit representation is the interface element method (Goodman at al., 1968; Gens et al., 1998; Garolera et al., 2013) in which the discontinuity is explicitly discretized with special elements inserted in-between element faces/edges. In this case additional degrees of freedom are introduced at the nodes to capture the discontinuous behavior of the displacement. On the other hand, the eXtended Finite Element Method (XFEM) (i.g. Deb & Das, 2010) represents implicitly the discontinuities. In this method,

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the discontinuity is given as the zero set of a level set function which cuts the elements in principle in arbitrary ways. The main advantage is therefore the flexibility to define discontinuities with complex geometries. In this case, appropriate enrichment functions have to be introduced near the discontinuity so as to capture the jump in the displacement field. In the Equivalent Continuum approach, the original discontinuous medium is substituted by a continuum one with a constitutive model that incorporates the effect of the intact material and that of the discontinuities, in other words, it defines an equivalent material in which the properties of the joint system are smeared out over a unit volume of rock. An elasticviscoplastic constitutive model of the multilaminate type (Zienkiewicz and Pande, 1977; Caballero et al., 2009) has been implemented, it includes the possibility of incorporating up to three discontinuity planes with given orientation and elastic and strength parameters. Advantages and limitations of each approach are highlighted by means of the numerical simulation of a jointed rock block subject to different loading conditions. Two academic cases are presented, one simulating the intersection of two discontinuities in X-shape subjected to different boundary conditions on the lateral faces to capture the jump in displacement/stresses across and at the intersection discontinuities. Second example simulates a Triaxial 3D loading on the rock block with a single discontinuity at different inclinations. Comparisons with theoretical solution demonstrate the accuracy and robustness of the two numerical approaches. 2 2.1

GENERAL DESCRIPTION OF NUMERICAL APPROACHES Equivalent continuum approach: Multilaminate model

The model formulation is composed of two main parts: the continuum (matrix) and the discontinuities, each of them defined by elastic-visco-plastic models which are then combined additively in terms of strains. Model is based on Caballero et al. (2009), it exhibits up to four hyperbolic yield surfaces, one for the continuum with particular hardening/softening laws and flow rules, plus up to three more for limiting the stresses on the discontinuity planes. Specific details can be found in Caballero et al. (2009) and González, et al. (2015). Figure 1 illustrates the general formulation of the model. As usual in multilaminate formulations (e.g. Zienkiewicz et. al., 1977), the static constrain is assumed, i.e the local stresses on the plane (tσ = [σn , τs , τt ]) are simply assumed equal to the projection of the global stress tensor (σ) on that plane by using the stress transformation matrix (T ). Each set of discontinuities is characterized by:

Figure 1. General formulation of multilaminate model.

Dip direction (α) and dip angle (β) of the normal to the plane (i). • Loading function (F (i) ) of the hyperbolic type in terms of normal and shear stresses on the plane. •

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Elastic-perfectly plastic behavior defined by the (i) (i) elastic stiffnesses: normal (kn ) and tangential (kt ) and the strength properties: apparent cohesion (c(i) ) and friction angle (φ(i) ) for each set of discontinuities. • Non-associated flow rule (P (i) ) in order to avoid excessive dilatancy upon shear sliding of the discontinuity plane. νρ(i) • Viscoplastic strain (˙tcε ) following the classical Perzyna formulation in terms of rates, with particular viscoplastic parameters for each discontinuity set as the viscosity (η(i) ) and the Perzyna exponent (N (i) ). •

Matrix behavior is characterized by: Hyperbolic yield surface (F) expressed in terms of the three stress invariants (p′ , J , θ). • A non-associated flow rule (P) in order to reducing volumetric dilatancy for high compressive confinements.

•

Hardening and softening behavior controlled by the evolution of the strength parameters (c′ , φ′ and p′T ) in terms of the deviatoric plastic strain. • Viscoplastic strain (˙εvp Matrix ) following the classical Perzyna formulation in terms of rates, with viscoplastic parameters for the matrix as the viscosity (η) and the Perzyna exponent (N ). •

As usual in multilaminate formulations, the strain rate of the plane is converted to a work-equivalent strain tensor rate of the continuum, which turns out related by the transposed matrix used for projecting the stress tensor, T (i) . The overall strain tensor rate of the system is then obtained by simple addition of those of the continuum plus the discontinuity families. The same procedure is applied to determine the elastic strain of the system. The global strain tensor (ε) is then obtained as the sum of the contributions of the elastic and visco-plastic strains. A stress-prescribed scheme is used for the numerical integration of the Multilaminate model following the proposal by Caballero et al., (2009). The model can be applied to materials exhibiting rate-dependent behavior, but it can also be used to recover an inviscid elastoplasticity solution when stationary conditions are reached. 2.2

Figure 2. Sum of the nodal enrichment functions in a typical triangular element cut by the interface Ŵh .

As for the elements cut by the interface (K ∩ Ŵh  = ∅) the displacement field is written as a linear combination of (1) plus a linear combination of n enrichment functions,

There are various possibilities for the enrichment shape functions to capture the strong discontinuities. In this work the following nodal enrichment functions is applied for simplicity,

Discrete approach: XFEM

The eXtended Finite Element Method (XFEM) is an implicit representation method to capture discontinuities in the mesh using the concept of level-set without a discrete localization needed by explicit representation methods. The main advantage of XFEM is the flexibility to define discontinuities with complex geometries. In this case, appropriate enrichment functions have to be introduced near the discontinuity so as to capture the discontinuities in the displacement field. Mathematical details of the XFEM formulation employed in this work and their implementation are given in Das et al., (2015) and Das et al., (2016). The most important concept in XFEM method is ‘enrichment’ which means that the displacement approximation is enriched (incorporated) by additional problem-specific functions. For example, for strong discontinuities such as rock joint/faults modeling, ‘Heaviside function’ is used to enrich nodes whose support element is cut by the joint/fault (Sukumar et al., 2003) whereas the near tip asymptotic functions are used to model the crack tip singularity (Sukumar et al., 2003). 2.2.1 Enrichment functions The displacement field on the standard elements is written as,

Denoting by Nj , j = 1, . . . , d + 1 the standard basis functions or shape function for an element.

e.g., it uses the product of the shifted Heavyside function and the standard shape functions. As an illustration, in Figure 2 the sum of the three enrichment functions is plotted for the case of a triangular element in 2D. 2.2.2 Matrix form For the sake of simplicity the elementary matrix for the linear case is written as,

where the index r refers to the standard degrees of freedom and the index a to the enrichment ones. Computation of matrices Kαβ proceeds as usual:

Each matrix block reads,

where npe is the number of nodes per element (4 for tetrahedra and 8 for hexahedra), α refers either to r (regular) or d 1 , d 2 , and d 12 (enrichment) functions, and the matrices Bi , i = 1, . . . , npe are computed as usual with the spatial derivatives of the shape funcα,β tions. Computation of surface integrals KS in (5) are explained in detail in Das et al., (2015).

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Figure 5. FE Geometry of example 1: (a) Multilaminate material to represent intersecting faults; (b) Fault planes in IE-FEM. Figure 3. Zero thickness interface element inserted into the continuum FE mesh.

Figure 4. Stresses and relative displacements in zero-thickness interface element formulation (IE-FEM). Adapted from Garolera et al., (2013).

2.3

Discrete approach: Zero-thickness interface elements

3.1 Intersection of two faults: X-shape

The more classical discrete representation of discontinuities is the interface element method (Goodman at al., 1968; Gens et al., 1998) in which the discontinuity is explicitly discretized with special elements inserted in-between element faces/edges. Mathematical details of the interface element method (IE-FEM) employed in this work and their implementation is given in Garolera et al., (2013) and Garolera et al., (2014). Zero-thickness joint or interface elements are finite elements introduced between adjacent continuum elements, with the special feature that they have one less dimension than the standard continuum elements, that is, they are lines in 2D, or surfaces in 3D (Figure 3).The integration of these elements is done through a local orthogonal coordinate system defined on the interface line or surface. The interface constitutive behavior is formulated in terms of the jump of the main variable across the midplane of the interface, and the corresponding forcetype conjugate variable. In the standard mechanical problem, those variables are the normal and tangential components of the relative displacements, and their counterpart stress tractions (Figure 4).

3

code. In this section, two academic examples are presented in order to highlight advantages and drawbacks of both approaches. The first example simulates the intersection of two faults in X-shape subjected to different boundary conditions on the lateral faces to capture the jump in displacement/stresses across and at the intersection fault planes. Second example simulates a Triaxial 3D loading on a rock block with a single discontinuity at different inclinations. Comparisons with theoretical solution demonstrate the accuracy and robustness of the two numerical approaches.

NUMERICAL EXAMPLES: RESULTS AND DISCUSSIONS

Discrete approaches using XFEM and Zero thickness interface elements (IE-FEM) as well as the equivalent continuum approach using the multilaminate model have been implemented in an in-house-Finite element

In this example, a column with two orthogonal intersecting fault planes as shown in Figure 5 is studied. The width, length and height of the column are 10m × 10m × 20m respectively. Mechanical properties of rock mass and faults stiffness parameters are the following: Young modulus (E) is 10 GPa, Poisson ratio (ν) is 0.0, fault normal and shear stiffness are KN = 1e4 GPa/m, and KT 1 = KT 2 = 1e-6 GPa/m respectively. In order to create a jump in stresses and displacements through the faults, two different types of boundary conditions on the lateral surfaces have been prescribed as shown in Figure 6. Prescribed displacements are of δx = δy = 0.050005 m. These displacements create a direct shear state of movement with respect to the faults planes. In case-1 (Fig. 6a) a displacement of 0.5 × δy is applied in Y-direction on the bottom right face which creates an asymmetric movement with regards to the fault plane XZ, while in case-2 (Fig. 6b), asymmetric movements are created with respect to both fault planes (XZ and YZ). These configurations have been created in order to evaluate the ability of the numerical approaches to represent the correct kinematic of the blocks. 3.1.1 Results of Case-1 Distributions of lateral displacement profiles for the case-1 are plotted in the Figure 7 which replicates the applied boundary conditions showed in Figure 6a. A sudden jump in displacements field across the faults is well captured using discrete IE-FEM (Fig. 7a). Using multilaminate model a smoothing jump is observed (Fig. 7b), which is a function of the element size affected by the faults.

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Figure 6. Lateral boundary conditions of example 1. (a) Case-1, (b) Case-2.

Figure 8. Lateral displacements along the lines ABC and DEF (Figure 7) for case-1 (inset showing zoomed view of displacement jump on faults). (a) X-Displacement, (b) Y-Displacement.

Figure 7. Lateral displacements for case-1 (deformed mesh with 10x factor). (a) Discrete IE-FEM, (b) Multilaminate model.

Computed displacement profiles along the line ABC (in Figure 7) which crosses the fault plane YZ (x = 5) at point B and along the line DEF which crosses the fault plane XZ (y = 5) at point E, are shown in Figures 8a and 8b, respectively. In the inset of Figure 8 there is a zoomed view showing the theoretical jump in displacements. It is noted that IE-FEM shows a perfect agreement with theoretical solution (X-jump of 5E-06 m and Y-jump of 2.5E-06 m). Multilaminate model shows an average displacement through the fault planes which is accurate enough to capture the kinematic movement of the blocks. Due to asymmetric movement of lateral surfaces in the Y-direction, the resulting stresses in this direction are non-uniform as shown in Figure 9. IE-FEM predicts a stress jump of 25 MPa between the blocks separated by the fault YZ (Fig. 9a). Multilaminate model also can predict the correct stress distribution at the left and right blocks (Fig. 9b) with an average stress along the elements representing the fault YZ. Normal stress distribution on the fault planes is also non-uniform as shown in Figure 10. Results of discrete XFEM approach are included in Figure 10 (panel b); they are taken from Das et al. (2016). Normal stress of 25 MPa is observed on the face of fault plane XZ located at the right side of the intersecting faults, all other faces on faults plane experienced uniform normal stress of 50 MPa. It is noted that normal

Figure 9. YY-Stress variation for Case-1. (a) Discrete IE-FEM (b) Multilaminate model.

stress results using Multilaminate model (Fig. 10c) are in close agreement with the IE-FEM results (Fig. 10a), however, XFEM results show a little dispersion (Fig.10b). A revision of the numerical implementation of XFEM approach is therefore required. 3.1.2 Results of case-2 Lateral displacement profiles for the Case-2 are plotted in the Figure 11, which replicates the applied boundary conditions showed in Figure 6b. It is noted that multilaminate model (Fig. 11b) predicts a smooth displacement field through the fault planes and is able to capture the kinematic movement of the blocks which are asymmetric with respect to both fault planes. Computed displacement profiles along the line ABC and line DEF (in Figure 11), are shown in Figures 12a and 12b, respectively. Again, it is observed that IE-FEM shows a perfect agreement with the theoretical jump solution (X-jump of 1E-05 m and Y-jump of 5.0E-06 m) and Multilaminate model shows an average displacement through the fault planes. Resulting stresses in X and Y direction are nonuniform for this case. Figure 13 shows the stress variation in X direction. It is noted that results of both IE-FEM and Multilaminate model are in good agreement. An abrupt stress jump of 50 MPa between the

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Figure 10. Normal stress on fault planes for Case-1. (a) Discrete IE-FEM, (b) Discrete XFEM and (c) Multilaminate model.

Figure 12. Lateral displacements along the lines ABC and DEF (Figure 11) for Case-2 (inset showing zoomed view of displacement jump on faults). (a) X-Displacement, (b) Y-Displacement.

Figure 13. XX-Stress variation for Case-2. (a) Discrete IE-FEM (b) Multilaminate model.

Figure 11. Lateral displacements for Case-2 (deformed mesh with 10x factor). (a) Discrete IE-FEM (b) Multilaminate model.

blocks separated by the fault XZ is predicted by IEFEM (Fig. 13a), while multilaminate model predicts a smoothed jump of stress (Fig. 13b). Finally, normal stress distribution on the fault planes is shown in Figure 14. Using IE-FEM a jump of the normal stress of 50 MPa is observed on both fault planes at the intersection between them (Fig. 14a). Using multilaminate model an average normal stress is predicted at the elements located in the intersection between both fault planes allowing a transitional normal stress variation on the fault planes. 3.2

Strength of a fault in triaxial compression

In this example the numerical simulation of a triaxial test on a rock block with a single fault at different inclinations is performed. Figure 15 shows the finite element geometry using multilaminate and XFEM approaches. The fault plane is inclined at an angle β

Figure 14. Normal stress on fault planes for Case-2. (a) Discrete IE-FEM, (b) Multilaminate model.

with the minor principal stress direction (σ3 ), inclination is varied between 20◦ to 85◦ . A hexahedral mesh of 9537 nodes and 8192 elements is employed. The shear strength of the fault is defined by the Mohr Coulomb law in elastic perfectly plastic conditions. Fault properties are normal and tangential stiffness of KN = 1e6 MPa/m and, KT = 1e4 MPa/m, apparent cohesion cf = 1 MPa and friction angle φf = 15◦ . Intact rock is elastic with a Young’s modulus of 1e4 MPa and Poisson’s ratio of 0.3.

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This tendency could be an effect of the proximity of the elements representing the fault plane to the boundary where lateral confinement is applied. A different behavior could be expected if the fault inclination is pivoting at the center of the column.

4 Figure 15. FE Geometry: (a) Multilaminate material; (b) Fault planes with different angles in XFEM.

Figure 16. Comparison of Fault strength obtained from analytical solution and XFEM and multilaminate analyses.

The model is constrained at the bottom surface in normal direction; a uniform vertical displacement δz of –0.024 m is prescribed on the top of the model and a constant confinement of σ3 = 5MPa is applied on the lateral surfaces. The strength of the rock sample with fault is considered to be the minimum pressure that has caused the slip of the fault plane based on Mohr-Coulomb criterion (onset of yielding). It is defined as,

Results of the rock mass strength using XFEM and multilaminate model are plotted in Figure 16. Rock mass strengths obtained from both numerical approaches are in good agreement with those of the analytical solution given in equation (7). There is a threshold value of the fault inclination under which the plane is not activated (this threshold value is the friction angle), and, immediately after that threshold, strength decreases with inclination increases until reaches the minimum strength at an angle of,

Academic examples presented in previous section show that both discrete and equivalent continuum approaches are able to represent the behavior of discontinuities in a good approximation. Main advantage of continuum approach is their simplicity, it is adequate for most practical analyses, and it delivers reasonably accurate results at a lower cost than is needed by discrete models (see also Lhasa et al, 2012). However, the response is smeared and the results are strongly dependent on the element size particularly in case of softening materials. In addition, regular meshes are recommended to discretize the elements representing the discontinuity. Discrete approach is theoretically more suitable to capture the localized opening/closing/sliding and stress representation along discontinuity planes. XFEM method allows an implicit representation of the discontinuities without changing the background mesh discretizing the continuum rock; this is their main advantage over the IE-FEM. However, discrete approaches are usually more demanding in the sense that they need more specialized software. Additional degrees of freedom (IE-FEM) and enrichment nodes (XFEM) are introduced to capture the discontinuous behavior of the displacement field, increasing the number of elements and nodes of the problem. For Oil & Gas industry a combined approach is recommended. Discontinuities (faults and fractures) will be represented differently depending on the scale with respect to the grid size (see Figure 17). Discontinuities larger than the grid cell or element size (typically faults) will be represented using discrete approaches (XFEM or IE-FEM). Discontinuities smaller than the grid cell size (typically fractures) will be represented with the equivalent continuum approach (multilaminate model), which can represent several sets of fractures contained in a cell in a smeared way. This combined methodology has been also recommended in the literature (e.g. Nguyen and Selvadurai, 1995; Bai et al. 1995) to simulate coupled Hydro-Mechanical behavior of fractured reservoirs.

5 Computed errors predicted by XFEM and multilaminate solutions are showed in Table 1.An error lower than 2% was obtained using XFEM, while multilaminate model gives larger errors, which are in general lower than 6. In spite of the higher errors, multilaminate model can deliver reasonably accurate results. It is noted in Table 1 that using multilaminate model, the error increases as the fault inclination also increases.

DISCUSSION

CONCLUSIONS

The basic features of the equivalent continuum and discrete approaches have been presented and discussed using two examples analysis. The applicability and relative merits and limitations of both of the approaches for the simulation of jointed rocks were presented. It was observed that both the approaches are reasonably good in predicting the real response.

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Table 1. Results of theoretical solution against XFEM and Multilaminate analyses. Strength

Error

Inclination (β) (Deg)

Theoretical (MPa)

Multilaminate (MPa)

XFEM (MPa)

Multilaminate (%)

XFEM (%)

20 30 40 45 50 52.5 60 70 80 85

27.60 10.08 6.98 6.39 6.13 6.10 6.39 8.07 14.36 27.60

26.92 9.77 6.74 6.14 5.87 5.83 6.11 7.64 13.58 26.07

27.12 10.00 6.94 6.37 6.09 6.07 6.37 8.04 14.35 27.59

2.44 3.13 3.51 3.88 4.17 4.34 4.42 5.29 5.43 5.53

1.71 0.84 0.55 0.43 0.70 0.53 0.40 0.36 0.10 0.03

Figure 17. (a) Fault representation using XFEM. (b) Fracture set representation using Multilaminate model.

The selection of one approach or the other is largely influenced by the scale of the problem. For Oil & Gas industry, behavior of faults can be modeled using a discrete approach when the number of faults is relatively small and their scale is larger than the background numerical mesh discretizing the domain. On the other hand, equivalent continuum formulations are more fitted to reproduce the behavior of large numbers of fractures and/or fractures at a smaller scale than the numerical discretization. REFERENCES Bai, M., Roegiers, J.C., and D. Elsworth. (1995). Poromechanical response of fractured-porous rock masses. Journal of Petroleum Science and Engineering, 13, 155–168. Caballero, A. Garolera, D., Carol, I. and Gens, A. (2009). Viscoplastic multilaminate model for jointed rock with stress-prescribed using a stress-prescribed LEGI scheme. International Conference on Rock Joints and Jointed Rock Masses, Tucson, Arizona, USA, January 7–8, 2009. Bai, M., Roegiers, J.C., and D. Elsworth. 1995. Poromechanical response of fractured-porous rock masses. Journal of Petroleum Science and Engineering, 13, 155–168. Das, K., Ausas, R., Carol, I. Rodrigues, E. Sandha, S., Vargas, P.E., González, N.A., Segura-Serra, J.M., Lakshmikantha, M.R. and Mello, U. (2015). Discrete Modeling of Multiple Discontinuities in Rock Mass using XFEM. ARMA 15ID46. Das, K., Carol, I. Sandha, S., Vargas, P.E., Rodrigues, E., González, N.A., Segura-Serra, J.M., Lakshmikantha, M.R. and Mello, U. (2016). Modeling of discrete intersecting discontinuities in rock mass using XFEM/Level

set approach. 1st International Conference on Energy Geotechnics ICEGT 2016. Deb, D., and Das, KC. (2010) Extended finite element method for the analysis of discontinuities in rock masses. Geotechnical and Geological Engineering, 28, 643–659. Garolera, D., Aliguer, I., Segura, J.M., Carol, I., Lakshmikantha, M.R. and Alvarellos, J. (2013). “Zero-thickness interface elements with H-M coupling, formulation and applications in geomechanics”. In XII International Conference on Computational Plasticity. Fundamentals and Applications COMPLAS XII. E. Oñate, D.R.J. Owen, D. Peric and B. Suárez (Eds). (pp. 1372–1383). Garolera, D.,Aliguer, I., Carol, I., Segura, JM.,Lakshmikantha, M R. and Alvarellos, J. (2014). Hydro-mechanical coupling in zero-thickness interface elements, formulation and applications in geomechanics. Rock Engineering and Rock Mechanics: Structures in and on Rock Masses (EuroRock-2014). Gens, A., Carol, I., and Alonso, E.E., (1988). An interface element formulation for the analysis of soil-reinforcement interaction. Computers and Geotechnics, 7:133–151. González, N.A. et al. (2015). Multilaminate model for fractured rocks. Repsol-IBM internal report. Goodman, R. E., Taylor, R. L., & Brekke, T. L. (1968). A model for the mechanics of jointed rock. Journal of Soil Mechanics & Foundations Div., 94 (SM3): 637–659, 1968. Latha, G.M. & Garaga, A. (2012). Elasto-plastic analysis of jointed rocks using discrete continuum and equivalent continuum approaches. Int. J. Rock mechanics. 53(2012) 56–63. Nguyen,T.S., and Selvadurai, A.P.S. 1995. Coupled thermalmechanical-hydrological behaviour of sparsely fracture rock: implications for nuclear fuel waste disposal. Internaional Journal of Rock Mechanics and Mining Sciee & Geomechanics Abstracts, 32(5), 465–479. Perzyna, P. (1966). Fundamental problems in viscoplasticity. Advances in Applied Mechanics, 9(C):243–377, 1966. Sukumar, N., Chopp, D., Fatigue, L. (2003). Crack Propagation of Multiple Coplanar Cracks with the Coupled Extended Finite Element/Fast Marching Method. International Journal of Engineering Science, 41(8), 845–869. Zienkiewicz, O. C. & Pande, G. N. (1977). Time dependent multilaminate model of rocks: a numerical study of deformation and failure of rock masses. Int. J. Numer. Anal. Meth. Geomech. 1, No. 3, 219–247.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Thermal-hydraulic modelling a Canadian deep geological repository P. Abootalebi & G.A. Siemens GeoEngineering Centre at Queen’s-RMC, Kingston, ON, Canada

ABSTRACT: Within Canada there are more than 2.5 million bundles of spent nuclear fuel with another approximately 2 million bundles to be generated in the future. Canada, and every country around the world that has taken a decision on management of spent nuclear fuel, has decided to on long-term containment and isolation of the fuel within a deep geological repository. At depth, a deep geological repository consists of a network of placement rooms where the bundles will be located within containers and surrounded by an engineered barrier system. Amongst other design aspects, the engineered barriers will transfer the thermal energy from the spent nuclear fuel to the surrounding geosphere. The barriers will be placed in a complex thermal-hydraulicmechanical-chemical environment. The environment will include competing gradients of groundwater pressure driving moisture into the repository and thermal gradients driving moisture out. A current design criterion of the repository is to keep temperatures of the container surface below 100◦ C. Therefore the thermal properties of the engineered barriers are a critical component of the system in terms of its efficiency and size. Barrier materials will be at variable saturation levels and temperatures over their design life. An experimental program was initiated to measure the thermal properties of a number of potential barrier materials under variable moisture and temperature conditions. In this paper the experimental methodology for thermal property measurement is presented along with preliminary results. Preliminary modeling of the Canadian concept for the deep geological repository is also presented. The results show the impact of coupled thermal-hydraulic properties on the surface temperature of the container.

1

INTRODUCTION

Global energy needs continue to rise along with the need for carbon-reduced energy sources to limit climate change effects. One viable energy source is nuclear power, which generates power using a carbon neutral source. Half of the electricity requirements of the province of Ontario, Canada (pop. 13 million) are met with nuclear power. Along with the benefits of nuclear power comes the ethical and environmental responsibility to safely care for the waste products. Within Canada there are more than 2.5 million bundles of spent nuclear fuel with another approximately 2 million bundles to be generated in the future. Canada, and every country around the world that has come to the decision on a long-term solution for nuclear waste, has decided deep geological repository. A deep geological repository (Figure 1) consists of a network of placement rooms at depth where the bundles will be located within containers and surrounded by an engineered barrier system. Amongst other design aspects, the engineered barriers will transfer the thermal energy from the spent nuclear fuel to the surrounding geosphere. The environment would likely include competing gradients of groundwater pressure driving moisture into the repository and thermal gradients driving moisture away from the used fuel container. A design criterion of the repository system is to keep the external surface temperature

of the used fuel container below 100◦ C (Maak 2006). Therefore the thermal properties of the engineered barriers are a key attribute of the system. The engineered barriers, composed of bentonite-based materials, will be at variable saturation levels and temperatures over their design life. Thus, it is necessarily to determine thermal properties of engineered barriers over a wide range of moisture contents (degree of saturations) and variable temperatures (25◦ C and 80◦ C). In this paper, the experimental methodology for thermal property measurement is presented along with preliminary results. Preliminary modeling of the Canadian concept for the deep geological repository is also presented. The results show the impact of coupled thermal-hydraulic properties on the container surface temperature over the lifetime of the deep geologic repository.

2 2.1

METRIALS AND METHODS Material description

The engineered barriers that surround the used fuel containers within the Canadian concept include highly compacted bentonite, dense back fill and gap fill. The container is surrounded by highly compacted bentonite, which is compacted to a dry density of 1.7 Mg/m3 . Between adjacent containers is placed a

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Figure 2. Compaction results to achieve dry density ρd = 1.7 Mg/m3 in terms of compaction pressure and force versus degree of saturation and gravimetric water content.

Figure 1. a) Canadian concept of a deep geological repository and b) Mark II placement room (after NWMO 2015).

spacer block made of dense backfill, which is composed of a mixture of crushed granite, illite clay and bentonite, compacted to a dry density of 2.1 Mg/m3 . The gap between bedrock and buffer box will be filled with gap fill material which is 100% bentonite composed of pellet size grains in the matrix with a dry density of 1.41 Mg/m3 . The gap fill and highly compacted bentonite specimens described within this paper were prepared using National Standard Bentonite acquired from Bentonite Performance Minerals LLC. 2.2 Specimen preparation Specimens are prepared using a methodology from Man et al. (2011) to achieve reliable moisture content and density conditions. The constituent bentonite is placed within an oven at 105◦ C for at least 24 hours. The material is removed from the oven, sealed, and allowed to come to thermal equilibrium with the laboratory. The mass of bentonite required for specimen preparation is removed and placed in a mixing bowl. Water is added to the bentonite via misting with a spray bottle to achieve the target moisture content. Following mixing, the soil is placed within two sealed bags in a fridge for at least 48 hours for moisture equilibrium. Each weekday the soil is mixed inside the bag to encourage suitable moisture distribution. Static compaction was selected for preparing thermal conductivity specimens in order to achieve uniform density over the wide range of moisture contents. However, due to high target dry density value (ρd = 1.7 Mg/m3 ) required for highly compacted bentonite, low saturation specimens were compacted in a General Electric 30,000 lb (130 kN) electromatic universal testing machine. Typical results in terms of compaction pressure and force versus degree of saturation and gravimetric water content are plotted in

Figure 2. Compaction force is a maximum at low saturation and decreases asymptotically from 90 kN to over 40 kN at Sr = 100%. Two test configurations are implemented for measuring thermal properties depending on the moisture content of the specimen. For higher moisture contents a two-sided test is used (Figure 3a) and at lower moisture contents a one-sided test methodology is used (Figure 3b). In the two-sided test, two 50 mm-diameter by 20-mm pucks are compacted and the sensor is placed between. A nominal normal stress is applied through the frame to ensure good contact between the soil and the sensor. For one-sided tests a special mould (Figure 3b) was constructed to allow for thermal property measurement without removal from the compaction mould. In some materials at low saturations, excessive disturbance occurred during removal from the twosided compaction mould. In Figure 3b the one-sided test compaction mould is shown with a slot cut into the side to allow for placement of the thermal conductivity sensor on the top face of the compacted specimen. During compaction the slot is covered to avoid soil spillage and loss of confinement. Figure 3b shows the compacted specimen with the thermal conductivity sensor in place. A block of insulation is placed above the specimen to limit thermal energy loss and an applied normal stress encourages contact between the sensor and the specimen. This type of test is termed a ‘one-sided test’ as the thermal conductivity sensor is only in contact with the test specimen on one side. A third methodology is used for testing thermal properties at elevated temperature. The same compaction method was followed for both one-sided and two-sided tests, but in this case the sample is wrapped up with plastic wrap and placed in ziploc (Figure 3c). The bag is sealed around the wire with tuck tape. Then the sample holder along with the specimen is placed in oven at 80◦ C along with a bowl of water to keep relative humidity close 100% and reduce moisture gradients. Thermal property measurement is performed in a standard manner after specimen equilibrates with the elevated thermal environment. Following placement in the oven thermal property measurements are performed periodically until thermal equilibrium is confirmed. Figure 4 shows an example of temperature drift detected by sensor over the 80 second test

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Figure 4. An example of temperature drift detected by sensor during thermal property measurement at different times following placement in the oven.

where
Tavg (τ) is the average temperature increase of the specimen surface in contact with the sensor surface,
Ti is the constant temperature difference that develops over the thin insulation layer covering the sensor, R0 is the resistance of the disk prior to heating at time (t) = 0 and α is the temperature coefficient of resistivity which is well-known for nickel. The temperature difference across the sensor’s insulating layer,
Ti , becomes constant over a short period of time
t, which can be estimated as:

Figure 3. Test procedures for measuring thermal properties: a) one-sided test and b) two-sided test and c) 80◦ C test.

during 4 different time intervals. For this test, the time required to reach thermal equilibrium was more than three hours. After the specimen is taken out of the oven the final moisture content of the specimen is measured and used to plot the results.

2.3 Thermal properties test interpretation The device used in the thermal property testing is a Hot Disk Thermal Constants Analyzer (Hot Disk 2014). The sensor (visible in Figure 3b) consists of an electrical conducting pattern in the shape of a double spiral etched out of the thin sheet of nickel. The nickel plate is covered on both sides with thin sheets of insulation. The sensor applies a constant thermal energy to the specimen and measures the surface temperature change. The experimental methodology and interpretation framework allows for measurement of thermal conductivity, thermal diffusivity as well as volumetric heat capacity during a single test. The temperature increase of the sample surface is measured by monitoring the total resistance of the hot disk sensor:

where δ is the thickness of the sensor’s insulating layer and κj is the thermal diffusivity of the insulating layer. Generally
t is less than 10 seconds in the experiments. By introducing dimensionless integration variable termed the characteristic time ratio, τ:

where t is the time measured from the start of transient recording, κ is the thermal diffusivity of the specimen and α is radius of sensor, it is possible to solve the differential equation of heat conduction in an isotropic material. Then temperature increase can be determined as a function of characteristic time:

where P0 is power output of hot disk sensor, K is thermal conductivity of sample, m is a number of concentric rings of sensor and I0 is the first kind modified Bessel function and D(τ) is geometric function of sensor.

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Figure 5. Thermal conductivity measurements of highly compacted bentonite as a function of degree of saturation at 20◦ C and 80◦ C.

By knowing the relationship between t and τ,
T (τ) can be plotted as function of D(τ) which result in a straight line and from slope of that line which is P0 /(π3/2 aK), thermal conductivity of the sample can be calculated. However the proper value of τ is generally unknown since it is related to thermal diffusivity of the sample. Thus, the final straight line from which the thermal conductivity is calculated, is obtained through an iterative process. 3

EXPERIMENTAL RESULTS

Figure 6. Thermal conductivity measurements of gap fill as a function of degree of saturation at 20◦ C and 80◦ C.

and continued by considering a representative crosssection. Comsol version 5.2 was used as a finite element software to model heat transfer.This is the first time numerical simulations of the current Canadian concept for deep geologic repository have considered the effects of moisture on the thermal response. The critical design consideration is surface temperature of the container. These models with constant thermal properties are used to bound the maximum and minimum temperature of the container at critical times of its use. 4.1 Buffer box model in air

Selected thermal conductivity results are plotted in Figure 5 and Figure 6 for highly compacted bentonite and gap fill respectively. The blue circles are room temperature data and the red diamonds are the thermal conductivity results for tests performed at 80◦ C. Room temperature tests were performed at 11 degree of saturations in triplicate. The 80◦ C tests were performed at 4 degree of saturations again in triplicate. The test results show thermal conductivity increases with increasing saturation in both highly compacted bentonite and gap fill. Good repeatability is indicated in the results with R2 > 0.97 for both materials. Comparing the Sr = 0% and Sr = 100% results shows indicates a 2-3 fold increase in thermal conductivity from dry to saturated. In highly compacted bentonite the relationship is linear. A Botzmann sigmoidal curve was used to fit the gap fill results. The gap fill, composed of bentonite pellets is prone to non-uniform distributions of saturation given the high density of the pellets and the low overall density of the material. The effect of temperature is notable in the gap fill but is undetectable in the highly compacted bentonite. The gap fill results indicate a 15–30% increase in thermal conductivity over the 60◦ C increase in temperature. The highly compacted bentonite results show the same trend and quantitative measurements were recorded in the 20◦ C and 80◦ C tests. 4 THERMAL-HYDRAULIC MODEL The thermal-hydraulic modelling efforts began with modeling an isolated component of the repository

The finite element mesh of the first model is shown in Figure 7a. Due to the symmetric shape of container half of the container in buffer box was modelled. In the buffer box model, there are two materials, which are highly compacted bentonite block and the outer copper surface of the used fuel container. Perfect contact between the container surface and the highly compacted bentonite is assumed. The initial temperature is set to 20◦ C of both materials. Boundary conditions for the transient model include heat energy applied to the inside of the container and the temperature at the outside of the buffer box. The heat source was modeled as a decay function based on the number of bundles within the container. The outside of the buffer box was set to 20◦ C. Results are given in Figure 7 including the temperature regime of the model at maximum container surface temperature (Figure 7b) and temperature versus time (Figure 7c). To verify the model, thermal properties from a Nuclear Waste Management Organization report (NWMO 2015) were initially used. Figure 7b shows maximum container surface temperature after 20 days was equal to 37.1◦ C. Figure 7c compared these results for container surface temperature for 50 years with NWMO (2015) and showed that results are in agreement. After verification, thermal properties of highly compacted bentonite based on experimental data for four different degrees of saturation were applied to the buffer box and the container surface temperature was modelled for 30 days. These results bound the possible maximum and minimum temperatures for this initial configuration. Results for this model showing the impact of saturation on the container surface

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Figure 8. Container Surface Temperature over 30 daysbuffer box model in air.

Figure 7. Buffer box model in air: a) Mesh developed through half of container b) Maximum container surface temperature reached after 20 days equal to 73.1◦ C c) Container surface temperature over 50 years compared with report by NWMO (Gue 2015).

temperature are plotted in Figure 8. The direct relationship between saturation and thermal conductivity is reflected in the model results. In the model where thermal conductivity associated with Sr = 0% was applied the maximum surface temperature of the container was 36.6◦ C. When increased to Sr = 100% the maximum temperature decreased to 29.2◦ C. 4.2 Buffer box model in deep geological repository The geometry and dimensions of one tunnel within the repository in room placement concept is shown in Figure 1b including the locations of the used fuel container, highly compacted bentonite, dense back fill and gap fill within the insitu rock. Because of the symmetric shape of the part of the repository where the containers placed, a section of the repository based on Figure 1b was selected which represents a deep geological repository at sedimentary rock. The section is shown in Figure 9a as well as the dimensions and

boundary conditions. Figure 9b shows mesh developed for repository and bedrock around, again extremely fine mesh was used for buffer box and container compared to surrounding geosphere. The height and width of the section were assumed to be 1000 m and 10 m respectively. The placement room at a depth of 500 m consists of two one-quarters of the buffer box on top of each other with the quarter of spacer block is attached to the side of each buffer box. A thin layer of gap fill material with thickness of 0.1 m was applied to the perimeter of both buffer boxes. An initial temperature that varied across the depth of the model from 5◦ C to 21◦ C (Guo 2010) was assumed for whole system. Constant temperature equal to 5◦ C and 21◦ C were applied at the surface and bottom of model during the transient phase. These symmetric boundary conditions were applied to the four left vertical boundary surfaces. The heat source from the decaying waste was applied to the containers and container surface temperature observed over the time. At first, the thermal properties of highly compacted bentonite, dense back fill, gap fill and rock were assumed to be the same as a report (NWMO 2015) at 0% degree of saturation for verification. The model was run model for 100 years and the results are compared in Figure 9c. The blue triangles and the green circles previous data on simulations performed by Comsol and Ansys software respectively. The red line is data from the current model, which agrees with the previous simulations and verifies the results. For considering the effect of a static moisture regime on the surface temperature of the container, the experimental data for all materials, including highly compacted bentonite, dense backfill and gap fill at 100% were used as for the thermal properties. Models were run for 100 years assuming and plotted as the blue line in Figure 10. This serves as a theoretical lower bound on the modelled temperatures for the configuration. Figure 10 shows that if all the material are assumed saturated, the maximum container surface temperature is 86.9◦ C, which is reached after 52.5 years (blue line). Further models considered the effect of degree of saturation of the highly compacted bentonite on the container. Focus was placed on this material since highly compacted bentonite surrounds the initially hot container and there is more potential for this material to dry out from the thermal gradients compared

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Figure 10. Container Surface Temperature over 100 yearsbuffer box model in deep geological repository.

than 100◦ C, the characterization of thermal properties of engineered barriers as a function of moisture content and temperature is a key component of the modelling. More efficient thermal transfer to the geosphere could impact the overall design and have direct impacts to the cost of the repository. In this paper, thermal properties of engineered barriers were reported and then used in thermal models of the Canadian concept of the deep geologic repository. The results show the impact of saturation on the maximum container temperature and can be used to bound the potential thermal regimes. Future models will consider the coupled response of the repository to competing thermal and hydraulic gradients. ACKNOWLEDGMENT Figure 9. Deep geological repository model: a) geometry and boundary condition b) Mesh developed through repository c) Container surface temperature over 100 years compared with previous models.

to other materials. The results are plotted in Figure 10 illustrating the increase in container temperature associated with decreasing the degree of saturation of the highly compacted bentonite. The maximum surface temperature increases to 92.4˚ C after 40 years for Sr = 0% in the highly compacted bentonite (red line). Increasing the thermal properties of the highly compacted bentonite (associated with Sr = 20% and Sr = 60%) caused notable decrease in the maximum container temperature and also delayed the timing of the maximum temperature. Thus there are incremental benefits to configuring the repository to increase the saturation of the bentonite barriers in both maximum temperature and timing.

5

CONCLUSION

The current concept for Canada’s inventory of spent nuclear fuel is a deep geological repository. The engineered barriers within repository will be under a wide range of phenomena, one of which is transient thermal gradients as the energy from the used fuel containers is transfer to the surrounding geosphere. Given design criterion of repository for temperatures to remains less

The support of the Nuclear Waste Management Organization (NWMO) in this research is gratefully acknowledged. REFERENCES Guo, R. 2015. Thermal Modelling of a Mark II container, Nuclear Waste Management Organization technical Report NWMO-TR-2015-06. Guo, R. 2010. Coupled Thermal-Mechanical Modelling of a Deep Geological Repository using the Horizontal Tunnel Placement Method in Sedimentary Rock using CODE_BRIGHT. Nuclear Waste Management Organization Technical Report NWMO-TR-2010-22. He, Y., 2005. Rapid thermal conductivity measurement with a hot disk sensor: Part 1. Theoretical considerations. Thermochimica acta, 436(1), pp. 122–129. NWMO. 2015. Progress Through Collaboration – Annual Report. 173 pp. Hot Disk. 2014. Hot Disk Thermal Constants Analyser – Instruction Manual. 135 pp. Maak, P. 2006. Used fuel container requirements. Ontario Power Generation Preliminary Design Requirements. 06819-PDR-01110-10000 R02. Man, A., Martino, J.S., Kim, CS., Priyanto, D.G. 2011. Characterization and improving the thermal conductivity of engineered clay barriers for sealing a deep geological repository. Waste Management, Decommissioning and Environmental Restoration for Canada’s Nuclear Activities, Toronto, Canada.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Behaviour of kaolinite and bentonite at elevated and lowered temperatures T. Ring, C. Leo & S. Liyanapathirana Western Sydney University, Sydney, NSW, Australia

ABSTRACT: Engineering applications which experience a change in the natural ground temperature are increasing. There is an established a link between mechanical behaviour, temperature, and stress history. Some models/relationships have been postulated, however, very few studies have been undertaken to compare and contrast responses based on the distinctive soil compositions. This paper presents some initial investigations into consolidation rate and thermal volume change for kaolinite and bentonite, two distinctive clays. Step loading tests were performed at various overconsolidation ratios, at temperatures between 5 to 50◦ C. One temperature cycle from 20 to 50◦ C was used to ascertain volume change. A clear influence of temperature on behaviour of both clays was observed, though not always in the same way. Elevated temperatures resulted in an increase in consolidation rate under normal consolidation predictably for both clay materials, however, at high overconsolidation rates, the nature of response appears to be more complex.

1

INTRODUCTION

Engineering applications experiencing a variation of the natural thermal state are increasing. These include high-level nuclear waste disposal (Ojovan, 2010), energy geostructures (Knellwolf et al., 2011), landfills (Abuel-naga and Bouazza, 2013), as well as advanced construction techniques such as soil freezing. The potential for heated prefabricated vertical drains to increase consolidation rate is also being explored (Pothiraksanon et al., 2010b). Design rules and guidelines related to thermal considerations are still limited (Laloui and Di Donna, 2011). This is a function of the complex nature of the thermo-poromechanical behaviour. Over the years, research has been expanding the understanding; however, it is still evolving. There have been a number of experimental works investigating the volume change produced by an alteration of the thermal state (Abuel-Naga et al., 2007, Sultan et al., 2002, Burghignoli et al., 2000, Cekerevac and Laloui, 2004, Cui and Tang, 2013). While the specifics of each test program varied, two general conclusions were drawn. When the effective pressure remains constant and the sample is under drained conditions; (1) normally consolidated clays contract when heated and the magnitude of contraction decreases with an increase in OCR (over consolidation ratio) up to a point where it can become dilated, (2) the volume change induced by heating is largely non-reversible (plastic). Some laboratory (Delage et al., 2000, Di Donna and Laloui, 2015) along with one field study (Pothiraksanon et al., 2010a), have investigated the clay consolidation rate under elevated temperatures. While the soil

types and procedures varied, they found consolidation rate increased with an increase in temperature. This work presents some initial findings from a planned comprehensive thermo-poromechanical investigation on the influence of mineral structure as it relates to the poromechanical behaviour under various thermal paths. Consolidation rates and volume change are the focus of this preliminary stage using a Rowe cell and a temperature of 5 to 50◦ C. One expansive and one non-expansive clay were chosen for this research to investigate the mineralogy/structural differences possibly contributing to different characteristics.

2 2.1

MATERIAL, EQUIPMENT AND EXPERIMENTAL PROCEDURE Material

Two different clays were used in this study. They were commercially available under the brand names ‘Clay Ceram’ and ‘Trugel 100’. X-ray diffraction was used to identify the major structures; they were kaolinite and quartz, and beidellite and quartz. Beidellite is colloquially known as bentonite. Due to kaolinite’s atomic and sheet structure (1:1 tetrahedral to octahedral), it has a very low cation exchange capacity (10–100 mmol/kg), specific surface area (5–20 m2 /g), and c-spacing (0.72 nm). This leads to a non-expansive and stable nature. Conversely, bentonite has a 2:1 sheet structure (tetrahedral to octahedral), this results in a high; cation exchange capacity (800–1200 mmol/kg), specific surface area (600–800 m2 /g), and c-spacing (1.2-2.1 nm) (Strawn,

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2015). These result in both its value as an engineering product and as a problematic soil with expansive behaviour. The kaolinite and bentonite plastic limits are: 30.0 and 46.4%, and the liquid limits are: 45.5 and 453%. 2.2

Equipment

A 75.5 mm Rowe cell was used for all consolidation tests. To control the test temperature the cell was fully immersed in a temperature controlled water bath. Temperature was logged separately using a digital temperature probe with a resolution of 0.1◦ C. Cell and back pressures were regulated by 3 MPa automatic pressure-volume controllers. The vertical displacement was monitored by a 25 mm linear variable displacement transducer. The data acquisition system was setup to provide a displacement resolution of 0.001 mm, although a drift of ±0.002 mm was common. When applicable, a 1 MPa pore pressure transducer was employed. Clisp Studio software was used to automate the controllers and log the data. Calibrations were performed on all instruments at ambient temperatures prior to testing. Calibrations of the complete system were also run at elevated and lowered temperatures to assess the impact on the equipment and instrumentation. As expected the temperature did affect some readings. Given the small magnitude (0.0013 mm/◦ C), it was only necessary to correct the vertical displacement for the volume change tests. 2.3

Experimental procedure

2.3.1 Consolidation rate tests and specimens To create the test specimens a slurry was mixed using dried powder and de-ionized water to a moisture content of 2x the liquid limit for kaolinite and 1.5x for bentonite. The slurry was then deaired under vacuum and agitated to remove air bubbles. From this point, two separate methods were used to prepare samples to the desired initial overconsolidation ratio. The kaolinite slurry was placed in a mold and under a pressure of 200 kPa. The sample was then trimmed to approximately 23 mm and placed in the Rowe cell. The bentonite slurry was placed directly into the Rowe cell. The cell was placed in the water bath set to 20◦ C. Placing the bentonite directly into the Rowe cell without prior consolidation was desirable for two reasons; it allowed for easier sample preparation (the low permeability made preconsolidation using a mold difficult and time consuming), the resulting final height (≈6–7 mm) rendered manageable test durations. Originally, kaolinite was prepared in the same manner, however at high overconsolidation ratios a longer consolidation time and magnitude was desired which was the impetus for the change. Once in the Rowe cell an effective pressure of 400 kPa was applied until primary consolidation was complete as observed by settlement. The effective pressure was then reduced to 50 kPa and allowed to

rebound creating an overconsolidation ratio (OCR) of 8, with the temperature set to the desired level (5, 20, 35, or 50◦ C). After temperature stabilization, the effective pressure was applied in steps at: 100, 200, 400, 800, and 1200 kPa. Constant temperature was maintained for the duration of the consolidation rate tests. Due to the low permeability of the bentonite, two-way drainage was used during testing. One-way drainage was used for kaolinite. Duration of each pressure step was consistent for each material; 1 hour for kaolinite and 24 hours for bentonite. Upon completion of the test, the effective pressure was reduced to 10 kPa and temperature set to 20◦ C, the samples removed, final heights and moisture content recorded. 2.3.2 Volume change test and specimens Separate specimens were created for investigating the volume change under thermal loading. Both kaolinite and bentonite were prepared in the same manner, similar to that of the bentonite consolidation rate samples. Firstly, a slurry was created then placed directly into the Rowe cell and consolidating to an OCR = 8. Two-way drainage was used for sample preparation and testing. Samples were prepared at a constant temperature of 20◦ C and pressures applied to achieve the desired overconsolidation ratio. Once primary settlement was complete the temperature was increased to 35 then to 50◦ C, and lowered back to 20◦ C before the next pressure step. At both temperature extremes the displacement was monitored and once stabilized the test was continued. A majority of the volume change occurred during the heating and cooling process. 3

MAIN RESULTS AND DISCUSSION

3.1 Consolidation rate The consolidation rate of each loading step was calculated using the log time method. These results for each temperature are presented in Figures 1 and 2. A trend line was used to determine the average percentage change per one degree temperature change and is presented in Table 1.All load histories produce an increase in the consolidation rate with the notable exception of the largest OCR for bentonite which exhibited the opposite response. The normally consolidated (NC) stages show a similar response for both materials with the consolidation rate increasing 1.1–1.9%/◦ C. When overconsolidated, the relation experiences greater variability, with an opposite behaviour for bentonite with an OCR = 4. This reversal in trend is not consistent with the kaolinite along with other findings that the settlement rate increases with temperature, although direct comparisons were not established. Therefore, this may reflect the true nature of highly overconsolidated bentonite or could be a function of other factors. Care was taken to reduce the impact of factors such as time and

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is the opposite to that of the other overconsolidated stages. A lesser understood factor is the molecular interaction between clay platelets and water molecules. This likely will vary based on the atomic structure but the direction of change should remain consistent throughout the tested temperature range within the context of each material. The physical expansion of the constituent soil parts may also contribute. These factors can act in a competing fashion with the overall behaviour dictated by the particulars of each case; material type, stress history, and temperature. Similarly, volume change with temperature is known to have a relation to stress history, which impacts the magnitude and direction of change (expansion or contraction). Changes in the compression index (Cc ) and recompression index (Cr ) were also investigated. No significant changes in Cc or Cr were noted for either material.

Figure 1. Kaolonite consolidation rate with temperature.

3.2 Volume change

Figure 2. Bentonite consolidation rate with temperature. Table 1. Consolidation average rate change in percent per degree increase. Loading

Kaolinite

Bentonite

OCR = 4 OCR = 2 OCR = 1 NC 800 NC 1200

1.7 4.2 2.4 1.1 1.1

–2.7 2.5 1.9 1.1 1.9

loading rates but variations in sample heights can complicate duplicating exact initial starting conditions. Additional tests are required to validate this response. Also, new preparation methods and test parameters will be considered to reduce these concerns. One clear contributor to the consolidation rate is the viscosity of the pore medium, in this case water. Values are readily available in engineering tables, with the viscosity increasing with temperature. Therefore, if this were the only factor, the change in rate of each pressure step should be the same for any material at the same void ratio. Each bentonite stage and kaolinite overconsolidated stages had similar void ratios as the settlement caused from each pressure step was small. However, the increase in consolidation rate is different amongst OCR = 1, 2, and 4 for both materials. Furthermore, the behaviour of bentonite at OCR = 4

Separate specimens were tested to assess the volume change characteristics of both kaolinite and bentonite at multiple overconsolidation ratios; 8, 4, 2, and 1. Samples were prepared at a constant temperature of 20◦ C and pressures applied to achieve the desired overconsolidation ratio. Once primary settlement was complete, the temperature was increased to 50◦ C then lowered back to 20◦ C before the next pressure step. A majority of the volume change occurred during the heating and cooling process. The temperature was left at the end of the range until the strain stabilized. During heating kaolinite experienced a reduction in volume for both normally consolidated stages (NC800 and OCR = 1) and the previous two stages (OCR = 2 and 4). The initial stage (OCR = 8) experienced minimal volume change. During cooling, the decrease in volume was plastic for all stages except OCR = 8 where it experienced swelling during cooling. Bentonite stages experienced similar behaviour during heating with little change for OCR = 1 and 4. Consolidation of 0.2% and 0.3% for OCR = 2 and NC800 respectively. The OCR = 8 stage experienced swelling during heating to 0.7% strain and further swelling during cooling for a total strain of 1.2%. Under cooling the remaining stages experienced a contraction of 0.6–0.9%. As observed in Figure 3 and Figure 4, both materials had a trend related to the pressure history. The higher the overconsolidation ratio the lower the vertical contraction, transitioning into a dilation at the highest OCR. Similar behaviour for saturated clays has been noted in multiple sources (Abuel-Naga et al., 2007, Sultan et al., 2002, Burghignoli et al., 2000, Cekerevac and Laloui, 2004). A noticeable difference between both materials was observed during cooling. Kaolinite stages which contracted exhibited little response during the cooling cycle, while the corresponding bentonite stages further

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Figure 3. Kaolinite thermal induced vertical strain.

Figure 4. Bentonite thermal induced vertical strain.

contracted. There is limited data available for saturated bentonite, however, those available are mainly conducted on unsaturated bentonite (Tang et al., 2008, Ye et al., 2013). Volume changes can take place in two fashions, reversible (elastic) and non-reversible (plastic). The elastic components comprise of the physical swelling of the constituent clay parts (soil particles and water). Both the soil particles and water will expand during heating and contract during cooling. Given the drained test conditions the water only contributes to an overall increase in volume if it is locked within the structure (diffuse double layer – bonded to the clay platelets) and not expelled to maintain constant void space. This may be the case at high OCR resulting in the dilation during heating. At lower OCR the expansion of the adsorbed water along with the soil particles may be offset by the expulsion of water not so tightly adhered to the soil structure. The plastic component requires a reorganization of the soil fabric. This is only possible where the pore water is expelled. Therefore, the forces bonding the water to the platelets needs to be less than the change in viscosity of the water to allow it to escape. This is the case under normally consolidated conditions as the pore water is already at the tipping point of retention within the soil structure and expulsion. As the OCR increases this becomes more difficult. Another consideration is an increase/decrease in the ability of the soil structure to retain water (adsorbed water – diffuse double layer) which may change with temperature. Although, it has been suggested that the effect of temperature on the thickness of the diffuse double layer is insignificant (Abuel-Naga et al., 2005). 4

CONCLUSIONS

Thermal consolidation and volumetric tests were performed on saturated kaolinite and bentonite clays at various overconsolidation ratios. Elevated temperature has a direct influence on the consolidation rate of bentonite and kaolinite. Increased temperature increases the consolidation rate with the notable exception of highly overconsolidated bentonite, which experienced the opposite response. This

exception requires further investigation. The magnitude of rate change was similar for normally consolidated stages but varies when overconsolidated. Given the opposite response at high OCRs, multiple mechanisms must be responsible for the rate change (viscosity of pore fluid and intermolecular bonds are suggested). No significant change in the compression index (Cc ) or recompression index (Cr ) were noted for either material. The stress history, namely overconsolidation ratio is responsible for either a thermal contraction or dilation. Normally consolidated stages experienced consolidation, while highly overconsolidated stages (OCR = 8) experienced dilation. REFERENCES Abuel-Naga, H. M., Bergado, D. T. & Bouazza, A. (2007) Thermally induced volume change and excess pore water pressure of soft Bangkok clay. Engineering Geology, 89, 144–154. Abuel-Naga, H. M., Bergado, D. T., Rujivipat, S. & Soralump, P. (2005) Thermal consolidation of soft Bangkok clay. Lowland Technology International, 7, 13–21. Abuel-Naga, H. M. & Bouazza,A. (2013) Thermomechanical Behavior of Saturated Geosynthetic Clay Liners. Journal of Geotechnical and Geoenvironmental Engineering, 139, 539–547. Burghignoli, A., Desideri, A. & Miliziano, S. (2000) A laboratory study on the thermomechanical behaviour of clayey soils. Canadian Geotechnical Journal, 37, 764–780. Cekerevac, C. & Laloui, L. (2004) Experimental study of thermal effects on the mechanical behaviour of a clay. International Journal for Numerical and Analytical Methods in Geomechanics, 28, 209–228. Cui, Y.-J. & Tang, A. M. (2013) On the chemo-thermohydro-mechanical behaviour of geological and engineered barriers. Journal of Rock Mechanics and Geotechnical Engineering, 5, 169–178. Delage, P., Sultan, N. & Cui, Y. J. (2000) On the thermal consolidation of Boom clay. Canadian Geotechnical Journal, 37, 343–354. Di Donna, A. & Laloui, L. (2015) Response of soil subjected to thermal cyclic loading: Experimental and constitutive study. Engineering Geology, 190, 65–76.

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Knellwolf, C., Peron, H. & Laloui, L. (2011) Geotechnical Analysis of Heat Exchanger Piles. J. Geotech. Geoenviron. Eng., 137, 890–902. Laloui, L. & Di Donna, A. (2011) Understanding the behaviour of energy geo-structures. Proceedings of ICE, 164, 184–191. Ojovan, M. I. (2010) An Introduction to Nuclear Waste Immobilisation, Burlington, Burlington: Elsevier Science. Pothiraksanon, C., Bergado, D. T. & Abuel-Naga, H. M. (2010a) Full-scale embankment consolidation test using prefabricated vertical thermal drains. Soils and Foundations, 50, 599–608. Pothiraksanon, C., Saowapakpiboon, J., Bergado, D. T., Voottipruex, P. & Abuel-Naga, H. M. (2010b) Soft ground improvement with solar-powered drainage. Proceedings of the Institution of Civil Engineers: Ground Improvement, 163, 23–30.

Strawn, D. (2015) Soil chemistry, Chichester, West Sussex, UK, Hoboken, NJ, USA : Wiley Blackwell, 2015. Sultan, N., Delage, P. & Cui, Y. J. (2002) Temperature effects on the volume change behaviour of Boom clay. Engineering Geology, 64, 135–145. Tang, A. M., Cui, Y. J. & Barnel, N. (2008) Thermomechanical behaviour of a compacted swelling clay. Geotechnique, 58, 45–54. Ye, W., Zhang, Y., Chen, Y., Chen, B. & Cui, Y. (2013) Experimental investigation on the thermal volumetric behavior of highly compacted GMZ01 Bent. Appl. Clay Sci., 83-84, 210–216.

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Analysis of cement-based thermal energy storages considering natural convection H. Hailemariam, D. Shrestha & F. Wuttke Marine and Land Geomechanics and Geotechnics, Kiel University, Kiel, Germany

ABSTRACT: One of the common technologies for balancing the energy demand and supply in district heating, domestic hot water production, thermal power plants and thermal process industries in general is thermal energy storage. In this study, the coupled thermo-hydro behaviour of a fully saturated cement-based thermal energy storage system for domestic applications modeled with the Finite Element method by taking in to account the effect of buoyancy-driven convection on the temperature and heat distribution within the storage system is presented. Thermal energy storage systems in water saturated condition are commonly analysed considering pure solid-solid, solid-water and water-water conduction. The significant heat transfer contribution from the buoyancy-driven convection induced due to flow in saturated media arising naturally from the effect of a density difference, resulting from a change in temperature or concentration of a medium, is commonly neglected. This consequently leads to the underestimation of the actual loading/unloading rates as well as the overdesigning of such systems. The results of an extensive experimental program for the determination of parameters used for the FE modeling are also presented.

1

INTRODUCTION

Thermal energy storage (Braun et al. 1981, Hesaraki et al. 2015), in particular sensible heat storage (Dincer et al. 1997) as compared to latent heat storage and thermo-chemical storage, has recently gained much interest in the renewable energy storage sector due to its comparatively low cost and technical development. Sensible heat storages work on the principle of storing thermal energy by raising or lowering the temperature of liquid (commonly water) or solid media, and do not involve material phase change or conversion of thermal energy by chemical reactions or adsorption processes as in latent heat and thermo-chemical storages respectively. Environmentally friendly renewable energy sources such as solar, geothermal and wind energy are typically harnessed for the purpose of sensible heat storage. Solid sensible heat storage systems (Laing et al. 2006, Laing et al. 2012) in the form of storage media such as concrete, rocks, geomaterials and cemented saturated porous media are nowadays typically used to capture solar thermal power. Such systems when used in domestic thermal energy storage applications are preferable when compared to sensible heat storage via liquids such as water as they provide low investment costs with high operability (Laing et al. 2006) and can be designed to bear loads as part of the sub-structure of buildings. In this research, the numerical analysis of a saturated cement-based porous media sensible heat storage

system, IGLU project1 , which aims at developing a solar thermal powered heat energy storage system for domestic dwellings, by considering natural convection is presented. The finite element software package COMSOL Multiphysics2 was used to couple the governing thermo-hydro equations discussed in Section 2 of this paper. The loading/unloading of the system is operated via an embedded heat exchanger system with a carrier fluid (in this case water). The system provides efficient flexibility in terms of economy, space requirements and operation as compared to other existing heat storage systems (Fig. 1). Two porous cement-based commercial thermal energy storage materials namely, Füllbinders L and M (SCHWENK Zement KG3 ) were used for our investigations. The experimental scheme for the determination of parameters included: thermal conductivity and specific heat using a transient line-source measurement technique; semi-quantitative phase content determination by combined X-ray diffraction (XRD) and X-ray fluorescence (XRF) analysis; mechanical 1

IGLU is an analysis, modeling and assessment of an intelligent and environmentally friendly geothermal long-term heat storage system project funded by the German Federal Ministry of Economy and Energy (BMWi) 2 COMSOL Multiphysics is a finite element analysis, solver and simulation software package for various coupled phenomena in physics and engineering applications 3 http://www.schwenk-zement.de/

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combining heat transfer equations in solid and fluid phases (Bejan 2004, Bejan & Lorente 2004).

Figure 1. Schematic representation of the sensible heat storage system of IGLU project.

strength parameters such as uni-axial and shear strength using uni-axial, one dimensional confined compression and tri-axial tests; and hydraulic properties such as hydraulic permeability or conductivity under controlled stress and temperature conditions using a specialised hydraulic permeability meter.

2 2.1

where, the subscripts m, s and f refer to the porous medium, solid and ?uid phases, respectively, n is porosity, ρ is density, C is the specific heat of the solid, Cp is the specific heat at constant pressure of the ?uid, λ is the thermal conductivity, Q is the heat source, T is temperature, t is time and ν is the flow velocity field. The buoyancy-driven convective flow velocity ν in Equation 1 is obtained by solving porous media fluid flow equations. Three fluid flow in porous media equations namely, the Richards equation (for flow in saturated and un-saturated porous media), the Darcy’s law (preferable for flow in porous media that is comparatively slow) and the Brinkman equations (for fast flow in porous media) are commonly used to analyse fluid velocity and pressure in porous media. In this study the Richards equation for a single phase flow (water) has been used to obtain the convective flow velocity ν and pressure p. According to Darcy’s law, the net flux across a face of porous media is given by:

FE MODELING Heat transfer governing equations

Conductive and convective modes of heat transfer generally govern the amount of heat energy transported through a sensible porous media heat storage system. Heat conduction occurs in the porous cement based storage material and the entrapped pore-water, AluPE pipe wall and the heat carried fluid (water) inside the Alu-PE pipe. Heat convection on the other hand occurs in the fluid entrapped in the saturated heat storage material and the heat carrier fluid in the Alu-PE pipes. The convective mode of heat transfer involves fluid flow accompanied with conduction, or diffusion, and is basically divided in to two processes. When the motion of the fluid arises from an external cause the process is termed as forced convection. Whereas, if no such externally induced flow exists and the flow arises naturally from the effect of a density difference, resulting from a concentration or a temperature difference in body forces such as gravity, the process is known as natural convection. In this study, only natural convection is considered. Under isotropic medium conditions, where local thermal equilibrium is ensured (Ts = Tf = T , where Ts and Tf are the temperatures of the solid and fluid phases respectively), heat transfer Equations 1–3 for the porous storage medium can be obtained by

where, ν is the Darcy velocity field, K is the saturated hydraulic conductivity of the porous medium, ρf is the fluid density, g is the gravitational acceleration, p is the pressure and ∇D is a unit vector in the direction of g. The pressure p is solved by inserting the Darcy’s law, Equation 4, in to the equation of continuity, Equation 5, and the Darcy velocity ν is obtained from Equation 4.

where, n is the saturated liquid fraction or porosity of medium and Qs is the strength of fluid source. For an incompressible fluid such as water the term ρf moves outside the divergence operator, and the continuity equation is expressed in terms of the storage coefficient S as:

Richards equation is commonly used for modeling variably saturated porous media. The model solves

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for the pressure p and the fluid velocity ν using the following equations:

Table 1. Material properties of the filling material and the heat exchanger. Heat exchanger

where, C is the specific capacity describing the changes in liquid volume fraction of porous medium for a variably saturated condition, Se is the effective saturation and Kr is the relative permeability. The analytical formulas of van Genuchten (1980) are typically used to model the retention characteristics of variably saturated porous media. Darcy’s linear relationship between flow velocity and pressure gradient is not applicable for porous media flow with high Reynolds number and high particle size. In such instances, the Brinkman model (which is an extension of Darcy’s model) can be used. Brinkman modified the Darcy’s law by adding a viscous term to account for the presence of a solid boundary. The unsteady Brinkman equation for viscous flow in a porous medium is given as:

where, µ is the fluid’s dynamic viscosity, K is the saturated hydraulic conductivity of the porous medium, µdv is the dilatational viscosity, F is a force term used to represent directed forces such as compressibility effects and gravity and Qbr is an optional mass source term used to model condensation in porous media.

Materials

Alu-PE composite* Fü. L ** Fü. M**

Density (kg m−3 ) Porosity (–) Thermal conduc. (W m−1 K−1 ) Specific heat (J kg−1 K−1 ) Hydraulic conduc. (x10−8 m s−1 )

1825 – 0.400

1583 0.543 0.960

1609 0.518 0.965

1261

2083.4

1957.1

–

11.95

7.13

* Carrier fluid density = 1000 kg m−3 , thermal conductivity = 0.58 W m−1 K−1 , specific heat = 4190 J kg−1 K−1 . ** Fully saturated condition.

Table 2. Chemical and mineralogical characteristics of the thermal storage materials (obtained by X-ray fluorescence and X-ray diffraction analysis). Porous material Materials

Fü. L

Fü. M

Lime + Limestone (wt.%) Portl. Cement 42.5 (wt.%) SiO2 (%) Al2 O3 (%) TiO2 (%) MgO (%) Fe2 O3 (%) CaO (%) P2 O5 (%) Na2 O (%) K2 O (%) MnO (%)

75 25 17.28 4.90 0.27 0.92 2.76 48.75 0.12 0.14 0.98 0.04

65 35 16.43 5.17 0.29 0.51 2.79 51.62 0.16 0.12 0.78 0.04

3 2.2 Boundary & initial conditions The following boundary and initial conditions are assumed to solve the governing equations: – An initial temperature of 20◦ C representing ground temperature is assigned to the porous medium, AluPE and carrier fluid giving the following condition: T = To = 20◦ C. – A constant inlet temperature of 90◦ C is assigned to the inlet of the Alu-PE pipe representing the temperature of the hot carrier fluid (water) during loading of the system. – A thermal insulation specifying a zero flux is applied to the outside boundary of the heat storage system as: n · (λm ∇T ) = 0, where n is the vector normal to the boundary. – Fluid flow across impervious boundaries is prevented with the following condition: n · ρf v = 0, where n is the vector normal to the boundary.

Porous material

EXPERIMENTAL PROGRAM & RESULTS

3.1 Tested materials In Tables 1 & 2 material properties and physiochemical analysis results of the two investigated cement-based thermal energy storage materials, Füllbinders L and M, is presented. The samples were prepared with a water to solids ratio of 0.8 and were then stored under water for 28 days. Storage in water ensures full saturation and prevents possible cracking of samples which may happen soon after sample preparation due to the hydration of cement.

3.2 Thermal properties The thermal conductivity and specific heat of the samples were measured with a Decagon KD2 Pro thermal needle probe transient line source measurement technique in accordance to ASTM D5334-08 (ASTM

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Figure 2. Thin sections of Füllbinder M (top-left), Füllbinder L (top-right) and 3-D view of Fü. L specimen (bottom).

2008) and IEEE 442 standards (IEEE 1992). Thermal needle probes SH-1, dual needle (with a length of 30 mm, dia. 1.3 mm and 6 mm spacing between needles) and TR-1, single needle (with a length of 100 mm and dia. 2.4 mm) were used to measure the thermal conductivity and specific heat of the samples at room temperature and atmospheric pressure, respectively. The sufficient length to diameter ratio of the probes ensure that conditions for an infinitely long and infinitely thin heating source are met. The recorded error for all measurements was kept well within the 0.015% limit. The KD2 Pro contains a linear heat source and a temperature measuring element with a resolution of 0.001◦ C, and calculates the thermal conductivity and thermal diffusivity of the medium using the following relations:

where, λ (W m−1 K−1 ) is the thermal conductivity of the sample, Q (W m−1 ) is a constant rate of application of heat, T (0 K) is the temperature response with time of the source, Ei is the exponent integral, r (m) is the distance between the heater and the temperature sensor, t (s) is the amount of time that has passed since the start of heating and D (m2 s−1 ) is the thermal diffusivity of the sample. 3.3 Thin section & hydro-mechanical properties Figure 2 shows thin section images of Füllbinders L and M taken with a microscope to study the porous material structure. For both materials, it can be noted that the pore structure is homogenously distributed

Figure 3. One dimensional confined compression test results at different curing times of Fü. L (top) and Fü. M (bottom).

Figure 4. Unconfined compression (uni-axial) test results.

along the solid skeleton providing a uniform thermal conductivity (mainly through the solid-solid cementitious contact points within the skeleton) and a uniform heat storage capability (mainly through the even distribution of entrapped pore water) across the storage materials. Results of one-dimensional confined compression tests, unconfined compression or uni-axial tests and drained tri-axial tests are presented in Figures 3–5 respectively.

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Figure 6. Results of hydraulic conductivity tests at different hydraulic gradients with a confining stress of 150 kPa.

Figure 5. Drained tri-axial test results on Fü. L specimen at different confining stress σ3 levels with peak shear strength parameters of c = 196.77 kPa and ϕ = 19.900 (specimen size: dia. = 10 cm and height = 20 cm) [p = (σ1 + 2σ3 )/3 and q = σ1 − σ3 ].

Both Füllbinders L and M show significant increase in mechanical strength with curing time, with Füllbinder M exhibiting a comparatively higher stiffness due to its higher cement binder content. The difference in the cement binder content in the two energy storage materials also plays a significant role in their thermal behaviour (Table 1). The higher cement binder content of Füllbinder M when compared with Füllbinder L, produces a medium with a relatively lower porosity and hence a lower amount of entrapped pore water when fully saturated. Consequently Füllbinder M has a higher thermal conductivity but a lower heat storage capacity when compared to Füllbinder L (Table 1). Figure 5 (bottom) shows failure mechanism of Füllbinder L samples at different confining stress σ3 levels in a drained tri-axial test. At lower confining stress levels the sample tends to fail by cracking diagonally. However, at higher confining stress levels the sample rather fails by bulging with minor or no visible cracking. This provides a valuable insight on the design load considerations for such storage systems when they are used as part of the sub-structure of buildings, as formation of major cracks along the storage material significantly lowers the effective thermal conductivity and hence seriously undermining the operation of the system. In Figure 6 results of hydraulic conductivity tests performed with a specialised hydraulic conductivity meter under controlled hydraulic gradient i and confining stress σ conditions are presented. As expected the measured hydraulic conductivity of both materials decreases with an increase in the applied confining stress due to a reduction in the effective porosity upon application of stress. Moreover, Füllbinder M with its comparatively lower porosity exhibits a lower hydraulic conductivity as compared to that of Füllbinder L. A good energy storage material should possess a moderate to good thermal conductivity, a moderate strength to provide load bearing capability but not too high so as to enable easy removal of energy storage material for future maintenance and repair operations as well as a homogeneous and highly porous structure

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Figure 7. Sensible heat storage system configurations with a helical (left) and vertical (right) Alu-PE fluid carrier pipes.

to provide a high heat storage capacity when saturated. Considering the experimental analysis results presented in Section 3, Füllbinder L is better qualified to be used as an energy storage material when compared to Füllbinder M and hence it has been selected for the majority of the numerical analysis presented in this study.

4

NUMERICAL ANALYSIS RESULTS & DISCUSSION

Two typical sensible heat storage system configurations are shown in Figure 7. In this research, the configuration with vertically oriented loading/unloading Alu-PE pipes (Fig. 7 right) is analysed. The system consists of an insulated cylindrical heat storage tank with a dia. of 1.1 m and a height of 1.04 m. The heating/cooling operation of the system is facilitated via embedded Alu-PE pipes with an inside dia. of 2 cm and a wall thickness of 2.5 mm. Water with up to a maximum temperature of 90◦ C is used as a carrier fluid. In Figure 8 the temporal temperature variation at the center of the sensible heat storage system during loading with a hot carrier fluid (water) at 900 C for different heat storage material types and operation conditions is presented. The variation in temperature with progress in time is analysed for: the two material types investigated in this study (Füllbinders L and M) (Fig. 8 top), the effect of convection considerations with hydraulic conductivities K = 0 – 1 × 10−2 ms−1 (Fig. 8 middle) and the effect of carrier fluid velocity or Reynolds number Re between 119.5–916.3 (inlet fluid velocities between 6.8–52.0 liters per hour respectively) (Fig. 8 bottom). The temporal variation in temperature for both Füllbinders L and M are closely matched due to similarities in their thermo-hydro properties, however, the variation in the temperature changes of the system is highly

Figure 8. Temporal variation of temperature for: Fü. L & M with Re = 458.2 (26 lph) (top), Fü. L with Re = 458.2 (26 lph) at different hydraulic conductivities (middle) and Fü. L with K = 1 × 10−3 ms−1 at different carrier fluid velocities (bottom) [Re = Reynolds number; lph = liters per hour; K = hydraulic conductivity].

affected by changes in the hydraulic conductivity of the porous media due to convection effects. The system temperature variations for the porous medium with no convection (pure conduction only) consideration and with convection K = 0 ms−1 consideration are almost the same. However, with an increase in the hydraulic conductivity of the porous medium,

282

Figure 9. (from top to bottom) FE-mesh and system outline, spatial temperature distribution after 5 hours, isothermal contours after 60 hours and spatial temperature distribution after 120 hours of loading via a carrier fluid at 90◦ C of the sensible heat storage system with no convection or pure conduction only (left) and with convection K = 1 × 10−2 ms−1 consideration (right) [heat storage material is Fü. L with Re = 458.2 (26 lph)].

the influence of convection in the temperature variation of the system increases significantly. Typically, the system with no convection considerations reaches near storage capacity (above 80◦ C) after around 100 hours of loading time, whereas, the system with K = 1 × 10−2 ms−1 reaches storage capacity within 24 hours of loading duration. Hence, for a porous

medium with lower hydraulic conductivity, the effect of convection on the temperature variation can be neglected by considering only pure conduction to simplify system analysis. Whereas, for a porous medium with a higher hydraulic conductivity, consideration of convection in the analysis of temperature changes upon loading/unloading enables an efficient system

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design with accurate estimation of loading/unloading rates, thus saving time and avoiding overdesign of the system. Natural convection, in addition to its effects on the temporal variation of temperature of the heat storage system, also plays a vital role in the spatial variation (temperature distribution) in the sensible heat storage system (Fig. 9). Assumption of a pure conduction yields in an even and a conservative distribution of temperature as shown in Figure 9 (left). This representation is far from reality, where the actual spatial temperature distribution of heat storage systems with higher hydraulic conductivities when natural convection is considered is as shown in Fig. 9 (right), with a higher temperature field across the inlet as compared to areas near the outlet of the carrier fluid during loading and vice versa. For the system considered in this research (Fig. 7 right) the effect of carrier fluid velocity or Reynolds number Re on the temporal and spatial variation of temperature across the sensible heat storage system is minor (Fig 8 bottom). However, for sensible heat storage systems with complex shapes of embedded fluid carrier pipes consisting of several twists or turns, changes in the carrier fluid velocity can significantly affect their operation. 5

CONCLUSIONS

The coupled thermo-hydro behaviour of a saturated sensible heat storage system for domestic heat storage applications was analysed numerically by considering the effect of buoyancy-driven convective heat flow. Results of extensive experimental analysis for the determination of parameters for numerical analysis are also presented. For sensible porous media heat storage systems with very low hydraulic conductivities, the effect of natural convection on the temporal and spatial variations of temperature during loading/unloading operations of the system is minimal and can be neglected for simplicity of analysis. However, for systems with considerable hydraulic conductivity, convective heat transfer plays a significant role with a resultant faster loading/unloading rates and a higher temperature field near the carrier fluid pipe inlet as

compared to the outlet while loading and vice versa. In such instances, consideration of natural convection provides accurate estimation of the loading/unloading rates and avoids the overdesign of the system.

ACKNOWLEDGEMENTS The authors gratefully acknowledge the funding provided by the German Federal Ministry for Economic Affairs and Energy (BMWi) under Grant numbers 0325547B and KF3067302HF3, as well as the support of Project Management Jülich (PTJ). REFERENCES Braun, J. E., Klein, S.A., Mitchell, J.W. 1981. Seasonal storage of energy in solar heating. Solar Energy 26(5): 403–411. Hesaraki, A., Holmberg, S., Haghighat, F. 2015. Seasonal thermal energy storage with heat pumps and low temperatures in building projects—a comparative review. Renewable and Sustainable Energy Reviews 43: 1199–1213. Dincer, I., Dost, S., Li, X. 1997. Performance analyses of sensible heat storage systems for thermal applications. International Journal of Energy Research 21(12): 1157–1171. Laing, D., Steinmann, W-D., Tamme, R., Richter, C. 2006. Solid media thermal storage for parabolic trough power plants. Solar Energy 80(10): 1283–1289. Laing, D., Bahl, C., Bauer, T., Fiss, M., Breidenbach, N., Hempel, M. 2012. High-temperature solid-media thermal energy storage for solar thermal power plants. Proceedings of the IEEE 100(2): 516–524. Bejan, A. 2004. Convection Heat Transfer (3rd ed.), New York: Wiley. Bejan, A., Lorente, S. 2004. The constructal law and the thermodynamics of flow systems with configuration, International Journal of Heat and Mass Transfer 47(14–16): 3203–3214. van Genuchten, M.Th. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal 44(5): 892–898. ASTM. 2008. ASTM 5334-08: Standard test method for determination of thermal conductivity of soil and soft rock by thermal needle probe procedure. IEEE. 1992. Guide for soil thermal resistivity measurements, Inc. New York, Inst. of Electrical and Electronics Engineers.

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Experimental and constitutive study of the thermo-mechanical behavior of an oil sand M. Mohamadi, E. Piotrowska & R.G. Wan Department of Civil Engineering, University of Calgary, Canada

ABSTRACT: The understanding of the thermo-mechanical behavior of oil sand deposits is of prime importance in the safe and economic design of thermal oil recovery processes in Alberta, Canada. The present study focuses on both the experimental and constitutive characterizations of the thermo-mechanical behavior of “Firebag” oil sand from the Athabasca area in Alberta, Canada. Isothermal triaxial compression tests at different levels of confining pressure and temperature were performed on samples obtained from a depth of approximately 270 m. Experimental results at ambient temperature show a quite brittle behavior with relatively large peak and residual strengths due to the initially dense and interlocked structure of the granular material. High temperatures were found to strongly increase the ductility and decrease the stiffness and strength of the samples. Based on the experimental results, a simple non-associated plasticity model is proposed to realistically describe the nonisothermal mechanical behavior of Firebag oil sands. The proposed model is built on the Mohr-Coulomb plastic limit enriched with constitutive features that enable it to capture important behavioral aspects of oil sands such as high peak strength and dilatancy. The adequacy of the model is verified through the simulation of laboratory triaxial test results at different temperatures. The model provides a consistent and yet simple framework for easy implementation into a coupled reservoir-geomechanics computer algorithm for thermal oil recovery processes.

1

INTRODUCTION

The thermo-mechanical behavior of oil sands is a topic of particular interest in western Canada due to the role it plays in the safety and economical aspects of steam injection oil recovery projects, among others. Generally speaking, the injection of high-pressure steam creates fractures that extend following both tensile and shearing modes in an oil sand reservoir.Although these failure processes are seen to be favorable for increasing the reservoir permeability and hence, the efficiency of oil production, fractures have to be avoided near the shale cap-rock which has to remain mechanically intact throughout the entire oil extraction process. Furthermore, coupled thermo-mechanical deformations induced by the propagating steam chamber within the reservoir produce surface heave that has to remain within the tolerable limits. As such, the need for the accurate description of the thermo-mechanical behavior of oil sands for evaluating in situ stress changes and deformations is indispensable. Reports of experimental results on the thermomechanical behavior of oil sands are quite scarce in the literature. Performing a series of isothermal triaxial compression tests at temperatures between 20 and 200◦ C, Agar et al. (1987) reported that the strength of Athabasca oil sands remains unchanged when the temperature is increased from 20 to 125◦ C and decreases upon further heating to 200◦ C. A small but measurable increase in the stiffness and dilatancy of the material at

elevated temperatures was reported in the same study. Kosar (1989) reported that the initial stiffness, peak strength and dilatancy of high fines content (51% of particles smaller than 0.074 mm) McMurray Formation oil sands increase when the testing temperature increases from 20 to 225◦ C. Based on multistage heating from 21 to 102 and 200◦ C followed by drained triaxial shearing at the end of each stage, Wong et al. (1993) reported that the peak strength of Cold Lake oil sands remains unchanged up to 102◦ C and increases pronouncedly at 200◦ C. In the same study, no major change in the volumetric strain response was observed at elevated temperatures. It is obvious that no consistent temperature-induced phenomenological mechanism can be identified from the results of the aforementioned studies. This, among others, has resulted into approximating the nonisothermal behavior of oil sands with isothermal elastic or elastoplastic models. For instance, Agar et al. (1987) adopted the very basic nonlinear elastic hyperbolic model developed by Duncan and Chang (1970) to describe the pre-peak behavior of Athabasca oil sand. Vaziri (1989) combined the same nonlinear elasticity model as used in Agar et al. (1987), with critical state soil mechanics concepts (Schofield and Wroth 1968) to develop a conceptual framework for describing the behavior of oil sands. However, no comparison with experimental or field data on oil sand behavior was made. Using Rowe’s stress-dilatancy theory along with the Mohr-Coulomb-type yield function, Wan et al.

285

(1991) proposed an elastoplastic model to describe the behavior of Cold Lake oil sand at two different temperatures. Subsequently, Samieh and Wong (1998) developed a constitutive model to capture the behavior of Athabasca oil sand at low confining pressures (50– 750 kPa). The central advantage of their model is the description of post-peak softening and shear dilation using the disturbed state concept, originally proposed by Desai et al. (1986). Li and Chalaturnyk (2005). used the strain-softening Mohr-Coulomb model that is available in the FLAC geomechanical simulator (Itasca Consulting Group 2011) to reproduce results of laboratory experiments on oil sands at ambient temperature. All of the above-mentioned constitutive models are based on isothermal elasticity/elastoplasticiy, and therefore are not suitable for describing the complex behavior of oil sands under non-isothermal conditions. It is worth mentioning that Wan et al. (1991) used variations of friction angle with temperature to incorporate temperature-dependence in their model. However, a consistent implementation of the temperature effects to describe diverse behavioral aspects of oil sands such as yielding, hardening and volume contraction was not performed. Given the lack of consensus among the experimental results and the oversimplified modeling approaches, as reviewed in the aforementioned previous studies, the focus of this paper is twofold. Firstly, the thermo-mechanical behavior of Firebag oil sand, obtained from Athabasca area in Alberta, Canada, is investigated experimentally in a series of highpressure and high-temperature triaxial tests. Secondly, based on phenomenological mechanisms observed in the above-mentioned lab experiments, a simple nonisothermal constitutive model is proposed to describe the effects of temperature on the mechanical behavior of Firebag oil sand. The model formulation is generic enough for describing the non-isothermal behavior of other oil sands or frictional granular material, and yet simple enough to be easily implemented in any commercial finite element packages. The latter computer implementation is currently under progress and will be described elsewhere.

Figure 1. Grain size distribution of the tested oil sands. Table 1. Mass percentage of bitumen and water in three oil sand samples (total mass of each sample is 130 gr). Sample No.

Bitumen content (%)

Water content (%)

1 2 3

14.4 4.9 12.5

3.0 9.4 4.3

the results of grain size distribution and Dean-Strak tests, respectively. A typical CT-image of one of the samples at its mid-height prior to testing is shown in Figure 2, wherein dark spots correspond to regions of low density. The existence of localized micro-cracks and diffuse zones of low density in this image reveals the initially disturbed structure of the sample, which is typical of all tested samples as described later in the paper. All samples of the present study were tested in the Rock Mechanics Laboratory at the University of Calgary using a high-pressure/high-temperature triaxial apparatus. Technical specifications of the apparatus are given in Mohamadi and Wan (2016), to which the interested reader is referred. 2.2 Testing procedure

2

EXPERIMENTAL STUDY

2.1 Tested material The oil sand samples tested in this study were obtained from the Athabasca oil sands deposit at the Firebag site, located 120 km northeast of Fort McMurray in Alberta, Canada. The samples were chosen from the middle McMurray formation at a depth interval of 268.5–274.5 m where the in-situ porosity as per the density logs, ranges from 30 to 34%. The initial conditions of the samples were characterized via X-ray computed tomography (CT) scanning and common geotechnical index tests related to grain size distribution and Dean-Stark. Figure 1 and Table 1 present

Consolidated drained triaxial compression tests were performed on oil sand samples (89 × 180 mm), at both ambient (T0 = 25◦ C) and elevated temperature (T = 130◦ C). The testing procedure at ambient temperature included an initial isotropic consolidation stage followed by shearing along a conventional triaxial compression stress path at a rate of 1 mm/hr. At elevated temperatures, testing included one more stage in which the specimen was heated prior to the shearing stage, while keeping the applied isotropic stress constant. The heating stage was performed in several sub-stages, each including an initial heating at a rate of 0.5◦ C/min followed by a stabilization sub-stage. Sample deformations were monitored during the latter sub-stage until a negligible change in the sample

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Figure 2. CT-image of an oil sand specimen at its mid-height showing sample disturbance.

dimensions was measured, at which point the testing was pursued. 2.3 Test results and discussions Figure 3 presents a typical set of responses for the samples tested under a confining pressure of 1 MPa, at both 25 and 130◦ C. The two samples (T12 S2 and T12 S5) tested at 25◦ C show identical initial stiffnesses and post-peak strengths, while their peak strengths are different. The latter is believed to be mainly due to variability in physical characteristics of the field samples. Furthermore, the peak strength of oil sands is known to be quite sensitive to sample disturbance (Agar et al. 1987). As for volume changes of the above-mentioned two samples it is observed that their initial compactions and subsequent constant-rate dilations in the pre-peak regime are quite similar. Turning to sample T12 S5, it is observed that the volume change is anomalously suppressed at an axial strain of 0.64%. This is attributed to difficulties associated with the local measurements of the deformations in the post-peak regime where the occurrence of non-homogeneous deformations is inevitable. Comparing results at 25 and 130◦ C, it is observed that heating causes a considerable decrease in the initial stiffness and peak strength, and a moderate decrease in the post-peak strength. Furthermore, sample T13 S2 reaches its peak strength at a larger axial strain (1.4%) as compared to those tested at ambient temperature, implying its enhanced ductility. Finally, heating seems to increase the maximum contractancy, as suggested by the volume change curves in Figure 3. Another noteworthy feature in Figure 3 is the initial upward concavity of the deviatoric stress-strain curves. The value of the deviatoric stress at the end point of these sections (see Figure 3(a)), are too large

Figure 3. Effects of temperature on shearing behavior of Firebag oil sands at the confining pressure of 1 MPa.

to be associated with the initial adjustment of the sample typically observed in the testing of rocks. In fact, such concave-upward segments of the stressstrain curve are attributed to pore and fissure closure in the Rock Mechanics literature (Goodman 1989). A more detailed experimental study regarding the source of these concave-upward features in the behavior of tested oil sands has been performed by the authors. The results, which are beyond the scope of the current paper, confirm that crack closure is indeed a major contributing factor to the formation of these early-stage non-linearities. In view of correcting for the crack closures, the initial section of the stress-strain and volume change curves of the tested oil sands have to be adjusted. Plots of deviatoric stress versus radial strain (not shown here) strongly suggest that the cracks are mostly horizontally oriented. As a result, the initial upward concavity is mainly due to axial deformations, and can be easily corrected following the conventional approach as per ASTM-D1883 (2007). The corrected

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stress-strain and volume change curves following this approach are shown later in Figure 5. Triaxial test results at the confining pressures of 3 and 5 MPa are not presented herein, due to limitations in the length of the paper. However, the general temperature-induced phenomenological mechanisms, i.e. decrease of the initial stiffness, peak and post-peak strength as well as the enhanced contractancy, are quite similar to those described earlier with regard to Figure 3. The proper description of these mechanisms entails recourse to a robust thermo-elastoplastic constitutive model, as described in the next section. 3

decreases at elevated temperatures. The temperaturedependence of the initial stiffness entails pressuredependence of the thermal properties that has to be accounted for using a coupled thermo-elastic rule (Graham et al. 2001, Mohamadi and Wan 2015). Assuming isotropic thermal strains, the coupling is invoked by additively decomposing the rate of elastic volumetric strain ε˙ ev into mechanical and thermal components as

CONSTITUTIVE STUDY

This section presents a non-isothermal constitutive formulation for describing the behavior of Firebag oil sands.The data obtained from lab experiments are used to extend a simple Mohr-Coulomb-based constitutive model, henceforth referred to as the reference model, whose elaborate description is given in Pietruszczak (2010). This extension is accomplished by incorporating temperature effects in the various components of the reference model such as temperature-dependence of the elastic and hardening rule, yield function and plastic flow rule, among others. Developed for describing the behavior of cohesionless soils, the reference model involves a few simplifying assumptions as: (i) no dependency of the yield locus or plastic potential on the Lode angle, (ii) exclusive strain-hardening behavior for both loose and dense samples, and (iii) no cap-type yield surface for the occurrence of the irrecoverable strains during isotropic loading. Adopting the above-mentioned assumption (i), the model formulation is herein presented in the triaxial stress/strain space where p = (σ1 + 2σ3 )/3, q = σ1 − σ3 , εv = ε1 + 2ε3 and εq = 2(ε1 − ε3 )/3 with σi and εi (i = 1, 3) being the major and minor principal components of the stress and strain tensor, respectively. With regard to assumption (ii), a simple form of the cohesion intercept is introduced in subsection 3.3 to adapt the model formulation to experimental observations made on the tested oil sands. Such a modification is useful for describing a strain-softening type of behavior, and shall be differentiated from the unified pressure- and density-dependent modeling approach, see e.g. Wan and Guo (1999). As for the assumption (iii), temperature-induced plastic mechanisms are also assumed to be only associated with the cone-type yield surface, i.e. Mohr-Coulomb. Finally, the components of the stress σ and the strain ε tensor are assumed positive in compression. The overdot associated with a variable denotes its rate, and the superscripts ‘e’, ‘p’designate the elastic and plastic components, respectively. 3.1 Thermo-elasticity As mentioned earlier, the initial stiffness of Firebag oil sands determined from triaxial compression tests

where K0 is the bulk modulus at reference temperature T0 and reference mean effective stress p0 . Other material parameters such as β1  = 1 and α1 describe variations of Young’s modulus with mean effective stress and temperature, respectively, while αT is the coefficient of volumetric thermal expansion of the solid skeleton. Eq. (1) preserves the path-independence of the thermo-elastic volumetric strains, that is the elastic volumetric strains do not depend on the order of the application of the incremental temperature and mean effective stress. The rate of elastic shear strain ε˙ eq is assumed to be purely mechanical, i.e. it is being merely induced by incremental deviatoric stress q˙ as

where ν is Poisson’s ratio. It is worth mentioning that the pressure-dependent shear modulus necessitates the dependence of bulk modulus on deviatoric stress (Hueckel et al. 1992), in order for the thermoelastic rule to be mechanically conservative. However, this type of coupling is trivial under monotonic loading (Zytynski et al. 1978), and has been neglected in the development of the present model. 3.2 Thermo-mechanical strength Results of triaxial compression tests show that both peak and post-peak strengths of Firebag oil sands decrease at elevated temperatures. Other researchers have reported that the peak strength of oil sand samples may remain unchanged, increase or decrease upon heating, e.g. see (Agar et al. 1987, Kosar 1989, Wong et al. 1993). The lack of consensus among these studies entails the use of a generic temperature-dependent mathematical expression to uniformly describe the

288

Eq. (4) is employed to define the family of yield loci f , i.e.

where MmT and ξmT represent suitable functions of the p plastic shear strain εq and temperature T , for prescribing hardening or softening in the behavior of oil sands, that is:

Figure 4. Non-isothermal MC criterion used to describe the peak strength of Firebag oil sands.

complex thermo-mechanical strength of oil sands. For simplicity sake, the well-known Mohr-Coulomb (MC) criterion is adapted here to serve as a non-isothermal strength limit. The MC criterion in terms of deviatoric stress (q) and mean effective stress (p) is given as:

where c0 and ϕ0 are cohesion and friction angle, both measured at the ambient temperature. An easy extension of Eq. (3) to non-isothermal conditions is obtained by assuming that the p-intercept, i.e. c0 / tan ϕ0 , remains unchanged at elevated temperatures (Mohamadi and Wan 2016). As such, the non-isothermal MC criterion is given by

where M0 is the stress ratio at incipient yielding at ambient temperature T0 , a is the evolution parameter controlling the pace of mobilization of friction angle ϕ0 , ξ0 and b are the material parameters for prescribing values of peak stress and strain, respectively, and α3 is a material parameter for controlling the degradation of ξ0 with temperature. The proposed expression for ξmT , Eq. (6b), is intended to capture the rapidly strain-softening behavior of oil sands as observed in the experiments. Such a description of the strain-softening phenomenon is linked to the loss of interlocked structure and conceivably interparticle bonding, and cannot be captured in conventional models including those based on merely mechanical state variables, i.e. pressure and void ratio. It is noteworthy that the strain-softening phenomenon in the aforementioned sense has to be complemented with the so-called strain localization analysis to thoroughly describe the observed post-peak behavior of the tested samples. The latter, however, requires a numerical analysis considering the triaxial test as a boundary value problem, and is beyond the scope of this study. 3.4

where α2 is a material parameter that can be used to describe temperature-insensitivity (α2 = 0), temperature-induced decrease (α2 > 0) or temperatureinduced increase (α2 < 0) of the strength. It is cautioned here that Eq. (4) is only a simple expression obtained from the curve fitting of experimental data and cannot be used to capture non-monotonic variations of strength with temperature. Figure 4 shows that the peak strength of Firebag oil sands are described quite satisfactorily as per Eq. (4).

Flow rule

Experimental observations on Firebag oil sand indicate that the initial contractile volume changes smoothly transform into dilatancy in a close proximity of the peak stress. Furthermore, it is observed that the maximum contractancy increases at elevated temperatures. These features can be adequately modeled by assuming a non-associated temperature-dependent flow rule as

3.3 Yield locus and hardening A key feature of the non-isothermal model is the existence of a thermoelastic limit whose evolution is used to describe the progressive deformation of oil sands. Herein, a similar mathematical form as that shown in

where ε˙p and σ are the rate of plastic strain and stress tensor, respectively, λ˙ is a positive plastic multiplier, T0 Mcv is slope of the critical state line in the q − p plane, T0 i.e. Mcv = 6 sin ϕ0cv /(3 − sin ϕ0cv ) with ϕ0cv being the

289

Table 2. Model parameters for Firebag oil sands. K0

β1

ν

ϕ0 (deg)

ϕ0cv (deg)

ξ0

d0

a

b

α1

α2

α3

αT

3100

0.33

0.11

41

38

4000

0.4

0.00003

500

0.981

0.1587

0.0761

–∗

∗

Not needed in the present study.

critical friction angle at ambient temperature T0 , d0 is a material parameter controlling the post-peak dilation rate, and pc is a constant representing the intercept of the plastic potential g with the p-axis at the current state of stress. 3.5 Thermo-elastoplastic constitutive equation Applying the consistency condition (f˙ = 0) to Eq. (5) and making use of Eq. (6) and (7), the positive plastic multiplier λ˙ can be obtained as:

where  are the Macaulay brackets such that x = x if x ≥ 0 and x = 0 if x < 0. Invoking the additive decomposition of the rate of total strain into elastic and plastic components, the thermo-elastoplastic constitutive equation in a stress-temperature-controlled program can be readily formulated as:

It is noteworthy that by setting αT = α1 = α2 = α3 = 0, and doing simple manipulations, Eq. (9) reduces to its isothermal counterpart as described in Pietruszczak (2010). 4 4.1

MODEL ASSESSMENT Determination of model parameters

The proposed model requires the evaluation of three elastic parameters, i.e. K0 , β1 and ν, six elastoplastic parameters, i.e. ϕ0 , ξ0 , d0 , ϕ0cv , a and b, and four thermal parameters, i.e. αT , α1 , α2 and α3 . The results of four drained isothermal triaxial compression tests,

performed at two temperatures and consolidation pressures, are needed to determine all model parameters. For a more accurate evaluation of these parameters, it is recommended that a testing program includes three different temperatures and confining pressures. The values of K0 , β1 and ν are easily determined from the initial slope of q − ε1 and εv − ε1 curves, as commonly done in geotechnical engineering. Variations of the initial slope of q − ε1 with temperature can be used to determine α1 . The values of ϕ0 , ϕ0cv and α2 can be determined using the procedure described in subsection 3.2. Assuming that elastic strain components are negligible compared to plastic ones, the hardening parameter a is determined by plotting MmT at ambient temperature versus εq in the pre-peak regime. Having determined ϕ0 and α2 , the values of ξ0 , b and α3 can be evaluated such that the peak strain and postpeak softening are precisely captured at both ambient and elevated temperatures. The value of d0 is chosen to describe the post-peak dilation rate. Finally, αT can be determined based on the heating test under constant isotropic stress prior to the shearing stage. All material parameters are reported in Table 2 for Firebag oil sand.

4.2

Simulation of drained triaxial compression tests

Model simulations as per Eq. (9) were employed to reproduce results of drained triaxial compression tests at different temperatures, on Firebag oil sands. Figures 5 and 6 present the comparison of model simulations with experimental results at confining pressures of 1 and 5 MPa, respectively. With regards to the stressstrain curves, it is observed that the initial stiffness as well as the peak and post-peak strengths are predicted reasonably well, both at the ambient and elevated temperature. It is only the peak strength corresponding to the test at the confining pressure of 1 MPa and temperature of 130◦ C that is underestimated. This, however, is due to the use of an average peak strength envelope, including experimental data from three different confining pressures, which has to be compatible with the special form of cohesion intercept as described in Eq. (6b). Turning to the volume change behavior in Figures 5 and 6 it is observed that both calculated and measured volumetric strains are in good agreement in the pre-peak regime, while the quality of the match in the post-peak regime deteriorates. The latter, as mentioned earlier in the paper, is attributed to non-objectivity of the post-peak response of the tested oil sands due to the occurrence of localized deformations. A numerical analysis considering the triaxial test as a boundary

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Figure 5. Comparison of model simulations (solid lines) and experimental measurements (symbols) at p0 = 1 MPa: (a) deviatoric stress vs axial strain and (b) volumetric strain vs axial strain.

value problem should be carried out in order to fully examine the localization phenomenon whereas model simulations in the present work were obtained at the element level. 5

CONCLUSIONS

The constitutive study of the non-isothermal behavior of geomaterials in the context of continuum theory of plasticity is usually performed based on the observed phenomenological mechanisms in the lab experiments. Such mechanisms cannot be consistently derived from previous studies on oil sands, given the presence of diverse sources of complexity governing their behavior. As a result, a series of high-pressure/-temperature triaxial compression tests were performed on Firebag oil sands, obtained from

Figure 6. Comparison of model simulations (solid lines) and experimental measurements (symbols) at p0 = 5 MPa: (a) deviatoric stress vs axial strain and (b) volumetric strain vs axial strain.

Athabasca area in Alberta, Canada. The results of lab experiments indicate that the initial stiffness as well as the peak and post-peak strength of the samples decrease at elevated temperatures, while their maximum contractancy increases. Based on these observations a simple MohrCoulomb-type constitutive model was extended to non-isothermal conditions. While maintaining simplicity, the temperature-dependency of elastic moduli, hardening rule, yield function and plastic flow rule were addressed. The new model was applied to successfully simulate the behavior of Firebag oil sand at different temperatures. Although being developed based on only one series of lab experiments, the proposed constitutive model is believed to be versatile enough for describing the nonisothermal behavior of other oil sand types.As ongoing

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research, the proposed model is currently being implemented in a commercial finite element package to test its efficiency and accuracy in simulating boundary value problems. ACKNOWLEDGEMENTS The authors would like to thank the Natural Sciences and Engineering Research Council of Canada (NSERC) and the CMG Foundation for providing financial support of this research through a CRD grant. Acknowledgment is also made to Suncor Energy for providing the oil sand cores from the Firebag in-situ project. REFERENCES Carraro, J. A. H., M. Prezzi, & R. Salgado (2009). Shear strength and stiffness of sands containing plastic of nonplastic fines. Journals of Geotechnical and Geoenviromental Engineering 135, 1167–1178. Chien, L. K. & Y. N. Oh (2002). Influence of fines content and initial shear stress on dynamic properties of hydraulic reclaimed soil. Canadian Geotechnical Journal 39, 242–253. Darendeli, M. B. (2001). Development of a new family of normalized modulus reduction and material damping curves. Ph.D. thesis, University of Texas at Austin. Drnevich, V. P. (1978). Resonant-column testing: Problems and solutions. Dynamic Geotechnical testing, 384–398. Hardin, B. O. & V. P. Drnevich (1972). Shear modulus and damping in soils measurment and parameter effects. Soils Mechanics and Foundations Division 98, 603–624. Hardin, B. O. & M. E. Kalinski (2005). Estimating the shear modulus of gravelly soils. Journal of Geotechnical and Geoenvironmental Engineering 131, 867–875. Iwasaki, T. an Tatsuoka, F. (1977). Effects of grain size and grading on dynamic shear moduli of sands. Soils and Foundations 17, 19–35.

Jamiolkowski, M., R. Lancellotta, & D. Lo Presti (1995). Remarks on the stiffness at small strains of six italian clays. Pre-failure Deformation of Geomaterials 1, 817–836. Menq, F. Y. (2003). Dynamic Properties of Sandy and Gravelly Soils. Ph.D. thesis, The University of Texas at Austin. Rahman, M. M. (2009). Modelling the influence of fines on liquefaction behaviour. Ph.D. thesis, The University of New South Wales at Australian Defence Force Academy. Rahman, M. M., S. R. Lo, & C. T. Gnanendran (2008). On equivalent granular void ratio and steady state behaviour of loose sand with fines. Canadian Geotechnical Journal 45, 1439–14561. Salgado, R., P. Bandini, & A. Karim (2000). Shear strength and stiffness of silty sand. Journal of Geotechnical and Geoenviromental Engineering 126, 451–462. Santamarina, J. C. & m. Aloufi (1999). small strain stiffness: A micromechanical experimental study. In Proceeding of pre-failure deformation characteristics of geomaterials. Tao, M., J. Figueroa, & A. Saada (2004). Influence of nonplastic fines content on the liquefaction resistence of soils in terms of the unit energy. In Cyclic behavior of soils and liquifaction phenomena. Tatsuoka, F., T. Iwasaki, &Y. Takagi (1978). Hysteretic damping of sands under cyclic loading and its relation to shear modulus. Soils and foundations 18, 26–39. Thevanayagam, S. (1998). Effect of fines and confining stress on undrained shear strength of silty sands. Journal of Geotechnical and Geoenviromental Engineering 124, 479–491. Wichtmann, T. & T. Triantafyllidis (2009). On the influence of the grain size distribution curve of quartz sand on the small strain shear modulus. Journal of Gerotechnical and Geoenviromental Engineering 135, 1404–1418. Yanagisawa, E. (1983). Influence of void ratio and stress condition on the dynamic shear modulus of granular media. Adv. in the mechanics and the flow of Granular Materials 2, 947–960. Yimsiri, S. & K. Soga (2002). Application of micromechanics model to study anisotropy of soils at small strains. Soils and Foundations 42, 15–26.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Effect of temperature and pressure on mechanical behavior of rock salt in underground storage caverns K. Khaledi, E. Mahmoudi, D. König & T. Schanz Chair of Foundation Engineering, Rock and Soil Mechanics, Ruhr-Universität Bochum, Germany

ABSTRACT: Assessing the material response of rock salt subjected to the cyclic thermo-mechanical loading conditions is essential for engineering design of underground storage caverns. In this paper, a coupled thermomechanical model is employed to describe the effect of temperature and pressure variations on the stress-strain behavior of rock salt around the underground cavities. In the numerical section, the operating condition of a typical compressed air storage cavern is first simulated. Then, the effects of cyclic pressure and temperature on the thermo-mechanical response of rock salt medium are investigated for this numerical problem and, finally, some important design aspects such as stability of the cavern and the long term serviceability will be evaluated.

1

INTRODUCTION

Underground caverns excavated in rock salt are recognized as the appropriate places to store energy in the form of compressed air or hydrogen. Rock salt is one of the prime alternatives for constructing the underground cavities because of its favorable properties. Low permeability, adequate thermo–mechanical properties and solubility in water are some of the unique features that make the rock salt distinguished from other rock materials. On the other hand, storing energy in the form of compressed air inside the underground salt caverns is recognized as a promising technique to meet the energy demand fluctuations in electricity power grids. This type of caverns are constructed using the solution mining technique and operate with daily cyclic periods. That means, the pressure and temperature applied to the inner boundary of salt cavern have rapid changes in comparison to the seasonal storage caverns. For this reason, it is essential to investigate the effect of thermo–mechanical cyclic loading on the stability and serviceability of storage systems. Obviously, accurate design of these underground cavities requires adequate numerical simulations which take into account the most important processes that could affect the performance of the system. However, rare investigations have been made to model the behavior of rock salt in storage caverns considering both cyclic mechanical and cyclic thermal loading. Therefore, design of salt caverns that work under cyclic loading conditions is still a challenging task. During the recent years, a limited number of experimental studies have been performed to assess the effect of cyclic loading on the mechanical behavior of rock salt with main focus on the fatigue failure and cyclic damage progress, e.g. see (Fuenkajorn and Phueakphum, 2010), (Ma et al., 2013), (Liu et al., 2014) and (Guo

et al., 2012). The main objective of this paper is to model the thermo–mechanical cyclic response of rock salt around the underground energy storage caverns. Furthermore, the stability and long-term serviceability of the system under the influence of cyclic loading condition are discussed. 2 THERMO-MECHANICAL CONSTITUTIVE MODELING OF ROCK SALT To describe the material response of rock salt, an elasto-viscoplastic-creep model has been employed in this paper. Under the small strain and strain additivity assumptions, the total strain rate is defined using the equation below.

where ε˙ el ij is the elastic strain rate obtained by the genvp eralized Hooke’s law. ε˙ ij and ε˙ cr ij are the viscoplastic strain rate and the creep strain rate, respectively. ε˙ th ij denotes the thermal induced strain rate.

2.1 Viscoplastic deformation The viscoplastic behavior of the rock salt has been described by (Desai and Varadarajan, 1987) model which is based on Perzyna’s viscoplasticity (Perzyna, 1966). In this model, the viscoplastic strain rate is defined through a non-associated flow rule as follows:

293

This quantity is related to the linear thermal expansion coefficient αs and the temperature changing rate T˙ :

2.4 Heat transfer in rock salt

Figure 1. The viscoplastic and creep potential functions as well as the failure and dilatancy boundaries of rock salt.

where
x = (x + |x|) /2 is the Macauley bracket. The fluidity coefficient µ1 and the stress exponent N1 are material parameters. F vp and Qvp are the proposed viscoplastic yield and potential functions by (Desai and Varadarajan, 1987), respectively. F0 is a reference value with the same unit as F vp . This model accounts for the compressibility and the dilatancy of rock salt in the stress space as well as the short-term failure. The compression behavior of rock salt in the stress space is separated from the dilative behavior through the dilatancy boundary. Fig. 1 shows the applied viscoplastic potential surface, dilatancy boundary and the failure boundary of rock salt in this paper. 2.2

Creep deformation

The creep deformation is described using the following equation:

The stress exponent N2 is a material parameter and µ0 denotes the value of fluidity coefficient at a reference temperature. R is the universal constant of perfect gas and Ts is the absolute temperature of rock salt. According to this equation, for any J2 > 0 and Ts > 0, a steady-state creep deformation occurs. Fig. 1 shows the creep potential surface Qcr applied in this study. In the compressibility domain(below the dilatancy boundary), the creep strain has only the deviatoric part and the volumetric creep deformation is assumed to be zero. However, when the stress state is in the dilatancy domain (above the dilatancy boundary), the irreversible time-dependent dilation occurs and volumetric creep strain increases. 2.3 Temperature induced deformation The term ε˙ th ij in Eq. 1 is the volumetric strain rate caused by the temperature change, which is considered as an additional strain tensor in the mechanical model.

The temperature fluctuation at the cavern boundary during the charge and discharge processes changes the temperature of the surrounding rock. To calculate the temperature distribution around the cavern, the heat transfer equation has to be solved. Assuming a constant thermal conductivity coefficient in Fourier’s law of heat conduction, the following heat transfer equation is solved to obtain the rock salt temperature over the time and space. In this paper, the finite element code Code–Bright is used (Code-Bright user’s guide, 2010) to solve the equation below:

where cs , ρs and ks are the specific heat, density and thermal conductivity of rock salt, respectively. In addition, Ts represents the rock salt temperature. 3

FINITE ELEMENT MODELING OF COMPRESSED AIR STORAGE CAVERN

To investigate the effect of thermo-mechanical cyclic loading on the behavior of salt cavern, a finite element model has been built using GiD software. GiD has been developed by the International Center for Numerical Methods in Engineering (CIMNE) and is used as the pre-processor and post-processor for the Code–Bright finite element solver (Code-Bright user’s guide, 2010). In this section, the practical data of Huntorf CAES plant is adopted to define the dimensions and working conditions of the model. In Huntorf plant, the compressed air is stored in two relatively identical storage caverns (i.e. in terms of dimension, depth and storage capacity). The total storage capacity of the plant is about 300000 m3 . However, to efficiently model the geometry of the cavern, some simplifications are required. In this study, only one of the caverns is selected for the simulation. The geometry and boundary conditions of the selected cavern are shown in Fig. 2a. As seen, the cavern has been idealized as a half cylinder with a radius of 18 m and a height of 150 m. The top and bottom of the cavern have the semi-spherical form. The axisymmetrical model with the height and width of 500 m is shown in Fig. 2a as well. With this assumptions, the storage volume of the simulated cavern is about 150000 m3 . On the upper boundary of the model, a load of 10 MPa is applied which represents the overburden load at the top of the model. The vertical displacement at the model bottom is restrained. The finite element discretization of the model is shown in Fig. 2b.

294

beginning of simulation, a load which is equal to the geostatic pressure is applied to the boundary of the cavern. The initial temperature of rock salt is assumed to be 50◦ C everywhere. Phase II : in order to model the excavation process, the applied mechanical loads to the inner boundary of cavern are gradually reduced to a minimum air pressure (in this example: 4.7 MPa). Assuming a leaching rate of 35 m3 /h and considering the time needed for debrining phase (Tryller and Musso, 2006), the whole construction phase lasts approximately 230 days. Additionally, the temperature of the inner boundary is reduced to 35◦ C in this phase. This temperature reduction is due to the heat transfer between brine and the rock medium during the leaching process (see Fig. 3). Phase III : in this phase, the thermo-mechanical cyclic loads resulted from the charge and discharge processes are simulated. It is assumed that, during the first 100 cycles, the cavern works under the normal operating conditions reported in (Cortogino et al., 2001). According to (Cortogino et al., 2001), the charge and discharge time of the cavern are 8 and 2 hours, respectively. Therefore, this simulation phase takes about 41 days (i.e. days: 230–271). The air pressure fluctuates between 4.7 MPa and 7.2 MPa, while, the temperature ranges between 30–70 ◦ C (see Fig. 3). Phase IV : after the first 100 cycle, an extreme loading scenario is defined and applied to the boundary of the cavern for another 100 cycles. The time duration of this simulation step is about 41 days (i.e. days: 271–312). The range of cyclic pressure drops down to 2.2–4.7 MPa in this phase. With this pressure reduction, the temperature cycles are obtained in the range 10–80◦ C (see Fig. 3). Figure 2. (a) Geometry and applied boundary conditions of the model (b) the finite element discretization of the model.

4

RESULTS AND DISCUSSION

The main objective in this section is to assess the performance of the simulated salt cavern under the influence of defined loading conditions. In the following, the temperature distribution around the cavern as well as the changes in mechanical stability and serviceability of the cavern are discussed. 4.1 Temperature around the cavern

Figure 3. The pressure and temperature applied to the cavern boundary during excavation and cyclic loading phases.

The following steps are performed to simulate the construction process and cyclic loading operation of the salt cavern: Phase I : initial stress state is considered to be isotropic (i.e. σxx = σyy = σzz ). Therefore, at the

Because of the temperature difference between the cavern’s inner boundary and the surroundings, the thermal energy is transferred through the rock salt medium by conduction. Because of this reason, the temperature distribution changes in the vicinity of the cavern. During the injection process the temperature of air inside the cavern increases. When the air temperature is higher than the surrounding rock, heat is transferred from the air to the rock. Therefore, the temperature of the surrounding rock salt rises up. Over the discharge time, because of the reverse heat transfer from the rock to the air, the rock salt temperature reduces.

295

In the following, the above-mentioned stability criteria are evaluated for the numerical example explained in the previous section. 4.2.1 “No-dilatancy” criterion The loading conditions of cavern have to be defined in a way that the stresses around the cavity remain in the compressibility zone. To determine the state of stress with respect to dilatancy boundary, the following safety factor is defined:

Figure 4. Variation of rock salt temperature at selected distances from the cavern boundary during cyclic loading phase.

Figure 5. Schematic definition of the stability criterion FS.

Figs. 4 shows the variation of rock salt temperature at three selected distances from the cavern boundary during cyclic loading phases. As depicted in this figure, during the cyclic loading operation, the average temperature of each cycle remains approximately 50◦ C (i.e. equal to the ground temperature). In addition, the temperature fluctuation in the rock only takes place in a narrow zone less than one meter thick. Inside this zone, the amplitude of temperature cycles reduces as the distance from the cavern’s boundary increases and finally, it approaches the ground temperature.

4.2

Stability of the cavern

In this section, the mechanical stability of the simulated cavern is investigated considering two criteria: 1. “No-dilatancy” criterion: this criterion indicates whether the stress state around the cavern is in the dilatancy zone or not. 2. “No-tensile stress” criterion: rock salt exhibits poor tensile strength. Therefore, no tensile stress should be experienced around the cavern.


J dil is the equation of dilatancy boundary in √2 the I1 − J2 plane shown in Fig. 1 and J2 is the second invariant of deviatoric stress tensor. Fig. 5 shows the schematic representation of “No-dilatancy” criterion. When FS < 1, the current stress state is below the dilatancy boundary. In this case, the opening of microcracks does not occur and subsequently, damage does not progress. In contrary, when FS > 1, the stress state locates beyond the dilatancy bounday. Thus, the operating condition of the cavern is not safe and cavern may experience long-time failure due to the damage progress. Fig. 6 compares the maximum value of FS around the cavern obtained for the normal operating condition and the low pressure cyclic loading. As it is observed, during the normal cyclic operation (i.e. phase III), the FS value is less than 0.9. That means, the internal pressure of the cavern in this loading scenario is high enough to keep the stresses below the dilatancy boundary. While, during the phase IV, where the internal pressure reduces drastically, the FS factor becomes more than one for the points located around the cavern. Thus, for this loading scenario, the stresses are in the dilatancy zone and the “No-dilatancy” criterion is not fulfilled. where

4.2.2 “No-tensile stress” criterion Rock salt has a poor tensile strength (i.e. around 1.8 MPa). The thermo–mechanical loading conditions have to be defined in a way that no tensile stress is experienced around the cavern. As shown in Fig. 3, for the point which are very close to the cavern wall, the air temperature during the low pressure working condition reduces to 10◦ C over the cyclic loading. This temperature reduction induces high thermal stresses in an area less than one meter thick around the cavern. Thus, due to the fast cooling and extra thermal contraction, the tangential component of stress becomes positive at the points which are very close to the boundary (in particular at the cavern roof). Fig. 7 shows the variation of principal stresses at cavern roof during excavation (days: 0–230), normal cyclic loading (days: 230–271) and extreme working condition (days: 271–312). As it is seen from this figure, the minimum principal (i.e. in this case the tangential stress) becomes positive during the last phase of simulation. Therefore, “Notensile stress” criterion is not satisfied for this loading condition.

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Figure 6. Contour plot of factor of safety FS at the end of (a) phase III (b) phase IV.

4.3

Serviceability of the cavern

The serviceability of the system is strongly related to the storage capacity of the cavern. If, for any reason, the volume of the cavern reduces significantly, the efficiency and the serviceability of the system will be in danger. For this reason, it is important to control the factors which may increase the rate of cavern closure. In this section, the volume loss of the cavern (VL) during the cyclic loading phase is evaluated for the defined loading scenarios. The volume loss of the cavern is calculated as:

where, V0 and Vt are the initial defined volume and the volume after time t, respectively. Fig. 8 shows the

changing of VL values for the defined loading scenarios in this paper. As it is observed, in phase IV, when the internal pressure drops down, the rate of volume convergence increases significantly in comparison to the normal working condition. In this case, the increased creep strain rate resulted from the higher deviatoric stresses accelerates the cavern closure. Thus, the rate of volume loss increases in this case. 5

CONCLUSION

In this paper, an elasto-viscoplastic-creep model has been employed to describe the stress-strain relation of rock salt under the influence of thermo-mechanical cyclic loading conditions. In order to investigate the effect of internal temperature and pressure on the stability and serviceability of cavern, its operation under

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serviceability of the system are affected by the internal pressure and temperature. The numerical example presented in this work demonstrates that the stability factors of the system are strongly governed by the internal pressure and temperature of the cavern. For this reason, these quantities should be set in a way that the stresses around the cavern satisfy the “No-dilatancy” and “No-tensile stress” criteria. ACKNOWLEDGMENT

Figure 7. The minimum principal stress at cavern roof during excavation (days: 0-230), normal cyclic loading (days: 230–271) and extreme working condition (days: 271–312).

Figure 8. The volume loss of cavern during normal operation (days: 230–271) in comparison to extreme cyclic loading (days: 271–312).

the normal and extreme loading conditions has been analyzed numerically. Obtained results show that during the normal operating condition, the applied loads to the rock salt medium generate only thermoelastic and steady-state creep deformations without any dilation. However, when the loading pattern of the cavern is changed to the extreme condition, the stability and

This work was performed in the frame of the project ANGUS+ funded by the Federal Ministry of Education and Research (BMBF) under Grant no. 03EK3022C. The authors are grateful for this support. REFERENCES Code-Bright user’s guide (2010). Department of the Geotechnical Engineering and Geosciences of the Technical University of Catalonia (UPC). Cortogino, F., K.-U. Mohmeyer, & R. Scharf (2001). Huntorf caes: More than 20 years of successful operation. In SMRI Spring Meeting, Orlando, 23-24 April, pp. 351–357. Desai, C. & A. Varadarajan (1987). A constitutive model for quasi-static behavior of rock salt. J. Geophys. Res 92, 445–456. Fuenkajorn, K. & D. Phueakphum (2010). Effects of cyclic loading on mechanical properties of Maha Sarakham salt. Eng. Geol. 112(1–4), 43–52. Guo, Y., C. Yang, & H. Mao (2012). Mechanical properties of Jintan rock salt under complex stress paths. Int. J. Rock. Mech. Min. Sci 56, 54–61. Liu, J., H. Xie, Z. Hou, C. Yang, & L. Chen (2014). Damage evolution of rock salt under cyclic loading in unixial tests. Acta Geotechnica 9, 153–160. Ma, L. J., X.Y. Liu, Q. Fang, H. F. Xu, H. M. Xia, E. B. Li, S. G. Yang, & W. P. Li (2013). A new elasto-viscoplastic damage model combined with the generalized HoekBrown failure criterion for bedded rock salt and its application. Rock. Mech. Rock. Eng. 46, 53–66. Perzyna, P. (1966). Fundamental problems in viscoplasticity. Rec. Adv. Appl. Mech 9, 243–377. Tryller, H. & L. Musso (2006). Controlled cavern leaching in bedded salt without blanket in Timpa del Salto. In SMRI Spring Meeting, Brussels, Belgium, 30 April-3 May.

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CTE analysis of saturated cement-based sensible heat storage materials H. Hailemariam, D. Shrestha & F. Wuttke Marine and Land Geomechanics and Geotechnics, Kiel University, Kiel, Germany

ABSTRACT: The linear coefficient of thermal expansion (CTE) of three cement based energy storage materials in saturated condition is determined experimentally. The CTE is a material property that indicates the extent to which a material expands or contracts upon heating or cooling respectively and plays a vital role in the thermohydro-mechanical analysis of sensible heat energy storage systems. Throughout their lifetime, sensible heat energy storage systems are subject to frequent temperature changes due to heating and cooling effects of loading and unloading of heat energy respectively. The different components of sensible heat energy storage system such as heating/cooling element, energy storage material, insulators and others, are constructed of different materials which possess un-equal CTE values, and hence produce extra stress in the system when heated or cooled. When unaccounted for, the extra stresses generated due to the heating/cooling processes may cause damage or failure of the thermo-hydro-mechanical system.

1

INTRODUCTION

With few exceptions, all solids expand or contract when heated or cooled respectively undergoing reversible dimensional changes on a macroscopic level due to a change in thermal vibrations that are always present in the crystal – which is known as thermal expansion or dilation. However the extent of expansion or contraction per degree of change in temperature is different for different materials. Analysis of the coefficient of thermal expansion (CTE) of porous materials is different from that of solids such as metals and ceramics due to the presence of pore water and/or pore air. In a porous multiphase material, thermal expansion of in situ pore water contributes to the volumetric change of the material due to a change in the ground surface temperature, thus influencing the stress field of the medium. In the past, several studies have been conducted on the thermal expansion of porous media and soils in particular. Agar et al. (1986) analysed both the drained and undrained thermal expansion coefficients for oil sands by means of heating experiments in the range of temperature between 20 and 300◦ C. Cui et al. (2000) described two phenomena produced during heating of saturated clays - namely, expansion of soil constituents (solid and water) and mechanical weakening of the contacts between soil aggregates. Saix et al. (2000) observed a contraction during heating of clayey silty sand under constant stress at 42, 160 and 800 kPa in a one dimensional confined compression test. On compacted FEBEX bentonite and Boom clay, Romero et al. (2005) observed a thermal expansion under low stresses. Analysis of CTE of the several components of a porous media based sensible heat storage system is of

utmost importance for the design and safe operation of such systems. However, the CTE is a much neglected material property and the level of material science is much more primitive. Furthermore, on top of the lack of experimental data of CTE analysis of porous media sensible heat storage materials, traditional methods of CTE determination assume a uniform temperature distribution within materials while heating or cooling, which is far from reality. The actual heat flow within sensible heat storage materials to-and-fro the sample via the heating/cooling element creates an inhomogeneous linearly varying temperature distribution within the sample. In accordance with this phenomenon, a thermal expansion and conductivity meter is used in this research to obtain the CTE of three commercial heat storage samples - namely, Füllbinders L and M (SCHWENK Zement KG1 ) and Dyckerhoff Dämmer S (Deuna Zement2 ). The samples were prepared with a sufficient diameter to length ratio to ensure a homogeneous linear variation of temperature within the materials while heating. The accuracy of the system was checked by testing standard materials of aluminum, stainless steel and brass with known CTE values, and a good agreement between the measured and the standard values was obtained. 2 THEORETICAL ANALYSIS The temperature dependent linear coefficient of thermal expansion α is calculated as per unit change in 1 2

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http://www.schwenk-zement.de/ www.deuna-zement.de

length with per unit change in temperature and is normally expressed as follows:

where, Lo is the initial sample height (length) at room temperature, L is the change in height (length) of sample due to a temperature change of T . This is an average coefficient of thermal expansion, which is the one normally provided in the literature, and is not the same as the differential form (dl/dt) of α. For practical applications specifying an average value of α is often adequate. Moreover, α is a function of temperature and hence when referring to α of a specific material, the temperature range over which the measurements were made is usually specified. Heating or cooling affects all the dimensions of a material, with a resultant volume change. The volume coefficient of thermal expansion αv represents the volume change of a material due to heating/cooling and is obtained as:

where, where Vo and V are the original volume and the volume change due to a temperature change of T respectively. Many materials have anisotropic values of α depending on the crystallographic direction along which CTE is measured. For materials in which the thermal expansion is isotropic, αv can be approximated as 3α. The mean CTE of the heat storage materials investigated in this research is calculated according to ASTM E831 (2006) guidelines for the determination of linear thermal expansion of materials by thermomechanical analysis as follows:

where, α is the mean coefficient of linear thermal expansion of the sample (×10−6 /0 C), αref is the mean coefficient of linear thermal expansion of reference material (x10−6 /0 C), k is calibration coefficient, Lo is the initial specimen length at room temperature (m), Lref is the change of reference material length due to heating (µm), Lref is the reference material initial length at room temperature (m), L is the change of specimen length (µm), T ref is the temperature difference over which the change in reference material length is measured (◦ C), T is the temperature difference over which the change in specimen length is measured (◦ C). In this study, Polyoxymethylene (POM) thermoplastic is selected as a reference material due to its high stiffness, low friction, excellent dimensional stability and known coefficient of linear thermal expansion.

Table 1. Properties of the heat storage materials. Porous material Properties

Fü. L*

Fü. M* Dä. S*

Density (kg m−3 ) Porosity (–) Thermal conduc. (W m−1 K−1 ) Specific heat (J kg−1 K−1 ) Modulus of elasticity (MPa)

1583 0.543 0.960 2083.4 1911.1

1609 0.518 0.965 1957.1 2751.5

1560 0.562 0.957 2162.8 1987.9

* Fully saturated condition.

3

EXPERIMENTAL PROGRAM

3.1 Tested materials In Table 1, obtained material properties of the three investigated cement-based thermal energy storage materials, Füllbinders L & M and Dämmer S, are presented. The samples were prepared with a water to solids ratio of 0.8 and were stored under water for 28 days. Storage in water ensures full saturation and prevents possible cracking of samples which may happen particularly on the specimen surface soon after sample preparation due to the hydration of cementing material. 3.2 Experimental set-up Determination of the thermal expansion coefficient of materials undergoing a thermal cycle requires the measurement of two physical quantities – namely, displacement and temperature. The three main technologies used for the measurement of CTE are interferometry, dilatometry and thermomechanical analysis. Interferometry works on the principle of measuring displacement of the specimen ends with optical interference techniques in terms of the number of wavelengths of monochromatic light. It is the most precise technique of the three methods and is capable of measuring CTE values lower than 5 × 10−6 /◦ C. Mechanical dilatometry techniques involve the application of heat to the specimen in a furnace and the measurement of the displacement of the specimen by means of an assembly of a sensor and push rods. The test precision is lower than that of interferometry and is generally suitable for materials with CTE above 5 × 10−6 /◦ C. Thermomechanical analysis measurements are made with a thermomechanical expansion meter consisting of a specimen holder, a transducer that measures the change in length of the specimen upon heating, a furnace or heating plate for uniform heating of specimen, a thermocouple or temperature sensing element and a means of data recording apparatus. The lower limit for CTE determination with this technique is 5 × 10−6 /◦ C. However, the method may also be used at lower or negative expansion levels with decreased precision & accuracy. In this research, a thermal expansion and conductivity meter which works on the principle of thermomechanical analysis is used (Fig. 1, top). The apparatus is

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a diameter of 50 mm and sufficient length of 40 mm to produce a linear variation of temperature within the samples while heating. In addition, the higher specimen length results in a greater length change signal upon heating or cooling and hence provides a higher CTE accuracy. Care was taken to ensure that the top and bottom faces of the samples are perfectly flat so that the minimum contact force applied over the samples is spread out uniformly over a wide enough surface area avoiding minor sample deformations. The accuracy of the system was checked by testing samples of aluminum, stainless steel and brass with known CTE values. For the porous material specimen shown in Figure 1 (middle), under isotropic medium conditions, where local thermal equilibrium is ensured (Ts = Tf = T , where Ts and Tf are the temperatures of the solid and fluid phases respectively), heat transfer Equations 5–8 can be obtained by combining heat transfer equations in solid and fluid phases (Bejan 2004, Bejan & Lorente 2004).

Figure 1. Thermal expansion measurement set-up (top), schematic representation (middle) and dimensional analysis (bottom) of the thermal expansion and conductivity cell.

modified to produce a homogenously linear temperature distribution within the specimen to represent the actual heat flow and distribution within sensible heat storage systems. The apparatus consists of a top heating plate, a bottom cooling plate and a reference disc with known thermal conductivity (Fig. 1, middle). The specimen is sandwiched between the top heating and reference plates. The plates consist of extremely thin PT 100 temperature sensors with an accuracy of 0.05◦ C. The system measures sample expansion or contraction with a TRS-0050 linear transducer with an independent linearity of 0.15% and repeatability of 2µm. The sample expansion tests were conducted under fully saturated condition by heating the top plate at a constant rate of 2◦ C/min within the temperature range of 22–75◦ C, as the materials are to be used for the purpose of a sensible heat storage system with a heat carrier fluid (water) for the loading/unloading operations of the system. The samples were prepared with

where, the subscripts m, s and f refer to the porous medium, solid and ?uid phases, respectively, n is porosity, ρ is density, C is the specific heat of the solid, Cp is the speci?c heat at constant pressure of the fluid, λ is the thermal conductivity, q′′′ (W m−3 ) is the heat production per unit volume, T is temperature, t is time and ν is the flow velocity field. For the system shown in Figures 1 (bottom), Equation 9 applies provided that T1 > T2 > T3 , ensuring that heat flow occurs from the top plate via the sample and reference disc to the bottom plate with a linear temperature gradient as the specimen is homogeneous, and T1 > Tambient > T3 , ensuring that heat flow from the environment does not penetrate to the specimen (Stegner et al. 2011, Sass & Stegner 2012).

The average sample temperature (at the center of the specimen) which corresponds to T1 , T2 and T3 can thus be obtained as:

where, T1 is the temperature of the top (heating) plate (◦ C), T2 is the temperature of the reference disc (◦ C),

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Table 2. Comparison of the measured and standard CTE (22–75◦ C) values of the reference materials.

Table 3. Measured CTE values of the three heat storage materials.

Material

Measured CTE*

CTE, Agil. Tech.*

Material

Measured CTE*

Aluminium Stainless steel Brass

23.77 14.54 19.87

23.60 14.90 19.10

Füllbinder L Füllbinder M Dämmer S

10.69 16.13 11.03

* ×10−6 /◦ C.

* ×10−6 /◦ C.

The thermal expansion test results of the reference materials matched closely with the standard CTE values proving the accuracy of the system. Similarly, a close match between experimental and numerical results is obtained for the heat flow and temperature distribution across the specimen and reference plate for all the materials. 4.2 Testing of heat storage materials

Figure 2. Analysis of reference plate temperature T2 of the studied invar alloy and the reference materials.

T3 is the temperature of the bottom (cooling) plate (◦ C), T is the average sample temperature (◦ C), λp and λv are the thermal conductivities of the sample and the reference disc respectively (W m−1 K−1 ), Sp , Sv andS23 are the distances (m) as shown in Figure 1 (bottom). The average sample temperature obtained using Equation 10 is used in the temperature calculations of Equations 3 & 4. 4

RESULTS AND DISCUSSION

4.1 Testing of reference materials Table 2 shows the observed and standard (Agilent Technologies 2002) CTE values of the three reference materials used in this study to verify the accuracy of the experimental results. The baseline correction due to expansion of the components of the system while heating was obtained by testing a specimen of an inert or low expansivity invar alloy. In Figure 2, the measured reference plate temperature T2 values of the three reference materials and invar alloy are compared with numerically obtained (using COMSOL Multiphysics3 ) reference plate temperature of a specimen with thermal property of an average of the invar alloy and the three reference materials used.

In Table 3 and Figure 3, results of thermal expansion tests on the three cement-based sensible heat storage materials obtained by heating the top plate at a constant rate of 2◦ C/min within the temperature range of 22– 75◦ C are presented. Since all the tests are conducted under drained condition, volume change caused by pore water expansion is negligible. Both Füllbinder L and Dämmer S exhibit a higher rate of expansion upon heating for average sample temperature range of up to 30◦ C followed by a gradual decrease afterwards due to material softening. However, Füllbinder M shows a consistent rate of expansion upon heating for the considered temperature range. Most solids exhibit a constant rate of expansion upon heating at lower temperature ranges, usually followed by an increase in the rate of expansion at very high temperature ranges. The results are also consistent with the properties and composition of the investigated heat storage materials. Both Füllbinder L and Dämmer S have a comparatively lower measured strength and modulus of elasticity, a lower cement binder content and a higher porosity when compared with Füllbinder M, and hence show a higher rate of softening or mechanical weakening of cementitious bonds and a decrease in the rate of expansion upon heating. Figure 4 shows the temperature distribution across Aluminium (reference material) and Füllbinder L (heat storage material) samples heated up to a temperature of 80◦ C. The results, obtained using COMSOL Multiphysics, show a homogenous and linearly varying temperature distribution across the samples. As expected, a higher temperature across the reference plate is recorded for the Aluminium specimen as compared with the Füllbinder L specimen due to its higher thermal conductivity. 5

CONCLUSIONS

3

COMSOL Multiphysics is a finite element analysis, solver and simulation software package for various coupled phenomena in physics and engineering applications

A thermal expansion and conductivity meter which works on the principle of thermomechanical analysis

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Figure 3. Plot of specimen expansion vs temperature at the top of specimen (top), specimen expansion vs temperature at the center of specimen (middle) and average CTE values vs the upper range of temperature used for calculating the average CTE (bottom) of the three heat storage materials [For the calculations of the average CTE values in the bottom figure, a bottom temperature range of 24◦ C is used for all points].

was modified to determine the linear coefficient of thermal expansion (CTE) of three cement based sensible heat storage materials in saturated condition by maintaining a homogeneously linear temperature distribution across the investigated materials. Unlike traditional CTE determination methods which assume a uniform temperature distribution in a material upon

Figure 4. FE-mesh and system outline (top), temperature distribution of the Aluminium reference material (middle) and temperature distribution across the Füllbinder L specimen and reference plate (bottom) [All temperature values shown are in ◦ C].

heating or cooling, the linear temperature distribution across the specimen represents the actual heat flow and temperature distribution within the porous medium of sensible heat storage systems upon loading/unloading operations via fluid carrier pipes. The findings of this research provide an accurate way of estimating the CTE of sensible heat energy storage materials, which plays a fundamental role in the thermo-hydro-mechanical analysis and design of such systems.

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ACKNOWLEDGEMENTS The authors would like to gratefully acknowledge the financial support provided by the German Federal Ministry for Economic Affairs and Energy (BMWi) under Grant numbers 0325547B and KF3067302HF3, as well as the support of Project Management Jülich (PTJ). REFERENCES Agar, J.G., Morgenstern, N.R., Scott, J.D. 1986. Thermal expansion and pore pressure generation in oil sands. Canadian Geotechnical Journal 23: 327–333. Cui, Y.J., Sultan, N., Delage, P. 2000. A thermo-mechanical model for saturated clays. Canadian Geotechnical Journal 37(3): 607–620. Saix, C., Devillers, P., El Youssoufi, M.S. 2000. Elément de couplage thermomécanique dans la consolidation de sols non saturés. Canadian Geotechnical Journal 37: 308–317. Romero, E., Villar, M.V., Lloret, A. 2005. Thermo-hydromechanical behaviour of heavily overconsolidated clays. Engineering Geology 81: 255–268.

ASTM. 2006. ASTM E831-06: Standard test method for linear thermal expansion of solid materials by thermomechanical analysis. Bejan, A. 2004. Convection Heat Transfer (3rd ed.), New York: Wiley. Bejan, A., Lorente, S. 2004. The constructal law and the thermodynamics of flow systems with configuration, International Journal of Heat and Mass Transfer 47(14–16): 3203–3214. Stegner, J., Nguyen, D., Seehaus, R., Sass, I. 2011. Development of a thermal conductivity and diffusivity meter for unconsolidated rocks. Proceedings of the 18. Tagung für Ingeniergeologie, Berlin (original in German). Sass, I., Stegner, J. 2012. Coupled measurements of thermophysical and hydraulical properties of unsaturated and unconsolidated rocks. Proceedings of the 37th Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, 30 Jan.–01 Feb., 2012. Agilent Technologies. 2002. Laser and Optics User’s Manual, Chap. 17, Material expansion coefficients.

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A laboratory investigation on the thermo-mechanical behaviour of thermal piles in sand A. Rafiei & C. Arya University College London, London, UK

S.W. James Cranfield University, Cranfield, UK

R.G. Correia University of Nottingham, Nottingham, UK

R. Fuentes University of Leeds, Leeds, UK

ABSTRACT: This paper reports on an investigation on the behaviour of base and shaft resistant piles embedded in sand subject to heating and cooling cycles. It describes the 1 g laboratory model developed at University College London. The test pile consists of a hollow stainless steel tube which is instrumented using Fibre Bragg Grating (FBG) sensors that allow measurement of strain and temperature profiles along the pile length and the surrounding soil. The pile is subjected to two heating-cooling cycles. Water held at 50◦ C is circulated inside the pile for 24 hours; this is followed by a 24-hour cooling period during which the temperature of the water is allowed to fall back to ambient conditions. The results show that small irreversible settlements occurred during this period. Additionally, it is found that the degree of freedom varies between 0.9 and 1.0 which indicate low levels of restraint are present. Nevertheless, considerable axial load and axial stress is induced in the pile. Moreover, significant shaft friction is mobilized during both heating and cooling periods.

1

INTRODUCTION

Thermal piles are a newly developed technology which not only provide structural support but also allow heat at shallow depths in the soil to be extracted from the ground during cold periods and excess heat from the overlying structure to be deposited in the ground during warm spells. This is achieved by circulating fluid through pipes embedded in the pile. If the temperature of the circulated fluid is lower than the soil, the fluid will absorb heat from the soil which can be subsequently recovered via a heat pump and used for heating. Alternatively, if the temperature of the fluid is higher than the surrounding soil, the ground can be used as a heat sink. Thermal piles are increasingly being used in major projects worldwide for heating and cooling purposes. However, despite the increasing number of installations, evidence of their thermo-mechanical performance is still rather limited. The research on thermal piles is mainly divided into 2 subjects: heat transfer within the pile and the surrounding soil and thermo-mechanical behaviour under combined loading conditions. The work reported in this paper addresses the later subject. Thermal loading induces additional strains and hence increases axial loads and stresses on the pile. These additional stresses

may compromise the safety of piles. Normally, to avoid the risk of failure, higher safety factors are used by designers. A significant amount of the research on thermal piles has been carried out in the field by a number of authors, most notably Laloui et al. (2006) and Bourne-Webb et al. (2009). However, in-situ tests are expensive, time consuming and also it is difficult to ascertain boundary conditions. Therefore, laboratory tests were used in this work. A 1 g small scale model was designed and developed to perform a series of monotonic and cyclic mechanical only, thermal only and thermo-mechanical loading tests. Due to space limitations, this paper only presents the results of the thermal only tests. Fibre Bragg Gratings (FBG), a type of point based fibre optic sensor, are used to monitor strain and temperature changes along the pile surface and inside the soil bed. Further details of the apparatus and test procedure are presented below. 2 APPARATUS An apparatus capable of assessing the behaviour of both shaft resistant and base resistant piles is developed. The tank is made from a 3 mm-thick steel

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sheet with an outer diameter and height of 500 mm. A polished round tube made of grade 304 stainless steel with an external diameter of 28 mm and height and wall thickness of 535 mm and 1.5 mm respectively is used to model the pile. The bottom of the model pile is capped by welding a base plate also of grade 304 stainless steel in order to allows water to be circulated inside the pile. For the shaft resistant test, the toe of the pile passes through a hole in the container base. Container and pile dimensions are chosen to make sure that the results obtained are not being affected by the boundary conditions. In the literature, the ratio between the pile diameter and the container diameter is chosen as a factor to minimize these boundary effects. As such, the ratio between the diameter of the container and model pile is 17.85 which lies near the limits specified by Parkin & Lunne (1982). Another boundary condition is introduced by Al-Mhaidib & Edil (1998), namely zone of influence, and determined that this is between 3D-8D for a pile installed in sand: this limit is also comfortably met in this test. The soil used in this study is a poorly graded uniform fine sand with a uniformity coefficient of 2.32 and a median grain size of D50 = 0.18 mm. The average specific gravity is 2.64 gr/cm3 and the maximum and minimum dry densities are 1.658 and 1.349 gr/cm3 respectively. A relative density of 57.6% is measured in all tests which classifies it as medium dense. The size of the sand grains in the reduced scale model is not scaled down with the rest of the system. Several recommendations are found in the literature based on the relationship between the pile diameter and median grain size. In this study, this ratio is equal to 155 which is above the recommended limits specified in the literature, namely 35 to 100 (King et al. 1984, Weinstein 2008). In order to prevent heat loss, an encapsulated fibreglass insulation jacket is used to cover the top and bottom surfaces as well as the sides of container. The insulation jacket has 8 mm thickness and a thermal conductivity value of 0.04 (W/m.K). A Techne compact water circulator model C-400 with temperature range of −20◦ C and +80◦ C is used to recirculate thermostatically-controlled water through tubes connected to the pile head. The circulator is not able to cool the water and this is achieved by simply allowing the water to fall back to room temperature. The model pile is instrumented using Fibre Bragg Gratings (FBG) which is one of the most commonly used point-based optical fibres. Application of Fibre Optic Sensors (FOS) for health monitoring of geotechnical structures including foundations and tunnels has increased significantly over the past decade. Application of FOS for in-situ installation of Thermal Piles is reported by Bourne-Webb et al. (2009). Using FOS instead of conventional monitoring instruments have several advantages including small size, high sensitivity, large bandwidth, automated and fast data acquisition, being immune to water and not using electrical signals (Iten, 2011). Typical strain resolution for distributed sensors is around 20µε while for pointbased sensors it is 1µε which has made point-based

Figure 1. Shaft resistant pile set-up.

sensors an accurate monitoring tool. The main reason for using FBG in this study is the multiplexing potential of FBG sensors where several sensors can be fabricated on a single fibre which reduces required space for the installation of fibres. In this study, two set of fibres each with 5 FBG sensors were fabricated at Cranfield University to monitor temperature, TP1-TP5, and strain along the pile surface, SP1-SP5. Moreover, 5 set of fibres each consisting of 4 FBGs are used to monitor the temperature in the soil bed at different levels and distances, T1-1 to T5-4 (Figure 1). Data collected for temperature variations in the soil is not presented in this paper though as the focus is on the pile itself. Pile head displacement is measured using a Linear Variable Differential Transformer (LVDT) with measurement range of ±7.5 mm and data collection frequency of 3 seconds. 3

EXPERIMENTAL PROCEDURE

A repeatable sample preparation method is used for both tests to reach a relative density of approximately 57%. Driving the pile in the sand bed was not an option as it would damage the fragile FBGs surface sensors despite using protective coatings. In order to perform the shaft resistant test, the pile is held in position at the centre of the container using a support at the pile head. Sand is poured into the container in 16 layers and each layer is levelled using a wooden tamper made particularly for this purpose. Temperature FBG sensors are placed at 5 levels. One end of the FBG sensor is placed next to the pile surface and it is laid on the sand until it is sealed to the container wall and the other end is attached to the laser box. Once the soil and sensors are in place, the inlet and outlet pipes are connected to the circulator and pipes are insulated to reduce the heat loss during water circulation. Before starting the

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Figure 2. Temperature changes along the pile (a) Shaft resistant pile (b) Base resistant pile.

test, the pile base support is removed which results in 0.05 mm (0.17% of the pile diameter) pile head movement due its self-weight. Water circulator is turned on and the temperature is raised to 50◦ C in less than 10 minutes. During each heating-cooling cycle, the temperature is kept constant for 24 hours at 50◦ C and then left to recover to room temperature for 24 hours and the same procedure repeated in the second cycle – see Figure 2. For the base resistant pile, the same procedure is applied with only one difference: Initially, the sand is poured in the container layer by layer until it reaches the height of 90 mm and then the pile base is placed on it after which a similar procedure as that of shaft resistant pile is repeated. The results are presented below. 4

RESULTS AND DISCUSSION

As previously noted, this paper only discusses the results of shaft and base resistant piles under thermal only loading. Both types of piles are not restrained either of the top or bottom and hence the only restraint is the surrounding sand. Pile temperature is increased from 22◦ C to 50◦ C and data has shown that variations in the temperature is seen at different depths during heating and cooling periods. Hence, instead of using absolute temperature values, constant room temperature at 22◦ C is considered as the reference and temperature variations from room temperature is

Figure 3. Observed strain distribution (a) Shaft resistant pile (b) Base resistant pile.

used as a more reliable tool (See Figure 2). For the shaft resistant pile, the maximum changes in temperature during heating and cooling periods are 31.09◦ C and −29.79◦ C from each particular period. These are recorded at TP5 and TP4 levels respectively which are approximately 8.5% higher than initial assumed value of T = 50 − 22 = 28◦ C. For the base resistant pile, slightly higher temperatures changes are recorded but the same trend is seen in both tests where the pile is heated up to 50◦ C within 10 minutes and kept at 50◦ C for 24 hours and then left to cool for 24 hours and same procedure is repeated in the 2nd cycle. Three type of strain values are used in the thermomechanical analysis of thermal pile systems. The first is the observed strain collected in the laboratory, shown in Figure 3. A residual strain of approximately 10 µε is seen in both tests. Lower strain values are obtained in the second cycle compared to the first one. Observed strain is compared with the free-state strain which is the product of temperature changes and thermal expansion coefficient of the pile material. In this study, a separate test is performed on free-state condition where the pile is heated up and cooled down without any soil restraint or end restraint and strain values collected are used as the free-state strain values. The difference between observed and free state strain is called Restrained Strain which represents the strain caused by the friction between pile and sand at the interface. It is this restrained strain that causes induced loads (Bourne-Webb et al. 2009).

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Figure 4. Degree of freedom variations along the depth (a) Shaft resistant pile (b) Base resistant pile.

A term called ‘degree of freedom’ is used as the ratio of observed strain over free strain to quantify the amount of restraint. The value of degree of freedom varies between 0 and 1, where 0 means maximum restraint. Existence of restraint will induce axial load and consequently additional induced stresses in the pile. Figure 4 shows the values of degree of freedom along the pile length achieved in both tests. For the shaft resistant pile, the maximum pile restraint is seen at the bottom of the pile. The maximum and minimum degrees of restraints are experienced at the end of first cooling and heating periods respectively. For the base resistant pile, similar trend as shaft resistant pile is seen for the heating and cooling cycles although there are less differences in the degree of freedom along its depth. In both tests, the value of degree of freedom varies between 0.9 and 1.0 which shows that a relatively small restraint is seen from the surrounding sand. Despite these small values of restrained strain and high degree of freedom, a significant axial load is induced in the pile from thermal loading. It is mainly due to the high thermal expansion coefficient of stainless steel and the magnitude of temperature changes in the pile. For the shaft resistant pile, the highest induced load during heating and cooling periods are 860N and 1050N respectively. During the cooling period, tension load is also observed – see Figures 5 and 6. This would be very significant for concrete piles. For the base resistant pile, lower induced axial load is applied to the pile due to the higher degree of freedom.

Figure 5. Induced axial force distribution along the pile (a) Shaft resistant pile (b) Base resistant pile.

Figure 6. Induced axial stress distribution along the pile (a) Shaft resistant pile (b) Base resistant pile.

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Figure 7. Pile head displacement (a) Shaft resistant pile (b) Base resistant pile.

Induced stress along the pile surface for both shaft and base resistant piles are shown in Figure 6. For the shaft resistant pile, the maximum induced stress in seen in the first cooling period at the bottom of the pile where it has reached up to −8.4 MPa. For the base resistant pile, the maximum induced stress is recorded at 95 mm depth as −5.57 MPa. Pile head displacements under thermal cycles for both shaft and base resistant piles are shown in Figure 7. For the shaft resistant pile, heave is seen during heating and settlement during cooling of the pile. Significant drop is seen during first cooling period where it has gone below the original starting point and again heaving happens due to heating and larger settlement up to 0.22 mm is seen in the second cooling period that shows the degradation of skin friction during heating and cooling cycles. This also explains why the induced load is lower in the second cooling cycle than in the first. Moreover, irreversible settlement is seen and hence, the assumption of perfect thermo-elastic behaviour does not hold. The base resistant pile shows a very similar trend where the maximum settlement is seen during the 2nd cooling period. In response to heave and settlement of the pile in the heating and cooling periods, shaft friction on the pile is mobilized to resist the movement. In order to determine the value of mobilised shaft resistance, the formula by Laloui et al. (2006) is used in this study. Four zones are defined for the mobilized shaft resistance from bottom of the pile between SP1 and SP2 called zone 1 to top of the pile between SP4 and SP5, zone 4.

Figure 8. Mobilised shaft friction at 4 zones along the pile for shaft resistant pile.

Mobilized shaft friction for the shaft resistant pile is shown in Figure 8. During 2 heating periods, higher magnitude of mobilized friction is seen in zones 1 and 3 during 1st heating period and in the 2nd heating period, higher values are seen in zones 2 and 4.

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At the end of cooling periods, higher magnitude of mobilized friction is seen during 2nd cooling periods in all zones except zone 3. This could be due to the higher magnitude of pile head displacements during the 2nd cooling period (Figure 7). Results presented in Figure 8 for shaft resistant pile is compared with the findings by Yavari et al. (2014) for test E2 for a shaft and base resistant pile. In terms of absolute magnitudes, lower magnitude of mobilized friction is seen byYavari et al. (2014), possibly due to the lower magnitude of temperature increase, reaching 35◦ C compared to 50◦ C in this study. Moreover, shaft resistant pile is expected to have higher mobilized friction and use the entire capacity of shaft friction due to the lack of support at the bottom compared to shaft and base resistant model. 5

CONCLUSIONS

A laboratory test for 2 types of shaft resistant and base resistant piles embedded in sand under thermal loading is presented. A novel monitoring technique using Fibre Bragg Grating optical fibre sensors is used to monitor temperature and strain on the pile surface and in the soil bed. It is found that small restraint is applied from the surrounding sand but due to the physical properties of the model pile and also due to the high temperature changes, significant axial loads and stresses are induced in the pile. In addition to compressive forces, considerable tensile force also develops in the pile. Irreversible pile head settlement is also seen for both shaft resistant and base resistant piles. Higher settlements are seen in the second cooling period compared to the first cooling period showing the signs of skin degradation under 2-way cyclic loading that are also evident from the distribution of induced loads at

different cycles. As part of the on-going research, the results presented in this study for thermal only loading will be used to assess the behaviour of piles under thermo-mechanical loading. REFERENCES Al-Mhaidib, A.I. & Edil, T. B. 1998. Model tests for uplift resistance of piles in sand. Geotechnical testing journal, 21(3), pp. 213–221. Bourne-Webb, P., J., Amatya, B., Soga, K., Amis, T., Davidson, C., Payne, P. 2009. Energy pile test at Lambeth College, London: Geotechnical and thermodynamic aspects of pile response to heat cycles. Géotechnique, 59(3), pp. 237–248. Iten, M. 2011. Novel applications of distributed fibre optic sensing in geotechnical engineering. PhD thesis. ETH Zurich. King, G.J.W., Dickin, E.A., and Lyndon, A.1984. The development of a medium size centrifugal testing facilities. Proceedings of The Application of Centrifuge Modelling to Geotechnical Design, Manchester, England, 24–46. Laloui, L., Nuth, M., Vulliet, L., 2006. Experimental and numerical investigations of the behaviour of a heat exchanger pile. International Journal for Numerical and Analytical Methods in Geomechanics, 30(8), pp. 763–781. Parkin, A. K., & Lunne, T. 1982. Boundary effects in the laboratory calibration of a cone penetrometer for sand. Proceeding of 2nd European Symposium on Penetration Testing, Netherlands National Society for Soil Mechanics and Foundation Engineering, May, pp. 761–768. Weinstein, G.M. 2008. Long-term behaviour of micropiles subject to cyclic axial loading. Ph.D. thesis, Polytechnic University, Brooklyn, New York. 373 pages. Yavari, N., Tang, A., M., Jean-Michel Pereira, J. M., Hassen, G. 2014. Experimental study on the mechanical behaviour of a heat exchanger pile using physical modelling. Acta Geotechnica, 9(3), pp. 385–398.

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Temperature dependence of elastic P- and S-wave properties of rocks: Applications to geothermal reservoir evaluation H.B. Motra & F. Wuttke Institute of Geosciences, Marine and Land Geomechanics and Geotechnics, Christian-Albrechts-University, Kiel, Germany

ABSTRACT: The rising cost of energy every year necessitates the development of alternative energy sources, and each development involves disturbance of a natural system, which must be analysed and predicted. Geothermal energy, energy stored within the Earth as heat, is a topic which has garnered attention in the recent past because of its potential as a powerful energy resource. Various models are used to predict the effect of development, but there is an extreme lack of quantitative information in the field of rock mechanics that is essential for this purpose. The thermal effect on rock that limit energy-resource recovery and development can be described briefly; each area need new research studies. In geothermal-energy exploration and production, questions arise concerning temperature and pressure effect on mechanical properties of reservoir rock. The increasing sophistication of seismic wave measurement, processing and recent experimental work on factors governing wave propagation in rocks has stimulated increased interest in the use of active seismic techniques to determine the in-situ physical state of crustal rocks for engineering applications. In this paper, we measured the elastic P- and S-wave velocities and the velocity anisotropy of geothermal core sample considering thermal gradients. The measurements were done at temperatures of up to 600◦ C and confining effective pressures of 100 MPa, corresponding to depths of ∼3000–4000 m. The measurements were carried out in a cubic multi-anvil pressure apparatus, using the pulse transmission technique. The effect of temperature and pressure act in opposite direction on most of rock properties. For example, P (Vp ) and S (Vs ) wave velocities, density, deformation modulus, such as Young’s modulus and bulk modulus, and shear modulus decrease with temperature. In addition, the correlated porosity and permeability with elastic seismic wave show that at increase with temperature. In this paper, we review experimental work showing how wave velocities in rocks are sensitive to parameters of interest to geothermal exploration; effective pressure, temperature, Young’s, bulk, shear moduli . From the results of temperature dependence P and S wave velocities and mechanical properties of rock possible approach to characterisation of geothermal reservoir systems.

1

INTRODUCTION

Reliable estimates of the physical properties of rock are required for exploration of hydrocarbon, geothermal, and mineral reservoirs, as well as for subsurface storage of nuclear waste or CO2 . Temperature is on of the factors that has a significant impact on the change in the mechanical properties of rock. Numerous laboratory measurements, mostly are sedimentary rocks, have been performed to determine the temperature dependence mechanical properties of rocks (R. and Homand 1979, Zhang et al. 2009, Hong et al. 2012, Tian et al. 2016). All these work tested a number of rocks deformation modulus, Poissons ratio, the tensile strength, compressive strength, cohesion and internal friction angle, viscosity, and other parameters and discussed the dependence of lateral pressure and high temperature on thermal expansions as well as the creep characteristics of the rock.

Temperature-dependent properties which may be important include: flow characteristics such as absolute and relative permeabilities; fluid-storage capacity, expressed in terms of porosity, involving such characteristics as bulk and pore compressibility and thermal expansions; properties of importance in well-log interpretation, for example,formation electrical resistivity factor and elastic-wave velocities; mechanical properties such as strength and deformation moduli. In addition, knowledge of the mechanical properties or rocks in high-temperature environments is useful for application of properties of geothermal reservoir characterization (Somerton 1992). There are number of important parameters that influence the mechanical properties of the rock mass like grain size and shape, density, porosity, anisotropy, pore water, confining pressure, temperature, weathering and alteration zones, bedding planes, and joint properties.

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The ultrasonic wave velocities is highly efficient, handy and reflects the mechanical properties of the tested object, which is widely used in rock sample testing. Experiments focussing on the temperature dependence of ultrasonic wave velocities in metamorphic rocks are rare. Laboratory measurement of temperature-dependent ultrasonic wave velocities of rocks at high temperatures have been performed by (Kern 1978, Punturo et al. 2005, Scheu et al. 2006). However, there experiments were not discussed the effect of temperature on the mechanical properties of rocks. Many researchers have found that seismic wave velocities (compressional P (Vp ) and shear wave velocities S (Vs )) is closely related to mechanical properties of rocks (Lama and Vutukuri 1978, Gaviglio 1989, Yasar and Erdogan 2004). In the present work Vp and Vs wave velocities of two core sample taken from area of the active geothermal field of Larderellol, Italy have been measured at elevated temperature and pressure. Results are reported for porosity, density, deformation, deformation moduli, permeability have been calculated in situ condition from Vp and Vs elastic wave velocities. Further, an attempt has been made in the present study is to correlate porosity, permeability, deformation moduli, density with Vp and Vs wave velocities.

2

SAMPLE DESCRIPTION

Two samples from Larderellol, Italy, were investigated. They were collected from the Carboli-11A and Puntone 4B core. The clasts for this analyses were chosen to be as representative as possible, in terms of density and homogeneity/heterogeneity of the Larderellol core. For the experiments cube-shaped specimens with 43 mm edge lengths were cut from these clasts.The orientation of the cube axes followed visible mesoscopic fabric coordinates where possible: X and Y are within

Figure 1. Thin section: Puntone-4B, amphibolite: composed by hornblende, biotite, quartz, plagioclase (opaques, apatite). Hbl-prevailing levels, 3–4 mm thick, regularly alternate to Bt+Qtz-prevailing levels of similar thickness. Grain size is small, planar schistosity.

the plane of magmatic layering (fluid flow), X is parallel to a shape preferred crystal orientation, if present, and Z is normal to the layering. Densities were calculated from mass and dimensions of the cubic specimen, the porosities being derived by mass/volume analysis. Two representative samples selected Puntone-4B (3289.6–3292.6 m depth core), of amphibolite: composed by hornblende, biotite, quartz, plagioclase (opaques, apatite) (Figure 1) and Carboli-11A (3594–3596 m depth core), schist with quartz prevailing on muscovite: an opaque granulation is pervasively dispersed in the rock also enhancing the schistosity. The bulk densities of these cylindrical samples are in good agreement with the densities of the cubic samples. The determined density values range of 2.75–2.91 g/cm3 corresponding to a open porosity range of 28.15–36.96 vol.%. This covers the density range from the most abundant to the maximum density observed for the block-and-ash flow deposits. 3

METHODOLOGY

The elastic VP - and VS -wave velocities and velocity anisotropies of the samples were determined experimentally. The measurements were conducted on cube-shaped specimens in a true triaxial multianvil press using the ultrasonic pulse-transmission technique (Figures 2 and 3). A state of nearly hydrostatic stress was achieved by pressing six pyramidal pistons onto the sample cubes. The special arrangement of the sample-piston-transducer assembly allows simultaneous measurements of compressional (P) and orthogonally polarized shear wave velocities (S1, S2). The end of each piston next to the specimen is surrounded by a furnace and heat is transmitted from the pistons to the specimen, allowing homogenous heating and temperature distribution within the large volume specimens, as has been confirmed by temperature measurements at different places within a test sample (Kern et al. 1997, Punturo et al. 2005, Scheu et al. 2006). Temperature is measured using thermocouples

Figure 2. Schematic draw of the triaxial multi-anvil press used to measure the elastic P- and S-wave velocities. The measurements were performed up to 100 MPa pressure and 600◦ C temperature (Scheu et al. 2006).

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placed in a cavity at the end of each piston very close (∼1 mm) to the specimen. The transducers (2 MHz and 1 MHz) are placed on the low-temperature side of each piston, and the travel time of the pulses through the specimen is obtained by subtracting the calibrated time needed for the pulse to travel to and from the specimen through the pistons from the total time measured by the transducers. Length and resulting volume changes of the sample cubes, due to changes of principal stress and temperature, are obtained by the piston displacement. The cumulative error in VP - and VS -wave is estimated to be around 1% (Kern et al. 1997, Punturo et al. 2005, Scheu et al. 2006, Wenk et al. 2008). 4

RESULTS

VP - and VS -wave velocities were measured simultaneously in the three structural directions. Measurements were performed first at room temperature up

Figure 3. True triaxial multianvil pressure apparatus at Kiel University to investigate mechanical and seismic rock properties at elevated stress and temperature conditions. a) Triaxial (multi-anvil) pressure apparatus for direct measurements of P and S-wave travel times. b) Reference system of a clay sample with regard to the polarisation directions of the various shear waves (see e.g. Kern et al. 1997, Wenk et al. 2008).

to 100 MPa, followed by measurements at the constant confining effective pressure of 100 MPa over the temperature range 20–600 ◦ C. The intrinsic effect of temperature on velocities is hard to determine, due to thermal expansion and the consequent loosening of structure. Figure 4a shows the change of the P-wave velocities and Vp anisotropy of the sample Carboli-11A as a function of temperature at 100 MPa. In addition, P-wave velocities measured in three direction decrease with increasing temperature from 6.32–5.62 km/s at room temperature to 5.03– 5.88 km/s at 600◦ C, it was similar to (Kern et al. 1997, Punturo et al. 2005, Scheu et al. 2006). Furthermore, The velocity anisotropy (A-Vp%) shows an inverse behavior; it increases with higher temperature from 11.63% at room temperature to 15.56% at 600◦ C. In general, the P-wave velocity decrease and velocity anisotropy increase at increasing the temperature for both samples. The mean P-wave velocities of both samples increase from 3,87–4.60 km/s at 20◦ C to 4.21–5.35 km/s at ◦ C. A similar behavior at increasing temperature was observed on the other samples. The Swave velocities show a similar trend. Figures 4b shows the Vs velocities of the sample Carboli-11A as a function of temperature. All three directional Vs velocities decreased from 3.80–3.60 km/s at room temperature to 3.63–3.49 km/s at 600 ◦ C, it similar to (Kern et al. 1997, Punturo et al. 2005, Scheu et al. 2006). Figure 5 shows average curve for theYoung’s E, bulk K and shear µ, moduli of the rock sample Carboli11A as a function of temperature from 20 to 600◦ C. Deviations from the moduli occur with changes in the Poisson’s ratio. This is because of the fundamental linkage between temperature and because of the elastic equations depends on VP - and VS with the elastic, bulk, and shear moduli. Concerning moduli parameter, high Poisson’s ratios give values below the Figure 5, and low Poisson’s ratios give higher values of moduli. Additionally, it is found that the moduli of metamorphic tested rock samples decreases with increasing

Figure 4. Elastic wave velocities as a function of temperature for the sample Carboli-11A. The measurements were carried out at 100 MPa pressure. (a) The compressional wave velocities (Vp) decrease with increasing temperature, whereas the anisotropy (A) increase. (b) The averaged shear wave velocities (Vs) decrease with increasing temperature.

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temperature from 20 to 600◦ C. It is apparent that temperature has a significant effect in decreasing these moduli properties. Furthermore, the mean bulk density, volumetric strain of both samples increase with the increasing the temperature. The mean porosity and

Figure 5. Average curves of Carboli-11A, for the field-scale Young’s E, bulk K, and shear µ moduli, in relation to temperature.

permeability of Carboli-11A is increase at the increasing temperature. In contrast, the mean permeability of sample Puntone-4B is approximately constant at increasing the temperature (Figure 6). It is found that, an average 10% increase in pore volume compressibility of Carboli-11A sample, upon increasing the temperature from room to 600◦ C, which is very close to to Puntone-4B sample observed change in bulk volume compressibility for the same metamorphic rock over this temperature range. Thus, if porosity did not change significantly over this temperature range. For the determination of density, volumetric strain, porosity and permeability, used th correlations function of these parameters wit the VP - and VS -wave velocities, which were measured in the laboratory with the dependence of temperature. The correlation function of porosity and permeability choose from literature of similar type of rock and minerals. In order to investigate the deformation behaviour here also evaluated the axail strain in the three direction and calculated the volumetric strain (see Figure 7). However, comparing the lateral strain parallel to the bedding with the axail strain it is obvious that the expansion behaviour of the sample is dominated by

Figure 6. Average curves for the bulk density, volumetric strain, porosity and permeability, in relation to temperature.

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Figure 7. Temperature-strain curves for Carboli-11A samples in axail and lateral direction.

the axail expansion in direction perpendicular to the bedding plane resulting in an overall expansion. 5

DISCUSSION

In this paper, the effect of temperature of rocks on their physical properties were discussed in details. These are the irreversible changes that occur upon heating rocks to their room temperature. The effects of temperature are considered to be the reversible changes that occur at increasing temperatures. In metamorphic rocks, increasing temperature generally leads to decreasing velocities. The main causes of the velocity change are: temperature dependence of the elastic properties of the rock-forming minerals and phase change of minerals; • temperature dependence of the elastic properties of the pore constituents and change of pore constituents (e.g., pore water) from a liquid to a gaseous state; • changes in the contact conditions at grains, crack boundaries, etc., resulting from variations of the interface effects and/or from different thermal expansion properties of rock-forming minerals. •

The decrease in elastic wave velocities with increased temperature could result in predicting higher porosities in using the time-average relationship. This is contradictory to some evidence that porosity tends to decrease with higher temperatures. The velocity anisotropy can be linked to the texture of the samples. Those with a high anisotropy show a pronounced shape preferred orientation and microcrystal sometimes in addition to layering within the groundmass of the sample. The effect of temperature on elastic and compressibility is substantially higher on the reservoir metamorphic rocks. Differences in mineral composition and lower porosity probably explain the differences in

elastic, bulk and shear moduli, behavior with respect to temperature changes. The mechanical properties of rocks calculation based on the analysis and using elastic wave data, is had measured at high temperature. In general, elastic, bulk shear moduli of the metamorphic rock samples shows decrease with the increasing temperature. It is concluded that moduli of reservoir rocks decreased substantially when pore-fluid pressure is decrease in high temperature reservoir. However, all the laboratory test be made at reservoir in-situ temperature for the propose of determine physical properties of rocks. The presented data set of density, volumetric strain porosity and permeability show that there is a clear trend of increasing porosity with increased for the selected area (Figure 6). The dependence of permeability on porosity, density and volumetric strain is generally explained by the assumption that a more connected pore space of rock matrix (pores and cracks) provides more efficient pathways for the fluid movement. The samples Carboli-11A show higher than average permeability for the these porosity and density, which supports the conclusion of that possibilities of the geothermal fluid migration. The ratio of axial stress and resulting axial strain gives a deformation modulus characterizing the deformation behaviour. Samples show an axial and a lateral deformation; relative change of dimension divided by relative change of axial length in stress direction is Poissons ratio; it represents a second property characterizing the deformation behaviour. The relationship between the Young’s, bulk and shear moduli as well as density, porosity, volumetric strain a nd permeability with elastic P- and S- wave velocities are valuable for understanding a geothermal reservoir evaluation. The data indicates strong correlation between these parameters. This paper consider that presented dataset can help reduce the technical and financial risk of drilling and exploiting deep geothermal drilling by in improving knowledge of the physical parameter in geothermal reservoir characterisation. Therefore, a deeper understanding of how mechanical parameters may be influence the migration fo fluid and change in mechanical parameter with respect to pressure and temperature is important. Knowledge of the mechanical properties at temperature of rock has become insincerely important with the wide-spread interest in physical process in underground geothermal reservoir. For meaningful analyses of mechanical properties, in addition to rock properties and their behaviour in high-temperature environment must be known. Some of these mechanical properties requiring knowledge of high-temperature behaviour of rock system include underground storage heat, disposal nuclear wast and geothermal reservoir evaluation.

6

CONCLUSIONS

Based on the experimental results, it is apparent that the interpretation techniques for the geothermal

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reservoir must take into account the effect of temperature on rock properties. The properties affected by temperature to be discussed include bulk and pore compressibility, P- and S-wave velocities. An example of the potential application of these mechanical properties would be the understanding of the response of a in-situ temperature effect at depth. At the 3000-4000 m depth samples from the potential geothermal reservoir of Larderellol, Italy. The aim of this study is to evaluate the mechanical behavior of rock based on the ultrasonic wave velocities as a function of temperature to serve as host materials to geothermal reservoir investigation. In order to determine mechanical properties of the reservoir rocks tested two core sections from the well at a safe depth, as well as using existing cores from metamorphic basement. This offered the opportunity to perform petrophysical laboratory analyses on core samples so as to define important mechnical characteristics of the reservoir host rocks, in particular seismic P- and S-wave velocities, physical and geomechanical properties. Rock samples were carried under simulated in-situ conditions at the high-pressure, high-temperature by in a cubic multianvil pressure apparatus, using the pulse transmission technique. Based on the results of this study, further investigation on laboratory measurement of permeability and porosity under in-situ temperature and pressure is necessary. The effect of the temperature on elastic wave velocities is one of the major issues to be investigated. Furthermore, the influence of temperature on the mechanical and chemical properties of rocks need to be further analysed and will be the topic of future work. REFERENCES

Hong, T., T. Kempka, X. Neng-Xiong, & M. Ziegler (2012). Physical properties of sandstones after high temperature treatment. Rock Mech. Rock Eng. 45, 1113–1117. Kern, H. (1978). The effect of high temperature and high confining pressure on compressional wave velocities in quartz-bearing and quartz-free igneous and metamorphic rocks. Tectonophysics. 44, 185–203. Kern, H., B. Liu, & T. Popp (1997). Relationship between anisotropy of p and s wave velocities and anisotropy of attenuation in serpentinite and amphibolite. Journal of Geophysical Research-Solid Earth. 102, 3051–3065. Lama, R. & V. Vutukuri (1978). Handbook on Mechanical Properties of Rocks. Clausthal: Trans. Tech. Publications. Punturo, R., H. Kern, R. Cirrincione, P. Mazzoleni, & A. Pezzino (2005). P- and s-wave velocities and densities in silicate and calcite rocks from the peloritani mountains, sicily (italy): The effect of pressure, temperature and the direction of wave propagation. Tectonophysics. 409, 55–72. R., H. & E. Homand (1979). Influence of temperature on the mechanical behavior of rocks. Proc. 4th Int. Cong. Rock Mech., Montreux. 110, 115–122. Scheu, B., H. Kern, S. O., & D. Dingwell (2006). Temperature dependence of elastic p- and s-wave velocities in porous mt. unzen dacite. Journal of Volcanology and Geothermal Research. 153, 136–147. Somerton, W. (1992). Thermal properties and temperaturerelated behavior of rock/fluid systems.Amsterdam: ELSEVIER. Tian, H., T. Kempa, S. Yu, & M. Ziegler (2016). Mechanical properties of sandstones exposed to high temperature. Rock Mech Rock Eng. 49, 321–327. Wenk, H., M. Voltolini, H. Kern, T. Popp, & M. Mazurek (2008). Anisotropy in shale from mont terri. Leading Edge. 1, 742–748. Yasar, E. & Y. Erdogan (2004). Correlating sound velocity with density, compressive strength and youngs modulus of carbonate rocks. Int. J. of Rock Mechanics and Mining Sciences. 41, 871–875. Zhang, L., X. Mao, & A. Lu (2009). Experimental study on the mechanical properties of rocks at high temperature. Science in China, Series E: Tech. Sci. 1, 979–985.

Gaviglio, P. (1989). Longitudinal wave propagation in a limestone: the relationship between velocity and density. Rock Mech Rock Eng. 22, 299–306.

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Inverse-volume pore pressure projection technique for the coupling of reservoir flow and geomechanics simulators P.E. Vargas & N.A. González Repsol Technology Centre, Móstoles, Madrid, Spain

C.N. Mena Paz, M. de Bayser & P.W. Bryant IBM-Research, Río de Janeiro, Brazil

J.M. Segura & M.R. Lakshmikantha Repsol Technology Hub, The Woodlands, Texas, USA

ABSTRACT: Coupling geomechanical reservoir models with fluid flow models improves accuracy when simulating phenomena relevant to production forecast, drilling and well integrity, and environmental impact (e.g. fault reactivation). A geomechanical model provides to a hydrodynamical model updated values of pore volume and permeability, and a hydrodynamical model in turn provides to a geomechanical model updates to the pore pressure, which then alters effective stress. The main challenge in coupling is the exchange of data. This work presents three different pore pressure projection schemes used for data exchange, that are based on weighted averages (inverse distance, volume, and by inverse of the volume). To validate the three methods, the pressure projected was compared with a hydrostatic pressure distribution while accounting for changes in the size of the surrounding cells of the hydrodynamical model. The weighting by the inverse of the volume shows the better agreement with hydrostatic pore pressure distribution of the three techniques presented. As a further demonstration, the three methods were compared within a small reservoir model with varying cell sizes, and the inverse volume method performs favorably. Finally an extension to the inverse volume method was developed, in which permeability is included in the weighting factors. Its effect is demonstrated in a benchmark system including both a reservoir and a nonpay region.

1

INTRODUCTION

Diverse scenarios require incorporating geomechanics effects into petroleum engineering analyses, leading to coupled geomechanics-reservoir modeling of the stress and pressure changes within one framework. The main challenge in coupling is implementation of data exchange (stresses & strains, and pore pressure data for both matrix and fractures) between the geomechanics and the flow simulator. Coupling of fluid flow and geomechanics models provides an accurate representation both of the dynamic model based on a geomechanics-guided update of pore volume and permeability, and of the geomechanical analysis based on an effective stress update. The geomechanical and the flow systems are coupled via the pore pressure term in the mechanical equilibrium equations and the time derivative of the volumetric strain in the flow equations, and also by the possible dependence of the material parameters like permeability and/or porosity with the stress state in the porous medium. The coupled problem can be solved

using iterative algorithms that require the resolution of fluid flow within a ‘reservoir simulation’ and also of a geomechanical ‘stress simulation’. The iterative algorithm is based on data exchange between the two simulators (see Fig 1). First the reservoir simulator provides the pressure changes to the stress simulator. The pressure change is transformed into loads in the stress simulator which computes in turn the resulting stress and strain changes. Stability of coupled formulations is extensively discussed in the literature by Hughes et al. (1986) and in the specific context of geomechanics by Haga (2011), Kim et al. (2011), Murad et al. (1994) and Wan et al. (2003). A scheme is required to transfer the pore pressure (from the flow simulator), calculated at the center of the cell, to the nodes (of the geomechanical simulator) of the finite element mesh. This transfer is known as Pore Pressure Projection. This work presents three different methods for pore pressure projection: inverse distance, volume average and inverse volume method. These names describe the weighting factor used to project pressure values

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Figure 1. Data exchange between flow simulator and geomechanical simulator for coupled models.

from cell centers to the nodes. For the inverse distance method the weighting factor is the distance between block-centered data and the nodal data. For the volume average and the inverse volume the weighting factor is determined by the sub-volumes that surround a node. The inverse volume method divides the finite element into sub-volumes according to the number of nodes of the element, associates each node to its corresponding sub-volume and pore pressure values, and finally computes the pore pressure by clustering around each element node weighted by the inverse volume.

Figure 2. Pressure projection scheme: Relation between the finite element mesh and the finite volume grid. Cell centered values indicated with the gray circles. Nodal values indicated with black circles.

The discrete space Wh is made up of continuous linear functions on τh , such that the pressure field is given by

2 TECHNIQUES TO PROJECT PORE PRESSURE Fluid flow and geomechanical simulations represent the domain as a grid of discrete cells. However, the Finite Volume Method (FVM) employed by fluid simulators calculates properties such as pressure at the centers of cells whereas the Finite Element Method (FEM) used by geomechanical simulators calculates forces and displacements at the corners (also called nodes). Therefore even if both grids coincide spatially the pressures that the FVM calculates at cell centers must be interpolated, or projected, to cell corners. In a hexahedral grid each corner is shared by up to eight cells and the pressure at this point is related to the pressures of these cells. Figure 2 shows the relation between the finite element mesh in which the mechanical problem is solved and the finite volume mesh in which the flow problem is solved. For simplicity we show the two dimensional (2D) case considering quadrilateral elements. The dashed arrows indicate where the cell-centered value would be included in the computation of the nodal values when a projection scheme is applied. Some schemes of pore pressure projection require the resolution of a linear system. An example is the L2 (
) projection, which is a natural option if a nodal value for the pressure is needed for accuracy or stability reasons. In this case the problem to be solved reads: ∼ Given ph ∈ P0 (τh ), find ph ∈ Wh such that ∀qh ∈ Wh

∼

From Equation 1 and the expression of ph in terms of the nodal basis functions N j , a linear system of equations in the nodal pressure coefficients and involving a mass matrix, is obtained, i.e.,

where each component of the mass matrix and the right hand side read

Possible variations that avoid the cost of solving a full linear system are to use a technique known as lumping of the mass matrix M (Bathe et al. 1976), in which the mass matrix is approximated by a diagonal matrix, or to use more simplified weighted averaging techniques, such as volume average, inverse volume and inverse distance. The projection of pore pressure from cell centers to the nodes with a weighted technique is calculated for known values (fi ) as:

where n = number of points with known values; fi = known value at point i; and wi = weight assigned to each point and defined in Sections 2.1, 2.2 and 2.3.

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Figure 4. Subdivision of cell with known center-cell pressure Pi in sub-volumes for Vertexk . Figure 3. Distance between point P and location of known values (P1, P2, P3 and P4).

The weighting factor wi (see Eq 5) is defined as

In the following subsections are described the weighting factor for inverse distance, volume weighted average and inverse of volume techniques.

2.1

where V = associated sub-volume to the known value Pi (see Fig 4).

Inverse distance

In the inverse distance technique the pore pressure at vertex P (see Fig 3) is calculated using a weighted average of the available values defined at the centers of the cells (P1, P2, P3 and P4). Shepard (1968) and Lam et al. (1983) define the weighting factor wi (see Eq 5) as

where d = distance between interpolation point and location of known value (see Fig 3). Explicitly, the distance in three dimensions is

2.3 Proposed Inverse volume weighted average The inverse volume technique uses the same definition of the sub-volume as in Section 2.2 (see Fig 4), and the weighting factor wi (see Eq 5) is defined as:

3 VALIDATION OF TECHNIQUES 3.1 Projected value, a matter of space location

where (x, y, z) = interpolation point coordinates and (xi , yi , zi ) = data point coordinate.

2.2 Volume weighted average In the volume weighted average technique, the pore pressure at each vertex is computed using sub-volumes (see Fig 4) for each concurrent element to the vertex in the model.

Figure 5 shows two different meshes with the same cell-center points P1, P2, P3 and P4. Pore pressure values at these points are known from theoretical variation or from a flow simulator. Figure 5 also exhibits points Pa and Pb with unknown values.These points correspond to the upperright vertex of cells with center located at P1. Depending on the mesh, the location of the upperright vertex of the shaded element (Pa or Pb) may vary, and therefore the pressure projected to this point (Pa or Pb) through the projection of the known cell-centered pressures may vary as well.

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Figure 5. Four center cell points P1, P2, P3 and P4 with known pressure in two different meshes. Hatched/shaded area corresponds to a cell with known pressure at center (P1) but unknown pressure at respective vertex Pa or Pb.

Figure 7. Theoretical values for hydrostatic pore pressure distribution in normalized space (rx , rz ) and pore pressure projected values based on theoretical values at corners, computed with three different techniques (inversed distance, inverse volume and volume).

Figure 6. Definition of normalized coordinates ri based on center-cell location of cells (P1, P2, P3 and P4) and location of upper-right vertex of shaded cell (P) in 2D system of coordinates.

Normalized coordinates (rx , ry , rz ) are used in the following sections to localize a projected value at given point P (see Fig 6).

When P is centered vertically between line P1-P2 and line P4-P3 (ry = 0.5) and centered horizontally between line P1-P4 and line P2-P3 (rx = 0.5), the projected value will be at the coordinate (rx = 0.5, ry = 0.5) inside the normalized space. The normalized axis ri is 0 when the length in i-axis (li ) is very small with respect to a neighbor cell length, and 0.5 when the length in i-axis is the same as that of the neighbor cell (Li = 2li ). 3.2

Projected values with different techniques

The techniques defined in Sections 2.1, 2.2 and 2.3 were applied in order to obtain projected values based on eight cell-centered pore pressure known values. The known pore pressure values follow from a hydrostatic pore pressure distribution. Values computed with each technique are shown in Figure 7 using normalized coordinates (rx , rz )

(see Eq 10). Also shown are the theoretical values for the hydrostatic pore pressure distribution in the normalized space (rx , rz ). The pore pressure distribution computed with the inverse volume technique show good agreement with theoretical values. The pore pressure distribution computed with inverse distance technique show agreement in the middle, close to rz = 0.5. The pore pressure distribution for the direct volume technique also shows good agreement only in the rz = 0.5 region.

3.3 Error analysis of projected values The values computed in section 3.2 were compared with hydrostatic pore pressure in order to evaluate the range of usability of each technique described in section 2. Figure 8, shows the error of the projection techniques (see Fig 7) when compared with the hydrostatic pore pressure distribution. The normalized axes rx and rz correspond to Equation 10. Figure 8 exhibits very good agreement (error less than 5%) between the pore pressure distribution resulting from the inverse volume projection technique and hydrostatic pore pressure distribution for all rz values. The inverse distance projection technique and the volume projection technique show good agreement only for rz values close to 0.5. In other words, when the heights of two neighboring cells are very similar the results are in good agreement with a hydrostatic distribution. When the heights are not similar, the error

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Figure 9. Reservoir geometry and position of vertical line of cells.

Figure 8. Error computed in normalized space (rx , rz ) for projected values using three different techniques (inverse volume, inverse distance and volume) with respect to the theoretical hydrostatic pore pressure distribution.

in the projected value may reach between 5% and 40% of a hydrostatic pore pressure distribution. 4

SYNTHETIC EXAMPLE

4.2 Comparison of results

Pore pressure projection techniques defined in Section 2 are applied to a small reservoir model that has diverse cell sizes to illustrate the geometrical weighting. 4.1

Figure 10. Pressure at nodes and cells of vertical line.

Description of the model

The reservoir contains a single vertical well (wellbore radius 0.5 ft) in the center, completed in all reservoir layers with production of 50,000 STB/D for 4,000 days. The 20 first and the last 18 time steps have a duration of 20 and 200 days each, respectively. The grid is 11 cells long in the X and Y directions and 5 cells high, as shown in Figure 9. In the X and Y directions the cells close to the well are smaller giving a higher resolution at a point where the simulation results in a more dynamic pressure state. In Z the cells are also smaller in the middle layers. The three different pressure projection procedures were tested on the 20th simulation step where there are already marked differences in the pressure distribution. The results are evaluated along a vertical and a horizontal line of cells in the reservoirs. The different heights in the model (see Fig 9) allows to capture the variation of results for each pore pressure projection technique applied.

4.2.1 Vertical pressure distribution Figure 9 also shows the vertical column of cells (in red) where the pore pressure is extracted for a comparative analysis. Figure 10 shows pore pressure projected values at vertices and the known values at the centers of the surrounding columns of cells. Projected values were computed with the techniques described in Section 2. Figure 10 shows that the inverse volume technique has the smoothest curve in between the curves of the cell centers, while the other two techniques show considerable variation. A divergence is observed at boundary cells due the lack of information to project values at the boundary of the model. Projected values with the inverse of distance or the direct volume techniques suffer a shift because of the irregularity of the mesh in z-axis. 4.2.2 Horizontal pressure distribution Figure 11 shows the horizontal row of cells (in red) where the known pore pressure is extracted in order to compare with the projected values using the techniques defined in Section 2. Figure 12 shows pore pressure projected values at vertices and the known values at the centers of cells.

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Figure 13. Variation of projected pore pressure in Vertex k, based on known cell-centered values Pi and Pj and their corresponding permeability (κi and κj).

Figure 11. Location of horizontal line of cells.

5.1 Proposed petrophysical weighting method Equation 11 shows the proposed petrophysical weighting scheme.

where pj is the pressure at node j. Each node j has associate a set of adjacent elements τj . Each adjacent element k in τj , has its own pressure Pk at center of the cell, sub-volume Vk (see Fig 4), and permeability norm ||κk || computed as

Figure 12. Pressure at nodes and cells of vertical line.

Projected values were computed with the techniques described in Section 2. Figure 12 exhibits that the inverse volume technique results in the best agreement with values at vertices regarding cell-centered known values. The inverse distance projection method and direct volume projection method give values different from those at the midpoints.

5

INFLUENCE OF PETROPHYSICAL PROPERTIES IN PORE PRESSURE PROJECTION

Weighting by permeability introduces petrophysical parameters into the otherwise geometrical scheme. By choosing weights proportional to permeability, pressure cells within regions of high permeability are more significant than those within regions of low permeability. In regions where the permeability field is homogeneous or nearly homogeneous, projection results are identical or nearly identical to purely geometrical methods (see Fig 13), respectively. 5.2 Application of proposed method

The numerical schemes used to solve the hydrodynamical equations tend to be relatively less accurate in regions of low permeability than in regions of high permeability. Also it is important to take into account that different values of permeability between neighbor cells (see Fig 13) could generate variation in projected pressure as well. Because of these shortcomings, a heuristic adjustment to the cell-to-node pressure projection method is proposed (Repsol/IBM, 2015), in which the norm of the permeability field is used as a weighting factor in the computation of nodal pressure.

Pore pressure projection techniques defined in Section 2 together with the petrophysical weighting scheme (Eq 11) are applied to a system comprised of a reservoir embedded within a nonpay region, and the projected values computed with these techniques are analysed. 5.2.1 Description of the model The reservoir contains a single vertical well (wellbore radius 0.25 ft) in the center, completed in all reservoir layers with production of 50,000 STB/D for 4,000 days. The grid geometry for the model is shown in Figure 14. The reservoir is highlighted in red.

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Figure 16. Comparison of Methods for Pore Pressure Projection: Subsidence at surface of the model; Dual Porosity And Multilaminate Model.

Figure 14. Grid geometry of the synthetic example (Dean et al. 2006).

Figure 17. Comparison of Methods for Pore Pressure Projection: Subsidence at top of the reservoir; Dual Porosity And Multilaminate Model. Figure 15. Comparison of Methods for Pore Pressure Projection: Average Reservoir Pressure; Dual Porosity And Multilaminate Model.

The grid geometry is equivalent to one published by Dean et al. (2006) excepting for the dual porosity model used in this work. As a consequence, to treat both the fractures and the matrix in the hydrodynamic model the number of grid-blocks in the Z direction is doubled from 12 in the original grid to 24. The well is also as published in Dean et al. (2006) but is connected only to the fracture cells. Horizontal and vertical permeabilities of the fractures within the reservoir are 100 mD and 0 mD, respectively. Horizontal and vertical matrix permeability values are 0.001 mD and 0.0001 mD, respectively. The dual porosity matrix-fracture coupling factor, σ, is 0.0076 ft-2 (Kazemy et al. 1976 & Schlumberger 2016). Outside the reservoir the permeability is zero. This benchmark case was run coupled with a fractured geomechanical, multi-laminate constitutive model. The reason for this approach is that in fractured models the permeability has a great impact on fluid flow and, in turn, pressure changes greatly influence the closure of fractures, which translates directly to a reduction in permeability in the fluid model.

In the geomechanical model, the material of nonproduction areas is stiff and not fractured. Rock mechanics properties are as follows: Poisson ratio is 0.25, and the initial in-situ density of the solid material is 2.7 g/cm3 . Within the reservoir the elastic modulus is 1e4 psi and outside the reservoir it is 1e6 psi, and the compressibility inside the reservoir is 1.5e4 psi−1 . Each cell has exactly one horizontal fracture family consisting of one fracture with an initial aperture equal to 0.0217 inches which results in an permeability of 0 mD in Z and 100 mD in X and Y according to Poiseuille flow assumption (Snow, 1965), shown in equation (13). The geomechanical mesh coincides spatially with the fluid simulation grid. The permeability of a fracture family is related to the permeability of a single fracture by

where a is the aperture size, s is the fracture spacing, and f is the fracture frequency. 5.2.2 Results In figures 15, 16 and 17 we can see the average pressure and the measured subsidence at the surface and at the top of the reservoir, with respect to simulation time,

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respectively. From the results we can see that although the three geometrical weighting methods resulted in different pressure profiles locally, at the global scale they behave similarly. However, to assess the impact of permeability weighting, we also ran the test with the inverse volume technique but with permeability weighting excluded. We can see that this resulted in different pressure and subsidence curves. 6

CONCLUDING REMARKS

Pore pressure projection is a fundamental task for petroleum engineering analysis when passing coupled information between the cell-centered values of flow simulators and the nodal values of geomechanical simulators. Three pore pressure projection schemes based on weighted averages were described in this work, inverse distance, volume, and inverse of the volume. Validation of these schemes showed that inverse volume weighted average has the best agreement when a hydrostatic pressure distribution is applied while accounting for changes in the size of the surrounding cells of the hydrodynamical model. Inverse distance and volume projection schemes shown good agreement only when the size of surrounding cells are very similar, when the heights in neighbor cells are not similar, the error in the projected value may reach between 5% and 40% of a hydrostatic pore pressure distribution. Evaluation of three pressure projection schemes accounting for both geometrical factors and petrophysical factors were performed. Testing on various systems indicates that the inverse volume weighting produces superior results and that weighting by permeability is indeed significant.

Hughes T.J.R., Franca L., Balestra and M. A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuka Brezzi condition. A stable Petrov Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comput. Methods Appl. Mech. Engrg., 59:85–99, 1986. Kazemi, H., Merrill Jr., L.S., Porterfield, K.L., and P.R. Zeman. 1976. Numerical simulation of water-oil flow in naturally fractured reservoirs, SPE-AIME Fourth Symposium on Numerical Simulation of Reservoir Performance, Los Angeles, CA, USA, SPE-5719-PA. Kim J., Tchelepi H.A., and Juanes R. Stability and convergence of sequential methods for coupled flow and geomechanics: Fixed-stress and fixed-strain splits. Computer Methods in Applied Mechanics and Engineering, 200:1591–1606, 2011. 20 Lam, N.S-N. 1983. Spatial Interpolation Methods: A Review. Cartography and Geographic Information Science 10 (2): 129–150. Murad M.A. and Loula A.F.D. On stability and convergence of finite element approximations of Biots consolidation problem. Comput. Methods Appl. Mech. Engrg., 37: 645–667, 1994. Wan J., Durlofsky L.J., Hughes T.J.R., and Aziz K. Stabilized finite element methods for coupled geomechanics reservoir flow simulations. SPE Res Simul Sym (SPE 79694), Houston, 3–5 Feb., pages 85–99, 2003. Repsol/IBM, 2015. Method of managing petro-chemical reservoir production and program product therefore. Patent filed in Europe and US. IBM Ref.: YOR920140126US1. REPSOL Ref.: PA00179 Schlumberger. 2016. Eclipse Black Oil Simulator Reference Manual. Shepard, Donald (1968). “A two-dimensional interpolation function for irregularly-spaced data”. Proceedings of the 1968 ACM National Conference. pp. 517–524. Snow, D. 1965. A parallel plate model of fractured permeable media. Ph.D. thesis, University of California, Berkeley, CA, USA

REFERENCES Bathe, K. J., & Wilson, E. L. 1976. Numerical methods in finite element analysis. Haga C.J.B. Numerical methods for basin-scale poroelastic modelling. Ph.D. Thesis, Univ. of Oslo, 2011.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Axisymmetric transient modelling of a suction caisson in sand: A numerical study B. Cerfontaine, F. Collin & R. Charlier Geomechanics and Engineering Geology, University of Liege, Belgium

ABSTRACT: This paper deals with the axisymmetric behaviour of a suction caisson installed in sand upon vertical monotonic and cyclic loading. A steel caisson is numerically modelled using the finite element code LAGAMINE. The Prevost model reproduces the cyclic behaviour of the soil, i.e. it captures the accumulation of deformation and pore water pressure within the soil. Coupled interface finite elements allow the modelling of the uplift behaviour of the caisson in both drained and partially drained conditions. Upon compression or traction loading, the suction caisson presents different modes of resistance: friction along the shaft, bearing capacity under the lid or the tip of the caisson, suction effect. The first part of this work describes the progressive mobilisation of these modes of resistance during monotonic simulations. The partially drained effect is particularly interesting since it drastically increases the resistance to transient loading. It proceeds from the transient consolidation process induced by the caissons loading. The second part describes the evolution of the settlement of the suction caisson upon different kind of cyclic loading signals. 1

INTRODUCTION

Offshore wind energy is a keystone in the struggle against global warming and the total offshore capacity is strongly increasing. Foundation design is a crucial issue to ensure economic viability of offshore projects and may represent up to one third of their total cost (Byrne and Houlsby 2003). Therefore there is a real need of innovative foundation techniques and design procedures. Among different types of foundations, suction caissons, also termed bucket foundations or suction anchors should be highlighted (Iskander et al. 2002, Houlsby et al. 2005). They consist of a hollow cylinder open towards the bottom. Their top (the lid) can be a stiffer plate or a dome. Installation of suction caissons is straightforward and does not require heavy equipment. Initially the caisson penetrates the seabed under its own weight. Water trapped inside is allowed to escape through an opening. It is pumped out afterwards, creating a differential of fluid pressure between inside and outside as shown in Figure 1. This differential of pressure digs the caisson into the soil (Senders and Randolph 2009). The foundation type may be monopod or multipod. In the first case, there is a single foundation per wind turbine subjected to a combination of horizontal and overturning moment (Achmus et al. 2013). In the second, the superstructure lies on a system of foundations. The large overturning moment is mainly transformed into a push-pull loading of the suction caissons (Senders and Randolph 2009). Therefore the behaviour of the caisson under large extraction load is one of the main issues (Houlsby et al. 2005).

Figure 1. Sketch of the installation process.

The cyclic nature of the loading complicates the problem since the behaviour of sand in this case is quite complex. It is widely studied in the fields of earthquake (Ishihara 1996) and offshore geotechnics (Rahman et al. 1977). The main outcome is the pore water pressure (PWP) and settlement accumulations with increasing number of cycles. This general behaviour is also observed for suction caissons experimentally (Kelly et al. 2006) and numerically (Cerfontaine et al. 2015). Therefore the modelling of this sand behaviour requires specific constitutive laws. This paper presents numerical drained and partially drained simulations of monotonic and cyclic loadings of a suction caisson embedded in dense sand upon vertical loading. The first objective is the deep understanding of the different mechanisms of resistance of

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the caisson upon monotonic loading and their interactions. The second objective is to understand the cyclic behaviour of suction caissons in the light of their monotonic response.

2 2.1

NUMERICAL MODEL Geometry

A sketch of the investigated suction caisson is provided in Figure 2. The studied behaviour is purely vertical then the mesh is axisymmetric. The cross section of the caisson is assumed circular. The diameter D of the caisson is equal to 7.8 m and its length L to 4 m. The caisson is made of a stiff lid (0.4 m thick), closing its upper aperture, and a more flexible skirt (0.1 m thick). The behaviour of sands is inherently non-linear and involves plasticity effects such as contractancy and dilatancy. Therefore elastic models are not sufficient. Classical elasto-plastic models are able to reproduce the monotonic behaviour of sands but not the cyclic one, involving plasticity during loading and unloading. The Prevost model is adopted in the following (Yang et al. 2003). This model is made of a yield and an arbitrary number of hardening surfaces discretising the field of hardening moduli. It takes into account the phase transition described in (Ishihara 1996). The evolution of the stiffness parameters with confinement (p′ ) is introduced. A full description of the model implementation into the finite element code LAGAMINE and calibration of parameters can be found in (Cerfontaine 2014). These parameters correspond to a very dense Lund sand (Ibsen and Jacobsen 1996). The phase transition line slope η¯ is equal to 1.15 and a cohesion shift pc to 5 kPa. The superficial sand layer outside the caisson is prone to liquefaction due to its low confinement. However modelling its post-liquefaction is meaningless in the scope of this study since it does not contribute significantly to the resistance of the foundation. It is modelled by a linear elastic soil layer (E, ν) = (10 MPa, 0.15). The depth of this layer is limited to 0.8 m. It includes the first two rows of elements. Similarly an elastic toe is also set up under the tip of the caisson as shown in Figure 2. It compensates the overestimated width of the skirt. A detailed justification of this approximation can be found in (Cerfontaine et al. 2015). The soil is assumed to be a very dense sand (relative density of 90%). The specific weight of the solid grains is equal to 26.5 kN/m3 , the porosity of the soil to 0.36 and its permeability to 5 · 10−12 m2 (corresponding to 5 · 10−5 m/s) (Andersen et al. 2008). The caisson is made of steel and assumed to remain elastic-linear. Its parameters are equal to (E, ν) = (200 GPa, 0.3). The 26 m × 24 m mesh is composed of 2364 hydromechanical coupled finite elements and 7085 nodes. A description of these elements can be found in (Gerard et al. 2008). Hydro-mechanical interface elements are

Figure 2. Zoom on the mesh adopted around the caisson.

Figure 3. Sketch of the loading applied to the caisson and initial stresses.

set up between the soil and the caisson. The installation phase of the suction caisson is not considered. 2.2 Boundary conditions and initial stresses The lower limit of the mesh is deemed impervious, i.e. it corresponds to a layer of consolidated clay under the sand layer for example. The right and upper sides of the mesh are considered drained. They respectively correspond to the continuity of the sand layer and to the transition between the sand layer and the sea. The sea level is considered to be 10 m over the sand layer. It is taken into account by a vertical pressure of 100 kPa applied at the top of the soil, as represented in Figure 3. The corresponding initial pore water pressures (PWP) are set up accordingly in the whole domain. Effective stresses are initialised within

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the soil (and the interface), due to its self weight. The coefficient of earth pressure at rest K0 is assumed equal to 1. 2.3

Loading of the caisson

The loading of the caisson consists of a stresscontrolled signal applied at the top of the lid, as shown in Figure 3. Monotonic loading is simply a positive (compression) or negative (traction) pressure applied uniformly at a constant rate. The cyclic loading is a more complex pressure signal and is described in the following. 2.4

Interface elements

The accurate modelling of suction caissons necessitates the use of hydro-mechanical coupled finite elements of interface. From a mechanical point of view, the soil-caisson shearing along the skirt is important especially in traction. In compression, the top of the caisson is in contact with the soil but this contact may be lost during the simulation and soil-caisson tractions can not exist. From the hydraulic point of view, the evolution of the PWP along the walls of the caisson modifies the maximum shearing available. Moreover the opening of a gap along the skirt introduces preferential paths for water flows. The interface element is extensively described in (Cerfontaine et al. 2015). The mechanical contact is enforced through a penalty method such that

where p˙ ′N is variation of effective contact pressure, KN a penalty coefficient (equal to 1010 N/m3 ) and g˙ N the variation of the distance between two sides of the interface. The effective contact pressure is obtained from the following relation

where pN is the total pressure at the soil-caisson interface and pw is the water pressure. The maximum shearing resistance is bounded by

where µ is the friction coefficient, equal to 0.5. When this maximum shear stress is reached, there is a free relative tangential displacement between the two sides of the interface. 3

Figure 4. Comparison of reaction components: Compression load Ftot .

MONOTONIC LOADING

Figure 5. Drained compression simulation: Variations of global reaction components.

diverge from their initial value. However the simulation is not undrained and they are able to dissipate progressively. A positive or negative variation of vertical load applied to the caisson is balanced by different components of reaction, described in Figure 4 in case of compression. The variation of total load applied on the upper part of the lid of the caisson is termed Ftot . The integral of the variation of PWP distribution on the lower part of the lid of the caisson is represented by Fpw . The integral of the effective normal contact stresses on this lower part are gathered into Flid . The integral of the variation of shear stresses along the skirt of the caisson is denoted Fin inside and Fout outside. In the following they are depicted with respect to the displacement of the top center of the caisson y. Stress-controlled simulations are carried out up to the local failure of a material point or to the global failure of the soil-caisson system. The post-failure behaviour of the system of foundations is not represented. Thence the maximum displacement remains limited. 3.1 Compression simulations

Two configurations of monotonic loading are considered : drained and partially drained. In the former, the loading rate is assumed very slow with respect to the PWP dissipation rate within the soil. Therefore the PWP are constant. In the second case, PWP generated

3.1.1 Drained configuration Drained results upon compression load are provided in Figure 5. The simulation underlines the sequential mobilisation of the reaction components. Up to 4mm of settlement, the main part of the total load Ftot

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Figure 6. Comparison of the settlement of the caisson and the surrounding soil for Ftot =4.3MN: Drained simulation.

Figure 7. Partially drained compression simulation, k = 5 · 10−12 m2 , rate of loading 0.4 MN/s: Variations of global reaction components.

applied to the caisson is sustained by the shearing that develops along the sides of the caisson. However shear stresses within the interface progressively reach their maximum value. Friction is not mobilised simultaneously on both sides of the skirt. Indeed, the soil-caisson relative displacement is lower inside since the soil settles with the caisson as depicted in Figure 6. This is due to the effect of the load transferred by the lid of the caisson and the shear mobilised depends on the soilcaisson relative displacement. Another consequence is the increasing confinement of the soil inside. Therefore the Fout component firstly reaches its maximum value but this latter increases due to the increasing confinement. Finally, further increments of total load applied are reported mainly under the lid and the tip of the caisson. 3.1.2 Partially drained configuration A partially drained compression simulation is illustrated in Figure 7. The total load is increased up to 4.3 MN at a rate of 0.4 MN/s and kept constant afterwards. The soil-caisson system is much stiffer in partially drained than in drained conditions. The displacement required to reach the same load is almost half in the partially drained simulation. This is due to the new component of reaction induced by the PWP generation Fpw . The loading compression of the suction caisson is nothing but a classical consolidation process. Variations of PWP are “trapped” inside the caisson due to its skirt, limiting their dissipation. The variation of the field of PWP generated within the soil upon a compression load is illustrated in Figure 9. The difference of pressure between inside the caisson and outside it is at the origin of Fpw . During the compression phase, the outer shearing Fout and suction Fpw are the main contributors to the resistance of the caisson as depicted in Figure 7. Indeed, the PWP inside are not yet dissipated and the behaviour is almost undrained. Therefore there is

Figure 8. Comparison of the settlement of the caisson and the surrounding soil for Ftot = 4.3 MN: Partially drained simulation.

nearly no effective stresses transferred by the lid to the soil and the relative displacement between the soil and the skirt is almost null inside as shown in Figure 8. The increasing of tip Ftip , lid Flid and inside shearing Fin components is delayed when the early generated PWP dissipate. At the end of the pushing phase, the PWP have time to dissipate and the settlement increases while the total load is kept constant. The load sustained by Fpw is transferred to the other components of resistance. The normal effective stress within the interface also increases du to the drainage process. Therefore the maximum value of shearing components also increases. This illustrates that the increase in stiffness and resistance is a purely transient effect. 3.2 Traction simulations In Figure 10, the pull drained simulation illustrates that only the two components of friction Fin and Fout ,

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Figure 9. Variation of the pore water pressure in the soil surrounding the caisson upon compression, partially drained case, Ftot = 4.3 MN, k = 5 · 10−12 m2 , rate of loading 0.4 MN/s.

Figure 11. Partially drained traction simulation: Variations of global reaction components, rate of loading 0.4 MN/s.

Figure 12. Influence of the permeability on partially drained results, pull rate 0.4 MN/s. Figure 10. Drained traction simulation: Variations of global reaction components.

actively contribute to the resistance to traction. The variation of Ftip is only due to the deconfinement of initial stresses and does not play an active role in the resistance. The contact is lost under the lid and effective traction stresses are not admissible. Therefore the lid component Flid is equal to zero. The difference of stiffness between inner and outer friction components proceeds from the uplifting movement of the soil inside the caisson. The relative soil-caisson displacement is reduced and so is the shear stress mobilisation. The outer friction is fully mobilised after an upward movement of 1.5 mm and a plateau is reached in Figure 10. Therefore the increasing load is sustained only by the mobilisation of shear stress within the inner interface. Simulation stops when it is fully mobilised and no additional load can be sustained. The partially drained simulation depicted in Figure 11 illustrates the increase of resistance obtained

by considering the fluid flow surrounding the caisson. Indeed, if the loading rate of the caisson is equal to 0.4 MN/s, the total load sustained for a displacement of −1.5 mm is increased by almost 50%. This phenomenon is supported by experimental (Byrne and Houlsby 2002) and numerical (Thieken et al. 2014) evidences. The negative variations of fluid pressure increase the normal effective stress within the soil-caisson interface and then the maximum friction available. The absolute value of Fout is slightly greater than in drained conditions.

3.3

Influence of soil’s permeability in traction

It was shown that the suction component can significantly increase the total resistance to traction load. Permeability of the soil and rate of loading both modify the available suction. Traction simulations for three order of magnitudes of permeability are illustrated in Figure 12. The stiffness of the soil-caisson system increases with decreasing permeability of the soil. Indeed, the

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negative PWP inside the caisson are less rapidly dissipated, maintaining a high differential of pressure. However the corollary effect is the generation of high pressure gradients leading to local liquefaction of the soil. For a similar applied traction load, the uplift displacement of the caisson also increases with increasing permeability. For the highest permeability, there are clearly two distinct phases. During the first phase (down to almost −1.5 mm), the stiffness of the caisson is only slightly different from the other simulations. This corresponds to the progressive mobilisation of friction along the caisson’s walls (inside and outside). After this point, the stiffness suddenly degrades. This actually corresponds to the full mobilisation of friction on the skirt inside and outside the caisson. The caisson slides upwards and suction Fpw is the only component of resistance. In this case, there is also a loss of contact between the lid and the soil, creating a gap. This gap is filled with water and the caisson acts like a piston.

4 4.1

Figure 13. Half-cycle analysis of the load signal ptot .

Table 1. Number of equivalent cycles, associated amplitudes and periods.

Number of cycles [−] ptot [kPa] T [s]

CYCLIC LOADING Loading

The cyclic load is applied in three phases.The first consists in applying monotonically a mean load ptot,mean = 20 kPa, in a drained fashion. This load corresponds to the weight of the wind turbine and the constant component of the storm. The second phase is the application of a cyclic loading around the mean load. Finally a 300s consolidation phase at constant initial mean load is simulated in order to allow dissipation of PWP and to compute a final settlement. The cyclic loading of the caisson originates from the effects of wind and waves acting on the offshore superstructure. A typical output of the analysis of a tripod superstructure to waves and wind is presented in Figure 14 (top figure). It is termed pseudo-random since it results from a numerical analysis by specialised software. It corresponds to a storm sample including an extreme event, i.e. the biggest load encountered by the superstructure during the storm. Only the vertical load applied by a leg of the superstructure is considered. Within the pseudo-random signal, high amplitude cycles alternate with the low amplitude ones and the effect of each type of cycle is difficult to isolate. A half-cycle analysis (Byrne and Houlsby 2002) is carried out to transform the pseudo-random signal into a sinusoidal equivalent one. A half-cycle is defined as the part of a signal between two successive crossings of its mean value, as shown in Figure 13. A half period T and a peak value ptot are associated to each half-cycle. Therefore an equivalent sinusoidal cycle of identical characteristics (T,ptot ) can be reconstituted. In this study, four types Ai of periods and amplitudes are identified in the pseudo-random load signal. They are supplied in Table 1. For each category Ai ,

A1

A2

A3

A4

50 4.5 4.6

28 13.5 11

4 22.5 11.6

1 40.5 11.1

Figure 14. Pseudo-random and equivalent cyclic load signals.

Ni cycles are identified in the pseudo-random signal. These equivalent cycles are ordered into equivalent load signals, as depicted in Figure 14. These signals mainly differ by the position of the extreme event, at the beginning, in the middle or at the end. A more detailed description of the method could be found in (Cerfontaine 2014).

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Figure 16. Evolution of the permanent displacement for four load signals (equivalent 1, equivalent 2, equivalent 3 and pseudo random). Figure 15. Comparison of cyclic variation of total pressure applied on the lid ptot and variation of mean pore pressure inside the caisson pw for two load signals: Equivalent 1 (up) and pseudo-random (down); total load applied to the caisson (solid black line), average PWP inside the caisson (dashed line).

4.2

Results

Figure 15 presents a comparison between the first equivalent and the pseudo-random load signals. The variation of the total load ptot around its mean value ptot,mean is represented as well as the averaged PWP under the lid of the caisson pw . The full response signal is difficult to analyse due to the large number of cycles. Therefore the envelope curve, i.e. the locus of local minima or maxima is represented for both ptot and pw . The tendency curve describes the long-term evolution of the PWP. If the process was totally reversible, the PWP should be equal to zero each time the cyclic amplitude ptot is equal to zero. However pw is not equal to zero, denoting a non recoverable part. The locus of all these non-recoverable parts describes the tendency response in Figure 15. It can be observed that the variation of PWP insidde the caisson pw is almost identical to the variation of the total load applied ptot . This is a consequence of the partially drained behaviour highlighted for monotonic simulations. A large part of the loading is sustained by a PWP variation which is hardly dissipated before the load reverses. Therefore the cyclic effective amplitude applied to the solid skeleton of the soil surrounding the caisson is much lower than the total cyclic amplitude applied on the caisson. Consequently this partially drained behaviour induces less stiffness degradation and settlement than a drained behaviour. Both response signals present a tendency to PWP accumulation. Such an observation is classical in undrained laboratory experiments on soil samples (Seed and Lee 1966) or in offshore engineering in

general (Cuéllar et al. 2014). This results from the plasticity of the soil, implying excess PWP in partially drained conditions. In the upper graph of Figure 15, it can be observed that a maximum accumulation arises after the extreme event. It is progressively dissipated afterwards during cycles of lower amplitudes. The cyclic loading of suction caissons can be decomposed into two parallel consolidation processes. The first, named short-term, consists of the immediate response of the soil to the variation of the applied load at the scale of a cycle. Variations of PWP are large since the load reverses before all PWP are dissipated. It is the origin of the “suction effect”. The displacement varies accordingly and is mainly recoverable. On the contrary the second consolidation process arises from the progressive dissipation of the accumulated PWP and is termed long-term. It results from the plastic contractancy of the soil and is responsible of the non-recoverable settlement. Accumulation of deformation during cyclic loading is also a classical results since it is linked to the accumulation of PWP. The trend of settlement accumulation is computed similarly to the trend of PWP. It is the locus of the settlements measured each time the total load applied is equal to its mean value. Only this trend is represented since the full response signal is illegible due to the large number of cycles. The evolution of this permanent settlement under the top centre of the caisson is represented in Figure 16. The maximum transient settlement encountered during the storm event (the global maximum) is also represented since it could affect serviceability. Results presented converge to a similar final settlement, justifying the pertinence of the half-cycle analysis method for the elaboration of a load signal. However there is a small divergence between them since the stress paths of material points are not identical for all load signals. One of the advantages of such a load signal is the clarification of the effect of each type of cycles

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(A1,A2,A3 or A4). The low-amplitude cycles lead to almost no plastic deformation. This is quite clear in results corresponding to Equiv. 3 load signal but totally impossible to observe in the pseudo-random response. The second batch of cycles (A2) exhibits a clear tendency of settlement accumulation which could be extrapolated to a larger number of cycles. The asymptotic non-linear evolution of the settlement is due to the progressive dissipation of the accumulated PWP, which is maximum during the extreme event. Therefore the sooner this event occurs, the sooner this asymptotic evolution starts. 5

CONCLUSIONS

Suction caissons represent an interesting competitive alternative to other types of foundations for offshore wind turbines. However their behaviour upon traction and cyclic loading is not entirely mastered and simplified methods for design should still be elaborated. This paper presents the results of monotonic and cyclic loading of a suction caisson embedded in dense sand. Upon traction, the main mechanism of reaction is the friction progressively mobilised along the skirt of the caisson. It is mobilised inside and outside the caisson in drained conditions (low pull rate). Upon high rate of loading, a consolidation process takes place, generating over- or under- pressures respectively with compression or traction loads. The transient differential of pressure between inside and outside the caisson creates a suction effect, increasing the resistance of the caisson in both traction and compression. It is of greater importance in traction than in compression. Permeability and loading rate strongly influence stiffness and resistance of the caisson. The cyclic loading of suction caissons is mainly partially drained. Therefore, the major part of the load variation is sustained by positive or negative variations of PWP within the soil inside the caisson and around it. The principal consequence is a low loading of the solid skeleton of the soil. All simulations present an accumulation of settlement during the cyclic loading of the caisson. However this settlement is reduced with respect to a purely drained behaviour. The accurate description of the mechanisms of resistance could lead naturally to a spring-dashpot macro-element, describing the behaviour of the caisson. This is already done in (Senders 2008) but the definition of the different parameters is still an issue. Moreover, the modelling of settlement accumulation upon cyclic loading requires the elaboration of a more complex non-linear law for the springs. REFERENCES Achmus, M., C.T.Akdag, & K.Thieken (2013). Load-bearing behavior of suction bucket foundations in sand. Applied Ocean Research 43, 157–165.

Andersen, K., H. Jostad, & R. Dyvik (2008). Penetration resistance of offshore skirted foundations and anchors in dense sand. Journal of Geotechnical and Geoenvironmental Engineering 134(1), 106–116. Byrne, B. & G. Houlsby (2002). Experimental investigations of response of suction caissons to transient vertical loading. Journal of the Geotechnical and Geoenvironmental Engineering 128(11), 926–939. Byrne, B. & G. Houlsby (2003, December). Foundations for offshore wind turbines. Philosophical transactions. Series A, Mathematical, physical, and engineering sciences 361(1813), 2909–30. Cerfontaine, B. (2014, september). The cyclic behaviour of sand, from the Prevost model to offshore geotechnics. Ph. D. thesis, University of Liege. Cerfontaine, B., F. Collin, & R. Charlier (2015). Numerical modelling of transient cyclic vertical loading of suction caissons in sand. Géotechnique 65(12). Cerfontaine, B., A. Dieudonne, J. Radu, F. Collin, & R. Charlier (2015). 3d zero-thickness coupled interface finite element: Formulation and application. Computers and Geotechnics 69, 124–140. Cuéllar, P., P. Mira, M. Pastor, J. Fernández Merodo, M. Baeß ler, & W. Rücker (2014, June).A numerical model for the transient analysis of offshore foundations under cyclic loading. Computers and Geotechnics 59, 75–86. Gerard, P., R. Charlier, R. Chambon, & F. Collin (2008). Influence of evaporation and seepage on the convergence of a ventilated cavity. Water Resources Research 44(5). Houlsby, G., L. Ibsen, & B. Byrne (2005). Suction Caissons for Wind Turbines. International Symposium on Frontiers in Offshore Geotechnics 75(September), 94. Houlsby, G., R. Kelly, & B. Byrne (2005). The tensile capacity of suction caissons in sand under rapid loading. In Frontiers in offshore geotechnics, pp. 405–410. Ibsen, L. & F. Jacobsen (1996). Lund sand no. 0. Technical report, Aalborg University. Ishihara, K. (1996, September). Soil Behaviour in Earthquake Geotechnics. Oxford University Press, USA. Iskander, M., S. El-gharbawy, & R. Olson (2002). Performance of suction caissons in sand and clay. Canadian Geotechnical Journal 584(may), 576–584. Kelly, R., G. Houlsby, & B. Byrne (2006). A comparison of field and laboratory tests of caisson foundations in sand and clay. Géotechnique 56(9), 617–626. Rahman, M., H. Seed, & J. Booker (1977). Pore pressure development under offshore gravity structures. Journal of the Geotechnical Engineering Division 103(December 1977). Seed, B. & K. Lee (1966). Liquefaction of saturated sands during cyclic loading. Journal of Soil Mechanics & Foundations Div 92. Senders, M. (2008). Suction caissons in sand as tripod foundations for offshore wind turbines. Ph. D. thesis, University of western Australia. Senders, M. & M. Randolph (2009). CPT-Based Method for the Installation of Suction Caissons in Sand. Journal of Geotechnical and Geoenvironmental Engineering 135(January), 14–25. Thieken, K., M. Achmus, & C. Schröder (2014, July). On the behavior of suction buckets in sand under tensile loads. Computers and Geotechnics 60, 88–100. Yang, Z., A. Elgamal, & E. Parra (2003). Computational model for cyclic mobility and associated shear deformation. Journal of Geotechnical and Geoenvironmental Engineering 129(12), 1119–1127.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Modelling the environmental impact of underground coal gasification B.D. Roullier, P.A. Langston & Xiang Ling Li Faculty of Engineering, University of Nottingham, Nottingham, UK

ABSTRACT: Underground coal gasification has the potential to access vast energy resources in a safe, economical and efficient manner, with many environmental advantages over traditional methods. Previous trials have led to local environmental issues concerning surface subsidence, groundwater contamination and water table depletion. The risk of such issues can be greatly reduced however, through a greater understanding of the coupled thermal, mechanical and hydraulic phenomena involved. Such an understanding allows operators to design gasifiers to reduce or completely eliminate these risks. Numerical simulations provide a cost effective means of investigating these issues. This paper uses the commercially available 2D discrete element code UDEC to model these effects. Initial results show agreement with field trial experience and previous predictions, despite a relative lack of available validation data. Future modelling aims to investigate the influence of a number of design decisions on environmental performance to produce guidelines for future operations.

1 1.1

INTRODUCTION UCG technology

Underground coal gasification (UCG) is an energy extraction technology in which coal is converted into a valuable synthesis gas (syngas) in-situ within an unmined coal seam. The syngas typically consists of a mixture of carbon monoxide, carbon dioxide, hydrogen, methane and water vapour. The syngas can be used as a fuel for gas fired power generation or industrial processes or can be converted into commodity chemicals or synthetic transport fuels. UCG operations involve drilling two wells down from the surface into the coal seam and connecting these with a horizontal channel to form a gas circuit. Oxygen is injected via one of the wells and the coal seam is ignited with the use of a burner inside the well casing. The flowrate of oxygen is controlled in order to promote gasification rather than combustion of the coal seam. Operating pressure is maintained at a level slightly below the local hydrostatic pressure. This both prevents the escape of syngas into the surrounding rock and causes a small inflow of groundwater into the cavity. The incoming water helps regulate temperatures and increases the concentration of hydrogen and methane in the syngas. After gasification is complete, product gases flow along the channel and are extracted from the second well. As the reaction proceeds the channel expands into a cavity, continually exposing fresh coal and prolonging the process. Eventually, the cavity grows too large for the coal seam, at which point gasification is ceased. Modern operations use a technique known as the Controlled Retracting Injection Point (CRIP), which allows several cavities to be formed from a single pair of wells. In CRIP UCG, when gasification

Figure 1. Schematic of CRIP UCG configuration and cavity.

of one cavity ceases, the injection point is retracted several metres and gasification begins again in a new cavity (Couch, 2009). A typical CRIP UCG setup is shown in Figure 1. 1.2 UCG advantages and disadvantages 1.2.1 Economic Coal is the most abundant fossil fuel on Earth, with economically recoverable reserves of over 800 billion tonnes and potential total resources of over 18 trillion tonnes (Self et al, 2012). Proven reserves alone

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account for approximately 7 billion GWh of thermal energy. In comparison, traditional oil and gas reserves represent approximately 2 billion GWh each, while unconventional oil and gas reserves (e.g. shale gas) are estimated to be around 8 billion GWh (World Energy Council, 2010). UCG allows for the exploitation of coal seams which are considered uneconomical by traditional methods due to their rank, depth or inaccessibility. As such, UCG could potentially access reserves of stored energy even greater than those afforded by unconventional oil and gas. Due to the more geographically ubiquitous nature of coal, UCG could provide a viable source of energy in many locations without access to indigenous oil and gas sources, for example the UK, Western Europe and Africa. In addition, the capital costs of a UCG operation are much lower than that of a traditional coal mine, as considerably less surface equipment is required. Capital and operating costs of commercial UCG would be similar to those of shale gas, however the current experimental state of the technology increases these costs somewhat. 1.2.2 Environmental Because of the nature of the syngas product, UCG has several environmental advantages over traditional coal use. Firstly, due to their low volatility, many of the contaminant species present in coal (e.g. lead, mercury, cadmium etc.) remain trapped underground. Second, the gaseous nature of the product allows for the use of highly efficient combined cycle gas turbines, which greatly improve energy efficiency compared to traditional pulverised coal power plants. Finally, due to the high carbon dioxide partial pressure of the syngas, UCG is ideal for connection to carbon capture and storage (CCS) facilities. In addition, the creation of the highly permeable cavity allows some of the captured CO2 to be stored on site. This is referred to as reactor zone cavity storage (RZCS) (Burton et al 2006). Despite these advantages, it is important to state that UCG is still a fossil fuel based energy source and should be seen as a bridging technology towards an eventual renewable energy system (Roddy & Younger 2010). 1.2.3 Social The principal social advantage of UCG over traditional mining is the greatly improved safety of miners. Because no workers are sent underground, the risk to life from cave-ins, flooding and explosions are eliminated. Other social benefits include a much smaller surface footprint (and hence a reduced landscape impact) as well as reductions in dust, noise and traffic. UCG also has the potential to create high tech jobs and revitalise the economies of regions which were previously dependent on coal mining. A particular issue with the social acceptance of UCG is the negative public perception of the technology. The key reasons for this are a lack of publically available information on the technology, concerns

around environmental issues, a perceived lack of process control and general distrust in fossil fuel operating companies (Shackley et al, 2006). UCG is also commonly compared to fracking, with many of the same issues presented despite the differences in the two technologies. 1.3

UCG environmental concerns

As with any fossil fuel extraction technology, there are concerns around the local environmental impact of UCG. Firstly because the gasification of coal removes solid material from underground, UCG can lead to surface subsidence above the cavity. Secondly, heavy metal pollutants and coal pyrolysis products remaining in the cavity can leach into surrounding groundwater resources. Finally, sub-hydrostatic operation can cause the depletion of local groundwater resources, leading to a lowering of the water table. All of these issues can however be reduced, if not entirely eliminated, through ensuring UCG operations are designed and sited appropriately. Key design parameters include coal seam depth, thickness and horizontal extent, cavity operating pressure and local water table depth and quality. The effects of each parameter are explained below: 1.3.1 Effects of coal seam depth The depth of the coal seam to be gasified has implications for both the economics and environmental impacts of a UCG operation. Deeper coal seams can operate under higher pressures, increasing methane yields (and therefore syngas quality) and CO2 partial pressure (aiding CCS). Below approximately 800 m, lithostatic pressure is high enough that CO2 exists as a supercritical fluid, allowing for RZCS. Increased depth reduces the extent of surface subsidence by increasing the amount of supporting overburden between the cavity and the surface. Finally, increased depth reduces the effects of groundwater contamination as deeper aquifers tend to be unpotable. On the other hand, drilling of wells is one of the largest capital expenses of a UCG project, and increases in depth greatly exacerbate this cost. 1.3.2 Effects of coal seam thickness and extent Increases in coal seam thickness and/or horizontal extent are beneficial as they increase the amount of coal that can be gasified by a single pair of wells. While cavity height tends to be determined by the height of the coal seam, width is usually limited by heat transfer effects. The length of a cavity is mainly determined by the spacing between wells. Longer spacings increase the amount of coal accessed, but also increase drilling costs, pressure losses and the chance of a cave-in blocking the channel. Cavity width, length and height are all positively correlated with subsidence extent, however this effect is greatly reduced with increasing depth. In coal seams with large horizontal dimensions, multiple UCG cavities can operate in parallel to exploit

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greater volumes of coal. A minimum separation distance is required in order to prevent cavities from merging, increasing the effective cavity width and exacerbating subsidence. The use of multiple cavities has a further benefit, in that produced gases can be blended to achieve a desired syngas composition. 1.3.3 Effects of operating pressure Increases in cavity operating pressure have a number of economic benefits as shown in section 1.3.1. Such increases also give rise a number of issues however. Firstly, excessive operating pressures can cause syngas to leak into the overburden rock. This both reduces the efficiency of the UCG process and provides a pathway for pollutants to enter groundwater. As mentioned previously, reduced pressures cause groundwater to flow into the cavity rather than gas to flow out. This reduces the risk of pollution, however it can increase the chance of water table depletion if drawdown rates are greater than the rate of replenishment. In addition, excessive rates of drawdown can lead to a quenching of the gasification reactions. In practice, cavity operating pressure is usually set to give a small net inflow of water. 1.3.4 Water table effects The depth of the water table below the ground’s surface has a profound effect on UCG cavity design. As operating pressure is usually set below local hydrostatic pressure, deeper water tables reduce the potential operating pressure of the cavity. In cases where the water table lies below the cavity, operating pressures can be set higher as there is no water present to be contaminated. In this case pressure is only limited by the need to minimise the loss of valuable syngas to the rock mass. Similar considerations arise where the local groundwater is unpotable. As deeper aquifers tend to be saline (and therefore unpotable), water table issues are often intrinsically related to cavity depth. 1.4

Environmental modelling of UCG

Subsidence, groundwater pollution and water table depletion are highly coupled processes depending on the thermal, chemical, hydraulic and mechanical behavior of the rock mass surrounding a UCG cavity. Due to the complexity of these issues, and the difficulties in observing physical processes occurring underground, numerical modelling is commonly used as a means to further understanding of the processes involved in UCG. A number of models have been produced over the past forty years which simulate a range of UCG aspects, including product composition (Daggupati et al 2012, Perkins and Sahajwalla 2008, Seifi et al 2011), cavity growth mechanics (Biezen et al 1996, Britten and Thorsness 1988, Sarraf et al 2011), subsidence (Morris et al 2009, Vorobiev et al 2008) and groundwater contamination (Yang and Zhang 2009). Despite their strong coupling, no model yet considers both subsidence and groundwater effects, though one is in development (Nitao et al, 2011).

1.5

Model aims

The model presented in this paper aims to predict, and therefore prevent, the coupled effects of subsidence, groundwater contamination and water table depletion caused by CRIP UCG.The model operates on a general basis rather than being site specific. The design aims to produce simulations which can run in under a week on a standard desktop PC. It is envisioned that the model will be used as a tool for investigating the influence of site design parameters on environmental issues. In addition, simulation results could be used as a ‘first pass’ filtering tool for the selection of sites for future, commercial UCG developments. The following section describes the design and development of the model. Section 3 presents initial model results alongside validation and verification studies. Section 4 discusses the advantages, disadvantages, challenges and limitations of the model methodology as well as potential future applications. Section 5 concludes the paper and suggests further developments and applications of the model.

2

MODEL DESIGN

The thermal, hydraulic and mechanical behaviour of the rock mass around a UCG cavity is simulated using the commercially available 2D Universal Distinct Element Code (UDEC v4.01) (Itasca Consulting Group 2004). UDEC is a combined finite difference – discrete element code which has been successfully applied to geotechnical problems in a range of fields, including tunneling (Solak, 2009), mining (Keilich et al, 2006), underground construction (Barton et al, 1994) and nuclear waste storage (Blum et al, 2009). UDEC approximates a highly jointed rock mass as an assembly of intact rocks (blocks) separated by discontinuities (joints). Blocks are further subdivided into triangular finite difference elements (zones) which allow the blocks to deform both elastically and plastically. Joints allow fluid to flow in the spaces between blocks. Pore pressures in the joints are driven by the weight of the rock blocks and act upon the surface of those blocks. As such, UDEC allows for full bi-directional coupling of mechanical and hydraulic effects. Heat conduction and thermally generated stresses are also simulated, giving one directional thermo-mechanical coupling. UDEC is not capable of simulating complex hydraulic phenomena such as dissolution. As such, groundwater contamination modelling must be achieved using alternative methods. An additional model is currently in development which uses the MODFLOW and MT3DMS codes (United States Geological Survey 2015) to predict contaminant motion based on permeability data taken from the results of the UDEC model. The UDEC model uses the plane strain assumption to model the 3D cavity as a 2D cross section. This

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Table 1. Design parameters used in the base case UCG model. Parameter

Value

Reason/Source

Cavity Width Cavity Height Cavity Depth Water Table Depth Operating Pressure Model Width Model Height Fine Zone Width Fine Zone Height Fine Joint Edge Length Coarse Joint Width Coarse Joint Height

12.4 m 14.2 m 98.4 m 27.6 m 555 kPa 310 m 126.8 m 37.2 m 56.8 m 0.8 m 31 m 5m

Lindblom et al, 1990 Lindblom et al, 1990 Lindblom et al, 1990 Mason et al, 1987 80% of hydrostatic 25 times cavity width See Fig. 2. 3 times cavity width 4 times cavity height Runtime considerations One tenth of model Runtime considerations

assumption both simplifies the model and speeds solution. On the other hand, the assumption can potentially lead to an overestimation of environmental damage as the cavity is effectively infinite in length. Given that the aim of the model is to predict the negative consequences of UCG, this overestimation is deemed to be acceptable as it provides an effective safety factor for gasifier design. The two dimensional geometry of the cavity is based on the Rocky Mountain 1 field trial site (Lindblom et al 1990). Model design parameters are given in Table 1. A dual scale representation of the rock mass is used to limit the number of blocks and zones in the model, considerably reducing solution times. In the region close to the cavity, the joint pattern is based on the discrete fracture network (DFN) as presented by Min et al (2004). This pattern allows for random variations in model behaviour whilst maintaining appropriate overall results. Far from the cavity, a horizontal brickwork pattern is used for simplicity. The geometry of the base case model is shown in Figure 2. The rock mass is modelled using a strain softening Mohr-Coulomb constitutive relationship. The strain softening representation is used as UDEC’s standard Mohr-Coulomb relationship does not fully realise plastic strains. Material properties are derived for sandstone using simulated triaxial compression testing as described in a previous paper (Roullier et al 2015). Rock mass permeability is calibrated against field data from the Rocky Mountain 1 site (Mason et al 1987). The temperature dependence of material properties is based on the work of Ranjith et al (2012). Temperatures are set at the cavity wall and vary with time over a 100 day period to simulate the consecutive stages of combustion, gasification and cooldown. The thermal model is set up to determine the maximum temperature experienced at each location over the entire period of operation. Rock material properties are then altered based on the maximum experienced temperature. Solution of the coupled thermal, hydraulic and mechanical models follows a ten step process: 1. Set up model geometry and material properties 2. Find initial hydromechanical equilibrium

Figure 2. Geometry and joint patterns used in the UCG model.

3. 4. 5. 6. 7. 8. 9. 10.

Excavate cavity volume Set cavity pressure equal to operating pressure Determine temperature profile around cavity Find hydromechanical equilibrium after operation Set cavity pressure equal to hydrostatic pressure Reset temperature profile to background levels Find hydromechanical equilibrium after cooling Analyse model results

The thermal part of the UCG model cannot be simulated at the same time as the mechanical or hydraulic parts due to the large difference in the characteristic timescales of these effects, as well as differences in the spatial discretization used in each aspect of the model (Itasca Consulting Group 2006).

3

RESULTS

Initial results of the coupled thermal, mechanical and hydraulic models show reasonable agreement with both field data and empirical predictions. Figure 3 compares the simulated subsidence profile for the Rocky Mountain 1 site with a simple empirical influence function (Brauner, 1973). Field measurement data is not available for this site as subsidence was considered of little importance during the trial. Data was available however, for the Hoe Creek 3 trial site (Ganow, 1984). Figure 4 compares simulation results with site measurements for this site. In both figures, average subsidence was found as the arithmetic mean

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Figure 5. Pore pressure distribution around Rocky Mountain 1 cavity. Pressure contours are in units of kilopascals. Figure 3. Comparison of simulated subsidence profile with empirical predictions for the Rocky Mountain 1 field trial.

Figure 4. Comparison of simulated subsidence profile with measured site data for the Hoe Creek 3 field trial.

of ten simulations while error bars are given as the standard deviation of these simulations. Model runtimes were found to average 54 ± 13 hours. Model results show reasonable agreement with both site measurements and empirical predictions. Simulated profile shapes are observed to be sharper than those given by empirical means, but to agree well with field measurements. In addition, the variability in simulation results is seen to be very large. The reasons for this variability are discussed in section 4. As well as subsidence, the coupled model produces results for both the hydraulic and thermal effects of UCG. Figure 5 shows the pore pressure distribution around a cavity based on the Rocky Mountain 1 geometry. As seen, the influence of UCG on groundwater pressures does not extend far from the cavity itself. A small cone of depression is seen up to approximately 5m from the cavity wall, and some distortion of the pressure distribution is seen directly above the cavity. Water table height was seen to be unaffected by UCG operation. This agrees with the results of modern UCG field trials, for example the Bloodwood creek trial site, in which negligible changes in groundwater pressures were observed (Green, 2015). Finally, the coupled model gives information on the temperature profile around the cavity. Figure 6 shows the maximum temperature experienced by each point around the cavity wall. It can clearly be seen that the

Figure 6. Simulated maximum temperature profile around Rocky Mountain 1 field trial site. Temperature contours are in units of Kelvin.

thermal penetration length of UCG is on the order of metres, in good agreement with the literature (Sarhosis et al, 2013, Yang, 2006). In addition to the results presented above, a number of further systems are currently being simulated to determine the validity of the model. Sensitivity analyses, parametric studies and further comparisons with field trials in both UCG and related fields (e.g. mining) are underway. Further plans involve the application of both the UDEC model and the contamination model (currently in development) to a range of potential site designs. Models will consider variances in cavity geometry, cavity operating conditions and local geology including the presence of faulting. 4

DISCUSSION

As seen in section 3, the results of the simulations show reasonable agreement with field trial data, yet a number of issues are observed. Firstly, as seen in Figure 3, simulations tend to give sharper subsidence profiles than empirical measures. It is believed that this discrepancy is due to the empirical methods not taking into the account the exact shape of the cavity. In effect, the curved roof of the modelled cavity acts to concentrate rock deformation across a

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smaller horizontal distance than would be given by the rectangular cavity of the empirical method. The close agreement between the simulated and measured profiles in Figure 4 support this explanation. A second issue is the high degree of variability in model results. Differences between two simulations for the same geometry are principally due to the random nature of the DFN pattern used in the fine mesh region. Model variability can therefore be reduced by decreasing the standard deviation of joint angle. Further reductions can be made by tightening convergence criteria; though this can lead to considerable decreases in solution speed and stability. Some degree of variability in model results is necessary however, to account for the inherent uncertainties in rock mass behaviour at real sites. Measured material properties of rock masses vary considerably, even for rocks of the same type acquired from the same site. These variations are caused by several mechanisms including the spatial variability of the rock mass, the inherent randomness of joint patterns and experimental error in the collection of material data. Simplifying assumptions in both numerical models and analytical theory also contribute to variability. (Cai et al 2011). Given these natural and modelled variabilities, it is recommended that any results based on this or other numerical models are repeated a number of times to ensure their validity. An additional complication with the model is the introduction of errors due to uncertainties in internal variables. As mentioned above, material properties for the rock mass are based on previous work into simulated compression testing. Although this method gives advantages over arbitrary selection of properties, it introduces uncertainty based on the errors in the simulated tests. Ideally material property data would be based on site investigations, but this is often too difficult and expensive to achieve. Joint material properties are chosen arbitrarily, based on suggestions in the literature. Due to the difficulties in examining rock masses without disturbing them, reliable joint material property data is rare. In addition, the Coulomb slip model used to represent joints in UDEC does not account for effects such as roughness or non-linear closure behaviour, further increasing uncertainty. Data on water table properties are available for many sites, however these must be assumed in cases where no data is given. In-situ stresses at sites are rarely reported due to the complication of measuring them. Modelled in-situ stresses are based on the weight of the overburden and assume a lateral earth coefficient of 0.5. This value is chosen arbitrarily from the literature and can vary considerably. UDEC specific values such as finite difference zone density and the magnitude of convergence criteria are often chosen by investigating how these values affect results and selecting values which give a compromise between accuracy, stability and runtime. As mentioned previously, a number of tests are currently underway to further examine the effects of various internal parameters on results and ensure the validity of the model.

Finally, model development is complicated by the lack of available verification data. The majority of past UCG trials took place in the 1980s or earlier, and many of the more recent trials are operated as commercial ventures (Bhutto et al 2013, Underground Coal Gasification Association 2011). As such, site measurement data is rare either because it was not collected at the time (due to technical limitations or lack of foreknowledge) or because it is considered to be commercially sensitive. Due to this lack of data it is difficult to compare model results with real world experience, considerably limiting the reliability of model predictions. In order to overcome this limitation, a number of verification models are being performed against processes with similar geometries to UCG, including mining and tunneling. These studies will go some way towards validating model results, however the considerable differences between these systems and UCG may reduce their usefulness. Further validation could be performed against future UCG operations, although these may also suffer from the issue of commercial sensitivity. In addition to subsidence and water table depletion, the aim of this model included simulation of groundwater contamination caused by UCG. As mentioned previously, this capability is currently being developed with the use of the MODFLOW and MT3DMS codes. Unlike the subsidence model, the lack of data is not an issue for the fluid model for two reasons: Firstly, fluid properties such as diffusivity are much easier to obtain than rock mass material properties. This is principally due to the relative ease with which these properties can be investigated in a laboratory setting. Unlike rock mass properties, fluid characteristics are also not site specific, with the exception of adsorption coefficients. The second reason refers to verification data. Groundwater compositions can be readily measured at trial sites using borehole sampling methods. In addition, many authorities place a legal requirement on operators to measure pollutant concentrations and the results are often in the public domain. As such, verification data for the pollution model should be much easier to find. A further advantage of the pollutant model is its relative simplicity. Compared to the UDEC model, the pollutant code is based on phenomena which are more readily understood, hence validation of model results should also be easy to achieve. Once the contaminant model is developed, the fully integrated UCG model will be complete. In addition to the validation and verification tests mentioned above, a number of tests will be performed to investigate how certain design choices affect the environmental risks of UCG. As mentioned in the introduction, these tests will focus on the influence of cavity geometry, operating conditions and water table properties. The effects of geological discontinuities (i.e. faults) will be modelled and investigations into multiple cavity, commercial scale operations will be performed. It is hoped that model results will show the expected trends in subsidence, groundwater pollution and water table depletion. Results from these tests could then be used

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to derive a set of guidelines for the appropriate siting and design of future commercial scale UCG operations, as well as proving the validity of the model for use in future predictive modelling of proposed UCG operations.

5

CONCLUSIONS

Underground coal gasification is seen to be a promising technology for both energy generation and industrial applications. UCG is shown to have a number of economic, social and environmental benefits over traditional coal extraction and use. As with all energy technologies however, there are environmental concerns associated with UCG. Due to the expense and difficulty of performing field scale UCG experiments, numerical models are commonly used to understand and predict these issues. Discrete element modelling is often used to account for the discontinuous nature of the rock mass around a UCG cavity. A coupled simulation of thermal, mechanical and hydraulic effects has been produced with the UDEC discrete element code in order to predict the local environmental impact of UCG. Initial results show good agreement with the literature for the prediction of surface subsidence and water table depletion as well as the effect of high temperatures on overburden rock. The variability in results is seen to be high; however this is on a scale comparable with the natural variability of rock. In addition, the reliability of model results is somewhat limited given the lack in available site data and verification studies. Further simulations are currently ongoing and it is hoped that these will demonstrate the validity of the model for use in future predictions of UCG behaviour. Investigations of the effects of varying site properties on environmental issues should give trends which can be used to produce a set of guidelines for future gasifier designs. It is envisioned that the final models could be used as a first pass screening tool to predict the environmental impacts of a number of proposed sites. This would allow further modelling efforts using high performance computing to focus only on those sites with a greater potential for safe and economically viable operation. Further uses of the model could also provide a similar function in related fields such as nuclear waste storage, oil extraction, geothermal energy and carbon capture and storage.

LIST OF ACRONYMS CCS – Carbon Capture and Storage CRIP – Controlled Retracting Injection Point DFN – Discrete Fracture Network RZCS – Reactor Zone Carbon Storage UCG – Underground Coal Gasification UDEC – Universal Distinct Element Code

REFERENCES Barton, N., By, T.L., Chryssanthakis, P., Tunbridge, L., Kristiansen, J., Loset, F., Bhasin, R.K., Westerdahl, H. & Vik, G. 1994: Predicted and measured performance of the 62m span Norwegian Olympic ice hockey cavern at Gjovik. International journal of rock mechanics, mining sciences and geomechanics. 31(6): 617–641 Bhutto, A.W., Bazmi, A.A. & Zahedi, G. 2013: Underground coal gasification: from fundamentals to applications. Progress in energy and combustion science 39: 189–214 Biezen, E.N.J. 1996. Modelling underground coal gasification. PhD Thesis. Delft University of Technology, The Netherlands Blum, P., Mackay, R. & Riley, M.S. 2009: Stochastic simulation of regional scale advective transport in fractured rock masses using block upscaled hydromechanical rock property data. Journal of hydrology, 369(3–4): 318–325 Brauner, G. 1973: Subsidence due to underground mining (in two parts) 1. Theory and practices in predicting surface deformation. Bureau of Mines, US Department of the Interior. Britten, J.A. & Thorsness, C.B. 1988: A mechanistic model for axisymmetric cavity growth during underground coal gasification. Journal of the American Chemical Society 33: 126–133 Burton, E., Friedmann, J. & Upadhye, R. 2006: Best practices in underground coal gasification. Lawrence Livermore National Laboratory, Livermore, USA Cai, M. 2011: Rock mass characterization and rock property variability considerations for tunnel and cavern design. Rock mechanics and rock engineering, 44: 379–399 Couch, G.R. 2009: Underground coal gasification, International Energy Agency Clean Coal Centre, 2009. Daggupati, S., Mandapati, R.N., Mahajani, S.M., Ganesh, A., Pal, A.K., Sharma, R.K. & Aghalayam, P. 2012: Compartment modelling and flow characterisation in nonisothermal underground coal gasification cavities. Journal of Industrial and Engineering Chemistry Research 51: 4493–4508 Ganow, H.C. 1984: Results of long term ground surface measurements at the Hoe Creek 3 site. Proc. 10th Underground Coal Gasification Symposium, Williamsburg, VA, USA. 12–15 August 1984 Green, M. 2015: UCG: Practical experience with UCG trials. Presented at the Coal Research Forum 26th annual meeting and meeting of the coal conversion division. Leeds, UK, 15th April 2015. Itasca Consulting Group Inc. 2004: UDEC – Universal Distinct Element Code v4.01. Itasca consulting group, Minneapolis, USA. Itasca Consulting Group Inc. 2006: UDEC – Universal Distinct Element Code v4.0 user’s guide. Itasca consulting group, Minneapolis, USA Keilich, W., Seedsman, R.W. & Aziz, N. 2006: Numerical modelling of mining induced subsidence. In: N. Aziz (ed), Coal 2006 – Coal operators conference, University of Woolongong & The Australian institute of mining and metallurgy, 2006: 313–326 Lindblom, S.R., Covell, J.R. & Oliver, R.L. 1990: Results of phase 1 post-burn drilling and coring, Rocky Mountain 1 underground coal gasification site, Hanna Basin, Wyoming. Western Research Institue, Laramie, USA. Mason, J.M., Oliver, R.L. & Moody, C.G. 1987: Geology and groundwater hydrology of the proposed Rocky Mountain 1 underground coal gasification site, Hanna, Wyoming. Western Research Institue, Laramie, USA.

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Min, K., Jing, L. & Stephansson, O. 2004: Determining the equivalent permeability tensor for fractured rock masses using a stochastic REV approach: Method and application to the field data from Sellafield, UK. Hydrogeology Journal, 12(5): 497–510 Morris, J.P., Buscheck, T.A. & Hao,Y. 2009: Coupled geomechanical simulations of UCG cavity evolution. Proc. 26th annual international Pittsburgh coal conference. 20–23 September 2009. Pittsburgh, USA Nitao, J.J., Camp, D.W., White, T.A., Burton, G.C., Wagoner, J.L. & Chen, M. 2011: Progress on a new integrated 3-D UCG simulator and its initial application. Proc. 28th annual international Pittsburgh coal conference. 12–15 September 2011. Pittsburgh, USA Perkins, G. & Sahajwalla, V. 2008: Steady state model for estimating gas production from underground coal gasification. Energy & Fuels 22: 3902–3914 Ranjith, P.G., Viete, D.R., Chen, B.J. & Perera, M.S.A. 2012: Transformation plasticity and the effect of temperature on the mechanical behaviour of Hawkesbury sandstone at atmospheric pressure. Engineering geology. 151: 20–127 Roddy, D.J. & Younger, P.L. 2010: Underground coal gasification with CCS: a pathway to decarbonising industry. Energy and Environmental Science 2010(3): 400–407 Roullier, B.D., Langston, P.A. & Li, X. 2015: Effects of joint geometry on the modelled material strengths of rock masses in the distinct element method. Proc. TC105 ISSMGE International Symposium on Geomechanics from Micro to Macro. 1–3 September 2014, Cambridge, UK. Sarhosis, V.,Yang, D., Sheng,Y. & Kempka, T. 2013: Coupled hydro-thermal analysis of underground coal gasification reactor cool down for subsequent CO2 storage. Energy Procedia. 40: 428–436. Sarraf, A., Mmbaga, J.P., Gupta & Hayes, R.E. 2011: Modelling cavity growth during underground coal gasification. Proc. 2011 COMSOL conference. 13–15 October 2011. Boston, USA.

Seifi, M., Chen, X. & Abedi, J. 2011: Numerical simulation of underground coal gasification using the CRIP method. The Canadian Journal of Chemical Engineering 89: 1528–1535 Self, S.J., Reddy, B.V. & Rosen, M.A. 2012: Review of underground coal gasification technologies and carbon capture. International journal of energy and environmental engineering 3:16 Shackley., Mander, S. & Reiche, A. 2006: Public perceptions of underground coal gasification in the United Kingdom. Energy Policy 34(18): 3423–3433 Solak, T. 2009: Ground behaviour evaluation for tunnels in blocky rock masses. Tunneling and underground space technology. 24: 323–330 Underground Coal Gasification Association. 2011: History of UCG. Retrieved 31/07/13 from: www.ucgassociation. org/index.php/ucg-technology/history-of-ucg United States Geological Survey. 2015: MODFLOW and related programs. Retrieved 04/02/16 from: http://www. water.usgs.gov/ogw/modflow Vorobiev, O., Morris, J., Antoun, T. & Friedmann, S.J. 2008: Geomechanical simulations related to UCG activities. Proc. 25th annual international Pittsburgh coal conference. 29 September – 2 October 2008. Pittsburgh, USA. World Energy Council (WEC) 2010: Survey of energy resources, World Energy Council, London, UK. Yang, L. 2006: Theoretical analysis of the coupling effect for the seepage field, stress field, and temperature field in underground coal gasification. Numerical heat transfer part A: Applications. An international journal of computation and methodology. 48(6): 585–606 Yang, L. & Zhang, X. 2009: Modelling of contaminant transport in underground coal gasification. Energy & Fuels 23(1): 193–201

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Stability analysis of large diameter boreholes using finite element modelling C. Morris, A. Cardoso & S. Raymackers GeoSea n.v, Zwijndrecht, Belgium

ABSTRACT: GeoSea n.v. is currently working on the development of windfarms requiring piles to be installed in hard clays and weak rocks. Drilling is required for pile installation and to optimize the installation it is preferable to drill without internal support measures. The authors have reviewed methods for assessing the stability of large diameter boreholes drilled in rock. Borehole stability is modelled using finite element modelling software PLAXIS 2D with the Hoek and Brown constitutive model. Results from these calculations are compared against methods from mining industry and well stability methods.

1

INTRODUCTION

2.1 Application of Hoek & Brown model

Monopile and piled jacket foundations are commonly used for offshore wind turbine generators (WTGs). Pile are installed in clay and sand by driving. GeoSea n.v. is currently working on projects where piles will be installed in very hard clays and weak sedimentary rocks. Driving unaided to design embedment in such ground conditions is unlikely to be feasible. Drilling will be required either to install piles as rock sockets or to aid driven installation. Due to the nature of offshore work, it is desirable that drilling can be done without support measures for the borehole, such as bentonite slurry. However the boreholes to be drilled are large, typically 2–8 m in diameter and a stability assessment of boreholes is required to ensure the installation method is viable. The authors required a suitable (analytical) method to assess borehole stability for numerous locations during project preparation. Locations which are thought to be critical could then be subject of further studies. This article discusses the literature review that was performed with the goal to find analytical models which could give an initial indication of borehole stability based on the rock mass properties and borehole diameter as well as the FE models that were made to analyze the global factor of safety. To conclude both analytical and FE models are compared and discussed. 2

The Hoek and Brown model takes into account the rock mass properties and the intact rock strength which govern the behavior and apparent strength of a rock mass. The rock mass properties are defined by the Geological Strength Index (GSI). Ground investigations in rock are typically made using rotary core drilling to extract samples. The GSI is a qualitative assessment of the rock normally made by the ground investigation supervisor. The GSI is based on a visual inspection of the rock considering the lithology, structure and condition of internal surfaces of the discontinuities. A high GSI corresponds unweathered, massive or intact rock with widely spaced discontinuities that have rough internal surfaces. The compression strength of intact rock is defined as the uniaxial compression strength (UCS), determined by unconfined compression or point load tests. Intact rock is typically stronger and stiffer than soil, behaving in a linear elastic manner until brittle failure. The Hoek and Brown failure criterion is defined as:

LITERATURE REVIEW

Stresses in the following paragraphs refer to effective stresses unless stated otherwise. The application of the Hoek and Brown (HB) rock model to this problem and other relevant experience from industry is examined.

where mi is a coefficient based on rock type, D is coefficient depending on the degree of disturbance and σci = UCS. The HB failure criterion is non-linear, however it can be approximated with reasonable accuracy by the

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Mohr-Coulomb model over a limited deviatoric stress range. An equivalent cohesion and friction angle can be calculated based on the UCS and GSI using the method defined by Hoek et al (2000). The onset of plastic failure is defined by the linear Mohr-Coulomb failure criterion:

The methods for well stability are concerned with identifying zones where hole enlargement beyond the drilled diameter is to be expected and for selecting appropriate drilling mud weights. Aadnoy (2010) recommends assessing wellbore stability by considering the stress conditions at the wall of the well: Radial stress: σr = Pw = borehole pressure Tangential stress: σθ = 2σa − Pw Vertical stress: σvo = overburden pressure

Gradient of σ1 with increasing confinement σ3 :

Hoek et al (2000) defines a critical internal support pressure for tunnels, above which the behavior of the rock mass is assumed elastic and no failure occurs:

This assumes stress in the rock to be hydrostatic. The radius of the plastic deformation zone, measured from the center of the tunnel:

where σa = estimated average horizontal stress Failure of the well is assumed to occur where the Mohr-coulomb failure criteria are exceeded, with the radial stress equal to the minor principal stress and the tangential stress equal to the major principal stress. Therefore estimation of the horizontal stress is critical for calculating tangential stress and the borehole stability. The radial pressure on the inside of the borehole provided by drilling mud is critical to the stability of the well. It is noted that wells for oil and gas are normally much deeper than the boreholes considered for pile installation and the in-situ lateral stresses and resulting tangential stresses are higher. 2.3 Sakurai critical strain method Sakurai’s critical strain concept can be used identify situations requiring special support consideration when the strain is above the critical strain value, as shown in Fig 1. The critical strain is calculated as:

Elastic inward radial deformations: The in-situ compression rock mass strength is calculated based on UCS and GSI: Total elastic and plastic inward radial deformation:

Where r0 = original tunnel radius, υ = Poisson’s ratio, E =Young’s modulus, p0 = hydrostatic soil pressure and pi = internal support pressure. The tunnel face provides support to the tunnel walls and the displacements from Eq (10) are not expected at the tunnel face. These values are reached approximately 1.5 diameters behind the tunnel face. Similar behavior is expected for drilled boreholes, with displacements increasing as the drill advances.

2.2 Wellbore stability methods Methods are used for estimating the stability of wells in the oil and gas industry. These wells are smaller diameter than boreholes being considered for installation of piles and drilling muds are normally used for internal support.

However, the critical strain only identifies when special support consideration is required and does not give detail on the behavior expected where the critical strain is exceeded. 2.3.1 Local stresses around the borehole Hoek et al (2000) discusses spalling failure that can occur in brittle rock. This can occur at tangential stress concentrations where the minor principle stress intersects the borehole wall and is manifested in the form of cracking, spalling and rock bursts. It is noted that case studies presented by Hoek et al (2000) are in hard rocks, which may not be entirely representative of the behavior of weaker, less massive sedimentary rocks considered for this study. The utilization of shear strength can be considered for an infinitely small soil wedge at the wall of the borehole, shown in Fig 2. The radial stress is zero because there is no radial confinement. The tangential stress is maximum at the borehole wall and expected to

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Table 1. Model revisions Description

Model variations

Base case model (DC02). K0 = 0.5, UCS = 10 MPa, GSI = 50%, D = 0.5, γ′ = 10 kN/m2 , mi = 17. Excavation in 2.5 m increments with FoS calculated for each depth. Same as DC02 with γ′ = 25 kN/m2

DC02A: Ø = 2 m DC02B: Ø = 4 m DC02C: Ø = 8 m

DC02B with K0 varied. DC02 extended to 100 m depth.

DC03A: Ø = 2 m DC03B: Ø = 4 m DC03C: Ø = 8 m DC04A: K0 = 0.75 DC04B: K0 = 1.0 DC07A: Ø = 2 m DC07B: Ø = 4 m DC07C: Ø = 8 m

Note: K0 = at rest earth pressure coefficient. Figure 1. Percentage strain for different rock mass strength for the Second Freeway, the Pinglin and the new Tielun Headrace tunnels in Tawain (after J.C. Chern reproduced from Hoek, 1998).

determined as the reduction required for a failure mechanism to form. 3.2 Model setup The borehole has been modelled axisymmetrically. The material properties in the base case model are uniform with depth in order to model diameter of the borehole as the main variable affecting stability. The drilling of the borehole is modelled as a staged excavation, excavated in 2.5 m depth increments. The FoS is analyzed after each excavation increment is assessed. The drilling method is assumed not to effect the borehole stability. The phreatic surface is modelled above the top level of the model. Structural geology features are not considered and the drilling process is assumed not to alter the rock properties. Details of the model revisions used for extracting results are given in Table 1.

Figure 2. The stresses acting on an infinitely small wedge ′ of rock at the borehole wall. σvo = overburden pressure, σθ′ = tangential stress, σr′ = radial stress.

be a function of in-situ lateral stresses present before drilling of the borehole. The utilization of the shear strength is expected to be maximum at the borehole wall, where the tangential stresses are highest and there is no radial confinement. The shear strength utilization is calculated as:

3 3.1

FINITE ELEMENT MODELLING (FEM) Global Factor of Safety (FoS)

The global failure mechanism will be modelled using the HB model in PLAXIS 2D. The global FoS is calculated using the safety analysis function, which reduces the material strength progressively. The (FoS) can be

3.3

Results

3.3.1 Global FoS Fig. 3 shows the FoS against failure over 100 m depth for 3 borehole diameters. The results confirm expectation that increasing depth and diameter reduce the borehole stability. The results suggest that for the rock properties considered there is safety margin against a global failure mechanism forming. The largest reduction of FoS with depth occurs in 0–40 m interval and beyond 40 m the decrease in FoS appears relatively stable with depth. This appears to be because a larger body of rock fails as the excavation depth increases while the slip surface that shear occurs on does not increase proportionally, shown in Fig. 4. Increased bulk density reduces the FoS, which is logical because the increased overburden stress results in increased tangential stress to be resisted by the rock. Fig. 5 shows the effect of increasing γ′ 5 kN/m3 . Results in Figure 6 indicate that the in-situ lateral stresses have a negligible influence on the global FoS.

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Figure 3. FoS for 2 m, 4 m & 8 m diameter boreholes from 0–100 m depth. Figure 6. Stability of a 4 m diameter borehole with K0 = 0.5 & K0 = 1.

Figure 4. Incremental displacements for DC02A at 2.5 m, 5.0 m & 7.5 m excavation depths.

Figure 7. Development of radial (left) and tangential (right) stresses around a 2 m diameter 40 m deep borehole (DC02A).

Figure 5. The influence of increased unit weight on FoS.

3.3.2 Local stresses The development of stresses around the borehole is examined at the end of excavation stages without reduction of strength properties. Excavation of the

borehole leads to an increase in tangential stress and a decrease in the radial stress around the borehole. The tangential stress is maximum at the borehole wall and the effective stresses decreases to zero at the borehole wall, as shown in Fig 7. Fig 8 shows that the tangential stresses are independent of the borehole diameter and are equal to twice the in-situ lateral stresses before excavation. Reduction in tangential stress occurs local to the base of the borehole because of different stress paths becoming available around the base of the borehole. The reduction occurs further from the borehole base for larger borehole diameters. The tangential stresses around the borehole are highly dependent on the in-situ lateral stresses. Fig. 9 shows tangential stresses around the borehole increase in direct proportion to the increases in K0 . This will result in higher utilization of the rock around the borehole.

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Figure 8. Tangential stresses over depth interval 20–40 m for DC02A, DC02B & DC02C. In-situ lateral stress before excavation shown as reference.

Figure 10. Shear strength utilization around a 2 m diameter 40 m deep borehole (DC02A).

4

DISCUSSION OF FEM AND COMPARISON WITH OTHER METHODS

4.1 PLAXIS 2D analysis

Figure 9. Tangential stresses over depth interval 20–40 m for 4 m diameter 40 m deep borehole. K0 = 0.5 for DC02B, K0 = 1.0 for DC04B.

Fig 10. shows the utilization of shear strength around the borehole. This indicates that the shear strength is fully utilized at the borehole wall below approximately 30 m depth. However, this occurs at very small strains and does not result in a global failure mechanism. It is assumed that full utilization of the rock shear strength local to the borehole wall will be manifested as cracking and spalling. This agrees with experience from the mining industry discussed by Hoek et al (2000). The effect of this on the drilling process of the borehole is uncertain. If a large quantity of rock is spalled it may impair the operation of the drilling equipment or require cleaning of the borehole prior to pile installation.

Results indicate that the relatively weak rock properties considered have a FoS > 2 against a global failure mechanism for 2–8 m diameter boreholes up to 100 m depth. The FoS decreases most in the 0–20 m depth interval and then decreases at a relatively stable rate with depth below 30 m. The FoS decreases with larger borehole diameter. The plastic construction stages of the model show that very low strains result from the staged excavation. The shear stresses at the borehole wall exceed the shear strength of the rock mass during the excavation stages, which is expected to cause localized failure in the form of cracking and spalling. The extent of this failure and whether it is self-limiting is not clear from the FE analysis. Hoek et al (2000) indicate that rock can continue to support load after cracking has occurred. Results show that tangential stresses at the borehole wall are twice the lateral in-situ stresses and is independent of borehole diameter. Therefore, accurate estimates of the lateral in-situ stress is important in determining if localized failure of the rock occurs. 4.2 Calculations based on tunnel stability from Hoek et al (2000) The borehole is assessed considering a diameter of 2 m, 40 m deep using Mohr-Coulomb properties using the formulas described in § 2.1. Results are shown in Fig 3. This can be compared with DC02B, which indicates that no plastic deformation is expected, however calculations using formulas of Hoek (2000) suggest that plastic deformation occurs. Model DC02B predicts a maximum inward radial displacement of the borehole wall of 0.14 mm, which is significantly less than shown in Fig. 11. Deformations

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The critical strain approach to assess borehole stability gives a more optimistic result than assessing the stability based on shear strength utilization from PLAXIS models. Additionally, this method does not account for the lateral in-situ stresses, which PLAXIS2D results and other methods indicate to be a critical factor. Therefore it is questionable whether this approach is suitable for assessing borehole stability. 4.4 Wellbore stability method

Figure 11. Inward radial deformation of borehole wall & radius of plastic zone.

The wellbore stability method from Aadnoy (2010) assesses the stability on the assumption that tangential stresses are double the in-situ lateral stress. This agrees with the results of PLAXIS2D analysis. Therefore it is reasonable to assume that the wellbore stability method will indicate localized failure in the same locations that PLAXIS2D shows 100% utilization of the rock properties. Calculations with this method are not performed in this paper. 5

Figure 12. Analysis of borehole stability with Sakurai critical strain.

shown in Fig 3. may overestimate the displacements close to the base of the borehole because calculations have not accounted for the 1.5 diameters required for displacements to develop. 4.3

Calculation with Sakurai critical strain

The critical strain is calculated using Eq. (12) and compared against the strain calculated based on the effective overburden pressure:

The in-situ strains are compared against critical strains over the depth range 10–100 m in Fig 12. 2 cases are considered: Case 1: UCS = 10 MPa; Case 2: UCS = 0.5 MPa. The in-situ strains for Case 2 are well below the critical strain, whereas the critical insitu strain is exceeded at approximately 40 m depth for Case 1.

CONCLUSION

A literature study was combined with FE modelling to find a suitable analytical model to assess borehole stability on numerous locations on a windfarm site, in order to spot the locations that require detailed modelling. Hoek and Brown model, Wellbore stability method and Sakurai critical strain method were discussed and a Plaxis 2D Hoek and Brown model was made to assess the stability of large diameter, unsupported boreholes in weak sedimentary rock. Results indicate that localized failure of the rock at the borehole wall due to exceedance of shear strength would occur at much lower rock strengths than a global stability failure of the borehole. Therefore, assessment of the global stability of the borehole appears less relevant than assessment of localized failure at the borehole wall. Literature from the mining industry indicates that the localized failure at the borehole wall will occur as cracking, spalling and rock bursts. Industry experience from assessing wellbore stability shows that failure at the borehole wall can result in borehole enlargement. Localized failure may have an adverse effect on the drilling and installation process. Therefore, assessment for localized failure is considered the most appropriate method for a first check of borehole stability for pile installation. The resistance against localized failure can be assessed using the Hoek & Brown failure criterion, setting the minor principal stress equal to a radial stress of zero and the major principal stress equal to the tangential stress. The tangential stress can be calculated as twice the lateral in-situ stress, which is in agreement with the recommendations for wellbore stability of Aadnoy (2010) and results of PLAXIS 2D modelling. Accurately estimating the lateral in-situ stresses is critical factor in estimating the resistance against localized failure.

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The Sakurai critical strain does not appear a suitable method for assessment of borehole stability. The results appear optimistic compared to PLAXIS 2D results for localized failure of the rock at the borehole wall. Furthermore, the Sakurai method does not take into account the lateral in-situ stresses. REFERENCES

Hoek, E (1998). Tunnel support in weak rock. Keynote address, Symposium of Sedimentary Rock Engineering, Taipei, Taiwan. Hoek, E. Kaiser, P.K. Bawden, W.F. 2000. Support of Underground Excavations in Hard Rock. CRC Press. Boca Raton. Sakurai, S. 1997. Lessons Learned from Field Measurements in Tunneling. Tunnelling and Underground Space Technology, Volume 12, Issue 4.

Aadnoy, S.B. 2010. Modern Well Design 2nd Ed. CRC Press. Boca Raton.

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Thermo-mechanical hypoplastic interface model for fine-grained soils Henning Stutz Institute of Geo-Science, Marine and Land Geomechanics & Geotechnics, Kiel University, Kiel, Germany

David Mašín Faculty of Science, Charles University in Prague, Prague, Czech Republic

Frank Wuttke & Boyke Prädel Institute of Geo-Science, Marine and Land Geomechanics & Geotechnics, Kiel University, Kiel, Germany

ABSTRACT: Thermo-active geo-structures e.g. gas-/oil-pipelines, high-voltage cables, energy-piles, nuclear waste disposals are exposed to temperature changes. These alterations have a significant effect to the behaviour of soil-structure interfaces. The model is an adaption of the thermo-mechanical hypoplastic model from Mašín & Khalili (2011) and Mašín & Khalili (2012). The reformulation is done by redefined tensorial definitions for the special case of soil-structure interfaces. The new thermo-mechanical interface model is used for the modelling of soil-structure interface under varying temperature. By applying different temperatures and conducting a parameter study it is be proven that the model can be used for modelling various thermo-mechanical loading paths. After the simulations of some selected stress and temperature paths the paper discusses the benefits and advantages by using an advanced model for soil-structure interfaces considering temperature effects.

1

INTRODUCTION

The temperature effects in soils are manifold and can have different impacts on the behaviour of interfaces. Thermo-active geo-structures gain more and more attention in the field of renewable energy production. Typical applications as nuclear-waste storage, deep and shallow geothermal applications imply new challenges for the geotechnical & geomechanical community. If structures are embedded into soils and the temperature fluctuates a temperature dependent interface zone is established around the embedded structure. Especially the modelling of energy pile must consider the these temperature dependences. The shaft friction and the performance of these geo-thermal foundations will be influenced by variations of the temperature. For example Di Donna & Laloui (2015), Bodas Freitas, Cruz Silva, & Bourne-Webb (2013) and Laloui, Nuth, & Vulliet (2006) emphasize the importance of the influence of the pile-soil interface for energy piles. The temperature can trigger especially in finegrained soils changes to the mechanical behaviour. In the case of soil-interface tests the experimental available data is scarce. Di Donna, Ferrari, & Laloui (2015) conducted sand-concrete and clay-concrete shear tests. In the sand-concrete shear test no effects of the temperature changes had been observed and measured. Whereas,

in the clay-concrete tests results show an increased shear strength with respect to an increasing temperature. Further a decreasing contractive behaviour with an increase in temperature is observed. Di Donna, Ferrari, & Laloui (2015) concluded that the effect of an increasing shear stress under an increasing temperature is a result of a thermal consolidation which the sample had undergone. Yavari, Tang, Pereira, & Hassen (2016) conducted tests with intermediate heated soils (5–40◦ C), which are typical for thermo-active geotechnical structures. The tested soil is a Kaolin clay. In contrast to the tests by Di Donna, Ferrari, & Laloui (2015) the samples were heated prior to the test which enables the tests to be performed without the effect of thermal consolidation. The results by the tests of Yavari, Tang, Pereira, & Hassen (2016) indicate negligible influences for the interface shear strength parameters. Nevertheless, Yavari, Tang, Pereira, & Hassen (2016) reported a softening behaviour for clay-concrete interfaces which are not observed in clay-clay direct shear tests. Xiao, Suleiman, & McCartney (2014) conducted interface shear tests with a silty soil. The results were compared with the standard direct shear tests for the same soil. They concluded that the shear behaviour in soil-soil as well as in soil-solid tends to increasing shear strength under increasing temperature. Whereas, Xiao, Suleiman, & McCartney (2014) are not describing the sample preperation in detail.

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From the perspective of continuum soil testing e.g. triaxial and odeometric soil testing several open questions have to be answered and should be emphasized by on-going interface research. Mašín & Khalili (2012) hypoplastic model considers the volume change caused by heating or cooling as fully reversible process. This process is described by a constant value of the thermal expansion coefficient αs . The findings by (Xiao, Suleiman, & McCartney 2014, Di Donna, Ferrari, & Laloui 2015, Yavari, Tang, Pereira, & Hassen 2016) doesnot show the same trend. Indeed the temperature at the interface have an impact for the soil-structure interface behaviour. Due to this reason, a thermo-mechanical hypoplastic constitutive interface model is proposed. This model is based on the thermo-mechanical hypoplastic models of Mašín & Khalili (2011) and Mašín & Khalili (2012). The model reformulation by preserving the tensorial notation of the model is done by an methodology presented in Stutz & Mašín (2015) and Stutz, Mašín, & Wuttke (2016). First the thermo-mechanical hypoplastic model (Mašín & Khalili 2012) is introduced briefly and the reduced stress and strechting tensors for interface condition are given. Latter the model is used to simulate different boundary conditions which are typical for soil structure interfaces.

where σˆ = σ/trσ, the two scalars are defined as:

where r is a model parameter. The scalar value of a is defined as:

Where ϕc is the critical state friction angle. α is given as:

Where λ∗ and κ∗ are model parameters. The second order constitutive tensor is then defined as:

where Y = 1 coincide with the critical stress condition of the Matsuoka–Nakai formulation. The limiting stress condition Y is defined as:

2 THERMO-HYPOPLASTIC INTERFACE MODEL 2.1 Hypoplastic thermo-mechanical model in general formulation The thermo-mechanical hypoplastic model developed by Mašín & Khalili (2011) is introduced briefly. The stress-strain rate hypoplastic equation is given as:

where σ˙ is the stress tensor, L and N the fourth and second order constitutive tensor, ε the strain tensor and fs and fd the barotropy and pyknotropy factors. Mašín & Khalili (2011) developed the thermo-mechanical model using the hypoplastic clay model Mašín (2005) as basis for the improvements of the model. The stress-stretching rate equation for the thermomechanical model is:

where the stress invariants are defined as:

the second order tensor m is calculated as:

using the factor F as:

The temperature related strain is given as: with

where is T˙ the temperature rate. The constitutive fourth-order tensor L is given as:

and the Lode angle defined as:

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the barotropy factor is calculated as:

Finally, the evolution of the state variable e (void ratio) is governed by:

and the pyknotropy factor:

For an detailed description of the hypoplastic thermomechanical model, see Mašín & Khalili (2011) and Mašín & Khalili (2012).

where pe is the Hvorslev equivalent pressure defined as:

2.2 Adaption of the model for interface behaviour The adaption of the full thermo-mechanical hypoplastic model described in Section 2.1 is done by using reduced stress and strain rate tensors. These are defined as:

where the reference pressure pr = 1 kPa. The temperature dependence values of λ∗ (T ) and N (T ) are calculated as: and for the strain

and

Parameters nt and lt control the position and slope of the Normal Compression Line (NCL) of heated soils. The tensorial terms HT is introduced by Mašín & Khalili (2012) to incorporate the collapse effect of the soil structure at constant effective stress for a heated soil. HT is given by (Mašín & Khalili 2012) as:

These reduced tensors account for simple shear conditions at the interface can be written in modified Voigt-Notation as:

with

By using the modifications of the standard tensorial operators used in the 3-D model from Section 2.1 and the reduced stress and stretching rate vectors the thermo-mechanical interface model is reformulated. A detailed description of the modified tensorial notation, which is used by the stress and strain rate vector is outside of the scope of the paper. The interested reader is referred to Stutz, Mašín, & Wuttke (2016) and Stutz & Mašín (2015). In respect to the difference in simple shear at an interface and a soil-soil shearing the influencing parameter is the surface roughness. Especially for fine-grained soils, the roughness is important. If this roughness exceed an critical value the shear failure localise in the soil specimen. Chen, Zhang, Xiao, & Li (2015) demonstrated, if the critical surface roughness is exceed the interfacial friction angle is equal to the soil-soil (internal) friction angle (Uesugi & Kishida 1986). Due to this the roughness is for the modelling of interfaces crucial. In hypoplastic interface models this is done e.g. Arnold & Herle (2006) by introducing a reference

Where fdSBS is defined as the value of fd at the State Boundary Surface (SBS) passing through the current stress point.

The fourth order tensor A is expressed as:

The collapse behaviour is controlled by an additional factor fu as:

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Table 1. Parameters used for the hypoplastic thermomechanical interface model. Parameter

Soil 1

CV

CNL

ϕc [◦ ] λ∗ κ∗ N r αs lt nt m e0 σ0 T

27.5 0.09 0.01 0.88 0.2 3.5 · 10−5 0 −0.01 2.5 0.5 300 var.

27.5 0.09 0.02 0.82 0.2 3.5 · 10−5 var. var. 2.5 0.45 300 40

27.5 0.09 0.04 0.82 0.2 3.5 · 10−5 var. var. 2.5 0.45 100 40

parameter for the roughness κr . Stutz & Mašín (2015) choose a different approach, by modifying r which is accounting for the shear stiffness. In clay hypoplasticity, the value of r is equal to (Mašín 2013):

Figure 1. τx − γx results for CNL simulation with different applied constant temperatures.

The value of r for the reduced shear stiffness (denoted as rr ) reads

where ν controls the proportion of shear and bulk stiffness and used here as a constant ν = 0.2. 3

SIMULATION OF INTERFACE FRICTION BEHAVIOUR

Typically, the behaviour of interfaces is tested under different conditions. In this paper two of these boundary conditions are examined. First, the Constant– Normal–Load condition (CNL) defined as σ˙n = 0, ε˙n  = 0. Secondly, the Constant-Volume condition (CV) which is defined as σ˙ n  = 0 and ε˙ n = 0. The availability of limited number of experimental tests related to Constant-Normal-Load tests are used in conjunction to model the effects by the new thermo-mechanical interface model. Using a generic set of parameters given in Table 1. The aim of this paper is to demonstrate the application possibilities instead of comparing measurement against experimental data. The parameters given in the Table 1 are artificial parameters for the evaluation of the models response. The reference temperature is 25◦ C. The results of the CNL simulation are given in Figure 1 and 2 using the parameters of Soil 1. The applied normal stress is σ0 = 300 kPa. The shear stress decreases slightly under increasing temperature, see Figure 1. Whereas, the normal strain εn results (see Figure 2) indicate an increasing normal strain εn by an increasing temperature. For modelling a different behaviour as

Figure 2. εn − γx results for CNL simulation with different applied constant temperatures.

Figure 3. τx − γx results for CV simulation with different applied constant temperatures.

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Figure 4. σn − γx results for CV simulation with different applied constant temperatures.

Figure 5. σn − γx results for CV simulation with parameter variation of nt at 40◦ C.

Figure 6. τx − γx results for CV simulation with parameter variation of nt at 40◦ C.

Figure 7. σn − γx results for CV simulation with parameter variation of lt at 40◦ C.

indicated by the experimental results from Di Donna, Ferrari, & Laloui (2015) another parameter set can be used, see Section 3.1. The behaviour using a Constant Volume boundary condition is illustrated in Figure 3 and 4. Decreasing shear stresses τx and normal stresses σn are the results by increasing temperature. In the next section the parameter variation is conducted to estimate the influence and behaviour of different model parameter which modify the thermomechanical behaviour of interfaces. 3.1

Parameter variation

Figure 5–8 show the results for the parameter variation of nt and lt under CV conditions. Those two parameters are the most important ones for modelling the thermo-mechanical interface response using the model proposed by Mašín & Khalili (2012) under constant temperature. The stress paths shown, are only monotonic shear and temperature tests.

Figure 8. σn − γx results for CV simulation with parameter variation of lt at 40◦ C.

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Figure 9. τx − γx results for CNL simulation with parameter variation of nt at 40◦ C.

Figure 12. εn − γx results for CNL simulation with parameter variation of lt at 40◦ C.

The parameter study is conducted under constant temperature of 40◦ C and a normal stress of 300 kPa. In all diverse figures it is observed that a positive sign of lt and nt will lead to a decrease of shear and normal stresses. Whereas, an negative sign will lead to an increasing shear stress and normal stress. Figure 9–12 show the results for the CNL boundary conditions. The simulated tests are conducted under 100kPa. As indicated for the CV conditions the CNL results indicate the same behaviour than the CV results. In all diverse figures it is observed that a positive sign will lead to a decreasing shear stress τ and normal stress σn . Whereas, a negative sign will invert the model behaviour. Figure 10. εn − γx results for CNL simulation with parameter variation of nt at 40◦ C.

Figure 11. τx − γx results for CNL simulation with parameter variation of lt at 40◦ C.

4

CONCLUSIONS

In this paper we present an interface constitutive model which can take into account isothermal conditions. Further the model is capable to model non-isothermal behaviour. For this purpose a hypoplastic formulation of Mašín & Khalili (2011) and Mašín & Khalili (2012) is used and the standard tensorial notation was preserved. By the use of reduced stress and strain rate vectors in combination with modified tensorial notations described in Stutz & Mašín (2015) Stutz, Mašín, & Wuttke (2016) the interface behaviour is modelled. The model can take into account all relevant influences which occur at an interface under thermal and mechanical loading. This is proven by the calculations of Constant-Normal-Load and Constant-Volume boundary conditions. The utilization of this model will contribute to the modelling of soil-solid interface in various conditions which are subjected to thermal and mechanical loading even for repeated loading cases.

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REFERENCES Arnold, M. & I. Herle (2006). Hypoplastic description of the frictional behaviour of contacts. Numerical Methods in Geotechnical Engineering, 101–106. Bodas Freitas, T. M., F. Cruz Silva, & P. J. Bourne-Webb (2013). The response of energy foundations under thermomechanical loading. 18th Intl Conf Soil Mechanics and Geotechnical Engineering, 3347–3350. Chen, X., J. Zhang, Y. Xiao, & J. Li (2015, jan). Effect of Roughness on Shear Behavior of Red Clayconcrete Interface in Large-scale Direct Shear Tests. Canadian Geotechnical Journal 52, 1122–1135. Di Donna, A., A. Ferrari, & L. Laloui (2015). Experimental investigations of the soil-concrete interface: physical mechanisms, cyclic mobilisation and behaviour at different temperatures. Can. Geotech. J., 1–44. Di Donna, A. & L. Laloui (2015). Numerical analysis of the geotechnical behaviour of energy piles. International Journal for Numerical and Analytical Methods in Geomechanics 39(8), 861–888. Laloui, L., M. Nuth, & L. Vulliet (2006). Experimental and numerical investigations of the behaviour of a heat exchanger pile. International Journal for Numerical and Analytical Methods in Geomechanics 30(8), 763–781. Mašín, D. & N. Khalili (2011). Modelling of thermal effects in hypoplasticity. Proc. 13th International Conference of the IACMAG 1(May), 237–245.

Mašín, D. & N. Khalili (2012). A thermo-mechanical model for variably saturated soils based on hypoplasticity. International Journal for Numerical and Analytical Methods in Geomechanics 36, 1461–1485. Mašín, D. (2005). A hypoplastic constitutive model for clays. International Journal for Numerical and Analytical Methods in Geomechanics 29, 311–336. Mašín, D. (2013). Clay hypoplasticity with explicitly defined asymptotic states. Acta Geotechnica 8, 481–496. Stutz, H., D. Mašín, & F. Wuttke (2016). Enhancement of a hypoplastic model for granular soil-structure interface behaviour. Acta Geotechnica, 1–13. Stutz, H. & D. Mašín (2016). Hypoplastic contact model for fine-grained soils (under review). Uesugi, M. & H. Kishida (1986). Soils and Foundations 26, 139–149. Xiao, S., M. T. Suleiman, & J. McCartney (2014). Shear Behavior of Silty Soil and Soil-Structure Interface under Temperature Effects. In Geo-Congress, Number GSP 234, pp. 4105–4114. Yavari, N., A. M. Tang, J. M. Pereira, & G. Hassen (2016). Effect of temperature on the shear strength of soils and soil/structure interface. Canadian Geotechnical Journal, 1–33.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

A novel cavity expansion-based analytical tool and its potential application for energy pile foundation Hang Zhou & Gangqiang Kong College of Civil and Transportation Engineering, Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing, China

Hanlong Liu College of Civil and Transportation Engineering, Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing, China College of Civil Engineering, Key Laboratory of New Technology for Construction of Cities in Mountain Area Chongqing University, Chongqing, China

Yuedong Wu & Guowei Li College of Civil and Transportation Engineering, Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing, China

ABSTRACT: Energy pile gradually adopted in many countries, which is compatible with the principles of sustainable development. Extensive field and laboratory experiments are being undertaken in order to evaluate its thermal-mechanical performance. However, there is no sound theoretical method to reveal the fundamental mechanism of energy pile, particularly in evaluating the pile capacity change due to the temperature change. This paper develops a potential useful analytical tool for analyzing the energy pile performance and in particular to quantify the stress changes at the pile-soil interface induced by the temperature change. The analytical tool is formulated by incorporating Laloui et al ’s Advanced Constitutive Model for Environment GeomechanicsThermal effect (ACMEG-T) into the Cavity Expansion Theory (CET), namely Thermal-Cavity Expansion Theory (TCET). The TCET has potential application in energy pile foundation and may provide a theoretical basis for developing design methods of energy pile capacity in the future. Keywords: Energy pile, Cavity Expansion Model, Thermoplasticity, Geo-thermal

1

INTRODUCTION

Energy pile is gradually adopted in many countries, which is compatible with the principles of sustainable development. It is instrumented with a closed-loop heat exchanger in general to transfer heat between the surrounding soil and upper building (Laloui et al. 2006, Brandl, 2006; Bourne-Webb et al. 2009; Stewart & McCartney 2013; and Ng et al. 2014). It takes advantage of the geothermal energy induced by season changes and reduces the use of fossil fuels. Compared with conventional GSHP, it is not only more cost-effective to install due to the dual purposes of the material, but also it may be more efficient heat exchangers for high thermal conductivity of concrete. However, the thermal expansion and contraction of the foundation or surrounding soil will led to the potential for foundation movements, which may influence the safety of the building. Therefore, the mechanisms of thermo-mechanical soil-structure interaction are very important. Several full-scale case histories are carried

out. Model test is also developed by some authors. These studies have shed light on the coupled loading conditions and temperature effects on the pile. However, the analysis focused on theoretical calculation method on bearing capacity of energy pile influenced by surrounding soils is little. In this paper, an analytical tool, namely ThermalCavity Expansion Theory (TCET), is presented by incorporating Laloui et al’s (2009) Advanced Constitutive Model for Environment GeomechanicsThermal effect (ACMEG-T) into the Cavity Expansion Theory (CET). The constitutive relations of ACMEGT are coupled with the stress equilibrium equation, continuity equation, as well as drained condition during cavity expansion to form a group of Partial Differential Equations (PDEs). The PDEs are transform into Ordinary Differential Equations (ODEs) using the similarity transformation technique. Unlike the complex FEM calculations, the ODEs can be easily solved through the commercial mathematical software with few seconds. The TCET provides a possibility to

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(2) the stress-strain relations are described by a constitutive model (ACMEG-T) (3) a consistency condition ensuring the current stress state stays on the loading surface (4) a continuity condition for the conservation of mass of the solid phase (5) drained conditions (undrained or drained during cavity expansion process) 3.1

Equilibrium equation

By ignoring the body force, the usual stress equilibrium equation can be expressed as:

where p′ = (σr′ + kσθ′ )/(k + 1), q′ = σr′ − σθ′ , uw is the pore pressure, σr′ , σθ′ is the radial and circumferential stress components respectively, k = 1 and 2 for cylindrical and spherical cavity expansion respectively, r is the radial position of soil particle.

Figure 1. Cavity expansion model.

quantify the stress changes at the pile-soil interface of energy pile foundation due to the temperature change. 2

Constitutive equation

CAVITY EXPANSION THEORY (CET)

Figure 1 shows a cavity (cylindrical or spherical cavity) with initial radius a0 , which represents the energy pile cross section, and initial internal pressure σ0 uniformly expands to another cavity with radius a under the condition of temperature changes in infinite thermoplasticity soil. The initial temperature of soil is T0 (before expansion)and then it increased to the value of T . The expansion induced by the increasing of temperature is investigated here and the case of cavity contraction induced by the decreasing of temperature beyond the scope of this paper and will not reported here The constitutive model for the soil is described by Laloui et al’s Advanced Constitutive Model for Environment Geomechanics-Thermal effect (ACMEG-T). Other definitions are identical to the conventional cavity expansion theory (Zhou et al, 2014, 2015, 2016). 3

3.2

GOVERNING EQUATION FOR CAVITY EXPANSION

The key problem for cavity expansion in thermoplasticity soil is to find the temperature-dependent cavity wall pressure-expansion relations. In fact, cavity expansion is initial and boundary value problem, which is a mixed problem. If the governing equations combined with the initial and boundary conditions are given, the problem could be solved. To establish the governing equations for cavity expansion, the following five conditions should be considered: (1) the stress around the cavity wall should satisfy the equilibrium equation

where the symbol (◦ ) is used to describe the material time derivative associated with a given soil particle, ,e , e K = Kref (p′ /p′ref )n , G = Gref (p′ /p′ref )n , Kref and Gref are the reference bulk and shear modulus, w is the radial velocity of soil particle, M is the slope of the critical line in q − p′ , α is the material parameter introducing the nonassociative behavior. plastic volume strain,

is the total

is the plastic volume strain

induced by the isotropic mechanism, is the plastic volume strain induced by the deviatoric mechanism. p′ref is the value of the effective mean pressure at which the reference hypoelastic modulus are measured. 3.3

Consistency equation

where the derivatives can refer to Laloui et al (2009) and will not be reported here. Other parameters are defined the same as Laloui et al.

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p

p

Note that the two variables λiso and λdev used here are slightly different from Laloui’s original definition. Since Laloui used the expressions in the form of incremental, while the author used the rate form in this p p p p p paper. Actually, λiso = λiso /dt, λdev = λdev /dt (λiso and p λdev are Laloui’s original variables). However, it has no influence on the derivation. Combining Equations (4) and (5), one can obtains:

Introducing the transformation relation in Equation (12) and note that a reference stress, p′r (=1 kPa) is used for normalizing the stress variables, the above equation can be sorted out as Ordinary Differential Equations (ODE). 4.1

Boundary conditions

Based on the cavity expansion theory, the following relations are established at the elastic-plastic (EP) boundary:

Furthermore, at the cavity wall, one obtains: 3.4

Continuity equation The above ODEs can be solved through the function of “ode45” in Matlab and a numerical solution can be calculated with a few seconds, which is more convenient than the finite element methods (FEM).

where υ is the specific volume of soil. 3.5 •

•

Drained condition

4.2 Transformation of the similarity solution into finite cavity expansion solution

For drained condition, one has:

For undrained condition, one obtains

3.6

Relations of three strain components

Another equation is about the three strain components realtions:

4

SOLUTION OF THE GOVERNING EQUATION

Based on the similarity technique proposed by Collins et al (1994), the above equations can be presented in a non-dimensional form. The following variable transformation is used as:

where R is the radius of the plastic zone at time t, W is the cavity wall expansion velocity.

Note that a finite cavity expansion (see Figure 1) is useful particularly in the interpretation of the energy pile problem. Therefore, the obtained similarity solution should be changed to the finite cavity expansion solution. In fact, this problem has been pointed by Collins and Yu (1996) that the response for the expansion of a cavity from the finite initial radius a0 is consistent with that for the soil in the region r ≥ a0 in the created cavity problem (a cavity expands from a zero initial radius cavity to a finite radius cavity ). Under this principle, the following relation is established:

where η and w(η) ˜ can be obtained from the similarity solution. Equations (15) actually represent cavity expansionplastic zone radius relations. With this relation, the solution for the finite cavity expansion problem can be completely determined. 4.3 Critical value of the cavity expansion radius at the start of the yield It is necessary to give the critical value of the cavity expansion radius for determining the surrounding soil whether is yield or not. It is known that there is no volume change in the elastic zone surrounding the cavity.

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In this case, the cavity wall circumferential strain can be expressed as (Cao et al., 2001):

where εθ,a is the cavity wall circumferential strain, a0 is the radius of the initial cavity wall, a is the radius of the cavity wall after expansion. With the condition of zero volume change, one has:

Note that:

Combining Equations (16), (17) and (18) leads to:

At the start of the yield
state, the stress variable p′b d ′ q is equal to qb = Mpb 1 − b ln p′ (p′b = p′0 ) and c,b
′ n e p . Thus, the critical value for G = Gb = Gref p′ b ref

cavity expansion radius ac can be obtained as:

If a < ac , the cavity expansion is in the elastic state or else it is in the plastic state. Thus, the complete cavity expansion relations can be summarized as: •

if a ≤ ac

•

if a > ac

5

Figure 2. Relations between normalized cavity wall radius with the undrained expansion-induced (a) radial cavity wall pressure, and (b) cavity wall excess pore pressure.

are selected for analyzing the temperature influence on the cavity wall pressure-expansion relations. In addition, both of undrained and drained conditions are considered for the cavity expansion. Additionally, only cylindrical cavity expansion (k = 1) is considered here though it is simple to obtain the spherical cavity expansion solution (k = 2).

NUMERICAL EXAMPLES

In this section, the stress mechanism of the cavity expansion in thermoplasticity soil is investigated through the proposed similarity solutions. The soil parameters used in the analysis is used the same as Laloui et al (2009) and will not reported here. The initial temperature of soil is 25◦ . Five typical increased value of temperature (60◦ C, 70◦ C, 80◦ C, 90◦ C, 100◦ C)

5.1 Undrained cylindrical cavity expansion First of all, the stress mechanism of the undrained cylindrical cavity expansion is presented. The stress distribution and the cavity wall pressure are very important to the energy pile and thus are provided in this section. Figure 2a and 2b plot the relations between normalized cavity wall radius with the expansion-

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very interested to be noted that the increased temperature leads to the decreasing of the value of the cavity wall pressure. In fact, the increasing of the temperature results in the decreasing of the preconsolidation pressure p′c . This actually indicates the overconsolidation ratio is gradually increased due to the temperature increasing. It is known from the conventional cavity expansion in MCC model that the cavity wall excess pressure may decrease with the increasing of the value of OCR under the small soil rigidity index condition. Therefore, this is reason for the decreased cavity wall pressure due to the temperature increased. Figure 3a and 3b show the radial effective stress and excess pore pressure distribution around the expanding cavity wall for undrained condition respectively. The normalized cavity wall radius is selected for 1.1 in the computation. It is seen that plastic zone and elastic zone exist around the cavity wall. The plastic zone is near the cavity wall, while the elastic zone is far from the cavity wall. The radial effective stress rapidly decreases with the increased normalized radial distance, while it changes slowly in the elastic zone. It is noted that higher value of temperature develops the higher value of the radius of the plastic zone. This is because the soil rigidity index (G/su ) increases with the increasing of the soil temperature. However, the radius of the plastic zone is not sensitive to the temperature changes. Additionally, the excess pore pressure rapidly vanishes in the plastic zone and the excess pore pressure in the elastic zone is zero, which is consistent with the conventional cavity expansion theory. 5.2 Drained cylindrical cavity expansion

Figure 3. Figure 3 Stress distribution around the expanding cavity wall for undrained condition (a) radial effective stress; (b) excess pore pressure.

induced radial cavity wall pressure and cavity wall excess pressure respectively. It is obviously found that the temperature has significant influence on both of the cavity wall pressure and cavity wall excess pore pressure. Furthermore, the cavity wall pressure increases with the increasing of the temperature value and it reaches the limit value when the normalized cavity wall radius a/a0 is close to the value of 5. In practice, the normalized cavity wall radius a/a0 for energy pile is very small since the temperature change results in slightly pile shaft expansion and thus the value of the contact pressure at the energy pile-soil interface may usually not reach the limit value. In addition, it is

Besides the undrained cylindrical cavity expansion, the drained cylindrical cavity expansion is also investigated in this paper. Figure 4 plots the relations between normalized cavity wall radius with the drained expansion-induced radial cavity wall pressure. Here, it is note that the cavity wall pressure is actually equal to the radial cavity wall effective stress since the pore pressure is zero during the drained cavity expansion process. Unlike the undrained cylindrical cavity expansion, the cavity wall pressure is not sensitive to the temperature changes though it slightly increases with the decreasing of the soil temperature. In addition, it is also found that the drained cylindrical cavity expansion in thermoplasticity soil needs larger value of normalized cavity wall radius than the undrained cylindrical cavity expansion to reach the limit state. Figure 5a shows the radial effective stress around the expanding cavity wall for drained condition respectively. The normalized cavity wall radius is also selected as 1.1. It can be seen that the radial effective stress is not sensitive to the temperature changes which is not identical to the undrained cylindrical cavity expansion. However, the radius of the plastic zone is also not sensitive to the soil temperature changes. In addition, the specific volume distributions around the expanding cavity wall for drained condition are also presented in Figure 5b. The initial specific volume of

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Figure 4. Relations between normalized cavity wall radius with the drained expansion-induced radial cavity wall pressure.

soil is chosen as 2. It can be found that the specific volume of soil in the elastic zone is not changed and equal to 2 since the mean effective stress is constant value during cavity expansion process. Furthermore, the specific volume of soil increases with the increasing of the normalized radial distance in the plastic zone until it reaches the value of 2 at the elastic-plastic boundary. It is interested to be noted that the specific volume increases with the increasing of the soil temperature near the cavity wall, while it decreases with the increasing of the soil temperature near the elastic-plastic boundary.

6

Figure 5. (a) radial effective stress and (b) specific volume distributions around the expanding cavity wall for drained condition.

CONCLUSION

This paper incorporates the thermoplasticity soil model (ACMEG-T) into the cavity expansion theoretical framework to form a new analytical tool, namely TCET, which may have potential useful in analyzing the energy pile performance, particularly in capturing the contact pressure changes at the pile-soil interface induced by the temperature changes. Since no analytical solutions for the cavity expansion in the thermoplasticity soil have been published previously, the present analysis serves the important purpose of providing a set of benchmark results that could underpin further more sophisticated analysis. The present solution provides an exact and realistic theoretical framework for revealing the influence of the temperature on the cavity expansion mechanism, and it also provides a valuable benchmark for validating numerous cavity expansion numerical methods involving the thermoplasticity model.

ACKNOWLEDGEMENTS The work is supported by the National Natural Science Foundation of China (No. 51378178, 51306080), and the Doctoral Program of Higher Education and Research Grants Council Earmarked Research Grants Joint Research (No. 20130094140001, MHKUST603/13, GRF617213). REFERENCES Bourne-Webb P J, Amatya B L, Soga K, et al. (2009). Energy pile test at Lambeth College, London: geotechnical and thermodynamic aspects of pile response to heat cycles. Géotechnique, 59(3): 237–248. Brandl, H. (2006). Energy foundation and other thermoactive ground structures. Géotechnique, 56(2): 81–122.

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Cao, L. F., Teh, C. I., & Chang, M. F. (2001). Undrained cavity expansion in modified Cam clay I: theoretical analysis. Géotechnique 51(4) 323–334. Collins, I. F., & Stimpson, J. R. (1994). Similarity solutions for drained a undrained cavity expansions in soils. Geotechnique, 44(1), 21–34. Collins, I. F., &Yu, H. S. (1996). Undrained cavity expansions in critical state soils. International Journal for Numerical and Analytical Methods in Geomechanics, 20(7), 489– 516. Laloui L, Nuth M,Vulliet L. (2006). Experimental and numerical investigations of the behavior of a heat exchanger pile. International Journal For Numerical Analytical Methods Geomechanics, 30: 763–781. Laloui, L., & François, B. (2009). ACMEG-T: soil thermoplasticity model. Journal of Engineering Mechanics, ASCE, 135(9), 932–944. Liu, H., Zhou, H., & Kong, G., (2016). Upper-bound solution for the flat cavity expansion model. Journal of Engineering Mechanics (accepted). Ng, C. W. W., Shi, C., Gunawan, A., and Laloui, L. (2014). Centrifuge modelling of energy piles subjected to heating and cooling cycles in clay. Géotechnique Letters, 4(4): 310–316.

Stewart, M.A. and McCartney, J.S. (2013). Centrifuge Modeling of Soil-Structure Interaction in Energy Foundations. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 140(4), 04013044-1-11. Zhou, H., Liu, H. L., Kong, G. Q., & Huang, X. (2014a). Analytical solution of undrained cylindrical cavity expansion in saturated soil under anisotropic initial stress. Computers and Geotechnics, 55,232–239. Zhou, H., Liu, H. L., Kong, G. Q., & Cao, Z. H. (2014b). Analytical solution for pressure-controlled elliptical cavity expansion in elastic-perfectly plastic soil. Geotechnique letters 4(April-June), 72–78. Zhou, H., Liu, H. L., & Kong, G. Q. (2014c). Influence of shear stress on cylindrical cavity expansion in undrained elastic-perfectly plastic soil. Geotechnique letters 4(JulySeptember), 203–210. Zhou, H., Kong, G., Li, P., & Liu, H. (2015). Flat cavity expansion: theoretical model and application to the interpretation of the flat dilatometer test. Journal of Engineering Mechanics, 142(1), 04015058. Zhou, H., Kong, G., & Liu, H. (2016). A semi-analytical solution for cylindrical cavity expansion in elastic-perfectly plastic soil under biaxial in-situ stress field. Geotechnique (accepted).

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Numerical analysis of heat conduction in granular geo-material using lattice element method Z.H. Rizvi, A.S. Sattari & F. Wuttke Geomechanics & Geotechnics, Christian Albrechts University, Kiel, Germany

ABSTRACT: Heat transfer in geo-materials especially in granular systems is important to a vast array of practical problems, yet is poorly understood even in the simplest case, such as conduction in dry state. This is due in part to the stress and contact heterogeneities inherent to these systems. Heat conduction in a packet bed is analyzed computationally based on lattice element method. A novel model is developed based on the Lattice Element Method, which not only sheds light on fundamental issues in heat conduction in particles, but also provides a valuable test bed for existing theories. By meshing the domain the material heterogeneity is directly included, and thus dynamic temperature distributions are obtained at the particle level. Comparison with existing experiments shows that this model yields a quantitatively accurate temperature field without the need for adjustable parameters or detailed microstructural information. This simple system is suitable for providing insight into such phenomena as reactor and underground energy and steam cable “hot spot” formation and spontaneous combustion of bulk reactive materials.

1

INTRODUCTION

The importance of heat transfer in granular materials has been brought up in many geotechnical engineering applications such as, geothermal energy storage, buried power cables, containment of radioactive waste, CO2 sequencing and hydrocarbon energy recovery. Traditionally, effective medium analogy is applied, assuming the porous media is homogeneous. Thermal analysis provides accurate results in bounded case with finite element method (FEM) and with boundary element method (BEM) in unbounded case. These methods, based on established continuum theory are high computational efficient for large scale problems. However, these methods cannot take in account for granular variation at spatial and particle level. Even, the heat conduction in solid phase presents problem in transient case. Many studies for heat transfer based on particle method have been proposed by researchers. Thermal particle dynamics method based on stress and contact heterogeneities has considered uniform particle bed. (Vargas & McCarthy 2001). Discrete element modelling with circular particles, pipe network model for transient analysis (Feng et al. 2008,2009) three dimensional random network model considering contact resistance (Yun & Evans 2010) multi scale model (Zhang et al. 2011), thermal contact model considering surface roughness (Zhou et al. 2012) have been studied. However all of these models are considering the particulate matter as circular which is far from reality in case of geo-materials. Recently, Laguere-Voronoi

based approach is applied to study heat transfer in open cell foam structure. (Randrianalisoa et al. 2015). In this paper we present an alternative approach for heat conduction in particulate matter based on lattice element method. This method involves Voronoi based techniques to divide the particle packing. The domain is seeded with nodes and then lattice network is obtained by connecting these nodes with 1D elements. These 1D elements connected in a three dimensional space thus reduces the 3D problem to 1D heat conduction. The method is applied to study heat conduction in vacuum. The heat transfer path is considered in the present modelling with conduction path depending upon the particle size. The results indicates that the Voronoi based approach is useful in understanding the mechanism of heat transfer in granular particles. 2

LATTICE ELEMENT METHOD

Behavior of geomaterials depends upon the properties and distribution of grains and binders. Therefore, morphology based simulations which accounts for material geometry itself is a growing trend. Various numerical models relying upon discrete structural components have been used to clarify crack nucleation and propagation within cement based binders. (Schlangen & Garboczi 1997). Voronoi based techniques for discretizing particulate materials in three dimension within the lattice model for fracture analysis is implied using randomly generated polyhedral. (Asahina & Bolander 2011)

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Lattice element method (LEM) is adopted from condensed matter physics as a method of discretizing continuum elastic media and are frequently used to simulate deformation and fracture. A LEM consists of a regular two or three dimensional network of a dimensional springs, connected to randomly distributed nodal sites, with each spring is govern by its own set of constitutive relations. Two type of spring models are used 1) Hookean spring model and 2) Born spring model. The first model exhibit central force interaction with constant Poisson’s ratio while the second introduces non-central two body interaction limiting the rotation freedom. A number of studies used beam-spring network thus enriching the material description with rotation degree of freedom. Lattice type models have been applied by Schorn using truss element, which require numerical measures to avoid instability. Bolander applied a beam lattice with a step wise softening law which was extended to 3D by Lilliu and termed is as “Delft lattice”. A parallel computation scheme is implemented to reduce the computational time and an interfacial transition zone (ITZ) is implemented to reduce the matrix strength. The majority of particulate models have been two dimensional with circular and fiber inclusions with a few spherical inclusions is investigated in a 3D simulation. Various failure criteria of element failure have been suggested including critical elastic stress, strain and energy. LEM is mostly associated with linear elastic fracture mechanics with a few attempts to include plasticity. Plasticity is assigned to the springs which results in anisotropic plastic deformations which in turns fails to account for conservation of volume. 3

REPRESENTATION OF HEAT TRANSFER WITH LATTICE ELEMENT

An in-house Lattice based code in under development to solve the heat transfer problem in steady and transient state. The solver can handle complex geometry and yield results in reasonable time.

3.2 Heat Transfer Formulation A lattice based contact conductance model is developed to simulate the heat transfer in granular assemblies in vacuum with consideration of the thermal resistance of smooth contact surfaces. The representation of heat transfer between spherical particles using DEM can be found in various scientific works (Feng et al. 2008, 2009). The discrete thermal element modelling of heat conduction in spherical particle systems using Pipe-network model is introduced by (Feng et al. 2008, 2009). Generally, the temperature Ti of each particle in the steady system should satisfy the following heat conduction equation. Under this condition, the heat flows into and out of the RVE are the same.

In which R denotes the granular RVE and qi represents the total heat exchange between particles i and others. Calculating qi requires heat exchange qji between two contact particles, which is given by

Where hij denotes the heat conductance between the two particles, Ti and Tj the temperatures of particles i and j, respectively. The analytical solution of heat conductance hij with perfectly smooth surfaces is presented by (Bahrami et al. 2005).

Where Fn is the magnitude of normal contact force between the two contact particles, and k is the thermal conductivity. re and Ee are the effective radius and the effective Young’s modulus, which are determined by,

3.1 Mesh Generation In the 2D and 3D model Voronoi polygons are used for the representation of the structured system. We apply a special form of the Voronoi tessellation called vectorizable random lattice (Lilliua-Mier 2003 & Moukarzel-Herrmann 1992), in order to obtain an initial configuration of the mesh. It is performed by first putting a regular grid onto the plane and throwing points randomly and independently in a square of the side length a centered on the plaquettes of the regular grid. Using these points for the Voronoi construction, the randomness of the tessellation can be controlled by tuning the value of the parameter a between 0 and the lattice spacing of the grid. After Voronoi construction, a customized Delaunay discretization code is developed based on the neighboring cells, accounting for lattice element springs or beams.

Figure 1. Representation of Voronoi cell and effective distance between two nuclei.

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Where ν is Poisson ratio. Application of Lattice Element into discrete element problem can provide better representation of heat transfer between irregular shaped particles. In this case ri and rj should be redefined as shown in figure (1). To scale up the heat transfer equation requires two conditions. The first assumption is that each i − j particle contact “feels” the same temperature for particle

i such that each heat contribution may be calculated from Eq. 2 and the total heat input Qi may be approximated as the sum of the interactions of particle i with each of its neighbors. The assumption is not correct if the heat storage term is incorporated. However it is conceptually simple and is found to be accurate in steady state condition. It is also assumed that heat transfer is possible through the network formed from connecting the nuclei of each Voronoi cell. The first two assumptions are independent of material property. The material parameter is introduced from the conductance between the two adjacent nuclei depends upon the re and Ee are the effective radius and the effective Young’s modulus Fn is the magnitude of normal contact force between the two contact particles. The second condition is that the temperature change is a gradual process and only the immediate cell can experience the change in one time step. Mathematically, this quasi-steady temperature criterion can be shown to be met by choosing a time-step sufficiently small. 4

Figure 2. Voronoi cell and Denulay triangulation of a 2D sample (a)(b)(c) and 3D(d)(e)(f) with different randomness factor (a) r = 0.01 (b) r = 0.4 (c) r = 0.7.

NUMERICAL TESTS AND DISCUSSION

Three numerical tests are performed based upon the developed model with regular and irregular packing of the granular assembly. These simulations are performed with 2D and 3D arrangement of particles. Three different packing arrangements are simulated,

Figure 3. 2D conduction heat transfer in granular material with particle shape factor of 20x20 mesh size a.) 0.01 b.) 0.4 c.)0.7 d.) 0.9.

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Figure 4. Mesh density test with different number of elements in a square plate [1, 1] a) 400 b) 2500 c) 10000 d) 22500.

Figure 5. Mesh density test with different number of elements in a cube block [1, 1, 1] a) 15 × 15 × 15 b) 30 × 30 × 30 c) 40 × 40 × 40.

the first one with a randomness of 0.01 which resembles a regular lattice case. The second simulation is performed with a randomness of 0.4 and the last one with a randomness of 0.7. The randomness factor controls the construction of Voronoi cell generation. The figure below snows the generated Voronoi and denulay triangulation diagrams for the considered region. 4.1

Illustrative examples

The effectiveness of the LEM heat transfer code is demonstrated with examples. Heat conduction in

Figure 6. Mesh density test with different number of elements in a prism block [1, 1, 3] a) 10 × 10 × 30 b) 20 × 20 × 40 c) 30 × 30 × 30.

granular materials are dominated by conduction and the flow path (Yun & Santamarina 2008) is defined by conduction path in granular material. Many particle based approaches to solve the problem had been proposed. Some of these approaches such as based of Discrete Element Method are limited with the shape and arrangement of particle. The other method based on molecular computation is computational intensive and requires the physical parameter calculation at molecular level. As the connections are defined between Voronoi cell and a heat conduction paths are developed which defines the heat conduction path, the method gives better picture of heat conduction in granular materials with limited computation power.

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The problem of heat conduction in granular material is presented. The Voronoi cells are generated in a range of [1, 1] square geometry. Randomness factors as mentioned above of 0.01, 0.4, 0.7 and 0.9 are applied. The number of Voronoi cells are increased from 20, 50 and 100 in each directions. The code is extended to simulate heat transfer in 3D granular media. 1D elements are chosen and the same scheme to discretize and the method for generation of Vornoi cells are adopted.Temperature boundary conditions are applied at two opposite faces and the rest were assumed to be isolated. Two different shapes, cube and prism were chosen for steady state heat transfer. The Voronoi particle randomness factor for these simulations are fixed at 0.7. The conductance between two particles is calculated from equation 3. 5

CONCLUDING REMARKS

The present work has developed a lattice based approach for thermal conduction in granular material. Each particle is modelled as a lattice which is connect by a simple 1D element connecting the Voronoi cell nucleolus with surrounding cells using Delaunay triangulation scheme. The model essentially neglects the heat storage term in the cells and thus simplifies the solution procedure. In comparison with the other particle methods i.e. Discrete Thermal Element Method, this lattice based approach predefines nucleolus and lattice connections. The algorithm is compatible with classical discrete element method which could be used to simulate thermo-mechanical problem. The method could be extended to simulate the transient heat transfer in granular materials with minor changes. Numerical simulations suggest that lattice based heat transfer method gives accurate and fast results for heat transfer in conduction for steady state problems. A detailed study for heat transfer in conduction based on lattice method is required for transient problems.

REFERENCES Asahina D., Bolander J.E.,”Voronoi-based discretizations for fracture analysis of particulate materials” Volume 213, Issues 1–3, 10 November 2011, Pages 92–99. Bahrami M., Culham J. R., Yovanovich M. M., Modeling Thermal Contact Resistance: A Scale Analysis Approach, J. Heat Transfer 126(6), 896–905 (Jan 26, 2005). Feng YT, Han K, Li CF, Owen DRJ (2008) Discrete thermal element modelling of heat conduction in particle systems: basic formulations. J Comput Phys 227(10):5072–5089. FengYT, Han K, Owen DRJ (2009) Discrete thermal element modelling of heat conduction in particle systems: pipenetwork model and transient analysis. Powder Technol 193(3):248–256. Lilliua G, van Mier J.G.M “3D lattice type fracture model for concrete” Volume 70, Issues 7–8, May 2003, Pages 927–941. Moukarzel, C. & Herrmann H.J. A Vectorizable random lattice, journal of statistical physics Vol,68.Nos.5/6 1992. Randrianalisoa J., Baillis D., Martin C.L., Dendievel R., Microstructure effect on thermal conductivity of open cell foams generated from the Laguere Voronoi tessellation method, International Journal of Thermal Sciences 98 (2015) 277–286. Schlangen E., Garboczi E.J. “Fracture simulations of concrete using lattice models: Computational aspects” Volume 57, Issues 2–3, May–June 1997, Pages 319–332. Vargas, W.L. & McCarthy, J.J. 2001. Heat conduction in Granular Materials AIChE Journal Vol 47, No. 5. Yun, T.; Evans, T. Three-dimensional random network model for thermal conductivity in particulate materials. Comput. Geotech. 2010, 37, 991–998. Yun, T.; Santamarina, J. Fundamental study of thermal conduction in dry soils. Granul. Matter, 2008, 10, 197–207. Zhang H.W., Zhou Q., Xing H.L., Muhlhaus H., A DEM study on the effective thermal conductivity of granular assemblies, Powder Technol. 205 (2011) 172–183. Zhou Q.,. Zhang H.W., Zheng Y.G., A homogenization technique for heat transfer in periodic granular materials, Advanced Powder Technology 23 (2012) 104–114.

ACKNOWLEDGEMENT This research project is financially supported by the research grant DuoFill provided by the Federal Ministry for Economic Affairs and Energy, Germany (ZIM grant number KF3067303KI3) and Federal state funding at University of Kiel.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Thermo-hydraulic coupled modelling: Analysis of thermal enhanced backfill structures and materials for near-shore power cables K. Sembdner Department of Geosciences, Kiel University, Kiel, Germany

H. Anbergen APS Antriebs-, Prüf- und Steuertechnik GmbH, Rosdorf, Germany

F. Wuttke Department of Geosciences, Kiel University, Kiel, Germany

ABSTRACT: Offshore wind power has been an expanding market during the last decade. The wind power stations are electrically connected via buried high voltage cable systems. Due to the electrical resistance of cables, thermal energy is emitted during current transport. The emitted heat damages and ages the cable, and weaken significantly the cable’s performance. A thermal enhanced backfill embedding the cable helps distributing the produced heat fast to the surrounding soil and protect the cable from excessive heating. Thermo-hydraulic coupled simulations have been carried out to analyse the influence of thermal enhanced backfill on the temperature distribution around these high voltage cables. A comparative study with different thermal backfill materials embedding a high voltage cable was performed, in order to identify suitable thermal backfill properties and its arrangement around the cable. For this purpose, three different numerical solutions have been used (OpenGeoSys, COMSOL, FEFLOW). The results show that heat distribution around high voltage cables is strongly influenced by thermal and hydraulic properties of the surrounding backfill and that a proper backfill is able to modify the heat dispersion according to requirements.

1

INTRODUCTION

Offshore wind power has been an expanding market of the last decade. Several offshore wind power plants have been constructed or the construction is in progress. These plants need to be connected via high voltage cable systems. While the energy transport onshore is often solved with over-head systems, offshore and nearshore buried cables are used. Due to the electrical resistance of cables, thermal energy is emitted during electrical energy transport. In order to be able to transfer a sufficient amount of current and simultaneously protect the cables from heat caused damages, the cable’s dimensions are enormous. The aim of this study is to increase the efficiency of power cables and/or reduce their required size, through a thermal enhanced backfill embedding the cable. Additionally ecological guidelines need to be taken into account to protect the heat-sensitive marine environment. Therefore, the german environmental authority (Bundesamt für Seeschiffahrt und Hydrographie) has prohibited to exceed a temperature rise of 2 K at a seafloor depth of 0.2 m (inside german’s exclusive economic zone) and 0.3 m (inside Lower Saxony’s wetlands), this prohibition is called the 2-Kelvin-Criteria

(BSH, 2007). The heat protection is particularly concentrated to the upper centimeters of the seafloor, since it exhibits the highest bioactivity compared to the lower depths of the seabed. In summary, the backfill material needs to provide a sufficient heat transport ability, to keep the high voltage cable cool and simultaneously comply with the ecological boundary conditions. Within the framework of a joint research project (KF3067306KI4) thermo-hydraulic coupled simulations have been carried out to analyze the influence of thermal enhanced backfill on the temperature distribution around high voltage cables inside the seafloor. The first fundamental study is a comparative study on the influence of the backfill’s material parameters on the heat transport. For this purpose simulations were performed with different backfill material and model geometries. The study consists of four scenarios, in which the high voltage cable is embedded in different enhanced backfill materials and without any backfill material. Additionally a hydraulic flow is induced. The temperature distribution around the cables is recorded for 168 hours at a maximum cable load, as a worst-case scenario. The simulations are performed by three finite element method (FEM) software solutions, namely: OpenGeoSys, COMSOL, FEFLOW.

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Table 1. Mesh parameters of the three different software solutions (for Model A).

Mesh Nodes Mesh Elements Element Type

2

OpenGeoSys

Comsol

FEFLOW

4211 8373 Triangular

14103 28385 Triangular

13059 24444 Triangular

METHODOLOGY

2.1

Software applications and numerical calculations

The three software solutions utilised are: OpenGeoSys, COMSOL, FEFLOW. They are all finite element method (FEM) based software solutions. The mesh parameters used by the three different software solutions are listed in table 1. For solving the groundwater flow coupled with heat transport, the following thermo-hydraulic coupled equations were used (Rühaak et al., 2015; Mottaghy & Rath, 2006; McKenzie et al., 2007; Rühaak, et al. 2008; Anbergen et al., 2015a):

Figure 1. Schematic model configuration, including boundary conditions and material parameter (after Anbergen et al., 2015b).

where λw , λs , and λeff are the thermal conductivities of water, soil solids, and the resulting bulk value, respectively; and ε is the porosity. The bulk volumetric heat capacity (ρc)eff (J m−3 K −1 ) is calcultated in the similar manner:

with where ρ is the density, c the heat capacity, ε the porosity. The indexes w, s and eff indicate the water and soil phase, respectively the bulk value.

Nomenclature Ss specific storage (m−1 ) ρ density (kg m-3) c specific heat capacity (J kg−1 K−1 ) T temperature (◦ C) λ thermal conductivity (W m−1 K −1 ) ∇ Laplace operator H heat sources (W m−1 ) Q fluid sources (s−1 ) K hydraulic conductivity (m s−1 ) h head (m) t time (s) Sw water saturation (–) L latent heat of fusion for bulk medium (J m−3 ) q Darcy velocity (m s−1 ) Indexes eff bulk value f fluid phase

2.2

Model configuration

Two different model configurations were used in this study. Their major difference is the trench design. Model A contains a uniform trench backfill, whereas model B has a combination of two backfilll material. Also, model A was solved by all three different software applications, while model B was solved only by Comsol.

The FEM code interpolates the bulk thermal conductivity linearly using porosity, the solid and fluid thermal conductivity (Anbergen et al., 2015a; Diersch, 2014; Comsol, 2013; Böttcher, 2014):

2.2.1 Model A The model area is a vertical cross-section through a power cable with the surrounding water and sediments. The area of interest is a square of 10 m × 10 m, see figure 1. The model is horizontally divided into halves. The upper half represents free seawater, the lower half the saturated seabed sediments. Inside the seabed the high voltage cable is embedded in a 1.64 m deep and 0.36 m wide trench filled with backfill material. Due to the legal constraints, a worst-case scenario is simulated in order to identify potential hot-spots in the surrounding sediments. Therefore, the outer surface of the cable is set to a constant temperature of 60◦ C, following assumptions of Brakelmann (2010). Brakelmann (2010) simulated a worst-case-scenario with a

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Figure 3. Three model scenarios of Model A: a) trench filled with backfill_1, b) trench filled with backfill_2, c) no backfill. Table 2. Material pameters of water, seafloor and backfill materials. Water Seafloor Backfill_1 Backfill_2 Figure 2. Schematic model configuration of the layered trench, filled with backfill_1 and backfill_2.

maximum electrical loading for a period of seven days (168 hours). This extensive energy transport resulted in a heating of the outer cable surface of 60◦ C. The temperature boundary conditions of the model area are set to constant 12◦ C, assuming no temperature change in the surrounding soil and water. With 12◦ C the boundary condition is set slightly higher than the mean annual bottom water temperature in the nearshore areas of the Northsea (Schulz, 2009), hence a worst case scenario is simulated. In order to simulate the water movement at the sea bed, a hydraulic flow from the left to right side of the model area is induced. Boundary conditions of different hydraulic heads are implemented (left hydraulic head of 10 m, right hydraulic head of 9 m). The model includes observationpoints at several depths under the seabed (0.2, 1 and 2 m). A special focus is on the depth of 0.2 m, for monitoring the compliance of the 2-Kelvin-Criteria. 2.2.2 Model B This model configuration contains a layered trench, in which two different kinds of backfill material are combined, see figure 2. Also the depth of the total trench is increased by 0.36 m to 2 m. All the other already described model configurations of Model A remain unmodified. 2.3 Model Scenarios Three model scenarios were simulated for Model A, see figure 3. The scenarios differ in the backfill material of the trench. In two scenarios the high voltage cable is embedded in backfill materials with different thermal properties. In the third scenario the cable is embedded in the seafloor, without any modified backfill. A fourth scenario is calculated for Model B; a layered trench combining two different backfill materials, as shown in figure 2. The material parameters of the backfill materials, water and seafloor are listed in table 2. The material

Heat Cond. (eff.), λ[W m−1 K −1 ] Heat Capacity, c[J kg −1 K −1 ] Porosity, ε [–] Hydraulic Cond., k[m s−1 ] Density, ρ[kg m−3 ]

0.58

1.43

1.00

2.00

4190 1273

1000

1000

1.00 –

0.25 0.30 1 × 10−6 1 × 10−8

1000 1800

1800

0.30 1 × 10−8 1800

parameters of the backfill materials backfill_1 and backfill_2 are almost identical, except for the heat conductivity of the saturated materials. Backfill_1 has a low effective heat conductivity of 1 W/mK, which is lower than that of the seafloor (1,43 W/mK). Backfill_2 has an effective heat conductivity of 2 W/mK, which is higher than that of the seafloor. 3 3.1

RESULTS Model A

The heat dispersion around the cable embedded in backfill_2 after 168 hours simulated with Comsol is shown in figure 4. The heat distributes in a circular shape around the heat source and expands its radius with increasing timesteps. The results in figure 4 calculated with Comsol stand exemplary for the other software solutions, which have shown very similar results for heat dispersion. For Comparison of the different software solutions and estimation of the accuracy of the results, the temperature at an observationpoint is analysed. The observationspoint is set at 0.2 m depth perpendicular to the cable’s center, for monitoring the compliance of the 2-Kelvin-Criteria. The temperature at this point is plotted versus time for all three software solutions (OpenGeoSys, Comsol and FEFLOW) and for the three scenarios: with backfill_1 (a), with backfill_2 (b) and without backfill (c). The scenario without backfill is shown in figure 5, here the cable is embedded in marine sediment. The

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Figure 4. Heat dispersion after 168 h with backfill_2, Comsol.

Figure 6. Heat development at 0.2 m seafloor depth versus time, with backfill_1.

Figure 5. Heat development at 0.2 m seafloor depth versus time, without backfill. Figure 7. Heat development at 0.2 m seafloor depth versus time, with backfill_2.

temperature increases with time for all three software applications. The 2-Kelvin-Criteria is slightly exceeded by OpenGeoSys and Comsol results. In both cases the temperature increases up to around 14.1◦ C. The FEFLOW results show no exceedance of the 2-Kelvin-Criteria for the calculated time period, the temperature’s maximum is 13,6◦ C. The temperature in the scenario b) (see figure 6) is also increasing with time, but the maximum temperatures are significantly lower compared to figure 5. Figure 7 shows the temperature development with the heat source embedded in backfill_2. In this scenario the temperature increase is the steepest and the maximum temperature is the highest for all three software solutions, compared to the other scenarios. Moreover all of the software solutions exceed the 2-Kelvin-Criteria.

In all of the scenarios the Comsol application calculated the highest temperatures, followed by OpenGeoSys and FEFLOW. However the deviations are smaller than 1 ◦ C. Figure 8 displays Isolines for the temperatures 15◦ C and 30◦ C around the cables of all three scenarios. It can be clearly noticed that the backfill_2 (b) is directing the heat flux towards the seabed surface. Additionally you can see, that the temperature plume is disturbed by the backfill materials, as their hydraulic conductivity is lower than that of the seafloor. 3.2

Model B

In figure 9 and 10, the temperature at different observationspoints for a layered trench and without any

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Figure 8. Temperature Isolines (15◦ C, 30◦ C) around the cable for the three scenarios of Model A: a) trench filled with backfill_1, b) trench filled with backfill_2, c) no backfill.

Figure 10. Heat development at different observationpoints (0.2, 1.0, 2.0 m beneath the seafloor) versus time, without backfill, solved with Comsol.

Figure 11. Temperature Isolines (15◦ C, 30◦ C) around the cable for Model B. Figure 9. Heat development at different observationpoints (0.2, 1.0 and 2.0 m beneath the seafloor) versus time, with layered backfill, solved with Comsol.

trench are displayed. Comparing these two results, it is obvious that the layered trench leads to a deviant temperature distribution. The upper layer of backfill_1 acts as isolating barrier for the upper part of the trench, to a very slight extent. As for the layered trench the temperature at the observationpoint in 0.2 m depth decreases by 0.01◦ C. But it seems, that the temperature is accumulating underneath the layer of backfill_1, as the temperature is raised by 0.5◦ C at the observationpoint at 1.0 m depth within the layered trench. Additionally the heat dispersion into the seafloor depth is strongly enhanced by backfill_2 underneath the cable. For the temperature at the observationpoint at 2.0 m depth is increased by 4.69◦ C. This effect of a redirected heat flow into the seafloor depth is also displayed in figure 11.

4

DISCUSSION

The figures 5–7 demonstrate that the temperature dispersion is obviously depending on the thermal parameters of the backfill. Thermally enhanced backfill in the trench, such as backfill_2, induces a faster heat transport. Even though this is favorable for the cable, as it leads to an enhanced cooling of the cable, the legal criteria (2-Kelvin-Criteria) is exceeded. Since a faster heat transport is mainly induced in an upwards direction. The backfill_1 might seem to be the best solution, as it is the only scenario complying with the 2-Kelvin-Criteria. But this first evaluation is misleading, because the backfill is insulating the cable, which conflicts with the need of the thermal energy dispersion. It is obvious that the first simulated solutions with Model A do not lead to the desired effect. Hence, further simulations were executed, where a layered

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trench was constructed (Model B). Here, the trench is filled with two different backfill materials. The upper part of the trench is filled with an insulating backfill (backfilll_1), to ensure a compliance with the 2-Kelvin-Criteria. The lower part of the trench is filled with a thermal enhanced backfill (backfill_2), to ensure a fast thermal energy dispersion. Yet the desired effects of the layered trench have only been achieved in parts. The fast thermal energy dispersion particularly to deeper areas of the seafloor has been accomplished. Yet the isolating effect of the upper backfill layer is much less pronounced than expected. This may depend on the thermal and hydraulic material parameters of backfill_1. A study with a variation of these parameters and the geometry of the layer is adviseable. Comparing the different software applications, certain variations in the results are detected, even though the calculations are executed with the same simulation parameter and model parameter input. These deviations may be based on different numerical solution algorithms, which are used by the different software applications. In spite of these discrepancies, the simulation results enable to evaluate at least tendencies of the temperature distribution around a high-voltage cable.

5

CONCLUSIONS AND OUTLOOK

The results of the three software solutions differ substantially. More benchmark studies, comparing the different software applications are needed. The temperature dispersion is strongly depending on the thermal parameters of the backfill and its arrangement. The results show, that a proper backfill is able to modify the heat distribution around the cable according to its requirements. Besides the simulation of the temperature distribution, further elaboration of the absolute heat-flux is needed. More in-depth studies are planned, as for example the simulation of heat flux around the cable. Only in this way the complete effect of thermally modified backfill material can be evaluated. Furthermore accompanying experimental studies are planned, in order to confirm or rectify the above presented simulation results. For this, thermal conductivity and heat capacity measurements of the modified backfill and sediments will be executed. Additionally an experimental setup as technikum experiment is planned, in order to measure the thermal plume around a cable directly.

ACKNOWLEDGEMENTS This research project is financially supported by the research grant “GeoMörtel” provided by BMWi (Bundesministerium für Wirtschft und Energie) & ZIM (Zentrales Innovationsprogramm Mittelstand) with the grant number: KF3067306KI4. REFERENCES Anbergen, H. Rühaak, W. Frank, J. & Sass, I. 2015a. Numerical simulation of a freeze–thaw testing procedure for borehole heat exchanger grouts. Canadian Geotechnical Journal 2015 – doi:10.1139/cgj-2014-0177 Anbergen, H. Sembdner, K. Kremmer, M. Christoffers, T. Metge S. 2015b. Untersuchungen der geothermischen Eigenschaften von Bettungsmaterialien für Near-Shore Kabeltrassen. Der Geothermie Kongress 2015, Essen Brakelmann, H. 2010. Kabelverbindungen innerhalb der Offshore-Windfarm Arcadis Ost 1 – Thermische und Magnetische Emission. Sachbericht Böttcher, N. 2014. Thermodynamics of porous media: nonlinear flow processes. Dissertation zur Erlangung des akademischen Grades Doktoringenieur (Dr.-Ing.), TU Dresden BSH, 2007. Standard – Konstruktive Ausführung von Offshore-Windenergieanlagen. Bundesamt für Seeschiffahrt und Hydrographie, Stand: 12.07.2007 Comsol 2013. Heat Transfer Module User’s Guide, Comsol Version 4.4 Diersch, H.-J.G. 2014. FEFLOW – Finite Element Modeling of Flow, mass and heat transport in porous and fractured media. Springer, Berlin, Germany McKenzie, J.M. Voss, C.I. Siegel, D.I. 2007. Groundwater flow with energy transport and water-ice phase change: Numerical simulations, benchmarks,and application to freezing in peat bogs. Advances in Water Resources 2007; 30:966–983 Mottaghy, D. Rath, V. 2006. Latent heat effects in subsurface heat transport modelling and their impact on palaeotemperature reconstructions. Geophys. J. Int. 2006; 164:236–245 Rühaak, W. Anbergen, H. Grenier, C. McKenzie, J. Kurylyk, B.L. Molson, J. Roux, N. Sass, I. 2015. Benchmarking Numerical Freeze/Thaw Models. Energy Procedia 08/2015 -doi:10.1016/j.egypro.2015.07.866 Rühaak, W. Rath, V. Wolf, A. Clauser, C. 2008. 3D finite volume groundwater and heat transport modeling with non-orthogonal grids using a coordinate transformation method. Advances in Water Resources 2008, 31(3):513– 524 Schulz, A. 2009. North Sea Atlas – Temperature, Salinity, Density and Heat Content – Monthly Means for the Period 1902 to 195. Bundesamt für Seeschifffahrt und Hydrographie, Hamburg und Rostock

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Development of laboratory system for cryogenic fracturing study M. Cha Texas A&M University, College Station, Texas, USA

N.B. Alqahtani King Abdulaziz City for Science and Technology (KACST), Riyadh, Saudi Arabia

B. Yao, X. Yin & Y.S. Wu Colorado School of Mines, Golden, Colorado, USA

T.J. Kneafsey Lawrence Berkeley National Laboratory, Berkeley, California, USA

ABSTRACT: The concept of cryogenic fracturing is that sharp thermal gradient developed on rock surface by subjecting cryogenic fluid creates strong local tensile stress and initiates fractures. Prior field tests suggest that field application with special equipment rated for cryogenic temperatures may bring in potential benefits. They did not, however, identify the fracture mechanisms at work in downhole conditions. We have developed experimental setups and procedures that are specifically designed to conduct cryogenic fracturing tests with confining stress, integrated cryogen transport, measurements, and fracture characterization. A true triaxial loading system is built to simulate reservoir stress levels and anisotropies. Temperature, borehole pressure, and liquid nitrogen can be monitored continuously. Acoustic and pressure-decay measurements are used to characterize fractures before and after the experiments. The laboratory design was able to effectively apply cryogenic fracturing to laboratory rock specimens. The characterization methods were able to capture rock property changes due to cryogenic fracturing.

1

INTRODUCTION

Cryogenic fracturing is based on the idea that a cold fluid can induce thermal fractures when brought into contact with a much warmer rock. When liquid nitrogen as a cryogen is injected into a rock with much higher temperature, the heat from the rock will quickly transfer to the cryogenic fluid. This rapid heat transfer, better known as a thermal shock, will cause the surface of the rock to contract and fail in tension, thus inducing fractures orthogonal to the contact plane of the cryogen and rock. The hydraulic fracturing practice uses mainly waterbased fluids, due to the general availability and low cost; however, a dependence upon water presents a number of advantages. Water can cause significant formation damage, which can occur as clay swelling and relative permeability effects stemming from capillary fluid retention (Mazza, 1997). The formation damage mechanisms inhibit hydrocarbon flow and impair production rates and recovery efficiency. Also, water used in large quantities may place stresses upon the local environments where fracturing activities occur. Finally, downhole injection of chemicals needed in water-based fracturing operations, including slickwater and gel, are environmentally controversial. In these

aspects, cryogenic fracturing have the potential to offer benefits. Cryogenic fracturing using liquid nitrogen can achieve extremely low temperatures and very strong thermally induced stresses. Grundmann et al. (1998) treated a Devonian shale well with liquid nitrogen and observed an initial production rate 8% higher than the rate in a nearby offset well that had undergone traditional fracturing with nitrogen gas. Unfortunately, subsequent production information was unavailable because the well had to be shut in for logistical reasons. To further advance the study of cryogen fluids on hydrocarbon producing formations, McDaniel et al. (1997) conducted simple laboratory studies where coal samples were immersed in cryogenic nitrogen. The coal samples experienced significant shrinkage and fracturing into smaller cubicle units, with the creation of microfractures orthogonal to the surface exposed to the cold fluid. The researchers found that repeated exposure cycles to the cryogen caused the coal to break into smaller and smaller pieces, or become rubblized. After 3 cycles of exposing the coal to liquid nitrogen and allowing the coal to ambient temperatures again, the coal was reduced to grain size particles. McDaniel et al. (1997) also conducted field experiments by re-stimulating four coal-bed methane (CBM) wells

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and one tight sandstone well with liquid nitrogen. The wells were retrofitted with stainless steel surface piping, manifolds, and wellhead component to prevent thermal contraction problems. A free hanging fiberglass tubing was used to inject the liquid nitrogen without compromising the casing integrity. The results were mixed: All 5 wells showed promising re-stimulating initial production rates 10–20 times the before-re-stimulation production average; however, those rates quickly dwindled. The CBM wells showed sustained 6 month re-stimulation production increase of 0–45%. The tight sand well initially had higher flow rates for 2 months after re-stimulating, but then had a 65% loss in production from pre restimulation performance. It is believed that the initial success in re-stimulating these wells was not that new fractures were created but that the damage from the gel filter cake of previous fracturing treatments were greatly reduced. In summary, fracturing with liquid nitrogen may be viable for the field and bring with it benefits in reducing the formation damage and water and chemical use. However, when it comes to the understanding of the cryogenic fracture mechanisms, few lab work has been done systematically. Research is required to better understand the mechanisms of cryogen fracturing process in controlled environment and how we can integrate it into our current fracturing technology, if cryogenic fracturing potential is proven high. A proper laboratory design of equipment is important to effectively capture cryogenic fracturing process. In this study, we developed a laboratory system for cryogenic fracturing under true triaxial loading conditions. It allows to characterize cryogenic fracturing processes in the laboratory in controlled environments, such as loading conditions and different cryogenic fracturing schemes. The devices and procedures are improved and optimized based on our understanding in cryogen and system behavior from our preliminary studies including Cha et al. (2014). 2

DEVICES FOR CRYOGENIC STIMULATION EXPERIMENTS

The laboratory system is mainly consisted of a triaxial loading system, a liquid nitrogen delivery, and measurement system. Compressed nitrogen gas source is used to either directly pressurize boreholes or to push liquid nitrogen into borehole at higher pressure. Setups for submersion tests and unconfined tests are not covered in this paper, but is detailed in Cha et al. (2014). 2.1

Cryogen delivery

Once an outlet is opened, liquid nitrogen is released out of a dewar by internal gas nitrogen pressure generated inside the dewar. This pressure is kept at relatively low levels ∼60–130 kPa by a pressure relief valve (Figure 1). The fluid injection system for cryogenic

Figure 1. Basic schematics of cryogenic fracturing setup (the loading device is not shown).

fracturing needs to be different from that for hydraulic fracturing. For cryogenic thermal fracturing, cryogenic fluid needs to keep flowing in order to cool the borehole down, because the specimen is much hotter and stagnant liquid nitrogen will quickly boil and vaporize. Compressed nitrogen gas was used to either push liquid nitrogen into borehole under higher pressure (“higher-pressure LN flow”) or directly pressurize boreholes for breakdown tests. Pressure can be applied as shown on the right-hand side of Figure 1. The cryogen transport lines should be able to withstand cryogenic temperature (down to −196◦ C in our study). Stainless steel 316 and brass generally provide such an ability as their brittleness-ductility transition temperature is lower than liquid nitrogen boiling point. However, stainless steel has higher pressure rating at the temperature. In case of tubing, it needs to be seamless annealed. Figure 1 shows that LN is flown directly from the dewar to the specimen borehole under low pressure (∼60–130 kPa). In order to have LN flow under higher pressure and flow rate, liquid nitrogen needs to be temporarily stored in a special container, as the Dewar cannot accommodate any high pressure. A vessel is specially built to temporarily store liquid nitrogen from dewar before it is pushed into the specimen borehole under higher pressure and flow using compressed gas nitrogen pressure. The vessel is made of annealed seamless stainless steel tubing with 5.1 cm OD, 4.1 cm ID, and 70 cm length (Figure 2). The 5.1 cm OD tubing is reduced to 0.64 cm OD tubing by multi-stage tube fitting reduction. The vessel tubing is rated for 7 MPa in ambient temperature, but 3.5 MPa is maximum recommended pressure at cryogenic temperature from the vendor. The vessel is heavily insulated to minimize heat transfer, and its internal storage volume is 1 liter (Figure 2). As mentioned above, unlike pressure-induced fracturing, e.g., hydraulic fracturing, cryogen need to keep flowing through in order to cool the borehole down. In order to achieve this, we devised two methods. The first one is placing a packer which has an inlet and outlet at the entrance of the borehole (Figure 1 & 3).

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Figure 2. Liquid nitrogen vessel for higher-pressure LN injection (Photo was taken before applying insulation). Figure 4. Cryogen flow-through at/around borehole (casing detached to show inner inlet pipe).

2.2 Measurements The measurements made include pressure, temperature, photography of specimens, and liquid nitrogen consumption. (a) Borehole & circular dent (b) Silicone pad, packer & gasket Figure 3. Locations where gaskets and packers are placed on the top surface of the block.

A gasket is used to seal between packers and the surface around boreholes. Some forces are applied on top of the packer to pressure-seal between the borehole and the packer/gasket. The gaskets that we used are made of PTFE, which resists temperatures down to −212◦ C. To provide good contacts between gasket and specimen surface, epoxy is applied to a gasket seat to fill any uneven surfaces to provide tight seal between gasket and specimen surface (Figure 3). The packer method is okay for low borehole pressure applications, but it leaks at higher borehole pressure. Thus, the 2nd method is putting a casing into a borehole, which turns out to be a robust solution for long stimulation and/or higher-pressure stimulation. 2.5-cm stainless steel tubing as a borehole casing is mounted to the borehole wall by epoxy for sealing and pressure rating at cryogenic temperature. Epoxy generally worked well for cryogenic fracturing, but could deteriorate after 3–5 times of uses. We also developed our innovative design that allow effective flow through with coaxial inlet and outlet (Figure 4). Insulation is applied between dewar and specimen inlet to minimize heat loss.

2.2.1 Temperature measurement Temperature measurement is a critical part to see performance and system behavior. T-type thermocouples were selected for range and accuracy. Thin thermocouples are placed into a borehole first before applying gaskets and packers. Then, packers are loaded by top load platen to create tight seal (Figure 3b). When using a casing, thermocouple wires are inserted into borehole between casing and borehole walls. One thermocouple is suspended in the borehole to see temperature at the borehole and know nitrogen phase state, and another is attached to the borehole wall to see actual conduction of temperature to the rock surface (Figure 5) 2.2.2 Pressure measurements Information of pressure in the borehole is important, and pressure and temperature are intimately related to each other. Operating a pressure transducer at cold temperature or exposing the sensor to cryogenic fluid will damage sensing elements of most pressure transducers, and cryogenic-rated pressure sensor that works in such an environment is very expensive. Pressure is measured using a pressure transducer attached to the end of a standoff pipe (Figure 1), where a vapor cushion is created to prevent conductance of the cold temperature to the sensor. The temperature at the top of the stand-off pipe remains above 0◦ C throughout

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Figure 7. Triaxial loading system: specimen and actuators inside the containment mounted in the press bed frame. Loading axes and specimen side numbers are shown.

Figure 5. Thermocouple attached to borehole wall.

Figure 6. Liquid nitrogen consumption vs. time.

the stimulation (Figure 13). The standoff pipe length should not be longer than necessary because a long narrow pipe can create drag force and thus may decrease responsiveness to fast-changing pressure. The length of standoff pipe can be reduced by decreasing the diameter of the pipe. Common inexpensive pressure transducers can be used to use with the standoff pipe. 2.2.3 Liquid nitrogen consumption The amount of LN leaving the dewar and flown through a borehole was monitored by placing the dewar on a scale. Typical data for liquid nitrogen consumption over time is shown in Figure 6. The nonlinear LN consumption vs. time shows that strong vaporization occurred at the beginning, which slowed the flow of LN. Then as the system cooled down, the flow rate of LN increases under the same amount of outlet opening.

2.3 True triaxial loading equipment A large specimen size (20 cm × 20 cm × 20 cm) are considered in order to create thermal gradient required for thermal tensile fracturing.

2.3.1 Triaxial loading device A true triaxial loading system was developed to simulate effects of stress levels and stress anisotropy on the characteristics of cryogenic fracturing. The containment is designed for the selected specimen size 20 cm × 20 cm × 20 cm.The triaxial loading (TX) system can load the specimen up to 30 MPa in x and y axes, and 40MPa in z axis, and can independently control loadings in the three axes. The two hydraulic pistons for x and y axes and the hydraulic press for z axis are powered by three pneumatic hydraulic pumps. Three heavy-duty ratchet tie-down straps (2300-kgf capacity each) surround the containment for extra safety. A practical advantage of our system is the vertical loading frame can be removed by rolling it away after unlocking it from the bed. This ability provides a user with space to work on specimens and inside the containment.An open system is adopted to better deal with any unexpected situation such as a cryogen spill and for ease of instrumentation (Figure 7). Silicone or PTFE pads are placed between rock specimens and the loading pad to provide uniform contacts and loading to specimen surface. PTFE and silicone pads resist temperature down to −212◦ C and −62◦ C, respectively. An automatic servo control system for load control is not available in our system nor required as our problem is quasi-static. Constant forces can be maintained by either manual control or in quasiautomatic manner using pressure relief valves attached to the hydraulic lines. In the manual control, a small additional amount of pressure is applied by pumping when certain amount of natural decay occurs. 2.3.2 Triaxial loading tests Forces exerted by the hydraulic pistons are calculated by multiplying hydraulic pressure in the hydraulic lines measured using pressure transducers by effective area of hydraulic pistons. Then the specimen stresses are obtained by dividing the piston forces by the specimen surface areas.

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Figure 8. Confining load tests – manual control of constant stress (isotropic stress 14 MPa).

Figure 10. Prominent fracture along the centers at the sides created due to repeated, acute anisotropic conditions.

Figure 9. Extrusion of the silicone pads under loadings (28 MPa loading).

Constant forces can be maintained by either the manual control or in the quasi-automatic manner using pressure relief valves in the hydraulic lines. Our hydraulic system can make use of pressure relief valves in the hydraulic lines to quasi-automatically control constant pressure, which needs less attention than the manual control. In the manual control, we manually pump small amount of pressure when certain amount of natural decay occurs. The manual control can be more accurate than quasi-automatic control, but require more attention to changes in pressure. Note that the test Figure 8 is manually controlled within ±2% of errors. Silicone pads are placed between the specimen surface and loading plates. The silicone pads appeared to function well in distributing the load on slightly uneven surfaces of specimens as we did not observe any specimen damages after loading tests. Especially, the top surfaces are rougher, and the silicone pads help distribute load over the surfaces. However, the pads inevitably extruded out the contact surfaces against rough surfaces at high confining stress (Figure 9), and damaged after repeated uses. The silicone pads resist temperature down to −62◦ C. In our short-term tests (less than an hour), this rating was sufficient as the block surface remained above this temperature. PTFE sheets are stiffer than the silicone pads, but is malleable enough at high pressure to accommodate

Figure 11. An example of synchronized unloading to avoid large stress anisotropic conditions, using pressure relief valves in the hydraulic system.

any local, undulating surfaces, and have exceptional temperature rating down to -212◦ C. A drawback compared to silicone pad is when the specimen is undulating more than a certain level, it cannot distribute load. In one of loading tests that we performed, unloading processes were abrupt and not perfectly synchronized in all three axes, which created acute anisotropic stress conditions in specimen. For example, the specimen was subjected to anisotropic condition where x and y axes are loaded to ∼14 MPa and z axis is loaded to ∼0 MPa due to unsynchronized rapid unloading for a couple of times (each time anisotropic condition lasted about 0.5 sec). This created prominent fractures (Figure 10). After this observation, we devised to make use of pressure relief valves to slowly and simultaneously unload the three axes as shown in Figure 11.

3

EXPERIMENTAL PROCEDURE

Cryogenic stimulation is performed by flowing liquid nitrogen from its source into boreholes of specimens. Baseline measurements of rock conditions relevant to fracture indication are done before any treatment,

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and then the same measurements are performed during treatments or after completing the treatments for comparison. Fracture assessments include breakthrough fracturing, acoustics, pressure decay tests, visual inspection, and CT. 3.1

Procedure

As mentioned previously, because the specimen is much hotter than liquid nitrogen, any stagnant condition will increase the borehole temperature rapidly. Thus, liquid nitrogen is continuously flowed through the borehole. Using our cryogenic fracturing apparatus under triaxial loading conditions, we performed two different cryogenic stimulation schemes. The first one is low-pressure liquid nitrogen flow, where liquid nitrogen is directly flowed from the dewar from a pressure difference between inside the dewar and outside the dewar upon opening the dewar’s release valve. Pressure ranges from 35–135 kPa in the borehole, depending on the internal pressure level inside the dewar. The other scheme is high-pressure LN flow, where liquid nitrogen is flowed through the borehole under higher pressure (2–2.8 MPa) for faster cooling in the borehole due to reduced film boiling effects. In high-pressure liquid nitrogen flow, there is also a pressure effect, which facilitates fracture opening by helping to reach tensile strength of the rock. Normally we apply the higher-pressure stimulation multiple times because our vessel for storing liquid nitrogen for higher-pressure injection is small (1 liter) (Figure 2), which makes each stimulation cycle very brief (1–2 min). 3.2

Fracture characterization

Fracture assessments are carried out by borehole pressure decay test, specimen breakdown pressure, and acoustic measurements. Borehole pressure decay is performed by applying a pressure to the borehole, shutting the borehole in, and monitoring the pressure decay. This was tested before cryogenic treatments as a baseline, and then tested between treatments and after completing cryogenic treatments for comparison. After all planned stimulation is completed for each specimen, specimens were subject to gas nitrogen (GN) pressure to fully fracture (“breakdown”) the specimen. These breakdown pressures are compared with baseline breakdown pressure of untreated specimen, and also with those of specimens that were treated in different situations. Breakdown tests are done at the last stage after all other tests and measurements are done as it will fully fracture to the surface. Elastic wave propagation are measured using ultrasonic transducers before and after the treatments. The post-stimulation measurements were done before applying breakdown pressure, so that we can know the effect of cryogenic stimulations. Elastic waves are governed by the mechanical properties of the medium. In particular, the wave velocity in jointed rock masses is a function of the density of fractures (Cha et al., 2009).

Figure 12. The bridge saw that was used to cut the large shale and sandstone blocks into cubic specimens (20 cm × 20 cm × 20 cm).

When other properties such as intact rock properties, density, and joint stiffness are the same, the wave velocity can be used as a monitoring tool for fracture generation. In addition, X-ray computed tomography (CT) scanning is used for fracture assessment before and after stimulations.

3.3

Specimen preparation

Shale and sandstone were collected from outcrops of producing formations. A fairly large specimen size (20 cm × 20 cm × 20 cm) is selected in order to create sufficient thermal gradient in the specimen for an extended time. Collected rock blocks are precisely cut into 20 cm × 20 cm × 20 cm cubic shapes using a laser-guided bridge saw (Figure 12). Then a 2.5-cm diameter wellbore was drilled by using a diamond imbedded coring drill bit with 2.6-cm outer diameter to a depth of 15 cm. Following drilling, a 2.5-cm stainless steel-316 tube (casing) were attached to the wellbore by applying epoxy after the thermocouples were placed inside the wellbore. The casing extends five centimeters into the wellbore. Mortar concrete blocks are used as surrogate for real rock. A fresh concrete with a water to cement ratio of 0.55, and sand to cement ratio of 2.5 was poured into the 20 cm × 20 cm × 20 cm mold and sealed in a plastic bag. After 24 hours, the seal and mold were removed and the concrete was cured under water (ASTM, 2014a). Index properties of intact rock were obtained for tested specimens. Permeability and porosity were measured using CMS 300 (CoreLab). Elastic constants were obtained from measurements of elastic wave velocities (Cha and Cho, 2007, ASTM, 2008b). Specific heat capacity was obtained by using a calorimeter. Splitting tensile strength and unconfined uniaxial compressive strength were obtained using procedures from the ASTM standards (ASTM, 2008a, ASTM, 2014b).

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Figure 14. Shrinkage and expansion of the specimen due to specimen cooling and warming, indicated from hydraulic pressure responses during low-pressure LN flow (followed by pressurization).

Figure 13. Temperature and borehole pressure during low-pressure LN flow (and borehole pressurization) under 14 MPa isotropic confining stress.

4

CRYOGENIC STIMULATION EXPERIMENTS

Following the procedures explained earlier, we performed experiments of low-pressure LN flow and higher-pressure LN flow. Some data is presented for temperature and pressure behavior in and around borehole, followed by assessment of generated fractures for a low-pressure LN stimulation. Figure 15. P-wave signature before (blue) and after (red) liquid nitrogen treatment in a concrete specimen (Side 1&3).

4.1

Low-pressure liquid nitrogen flow through borehole

4.2 Fracture assessment and characterization

In this scheme, low pressure LN is discharged (70 ∼ 135 kPa) naturally from a liquid nitrogen dewar and injected into borehole to initialize fractures at the borehole by thermal shock. Liquid nitrogen was injected until borehole and borehole wall was fully cooled down to the nitrogen boiling point (Figure 13). Although not included in the initial plan, when the liquid nitrogen injection was stopped, we applied gas nitrogen pressure to the borehole, pressurizing it at about 3 MPa (Figure 13a). During the pressurization period (about 20 seconds), rapid temperature increase is observed following the adiabatic compression of gas (Figure 13b). This gas nitrogen pressure is in an attempt to open up cracks generated by the thermal shock. Contraction and expansion of specimens were observed from pressure responses of the hydraulic system (Figure 14). When the specimen was cooled down, the specimen shrank and the pistons in contact with the specimen lost pressure at a faster rate than at the steady-state condition. When the temperature of the specimen increases, the specimen expands and the piston starts to pick up pressure, making the hydraulic pressure increase. Each jump represents manual pumping to make up for pressure decay in hydraulic lines to keep ∼14 MPa.

Several methods are applied to check whether fracture has been created by cryogenic stimulations. They include the pressure decay, acoustic waves, and breakdown fracturing, etc. 4.2.1 Acoustic waves Elastic wave data is collected to obtain parameters on changes in specimen stiffness and quality by waveform comparisons.Acoustic signals were measured between Faces 1&3 and 2&4 (pairs of opposing faces). For each set of faces, acoustic measurements were conducted at twelve locations (Figure 15). We observed that acoustic velocities and amplitudes decrease after cryogenic stimulations, indicating fracture creation in the specimens. 4.2.2 Post-stimulation breakdown fracturing by borehole pressure When stimulations are finished for each specimen, specimens were subject to gas nitrogen (GN) pressure to fully fracture (“breakdown”) all the way to the block surface (Figure 16b). These breakdown pressures are compared with baseline breakdown pressure of untreated specimen (Figure 16a). Breakdown tests are done at the last stage after all other tests and measurements are done as it will fully fracture to

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data were gathered from cryogenic fracturing tests on triaxially stressed rock blocks by using the newly developed system proves that the system works adequately. With this device developed, high-quality data can be obtained to provide better understanding in cryogenic fracturing, and develop and improve the process toward field applications. As waterless or reduced-water technology is sought for more than ever, this technology should be sought for systematically in the lab. ACKNOWLEDGEMENT Support for this research was provided by Research Partnership to Secure Energy for America (RPSEA) (Grant no. 10122-20). REFERENCES Figure 16. Post-stimulation fracturing by nitrogen gas.

the surface. A result shows that cryogenic treatment decreases breakdown pressure (PBD) level by low pressure liquid nitrogen flow-through (Figure 16). 4.2.3 Borehole pressure decay test Any permeability enhancement was assessed by comparing of pressure decay over time in a borehole before and after cryogenic stimulation. Pressure decay test results show that low and high-pressure liquid nitrogen stimulations increase permeability of stimulated specimens. In one test, low-pressure LN flowed for 30 min resulting in a significant increase in permeability indicated by a rapid pressure decay. Cycles of higher-pressure stimulation under triaxial loading also led to significant permeability enhancements. It is found that specimen temperature and confining stress play noticeable role in pressure decay profile. Detailed pressure decay results and analysis are in Alqatahni et al. (2016) 5

CONCLUSIONS

We built a laboratory system for controlled cryogenic fracturing study under tri-axial loading conditions, which mainly consist of a true triaxial loader, liquid nitrogen delivery/control, and measurement/ characterization system. The true tri-axial loading (TX) system can load to reservoir confining stresses level on 20 cm × 20 cm × 20 cm cubic blocks, and independently control loadings in the three axes, and keep constant pressure to specimens. It is an open-system with movable z-axis frame. The cryogen delivery and control system allows pressurized and unpressurized liquid nitrogen flow through borehole, with borehole gas pressurization as necessary. Our characterization tools, such as acoustics, breakdown fracturing, and pressure decay tests, are able to effectively capture created fractures and permeability changes. Initial

Alqatahni, N. B., Cha, M., Yao, B., Yin, X., Kneafsey, T. J., Wang, L., Wu, Y.-S. & Miskimins, J. L. (2016) Experimental Investigation of Cryogenic Fracturing of Rock Specimens under True Triaxial Confining Stresses. SPE Europec featured at 78th EAGE Conference and Exhibition, Vienna, Austria, 30 May–2 June 2016. SPE180071-MS. ASTM (2008a) ASTM D3967 Standard Test Method for Splitting Tensile Strength of Intact Rock Core Specimens. ASTM (2008b) D2845-08 Standard Test Method for Laboratory Determination of Pulse Velocities and Ultrasonic Elastic Constants of Rock. ASTM International. ASTM (2014a) ASTM C192/C192M Standard Practice for Making and Curing Concrete Test Specimens in the Laboratory. ASTM (2014b) ASTM D7012 Standard Test Methods for Compressive Strength and Elastic Moduli of Intact Rock Core Specimens under Varying States of Stress and Temperatures. Cha, M. & Cho, G. C. (2007) Compression wave velocity of cylindrical rock specimens: engineering modulus interpretation. Japanese Journal of Applied Physics Part 1Regular Papers Brief Communications & Review Papers, 46, 4497–4499. Cha, M., Cho, G. C. & Santamarina, J. C. (2009) Longwavelength P-wave and S-wave propagation in jointed rock masses. Geophysics, 74, E205–E214. Cha, M., Yin, X., Kneafsey, T., Johanson, B., Alqahtani, N., Miskimins, J., Patterson, T. & WU,Y.-S. (2014) Cryogenic fracturing for reservoir stimulation – Laboratory studies. Journal of Petroleum Science and Engineering, 124, 436– 450. Grundmann, S. R., Rodvelt, G. D., Dials, G. A. & Allen, R. E. (1998) Cryogenic Nitrogen as a Hydraulic Fracturing Fluid in the Devonian Shale. SPE-51067-MS. SPE Eastern Regional Meeting. Pittsburgh, Pennsylvania, Society of Petroleum Engineers. Mazza, R. L. (1997) Liquid CO2 improves Fracturing. Hart’s Oil and Gas World, 22. McDaniel, B. W., Grundmann, S. R., Kendrick, W. D., Wilson, D. R. & Jordan, S. W. (1997) Field Applications of Cryogenic Nitrogen as a Hydraulic Fracturing Fluid. SPE 38623. SPE Annual Technical Conference and Exhibition. San Antonio, Texas, 1997 Copyright 1997, Society of Petroleum Engineers, Inc.

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Steady state vs transient thermal conductivity of soils H. Hailemariam, D. Shrestha & F. Wuttke Marine and Land Geomechanics and Geotechnics, Kiel University, Kiel, Germany

ABSTRACT: Precise determination of thermal conductivity of porous media or soils in particular is vital in performing analysis and modeling operations in a range of fields of engineering, agriculture, hydrology etc. Depending on the type, thermal properties and medium temperature, steady state or transient techniques are employed to obtain the thermal conductivity of soils. Although several studies have been carried out in the past to assess the suitability and accuracy of each technique, there is an evident lack of assessment of the two methods for a wide range of soil types as well as verification of the results against widely applicable soil thermal conductivity prediction models. In this document, the result of thermal conductivity study on three fine-grained and five coarse-grained soils analyzed using steady state and transient techniques in a two-phase dry soil condition is presented. The steady state and transient measurements of each soil are further compared with the prediction of seven models of soil thermal conductivity and the suitability as well as the accuracy of both methods is assessed.

1

INTRODUCTION

Thermal conductivity plays a significant role in engineering applications such as the operation of small and large scale seasonal thermal energy storage, embedding of underground power cables in selected porous media, nuclear waste disposal facilities, heat exchanger piles of structures, assessing the effect of berms on the heat loss from thermal energy storage tanks etc (Doughty et al. 1983, Hart & Whiddon 1984, Rosen & Hooper 1989). Several methods exist for measuring soil thermal conductivity (Mitchell & Kao 1978). These methods of measuring soil thermal conductivity fall into one of two categories: steady state or non-steady state (transient methods) (Mitchell & Kao 1978, Farouki 1981). Steady state methods involve the application of one-directional heat flow through a specimen and the observation of power or temperature difference across the sample when a steady state is reached (Mitchell & Kao 1978, Farouki 1981, Low et al. 2013). The thermal conductivity of the specimen is then obtained using Fourier’s Law. Generally, steady state techniques are helpful when the temperature of the specimen does not change with time. However, the main limitation of steady state methods is that a well-engineered experimental setup as well as ample time is needed for establishing a steady state condition. Steady state techniques are furthermore widely classified as absolute or comparative methods (Alrtimi 2014). The former includes the guarded hot plate method, unguarded hot plate method and the heat flow meter technique, where the determination of power and temperature distribution across the specimen is directly obtained from the input power and temperature parameters. The latter

includes methods such as the guarded comparative longitudinal heat flow technique, which uses a series of reference materials of known thermal conductivity aligned in series with the specimen (Momose et al. 2008). Transient methods on the other hand involve applying heat to the specimen and monitoring temperature changes over time, and then after using the transient data to determine the thermal conductivity, usually by applying analytical solutions to the heat diffusion equation (Mitchell & Kao 1978, Farouki 1981, Low et al. 2013, Alessandro 2007). The method by which the transient data is analyzed can significantly affect the obtained thermal conductivity. Transient methods of measuring thermal conductivity provide better versatility as compared to steady state methods because of their ease of use and the required short measurement time. Most commonly used transient methods include the hot wire method, transient plane source method and the thermal needle probe (single or dual probes). The probe methods have been more commonly used for the past 50 years (Farouki 1981). Several researchers have performed studies on steady state and/or transient methods of thermal conductivity determination independently and/or in joint combination (Low et al. 2013, Alrtimi 2014, Mohsenin 1980, Hooper & Lepper 1950, Sass et al. 1984). However, there is a noticeable lack of evaluation of the two methods for a wide range of soil types as well as comparisons with existing widely known theoretical and semi-empirical thermal conductivity prediction models. The focus of the body of work presented in this manuscript is to contribute to the existing literature and to provide users with a comprehensive comparison between experimental steady state and transient

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techniques as well as theoretical and semi-empirical models of thermal conductivity prediction for a wide range of soil types. For this purpose, the steady state and transient thermal conductivities of three fine-grained and five coarse-grained soils in two-phase dry condition, obtained using a steady state thermal conductivity meter and a transient thermal needle probe respectively, are analyzed experimentally.The results are then compared with seven theoretical and semi-empirical models of thermal conductivity, and the accuracy as well as suitability of each experimental technique is assessed. 2 THEORETICAL & SEMI-EMPIRICAL ANALYSIS Three theoretical models (volume fraction & logmodels (Yun & Santamarina 2007) and cubic cell model (Gori & Corasaniti 2004)) and four semiempirical models (Johansen 1975, Gavriliev 2004, Côté & Konrad 2005 and Lu et al. 2007 models) have been used in this research to verify the experimental steady state and transient thermal conductivity measurements. Details of each thermal conductivity prediction model are presented in the following sections.

the geometric mean as given by Equation 3 (Farouki 1981). The geometric mean (GM) equation has been widely used for predicting two-phase thermal conductivity of porous media (Farouki 1981, McGaw 1969). Several researchers (Johansen 1975, Côté & Konrad 2005, Lu et al. 2007) have also adopted the geometric mean method in the development of semi-empircal models with satisfactory accuracy.

Hashin & Shtrikman (1962) proposed the relations given by Equations 4 (HS-U) & 5 (HS-L) for the upper λu and lower λl bounds of thermal conductivity respectively.

According to the cubic cell model (Gori & Corasaniti 2004), the effective dry soil thermal conductivity can be obtained as:

2.1 Theoretical models Numerous theoretical approaches have been developed to model the thermal conductivity of two-phase soils based on the volumetric proportions of the different phases as well as the texture/fabric within the medium (Farouki 1981, Yun & Santamarina 2007, Abuel-Naga et al. 2008). Unlike most empirical models, the validity of theoretical models is not limited to specific conditions and they can be used to predict thermal conductivity for a wide variety of soil types (Abuel-Naga et al. 2008). The parallel and series heat flow models can be considered as the upper and lower bounds of theoretical models, respectively (Farouki 1981, Abuel-Naga et al. 2008). The two-phase parallel λParallel and series λSeries thermal conductivities are given by Equations 1 & 2 respectively (Farouki 1981).

where, n is soil porosity, λf is the fluid thermal conductivity (water, λw = 0.594 W m−1 K−1 or air, λa = 0.024 W m−1 K−1 at 20◦ C, for saturated or dry soil states respectively), λs is the thermal conductivity of solid soil particles. At low λs /λf ratios, parallel flow dominates, while, at higher λs /λf ratios, it is series flow which dominates (Farouki 1981). An important and useful ‘average’ of the parallel and series heat flow models is obtained by taking

Yun & Santamarina (2007) fitted the volume fraction (VF) model (equivalent to the Complex Refractive Index Method, CRIM) and the log-model for obtaining the effective dry thermal conductivity of soils as given by Equations 7 & 8 respectively.

Figure 1 shows plot of two-phase dry thermal conductivity of a soil with a quartz fraction q = 0.70 (taken as the average of the eight soils used in our study), obtained using the different theoretical models for a wide range of soil porosity. 2.2 Semi-empirical models Several semi-empirical models exist for estimating soil thermal conductivity as a function of water content, porosity and other hydro-mechanical parameters (Farouki 1981, Johansen 1975, Côté & Konrad 2005, Lu et al. 2007, Kersten 1949, Van Rooyen & Winterkorn 1957). However, although most of the models provide better accuracy as compared to theoretical

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Figure 1. Thermal conductivity λ vs porosity n of a soil in dry state obtained using theoretical models [VF is the volume fraction model, GM is the geometric mean model and HS-U & HS-L are the upper and lower bounds of the Hashin & Shtrikman model respectively].

models, they are generally limited to specific soil types under specific boundary conditions. Johansen (1975) proposed a semi-empirical relationship to obtain dry thermal conductivity of natural soils λd (W m−1 K−1 ), based on soil dry density ρd (kg m−3 ) and density of soil solids ρs (kg m−3 ), Equation 9.

Johansen also proposed that the thermal conductivity of soil grains λs (W m−1 K−1 ) could be determined using a geometric mean function, Equation 10, based on the fraction quartz content of the total soil q and thermal conductivities of quartz, λq = 7.7 W m−1 K−1 , and other minerals, λo = 2.0 W m−1 K−1 or 3.0 W m−1 K−1 for soils with q > 0.2 or q ≤ 0.2 respectively (Johansen 1975, Lu et al. 2007, Clauser & Huenges 1995).

The value of λs for all the models used in this study was obtained by calculating the quartz fraction based on the coarse grain fraction of each soil using Equation 10 (Lu et al. 2007, Peters-Lidard et al. 1998). Gavriliev (2004) suggested an empirical relationship for estimating dry thermal conductivity of mineral soils λd (W m−1 K−1 ) based on dry density ρd (g cm−3 ), Equation 11. The relationship is valid for mineral soils with dry density lower than 2 g cm−3 .

Côté & Konrad (2005) suggested a new empirical equation for the dry thermal conductivity of soils λd (W m−1 K−1 ) as:

Figure 2. Thermal conductivity λ vs porosity n of a soil in dry state obtained using semi-empirical models [Lu et al. model is valid for porosity n (0.2 < n < 0.6)].

where, χ (W m−1 K−1 ) and η are parameters for particle shape effects with values of 1.70 W m−1 K−1 and 1.80 for crushed rocks, 0.75 W m−1 K−1 and 1.20 for natural mineral soils, and 0.30 W m−1 K−1 and 0.87 for organic fibrous soils. Lu et al. (2007) suggested a simple linear function, Equation 13, that describes the relationship between thermal conductivity at dry condition λd (W m−1 K−1 ) and porosity n (0.2 < n < 0.6) for mineral soils, based on two empirical parameters a and b, as the magnitude of heat transfer in dry soils is related to soil porosity. Lu et al. calculated values of 0.56 and 0.51 for empirical parameters a and b, respectively, by fitting heat pulse measured data with Equation 13.

Figure 2 presents plot of two-phase dry thermal conductivity of a soil with a specific gravity Gs = 2.654 (taken as the average of the eight soils used in our study), obtained using the different semi-empirical models for a wide range of soil porosity. 3

EXPERIMENTAL PROGRAM

3.1 Tested soils Three silty clay soils (referred here as silty clays A-C) and five sandy soils (referred here as sands A-E) were investigated. The common geotechnical properties of the soils (obtained following ASTM D420–D5876 (2001)) are listed in Tables 1 and 2. 3.2 Determination of steady state thermal conductivity Heat transfer phenomena play a vital role in many problems which deal with transport of flow through a porous medium. Under isotropic medium conditions, where local thermal equilibrium is ensured

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Table 1. Geotechnical properties of the studied fine-grained soils. Silty clay soil

A

B

C

Gravel (%) Sand (%) Silt (%) Clay (%) Gs (–) LL (%) PI (%) ρd (g cm−3 ) USCS

16.1 8.8 58.2 16.8 2.67 34.6 14.81 1.49 CL

14.9 12.2 52.5 20.2 2.67 43.1 19.45 1.43 CL

2.8 7.1 65.4 24.6 2.62 48.2 23.19 1.38 CL

Gs specific gravity, LL liquid limit, PI plasticity index, ρd dry density, USCS unified soil classification system.

Figure 3. Steady state thermal conductivity measurement setup.

Table 2. Geotechnical properties of the studied coarsegrained soils. Sand

A

B

C

D

E

Gravel (%) Sand (%) Silt (%) Clay (%) Gs (–) D50 (mm) D10 (mm) Cu (–) Cc (–) ρd (g cm−3 )

9.62 90.27 0.11 0 2.65 0.64 0.27 3.00 0.77 1.73

0 100 0 0 2.65 0.36 0.21 1.81 1.05 1.52

4.78 95.16 0.06 0 2.66 0.60 0.27 2.63 0.88 1.77

5.69 94.14 0.17 0 2.66 0.40 0.21 2.19 0.99 1.77

9.54 89.95 0.51 0 2.65 0.50 0.22 2.72 0.83 1.76

Gs specific gravity, D50 grain diameter at 50% passing, D10 grain diameter at 10% passing, Cu coefficient of uniformity, Cc coefficient of curvature, ρd dry density of soil

(Ts = Tf = T , where Ts and Tf are the temperatures of the solid and fluid phases, respectively), Equations 14–17 can be obtained by combining heat transfer equations in solid and fluid phases (Bejan & Lorente 2004, Bejan 2004). Figure 4. Schematic representation of steady state thermal conductivity cell (top) and dimensional analysis (bottom).

where, the subscripts m, s and f refer to the porous medium, solid and fluid phases, respectively, n is soil porosity, ρ is density, c is the specific heat of the solid, cp is the specific heat at constant pressure of the fluid, λ is the thermal conductivity, q′′′ (W m−3 ) is the heat production per unit volume, T is temperature, t is time and v is the seepage velocity. A steady state thermal conductivity and diffusivity meter was used to obtain the steady state thermal

conductivity of the investigated soils in dry condition. The apparatus consists of a control panel, loading machine, data acquisition and data analysis software, a top heating plate, a bottom cooling plate and a reference disc with known thermal conductivity, Figures 3 & 4.The specimen has a diameter of 100 mm and a height of 30 mm, and is sandwiched between the top heating and reference plates, Figure 4. The plates consist of extremely thin PT 100 temperature sensors with an accuracy of 0.05◦ C. The system measures sample deformation with a TRS-0050 linear transducer with an independent linearity of 0.15% and repeatability of 2 µm. The thermal conductivity of the specimen can be calculated from the temperatures, distances and the known thermal conductivity of the reference plate,

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as the temperature gradient within a homogeneous body is linear (Stegner et al. 2011, Sass & Stegner 2012). In contrast to the divided bar apparatus (such as King et al. (1982)), the temperature sensor is built-in directly into the reference plate, thus lowering contact resistances. For the system shown in Figures 3 & 4, Equation 18 applies provided that T1 > T2 > T3 , ensuring that heat flow occurs from the top plate via the sample and reference disc to the bottom plate, and T1 > Tambient > T3 , ensuring that heat flow from the environment does not penetrate to the specimen (Stegner et al. 2011, Sass & Stegner 2012). The steady state thermal conductivity and average sample temperature are expressed in Equations 19 & 20 respectively. Figure 5. KD2 Pro thermal needle probe setup.

where, λ (W m−1 K−1 ) is the thermal conductivity of the sample, D (m2 s−1 ) is the thermal diffusivity of the sample, r (m) is the radial distance to the line source, t (s) is the amount of time that has passed since heating has started and Ei is an exponential integral (transcendent mathematical function). For a large measuring time, the exponential integral is usually approximated by the following expression: where, T1 is the temperature of the top (heating) plate (◦ C), T2 is the temperature of the reference disc (◦ C), T3 is the temperature of the bottom (cooling) plate (◦ C), Tav is the average sample temperature (◦ C), λp and λv are the thermal conductivities of the sample and the reference disc respectively (W m−1 K−1 ), Sp , Sv and S23 are the distances (m) as shown in Figure 4 (bottom). 3.3

Determination of transient thermal conductivity

The transient thermal conductivity of the studied soils was measured with a Decagon KD2 Pro thermal needle probe, based on transient line source measurement in compliance to ASTM D5334-08 (2008) and IEEE (1992) standards, Figure 5. A thermal needle probe (TR-1) with a diameter of 2.4 mm and a length of 100 mm was used to measure the transient thermal conductivity of the soils. The sufficient length to diameter ratio ensures that conditions for an infinitely long and infinitely thin heating source are met, and the measurement error recorded for all samples was kept well below the 0.015% limit. The KD2 Pro includes a linear heat source and a temperature measuring element with a resolution of 0.001◦ C. The physical model behind the measurement method is based on the application of heat at a constant rate Q (W m−1 ) to an infinitely long and infinitely small line source. The temperature response of the source over time is described as:

where, γ = 0.5772. . . is Euler’s constant and α = r 2 / 4Dt. For a large enough time, the terms beyond ln α in the series become negligibly small and the graph of T vs ln t becomes linear with slope equal to Q/4πλ. Hence, the thermal conductivity of the medium can be computed as:

4

RESULTS AND DISCUSSION

4.1 Analysis of steady state conduction test parameters In Figure 6, the measured values of reference disc temperature T2 required for obtaining the steadystate thermal conductivity of the investigated soils are plotted. For all the measurements, a top heating plate temperature of 30◦ C and a bottom cooling plate temperature of 20◦ C were applied. Generally, the coarse-grained soils exhibit a higher measured value of T2 and hence a higher thermal conductivity λ near steady state condition, Figure 6. This is attributed mainly to the higher quartz fraction q and lower porosity n (higher dry density ρd ) of the sandy soils as compared to the silty clay soils. The results comply well with previous findings which state that soils with the highest quartz fraction exhibits the highest thermal conductivity and vice versa

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Figure 6. Observed values of reference disc temperature T2 for the fine-grained soils (top) and coarse-grained soils (bottom).

(Johansen 1975, Côté & Konrad 2005, Lu et al. 2007, Abu-Hamdeh & Reeder 2000). Moreover, second only to moisture content, dry density plays a significant role in soil thermal conductivity (Salomone et al. 1984, Salomone & Kovacs 1984, Salomone & Marlowe 1989). With an increase in the soil’s dry density, the number of soil particles packed per unit volume increases creating higher number of contact points between the soil grains. As a result the heat flow path and consequently the thermal conductivity of the resulting soil mass are increased. In particular, sand B exhibits the lowest measured T2 and hence a low thermal conductivity when compared to the other sands due to its comparatively high porosity (lower dry density) and poor gradation (uniform soil). Unlike poorly graded soils, well graded soils have a good distribution of coarse-grained matrix bridged by finer particles, which in turn increases the number of soil particles packed per unit volume and the number of contact points, resulting in a higher soil thermal conductivity. 4.2

Steady state and transient thermal conductivity results

Figure 7 shows plot of experimental results of thermal conductivity measurements of the investigated soils as compared to the different theoretical and semiempirical prediction models of two-phase dry thermal conductivity of a soil with a quartz fraction q = 0.70

and a specific gravity Gs = 2.654 (taken as the average of the eight soils used in our study). As expected, all the measured thermal conductivity values fall in between the series (lower bound) and parallel (upper bound) as well as the Hashin & Shtrikman lower and upper bounds of heat flow conditions, Figures 1 & 7. Overall, with the exception of the Gavriliev (2004) model, the semi-empirical models, Figure‘7 (bottom), provide better accuracy of prediction of the experimental results of steady state and transient measurements for both sands A, C, D & E (with relatively higher dry density) as well as sand B and silty claysA-C (with relatively lower dry density). However, the theoretical models, Figure 7 (top), provide much lower accuracy of prediction than the semi-empirical models, with the log and volumetric fraction (VF) models fitting comparatively better with the experimental results when compared to the prediction of the cubic and geometric mean (GM) models. The cubic cell model significantly underestimates the measured thermal conductivity values, while, the GM model overestimates the measured thermal conductivity of all soils. GM model only gives satisfactory results when the ratio of thermal conductivity of solids to fluids λs /λf < 15 (Côté & Konrad 2005b). In a two-phase dry condition, where air is the fluid, λs /λa > 100 leads to a significant overestimation of thermal conductivity by GM model (Farouki 1981, Johansen 1975). The lack of accuracy of prediction of two-phase thermal conductivity of soils using theoretical solutions based on properties such as geometry, porosity and volumetric fractions is mainly attributed to their inability to quantify factors such as the microstructure, gradation and soil texture (when having higher ratios of thermal conductivity of solid particles to air λs /λa > 100), which play significant role in the thermal conduction of dry soils (Farouki 1981, Johansen 1975). 4.3 Comparison of steady state and transient thermal conductivity with prediction models The accuracy of the steady state and transient thermal conductivity test results is checked by comparing the root mean square error (RMSE) between the prediction models and experimental results. The RMSE and is calculated using the following equation:

The findings illustrate that both the experimental steady state and transient thermal conductivity measurements are rated to be of high accuracy according to the semi-empirical models (Johansen (1975), Côté & Konrad (2005) and Lu et al. (2007) models in particular). This result is to be expected as most semiempirical models are calibrated to account for factors such as soil fabric, gradation and texture in addition to the commonly used parameters such as porosity,

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Figure 8. Bar chart of RMSE between model prediction and experimental results.

when compared with both the Côté & Konrad (RMSE of 0.028 W m−1 K−1 to 0.036 W m−1 K−1 ), Lu et al. (RMSE of 0.028 W m−1 K−1 to 0.044 W m−1 K−1 ) and log models (RMSE of 0.038 W m−1 K−1 to 0.042 W m−1 K−1 ), Figure 8. Whereas, the transient thermal conductivity measurements are more accurate when compared with the Johansen model (RMSE of 0.029 W m−1 K−1 to 0.034 W m−1 K−1 ). 5

Figure 7. Thermal conductivity λ vs porosity n comparisons of experimental results with theoretical (top) and semi-empirical (bottom) model prediction [steady state and transient results are shown with gray and no fill markers respectively].

grain geometry as well as volumetric fraction (Farouki 1981, Johansen 1975, Côté & Konrad 2005, Lu et al. 2007 and others). Bettered only by the semi-empirical models, the experimental results comply well with the prediction of the log and to a lower extent the VF theoretical models used in our study, as both models were calibrated based on soil thermal conductivity data by Yun & Santamarina (2007). Furthermore, when evaluating the accuracy of the steady state and transient thermal conductivity experimental results, the steady state thermal conductivity measurements provide the most accurate results

CONCLUSIONS

The thermal conductivity of three fine-grained and five coarse-grained soils was analyzed experimentally using steady state and transient techniques in a two-phase dry soil condition. The steady state and transient thermal conductivity measurements of each soil were then compared with the prediction of seven models of soil thermal conductivity and the suitability as well as accuracy of both methods was assessed. As expected, with both thermal conductivity measurement techniques, majority of the sandy soils exhibited a higher measured thermal conductivity than the silty clay soils, due to their higher quartz fraction and higher dry density (lower porosity). When assessing the accuracy of the two techniques of thermal conductivity measurement, the steady state thermal conductivity technique provides the most accurate results when compared with both the Côté & Konrad (RMSE of 0.028 W m−1 K−1 to 0.036 W m−1 K−1 ), Lu et al. (RMSE of 0.028 W m−1 K−1 to 0.044 W m−1 K−1 ) and log models (RMSE of 0.038 W m−1 K−1 to 0.042 W m−1 K−1 ). Whereas, the transient measurements are more accurate when compared with the Johansen model (RMSE of 0.029 W m−1 K−1 to 0.034 W m−1 K−1 ). ACKNOWLEDGEMENTS The authors would like to acknowledge the financial support provided by the German Federal Ministry for Economic Affairs and Energy (BMWi) under Grant numbers 0325547B and KF3067302HF3, as well as the support of Project Management Jülich (PTJ).

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REFERENCES Abu-Hamdeh, N.H., Reeder, R.C. 2000. Soil thermal conductivity: Effects on density, moisture, salt concentration, and organic matter. Soil Sci. Soc. Am. J. 64: 1285–1290. Abuel-Naga, H.M., Bergado, D.T., Bouazza, A. 2008. Thermal Conductivity Evolution of Saturated Clay under Consolidation Process. Int. J. Geomech. 8(2): 114–122. Alessandro, F. 2007. An apparatus for the routine measurement of thermal conductivity of materials for building application based on a transient hot-wire method. Applied Thermal Engineering 27(14–15): 2495–2504. Alrtimi, A.A. 2014. Experimental Investigation of Thermal Conductivity of Soils and Borehole Grouting Materials. Ph.D. diss., School of Civil Engineering and Geosciences, Newcastle University, November 2014. ASTM. 2011. D420–D5876: Annual book of ASTM standards. Volume 04.08 Soil and Rock (I): D420–D5876 and Volume 4.09 Soil and Rock (II): D5877—latest, West Conshohocken, Pennsylvania, United States. ASTM. 2008. 5334-08: Standard test method for determination of thermal conductivity of soil and soft rock by thermal needle probe procedure. Bejan, A., Lorente, S. 2004. The constructal law and the thermodynamics of flow systems with configuration. Int. J. Heat Mass Transfer 47: 3203–3214. Bejan, A. 2004. Convection Heat Transfer. 3rd ed., Wiley, New York. Clauser, C., Huenges, E. 1995. Thermal conductivity of rocks and minerals. In Rock physics and phase relations:A handbook of physical constants, American Geophysical Union, pp. 105–126. Côté, J., Konrad, J.M. 2005. A generalized thermal conductivity model for soils and construction materials. Can. Geotech. J. 42: 443–458. Côté, J., Konrad, J.M. 2005b. Thermal conductivity of basecourse materials. Can. Geotech. J. 42: 61–78. Doughty, C., Nir, A., Tsang, C.F., Bodvarsson, G.S. 1983. Heat storage in unsaturated soils: Initial theoretical analysis of storage design and operational method. Proceedings of the International Conference on Subsurface Heat Storage in Theory and Practice, Stockholm, Sweden. Farouki, O.T. 1981. Thermal properties of soils. CRREL Monograph 81-1, US Army Corps of Engineers, Cold Regions Research and Engineering Laboratory, Hanover, N.H. Gavriliev, R.I. 2004. Thermal properties of soils and surface covers. in: D.C. Reston (ed.), Thermal analysis, construction, and monitoring methods for frozen ground, ASCE, VA, vol. 492, pp. 277–294. Gori, F., Corasaniti, S. 2004. Theoretical prediction of the thermal conductivity and temperature variation inside Mars soil analogues. Planet. Space Sci. 52: 91–99. Hart, G.K., Whiddon, W.I. 1984. Ground source heat pump planning workshop. Summary of Proceedings, Palo Alto: Electric Power Research Institute, EPRI Report RP 2033-12. Hashin, Z., Shtrikman, S. 1962. A Variational approach to the theory of the effective magnetic permeability of multiphase materials. J. Appl. Phys. 33(10): 3125–3131. Hooper, F.C., Lepper, F.R. 1950. Transient heat flow apparatus for the determination of heating piping and air conditioning. American Society of Heating andVentilation Engineering 56. Kersten, M.S. 1949. Thermal properties of soils. Bulletin 28, Engineering Experiment Station, Minneapolis: University of Minnesota.

Johansen, O. 1975. Thermal conductivity of soils. Ph.D. diss., Norwegian Univ. of Science and Technol., Trondheim (CRREL draft transl. 637, 1977). King, M.S., Pandit, B.I., Hunter, J.A., Gajtani, M. 1982. Some seismic, electrical and thermal properties of subseabottom permafrost from the Beaufort Sea. Proceedings of the Fourth Canadian Permafrost Conference, Ottawa, pp. 268–273. Low, J.E., Loveridge, F.A., Powrie, W. 2013. Measuring soil thermal properties for use in energy foundation design. Proceedings of the 18th International Conference on Soil Mechanics and Geotechnical Engineering, Paris, France. Lu, S., Ren, T., Gong, Y., Horton, R. 2007. An improved model for predicting soil thermal conductivity from water content at room temperature. Soil Sci. Soc. Am. J. 71(1): 8–14. McGaw, R. 1969. Heat conduction in saturated granular materials. Special Rep. No. 103, Highway Research Board, pp. 144–131. Mitchell, J.K., Kao, T.C. 1978. Measurement of soil thermal resistivity. Journal of the Geotechnical Engineering Division 104: 1307–1320. Mohsenin, N.N. 1980. Thermal properties of foods and agricultural materials. Gordon and Breach, Science Publishers, Inc.: New York, pp. 407. Momose, T., Sakaguchi, I., Kasubuchi, T. 2008. Development of an apparatus for measuring one-dimensional steadystate heat flux of soil under reduced air pressure. European Journal of Soil Science 59(5): 982–989. Peters-Lidard, C.D., Blackburn, E., Liang, X., Wood, E.F. 1998. The effect of soil thermal conductivity parameterization on surface energy fluxes and temperature. J. Atmos. Sci. 55: 1209–1224. Rosen, M.A., Hooper, F.C. 1989. A model for assessing the effects of berms on the heat loss from partially buried heat storage tanks. Proceedings of the 9th International Heat Transfer Conference, Jerusalem, Israel, August 19– 24, 1989. Salomone, L.A., Kovacs, W.D., Kusuda,T. 1984.Thermal performance of fine-grained soils. Journal of Geotechnical Engineering 110(3): 359–374. Salomone, L.A., Kovacs, W.D. 1984. Thermal resistivity of soils. Journal of Geotechnical Engineering 110(3): 375–389. Salomone, L.A., Marlowe, J.I. 1989. Soil rock classification according to thermal conductivity. Palo Alto: Electric Power Research Institute, EPRI CU-6482. Sass, J.H., Stone, C., Munroe, R.J. 1984. Thermal conductivity determinations on solid rock – a comparison between a steady-state divided-bar apparatus and a commercial transient line-source device. Journal of Volcanology and Geothermal Research 20(1–2): 145–153. Sass, I., Stegner, J. 2012. Coupled measurements of thermophysical and hydraulical properties of unsaturated and unconsolidated rocks. Proceedings of the 37th Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, Jan. 30–Feb. 1, 2012. Stegner, J., Nguyen, D., Seehaus, R., Sass, I. 2011. Development of a thermal conductivity and diffusivity meter for unconsolidated rocks. Proceedings of the 18. Tagung für Ingeniergeologie, Berlin. (original in German). Van Rooyen, M., Winterkorn, H.F. 1957. Structural and textural influences on thermal conductivity of soils. Highway Research Board Proceedings 39: 576–621. Yun, T.S., Santamarina, J.C. 2007. Fundamental study of thermal conduction in dry soils. Granul. Matter 10(3): 197–207.

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Determination of time-dependent undrained shear strength of mining landfill M. Uhlig & I. Herle Chair of Soil Mechanics and Foundation Engineering, Institute of Geotechnical Engineering, Faculty of Civil Engineering, Technische Universität Dresden, Dresden, Germany

C. Karcher RWE POWER AG, Bergheim, Germany

ABSTRACT: Today, more than a quarter of the energy produced worldwide is based on coal. In Germany in 2014, lignite is the main resource for energy production. Lignite is mined in open-pit mines. With openpit mining, the overburden of the coal must first be removed. Normally, the material from the upper layers is transported to the other side of the open-pit mine. There the material is deposited, filling the existing excavation. If the material is fine grained and the consistency index is low then in the first step dams have to be built and the wet material can be filled in behind to create a polder. Many dams and polders create together a large slopesystem, with a height from the coal base to the original surface elevation. This slope-system can be as high as 400 m. For engineering and planning these dams and polders, shear parameters (for example the undrained shear strength) of the involved materials are necessary. Furthermore, the undrained shear strength changes over time should be taken into account because the freshly dumped material is consolidating. In this paper two models are presented showing how the undrained shear strength can be calculated using the initial state of the soil, statistics and finite element analysis or analytical approach. For the finite element model the determination of the soil consistency is the basis for the statistical analysis. From the statistical analysis the void ratio can be calculated. Using this variable and the parameters of the hypoplastic soil model by Mašín, consolidation simulations are performed. Finally, time-dependent void ratios are used to determine the undrained shear strength. The second model uses analytical equations of the consolidation problem to calculate the effective stress. From the effective stress the undrained shear strength can be determined. A comparison of both models is also presented on example calculations.

1

INTRODUCTION

In open-pit mines the majority of the excavated material is overburden, which overlays the desirable lignite. In West-Germany near Cologne, the material is excavated with bucket-wheel excavators. This material is then transported by belt-conveyors to the other side of the mine. There it can be deposited using a spreader, which lifts the material by belt conveyors to a specific height and then lets the material to fall free to the surface. With dry coarse grained material no preparation has to be done because it builds natural angles of repose. However, with soft and wet fine grained soils this procedure can not be done without preparing dams and polders, otherwise the material would flow away. To separate the soils in open-pit mines in North Rhine-Westphalia there is a central collection station for all belt conveyors coming from different operating levels (excavators) and belt conveyors to the spreaders at different levels. In this station it is possible to couple belt conveyors coming from the excavators and going to the spreaders with each other so that every spreader can get the required material at any given time.

The company developed sections to define where the soft and liquid fine grained soil, that need to be filled behind dams made of sand or gravel, have to be dumped. After the soft material has been filled in, the polders are covered by stiffer clays. Another layer of sand cover is used to build a surface, where the heavy spreader can be safely driven. Figure 1 shows a typical section of a completed polder and a dam. The yellow areas are coarse grained soils, which have equal or less than 30% of fine (so called M1-material). Materials with more than 30% fine grains are divided into two different material classes: the material class M2T is a fine grained material which builds an angle of repose during its deposition, hence the consistency varies from stiff to hard. This material, shown in Figure 1 in brown, is in an overconsolidated state and exists predominately in the form of lumps. Mostly, these are high plasticity clays. The class M2N (in Figure 1 in red) includes wet and soft or liquid soils, which are not able to build any reasonable angles of repose. Normally, these materials are mixtures of fine sand with silt or clay, low plasticity silts or clays with a high water content.

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Figure 1. Section of a deposition. Blue 1-D column used for calculations.

Each of these sections forms one level. On each level a spreader deposits the material evenly across the width of the mine.The height of each level is always the same. The spreader drives continuously forwards and backwards, finishing a horizontal section across the width of excavated area. Layers are stacked building the complex temporary slope which changes every day as the deposition moves on. These slopes go from the bottom of the lignite level up to the natural ground level or above it. The slope-system can reach heights of more than 400 m. The slopes and sections have to be engineered and designed to be safe. First, the slopes must be stable under their own weight. Also, the slopes must be designed for the load of the spreaders on the freshly deposited soils (mostly 3 months old). Calculations of the slope stability for fine grained soils can be split into two models. If the soil is loaded almost immediately after its deposition being fully saturated and unconsolidated, the load on the surface will produce excess pore water pressures. Undrained shear strength cu is meaningful for the design in this case. If the soil is fully consolidated the load is completely carried by the grains; the soil is drained and the effective shear parameters ϕ′ and c′ can be used. During the consolidation process the soil shear strength changes between these two extremes. The undrained shear strength is a conservative value here, therefore it is used in the sequel to describe the evaluation of the shear strength during the consolidation. 2

UNDRAINED SHEAR STRENGTH

The undrained shear strength cu depends on state of the soil, which can be expressed in void ratio and effective stress. During consolidation, the soil state changes. In normally consolidated soils the void ratio decreases while the undrained shear strength increases. Commonly, to determine the undrained shear strength of a soil different tests can be performed. In situ direct investigation methods such as cone penetration or shear vane tests can be carried out to determine cu . Alternatively undisturbed samples can be taken out of the field. The samples can then be tested in the laboratory using triaxial apparatus (UU-test), falling cone or shear vane tests. However, it is usually not possible to test the soil in several subsequent time increments (for instance 1 week) to validate the undrained shear strength changes over time because the costs of such

an extensive testing would be too high. Additionally, it may be dangerous to enter freshly dumped deposits with very low undrained shear strength to acquire samples for testing. For this reason, it is necessary to develop models to predict the undrained shear strength. The undrained shear strength can be calculated from the effective critical friction angle ϕc′ using the critical state soil mechanics theory (Schofield et al. ). In this case, the undrained shear strength cu is, as shown in equation 1, the half of the deviator stress q, which follows from the slope of critical state line M at a particular mean effective stress p′ :

M is a function of the critical friction angle ϕc′ in triaxial compression:

The effective mean pressure p′ can be obtained from a particular constitutive model. Using the Modified Cam Clay model,

where p′i is the actual effective mean pressure, ηp is the isotropic overconsolidation ratio (p′0 /p′i ), r is the pressure ratio between the normal compression and critical state line p′0 /p′cs and  is a ratio of the compression λ and swelling index κ, both defined in a (ν)-ln(p′ )-space:

The specific volume ν is defined as:

All mentioned quantities are depicted in Figure 2. The red point represents the actual specific volume (νi ) and the corresponding pressure (p′i ). The soil state is overconsolidated, the maximum previous pressure is defined by p′0 . If the behaviour is assumed to be undrained, the specific volume remains constant and shearing of the soil results in the critical state at pressure p′cs . Using equations 1 and 3 with r = 2 (Wood 1990) and simplifying the equation for a normally consolidated soil (p′i = p′0 ), the undrained shear strength cu1 can be calculated from:

In the hypoplastic soil model for fine grained soils according to Mašín (Mašín 2005), p′0 is defined

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surface, j as a control variable ( j = 1, 2, 3, …), h as the height of the column and cv as the consolidation coefficient:

Figure 2. Definitions of the quantities in the Modified Cam Clay model.

Directly after surface loading (t = 0) the total stress is equal to the pore water pressure. This means that the initial pore water pressure distribution due to the load at the top is a rectangle. After a very short time the pore water pressure at the boundaries becomes zero. In the case of a deposit of a significant height, however, the self-weight effect is an important factor. For this problem equation 9 describes the analytical solution (Lee 1979, Lee & Sills 1981). γ ′ is the effective unit weight of the material and n is a control variable (n = 1, 2, 3, …).

differently and the undrained shear strength follows from:

Herein p∗e is the Hvorslev equivalent pressure (see Figure 2). This pressure is defined in a double logarithmic space of specific volume and mean pressure. 3 ANALYTICAL SOLUTION The following analysis is performed for the case of a 1D consolidation. This means that water can only flow vertically like in oedometer tests. Also, the deformations are only possible in the vertical direction. This condition occurs roughly in the centre of a polder as illustrated by the blue column in Figure 1. Closer to the dams, which are made of more permeable material, there are also horizontal drainage paths, which decrease the consolidation time. The 1D case is therefore the most conservative one. The solutions of the consolidation problem follow from the underlying partial differential equations. The following conditions and assumptions apply: 1. 2. 3. 4.

drainage on both sides (top and bottom) permeability is constant stiffness is constant load at the top is constant

Well known and often used is the solution by Terzaghi, which represents the simple case in which the column is loaded on top with a constant stress. The soil itself is weightless. The analytical equation can be found in different books, e.g. (Atkinson and Bransby 1977) or (Verruijt 2012). The analytical equation for the pore water pressure at time t and at a depth z is shown in equation 8, using σ as the stress on the

For the self-weight consolidation, the initial pore water pressure distribution is a triangle. Thus, the pore water pressure at the top boundary is zero from the beginning. Analogously to the case of constant load at the top, the bottom value becomes zero after a short time. Using the conditions mentioned before, the pore water pressures can be calculated as a superposition of m different loads (u1,m ) and the self weight (u2 ) consolidation. The summation must be done time tand depth z-wise. While the total pressure is known and the pore water pressure follows from the mentioned equations, the effective vertical stresses σv′ can be calculated from:

Here, a K0 -condition defined by Jaky:

can be assumed. In the last step the mean pressure can be inserted into equation 1 to obtain the time-dependent undrained shear strength.

4

NUMERICAL SOLUTION

The basis for this procedure is a set of laboratory tests on samples taken from the spreader to determine the

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continuous distribution was approximated with a discrete distribution using ni intervals. Figure 3 shows an example with 36 intervals. For each interval an IClog value (centre of interval) and a frequency f (height of bar) is known. From the IClog -values the water content can be calculated using equation 12 and the average of the liquid limits and the plastic limits of all samples. Using the water content, the void ratio was determined from:

Figure 3. IClog -distribution continuous (red line) and discrete (blue bars – ni = 36 intervals).

initial state. The obtained water content in situ w, the liquid wL and plastic wP limit can be used to calculate a logarithmic consistency index IClog :

Under the assumption that the IClog -values of all samples follow a normal distribution, see Figure 3, the mean µ and standard deviation σ can be determined. The statistical distribution represents the initial consistency of the soils in the deposits. Subsequently, the finite element method is used to solve the consolidation problem. The 1D calculations were done by the software Tochnog (2013). The hypoplastic model for fine grained soils according to Mašín (2005) was used. The constitutive model reproduces the non-linear soil behaviour and includes barotropy and pycnotropy. For the basic formulation five parameters are necessary, they can be determined by mechanical laboratory tests (oedometer, CU-triaxial or direct shear box test) and are listed below: • • • • •

ϕc′ , critical friction angle N , logarithmic specific volume at 1 kPa λ∗ , slope of the normal compression line κ∗ , slope of the reloading line r, initial shear stiffness.

N , λ∗ , κ∗ are defined in a double-logarithmic space of specific volume and mean pressure. The model has the same boundary conditions as the analytical model described in section 3. The soil column has an initial effective stress of 5 kPa corresponding to the initial load at the top. To simulate the dumping, the gravity force is increased from 0 (initially) to 1g within a few days (depending on the real dumping time). The initial void ratios were calculated as follows: First, the continuous distribution of IClog of samples from the open-pit mine were considered. This

including the average of the grain density ρs of all samples and the water density ρw . For all calculations full saturation (Sr = 1) was assumed. Finally, for each of the calculated void ratio a simulation of 1D consolidation is performed. During the consolidation process the void ratio is changing continuously with time and depth. From this void ratio the equivalent Hvorslev pressure can be calculated:

Subsequently, the undrained shear strength can be determined from equation 7. For every simulation nd points at different depths are considered for output. Thus nd void ratios are available for nt time steps and ni simulations. As a result of all simulations ni · nd · nt undrained shear strengths are obtained. A further simplification of the results is needed. The focus of the presented analysis is on the time effects. Therefore the influence of the depth and the initial state can be averaged using the following. First the average of cu from surface level to the bottom of the column was calculated for every time step and simulation, denoted as cu . Herewith, the results are reduced to ni · nt undrained shear strengths. In the next step, the frequency f of each initial void ratio (IClog -interval) is used to sum all ni simulations. The idea behind is the following: if a void ratio is rare in the deposition, then the undrained shear strength, calculated from this void ratio is also exceptional. On the contrary, a void ratio measured often in the field (i.e. close to the peak of the IClog distribution) must be reflected in a corresponding calculated undrained shear strength with a high probability. Consequently, the frequencies of void ratios from the initial IClog -distribution have to be correlated directly with the calculated undrained shear strengths. Figure 4 demonstrates the procedure. Figure 4a shows ni (here 36) intervals (ordinate) and the frequency of each interval (abscissa). This corresponds directly to Figure 3. Each interval represents a IClog -value or initial void ratio for one simulation. Figure 4b shows the calculated cu -values for each interval after a certain time (in Figure 4 one month). Then, new cu -intervals should be created in a new diagram showing the frequency f over the undrained shear strength

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Table 1. Properties of the material for analytical model for reference set (ref) and the parameter study sets (para 1 to para 4).

ref para 1 para 2 para 3 para 4

Es [kPa]

k [m/s]

ϕc′ [–]

equation for cu

5000 5000 5000 10 000 5000

1 · 10−7 1 · 10−7 1 · 10−7 1 · 10−7 1 · 10−8

27◦ 27◦ 20◦ 27◦ 27◦

7 6 7 7 7

Figure 4. Procedure to determine the discrete distribution of cu .

cu (Figure 4c). The frequencies of the cu -intervals have to be calculated using the frequencies fi from Figure 4a from all cui -values in Figure 4b which are located in the cu -interval. For example the red box represents the cu -interval from 200 kPa and higher. Three values of cu are in between. The sum of the frequencies in the red box on Figure 4a is equal to the height of the red bar on Figure 4c. In this way a complete discrete distribution of cu can be created. In the last step, this discrete distribution can be transformed in a continuous log-normal distribution and the distribution characteristics can be calculated. Here only the median value is discussed as a representative value (Herle et al. 2011). In such a way calculated undrained shear strength depends only on time. 5

EXAMPLE

The chosen parameter sets originate from the openpit mine. As a simplification, the parameters of both fine grained layers (see Figure 1) are summed togethers (M2T + M2N = M2). The cover layer, shown in yellow in Figure 1, is simulated as a load at the top. Time starts (t = 0) with the deposit of the M2material. The M2-material is completely deposited in 3 days after t0 . Another 3 days later (t = 6 d) the cover layer is installed. This layer loads the M2-material with 130 kPa. The soil density was considered equal 1.8 g/cm3 . The soil own weight for both, analytical approach and numerical analysis, is assumed to be the same. 5.1 Analytical method The applied parameters are summerized in Table 1. They represent a clay silt mixture (M2-material). Using the reference parameter set the calculated pore water pressure distribution is shown in Figure 5. As discussed previously the pore water pressure distribution at the beginning is a triangle because the

Figure 5. Pore water pressure distribution at different times.

load due to own weight is completely carried by pore water pressure. Beginning from the bottom, the consolidation starts and proceeds very quickly as can be seen by comparing curves with time 0.01 d, 0.5 d and 5.99 d in Figure 5.All these lines are solid and represent only the self-weight consolidation. Then the cover is installed and the load at the top is added and reflected in the pore water distribution (curve 6.01 d). The maximum pore water pressure moves up with time (see 6.01 d to 30.0 d) and after a certain period stabilizes at the middle, which corresponds to the point with the longest drainage path. Finally the pore water pressures decreases to zero (360 d and 720 d), the soil is now fully consolidated. At both ends the undrained shear strength changes very fast. In Figure 6, the curves for 0.01 m and 22.69 m show clearly this effect. Furthermore both curves are the boundaries for the minimum and maximum final shear strength. The shear strength increases from top to the bottom, due to the effect of the own weight. Additionally, in Figure 6 the average undrained shear strength cu calculated over 6 heights is shown as a black dashed curve. A parameter study was performed to evaluate the uncertainty of the input parameters. Figure 7 presents the results of this parameter study (the reference set is

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Table 2. Parameters of the material for the FEM-model. N [–]

λ∗ [–]

κ∗ [–]

ϕc′ [–]

r [–]

k [m/s]

0.82

0.07

0.004

27.0◦

0.4

1 · 10−7

Table 3. Parameters for calculating the initial void ratio.

Figure 6. Undrained shear strength at different depths (reference parameter set).

IClog -distribution

Atterberg limits

grain density

µ [–]

σ [–]

wL [%]

wP [%]

ρs [g/cm3 ]

0.56

0.25

44.0

21.0

2.52

final undrained shear strength but it increases the consolidation time. Reducing the permeability 10 times increases the consolidation time by a factor of 10. As it can also be seen in Figure 7 (purple curve), in the first 100 days no evident increase of cu in the middle of the soil column can be observed. 5.2

Figure 7. Influence of different parameters: Curves for depths of 11.40 m (solid lines) and 22.69 m (dashed lines).

shown the with blue curves). The calculation results are presented at two different depths. The results for the point in the middle of the 1D column (11.4 m) are shown with solid lines. Additionally, a point 1 cm above the bottom (22.69 m) was chosen. The results for this point are shown in Figure 7 with dashed lines. The green curves show the cu values calculated using equation 6 (according to the Modified Cam Clay model). The value of λ is 10 times greater than of κ. This equation yields the highest final shear strength (green lines in Figure 7). However, the difference is smaller than 10% comparing with the reference set. Decreasing the critical friction angle (red lines) the final undrained shear strength decreases too. The consolidation time is not affected by the variation of ϕc or using equation 6 (Modified Cam Clay model). The oedometric modulus of 10 000 kPa does not change the

Numerical method

In all simulations, the parameter set from Table 2 was used. These average values were obtained from laboratory test results using 6 representative soils from the open-pit mine. In the FEM code the permeability k was the same as in the analytical model. The initial void ratios are calculated from a given IClog -distribution (see section 4) and the liquid and plastic limit. For the simulations the IClog -distribution was split into ni = 36 intervals (see Figure 3). For each initial void ratio a consolidation simulation was performed using FEM. The void ratios were calculated for nd = 22 points (with a vertical distance of 1 m between the points) in a 1D column over a given time period. As previously discussed, the undrained shear strength cu can be calculated from these void ratios as an average of all 22 points. Using the statistical weighting (see section 4) the median undrained shear strength was calculated. Figure 8 shows the result of the simulation. The analytical result in Figure 8 uses the cu of 22 points in each calculated time step.This curve is principally the same as shown in Figure 6, the only difference is the number of calculated points. As can be seen in Figure 8 the numerical curve starts and ends with a higher cu than the analytical calculation. The reason can be explained with help of Figure 9. Here the changes of specific volume (1 + e) over effective stress are shown. As mentioned before, one simulation is performed for a number of different initial void ratios. The initial void ratios are decreasing during consolidation as can be seen in Figure 9. E.g., starting at a void ratio of 1.02 (blue points), which represents the IClog of 0.09, the normal compression line is reached very quickly

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The explanation is the stiffness, which changes with effective stress in case of hypoplastic model. 6

CONCLUSIONS

In this paper two methods for calculating timedependent undrained shear strength of mining landfills are presented. Comparing the analytical and numerical method the following remarks can be formulated: The analytical solution performs very well, showing the basic effects and many variations of parameters can be calculated very fast (several minutes). • Numerical model can take into account variable stiffness or permeability changing with stress (and/or density). Furthermore, the initial state of the soils (normal consolidated or overconsolidated) can be considered. • The analytical model yields a conservative estimate, whereas the FEM using statistc distributions can produce more realistic results (at a higher computational cost). •

Figure 8. Undrained shear strength for numerical (num) and analytical (ana) model.

REFERENCES

Figure 9. Trend of specific volume (1 + e) with effective vertical stress for different initial states in a simulation.

and is followed afterwards. If the initial void ratio is smaller the normal compression line is reached at a higher effective stress. In some cases (see e0 = 0.41 – black dots), the normal compression line is even not reached at all because the maximum effective stress is too small. In this way, the overconsolidated states are included in the numerical calculation. This effect results in higher cu values in FEM when comparing both models. In the analytical model, the soil state is following only the normal compression line. Further differences between the analytical and the numerical model can be noticed in Figure 8. The permeability was the same for both models but the numerical model reaches a fully consolidated state faster.

Atkinson, J. & P. Bransby (1977). The Mechanics of Soil – An Indorduction to Critical State Soil Mechanics. Herle, I., D. Mašín, V. Kostkanova, C. Karcher, & D. Dahmen (2011). Experimental investigation and theoretical modelling of soft soils from and mining deposits. In International Symposium on Deformation Characteristics of Geomaterials, September 1–3, 2011, Seoul, Korea. Lee, K. (1979). An Analytical and Experimental Study of large Strain Soil Consolidation. Ph. D. thesis, University of Oxford. Lee, K. & G. Sills (1981). The consolidation of a soil stratum, including self-weight effects and large strains. International Journal for Numerical and Analytical Methods in Geomechanics 5, 405–428. Mašín, D. (2005). A hypoplastic constitutive model for clays. International Journal for Numerical and Analytical Methods in Geomechanics 29(4), 311–336. Schofield, A., P. Wroth, L. in Engineering, at Cambridge, & University. Critical State Soil Mechanics. Tochnog (2013). version 16, [finite element method software]. http://www.feat.nl/. Verruijt, A. (2012). Soil Mechanics. Delft University of Technology. Wood, D. M. (1990). Soil Behaviour and Critical State Soil Mechanics. Cambridge University Press.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Enhancement of soil thermal conductivity in dry condition D. Shrestha, H. Hailemariam & F. Wuttke Marine and Land Geomechanics and Geotechnics, Kiel University, Germany

ABSTRACT: The efficiency and performance of an underground power cable is strongly influenced by thermal conductivity of soil in which it is placed. Most soils have extremely low thermal conductivity in dry state as compared to that in saturated condition. It is essential to improve the thermal conductivity in dry state for the optimum performance and safe operation of the cable, as backfill soils dry due to continuous heat generated from the cable. This paper presents extensive laboratory study to develop backfill soils with higher dry thermal conductivity by modifying grain size distribution into fuller curve gradation. Experimental results clearly show a significant improvement of the thermal conductivity of modified soils. The improvement is attributed to fuller curve gradation which contributes to obtain lower porosities and improve interparticle contacts. A result of thermal simulation run for single cable clearly shows large improvement in heat dissipation for modified soil as compared to unmodified soil.

1

INTRODUCTION

Soil thermal conductivity plays preponderant role in geo-engineering applications including thermal effects, such as embedding of underground power cables, small and large scale seasonal thermal ground energy storage, oil and gas pipelines, heat exchanger piles and nuclear waste disposal facilities. The efficiencies and performances of some applications such as underground power cable and energy piles are strongly affected by soil saturation conditions; especially low saturation conditions, which alone can negatively affect the overall soil thermal conductivity. Thus, it limits further possibility to extend their application in hot-arid environments region, where extreme environmental conditions such as high air temperature, high evapotranspiration rate and poor rainfalls result low saturation condition and poor recharge of underground water and thus high thermal resistance. Therefore, it is essential to improve the soil thermal conductivity to enhance the performance of such applications. High voltage underground power cable, alternatives to overhead power cable, needs proper burial. The performance of an underground power cables is critically influenced by the thermal conductivity of the medium in which it is placed, as well as by the thermal properties of the cable itself. Heat is propagated due to power losses in the conductors, insulation, sheath and other components of the cable system (Sandiford 1981, Mozan et al. 1997 & Afa 2010). The main role of backfill materials is to

dissipate the heat into the surrounding environment for the efficient and safe operation of the cable. Thus, the thermal conductivity of backfill soil should be, in principle, higher than surrounding soil in dry as well as wet state.The thermal conductivity of the backfill soils are highly moisture dependent. Typically their thermal conductivity decreases by five- to ten-fold when the soil moisture is decreased to zero (Adams & Baljet, 1968). It is due to fact that the water bridges formed between soil solid particles improve contact between the particles and thermal conductivity of water is 25 times larger than that of air. The reduction in thermal conductivity as a result of low saturation largely influences the current carrying capacity of the underground cables (Sandiford 1981, Len & Anders 2008) as well as cable life (Karahan & Kalenderli 2011). On the other hand, energy piles used as ground heat exchanger loss their efficiency up to 40% in dry conditions as compared to that in fully saturated conditions (Venuleo et al. 2016). The goal of this paper is to compensate such reduction by improving the thermal conductivity of backfill soils for lower saturation conditions. Soil thermal conductivity depends on several factors such as soil fabric (refers particle shape and size), porosity, water content, packing density, mineral composition and temperature (Vries 1963, Johansen 1977, Farouki 1981, Rao & Sing 1999, Côté & Konrad 2005a). As explained by Yun (2007) and Nasirian (2015), a bigger particle size, well graded grain size distribution, higher solid thermal conductivity, lower porosity, saturation and effective stress are the factors to enhance thermal conduction and thus

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increase the thermal conductivity of soils. In dry soils, heat mainly transfers via solid inter-particle contacts and thus, thermal conduction is controlled by number of contacts per volume and its quality. The number of contacts per particle and contact quality depends on the particle shape, grain size distribution and packing density. Keeping these facts in consideration, the grain size distribution of soil was modified into fuller curve gradations to achieve the goal. The fuller curve gradations (Fuller & Thomsan 1907) consists of wide range of particle arrangement (coarse to fine particles) contribute to obtain lower porosities (or dense mixes) and improve inter-particle contacts. The fine grains act as thermal bridges between the grains to increase the overall thermal connectivity of the soil solid matrix. In order to validate these assumptions, the thermal conductivity of unmodified and modified backfill soil samples was measured in dry conditions. The measured thermal conductivity data were also compared with existing theoretical and semi-empirical models applicable to natural soils and crushed rocks to analyse the thermal improvement of modified soils. Furthermore, thermal simulation was carried out for single cable using Finite Element Methods software (Comsol multiphysics) to observe the heat dissipation characteristics with the modified soils.

2

EXPERIMENTAL PROGRAM

2.1 Analysed soil The thermal conductivity of unmodified sand samples and modified sand samples was measured and compared at dry conditions. Two different types of sands referred in this paper as sand A (from Weimer, Germany), and sands B (from Kiel, Germany) were selected for this study. The gradation of both sands was modified to three different fuller curve gradations of 2 mmF, 4 mmF and 8 mmF. There were altogether six modified soils, three from each sand. The modified soils of 8 mmF, 4 mmF and 2 mmF have maximum particle size of 8 mm, 4 mm and 2 mm respectively. Selection of bigger size particles was done on the basis that bigger particles enhance the thermal conduction. The fine soils, sodium bentonite in this study, was added to complete fuller curve gradation attaining particle size lower than 125 µm. It acts as inter-granular bridges to increase the overall thermal connectivity of the soil solid matrix. The particles size distribution of all sands and modified sands are presented in Figure 1. A total of 33 samples including 8 unmodified sand samples were analysed with measurement of thermal conductivity. All the samples were oven dried and the bulk density was controlled. The measurements were done at room temperature and atmospheric pressure conditions and were repeated at least three times for each sample.

Figure 1. Particle size gradation.

2.2 Soil thermal conductivity measurement The thermal conductivity of studied mixes was measured with a thermal needle probe, Decagon KD2 Pro, based on transient line source measurement in compliance to ASTM D5334-08 [23] and IEEE standards [24]. The sufficient needle length to diameter ratio ensures that conditions for an infinitely long and infinitely thin heating source are met. The measurement error recorded for all samples was kept well below the 0.015% limit. The KD2 Pro includes a linear heat source and a temperature measuring element with a resolution of 0.001◦ C, and computes the thermal conductivity of the analysed material by the following equation,

where λ (W m−1 K−1 ) is the thermal conductivity of sample, Q (W m−1 ) is a constant rate of application of heat, T is the temperature response of the source over time, and t (s) is the amount of time that has passed since heating has started.

3

RESULTS AND DISCUSSION

3.1 Experimental results analysis Figure 2 shows thermal conductivity results as a function of porosity in dry state for all studied mixes. As expected the thermal conductivity values increase with a decreasing porosity. In this case, the thermal conductivity is increased exponentially with decreasing porosity. The experimental results clearly show the significant improvement in thermal conductivity for dry conditions. About two to threefold increment in dry λ is noticed in all modified sand samples at porosity less than 0.3.The thermal conductivity values of dry

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Figure 2. Thermal conductivity as function of porosity in dry state for modified (fuller) and unmodified sands.

Figure 3. Thermal conductivity with respect to relative density in dry state for modified (fuller) and unmodified sands.

unmodified sand obtained in this study are lower than 0.4 W m−1 K−1 , range from 0.28–0.39 W m−1 K−1 for the porosities between 0.45 and 0.3). For modified sands the measured dry λ ranges from 0.4–1.1 W m−1 K−1 for porosities between 0.35 and 0.2, which is significantly higher than that of ordinary dry soils. As increase in the maximum particle size of fuller gradation from 2 mm to 8 mm, the decrease in porosity was observed and lowest porosities of 0.2 are attained with 8 mm fuller gradation of both sand samples. However, the dry thermal conductivity values for the same porosity are not remarkably affected by maximum particle size of fuller gradation. For example, thermal conductivity values are 0.59 W m−1 K−1 , 0.61 W m−1 K−1 and 0.60 W m−1 K−1 at a porosity of 0.27 for 8 mmF, 4 mmF and 2 mmF fuller gradations respectively. In terms of relative density, the improvement in the thermal conductivity of modified sand samples can be distinctively observed as unmodified and modified sand samples have different minimum and maximum porosities. Minimum and maximum porosities are in range of 0.20–0.21 and 0.31–0.35 respectively for the modified sand samples while those for sand samples are 0.31 and 0.45 respectively. In Figure 3, the thermal conductivity is gradually increased for unmodified soil as compared to modified soil. Densification of soil affects significantly to improve the thermal conductivity in case of modified soil as compared to unmodified soil. However, the modified soil has higher conductivity even in loose state than unmodified soil. Figure 4 shows improvement in thermal conductivity (I), calculated using Equation 2, with respect to relative density. The thermal conductivity values are increased by 50–180% in all state from loose to dense. As expected 8 mmF has higher thermal conductivity than others which confirm the bigger particle sizes

enhance thermal conduction. The thermal conductivity is decreased with decrease in maximum particle size and consequently 2 mmF has lower thermal conductivity.

The significant increase in thermal conductivity with reduction in porosity reflects the increase in the number of contacts per volume and the improvement in heat conduction efficiency. Wide range of particle arrangements in fuller gradation tends to attain denser packing and a higher coordination number as number of contacts per unit volume helps to improve the quality of contacts. Due to larger surface area, the fine particles act as thermal bridge at contacts to improve quality of contacts. The fuller curve gradation is one of the most influential parameters which can be used to improve dry thermal conductivity for granular type soils. 3.2 Comparison with semi-empirical models Several semi-empirical models exist for estimating soil thermal conductivity as a function of water content, porosity and other hydro-mechanical parameters (Kersten 1949, Van Rooyen & Winterkorn 1957, Johansen 1975, Farouki 1981, Côté and Konrad 2005, Lu et al. 2007). However, although most of the models provide better accuracy as compared to theoretical models, they are generally limited to specific soil types under specific boundary conditions. Johansen (1975) proposed a semi-empirical relationship, Equation 3, to obtain dry thermal conductivity of natural soils λd (W m−1 K−1 ), based on soil

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Figure 4. Improvement in thermal conductivity with respect to relative density in dry state.

Figure 5. Comparison of experimental results with semi-empirical models for dry condition.

dry density ρd (kg m−3 ) and density of soil solids ρs (kg m−3 ).

Côté and Konrad (2005) suggested a new empirical equation for the dry thermal conductivity of soils λd (W m−1 K−1 ) as:

where, χ (W m−1 K−1 ) and η are parameters for particle shape effects with values of 1.70 W m−1 K−1 and 1.80 for crushed rocks, 0.75 W m−1 K−1 and 1.20 for natural mineral soils, and 0.30 W m−1 K−1 and 0.87 for organic fibrous soils. Gavriliev (2004) suggested an empirical relationship for estimating dry thermal conductivity of mineral soils λd (W m−1 K−1 ) based on dry density ρd (g cm−3 ), Equation 3. The relationship is valid for mineral soils with dry density lower than 2 g cm−3 .

Lu et al. (2007) suggested a simple linear function, Equation 5, that describes the relationship between thermal conductivity at dry condition λd (W m−1 K−1 ) and porosity n (0.2 < n < 0.6) for mineral soils, based on two empirical parameters a (=0.56) and b (=0.51), as the magnitude of heat transfer in dry soils is related to soil porosity.

Figure 5 shows measured thermal conductivity values against porosity and trends predicted with

Figure 6. Predicted versus measured dry thermal conductivity of modified soils.

empirical thermal conductivity models. All the models underestimate the measured thermal conductivity of modified sands except Gavriliev model which predicts quite close to measured λ at porosity greater than 0.27. This is probably due to the fact that the models are primarily based on dry density (or porosity) of media and lack considerations of inherent presence of contacts and bulk conductivity of each constituent in dry soils. Figure 6 presents the comparison between the measured and predicted thermal conductivity data from five models. The measured λ of modified soil are larger than predicted data from all models. However, these models are able to predict for the unmodified

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Figure 7. Temperature (◦ C) distribution around underground cable with sand (left) and modified sand (right) at 24, 72 & 120 hours (2nd row to bottom) for dry condition. Geometry of model with mesh generation (top).

soil.The root mean square, RMSE and bias in model prediction were calculated as:

where m is the number of measurements, and λm and λp are the measured and predicted values of dry thermal conductivity λd , respectively. The RMSE and bias for the modified sands were: 0.333 W −1 K−1 and 0.289 W −1 K−1 for Johansen model, 0.382 W −1 K−1 and 0.332 W −1 K−1 for Côté and Konrad: soils, 0.202 W −1 K−1 and 0.139 W−1 K−1 for Côté and Konrad: crushed rocks,

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Table 1. Thermal property of the simulated geometry. Material

Thermal Heat capacity at Conductivity Density constant pressure λ [Wm−1 K−1 ] ρ [kgm−3 ] Cp [Jkg−1 K−1 ]

Soil 0.18 Sand 0.36 Modified-sand 1.0

1450 1650 2000

900 800 800

0.187 W −1 K−1 and 0.106 W −1 K−1 for soil Gavriliev, and 0.386 W −1 K−1 and 0.328 W−1 K−1 for Lu model. The RMSE of Johansen model, Lu model and Côté and Konrad model are considerably higher than that of other two models. Figure 8. Temperature versus time at two observation points for sand and modified sand.

3.3 Temperature distribution around underground cable The thermal simulation for single cable has been carried out using Finite Element Methods software (Comsol multiphysics) to observe the heat dissipation characteristics around underground cable with unmodified and modified backfill soil. Figure 7 (top) shows geometry of model with mesh generation, which consists of single cable, directly buried in the trench at 1.3 m depth. The trench has a width of 0.5 m and depth of 1.5 m, while the size of the model, which represents surrounding soil, is 6 m in width and 5 m in height. The trench first was first filled with sand and then with modified sand for the simulation. The properties of material, used in this simulation, are presented in Table 1. The geometry was simulated in 2-D environment, while the influence of air thermal conductivity was taken into consideration. Each material was assumed to be homogeneous with constant thermal conductivity and a constant specific heat.The cable temperature was fixed at 90◦ C, maximum temperature the underground power cable can reach. At the boundary between trench and surrounding soil, continuity of heat flux and temperature was assumed. The soil surface and other three sides were represented as an isothermal boundary at the temperature of 20◦ C and 15◦ C respectively. The transient heat transfer equation was solved numerically for 200 hrs using the Cosmos Multiphysics software. Figure 7 (2nd row to bottom) shows the outputs of simulation showing the temperature distribution for 24 hrs, 72 hrs and 120 hrs respectively with unmodified sand (left) and modified sand (right). The results clearly indicate the large improvement in heat dissipation for the modified soils which helps to prevent the cable overheated and thus prevent the cable failure and extend their life. Two observation points OP-1 & OP-2 were plotted at depth of 0.5 m & 1.5 m respectively as shown in Figure 7 (top) to observe the temperature rise characteristics within the selected period of 200 hrs.

Figure 8 shows temperature increment with respect to time at two selected points for unmodified and modified sands. The heat dissipations in case of modified sand are faster as compared to unmodified sand in both observation points. At OP-2, there is abrupt change in temperature in the beginning and 63◦ C is reached in just 30 hrs for modified sand, whereas 200 hrs are needed to reach the same temperature for unmodified sand. Then-after the temperature increases steadily after 50 hrs and 100 hrs for modified and unmodified sand respectively. The temperature is gradually increasing at OP-1 and reaches to 50◦ C and 32◦ C for modified and unmodified sand respectively in 200 hrs.

4

CONCLUSION

In this study, backfill materials with high thermal conductivity in dry state were developed and analysed.The modification of grain size distribution into fuller curve gradation shows a strong effect on increasing thermal conductivity of sand for dry condition. Comparing the thermal conductivity of modified sand with that of unmodified sand shows improvement upto 180%. Hence, the backfill materials developed in this study can be efficiently used to bury high voltage underground cables under all moisture conditions; as well graded soils have a great capability to hold moisture content (Adams & Baljet 1968, Moya et al. 1999) and good thermal stability (Adams & Baljet 1968, Radhakrishna et al. 1980). The work presented in this study also confirms previous finding such as the decrease in thermal conductivity with increase in soil porosity, particle size distribution influence on dry thermal conductivity, improvement of quality of contacts due to addition of fine particles which in turn enhances thermal conduction. The output of thermal simulation done in this study for underground cable

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clearly indicate the large improvement in heat dissipation for the modified soils which helps to prevent the cable overheated and thus extend the cable life. Reasonable agreement could not be obtained with existing semi-empirical models while comparing with experimental results. The work in this research can be used further to develop a complete set of prediction model over the full range of saturation.

ACKNOWLEDGMENT The authors wish to acknowledge the financial support provided by the German Federal Ministry for Economic Affairs and Energy (BMWi) under Grant numbers KF3067302HF3 and 0325547B.

REFERENCES Adams, J.I. & Baljet, A.F. 1968. Thermal behaviour of cable backfill materials, IEEE Transaction on Power Apparatus and Systems 87(4): 1149–1161. Afa, J.T. 2010. Subsoil temperature and underground cable distribution in Port Harcourt City, Res. J. Appl. Sci. Eng. Technol. 2(6): 527–531. ASTM. 2008. Standard test method for determination of thermal conductivity of soil and soft rock by thermal needle probe procedure, ASTM 5334-08. Côté, J. & Konrad, J.M. 2005a. A generalized thermal conductivity model for soils and construction materials, Can. Geotech. J. 42: 443–458. de Len, F. & Anders, G.J. 2008. Effects of backfilling on cable ampacity analyzed with the finite element method, IEEE Transactions on Power Delivery 23(2): 537–543. de Vries, D.A. 1963. Physics of plant environment, In W.R. Van Wijk (eds.), Thermal properties of soils: 210–235. Amsterdam: North-Holland Publ. Co. Farouki, O.T. 1981. Thermal properties of soils, CRREL Monograph 81-1, US Army Corps of Engineers, Cold Regions Research and Engineering Laboratory, Hanover, N.H. Fuller, W.B. & Thomsan, S.E. 1907. The laws of proportioning concrete, Trans. ASCE 59(2): 67–143. Gangadhara Rao, M.V.B.B. & Singh, D.N. 1999. A generalized relationship to estimate thermal resistivity of soils, Can. Geotech. J. 36: 767–773.

Gavriliev, R.I. 2004. Thermal properties of soils and surface covers, In D.C. Reston (ed.), Thermal analysis, construction, and monitoring methods for frozen ground: 277–294. VA: ASCE. IEEE. 1992. Guide for soil thermal resistivity measurements, Inst. of Electrical and Electronics Engineers, Inc. New York. Johansen, O. 1975. Ph.D. diss. Norwegian Univ. of Science and Technol, Thermal conductivity of soils. Trondheim (CRREL draft transl. 637, 1977). Karahan, M. & Kalenderli, O. 2011. Heat transferEngineering applications, In V. Vikhrenko (eds.), Coupled Electrical and Thermal Analysis of Power Cables Using Finite Element Method: 205–230. Croatia Kersten, M.S. 1949. Thermal properties of soils. Engineering Experiment Station Bulletin 28, University of Minnesota, Minneapolis. Lu, S. Ren, T. Gong, Y. & Horton, R. 2007. An improved model for predicting soil thermal conductivity from water content at room temperature, Soil Sci. Soc.Am. J. 71: 8–14. Moya, R.E.S. Prata, A.T. & Cunha Neto, J.A.B. 1999. Experimental analysis of unsteady heat and moisture transfer around a heated cylinder buried into a porous medium, International Journal of Heat and Mass Transfer 42: 2187–2198. Mozan, M.A. El-Kady & Mazi, A.A. 1997. Advanced thermal analysis of underground power cables, Record of the Fifth International Middle East Power Conference MEPCON’97, Alexandria, Egypt: 506–510. Nasirian, A. Cortes, D.D. & Dai, S. 2015. The physical nature of thermal conduction in dry granular media, Géotechnique Letters 5: 1–5. Radhakrishna, H.S. Chu, F.Y. & Boggs, S.A. 1980. Thermal instability and its prediction in cable backfill soils, IEEE Transactions on Power Apparatus and Systems 99(3): 856–867. Sandiford, P. 1981. Cable backfill materials-state-of-the-art, Proceedings of the Symposium on Underground Cable Thermal backfill, Toronto, Canada: 3–9. Van Rooyen, M. & Winterkorn, H.F. 1957. Theoretical and practical aspects of the thermal conductivity of soils and similar granular systems, U.S. Highway Research Board, Bulletin 159: 58–135. Venuleo, S. Laloui, L. Terzis, D. Hueckel, T. & Hassan, M. 2015. Effect of microbially induced calcite precipitation on soil thermal conductivity, Géotechnique Letters 00: 1–6. Yun, T.S. & Santamarina, J.C. 2007. Fundamental study of thermal conduction in dry soils, Granul. Matter 10(3): 197–207.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Heat energy recovery from waste water in the Glasgow Subway system N. Hytiris, K. Ninikas & R. Emmanuel Glasgow Caledonian University, Glasgow, Scotland, UK

P.L. Younger University of Glasgow, Glasgow, Scotland, UK

ABSTRACT: This paper investigates the feasibility of utilizing the waste subsurface water ingress inside the Glasgow Subway system. At present this unused excess water is being discharged into the city’s drainage system as waste. This valuable resource could be channeled through a water source heat pump to produce heat energy for domestic or public use. A study was carried out in order to calculate the heat contained in the water. Water flow and water temperature were recorded over a full year within fifteen different places around the network of underground tunnels. A feasibility study to review the number of support factors that could profit the subway system was undertaken as well. Options were discussed and a selection of a site inside the tunnels for a pilot study was decided. The findings of this study are expected to develop an appropriate renewable solution and design a cost effective heat pump system. This waste water will be collected and used to recover heat energy. During this process energy will be produced from a waste product using a sustainable and environmental friendly method.

1

INTRODUCTION

The need for replacing conventional fuel finding alternative sources becomes day by day bigger. A basic factor that led the UK government into more environmental friendly ways of heating are the obligation of reducing the CO2 emissions in 1990’s levels by 2020 (Scottish Government, 2012) and to fully decarbonise heating until 2050 (Department of Energy & Climate Change, 2013). Ground source heat pump (GSHP) systems have shown potential to reduce energy consumption and as result a CO2 reduction of more than 50% compared with conventional heating systems (electricity, oil). A study was carried out from May 2014 until April 2015 in the Glasgow Subway system to investigate the possibility of using the water ingress inside Glasgow’s Subway tunnels for space heating and Domestic Hot Water (DHW) through a water source heat pump (WSPH). The Glasgow Subway forms a circle in the centerwest of the city. The entire passenger railway is underground, contained in twin tunnels, allowing clockwise circulation on the “outer” circle and counterclockwise on the “inner”. Fifteen stations are distributed along the route length of just over ten kilometers. The river Clyde dissects the circular route, with eight stations in the North and seven in the South as shown in Figure 1.

Figure 1. A typical Glasgow Subway map.

2

BACKGROUND

Heat pumps have always been the key technology in the use of excess heat in lower temperatures. They use compression (the same principal as a refrigerator) to extract tepid low grade heat to produce heat for space and/or water heating in general. They can also be reversed to produce cooling. Heat pumps, as shown in Figure 2, are designed to move thermal energy opposite to the direction of spontaneous heat flow by absorbing heat from a cold space and releasing it to a warmer one. A heat pump uses some amount of external power to accomplish the work of transferring

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Figure 2. A typical water source heat pump (WSHP).

Figure 4. A typical sump located between the rail tracks in the Glasgow Subway system.

network adjacent to the vicinity of the nearest Subway station. The two most critical measurements are the water flow and the water temperature in each sump. Some additional data were collected at the same time in order to help us evaluate the water flow through out a year (Average Glasgow temperature, humidity, and precipitation).

Figure 3. Sump locations in the Glasgow Subway system.

energy from the heat source to the destination (space heating/hot water).

3

METHODOLOGY

A series of measurements were undertaken from May 2014 to April 2015 and these consisted of the following: measurements of temperature and flow of the ingress water, consideration of geological and geotechnical parameters to identify sites suitable for heat pump locations. During this period, the seasonal variations of the water ingress were identified. Water sampling was carried out at all sumps for the chemical analysis of the water regime. The 21 sumps located inside the tunnel system that were monitoring are displayed in Figure 3. In addition to the above, atmospheric data were also compiled in order to monitor the Glasgow weather changes i.e. do temperature, humidity, atmospheric pressure and rainfall. This was done by using Glasgow Caledonian University’s meteorological station to collect the readings for each day of the site visits. A monthly meteorological table was also produced to parallelize the tunnel conditions with the Glasgow climate conditions. The sumps (Figure 4) are generally flat bottomed rectangular chambers formed either within the tunnel invert or station platforms and range from 0.50 m to 2.50 m in depth from access level. The pumping stations inside each sump are generally equipped with two submersible pumps. The excess water from the tunnels is being pumped out and discharged into the

3.1 Water flow measuring methods 3.1.1 First method of water flow measurement (Drop test) In each sump there is a probe that when the water reaches a certain level the pump starts pumping the water out of the sump. This period is called “active time”. When the pump will stop functioning; it takes some time before the water flux will raise (inside the sump) the water level up to a point that the pump will start working again. This period is called “inactive time” and this is the actual water flow. Given that the dimensions of each sump are known; the water flux can be calculated by measuring the water level inside the sump (Figure 6) between the “active time” and the “inactive time”. The higher water level (when pump starts working) and the lower level (when pump stops working) are thus measured (Figure 5). This height difference multiplied by the area (surface) of the sump, gives us the water volume that is being pumped out. Dividing this volume by the time (seconds) that the pump is active gives the discharged volume during the active time of the pump. From the lower point when the pump has stopped the time that the water takes to reach again the highest point in the sump is being measured (until the pump will start working again). This depth raised multiplied by the sump surface gives us the water volume that inflows the sump in a specific period of time (F). This is the average water flux in each sump. At least two readings are taken during each visit in each sump are taken to have more data and therefore more accurate averages of the water flux.

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Figure 7. The ultrasonic flow meter showing the water flux (l/s). Figure 5. Measuring the sump water level.

Figure 6. Two consecutive water flow measurements in sump No. 1.

Readings were taken with a rigid measuring stick as well as with an automated depth meter, in which a water sensitive sensor at the end of the measuring cord completes a circuit when it touches the water level, sounding a buzzer. This calibrated cord indicated the distance from the both water levels to the surface. 3.1.2 Second method of water flow measurement (Ultrasonic flow meter) In order to crosscheck the water flux in each sump a second method was used as well. A flow meter (Dynasonics TFX/DMS 1002 ultrasonic flow meter with clamp on pipe transducer) (Figure 7) was used providing more accurate water flow measurements. The device was calibrated prior to each measurement inputting in the software the pipe material (uPVC or steel), the diameter of the pipe (∅120 or ∅160) and the liquid (water). The portable transducers (Figure 8) were clamped onto the pipe applying also liquid silicon to the transducers to assist “reading” the flux.

Figure 8. The transducers clamped onto the discharge pipe.

3.2 Temperature measurements Water temperature is being measured inside each sump and also from all the water inlets into the sump and the average is calculated. A digital probe thermometer (Tiny Tag, TGP4020, range = −40◦ + 125◦ C, accuracy = ±0.35◦ C in the 0–60◦ C range) was used to record the temperature every 10 sec. The thermometer is kept in place for 2 minutes (as a minimum) so the minimum 12 temperature measurements were received from each measuring point (Figures 9 & 10). Atmospheric data were compiled in order to identify if the weather changes i.e. atmospheric temperature, pressure and rainfall, had any effect on the subsurface tunnel water. This was undertaken by using the University’s meteorological station. 3.3 Water flow and water temperature readings Water flow and water temperature readings were taken from May 2014 to April 2015. These were compared with the average Glasgow temperature and humidity

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Table 1. Readings from sump 1. Sump No: 1 WF1: Water flow WT1: Water Temp. GMT: Glasgow Mean Temp. GMH: Glasgow Mean Humid.

Figure 9. The digital thermometer.

Month

Year

WF1 (l/s)

WT1 (◦ C)

GMT (◦ C)

GMH (%)

May June July August September October November December January February March April

2014 2014 2014 2014 2014 2014 2014 2014 2015 2015 2015 2015

6.7 6.3 5.3 3.9 1.9 1.8 1.8 2.0 2.1 2.2 1.5 1.6

14.17 13.45 14.95 16.03 15.40 16.13 13.72 13.20 14.13 12.12 12.81 14.02

11.40 16.70 15.80 16.00 15.00 12.00 10.00 04.10 05.80 05.70 05.40 09.40

80 83 77 88 67 67 75 96 77 80 81 68

Table 2. Heat Loads for six Subway stations (Accord. BS EN: 12831). Station name

Total design heat load (W)

Total design heat load (kW)

Kelvinbridge St. George’s Cross Cowcaddens Buchanan Street Kelvinhall Hillhead

4755 5185 3369 3778 2599 6641

4.8 5.2 3.4 3.8 2.6 6.6

Figure 10. The same digital thermometer inside the sump taking readings.

The heat energy H (in kW) can be calculated from the following formula (Banks, D. 2009): the same days where the readings were taken. InTable 1 are displayed the result from the sump that has been chosen for the trial.

3.4

Subway station’s heat demand & heat energy output from the water

A constant water flow has been monitored in three out of twenty one sumps. Those are: 1, 2 & 17A. The following five stations are the closest ones to the three sumps with the highest and constant water flux: Buchanan Street, Cowcaddens, St. Georges Cross, Kelvinbridge and Hillhead. (See Figure 3). To assess where heat output can be delivered and used, a heat load calculation (in kW) for all the Station has been completed (Table 2). The calculations have been done according the BS EN: 12831-2003. St. Georges Cross subway station has been chosen for the pilot installation of a Water Sourced Heat Pump (WSHP). This station is in the closest proximity from the source point (water sump no.1) to the sink point (station’s ticket office).

(1)

H = Q ∗ ρSvc ∗ t 3

Q: Water flow of the system (m /s) ρ: Density of the water 1000 (kg/m3 ) Svc: Heat capacity of water 4.18 (kJ/kg ∗ K) t: Temperature difference (◦ C) Example: If we take the average water flow from May 2014 to April 2015 for sump 1 (Table 1), which is 3.07 l/s = 0.00307 m3 /s, we can estimate the output. H = 0.00307 ∗ 1000 ∗ 4.18 ∗ 4 = 51.33 kW St. Georges Cross station’s heat load is 5.2 kW (Table 2), so a selection of a system to provide heating and Domestic Hot Water (DHW) is feasible according to the heat energy output from sump 1. Table 3 is an example of the calculation of St. Georges Cross station thermal needs according BS EN 12831:2003. A basic design for this pilot installation has been undertaken and a water source heat pump (WSHP) of 9 kW output is required to meet the Subway stations heating and domestic hot water demand (DHW).

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Table 3. Thermal needs of St. Georges Cross Subway station. Transmission heat load St. George’s Cross room name

W

W

Higher temperature factor f p.u.

Ticket-Office Hallway (Ground) Hallway (Upper) Canteen Female Toilet Male Toilet Store Total

845.62 448.60 337.90 987.77 276.31 276.31 377.76 3550.28

215.37 74.72 36.62 232.25 78.83 78.83 31.36 747.98

1 1 1 1 1.6 1.6 1 –

T ,i

Ventilation heat load V ,i

Figure 11. St. Georges Cross station drawing.

This case study will feed four new low temperature fan coil radiators which will be sufficient to heating the station replacing the existing four electric radiators (2 kW each) (Figure 11). This system is expected also to provide cooling as a by-product during summer months.

4

DISCUSSION & CONCLUSIONS

Out of the 21 sumps inside the Glasgow subway system; only in three there is a constant water flux. Because of the position of Glasgow, north of the UK, it is common that heating starts even from September. Currently the Subway stations are heated with electric radiators where the energy cost and the CO2 emissions from the use of electricity are high. A WSHP generally can perform with seasonal performance factor (OFGEM) of 2.80 (Energy Saving Trust). The (Coefficient of Performance CoP) can be up to 4. The higher COP equates to lower operating costs. It is feasible to install a WSHP in four Subway stations to cover its thermal needs. St. Georges Cross Subway station was chosen, and the first WSHP has been installed in the ticket office

Heating-up capacity RH ,i

Total design heatload HL,i

W

W

239.20 82.81 40.56 257.40 58.24 58.24 80.21 816.66

1300.19 606.13 415.08 1477.43 448.32 448.32 489.33 5185

to accommodate the space heating and the domestic hot water for the station. This was the first installation which is expected to prove the efficiency of the suggested system before scaled up in the other stations in the Subway system. A basic design for this system was undertaken and the installation has been completed in November 2015. A WSHP of 9 kW has replaced the station’s heating system to cover the heating demand and DHW (Domestic Hot Water). The old four electric radiators that were providing only heating for this station have been replaced by four new low temperature fan coil radiators (with a return temperature of 45◦ C). This system is covering the space heating, the DHW and is expected to provide as a by-product cooling during summer months. A COP for a return temperature of 45◦ C and inlet air temperature) of 5◦ C is around 3. This means that for every kW of energy spent through the compressor the heat energy output is 3 kW. It is expected with the same return temperature of 45◦ C and inlet air temperature of 13.5◦ C even during December to have a COP of more than 4, which means that the energy consumption will be reduced approximately 75% compared to the existing system. The CO2 emissions are expected to be reduced more than 60%.

NOMENCLATURE Water Source Heat Pump (WSHP), Domestic Hot Water (DHW), Carbon Dioxide (CO2), Coefficient of Performance (COP). British Standard (BS), European Norm (EN), Kilowatt (kW).

ACKNOWLEDGMENTS This research was funded through a Knowledge transfer Partnership (KTP) scheme operated by Innovate UK. The partnership members are Glasgow Caledonian University (GCU) and Strathclyde Partnership

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for Transport (SPT). The authors would also like to thank the following from the SPT: Mr. Gordon McLennan, Mr. Charles Hoskins and Mr. Stuart McMillan whose belief in the approach described herein made it possible for us to carry out the work. REFERENCES Banks, D. 2009. An introduction to thermogeology ground source heating and cooling, Wiley-Blackwell, Second Edition. 93–99 Coefficient of Performance CoP, http://hyperphysics. phy-astr.gsu.edu/hbase/thermo/heatpump.html

Department of Energy & Climate Change, March 2013, the future of Heating: Meeting the challenge. See https://www.gov.uk/government/uploads/system/uploads/ attachment_data/file/190149/16_04-DECC-The_Future_ of_Heating_Accessible-10.pdf Energy Saving Trust, our calculations, http://www.energy savingtrust.org.uk/content/our-calculations OFGEM, seasonal performance factor, https://www. ofgem.gov.uk/key-term-explained/seasonal-performancefactor-spf Scottish Government 29 March 2012, Scotland beats 2011 green energy target. See http://www.scotland.gov.uk/ News/Releases/2012/03/geenenergytargets29032012.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Potential of nano material (SiC) for improving the thermal properties of sand Z.H. Rizvi, K. Sembdner, A.S. Sattari & F. Wuttke Geomechanics & Geotechnics, CAU Kiel, Germany

ABSTRACT: For the present study, two different SiC particles sizes with average diameter of 63 nm and 125 nm were mixed with medium sand and measurements were performed. Thermal conductivities of mixtures were measured by the transient hot-wire technique. Classical models were used to predict the thermal conductivity of the mixes. Test were performed to observe the improvement in mechanical properties such as shear strength and consolidation. Finally, a numerical model is setup to observe the improvement in heat dissipation with the modified sand SiC mix. The possible mechanism of the thermal conductivity enhancement in nanoparticle sand mixture is discussed.

1

2

INTRODUCTION

Soil thermal properties play an important role in many engineering projects and heat transfer situation in the soil i.e. roads, airfields, pipelines, buildings in cold regions and underground power cables. Thermal conductivity of soil varies predominantly with type of soil, grain size distribution, soil texture, porosity, moisture content and temperature, etc. Porosity and the moisture content are the dominating factors on the thermal conductivity. Some studies [Ochsner & Horton 2011, Usowicz 1995] suggest that the thermal conductivity is more closely correlated with air-filled porosity than with volume fraction of water. In fine grain soils aggregate structure that forms pore network with relatively large continuous and interconnected inter-aggregate pore spaces (10−3 to 10−6 m) and very small intra-aggregate pore spaces between the textural grains (10−9 to 10−6 m) highly influence the thermal conductivity. These inter and intra-aggregate pores store air or water in dry and saturated conditions respectively [Carminati et al. 2008, Horn et al 2005, McGarry et al. 2000]. To improve the thermal conductivity, Nano material is suitable due to its size, large surface to volume ratio and high thermal conductivity to fill these inter and intra aggregate pores. To our knowledge no comprehensive studies have been performed to improve soil thermal conductivity using Nano material (SiC 125 63). Therefore, the aim of the work was to observe the enhancement in the thermal conductivity of dry sand, which acts as a bottle neck in many engineering applications.

EXPERIMENTAL

2.1 Thermal conductivity measurements Different measurement techniques of the soil thermal conductivity have been presented in detail[Mitchell & Kao 1978]. These methods are broadly classified as: steady heat flow method and transient heat flow method. The steady heat flow method requires a long testing time to setup the thermal equilibrium. Therefore, based on the transient theory, KD2 pro thermal property analyzer is used for measurements (Decagon Devices, Inc. USA). The sensor needle can be used for measuring thermal conductivity of soil in the range of 0.02–5 W/m-K with an accuracy of ±2%. Each measurement cycle consists of 900 s. During the first 60 s, the instrument will equilibrate; heating and cooling of sensor needle for 420 s each then follow. At the end of the reading, the controller computes the thermal conductivity using the change in temperature
θ–time data from

This instrument follows the ASTM D5334 and IEEE 442-1981 standards. For calibration of the probe thermal conductivity of distilled water, glycerin and ethylene glycol were measured. The measured values for distilled water, glycerin and ethylene glycol were 0.614, 0.289 and 0.257 W/m-K, respectively, which are in agreement with the literature values of 0.613, 0.285 and 0.252 W/m-K, respectively, within ±2% accuracy.

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Figure 1. Grain size distribution of Duofill sand.

At each point at least three measurements were performed. The uncertainty of the calculated (measured) thermal conductivity was calculated from the uncertainty value of experimental data and was estimated to be lower than 5%. The thermal conductivity calculated from experimental data was based on several assumption such as the long heat source treated as an infinitely long heat source and the medium is homogeneous, isotropic, and at uniform initial temperature. SiC/Sand mixture up to 5% weight percentage were used for thermal conductivity measurements for two different types of SiC Nano particles (63 nm and 125 nm). The investigated sand, called Duofill sand, has a Quartz content of more than 98.7% and an air-dried moisture content of lower than 0.1%. Particle-size distribution was determined by sieving for sand (Figure 1) [ASTM D422]. SiC/Sand mixture with two different particle sizes were prepared. The particle size between 125 micron to 63 micron is termed as 125 while size below 63 micron is tagged as 63. 2.1.1 Theoretical models At present, there is no theory to predict the thermal conductivity of the sand nano-material mix. From the experimental results of many researchers, it is known that the thermal conductivity of nanomaterial depends on the surface area, shape of the nanomaterial & the temperature [Murshed et al. 2008, Choi et al. 2001]. It is also established that the thermal conductivity of soils depend upon various factor i.e. type of soil, particle size distribution soil structure, porosity, saturation degree and temperature [Johansen 1975, Donazzi 2001]. Many equations have been proposed for the thermal conductivity of the thermal conductivity of a multiphase soil mixtures [Gemant 1950, Russell 1935, Eucken 1932]. However, validity and application of these equations are limited to specific system. Maxwell’s [Maxwell 1881] equation of randomly distributed solid sphere (kSiC ) in a continuous soil media (Ksand ) is applied

This equation is strictly applicable only when weight percentage is small, since it was derived on the assumption that the solid spheres are far enough apart that they don’t mutually interact. The Hamilton and Crosser [Hamilton & Crosser 1962] equation for computing the thermal conductivity of solid mixture for non-spherical particles was applied. This model considers the effect of the shape as well as that of the fraction percentage of the dispersed particle. This complicated model can predict the thermal conductivity of solid suspensions containing micrometer or millimeter-size particles. Therefore, it is used to predict the behavior in dry case. It is assumed that the sand is a continuous media and Nano particles are evenly disperse. Homogeneity of the mixture is achieved by thorough mixing and the then validated with density tests. 10 samples were collected and measured from a mix type. If the results don’t match within 2% of error range it is again homogenized till it achieves the homogeneity criteria. The equation is expressed as

where φ is the volume fraction of the particle and n is the shape factor. It can be calculated empirically by

where k is the sphericity, which is defined by the ratio of the surface area of a particle to that of a sphere with the same volume as the particle. The sphericity of a spherical particle is 1, while that of a cylindrical particle is 0.5. So the smaller the sphericity of the particle, the larger the shape factor will be. Sphericities of 1 and 0.5 were used for SiC 63 and 125, respectively, in the Hamilton and Crosser equation to calculate the effective thermal conductivities.

3

RESULT & DISCUSSIONS

Figure 2 shows some of the thermal conductivity data obtained for the Duofill sand with SiC 63 and SiC 125 varying percentages. It is apparent that the thermal conductivity of Sand-SiC nanomix increases nonlinearly with increase in percentage of SiC content in the mix. Significant improvement is observed in case of SiC 63 with 5% weight content. SiC 63 increases the thermal conductivity more than SiC 125 due to larger surface to volume ratio of the Nanoparticles. Also, the smaller size allows to achieve a higher density by filling the inter and intra granular pores. Although, there is no theoretical model for the sand/SiC mix, Hamilton and crosser model acts as lower and upper bound for the prediction of thermal conductivity. For SiC 63 in Duofill sand mix, a thermal conductivity increase of 24.4% at a weight percentage of 5% is observed. Figure 2 provides an increase in thermal conductivity for both sand mixtures with SiC 63 and SiC 125.

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more heat to transfer, with higher grain to grain contact. Sand/SiC 63 shows more improvement as finer SiC particles are filling the intra granular voids and improving the quality of contact among the grains.

4

Figure 2. Percentage enhancement of thermal conductivity of Duofill sand (DS) with weight percentage of SiC nano particles (SiC-63 and SiC-125).

Figure 3. SEM image of showing two kinds of SiC (a) SiC 63 and (b) SiC 125.

CONCLUSION

To investigate the thermal properties of SiC/Sand mixture, sand mixtures with two different SiC (63 and 125 nm) were prepared and the thermal conductivity was measured. The thermal conductivity measurements suggest that the small amount of SiC particles improve the thermal property of the sand. At low weight fraction range, the thermal conductivity enhancing ratios increase linearly with weight fraction of solid particles. SiC with 63 micron particles size have a large surface area per volume, therefore, an improvement in the effective thermal conductivities of the mixtures is expected with decreasing particle size. The thermal measurement results have been compared with the Hamilton & Crosser model. The model behaves as a low and upper bound for most of the measurements. A further investigation is required to develop a model for Sand/SiC mixture.

ACKNOWLEDGEMENT This research project is financially supported by the research grant DuoFill provided by the Federal Ministry for Economic Affairs and Energy, Germany & ZIM by grant number KF3067303KI3. Figure 4. SEM image of (a) Sand-SiC 63 and (b) Sand-SiC 125 showing thermal bridge formation in both mixes.

REFERENCES

In the calculation of Hamilton and Crosser model, the thermal conductivities of sand was obtained from experimental results as 0.34 W/m.K Duofill sand. The effect of boundary scattering of phonons and/or electron in micro and nano scale regime is well known. We assumed the thermal conductivity of SiC particles as 490 W/m.K based on reported value in literature. As the heat transfer in dry soil is dominated by conduction through grain to grain contact mechanism, it was expected that the heat transfer will be more with the filling of the void with high conductive material. The advantage of nano particles is that it cannot only fill inter granular pores but also the intra granular pores thus increasing the thermal conductivity. Scanning Electron Microscopy (SEM) images show that with addition of SiC 63/125 a thermal bridge is between the sand grains is formed. Thus allowing

T.E. Ochsner, R. Horton, T. Ren, A new perspective on soil thermal properties, Soil Sci. Soc. Am. J. 65 (2001) 1641– 1647. B. Usowicz, Evaluation of methods for soil thermal conductivity calculations, Int. Agrophys. 9 (2) (1995) 109–113. A. Carminati, A. Kaestner, P. Lehman, H. Flühler, Unsaturated water flow across soil aggregate contacts, Adv. Water Res. 31 (2008) 1221–1232. R. Horn, A. Smucker, Structure formation and its consequences for gas and water transport in unsaturated arable and forest soils, Soil Till. Res. 82 (2005) 5–14. D. McGarry, B.J. Bridge, B.J. Radford, Contrasting soil physical properties after zero and traditional tillage of an alluvial soil in semi-arid subtropics, Soil Till. Res. 53 (2000) 105–115. Mitchell J.K., Kao TC (1978) Measurement of soil thermal resistivity. J Geotech Eng ASCE 101(GT10):1307–1320. ASTM D 5334-00. Standard Test Methods for Determination of Thermal Conductivity of Soil and Soft Rock by Thermal Needle Probe Procedure. vol. (04)08. ASTM, 100 Barr-Harbor Dr., West Conshocken, PA 194282059, 2000.

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IEEE STD 442-1981. IEEE Guide for Thermal Resistivity Measurements, The Institute of Electrical and Electronics Engineers, Inc., 345 East 47 Street, New York, NY 10017 Standard Test Method for Particle-Size Analysis of Soils, ASTM D422 – 63(2007) S.M.S. Murshed, K.C. Leong, C. Yang Thermophysical and electrokinetic properties of nanofluids – a critical review Appl. Therm. Eng., 28 (2008), pp. 2109–2125 S.U.S. Choi, Z.G. Zhang, W. Yu, F.E. Lockwood, E.A. Grulke Anomalous thermal conductivity enhancement in nanotube suspensions Appl. Phys. Lett., 79 (2001), pp. 2252–2254 O. Johansen Thermal conductivity of soils. PhD. Thesis, University of Trondheim, Trondheim, Norway (1975)

F. Donazzi, Soil thermal and hydrological characteristics in designing underground cables. Proc IEE 123:506–516 A. Gemant, Journal of Applied Physics. 21 750 (1950) H.W. Russell, Journal of American ceramics Society. 18 1 (1935) A. Eucken, Forsch. Gebiete Ingenieurw, B3, VDI-Forschungsheft, 353 (1932) J.C. Maxwell “A Treatise on Electricity and Magnetism” (second ed.) Clarendon Press, Oxford, UK (1881) R. L. Hamilton and O. K. Crosser, “Thermal Conductivity of Heterogeneous Two-Component Systems,” Industrial & Engineering Chemistry Fundamentals,Vol. 1, No. 3, 1962, pp. 187–191

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Bearing capacity and settlement of raft-pile foundations under cyclic loading Ilizar T. Mirsayapov & Marat I. Shakirov Kazan State University of Architecture and Engineering, Kazan, Russia

ABSTRACT: Developed raft-pile foundation settlement calculating method under cyclic loading, considering joint deformation of ground base, piles and raft grillage. Depending from the loading cycle, cyclic loading leads to a redistribution of load between the elements of the raft-pile foundation, ground base at various levels from the grillage raft foundation and ground massive in the space between piles. This calculation method takes into account the specificity of raft-pile foundation elements stress-deformed state and shows good agreement between the calculated and factual researched parameters values.

1

INTRODUCTION

In modern conditions at construction of buildings and structures, trend of increasing loads to the ground base and using as a base weak grounds contributed to the fact, that one of the common ways to increase bearing capacity and reduce settlement, using raft-pile foundations. This foundations and their ground bases together with static, exposed to cyclic loads, which in some cases are the main, determine safety using of buildings and structures. Herewith the question of cyclic loads influence to the plate-pile foundations behavior researched not enough. In this regard were conducted experimental and theoretical researches of raft-pile foundations under cyclic loading.

2

EXPERIMENTAL RESEARCHES

Laboratory studies were carried out in a steel tray with the same length, width and height equal to 1.0 m. As the raft in raft-pile foundation used reinforced concrete plate with dimensions 400 × 400 × 40 mm. Piles modeled by hollow plastic tubes (compressive strength R = 92.0 MPa; deformation modulus E = 700 MPa) with a diameter equal to 7 mm, wall thickness 1 mm and length 400 mm. As the ground base were used sandy loam with a density ρ = 1.4 t/m3 and humidity W = 11%. Were fixed foundation and ground base settlement values at different points from plate, and also deformations in pile models and ground base during cyclic loading. In the system “raft-pile foundation – the ground base” under cyclic loading jointly deform materials with different strength and deformation properties and loading conditions. Herewith

Figure 1. Efforts in piles diagram at different number of cycles, H (Pmax = 1000 kg, ρp = 0.5).

deformation of all system elements takes place in connected conditions. When the load is applied to the plate grillage, at the load initial stages, takes place a ground compaction

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At cyclic loading, bearing capacity reducing of raft-pile foundation model based on the experimental researches results described by the equation of regression:

Figure 2. Ground stress diagrams at different number of cycles, kPa (Pmax = 1000 kg, ρp = 0.5).

throughout the depth of compressible thickness. Further cyclic loading leads to an increasing of plastic deformation zones, which are combined in the area, capturing all the entire upper part of the ground base. At cyclic loading takes place changing efforts in pile models. From piles effort diagram in (Fig. 1) can be seen, that with increasing number of cycles increase efforts on the entire length of the piles. Figure 2 shows the stress diagrams at different zones in the space between piles. With the increasing of the loading cycles number, occurs stress decreases in the ground at different levels from grillage, herewith the greatest stresses are fixing directly under the plate. To the free deformation of plate grillage ground base prevent piles, and the piles free deformation limited by plate grillage ground base. As a result of such joint deformation take place a redistribution of forces between the raft-pile foundation elements during cyclic loading. Measured in the step cyclic loadings base settlements, after different numbers of repeated load, change similar as ground deformation in the space between piles. After various numbers of cycles, ground base settlement changes analyze shows that the main settlement increment occurs by increasing their residual part. The settlement increase compare to the first loading cycle up to 30%. (Mirsayapov I.T. & Shakirov M.I. 2014, Mirsayapov I.T. & Shakirov I.F. 2015)

3

FOUNDATION BASE CALCULATION MODEL

Raft-pile foundation settlement changing patterns under cyclic loading can be expressed in a regression equation received by experimental researches:

where S1 = raft-pile foundation settlement under static load; Pmax = maximum cycle load; N = number of cycles at the limit of bearing capacity.

Pst = bearing capacity of raft-pile foundation model under static loading; N = number of cycles at the limit bearing capacity (Mirsayapov I.T. & Shakirov M.I. 2012). The limit value of the cyclic load, sensing by raft-pile foundation, depends from joint deformation conditions of ground, piles and plate grillage, and their strength and deformation properties. Sress-strain pile base condition of raft-pile foundation is very complicated. In this bases, together deform materials with a different strength and deformation properties. Deformation development of pile base under cyclic loading will take place in the conditions of ground and piles interaction in connected conditions: a) to the free deformation of the ground is constrained by piles; b) to the free deformation of the piles prevents the surrounding ground. As a result of this interaction between the elements in the pile base occurs is an additional stress state and take place a redistribution of efforts between the ground and the piles under cyclic loading. The stress in the piles increases, but stress in the ground reducing between the reinforcing elements compare to the first cycle. Then current stress in pile base are presented as:

max σpmax (N1 ), σgr (N1 ) = maximum stress at the first loading cycle in the piles and ground respectively; max σpmax (N1 ), σgr (N1 ) = additional stresses in the pile base during the process of cyclic stressing in the piles and ground respectively. In the pile base, pile due to its grip along the side surface with surrounding ground becomes an internal communication, preventing to the free ground deformation in the space between piles under cyclic loading. Straitened vibrocreep ground deformations leads to the appearance in the pile base more balanced internal stresses. In the ground occurs tensile stresses, and in the piles – compression stresses. Under the vibrocreep deformation difference influence between the free ground and piles, straitened vibrocreep ground deformation in the space between piles represented as

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εpl (N ) = additional (residual) vibrocreep pile base gr deformations; εpl (N ) = free ground vibrocreep deforp mation; εpl (N ) = free pile material vibrocreep deformation. Then averaged additional tensile stresses in the ground accepted:

Eo′ (N ) = ground deformation modulus under cyclic loading; For piles εpl (N ) elastic deformation, and therefore there are compressive stresses:

Ep (N ) = the pile material elastic modulus. Efforts equilibrium equations from the additional stress state symmetrical pile base has the form:

Figure 3. Interaction design scheme of raft-pile foundation with the ground massive.

where Ap = the total piles cross-sectional area in the limit field of the foundation pile base; Agr = foundation ground base area. From (8) after a number of simplifications, obtained analytical expressions for determining the additional (residual) stresses: – in the ground between the pile space

– in piles

Figure 4. Interaction design scheme of single pile with a homogeneous ground massive with the sizes 2A × 2B. gr

εpl = ground vibrocreep deformation; Ap1 = one pile cross-sectional area; h = the total number of piles in the calculated base area. 4

EQUILIBRIUM AND MECHANICAL STATE EQUATIONS

For an analytical description non-free deformation of the system elements, adopted calculation schemes (Figs. 3, 4) and developed ground and pile-ground system mechanical state equations, as well as the efforts equilibrium equations. The joint solution of these equations allows to obtain the required settlement and the bearing capacity values of raft-pile foundation under cyclic loading.

To simplify the calculation, accepted design scheme which consists from the pile, surrounding it ground and the part plate grillage, attributable to one pile. The main stress-strain state components behavior of such a cell will match to behavior of the pile as part of raft-pile foundation (Figs. 3, 4). The cell dimensions = 2A × 2B × L, pile dimensions = 2a × 2b × l. On the borders of a cell taken free vertical movement conditions.At the bottom of the cell accepted complete lack of movement. To solve the task it is necessary to find the four unknown – p1 , p2 , p3 , and τ0 (Figs. 3, 4). Using the forces equilibrium equations on the pile and the whole

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diagrams (Fig. 5) at intersection point, which can be calculated by the formula:

where c(N ) = ground cohesion under cyclic loading, takes in accordance with [19]: Figure 5. Mobilized shear stress and limit shear stress diagrams.

cell, equality movements of ground and at the heel and top piles level, obtain a system of equations:

Depending from the pile length, to heel level may account different share of the load, since in the case of increasing the length of the pile, increasing the lateral surface area. Stress occurring in the soil under the raft can be found by the formula:

Stress level appearing at the top of the pile can be expressed as follows:

Here:

E – soil shear modulus; 2 · (l + v) where k(l) = dimensionless coefficient taking into account the effect of the depth of a rigid stamp application on its length; ω = coefficient taking into account the shape of the die; v = Poisson’s ratio; α = 5/l, l = pile length. Stress under the heel of the pile can be calculated using the formula: G=

The solution of the system allows to find the settlement value, as well as the stresses arising in the pile trunk, in the ground under the grillage and in end of the piles under cyclic loading. Limit equilibrium zones, taking into account the rigidity of the pile material, determined by the mobilized shear stress (τ(N )) and the shear stress limit

Shear stress τ0 (N ) can be expressed as follows:

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Calculation results comparisons with the experimental values are shown in figures 1, 2, 5, 6. As can be seen from the figures, there is good agreement between the calculated and experimental stress and settlement values (deviation of no more than 15%). REFERENCES

Figure 6. Compare of experimental and calculated raft-pile model settlement values under cyclic loading (Pmax = 1000 kg, ρp = 0.5).

Raft-pile foundation settlement can be calculated by the formula:

Ground base bearing capacity in depending from the ratio τ(N ) ≤ τ ∗ (N ) is estimated by conditions

Function σ1u (N ) accepted

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Mirsayapov I.T., Koroleva I.V. (2010). Features of the deformation of clayey soils under cyclic triaxial compression. International journal of Geotechnics, No. 6. 64–67. Mirsayapov I.T., Shakirov M.I. (2012) Bearing capacity and settlement patterns raft-pile foundations under cyclic loading. Integration, partnership and innovation in building science and education: the International Collection of papaers. Scien. Conf. 2 t. Vol. 2, 528–531. Mirsayapov I.T., Shakirov M.I. Plate-pile foundations under cyclic loading // Geotechnics Belarus: Science and Practice. 2013. P. 314–320. Mirsayapov I.T., Shakirov M.I. (2014) Experimental study of bearing capacity and the settlement of bases raft-pile foundations under cyclic loading. Perspective directions of development of the theory and practice of rheology and soil mechanics. Proceedings of the XIV International rheology Symposium, 68–74. Mirsayapov I.T., Shakirov M.I. (2014) Research of the cyclic loading effect on model combined raft-pile foundation construction. Forming environment of life: the International Collection of papaers. Scien. Conf., 423–429. Mirsayapov I.T., Shakirov I.F. (2015) Selecting the type of foundations and basements of multifunctional complex “Fatikh, Amir and Khan” in the Fatikh Amirhan street in Kazan. Journal News of the KSUAE, 86–92. Mirsayapov I.T., Koroleva I.V. (2016) The strength and deformability of clay soils under the regime spatial stress state in view of cracking. Grounds, foundations and soil mechanics, No. 1. 16–23. Voznesensky E.A. (1997) The behavior of ground under dynamic loads. MGU, 286. Zaretsky Yu.K. (1989) Lectures on modern soil mechanics. Rostov-na-Donu: University Press, 607.

CONCLUSIONS

Represented calculation method takes into account the specificity of raft-pile foundation elements stressdeformed state under the action of cyclic loading.

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Calculation model of foundation base settlement at the static and cyclic regime loading Ilizar T. Mirsayapov, Irina V. Koroleva & Danil D. Sabirzyanov Kazan State University of Architecture and Engineering, Kazan, Russia

ABSTRACT: The article presents results of experimental and theoretical researches of the clay ground bases soils under triaxial long-static, cyclic and regime static-cyclic loading. Described the source and transformed the clay ground deformation diagrams for long-static, cyclic-static and modal prolonged cyclic loading. Test results are presented and processed in the form of graphs and used for comparison with theoretical studies. Based on the analysis of the transformed strain diagrams developed engineering method for calculating ground settlement, based on the method of layering summation taking into account spatial changes of stress – strain state of the ground in the process of regime static and cyclic loading. At the end of the article compares the results of triaxial with a trough tests at long-static, cyclic and static and modal prolonged cyclic defor-mation of the clay base raft foundation.

1

INTRODUCTION

In real conditions, the construction and operation of the load on the foundation soil is applied in stages as the construction of buildings and structures. At this stage of the active loading during the construction stage transformed into stages sequential alternation of long static and cyclic loading, if the building or construction equipment is installed, which create a dynamic impact on the ground base. The maximum and minimum values of cyclic loading and prolonged static load depends on the technology and mode of equipment operation. However, existing methods of calculation can not to take into account the particular strain of foundations under such loadings. Based on that, there is a need to develop a method for calculating bases at regime-static cyclic loading. This is particularly relevant for the grounds composed of clay grounds, as in this case, the stress – strain state varies with time and depends on the previous history of the loading. Scheme strained substrate conditions and calculation mode shown (Mirsayapov & Koroleva 2011).

2

EXPERIMENTAL RESEARCHES

In connection with the foregoing at the Department “Bases and foundations, dynamics of structure and engineering geology” in KSUAE were carried out experimental studies of the clay ground under triaxial static, cyclic and regime loading. Were tested clay ground samples with the following characteristics: W = 23%; Wp = 22.8%; WL = 40.1%;

Figure 1. Dependence of vertical stress from vertical deformation under triaxial short-term cyclic loading.

ρ = 1.94 g/cm3 ; Ip = 17.3%; IL = 33%. Samples twins were prepared in accordance with GOST 30416-96. According to the results of experimental studies obtained graphic dependences between the intensity of tangential stresses τi and the intensity of shear strain γi , between the axial stress σz and axial strain εz , between the bulk stresses σm and volume deformations εv ; changes of linear module E0Z , bulk modulus Kv and the shear modulus G with time (Mirsayapov & Koroleva 2009, Mirsayapov & Koroleva 2010, Mirsayapov, Koroleva & Sabizyanov 2013, Mirsayapov, Koroleva & Sabizyanov 2014). Figure 7 shows the change in strength at various lateral pressures of 0.08 MPa and 0.16 MPa. Graphs show changes in the short-term strength of triaxial static, long static, short-term cyclic loading points and showed the values strength at the regime long triaxial static and cyclic loadings. The graphs show that the strength of the clay samples at regime-static cyclic

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Figure 5. Loading mode under triaxial regime prolonged static and cyclic loadings. Figure 2. Dependence of vertical deformation from number of cycles under triaxial cyclic loading.

Figure 6. Dependence of vertical deformation under triaxial prolonged static loading. Figure 3. Dependence of vertical stress from triaxial prolonged static loading.

Figure 4. Dependence of vertical stress from time under triaxial prolonged static loading.

loading is significantly different from the strength of the long-term static and cyclic loading. As can be seen from the graphs at viewed regimes take place changing of all bases parameters, characterizing the stress and strain state of the ground in time, which allows to conclude about necessity to develop a new parameter characterizing the mechanical condition and about necessity to create calculation models. As this parameter is accepted analytical diagram of ground deformation in the coordinates ≪σ1 − ε1 ≫ for triaxial (where σ1 , ε1 vertical stress (deviator) and linear deformation under triaxial compression).

Figure 7. Change the regime of loading strength: a) for the lateral pressure of 0.08 MPa; b) for the lateral pressure of 0.16 MPa.

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Figure 8. Initial ground deformation diagram with short-term static triaxial loading. Figure 9. Original and transformed ground deformation diagram long triaxial static loading.

3 ANALYTICAL DIAGRAM OF GROUND DEFORMATION UNDER TRIAXIAL COMPRESSION

Ground creep deformation at given moment of time at long static loading are determined by the formula:

Based on the graphs (Figs. 1–7) were built initial diagrams (phase diagram) of ground deformation at short triaxial static loading. As a limit point to the coordinates (σ) takes the value of ground tensile strength σ1 = Rgr,u (deviator) under triaxial short-term static compression. Limit point on the y-axis (ε) takes the value of linear deformation εu1 = 0.0869. View of diagram shown in figure 8. At clay ground state diagrams under triaxial long static loading as initial used stress-strain diagram ≪σ1 − ε1 ≫ for the case of short-term triaxial static loading. Transforming the initial phase diagram under triaxial short-term static loading, obtain analytical dependences for the description diagrams of the clay ground deformation under triaxial prolonged static loading. By the form of transformed diagram taken similar initial phase diagram based on the following provisions (Fig. 9): – Limit point of the vertical pressure at the top of diagram accept stress in the ground, which is equal to the limit prolonged resistance under triaxial load action Rgr,long − (t, τ) and deformation, answer to deformations at the top of the state diagram under triaxial short-term static loading εgru,red = εgru ; – To limit point, define the limits of state diagrams on the y-axis, deformations equal to limit deformations under triaxial short-term static loading εgr,red = εgr,R , and on major dependencies calculate by (1) stresses in the ground; – The origins of diagrams taken offset to value, equal to the creep deformation at the viewing moment of time: εpl (t) – at long static loading; – Obtained tilt angles deformation diagrams taken in view of the changes of the clay ground module deformation under triaxial long static loading. The dependence of vertical pressure (deviator) limiting point at the top of diagram and the loading time under triaxial long static loading takes the form:

f (t1 t0 ) = 1 − e−γ(t − t0 ) = growth creep deformation function; γ = ground creep parameter.

c∞ (t1 τ) = ground creep limit measure at time t. At viewing the clay ground state diagrams under triaxial cyclic loading as initial were used stress-strain diagram ≪σ1 − ε1 ≫ for the case of short-term triaxial static loading. By transforming the initial state diagram under triaxial short-term static loading, obtain analytical dependences for the description of clay ground deformation diagrams under triaxial shortterm cyclic loading. Transformed diagram form taken similar to initial state diagram based on the following provisions (Fig. 10): – Vertical pressure limit point takes from the top of ground stress diagram, which is equal to the limit of endurance under triaxial cyclic loading Rgr,long (t, τ) and deformation answering to deformation at the top of state diagram under triaxial cyclic loading εgru,red = εgru ; – For limit point, which define the state diagram limits at the Y-axis, deformation equal to limit deformation under short-term triaxial cyclic loading εgr,red = εgr,R , and stress in the ground calculate by the major dependencies (4); – Diagram start coordinates taken offset to value, which equal to vibrocreep deformations at viewing loading cycle: εpl (N ) – at short-term cyclic loading; – Obtained deformation diagram tilt angles, which taken with changes of the clay ground deformation module under triaxial short-term cyclic loading. The dependence between the limiting point of the vertical pressure at the top of the state diagram and the loading cycles number under cyclic loading takes the form:

α = values obtained by experiments.

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Figure 10. Initial and transformed ground deformation diagram under triaxial cyclic loading.

β = values obtained by experiment; N = number of cyclic loadings. Ground creep deformation in viewing cycle at short cyclic loading determine by the formula:

f (N ) = 1 − e−γ(N − N0 ) = growth creep function; γ = ground creep parameter under cyclic loading;

c∞ (t1 τ) = limit ground creep measure. Analytical dependences for describing ground deformation diagrams at regime triaxial loading are obtained by transforming dependencies (1–6) for triaxial long static and cyclic loading (Fig. 11). In the ground deformation regime description under triaxial loading is necessary to consider the influence from vertical pressure (σ1 ) of the previous block for strength, modulus and relative deformation at the top of the diagram in the subsequent loading after the regime change. Within each block, in which develops regime loading, changing deformation diagrams described by the same formulas as for cycling or long – static loading, but appropriate for each block σi , Ni or Ti and taking into account the change in the strength and deformability of the previous blocks. It is necessary to take into account two specific case when: – at first acting the long – static loading σ1 (t), and then cyclic loading; – at first acting cyclic loading σ1 (N ), and then prolonged static loading. In the first case, the overall durability increases as compared with that, when cyclic loading is being with the stress value σ1 (N ). This is due to with increasing the effective destruction of the ground surface energy on the first stage load due to recovery and the increasing of coagulation bonds (Mirsayapov & Koroleva 2016). In the second case, strength reduction at the transition to the block with prolonged static load will be extremely slow. This is explained by “delay effect” of

Figure 11. Initial and transformed ground deformation diagrams at regime alternating static and cyclic loading.

fatigue cracks in the equilibrium limit planes in the calculated ground volume (Mirsayapov & Koroleva 2016). Thus, at transforming the initial diagram for the case of regime loading must be taken into account the influence of alternation long-term static and cyclic loads. In the limits of starting block, independently from sequence from loading block, transformed diagrams obtain similarly to not regime long-static and cyclic loading. In each subsequent block take place further deformation diagram transforming, but the initial diagram for each of them is an transformed diagram at the end of the previous block. Top coordinates of transformed diagrams at the beginning of each subsequent block depends from the level of stress in the preceding block and the sequence alternation of blocks with different types of loading.

4

CALCULATION MODEL OF FOUNDATION BASE SETTLEMENT

Based on the analysis of the transformed strain diagrams developed the engineering method for calculating ground base settlement, which based on the method of layering summation with taking into account changes in the spatial stress – strain state of ground in the process of triaxial long-static, cyclic and regime static – cyclic loading. Accepted volumetric stress state of foundation base ground presented in figure 12. Breaking base compressible thickness to the layers, for each layer based on (Fig. 12) for the stress deviator (σ1 ) determine the

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Figure 12. Stress state scheme of the foundation base during the regime loading.

Figure 14. Raft foundation comparing settlements graphs: a) at long static loading; b) under cyclic loading; c) at the regime-static-cyclic loading.

layer; εz,i (t, τ) = axial strain increment of i-th layer under the static load action; t = time appropriate to the moment of observation; t0 = application time of the load. – at triaxial cyclic loading:

Figure 13. Calculation scheme for determining ground base settlement during the regime loading.

εz,i (N ) = axial strain increment of i-th layer under cyclic loading action; – under triaxial regime prolonged static and cyclic loading:

deformation εz,i appropriate to value of vertical pressure, and then the deformation values at the limits of the compressible thickness summed up. Thus, the base settlement calculate according to the formulas:

m = the number of cyclic loading blocks; k = the number of long-term static loading blocks.

– with triaxial prolonged static loading:

n = the number of layers in which divide compressible base thickness; hi = the thickness of the i-th

Comparing theoretical and experimental researches results graph of raft foundation model settlement (with dimensions of 0.4 × 0.4 m) on clay ground base in a laboratory tray (tray with the size of 1 × 1 × 1 m) the ground characteristics that defined above, for the triaxial loading conditions are shown in figure 14.

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5

CONCLUSIONS

Based on the analysis of the transformed strain diagrams developed the engineering method for calculating ground base settlement, which based on the method of layering summation with taking into account changes in the spatial stress – strain state of ground in the process of triaxial long-static, cyclic and regime static-cyclic loading. As seen from figure 14, comparing the results of triaxial with a trough tests at long-static, cyclic and static and modal prolonged cyclic deformation of the clay base raft foundation shows a good agreement between the calculated and experimental settlement data.

REFERENCES Mirsayapov I.T., Koroleva I.V. (2011). Bearing capacity of foundations and rainfall with prolonged loading. Integration, partnership and innovation in building science and education: the International Collection of papers. Scien. Conf. 2 t. Vol. 2, 342–347.

Mirsayapov I.T., Koroleva I.V. (2009). Research strength and deformability of clay soils with prolonged triaxial compression. Proceedings of the Kazan State Architectural University. No. 2 (12), 167–172. Mirsayapov I.T., Koroleva I.V. (2010). Features deformation of clayey soils under cyclic triaxial compression. International Journal of Geotechnical. No. 6, 64–67. Mirsayapov I.T., Koroleva I.V., Sabizyanov D.D. (2013). Strength and deformation of clayey soils under triaxial modal alternating static and cyclic loading. Geotechnics Belarus: Science and Practice, 297–304. Mirsayapov I.T., Koroleva I.V., Sabizyanov D.D. (2014). Warp clay soils combined with the regime and the longterm cyclic loading. Perspective directions of development of the theory and practice of rheology and soil mechanics. Proceedings of the XIV International Symposium on rheology, 130–135. Mirsayapov I.T., Koroleva I.V. (2016). The strength and deformability of clay soils under the regime spatial stress state in view of cracking. Grounds, foundations and soil mechanics, No. 1, 16–23 Voznesensky E. A. (1997). The behavior of soils under dynamic loads. MGU, 286. Zaretsky Yu.K. (1989). Lectures on modern soil mechanics. Rostov-na-Donu: Pabl growth. University Press, 607.

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The role of high-pressure flow-through experiments for evaluating the mechanical behaviour of gas hydrate-bearing soils C. Deusner, E. Kossel, N. Bigalke & M. Haeckel GEOMAR Helmholtz Centre for Ocean Research Kiel, Kiel, Germany

S. Gupta Technical University Munich, Garching bei München, Germany

M. Freise, H. Anbergen & T. Wille APS GmbH Wille Geotechnik, Rosdorf, Germany

ABSTRACT: Results from two recent field trials, onshore in the Alaska permafrost and in the Nankai Trough offshore Japan, suggest that natural gas could be produced from marine gas hydrate reservoirs at compatible yields and rates. However, both field trials were accompanied by different technical issues, the most striking problems resulting from un-predicted geomechanical behaviour, sediment destabilization and catastrophic sand production. So far, there is a lack of experimental data which could help to understand relevant mechanisms and triggers for potential soil failure in gas hydrate production, to guide model development for simulation of soil behaviour in large-scale production, and to identify processes which drive or, further, mitigate sand production. We use high-pressure flow-through systems in combination with different online and in situ monitoring tools (e.g. Raman microscopy, MRI) to simulate relevant gas hydrate production scenarios. Key components for soil mechanical studies are triaxial systems with ERT (Electric resistivity tomography) and high-resolution localstrain analysis. Sand production control and management is studied in a novel hollow-cylinder-type triaxial setup with a miniaturized borehole which allows fluid and particle transport at different fluid injection and flow conditions. We further apply a novel large-scale high-pressure flow-through triaxial test system equipped with µ-CT to evaluate soil failure modes and triggers relevant to gas hydrate production and slope stability. The presentation will emphasize an in-depth evaluation of our experimental approach, and it is our concern to discuss important issues of translating laboratory results to gas hydrate reservoirs in nature. We will present results from high-pressure flow-through experiments which are designed to systematically compare soil mechanical behaviour of gas hydrate-bearing sediments in relevant production scenarios focusing on depressurization and CO2 injection. Experimental data sets are analyzed based on numerical models which are able to simulate coupled process dynamics during gas hydrate formation and gas production.

1

INTRODUCTION

In marine sediments and permafrost soils gas hydrates can be present in large amounts and at high relative saturations. Gas hydrate formation can occur whenever pressure-temperature (p-/T-) conditions are inside the gas hydrate stability region, and gas hydrate forming components such as CH4 or CO2 are available in sufficient amounts. Dependent on gas hydrate saturation and gas hydrate-sediment particle fabrics, the presence of gas hydrates contributes to marine sediment stiffness and strength, and it is important to understand and quantify this contribution for reliably predicting sediment mechanical behavior and assessing risks of ground subsidence or slope failure. The lack of knowledge and simulation tools to predict dynamic mechanical behavior of gas hydratebearing sediments became apparent in recent gas hydrate production field trials, onshore in the Alaska

permafrost (Schoderbek et al., 2013) and in the Nankai Trough offshore Japan (Yamamoto, 2013). Both tests were accompanied by substantial sediment yielding and sand production events, which were, however, following different patterns. In the onshore field test, natural gas production was initiated after N2 :CO2 mixed gas injection and gas-hydrate exchange, and further enhanced through stepwise depressurization. In this field test, sand production was initially very high. Substantial technical problems occurred, including failure of technical components and extended production shutdown intervals. However, sand production rates decreased with ongoing gas production. In the first offshore field test in the Nankai Trough, gas production was achieved through depressurization only. In contrast to the results from the onshore permafrost test, sand production was low during early production and could be managed with applied standard technical means. However, after a few days,

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sudden and catastrophic sand production occurred, and the production test had to be canceled pre-maturely. The reasons for this distinct test specific behavior are currently unknown and might be related to numerous factors, such as site and reservoir characteristics, geological heterogeneities, gas hydrate alteration and dissociation dynamics, technical issues, or dynamic thermo-hydro-chemo-mechanical process coupling. Gas hydrates contribute to sediment or soil mechanical behavior in various ways, and effects might be defined as primary and secondary, respectively. Primary effects result from direct and quasi-static interaction of gas hydrates and soil particles, and define sediment behavior in terms of soil stiffness and strength. The understanding of geotechnical behavior of gas hydrate-bearing sediments in this sense has improved tremendously in recent years, and with our current understanding, gas hydrates contribute to sediment strength by changing friction and dilatancy, Soil critical state models were successfully applied to simulate soil plastic yielding (Klar et al. 2013). Today, the availability of experimental tools and methods to analyze and visualize micro-structuring of gas hydrate-bearing sediments helps to develop physical understanding and improve constitutive models of bulk sediment behavior. For example, recent experimental studies on microscale gas hydrate-sediment structures have demonstrated the presence of a water layer between gas hydrates and quartz sand particles independent of gas hydrate formation methods (Chaouachi et al. 2015), which has implications for understanding strength of gas hydrate-bearing soil in terms of assumed cohesion and cementation. In contrast to primary effects, secondary, non-direct mechanical effects result from strong and dynamic thermo-hydrochemo-mechanical process coupling. This definition emphasizes that under relevant non-equilibrium conditions with dynamic gas hydrate formation, alteration or dissociation, sediment mechanical stability becomes eventually dominated by multiphysics parameters such as hydraulic properties (e.g. absolute and relative permeability changes) or flow dynamics (e.g. multiphase fluid flow, gas migration or holdup). Quantitative effects emerging from multiphysics coupling are extremely complicated to predict, and coupled secondary effects could easily overprint simplified sediment stability and failure predictions based on quasi-static primary effects. It is an important task to reveal and disentangle multiphysics effects, understand process coupling and resolve mechanistic details, and this importance is increasingly recognized. For example, large-strain deformation under deviatoric loading, and dynamic stress-strain behavior during depressurization or thermal stimulation was studied in triaxial experiments (Hyodo et al. 2013, 2014, Song 2014, Ghiassian and Grozic 2013). In the very recent past there have also been the first attempts to carry out studies on undisturbed pressure cores, which will clearly advance the field towards a much better understanding of the mechanics of the gas hydrate-bearing soils (Inada

and Yamamoto 2015, Santamarina 2015, Yoneda et al. 2015). Numerical gas hydrate reservoir simulators have been used to study coupled processes during and after gas production from gas hydrates, and there is strong effort to build-in soil mechanical constitutive models and improve model couplings. Recently, a gas hydrate reservoir simulation algorithm was developed and applied for modelling particle mobilization and sand production as observed in the field trial offshore Japan (Uchida et al. 2015). A novel hydrogeo-mechanical gas hydrate simulator was developed recently at TU Munich (Gupta et al. 2015). It was calibrated and tested by matching experimental data from high-pressure flow-through triaxial experiments simulating gas hydrate formation and dissociation under isotropic compression at variable total and effective stresses and with dynamically changing gas hydrate saturations. Using high-pressure flow-through triaxial experiments in combination with numerical simulation is the most direct and promising approach to understand multiphysics coupling and to improve physical process knowledge. High-pressure flow-through experimental systems, and different online and in situ monitoring tools have been successfully applied for testing various strategies for gas production from gas hydrate-bearing sediments (essentially depressurization, thermal stimulation and gas hydrate exchange after injection of CO2 or CO2 -rich mixed gases). We used our NESSI system (N atural Environment Simulator for Subseafloor I nteractions) to study different CO2 injection schemes and to improve gas hydrate exchange and natural gas production from gas hydrate-bearing soils (Deusner et al. 2012). The NESSI system is used in combination with Raman spectroscopy and IR-based gas analysis. These tools allow time-resolved monitoring of multiphase fluid flow (e.g. water, gas, liquid CO2 ) as well as phase compositions (e.g. pure or dissolved compounds, mutual solubilities). Tomography techniques have been applied for disturbance-free and high-resolution analysis of process dynamics and influence of heterogeneities in gas-hydrate bearing soils. Magnetic resonance imaging (MRI) was applied to study phase distributions and permeability changes during gas hydrate formation (Kossel et al. 2014) and gas hydrate exchange after injection of CO2 . Electrical resistivity tomography (ERT) was applied to map fluid and solid phase distributions (Priegnitz et al. 2013). Further, X-ray CT was applied to visualize gas hydrate sediment structures and analyze permeabilities (Kneafsey et al. 2014, Kneafsey et al. 2011). To better understand dynamic and coupled thermohydro-chemo-mechanical processes relevant to gas hydrate-bearing soils, we have developed novel highpressure flow-through triaxial systems for large samples. The novel systems are used in combination with µCT or ERT, respectively, high-resolution local-strain measurement and continuous fluid composition monitoring with flow-through sensors, as described above. One system is equipped with a miniaturized perforated

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borehole, which allows passage and sampling of both fluids and solids. Major research objectives are to experimentally simulate coupled processes relevant to gas-charged or gas hydrate-bearing sediments in the context of slope stability and natural gas production. The experimental systems allow inducing and monitoring large-strain visco-elasto-plastic deformation, particle fluidization and sand production on different scales (pore-scale to bulk scale). Experimental data are used to develop and test numerical codes, and to define constitutive models based on high-resolution micro-scale data. Here, we present details about the novel triaxial flow-through systems which were developed for studies of gas hydrate-bearing or gas charged soils and sediments, but might also be suitable for a range of related scientific topics in geomechanics and geotechnics. We further present results from experimental and numerical studies on depressurization, CO2 - or CO2 mixed fluid injection and gas hydrate exchange from high-pressure flow-through experiments. We briefly define upcoming test cases. Preliminary test data with triaxial-CT and triaxial-ERT systems will be presented during ICEGT 2016. 2

MATERIAL AND METHODS

2.1 Sample preparation and mounting Sediment samples were prepared from quartz sand (initial sample porosity 0.35, grain size 0.1–0.6 mm, G20TEAS, Schlingmeier, Schwülper, Germany), and mixed with deionized water. The partially water saturated and thoroughly homogenized sediments were filled into the triaxial sample cell equipped with a Viton sleeve to obtain final sample dimensions of 380 mm in height and 80 mm in diameter. Sample geometry was assured using a sample forming device. The sample was cooled to 2◦ C after the triaxial cell was mounted inside the pressure vessel. Initial water permeability of gas hydrate-free sediment was 50 × 10−11 m2 .

2.2 Gas hydrate formation Prior to gas hydrate formation the sediment sample was isotropically consolidated to 2 MPa effective stress under drained conditions. The sample was flushed with CH4 gas and, subsequently, pressurized with CH4 gas. During pressurization with CH4 gas and throughout the overall gas hydrate formation period, formation effective stress conditions were maintained using an automated control algorithm. The formation process was continuously monitored by logging CH4 gas pressure. Mass balances and volume saturations were calculated based on CH4 gas pressure and initial mass and volume values. After completion of gas hydrate formation, the sample was cooled to −5◦ C and stress control was switched to constant total isotropic stress control before the sample pore space was

de-pressurized to atmospheric pressure and remaining CH4 gas in the pore space was released. System re-pressurization and water saturation of pore space was achieved by instant filling and re-pressurization with pre-cooled (−1◦ C) saltwater medium according to seawater composition. Hydrate dissociation during the brief period of depressurization was minimized by taking advantage of the anomalous self-preservation effect, which reaches an optimum close to the chosen temperature (Stern et al. 2003). After completion of gas – water fluid exchange, the sample temperature was re-adjusted to 2◦ C.

2.3 Flow-through experiments Experiments were carried out in the custom-made high pressure apparatus NESSI (N atural Environment Simulator for Sub-seafloor I nteractions, Deusner et al. 2012), which was equipped with a high-pressure triaxial cell mounted in a 40 L stainless steel vessel. All wetted parts of the setup are made of stainless steel. Saltwater medium was supplied from reservoir bottles (DURAN, Wertheim, Germany) using a HPLC pump S1122 (SYKAM, Fürstenfeldbruck, Germany). Pressure was adjusted with a back-pressure regulator valve (TESCOM Europe, Selmsdorf, Germany). Experiments were carried out in upflow mode with injection of CH4 gas and seawater medium at the bottom of the sample prior and after gas hydrate formation, and fluid discharge at the top of the sample during depressurization. Axial and confining stresses, and sample volume changes were monitored throughout the overall experimental period. Pore pressure was measured in the influent and the effluent fluid streams close to sample top and bottom. The experiment was carried out at constant temperature conditions. Temperature control was achieved with a thermostat system (T1200, Lauda, Lauda-Königshofen, Germany). Produced gas mass flow was analyzed with mass flow controllers (EL FLOW, Bronkhorst, Kamen, Germany). For control purposes, bulk effluent fluids were also collected inside 100 L gas tight TEDLAR sampling bags (CEL Scientific, Santa Fe Springs CA, USA). The sampling bags were mounted inside water filled sampling containers. After expansion of the effluent fluids at atmospheric pressure, overall volume was measured as volume of displaced water from the containers.

2.4 Numerical modelling To simulate gas hydrate formation and dissociation processes in the lab-scale triaxial compression experiment described in Section 2, we use the mathematical model and the numerical simulator developed by Gupta et al. (2015). This model considers kinetic hydrate phase change and non-isothermal, multiphase, multi-component flow through porous medium. The model accounts for the effect of hydrate phase change on the mechanical properties of the soil, and also for the effect of soil deformation on the fluid-solid

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interaction properties relevant to reaction and transport processes (e.g., reaction surface area, permeability, capillary pressure).

3

NOVEL EXPERIMENTAL SYSTEMS

3.1 Triaxial-CT 3.1.1 CT system In close collaboration APS and GEOMAR develop a new kind of triaxial test system combined with computer tomography. In contrast to existing triaxial CT systems, the triaxial cell is fixed and the CT scanner itself moves around the sample. Due to a high-precision alignment system, high-resolution tomography becomes feasible. As the cell is not in motion, the accuracy of the permeability and shear tests performed increases substantially compared to “moving cell” solutions. The thermodynamic processes of the gas hydrate formation and dissociation can be observed, as well as CO2 injection and capturing. The system is designed for cell pressures up to 40 MPa. Therefore a special cell was constructed that allows the application of the cell pressure while remaining transparent for the X-ray tomography. As the system is currently in the patent process, further information and first testing results will follow soon.

3.1.2 Evaluation Software Besides the experimental part of the CT-tests, the evaluation of the acquired data is a crucial task of the project. Commercial and open-source software solutions are available, but they are limited in the meaning of objectivity. For the evaluation a manual definition of the distinct phases (water, matrix, air, gas hydrates) is needed. The user defines the phases according to his experience and thus with eventual errors and mistakes. In order to ensure an objective definition of the phases a new program was developed based on machine learning technology (Chauhan et al. 2015, Chauhan et al. 2016). The algorithm learns from the data sets itself which phases are tomographically recorded. The phases are clustered and evaluated by their volumetric content. As there are several possibilities of suitable solver-algorithms, a module is incorporated that allows to select and to compare the results of different solver types. Depending on the specimen structure, the results of the different solvers scatter, in some cases substantially. The results of the machine learned analysis are visualized in 2D or 3D (see Fig. 1). Applying the histogram method, the volumetric distribution of the phases is calculated. Besides the absolute value of phase volumes, an evaluation of the pore-size distribution is implemented as well. The constructed pore model can be exported from the program for subsequent pore network and flow simulations, as well as for further elaboration and finite element analysis.

Figure 1. 2D segmented images and volume rendered plot of a respective sample using unsupervised networks (after Chauhan et al. 2016).

3.2 Triaxial-ERT The system combines ERT and local deformation measurements (Fig.2). The triaxial test unit is designed for mounting of large samples (diameter 150 mm, height maximum 400 mm) and can be operated up to 40 MPa. Coupled fluid flow – mechanical loading tests can be performed with a perforated central well. Thus, scenarios of flow- or load-induced deformation and sand production can be simulated. The loss of sample solids through visco-plastic yielding or particle migration leads to local straining rather than homogeneous bulk deformation. Heterogeneous deformation is monitored at high-resolution using electromagnetic sensors. ERT is applied to simultaneously acquire information about heterogeneous phase distributions (e.g. spatial gas hydrate saturation, zones of gas hydrate dissociation and gas release, gas migration pathways, fractures, gas holdup regions, etc.). Combining tools, bulk sample behavior can be correlated with physically relevant heterogeneous processes. 4

RESULTS AND DISCUSSION

4.1 Depressurization experiments Depressurization of gas hydrate-bearing reservoirs is the most mature approach for natural gas production from gas hydrates. Depressurization refers to a technical decrease in hydrostatic or pore pressure at a well using pumps. Obviously, depressurization changes effective stresses, induces fluid flow and phase changes, and gas hydrate saturations are effected relative to gas hydrate stability conditions. After shutdown of pumps, hydrostatic pressure will recover, with recovery rate being dependent on multiple factors including geological and sedimentological settings, permeability and reservoir dimensions. First triaxial experiments on dynamic gas hydrate formation and dissociation were done without allowing particle flow (Fig.3), i.e. sediment particles were

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often irreversible blocking. For similar reasons, nearwell flow assurance might become a major issue in field application, and flow management and filtration means must be carefully chosen. The triaxial experiments were focused on dynamically altering gas hydrate saturations during gas hydrate formation or gas hydrate dissociation and dissociation induced gas flow in a water saturated sample. Pressure and loading constraints were chosen to mimic gas hydrate formation in weakly consolidated sediment which is confined by low-permeability layers at its upper boundary. Thus, usually effective stress is controlled during gas hydrate formation, and total stress is controlled during depressurization (Fig.4). Experimental data from isotropic compression experiments were used to calibrate a fully coupled numerical simulator, soil constitutive behavior was defined in the framework of poro-elasticity. CompositeYoung’s modulus of gas hydrate-bearing sediment was modeled with additive soil and gas hydrate contributions, and it was found that composite modulus depends almost linearly on Sh during gas hydrate formation, while during the hydrate dissociation period the dependence of Esh on Sh is smaller. Further experiments at different gas hydrate saturations have been carried out (Fig.5), and experimental data are now used to further develop the model approach and parameterization.

4.2 Gas hydrate-exchange experiments

Figure 2. Scheme of high-pressure flow-through triaxial test system with electromagnetic sensors for local strain analysis, ERT and perforated well.

retained by the use of filter plates. The obligatory use of filter plates was problematic, since gas hydrate formation, water freezing or multiphase fluid flow caused substantial problems with permeability and

The application of gas-hydrate exchange for natural gas production was discussed extensively in recent years, advantages essentially seen as being an emission neutral energy production technology and as a cure of depressurization induced process problems such as sediment cooling from endothermic gas hydrate formation. It was considered that gas hydrate exchange could also contribute to mechanical integrity during gas hydrate production by keeping gas hydrate-soil fabrics untouched. Although this certainly is a very idealized assumption, results from the Ignik Sikumi field test suggest, that gas hydrate exchange might at least partly prevent excessive sand production. At the moment, the mechanical consequences of CH4 -CO2 hydrate exchange, even under most ideal assumptions are not understood, and different injection strategies and reaction proceedings (gaseous, liquid or supercritical CO2 injection, N2 :CO2 injection, continuous or discontinuous injection, mixed gas hydrate formation, etc.) will influence mechanical behavior in a very complicated and coupled way. The role of gas hydrate conversion for sediment mechanics is a very central topic for applying the new triaxial systems with tomography.

4.3

Important test cases

4.3.1 Slope stability Sub-marine slope stability is affected by different factors, and slope failure and sub-marine avalanches

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Figure 3. Experimental scheme for depressurization experiments.

Figure 4. Converted data from dynamic gas hydrate formation and dissociation experiments.

could be triggered by different mechanisms. The influence of gas migration, gas holdup, and gas charging of sediments is long recognized as an important factor, although mechanistically many unknowns remain. The impact of gas hydrates in slope stability is less well defined. As a primary effect, gas hydrates tend to increase sediment shear strength and could oppose destabilization. However, in a dynamic marine setting with processes as active gas ascent and seeping, or gas hydrate dissociation the presence of gas hydrates could well be destabilizing (e.g. by enabling pore pressure increase from acting as a low permeability barrier and causing sediment effective unloading, gas release from gas hydrate dissociation or defining failure planes). To improve the understanding of mechanical effects of gas charging, gas migration and gas hydrate dissociation for slope stability, the new flow-through triaxial systems with tomography will used to simulate relevant gas flow and gas release dynamics and investigate mechanical response on micro- and bulk scale. The objective is to improve coupled process understanding and constitutive laws used for mechanical modeling.

Figure 5. Raw data from dynamic gas hydrate formation and dissociation experiments with different initial gas hydrate saturations.

4.3.2 Sand production The mechanisms and progress patterns of sand migration observed in field trials are not understood, and the phenomenon could potentially be explained by transient particle fluidization or plastic flow. To improve the understanding of sand production, and to define criteria and triggers for catastrophic soil failure, samples of gas hydrate-bearing sediments with different grain size distributions and gas hydrate saturations will be investigated under different deviatoric loading and flow conditions. Tomographic systems will be used to analyze phase distributions and soil-hydrate fabrics on the small (mm to cm) to micro-scale (few µm) in order to define zones and progression of initial disturbance, and to dynamically monitor transition of initial local disturbance to bulk failure. Certainly, studies to improve mechanistic understanding of sand

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production will be extended to study technical means of sand production management (e.g. application of sand screens or improved depressurization schemes avoiding peak shear loading on the particle scale). Also, the effect of different injection and gas hydrate formation and exchange schemes will be tested. ACKNOWLEDGEMENTS This work was further funded by the German Federal Ministries of Economy (BMWi) and Education and Research (BMBF) through the SUGAR project (grant No. 03SX250, 03SX320A & 03G0856A), and by DEA Deutsche Erdoel AG. The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/20072013) under the MIDAS project, grant agreement n◦ 603418. We gratefully acknowledge the support for S. Gupta by the German Research Foundation (DFG), through project no. WO 671/11-1. REFERENCES Chaouachi, M., Falenty, A., Sell, K., Enzmann, F., Kersten, M., Haberthuer, D., & Kuhs, W. F. 2015. Microstructural evolution of gas hydrates in sedimentary matrices observed with synchrotron X-ray computed tomographic microscopy. Geochemistry Geophysics Geosystems 16: 1711–1722. Chauhan, S., Rühaak, W., Khan, F., Enzmann, F., Mielke, P., Kersten, M., & Sass, I. 2016. Processing of rock core mi-crotomography images: Using seven different machine learning algorithms. Computers & Geosciences 86: 120– 128. Chauhan, S., Rühaak, W., Sass, I., Anbergen, H., Kabdenov, A., Freise, M. & Wille, T. 2016. A new software collection for 3D processing of X-ray CT images. Proceedings 1st International Conference on Energy Geotechnics and Geotechnics, 29th–31st August 2016, Kiel Deusner, C., Bigalke, N., Kossel, E., & Haeckel, M. 2012. Methane Production from Gas Hydrate Deposits through Injection of Supercritical CO2 . Energies 5: 2112–2140. Ghiassian, H. & Grozic, J. L. H. 2013. Strength behavior of methane hydrate bearing sand in undrained triaxial testing. Marine and Petroleum Geology 43: 310–319. Gupta, S., Helmig, R. & Wohlmuth, B. 2015. Nonisothermal, multi-phase, multi-component flows through deformable methane hydrate reservoirs. Computational Geosciences, 1–26doi:10.1007/ s10596-015-95209, URL http://dx.doi.org/10.1007/ s10596-015-9520-9. Hyodo, M., Li, Y., Yoneda, J., Nakata, Y., Yoshimoto, N., & Nishimura, A. 2014. Effects of dissociation on the shear strength and deformation behavior of methane hydratebearing sediments. Marine and Petroleum Geology 51: 52–62. Hyodo, M., Yoneda, J., Yoshimoto, N., & Nakata, Y. (2013). Mechanical and dissociation properties of methane

hydrate-bearing sand in deep seabed. Soils and Foundations 53, 299–314. Inada, N. & Yamamoto, K. 2015. Data report: Hybrid Pressure Coring System tool review and summary of recovery result from gas-hydrate related coring in the Nankai Project. Marine and Petroleum Geology 66, 323–345. Klar, A., Uchida, S., Soga, K., &Yamamoto, K. 2013. Explicitly Coupled Thermal Flow Mechanical Formulation for Gas-Hydrate Sediments. Spe Journal 18, 196–206. Kneafsey, T. J. & Moridis, G. J. (2014). X-Ray computed tomography examination and comparison of gas hydrate dissociation in NGHP-01 expedition (India) and Mount Elbert (Alaska) sediment cores: Experimental observations and numerical modeling. Marine and Petroleum Geology 58: 526–539. Kneafsey, T. J., Seol, Y., Gupta, A., & Tomutsa, L., Permeability of Laboratory-Formed Methane-Hydrate-Bearing Sand: Measurements and Observations Using X-Ray Computed Tomography. Spe Journal 16: 78–94. Kossel E., Deusner C., Bigalke N., & Haeckel M. 2014. Experimental investigation of water permeability in quartz sand as function of gas hydrate saturation. Conference Proceedings of the 8th International Conference on Gas Hydrates, Peking, China. Priegnitz, M., Thaler, J., Spangenberg, E., Ruecker, C., & Schicks, J. M. 2013. A cylindrical electrical resistivity tomography array for three-dimensional monitoring of hydrate formation and dissociation. Review of Scientific Instruments 84. Santamarina, J. C., Dai, S., Terzariol, M., Jang, J., Waite, W. F., Winters, W. J., Nagao, J., Yoneda, J., Konno, Y., Fujii, T., & Suzuki, K. 2015. Hydro-bio-geomechanical properties of hydrate-bearing sediments from Nankai Trough. Marine and Petroleum Geology 66, 434–450. Schoderbek, D., Farrell, H., Hester, K., Howard, J., Raterman, K.,Silpngarmlert, S., Martin, K., Smith, B. & Klein, P. (October 1, 2008–June 30, 2013). ConocoPhillips gas hydrate production test final technical report. Technical report, ConocoPhillips, URL http://www.netl.doe.gov. Song, Y. C., Yu, F., Li, Y. H., Liu, W. G., & Zhao, J. F. 2014. Mechanical property of artificial methane hydrate under triaxial compression. Journal of Natural Gas Chemistry 19: 246–250. Stern, L. A., Circone, S., Kirby, S. H., and Durham, W. B., 2003. Temperature, pressure, and compositional effects on anomalous or “self ” preservation of gas hydrates. Canadian Journal of Physics 81: 271–283. Uchida, S., Klar, A., & Yamamoto, K. 2015. Abstract Sand migration modeling in hydrate-bearing sediments presented at 2015 Fall Meeting AGU, San Francisco, Calif., USA, 14–18 Dec Yamamoto, K. 2013. Japan completes first offshore methane hydrate production test – methane successfully produced from deepwater hydrate layers. Fire in the ice: Department of energy, office of fossil energy, national energy technology laboratory. Methane Hydrate News Letter 13, No. 1–2. Yoneda, J., Masui, A., Konno,Y., Jin,Y., Egawa, K., Kida, M., Ito, T., Nagao, J., & Tenma, N. 2015. Mechanical properties of hydrate-bearing turbidite reservoir in the first gas production test site of the Eastern Nankai Trough. Marine and Petroleum Geology 66: 471–486.

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Influence particle size on strength of gas hydrate cemented granular materials B.N. Madhusudhan & C.R.I. Clayton Faculty of Engineering and the Environment, University of Southampton, UK

ABSTRACT: Quantifying the effect of gas hydrates on engineering properties of sediments is essential to assess its role as triggering mechanism for submarine slope instabilities, potential energy resource or accelerating climate change. Previous studies show cementation due to presence of gas hydrate in deep ocean sediments or permafrost influences the seismic wave velocities of host sediment. This study examines the effect of particle size on the strengths of gas hydrate cemented granular materials using our recently developed gas hydrate triaxial apparatus. Cylindrical specimens of given porosity, methane hydrate content were prepared using ‘excess gas method’ and sheared undrained at constant effective stress and rate of shearing for sands. These tests were then compared with their corresponding host sediments with no hydrates. The stress strain behaviour indicates the host soils exhibits stiffer behaviour due to presence of hydrates similar to structured soils of sensitivity greater than 10. However, the change in strength behaviour of the disseminated gas hydrate sediments is significantly influenced by the particle size, in terms of their specific surface and grading of the granular material regardless of similarity in the hydrate concentration. Keywords: laboratory tests, sands, methane hydrate, fabric/structure of soils

1

INTRODUCTION

The role of methane hydrate as one of mechanisms sought to understand triggering of huge underwater landslides that could trigger tsunami in oceanic sediments (Urlaub et al., 2013) has driven researchers to understand their occurrence, morphology and stressstrain behaviour in order to model submarine slopes and assess the future risks (Talling et al., 2014). Quantifying the engineering properties of gas hydrate is also essential to accurately assess its role as potential energy source and climate change accelerator (Mascarelli, 2009). Methane hydrates are ice like structures that naturally occur in deep ocean sediments and permafrost that forms within stability zone, governed by specific thermobaric range (Fig. 2). The major factors influencing their occurrence, distribution, and morphology are sediment size and geological structure (Brewer et al., 1997; Clennell et al., 1999), porosity and permeability of the host sediment (Collett, 1993) and source of methane gas. Depending on these factors, the gas hydrate could occur in disseminated, nodular and hydrate sheets/veins (Malone, 1985). Disseminated gas hydrates are known to occur in high permeability soils (Collett, 1993; Booth & O’Leary, 1991), wherein the above factors govern the hydrate saturation. Disseminated hydrates formed within pore space of a granular media could be classified into two different micro-morphologies (Clayton et al., 2010),

which is dependent on location of water within the pore space of the media. Hydrate may form within the pore water, acting as additional mineral grains with the voids, termed pore filling or it could occur as cement between grains, formed via the initial capillary water bridge between two grains, termed frame supporting or cementing by Clayton et al. (2010). Previous studies by Clayton et al. (2010) and Priest et al. (2009) on measuring wave velocities by forming hydrates using ‘excess water method’ did not have significant effect on measured wave velocities in sands, whereas using ‘excess gas method’ for same target hydrate content led to rapid increase in the wave velocity. Clayton et al. (2010) also demonstrated that, for a given hydrate saturation, relative density and effective stress, coarser grained quartz sand were twice stiffer than the finer grained ones.This paper aims to demonstrate the above reported effect of grain size on the strength behaviour of disseminated gas hydrate bearing sediments.

2

EXPERIMENT METHODOLOGY

Gas hydrate triaxial apparatus was specially built by the authors at University of Southampton as part of research assessing impact of Arctic climate change on increasing the risk of slope instability. Figure 1 shows the schematic layout of the apparatus and associated accessories to apply appropriate thermobaric

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Figure 1. Schematic of the gas hydrate triaxial apparatus.

conditions to create and test gas hydrates bearing sediments. Disseminated methane hydrate was formed within pore space of selected granular materials using the thermobaric controllers under conditions of constant host sediment void ratio, effective stress and stress history. 2.1

Host materials

In order to study the effect of particle size on strength behaviour of gas hydrate bearing sediments, uniform Leighton Buzzard sand representing coarse (Leighton Buzzard B or LBB, Clayton et al., 2004) and fine (Leighton Buzzard E or LBE, Clayton et al., 2005) grained uniform sediment particle sizes were chosen for this study. Details regarding the index properties of the materials used in testing can be found in Clayton et. al (2010). 2.2

Figure 2. Thermobaric path used to form methane hydrates by ‘excess gas method’.

pressure of 10 MPa (point A to B, Fig 2) with an effective stress of 250 kPa, before cooling to 2◦ C to form hydrate (point B to C, Fig. 2). Temperature, back pressure and effective stress conditions were maintained at point C for at least 48 h, to allow complete hydrate formation. Small cycles of stain controlled loading tests upto 0.5% axial strain was conducted at 12h, 24h, 36 and 48h to determine the comparative strength evolution during hydrate formation process. The rate of strain used was 0.2% per hour. During the process of hydrate formation and thereafter, the loadram was always kept in contact with the sample at a stress of 15 kPa.

Hydrate formation

Cylindrical triaxial specimens of 70 mm diameter and 140 mm height moist sands, mixed with known amount of water and cured overnight in sealed bag, were prepared using moist-tamping method (Ladd 1978). A known amount of water, ∼2.5% to induce 10% hydrate saturation in the granular pore space was used for this comparative study. Care was taken to see no spillage of the sand particles occurred and sample was encased in Butyl membranes in order to avoid any leakage at high pressures. The volumes, dry densities and void ratio for the specimens for LBB sand was 551 cm3, 1706 kg/m3 and 0.553 respectively, whilst for the specimens for LBE sand was 520 cm3, 1616 kg/m3 and 0.640 respectively. After forming the specimen by moist tamping, the specimen it was taken through the methane hydrate/water phase to initiate hydrate formation, by injecting methane at 20◦ C to attain a back

2.3 Hydrate content Calculating the percentage pore space occupied by methane hydrate formed by using excess gas method has been described by Clayton et al. (2005, 2010). The degree of hydrate saturation at the end of gas hydrate formation under ‘drained’ conditions could be calculated on the assumption that all the water in the sand pore space had been converted to hydrate under the thermobaric condition (Sultaniya et al., 2015). Considering the molar ratio of methane to water to be 1 : 5.75 (Sloan and Koh, 2007), mass of the added water and porosity of the sand specimen, the hydrate saturation (Sh) can be calculated by using the expression proposed by Sultaniya et al. (2015):

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where Mw = molar mass of water (18.015 g/mol); Mhy = molar mass of methane hydrate (119.63 g/mol), mw = mass of pore water; ρhy = mass density of methane hydrate (917 kg/m3), n = specimen porosity, and VT = total specimen volume.

2.4 Strength testing Strain controlled triaxial undrained shearing test was performed on host sands without hydrates and with 10% hydrate (after hydrate formation) at constant temperature of 2◦ C. The samples were sheared at constant shearing rate of 0.2% per hour until constant strength was reached for all the samples. The specimen temperature and cell volume was also measured and monitored during the shearing process. 3

RESULTS AND DISCUSSION

3.1 Effect of hydrate formation As mentioned in earlier, gas hydrate was formed over a period of 48 hours in the pore space by supplying constant methane back pressure, whist measuring the specimen temperature at bottom (Fig1). The time calculated for hydrate formation is time since the specimen temperature reaches 2◦ C, even though the cell fluid temperature reached the designated temperature (Sultaniya et al., 2015). Figure 3 shows the evolution of the strength due to hydrate formation in both LBB and LBE sands by performing small cycles of strain on to the sample (0.5%), tested at 24, 36 and 48 hour. The figure clearly indicates the evolution of hydrate cementation within the pore space with time. In case of LBB sand (coarse grained) there is significant increase in the strength at strain below 0.3% regardless of the time after hydrate begins to form, however since the cementation is not yet complete after 24 hr, the strength is lesser in comparison to that after 48hrs beyond 0.3% strain. At 0.4% strain the strength attained by the LBB sand were 180 kPa (no hydrate), 1175 kPa (24hr) and 1770 kPa (48 hr), indicating that the strength of sand increases greater than 6 times within 24hr of hydrate formation and after 48 hr there is 10-fold increase in the coarse sand sediment strength hosting 10% hydrate in their pore space. LBE sand on other hand also show significant increase in strength for 48 hr and 36 hr testing before 0.2% strain, but it is interesting to note that the specimen behaves significantly stiffer when tested after 36 and 48h in comparison to the 24 hr below 0.17% strain. At 0.4% strain the LBE sand attained 107 kPa, 300 kPa, 950 kPa and 1050 kPa strength when tested with no hydrate, after 24 hr, 36 hr and 48 hr respectively. As noted earlier the strength of LBE sand due to hydrate cementation increases 3 times after 24hr of hydrate formation and greater than 5 times after 36hr. There is not significant gain in strength when sample is left for 48hr to form hydrate indicating that most of the hydrate cementation occurs before 36 hours.

Figure 3. Strength evolution of a) LBB sand and b) LBE sand during hydrate formation.

The significant mobilisation of the strength beyond 0.3% strain for the hydrate bearing LBB sand and beyond 0.17% for the hydrate bearing LBE sand indicates either that the contribution of the cementation between the grains to the global strength is attained only after there is initial yielding of the specimen or that the sample could have misaligned (Gasparre et al., 2014) due to hydrate growth in its pore spaces, even though the sample was prepared carefully to form perfect cylinder and the loadcell was in contact throughout the process of hydrate formation. Previous studies on the effect of given hydrate cement (10%) on stiffness of LBB and LBE sand (Clayton et al., 2010) show that at effective stress of 250 kPa, LBB sand was twice stiffer than that of LBE sand.

3.2 Effect of particle size on strength behaviour The effect of particle size on the stress strain behaviour of gas hydrate cemented sediments was examined by triaxial undrained shearing tests on hydrate bearing Leighton Buzzard B and E sands and comparing it with uncemented their counterparts at similar porosity and stress levels. The strength behaviour is expressed as stress ratio, deviatoric stress (q) to mean effective stress (p′ ), variation with deformation, axial strain on the sample in figure 4 for all the specimens tested with and without cementation due to hydrate. Both the coarse (LBB) and fine (LBE) grained sands show

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sharp increase in strength at very early stage of shearing, below 1% strain due to hydrate cementing the grains and thereafter the deviatoric stress begins to drop as the sample deforms further until the sample reaches constant deviatoric stress beyond 10% axial strain. Hydrate cemented Leighton Buzzard B sand exhibited peak dilative behaviour similar to a dense sand or heavily overconsolidated soil, whereas its uncemented counterpart exhibit loose sand behaviour indicating the significant effect of hydrate cement on the sediment behaviour. Leighton Buzzard E sand, on the other hand exhibited slight peak dilative behaviour similar to a medium sand or lightly overconsolidated soil, whereas its uncemented counterpart exhibit loose sand behaviour. Both the sands used for this study have been extensively characterised and tested at the University of Southampton (Abbireddy et al., 2009; Clayton et al., 2010). From these studies, it is known that Leighton Buzzard B had a higher uncemented stiffness than Leighton Buzzard E at the same stress level and relative density and for 10% hydrate cemented Leighton Buzzard B had twice the stiffness to that of Leighton Buzzard E. The mechanism explained by Clayton et al., (2010) was that since the hydrate replaces the water, assuming 100% hydrate replacement (Priest et al., 2005), the contact area between two particles, previously bridged by capillary water is replaced by hydrate cement (Fig. 5). Since the cemented surface area is greater for Leighton Buzzard B sand in comparison to Leighton buzzard E sand, it explains why the higher strength for a coarser particle when sheared at same hydrate content, effective stress and relative density. 3.3

Figure 4. Stress-strain behaviour of LBB and LBE sands with and without 10% hydrate.

Figure 5. Disseminated hydrate formation between two sand grains using ‘excess gas method’ after Clayton et al. (2010).

Effect of shearing disseminated hydrates

The stress paths of all the specimens tested with or without hydrate, sheared undrained, are shown in Figure 6. The stress paths indicate that there is minimal pore pressure developed during the undrained shearing of cemented hydrate and the effective stress is similar to the total stress. This indicates that the hydrate cement simply begins to rupture beyond the peak strain and hence there is gradual reduction in the strength with increasing deformation on the sample. 4

CONCLUDING REMARKS

This paper has presented the results of experiments conducted to investigate the strength behaviour of hydrate cemented sands, tested using new gas hydrate triaxial apparatus built for this specific purpose. Using the excess gas method to form disseminated hydrates, the formation of hydrates induced cementation between the particles and thus they exhibit stress strain behaviour similar to over consolidated soils. For a given hydrate content, relative density and effective stress coarse grained quartz sand show higher strength in comparison to finer grained sand. Small cycles of strength tests performed at regular intervals reveal that

Figure 6. Stress path of the specimens tested.

the hydrate formation process took upto 36 hours and beyond that there the gain in strength is marginal. The difference in the strength behaviour of similar hydrate bearing sediments due to particle size and perhaps morphology (future study) reveals that the particle surface area available for the cementation along with hydrate content and porosity can be quantified and incorporated in modelling.

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REFERENCES Abbireddy, C. O. R., Clayton, C. R. I. & Huvenne, V. A. I. 2009.A method of estimating the form of fine particulates. Géotechnique 59(6): 503–511. Booth, J. S. & O’Leary, D. W. 1991. A statistical overview of mass movement characteristcs on the North American Atlantic outer continental margin. Marine Geores. Geotechnol. 10(1): 1–18. Clayton, C. R. I., Theron, M. & Vermeulen, N. J. 2004. The effect of particle shape on the behaviour of gold tailings. In Advances in geotechnical engineering: the Skempton conference. London: Thomas Telford. Clayton, C. R. I., Priest, J. A. & Best, A. I. 2005. The effects of disseminated methane hydrate on the dynamic stiffness and damping of a sand. Géotechnique 55 (6): 423–434. Clayton, C. R. I., Priest, J. A. & Best, E. V. L. 2005. The effects of hydrate cement on the stiffness of some sands. Géotechnique 60(6): 435–445. Clennell, B. M., Hovland, M., Booth, J., Henry, P. & Winters, W. J. 1999. Formation of natural hydrates in marine sediments: 1. Conceptual model of gas hydrate growth conditioned by host sediment properties. J. Geophys. Res. 104, (B10): 22 985–23 003. Collett, T. S. 1993. Natural gas hydrates of the Prudhoe Bay and Kuparuk River area, North Slope, Alaska. AAPG Bull. 77 (5): 793–812. Gasparre A, Hight DW, Coop MR, Jardine RJ. 2014. The laboratory measurement and interpretation of the smallstrain stiffness of stiff clays. Géotechnique 64 (12): 942– 953.

Ladd, R. 1978. Preparing test specimens using undercompaction. Geotechnical Testing Journal, 1 (1): 16–23. Malone, R. D. 1985. Gas hydrates. DOE/METC/SP-218. Washington, DC: US Department of Energy. Mascarelli, A. 2009. A sleeping giant? Nature Reports Climate Change, 3: 46–49. Priest, J. A., Best, A. I. & Clayton, C. R. I. 2005. A laboratory investigation into the seismic velocities of methane gas hydrate bearing sand. J. Geophys. Res. Solid Earth 110 (B4): B04102. Priest, J.A.,. Rees, E.V. L and Clayton. C. R. I. 2009. Influence of gas hydrate morphology on the seismic velocities of sands. J. Geophys. Res., 114: B11205. Sloan, E. D., and Koh, C. A. 2007. Clathrate Hydrates of Natural Gases, 3rd ed., CRC Press, Taylor and Francis Group, New York. Sultaniya, A. K., Priest, J. A. and Clayton, C. R. I. 2015. Measurements of the changing wave velocities of sand during the formation and dissociation of disseminated methane hydrate. J. Geophys. Res. Solid Earth, 120: 778–789. Talling, P, Clare, M, Urlaub, M, Pope, E, Hunt, J.E, Sebastian, W. 2014. Large Submarine Landslides on Continental Slopes: Geohazards, Methane Release, and Climate Change. Oceanography, 27 (2): 32–45. Urlaub, M., Talling, P. J., Masson, D. G. 2013. Timing and frequency of large submarine landslides: implications for understanding triggers and future geohazard. Quaternary Science Reviews, 72: 63–82.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Sand production modeling of the 2013 Nankai offshore gas production test S. Uchida Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, Troy, USA

A. Klar Faculty of Civil and Environmental Engineering, Technion – Israel Institute of Technology, Haifa, Israel

K. Yamamoto Methane Hydrate Research & Development Group, Japan Oil, Gas and Metals National Corporation, Chiba, Japan

ABSTRACT: A better understanding of the behavior of gas hydrate-bearing sediments during gas extraction is a vital step towards realization of long-term gas production for the future. In March 2013, the world first trial of gas production from offshore hydrate-bearing sediments by depressurization method was conducted at the Eastern Nankai Trough site, Japan. While the operation was successful in producing gas, after six days it suddenly encountered a large amount of sand migration into the well, a phenomenon known as sand production, leading to a premature termination of the operation. This incident has highlighted the importance of development of sand migration model within hydrate-bearing sediments and understanding of the geomechanical behavior of hydrate-bearing sediments with the effect of sand migration during gas extraction. This paper presents the overview of the recently developed thermo-hydro-mechanically coupled formulation that entails sand migration in gas hydrate-bearing sediments. The formulation is then applied to simulate the 2013 Nankai production test in wellbore scale, including history matching of produced water and gas. The amount of produced sand at the end of the test is also matched and the effects of sand migration on geomechanical behavior are investigated.

1

INTRODUCTION

Methane hydrate has been attracting international interest because of its potential as an abundant and widespread source of natural gas that could meet many decades worth of global energy demands. As of today, only a few short-term field trials have been successful in producing gas, namely at the Mallik site, Canada, in 2007 and 2008 (1), at the Mount Elbert site, USA, in 2007 (2), at the Ignik Sikumi site, USA, in 2012 (8) and at the Nankai Trough site, Japan, in 2013 (12). Having learned lessons from the past field trials, it was hoped that the 2013 Nankai gas production test operated by Japan Oil, Gas and Metals Corporation (JOGMEC) would be a long-term success but it was on the sixth day that sand production (excessive migration of sand into the well) occurred despite the presence of sand screen, leading to an untimely abandonment of the well. Therefore, establishing a commercially viable and sustainable method of methane gas production from gas hydrate-bearing sediments still remains as a major challenge. Motivated by the premature termination of the test, the authors have recently developed a coupled thermo-hydro-mechanical sand production model in gas hydrate-bearing sediments (9). The developed model is the extension of existing thermohydro-mechanical simulator for gas hydrate-bearing

sediments by 4) together with sand migration models (7). The highlight of the developed formulation is its coupled manner of incorporation of sand migration features such that grain detachment causes stress reduction, sediment shear deformation induces grain detachment and grain migration alters multiphase fluid pressure and temperature profiles. This paper presents a brief summary of the developed thermo-hydro-mechanical sand production formulation in gas hydrate-bearing sediments and its application to the field production test conducted at the offshore Eastern Nankai Trough in 2013. This work is a part of Research Consortium for Methane Hydrate Resources in Japan (MH21), supported by JOGMEC. 2

COUPLED THERMO HYDRO MECHANICAL FORMULATION FOR SAND MIGRATION IN GAS HYDRATE-BEARING SEDIMENTS

This section briefly describes the derivation of the developed coupled thermo-hydro-mechanical formulation for sand production. The detailed explanations can be found in 9). 2.1

Solid mass balance

Since the solid volume is no longer constant when considering sand migration, three states for solids are

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Figure 1. An elementary volumetric cube representing solid states, mixture and concentrations.

introduced: [1] flowing solids (fs) that are currently flowing with fluid; [2] stable solids that are still part of the original soil skeleton and thus intact (ssi); and [3] solids that are settled after flowing (sst). A simple volumetric cube incorporating these states is shown in Fig. 1 where the subscripts w, g and h are for water, gas and hydrate, respectively. A grain is assumed to flow with water or gas. Thus, the concept of mixture is introduced as water-flowing solid mixture (wm) and gas-flowing solid mixture (gm). The volumetric concentrations of the flowing solids in the watermixture (fs|wm) and gas-mixture (fs|gm) are defined V V s s as cwm = Vw +fs|wm and cgm = Vg +fs|gm , which are also Vfs|wm Vfs|gm illustrated in Fig. 1. The mixtures are assumed to hold the same superficial velocity as their corresponding fluids, that is, qwm /Vwm = qw /Vw and qgm /Vgm = qg /Vg where q is the discharge vector. Assuming the Darcy’s law is valid for the sole fluid, the discharge of flowing solids can be given by:

where V is the control volume, ǫv is the volumetric strain (compression negative), n is the porosity (=Vv /V ), βs is the thermal expansion coefficient of soil grains and T is the temperature. This leads to a change in the storage term equations of water, gas and hydrate. Together with: [1] the capillary pressure equation Pc (Swe ) derived from the model by 11), where Swe is the effective water saturation; and [2] the pore space condition (i.e. dSw + dSg + dSh = 0 where S is the saturation), the incremental form of five unknowns, Pw , Pg , Sw , Sg and Sh can be solved as simultaneous equations. For example, dPw is given by:

S

where D = KSww + Kgg − where µ is the viscosity, Kh is the intrinsic permeability tensor with the effect of hydrate, k r is the relative permeability factor, P is the pressure, ρ is the density and g is the gravity vector. The mass of the solids in a control volume is not affected by the change in the solid state by itself. Rather, it is altered only by mass divergence of the flowing solids:

where m is the mass, t is the time and the subscript s is for solids. 2.2

Hydro-sand migration coupling

The solid mass change results in the change in the void volume:

Sg Pc′ , Kg (Sw + Sg )(1−Swr −Sgr )

Sw Sg Pc′ , Kw Kg (Sw + Sg )(1−Swr −Sgr )

Ŵ=1−

Swr and Sgr is the degrees of residual water and gas saturation (discussed later), K is the bulk modulus, M is the molecular mass, Nh is the number of water molecules to constitute one hydrate molecule with one gas molecule (i.e. Mh = Nh Mw + Mg ) and Rh is the rate of hydrate formation/dissociation (dissociation positive) determined by the current Pg and T such as the firstorder kinetic model of 3). Equation (4) clearly shows how the variable is affected by five components: fluid flow, mechanical deformation, hydrate formation/dissociation, temperature change and sand migration, which are represented by a large square bracket in the right-hand side of the equation. Considering hysteresis nature of the multiphase media and also the presence of hydrate, the effective water saturation is defined as:

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It should be noted that, at in-situ condition, there is no gas present as any residual gas should form hydrate under the pressure-temperature condition. The residual gas saturation shall then increase according to developing gas in pores (without exceeding the gas saturation itself) and shall never decrease. This development of residual gas saturation can be modeled by:

where Sgr0 is the maximum residual gas saturation and Sg,max is the historical maximum of the varying gas saturation during gas production operation.

where ǫ is the strain vector, Dehs is the elastic stiffness matrix of hydrate-bearing soil continuum (i.e. Dehs = Deh0 Sh + Des ), g is the plastic potential, f is the yield function, ξ is the hardening parameters in a vector form, δ = (1, 1, 1, 0, 0, 0)T and β∗ is the volumetric mean of grain and hydrate thermal expansion coefficient (i.e. β∗ = (1 − n)βs + nSh βh ). This expression states that the effective stress change can be caused by soil straining, hydrate dissociation, temperature change and grain detachment, which are represented by each large square bracket on the right hand side of the equation.

2.3 Mechanical-grain detachment coupling

2.4 Thermo-sand migration coupling

The effective stresses are defined as the stresses that are carried by the intact solids. When a grain is detached from the skeletal intact solids, the grain is no longer part of the intact solid continuum. Therefore, the part of the effective stresses can be released upon grain detachment, leading to stress relaxation. The magnitude of the released stresses should depend on both the current effective stresses and the fraction of the detached grain to the intact solids. Thus, introducing a proportionality factor ω1 , the effective stress change due to the grain detachment is:

As flowing solids carry heat, the sand migration contributes to the convection term:

where cT ∗ is the volumetric mean of specific heats, that is, cT ∗ = (1 − n)ρs csT + n(Sw ρw cwT + Sg ρg cgT + Sh ρh chT ). Introducing the above term into the energy-balance equation within gas hydrate-bearing sediments results in:

where σ ′ is the effective stress vector and dmssi is the change in the mass of intact solids (negative denotes grain detachment) per control volume. Introducing the above expression into a hydrate-dependent elastoplastic constitutive model results in:

where K T ∗ is the bulk thermal conductivity tensor which can be obtained by a similar manner to cT ∗ , H is the enthalpy of methane hydrate (H > 0 and Rh is positive/negative depending on hydrate dissociation/formation, respectively) and σ ′ dǫp is the mechanical energy dissipation because of plastic deformation. The expression implies that the temperature change is caused by conduction, convection of water and gas, hydrate formation/dissociation, plastic mechanical deformation and convection of sand migration, each of which is represented by the large square bracket on the right-hand side of the equation.

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3

SOLID STATE CHANGE: DETACHMENT, SETTLING AND LIFTING

This section summarizes the suggested mechanisms and corresponding mathematical representations for the state change of solids by detachment (from ssi to fs); settling (from fs to sst); and lifting (from sst to fs) by 9). 3.1 Grain detachment For grain detachment, the following five mechanisms are assumed. First, grains are detached from the intact soil skeleton when hydraulic gradient exceeds its critical value. Second, when hydrate is present in pores, grain detachment should be harder to occur. Third, the flowing grain does not switch the media while flowing. Forth, the active fluid (i.e. fluid that has greater hydraulic gradient than its critical value) realizes the detachability potential into an actual detachment in proportion to relative pore occupancy to multiphase fluids. Fifth, the detachability potential increases as a result of shearing deformation. These assumptions can be expressed together as:

Figure 2. Model geometry and boundary conditions.

where ω2 is the controlling parameter for the rate of detachment (dimension of time−1 ), M dtc is the detachability potential, H (x) is the heaviside step function, i is the hydraulic gradient of a fluid (water or gas) and icri is the critical hydraulic gradient, which is influenced by the hydrate saturation through:

where icri0 is the critical hydraulic gradient for grain detachment without hydrate and ω3 is the increasing factor of the critical gradient with hydrate. The first term of the right-hand side of Eq. (12) is for waterinduced flowing solids mfs|wm and the second term is for gas-induced flowing solids mfs|gm . The detachability potential increases with shearing deformation but actual detachment itself reduces the potential such that:

3.2 Grain settling and lifting Considering that the settled solids are no longer part of soil skeleton, they should be easier to initiate flowing compared to the solids of intact skeleton. Thus, introducing another proportionality factor ω5 (0 ≤ ω5 ≤ 1), the mass of settled solids becomes:

i

where Hw = H ( ω5iwicri − 1) and Hg = H ( ω5gicri − 1). The w g first two terms of Eq. (15) represent settling and the last term is for lifting. Unlike grain detachment, grain lifting does not directly affect soil effective stresses. 4

where ω4 is the model parameter that gives the increase in the potential due to shearing deformation and ms0 is the initial intact solid mass equal to the initial solid mass (i.e. mssi0 = ms0 ).
It can  be seen that grain mssi detachment ceases when ln ms0 becomes equal to −ω4 ǫd .

4.1

NUMERICAL SIMULATIONS OF THE 2013 NANKAI GAS PRODUCTION TEST Model geometry and in-situ conditions

The model geometry and the boundary conditions used for the wellbore-scale simulations of the 2013 Nankai offshore test are shown in Fig. 2. The wellbore is assumed to be constructed instantaneously in time without disturbing the in-situ stresses. The wellbore

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boundary for displacement is fixed in the radial direction but smooth in the vertical direction, that for fluid flow is only permeable inside the production zone and that for heat is insulated. The seabed is assumed to be at 1000 m from the mean sea level. The production zone is between −278 and −308 m from the seabed. Figure 3 provides (a) hydrate saturation profile and (b) geometric mean permeability profiles with (red line) and without (black line) hydrate. Between Figs. 3a and b, the soil classification is shown. From the in-situ measurement, it is found that the sediments are highly stratified with alternating sand and clay layers. The measurement was conducted approximately every 50 cm deep interval but the model mesh is slightly coarser (e.g. 90 cm around the production zone and on average 400 cm above and below the production zone). In order to incorporate the strata in terms of fluid flow, the horizontal permeability without hydrate for a given element is averaged by:

Figure 3. Hydrate saturation and permeability profiles used in the simulations.

where α is the scaling factor for the overall permeability to be used later for history matching, khr,j is the measured horizontal permeability without hydrate, zj is  the measurement interval and j zj is the element vertical size. In contrast, the vertical permeability without hydrate is:

For an element level, therefore, the permeability tensor is defined as:

This facilitates the presence of a thin clay layer. In the analysis, the horizontal permeability is on average found to be approximately 200 times greater than the vertical permeability. As a boundary condition, the well pressure decreases according to the recorded value as shown in Fig. 4. The starting time of the simulation is set at 4 am on 12 March, 2013. The thermocline is set to be 0.272 K/m and 278.8 K at the seabed based on the insitu measurement. The salinity is assumed to be 3%. Accordingly, the profiles of the water pressure and the phase equilibrium pressure at in-situ are obtained and shown in Fig. 5. The lower boundary of the hydrate stability zone coincides with the location where hydrate is inferred non-existent albeit sand layers. 4.2

Soil properties and other physical properties

To capture the geomechanical behavior of the Nankai sediments, the soil model by 10) is utilized to match

Figure 4. Recorded depressurization conducted during the 2013 Nankai test.

Figure 5. Hydrate phase boundary at the Nankai site.

the soil responses, both shear and volumetric, of the Nankai sand and clay, making the use of the model’s versatility. For the Nankai sand, drained triaxial compression test data by 5) while, for the Nankai clay, undrained triaxial compression test (preceded by K0 consolidation) data by 6) are calibrated. The results (normal lines) including the experimental data (dotted lines) are shown in Fig. 6. The calibrated model

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parameters are summarized in Table 1. Other physical parameters used for the simulation such as the thermal conductivity of water, gas and hydrate are presented in 9). 4.3

History matching of the 2013 Nankai production test

Figure 7 illustrates the histories of (a) gas production, (b) water production and (c) sand production. The dotted lines represent the recorded values during the Nankai 2013 operation. The normal lines represent the best-fitted results, obtained from a series of recursive analyses. Since production history is predominantly influenced by the in-situ permeability, the water production is first equated. This is because a large fraction of pore space is occupied by water. In other words, the

water production history is less affected by the relative permeability. Subsequently, the gas production history is matched by adjusting the relative permeability factor. Finally the sand production is matched by varying sand migration related parameters. The overall permeability is adjusted to match the water production history by changing the value of α described in Eqs. (16) & (17). Thus, the anisotropic nature in the permeability is unaffected. In other words, the value α swifts the permeability profiles illustrated in Fig. 3b leftwards when α < 1 and rightwards when α > 1. For the best matching, α is determined to be 1/8. Based on α = 1/8, the gas production history is matched by altering the relative permeability curves, of which the best matched case is shown in Fig. 8. The relations are derived based on vanGenuchten (1980) formula and the parameters are found to be a = 0.55, b = 3.5 and c = −0.05. In addition, the residual saturations defined in Eq. (5) are determined to be Swr = 0.2 and Sgr0 = 0.012. The recorded history of sand production is not available and thus this study seeks to match the overall production at the end of six day operation, known to be approximately 27 m3 . Grain detachment occurs when the hydraulic gradient exceeds the critical gradient and its amount depends on the potential which is cumulative deviatoric strain as described in Eqs. (12) & (14), respectively. Considering there are currently flowing and settled solids, the detached solid volume is always Table 1. Soil parameters used for the Nankai soils.

Figure 6. Deviatoric and volumetric behaviors of (a) Nankai sand and (b) Nankai clay.

Parameter

Sand

Clay

Void ratio e0 = n/(1 − n) Slope of critical state M Compression line λ Swelling line κ Poisson’s ratio ν Preconsolidation stress p′cs

0.82 1.40 0.16 0.025 0.28 5.0 MPa 0.29 MPa 10 45 Sh 0.8 MPa 320 MPa 15

0.72 1.32 0.20 0.05 0.23 −0.012z(m) +

Subloading factor u Yield surface expansion p′cd Sh dependent modulus Eh0 Degradation factor m

Figure 7. Production histories and simulation results.

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960 – – –

Figure 8. Relative permeability and capillary pressure relations used in the simulation. Table 2. Sand migration related parameters used for the analyses. Parameter

Value

Stress reduction factor ω1 Rate of detachment ω2 Critical gradient factor ω3 Shear to detachability ω4 Grain settling factor ω5 Critical gradient icri0

1.0 0.1 hour−1 1.0 1.0 0.5 5.0

Figure 9. Thermo-hydro behavior of the sediments.

greater than the produced solid volume. When ǫd is known, therefore, a rough estimation of produced volume is feasible. Table 2 lists the sand migration related parameters employed for the best matching analysis. 4.4 Thermo-hydro-mechanical studies during the 2013 Nankai production test Figure 9 presents the thermo-hydro behavior of the Nankai hydrate-bearing sediments during the production test: (a) hydrate saturation profile; and (b) temperature profile at the elapsed times of 3 and 6 days. As can be seen, hydrate dissociation does not uniformly occur due to the differences in the permeability and temperature. The area with lower temperature corresponds to the area with greater hydrate dissociation. It is evident that a greater hydrate dissociation occurs in the layers adjacent to the low initial Sh (cf. Fig. 3), where adequate heat convection is available. Figure 10 presents the mechanical behavior of the hydrate-bearing sediments in terms of (a) stress ratio q/p′ where q is the deviator stress and p′ is the mean effective stress;and (b) displacement magnitudes, that is, |u| = ur 2 + uz 2 , with the arrows indicating its magnitudes and directions, at the elapsed times of t = 3 and 6 days. The change in the stress

Figure 10. Mechanical behavior of the sediments.

ratio implies whether the sediment deformation is shearing-oriented (q) or volumetric-oriented (p′ ) (or consolidation-oriented). The sediments around the well inside the production zone appears to deform in volumetric manner, whereas the layers with relatively high Sh tend to deform in shearing manner. This is because the hydrate dissociation occurred in the layers with low Sh induces stress relaxation and subsequently the stiffer sediments (i.e. layers with high Sh ) carry the redistributed stresses. From the arrows in Fig. 10b, large vertical deformation is evident just above the production zone and large radial deformation is noticeable

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the stress redistribution from the low Sh layers. It is also shown that a significant shearing deformation as well as sand migration appeared to occur at the depth of approximately −300 m. REFERENCES

Figure 11. Sand migration of the sediments.

in the sediments away from the wellbore, particularly at r ≈ 10 m. Figure 11 presents: (a) the snapshot of the normalized flowing solid volume; and (b) the normalized detached solid volume (i.e. change in the intact) at the elapsed times of 3 and 6 days. The values of the settled solids Vsst /V are negligibly small and most of Vfs are flowing with water. Comparing Figs. 11a & b, the values of Vfs /V away from the well are almost identical to those of −Vssi /V . This implies that, even though the solids are detached in the region, they have hardly moved towards the well due to the slow fluid velocity. The lowest possible value for Vssi /V is n − 1 = −0.65 when all the solids are detached. This implies that the amount of detached solids are around 5% near the well. At the depth of −300 m, detachment occurs as far as 20 meters from the well and this location corresponds with the layers with high q/p′ , implying that shearing deformation contributes to the sand migration and eventually sand production. 5

SUMMARY

This paper presented the overview of the coupled thermo-hydro-mechanical formulation for sand migration in gas hydrate-bearing sediments and its application to the 2013 Nankai offshore gas production test. The formulation was able to achieve good history matching of the 2013 Nankai test for gas, water and sand production. Through wellbore-scale thermohydro-mechanical studies, it is found that the layers with high Sh deformed in shearing manner caused by

Dallimore, S. R., J. F. Wright, K. Yamamoto, & G. Bellefleur (2012). Proof of concept for gas hydrate production using the depressurization technique, as established by the jogmec/nrcan/aurora mallik 2007-2008 gas hydrate production research well program, mackenzie delta, northwest territories, canada. Bulletin of the Geological Survey of Canada 601, 1–15. Hunter, R. B., T. S. Collett, R. Boswell, B. J. Anderson, S. A. Digert, G. Pospisil, R. Baker, & M. Weeks (2011). Mount Elbert Gas Hydrate Stratigraphic Test Well, Alaska North Slope: Coring operations, core sedimentology, and lithostratigraphy. Marine and Petroleum Geology 28(2), 311–331. Kim, H., P. Bishnoi, R. Heidemannn, & S. Rizvi (1987). Kinetics of methane hydrate decomposition. Chemical Engineering Science 42(7), 1645–1653. Klar, A., S. Uchida, K. Soga, & K. Yamamoto (2013). Explicitly coupled thermal-flow-mechanical formulation for gas hydrate sediments. Society of Petroleum Engineers Journal 18(2), 196–206. Masui, A., H. Haneda, Y. Ogata, & K. Aoki (2007). Mechanical Properties of Sandy Sediment Containing Marine Gas Hydrates in Deep Sea Offshore Japan Survey drilling in Nankai Trough. In Seventh ISOPE Ocean Mining Symposium, Lisbon, Portugal, pp. 53–56. International Society of Offshore and Polar Engineers. Nishio, S., E. Ogisako, & A. Denda (2009). Geotechnical properties of core samples recovered from seabed ground in East Nankai Trough. Journal of Geography 118(5), 955–968. Papamichos, E., I. Vardoulakis, J. Tronvoll, & A. Skjaerstein (2001). Volumetric sand production model and experiment. International Journal for Numerical and Analytical Methods in Geomechanics 25, 789–808. Schoderbek, D., H. Farrell, K. Hester, J. Howard, K. Raterman, S. Silpngarmlert, K. L. Martin, B. Smith, & P. Klein (2013). ConocoPhillips Gas Hydrate Production Test. Technical report, US Department of Energy. Uchida, S., A. Klar, & K.Yamamoto (2016). Sand production model in gas hydrate-bearing sediments. International Journal of Rock Mechanics and Mining Sciences 86, 303–316. Uchida, S., K. Soga, & K. Yamamoto (2012). Critical state soil constitutive model for methane hydrate soil. Journal of Geophysical Research 117, B03209. van Genuchten, M. (1980). A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil and Science Society of America Journal 44, 892–898. Yamamoto, K., Y. Terao, T. Fujii, I. Terumichi, M. Seki, M. Matsuzawa, & T. Kanno (2014, may). Operational overview of the first offshore production test of methane hydrates in the Eastern Nankai Trough. In Offshore Technology Conference, Huston, USA.

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A small pore size effect on dissociation behavior of gas hydrates in fine-grained sediments Taehyung Park, Hak-Sung Kim & Tae-Hyuk Kwon Department of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology (KAIST), South Korea

ABSTRACT: As capillarity in small pores is known to affect dissociation of gas hydrates, the dissociation behavior of gas hydrates in fine-grained sediments need to be clearly understood for successful practices of resource recovery. Therefore, this study investigated the dissociation behavior of gas hydrates in different sized pores of host sediments. Gas hydrates were synthesized from a partially water-saturated conditions in a sand sample and a natural fine-grained sediment sample cored from Ulleung Basin (UB), offshore Korea, and these hydrates were thermally dissociated under a constant volume condition while monitoring the pressure and temperature. The dissociation of gas hydrate in the fine-grained sediments occurred at the lower temperature than the bulk equilibrium by ∼1.5◦ C. When compared with the pore size distribution obtained by the mercury intrusion porosimetry, gas hydrate was preferentially formed in small pores for a given range due to the initial water locations in partially water-saturated conditions.

1

INTRODUCTION

Gas hydrates are ice-like crystalline structure comprised of hydrogen bonded water cages with gas molecules inside (Sloan, 1998). These are naturally formed under high pressure and low temperature conditions (Sloan, 1998). In deep ocean sediments where those conditions are satisfied, abundant amount of natural gas hydrates exist in continental margins and permafrost regions (Sloan and Koh, 2008). As energy use and fossil fuel consumption increase from decade to decade, gas hydrate deposits in oceanic sediments have been spotlighted as prospective energy resource for the large amount of methane (Lee et al., 2003). Potential reserves of natural gas hydrates are over 1.5 × 1016 m3 all over the offshore earth areas (Makago et al., 2007). Additionally, gas hydrates have been considered as one of the possible solutions for carbon dioxide (CO2 ) mitigation. By the formation of a CO2 hydrate layer in subsurface, CO2 hydrate can also function as a cap-rock structure which provides the secondary shield to prevent the leakage of CO2 (Tohidi et al., 2010). For successful practices of methane recovery from hydrate deposits or CO2 storage using hydrates, better understanding of the dissociation behavior and the phase equilibrium of gas hydrates in natural sediments is required (Lee et al., 2007, Uchida et al., 2004). For these reasons, there have been numerous studies to understand the phase equilibrium of gas hydrates in porous media; previous studies found that dissociation pressure of gas hydrates were higher in small pores than that in a bulk phase, which means the inhibition

effect on hydrate equilibrium conditions (Handa and Stupin, 1992; Uchida et al., 1993; Tohidi et al., 2001; Anderson et al., 2003; Uchida et al., 2002). Despite of numerous gas hydrate studies in porous media, there have been lack of experimental data on the dissociation behavior of gas hydrates in natural fine-grained sediments as most of the previous studies were conducted using porous silica gels. Therefore, in this study, we investigated the dissociation behavior and the equilibrium conditions of CO2 hydrate in the sediments with different pore sizes, including a fine sand and a natural clayey silt sample cored from the Ulleung Basin (UB), offshore South Korea. 2 2.1

EXPERIMENTAL PROGRAM Materials

CO2 gas (commercial-grade with the purity of 99.9%, Sam-Oh Gas Co., South Korea) was used for CO2 hydrate formation in this study. Fine sand (Ottawa F110) was selected as representative coarse-grained sediments, as shown in Figure 1a. A natural finegrained sediment sample retrieved from Ulleung Basin, located in the southwestern part of the East Sea of South Korea was used for the experiment, as shown in Figure 1b. Detailed descriptions of the sediment samples are available in previous references (Kwon et al., 2011; Kim et al., 2013). The basic properties of the tested samples, including mean particle diameter (D50 ), specific gravity (Gs ), specific surface area (Sa ), porosity, and water saturation (Sw ), are described in Table 1.

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Table 1. Properties of the sediments Fine sand (Ottawa F110) (Kwon et al., 2008)

Natural UB sediment (Kim et al., 2013)

Mean diameter, D50 = 120 µm Specific gravity, Gs = 2.65 Specific surface area, Sa = 0.019 m2 /g Porosity = 0.41 Water saturation, Sw 0.46

Mean diameter, D50 = 4.83 µm Specific gravity, Gs = 2.52 Specific surface area, Sa = 32.09 m2 /g (dry method) Porosity = 0.61 Water saturation, Sw = 0.52

Figure 3. Temperature and pressure conditions of CO2 hydrate in sand sample during 1st heating, 2nd cooling and 3rd heating procedures. Figure 1. (a) Microscopic image of the fine sand (Ottawa F110) sample and (b) scanning electron microscope (SEM) image of the natural UB sediment.

Figure 2. Schematic diagram of experimental setup.

A proper amount of deionized water (DIW, 18 M
cm) was prepared to partially saturate the sediments and form CO2 hydrates. 2.2

Experimental Apparatus

The experimental setup was designed to measure the dissociation temperature and pressure of CO2 hydrate in the sediments. These experimental setup is graphically described in Figure 2.A cylindrical, transparent high pressure cell made of polycarbonate with a volume of 3.18 cm3 was used for this study. During whole experimental procedures, the cell was submerged in the temperature-controlled bath (RW-2025G; Lab Companion, South Korea) to control the temperature of the cell. A platinum resistance thermometer (Pt100; Hankook Electric Heater, South Korea) was placed at the center of the sediment inside the cell and two pressure transducers (PX302; Omega, United States) were connected to the cell. For real time monitoring of the temperature and pressure conditions, the data acquisition unit (34970A; Agilent, United States) was used.

2.3 Experimental Procedures Each sample was mixed with DIW and the mixture was hand-tamped in the cell to achieve a partially saturated condition. The porosity of 0.41 and 0.61 was achieved for the fine sand and natural UB sediment, respectively (Table 1).The cell was flushed with pure CO2 gas several times to remove the residual air inside the reaction cell. CO2 gas was then injected and pressurized to 3 MPa. The temperature of the cell was lowered to 274.15 K. CO2 hydrate nucleation took place, and the pressure and temperature was maintained for 24 h until forming a sufficient amount of CO2 hydrate. Hydrate nucleation was confirmed by appearance of a temperature peak where an exothermal reaction takes place. After 24 h, the temperature of the reaction cell was increased in steps of 0.5◦ C every 6 h under a constant volume condition (i.e., isochoric heating). When the temperature exceeded the equilibrium temperature, hydrates started to melt due to the increased temperature. The pressure also increased as the dissociation of CO2 hydrate released free CO2 gas. Thereby, the pressure and temperature were tracked to obtain the hydrate phase equilibrium. Such step-wise heating was continued until complete dissociation of CO2 hydrate (i.e., 1st heating cycle). Then, the reaction cell was cooled again to 0◦ C for CO2 hydrate formation (i.e., 2nd cooling cycle). The aforementioned dissociation procedure was repeated to make sure the experiment results shows the repeatability (i.e., 3rd heating cycle).

3 3.1

RESULTS AND DISCUSSION Dissociation behaviors of CO2 hydrate in fine sand and fine grained sediment

Figure 3 and Figure shows the pressure-temperature trances during the experiments with the fine sand and UB sediment samples, respectively. CO2 hydrate in the fine sand sample started to dissociate at 5◦ C, 2.25

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Figure 4. Temperature and pressure conditions of CO2 hydrate in UB natural sediment sample during 1st heating, 2nd cooling and 3rd heating procedures.

MPa during 1st heating process, in which the pressuretemperature trance (or PT trace) followed the phase boundary of pure CO2 hydrate in a bulk condition (or bulk phase boundary). As expected, CO2 hydrates formed in find sand sample did not experience any capillarity effect due to the large enough pore sizes larger than 1 µm. This is consistent with with an earlier work (Kwon et al., 2008), confirming the validity of our experimental procedures and measurements. While the dissociation conditions of CO2 hydrate in fine sand sample was indistinguishable to those of pure CO2 hydrate, the dissociation of CO2 hydrate in the natural UB sediment started at 5.6◦ C, 2.8 MPa which was at a lower temperature than the bulk phase boundary. Natural UB sediment showed a pronounced capillary effect depressing the melting point of CO2 hydrate in fine-grained sediments. 3.2

Capillary effect of fine-grained sediments on dissociation behavior of CO2 hydrate

Association of water molecules with mineral surfaces in the fine-grained sediments becomes dominant in small pore sizes, which lowers the water activity and leads to the depression of melting temperature of ice crystals. Such melting temperature depression has been widely observed in ice melting or water freezing in fine-grained sediments. Likewise, due to the decreased water activity by capillarity in small pores, CO2 hydrate equilibrium condition was inhibited in fine-grained sediments with the melting temperature depression, as shown in Figure 4. The depression of melting temperature (Tdep ) in porous media from bulk conditions (Tbulk ) can be estimated by GibbsThomson equation (e.g., Anderson et al., 2003; Kwon et al., 2008):

where γhw is the surface tension between CO2 hydrate and water, mh is the molar mass of the CO2 hydrate,

Figure 5. Shift of phase boundaries of CO2 hydrate in small pore sizes (calculated from Gibbs-Thomson equation) and dissociation behavior of CO2 hydrate in natural UB sediment.

Figure 6. Pore size distribution of natural UB sediment analyzed by mercury intrusion porosimetry.

ρh0 is the density of CO2 hydrate, and Lf is the latent heat of dissociation of CO2 hydrate. In this study, Tdep were calculated using previously reported data: γhw = 0.030 N/m, mh = 174 g/mol, ρh0 = 1065 kg/m3 , and Lf = 65.2 kJ/mol (Anderson et al., 2003; Kwon et al., 2008). The phase boundaries considering the melting point depression (Tdep ) by different pore sizes were superimposed with the bulk phase boundary in Figure 5. It appeared that the hydrate-containing pore size of the natural UB sediment was in the range of ∼50–70 nm. This implies that CO2 hydrate formation and dissociation in fine-grained sediments is affected by capillarity while those in coarse-grained sediments may not be affected. Figure 6 shows the pore size distribution of the natural UB sediment measured by the mercury intrusion porosimetry (MIP). The MIP results showed that the pore size of the natural UB sediment ranged from 10 nm to 10 µm. Whereas, our experimental data (Figure 5) indicated that the hydrate-containing pores sized ∼50–70 nm. This implies the preferential formation of

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CO2 hydrate in small pores of fine-grained sediments. This was possibly attributed to the initial location of water when hydrates were nucleated, as water favors small pores in partially water-saturated conditions due to the capillarity.

ACKNOWLEDGMENTS This work was partially supported by This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (No.20152520100760).

REFERENCES Anderson, R., Llamedo, M.,Tohidi, B. & Burgass, R. W. 2003. Experimental measurement of methane and carbon dioxide clathrate hydrate equilibria in mesoporous silica. The Journal of Physical Chemistry B, 107, 3507–3514. Bergman, P. D. & Winter, E. M. 1995. Disposal of carbon dioxide in aquifers in the US. Energy Conversion and Management, 36, 523–526. Kim, H.-S., Cho, G.-C. & Kwon, T.-H. 2013. Effect of CO2 hydrate formation on seismic wave velocities of finegrained sediments. Geochemistry, Geophysics, Geosystems, 14, 1787–1799. Kwon, T.-H., Kim, H.-S. & CHO, G.-C. 2008. Dissociation behavior of CO2 hydrate in sediments during isochoric heating. Environmental science & technology, 42, 8571– 8577.

Lee, J. H., Kim, H. & Choi, S. C. Effects of phase-equilibrium temperature and pressure on the thickness decision of a methane hydrate container. Key Engineering Materials, 2007. Trans Tech Publ, 2782–2785. Lee, S., Liang, L., Riestenberg, D., West, O. R., Tsouris, C. & Adams, E. 2003. CO2 hydrate composite for ocean carbon sequestration. Environmental Science & Technology, 37, 3701–3708. Makogon, Y., Holditch, S. & Makogon, T. 2007. Natural gashydrates—A potential energy source for the 21st Century. Journal of Petroleum Science and Engineering, 56, 14–31. Shahnazar, S. & Hasan, N. 2014. Gas hydrate formation condition: Review on experimental and modeling approaches. Fluid Phase Equilibria, 379, 72–85. Sloan, E. D. 1998. Gas hydrates: review of physical/chemical properties. Energy & Fuels, 12, 191–196. Sloan JR, E. D. & Koh, C. 2007. Clathrate hydrates of natural gases, CRC press. Tohidi, B., Anderson, R., Clennell, M. B., Burgass, R. W. & Biderkab, A. B. 2001. Visual observation of gas-hydrate formation and dissociation in synthetic porous media by means of glass micromodels. Geology, 29, 867–870. Tohidi, B., Yang, J., Salehabadi, M., Anderson, R. & Chapoy, A. 2010. CO2 hydrates could provide secondary safety factor in subsurface sequestration of CO2. Environmental science & technology, 44, 1509–1514. Uchida, T., Ebinuma, T., Takeya, S., Nagao, J. & Narita, H. 2002. Effects of pore sizes on dissociation temperatures and pressures of methane, carbon dioxide, and propane hydrates in porous media.The Journal of Physical Chemistry B, 106, 820–826. Uchida, T., Takeya, S., Chuvilin, E. M., Ohmura, R., Nagao, J.,Yakushev, V. S., Istomin, V. A., Minagawa, H., Ebinuma, T. & Narita, H. 2004. Decomposition of methane hydrates in sand, sandstone, clays, and glass beads. Journal of Geophysical Research: Solid Earth, 109.

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Experimental and numerical studies on geomechanical behavior of various gas hydrate-bearing sediments in China X.G. Xie & Y.F. Leung The Hong Kong Polytechnic University, Hong Kong, China

S. Uchida Rensselaer Polytechnic Institute, New York, USA

J.S. Lu, D.L. Li & D.Q. Liang Guangzhou Institute of Energy Conversion, Guangzhou, China

ABSTRACT: Gas hydrates exist in pores as a solid, bonding surrounding soil grains together and also densifying the host sediments. As a result, hydrate-bearing sediments exhibit stiffer, stronger and more dilatant behavior than hydrate-free sediments. This paper presents experimental and numerical studies to capture these features of the geomechanical behavior of hydrate-bearing sediments. The experimental data includes triaxial tests on reconstituted soils of South China Sea and synthetic samples of carbon dioxide hydrate-bearing soils, while the critical state-based soil constitutive model is calibrated using an optimization-based technique. The results show that the critical state-based model is capable of predicting shearing response of the hydrate-bearing sediments under different confining stresses, drainage conditions and degrees of hydrate saturation. It is also found that the influence of gas hydrates manifests itself mainly through enlargement of the initial yield surface. The corresponding model parameters are presented for the host sediments in China, which can be adopted for the simulation of future gas exploration and gas production in China.

1

INTRODUCTION

Gas hydrate is a crystalline formed by the intrusion of gas (e.g. methane or carbon dioxide) into water under high pressure and low temperature. These conditions are often found in deep offshore or permafrost regions, where gas hydrate-bearing sediments are formed. Compared with hydrate-free sediments, higher strength, stiffness and dilatancy can be observed in hydrate-bearing samples due to grainbonding and/or pore-filling effects (Masui et al. 2005, Masui et al. 2007, Miyazaki et al. 2011, Hyodo et al. 2013). As a result, it is difficult to accurately predict the geomechanical behavior of gas hydratebearing sediments. The importance of investigating the geomechanical behavior of the sediments has been highlighted by the large deformations around the well encountered in several field-scale gas production tests from gas hydrate-bearing sediments (Dallimore et al. 2008, Yamamoto et al. 2014, Schoderbek et al. 2013). In recent years, China has invested heavily on gas hydrate-related researches. It is estimated that China has over 200 billion tonnes of oil equivalent (TOE) reserves of methane hydrate deposits, 35% of which reside in South China Sea region, with the rest in permafrost regions of Tibetan plateau and Heilongjiang Province (Wang et al. 2010). In South China Sea alone,

the reserve amounts to half of the sum of petroleum and natural gas in the mainland (Geng 2012). Cores had been drilled in northern South China Sea in 2007 and 2013, while in-situ methane hydrate-bearing samples have been retrieved at Tibetan plateau in 2009. The first part of this paper presents undrained triaxial compression tests on hydrate-free and methane hydrate-bearing samples of South China Sea sand. Subsequently, a brief description of the critical statebased soil model is presented. The model is incorporated into an optimization-based calibration approach, which allows determination of the critical state parameters. The approach is also applied to tests conducted by other Chinese researchers, and the favorable comparisons between experimental data and simulation results demonstrate that the critical state-based model is applicable to both methane and carbon dioxide hydrate bearing sediments. 2 TRIAXIAL EXPERIMENT ON RECONSTITUTED SAMPLES FROM SOUTH CHINA SEA 2.1 Apparatus The depth of the gas hydrate stability zone in South China Sea extends to 1200–2300 m from sea surface

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sample preparation process is introduced as follows. First, the sand was mixed with a predetermined amount of water to achieve targeted degrees of hydrate saturation (Sh ). Second, the moist sand was put into a mold, 50 mm in diameter and 100 mm in height, covered by 1 mm thick rubber membrane. Third, in order to let the hydrate-free sample stand by itself, the sample was vacuumed from the top and covered. Fourth, the cell pressure and the back pressure were gradually increased as pressurized methane gas was injected into the inner cell. The cell pressure was kept 3 MPa higher than the back pressure (i.e. gas pressure) during the gas injection process, and the back pressure was eventually increased to 12 MPa. Fifth, when pressurization was completed, temperature of the confining fluid in the cell was lowered to 275 K so that the desired temperature and pressure conditions to form methane hydrate were fulfilled. Finally, the back pressure and temperature were kept constant for 24 hours to ensure that all the water in pores to react with the methane gas. In other words, after 24 hours the pores of the sample was filled with either formed hydrate or gas (no water). The degree of hydrate saturation was calculated assuming that one floating CH4 molecule is caged in 6 H2O molecules (i.e. n = 6 in CH4·nH2O). Three samples were prepared: one is hydrate-free specimen and the two hydrate-bearing specimens with hydrate saturations of 36% and 42%.

Figure 1. Triaxial apparatus used in this study.

Figure 2. Schematic diagram of the apparatus used in this study. (1) computer; (2) confining fluid thermostatic tank; (3) data logger; (4) vacuum pump; (5) circulation pump; (6) load cell; (7) specimen; (8) buffer tank; (9) methane gas; (10) water pump for inner cell; (11) gas pump; (12) confining pressure pump; (13) hydraulic oil pump for axial load.

and approximately 100 m from seabed (Trung 2012, Wu et al. 2008), where the pressure is over 10 MPa, temperature is around 275 K (Wu et al. 2005), and the effective stresses is in the range of 1 MPa. In order to simulate these pressure and temperature conditions, a triaxial apparatus that could sustain high pressure and provide low temperature during shearing is assembled at the Guangzhou Institute of Energy Conversion, China. The cell of this apparatus could resist a pressure up to 30 MPa while the loading arm capacity is 250 kN. The apparatus is also equipped with a thermostatic tank which controls the temperature of the confining fluid from 243 K to 323 K with an accuracy of 0.5 K, by circulating 50% ethylene alcohol solution. Synthesized hydrate-bearing samples can be formed and sheared within the same chamber. Possible dissociation or depressurization during transportation is thus avoided. Figure 1 shows the apparatus and Figure 2 shows the schematic diagram of the test setup. 2.2

Sample preparation

Sand from gas hydrate-bearing layer in South China Sea was used as host sediments in this study and partial water saturation (PWS) method was adopted to form methane hydrate within sediment pores. The

2.3 Triaxial compression test results In the three tests, cell pressure was 15 MPa while the gas pressure was 12 MPa, keeping the effective confining pressure σc′ to be 3 MPa. The temperature inside the cell was kept at 275 K during shearing. A constant strain rate of 0.2%/min was adopted. Figure 3 presents the development of deviator stress with axial strain. It can be seen that the existence of hydrate strengthened the sediments by approximately three times for Sh = 36 % and four times for Sh = 42 % sample, respectively. The hydratebearing samples also showed increase in the stiffness. The hydrate-bearing specimens are associated with more dilatant behavior upon shearing, as shown by the strain-softening response post-peak. These corroborate the previous findings of geomechanical behavior of gas hydrate-bearing sediments by Masui et al. (2005), Masui et al. (2007), Miyazaki et al. (2011), Hyodo et al. (2013), etc. 3

METHANE HYDRATE CRITICAL STATE MODEL

Uchida et al. (2012) developed the methane hydrate critical state (MHCS) model based on the critical state framework (Roscoe et al. 1958, Roscoe & Burland 1968) and the model is able to capture the essence of geomechanical behavior of hydrate-bearing sediments. The main features of the model are: (a) to incorporate the strength increase due to hydrates

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where u is the material parameter that incorporates pre-yield plasticity. The fourth feature (d) leads to addition of the hydrate effect on the elastic stiffness as

where K ′ is the soil bulk modulus which is function of the mean effective stress in the critical state framework, ν is the Poisson’s ratio, Eh0 is the material property that determines the effect of hydrate on stiffness. Therefore, in addition to the conventional critical state model, the MHCS model employs four hydrate-dependent parameters (α, β, m andEh0 ) and one hydrate-free parameter (u). 4

MODEL CALIBRATION

4.1 Testing database Figure 3. Triaxial test result on methane hydrate bearing South China Sea sand.

by enlarging the yield surface of the hydrate-free sediments, which implicitly leads to the increase in dilatancy; (b) to capture shearing-induced degradation effect of mechanical contribution from hydrates; (c) to exhibit smooth transition from linear elastic to plastic behavior; and (d) to include the effect of hydrates on the elastic stiffness. The first and third features lead to modification of the conventional critical state yield function (Roscoe & Burland 1968) such that:

where f is the yield function, q is the deviator stress, M is the stress ratio at the critical state, p′ is the mean effective stress, p′cs is the yield stress for hydrate free specimens, R is the subloading ratio (described later) and p′cd is the strength and dilatancy enhancement due to hydrates, which is defined as:

where α and β are model parameters and Shmec is the mechanical hydrate saturation. This mechanical hydrate saturation is utilized to represent the second feature (b) such that:

p

where ǫd is the plastic deviatoric strain and m is the material parameter that determines the relationship between the degradation effect and the plastic deviatoric strain. The subloading ratio is introduced in Eq. (1) for the third feature (c) , and its form was first suggested by Hashiguchi (1989), with its evolution given by:

In order to simulate the experiments on hydratebearing sediments in China, a database is established consisting of the results shown in Figure 3 and triaxial compression tests by other Chinese researchers reported in the literature. The database includes tests on both methane and carbon dioxide hydrate-bearing soils. Details of these experiments are listed in Table 1. 4.2

Calibration method

As stated in Section 3, the parameters of MHCS model can be classified into two groups, hydrate-free parameters {M , λ, κ, ν, pcs , u} and hydrate-dependent parameters {m, Eh , α, β}. For each study listed in Table 1, hydrate-free parameters are calibrated with hydratefree specimens (Sh = 0) before hydrate-dependent parameters are derived based on hydrate-bearing specimens. The calibration process is essentially an optimization problem, whose target is to obtain the ‘optimal’ set of MHCS model parameters that would lead to minimum differences between the experimental data and the simulated curve. In this study, one of the most efficient optimization methods, Differential Evolution (DE) (Storn & Price 1997), is adopted to find this best set of parameters. DE is a derivative-free optimization technique and is conceptually similar to other evolutionary algorithms such as genetic algorithm. In the DE optimization process, a population of N candidate solutions is first generated randomly (Section 4.2.1). The candidate solutions are vectors of MHCS parameters, known as trial vectors. The algorithm then explores the search space by vector difference of the various candidate solutions. At each iteration or generation, ‘mutant vectors’ are formed by linear interpolation or extrapolation of trial vectors randomly selected from the population. A new generation of trial vectors is then formed by the ’crossover’ process, whereby the components of mutant vectors are mixed with those of the trial vectors in the previous generation (Section 4.2.2).

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Table 1. Conducted triaxial compression tests on hydrate bearing sediments in China Hydrate type

σc′ (MPa)

Sh

Test

Specimen type

Reference

Methane

3 1, 2, 4 1, 1.5, 2

0, 36, 42% 0, 16, 36, 56% 0, 20, 37, 51%

Undrained

Gas saturated Water saturated Water saturated

This study Sun et al. (2013) Wei et al. (2011)

Carbon dioxide

Drained

A new generation of trial vectors (U) is formed by the crossover of old trial vectors (X) and the mutant vectors (V):

Table 2. Parameter range for the optimization Type

Parameter

Min

Max

Hydrate free

M λ κ u ν pcs (MPa) m Eh0 (GPa) α (MPa) β

1.0 0.1 0.001 1.0 0.10 3 1 0.01 1 0.1

1.7 0.4 0.3 5.0 0.40 20 50 10. 200 5.0

Hydrate dependent

where Cr (0 < Cr < 1) is the crossover probability. jrand is a value from 1 to 6 (the number of parameters) which ensures at least one element is from the mutant vector.

Fitness of Xi,G (parent, in generation G) and Ui,G+1 (child, in generation G + 1) are evaluated and compared through the ‘selection’ process. The fitness determines the survivability of the particular solution – the fitter solutions stay in the population, while the weaker ones will be discarded. In the current context, the fitness is defined by a cost function (Section 4.2.3). The comparison is performed for each candidate solution (i from 1 to N ), and the processes are iterated until the population converges to a global optimum solution (Section 4.2.4). The following subsections describe the details of the optimization procedures.

4.2.3 Selection The fitness of vectors Xi,G and Ui,G+1 are compared through a cost function to determine their survivability. In simple words, the set of parameters that lead to closer match with the experimental data is the better (fitter) solution, and will remain in the population. Since only deviator stress data is available, the cost function is defined in the current study as:

4.2.1 Initialization The population size of candidate solution, N , is set to be 10 times the number of parameters to be optimized (Storn & Price 1997). In this study, 6 hydrate-free parameters are considered, and therefore a population consisting of 60 trial vectors {X1 , X2 , . . ., X60 } is randomly generated. In this process, the upper and lower bounds must be specified and their values are summarized in 4.2.2.

where c is the number of cases (with different confining stresses or hydrate saturations) considered. C1 (X) and C2 (X) indicate the differences between experimental and simulation curves. C1 (X) is the error of deviator stress curve and C2 (X) is the deviation of the slope of deviator stress curve concerned. C(X) is compared with C(U) and the vector that leads to the lower cost C will stay in the population while the other one is discarded.

4.2.2 Mutation and crossover To form a mutant vector (Vi ), three different trial vectors need to be randomly selected from the population (Xr0 , Xr1 and Xr2 ). The difference between Xr1 and Xr2 is then scaled by a factor F through interpolation or extrapolation, and the scaled difference is added to Xr0 to become the mutant vector. Mathematically, this process is expressed as:

4.2.4 Convergence In this study, when the populations have converged to the same solution (i.e. X1 = X2 = · · · = X60 ), the optimization is complete. The resulting solution is the calibrated parameter set that produces the closest match with experimental data. 4.3

Calibration results and discussions

Table 3 summarizes the calibrated parameters obtained from the optimization. The average value of each

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Table 3. MHCS parameters from optimization This study

Sun et al. (2013)

Yan et al. (2012)

Wei et al. (2011)

M λ κ u v pcs (σ3′ ) (MPa)

1.7 0.37 0.007 1.8 0.10 14.5

1.7 0.4 0.017 4.6 0.1 9.0 (1) 14.1 (2) 15.0 (4)

1.15 0.1 0.002 2.3 0.1 3.0 (1) 3.1 (2) 3.2 (3)

1.23 0.4 0.009 3.7 0.4 3.0 (1) 4.6 (1.5) 7.3 (2)

m Eh0 (GPa) α (MPa) β ∧ C1F # C1B

2 10 183 1.1 2% 16%

30 4 29 0.9 5% 13%

4 10 32 0.6 3% 9%

1 1 11 0.9 2% 9%

Parameters

ˆ Average C1 for hydrate free specimens # Average C1 for hydrate bearing specimens

Figure 4. Triaxial compression test on South China Sea sand (this study).

C1 is also presented. Compared to the experimental data, the model results in less than 5% deviation for hydrate-free specimens and less than 16% deviation for hydrate-bearing specimens. Figure 4 to Figure 7 show the comparisons between experimental data and model simulations. The results clearly demonstrate that the MHCS model, which is simple extension of the critical state model, can capture the essence of the geomechanical behavior of methane hydrate-bearing sediments. It is also worth noting that although the MHCS model was developed for methane hydratebearing sediments, it is also applicable to carbon dioxide hydrate-bearing sediments.

Figure 5. Triaxial compression test by Sun et al. (2013) and MHCS simulation.

5

CONCLUSIONS

This paper presents triaxial tests conducted on methane hydrate-bearing soil, synthesized with sands recovered from South China Sea. Under the same effective confining pressure, the stiffness and peak strength are found to increase with increasing degrees of hydrate saturation. Strain-softening behavior is also observed in the gas hydrate-bearing specimens.

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Figure 6. Triaxial compression test by Yan et al. (2012) and MHCS simulation.

A global optimization method, DE, was adopted in the study to verify the applicability of the MHCS model. Favorable matching was achieved, even though the model only introduces 4 hydrate-dependent parameters and 1 hydrate-free parameter in addition to the conventional critical state model parameters. Moreover, the study shows that the model can be applied to represent the behavior of carbon dioxide hydrate

Figure 7. Triaxial compression test by Wei et al. (2011) and MHCS simulation

bearing-sediments. The good comparisons between model simulations and tests from various sources demonstrate the generality of the model. ACKNOWLEDGEMENTS The authors would like to acknowledge the financial supports from the Hong Kong PhD Fellowship

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Scheme, Rensselaer Polytechnic Institute Junior Faculty Startup Fund, Chinese Academy of Science (Grant No. KGZD-EW-301), National Oceanic Geological Special Project (Project No. GHZ2012006003) and National Natural Science Foundation of China (Grant No. 41276043, 51474197). REFERENCES Dallimore, S.R., Wright, J.F., Nixon, F.M., & Schlumberger, K.K. (2008). Geologic and porous media factors affecting the 2007 production response characteristics of the JOGMEC/NRCAN/AURORA Mallik Gas Hydrate Production Research Well. In Proceedings of the 6th International Conference on Gas Hydrates. Vancouver. Geng, W.H. (2012). Combustible ice’s commercial exploration timetable. Land and Resources Information, 2012(7), 23–25. Hashiguchi, K. (1989). Subloading surface model in unconventional plasticity. International Journal of Solids and Structures, 25(8), 917–945. Hyodo, M., Yoneda, J., Yoshimoto, N., & Nakata, Y. (2013). Mechanical and dissociation properties of methane hydrate-bearing sand in deep seabed. Soils and Foundations, 53(2), 299–314. Masui, A., Haneda, H., Ogata, Y., & Aoki, K. (2005). Effects of methane hydrate formation on shear strength of synthetic methane hydrate sediments. In Proceedings of the Fifth International Offshore and Polar Engineering Conference ISOPE. Seoul. Masui,A., Haneda, H., Ogata,Y., &Aoki, K. (2007). Mechanical properties of sandy sediment containing marine gas hydrates in deep sea offshore Japan. In Proceedings of the seventh International Offshore and Polar Engineering Conference ISOPE Ocean Mining Symposium. Lisbon. Miyazaki, K., Masui, A., Sakamoto, Y., Aoki, K., Tenma, N., & Yamaguchi, T. (2011). Triaxial compressive properties of artificial methane-hydrate-bearing sediment. Journal of Geophysical Research: Solid Earth, 116(B6), B06102. Roscoe, K.H., Schofield, A.N., & Wroth, C.P. (1958). On the yielding of soils. Geotechnique, 8(1), 22–53. Roscoe, K.H. & Burland, J.B. (1968). On the generalized stress-strain behavior of wet clays. Engineering Plasticity (p. 535-609). Cambridge University Press.

Schoderbek, D., Farrell, H., Hester, K., Howard, J., Raterman, K., Sipngarmlert, S., Martin K., Smith, B., & Klein, P. (2013). ConocoPhillips gas hydrate production test final technical report. United States Department of Energy. Storn, R. & Price, K. (1997). Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11(4), 341–359. Sun, Z.M., Zhang, J., Liu, C.L., Zhao, S.J., & Ye, Y.G. (2013). Experimental study on the in situ mechanical properties of methane hydrate-bearing sediments. Applied Mechanics and Materials, 275, 326–331. Trung, N.N. (2012). The gas hydrate potential in the South China Sea. Journal of Petroleum Science and Engineering, 88, 41–47. Uchida, S., Soga, K., & Yamamoto, K. (2012). Critical state soil constitutive model for methane hydrate soil. Journal of Geophysical Research: Solid Earth, 117(B3), B03209. Wang, Z.M., Qu, H.L., & Jian, Z.J. (2010). Combustible ice’s distribution and development status in China. Energy Conversion, 334(5), 4–5. Wei, H.Z., Yan, R.T., Chen, P., Tian, H.H., Wu, E.L., & Wei, C.F. (2011). Deformation and failure behavior of carbon dioxide hydrate-bearing sands with different hydrate contents under triaxial shear tests. Rock and Soil Mechanics, 32(Supp. 2), 198–203. Wu, N.,Yang, S., Zhang, H., Liang, J., Wang, H., Su, X., & Fu, S. (2008). Preliminary discussion on gas hydrate reservoir system of Shenhu Area, North Slope of South China Sea. In Proceedings of the 6 th International Conference on Gas Hydrates. Vancouver. Wu, S. G., Zhang, G. X., Huang, Y. Y., Liang, J., & Wong, H. K. (2005). Gas hydrate occurrence on the continental slope of the northern South China Sea. Marine and Petroleum Geology, 22(3), 403–412. Yamamoto, K., Terao, Y., Fujii, T., Terumichi, I., Seki, M., Matsuzawa, M., & Kanno, T. (2014). Operation overview of the first offshore production test of methane hydrates in the Eastern Nankai Trough. In Offshore Technology Conference. Houston. Yan, R.T., Wei, C.F., Wei, H.Z., Tian, H.H., & Wu, E.L. (2012). Effect of hydrate formation on mechanical strength of hydrate-bearing sand. Chinese Journal of Geotechnical Engineering, 34(7), 1234–1240.

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A new software collection for 3D processing of X-ray CT images S. Chauhan, W. Rühaak & I. Sass Technische Universität Darmstadt, Institut für Angewandte Geowissenschaft, Fachgebiet, Angewandte Geothermie, Darmstadt Deutschland

H. Anbergen, A. Kabdenov, M. Freise & T. Wille APS Antriebs-, Prüf- und Steuertecknik GmbH, Rosdorf, Germany

ABSTRACT: The identification of accurately segmented phases in images observed through X-ray microcomputer tomography (XCT) is vital towards characterizing uncertainties involved in determining the geometries of pore network. Currently popular methods such as histogram, thresholding which are commonly used for XCT image segmentation exhibit a number of shortfalls. In this paper a new software is proposed, which is based on machine learning (ML) techniques, for the 2D/3D visualization of XCT data. The segmentation and classification of different phases are based on feature vector selection. Hence relative porosities and trends in pore size distribution can be computed. In this study, the computational performance is optimised using correlation-based feature vector selection, demonstrated using unsupervised, supervised and ensemble ML techniques. Furthermore, accuracies of ML techniques are accessed based on entropy, purity, and receiver operation characteristics.

1

INTRODUCTION

The APS GmbH is developing a new triaxial testing system for methane hydrate research. Embedded in the latest research project “SUGAR 3” a high-pressure triaxial system is equipped with high-resulution X-ray computer tomography (XCT). In order to get most accurate results, a new software solution was developed that analyses objectively obtained XCTimages. This software solution was developed in cooperation between APS and the Institute of Applied Geothermal Science of the Technische Universität Darmstadt. Accurate segmentation of the phases from the XCT rock images are the main building block for a reliable prognosis of the transport processes, elastic and electric properties; simulated using digital rock physics (DRP) models (Fusseis et al., 2014; Chauhan et al., 2016;). The segmentation problem is reduced to the need to quantify the binary solid–void phase distribution (i.e., a binarization problem) when modelling fluid transport at the pore scale. However, Leu et al. (2014) recently performed a sensitivity study in which they showed that even a small bias in the accuracy of the binarization may lead to a significant error in the calculated permeability. Binarization is an essential prerequisite of DRP studies, but there are few accurate and fast binarization algorithms that are not biased by manual (subjective) interventions by the user. Choosing an appropriate scheme to binarize an image is key to characterizing a porous space with a good degree of

accuracy and therefore decreasing the magnitudes of the uncertainties involved in determining the geometries of pore networks (Chauhan et al., 2016). Machine learning (ML) techniques provide a promising alternative to segment and classify different voxel phases from XCT rock images. The software tool we propose used unsupervised, supervised and ensemble classifier techniques to extract relative porosity and pore size distribution 3D XCT gray scale images. The study validated the accuracy and performance of these ML techniques. 2

EXPERIMENTAL APPROACH

For this study we used a volcanic rock Andesite and Rotliegend Sandstone taken from Tongariro National Park, New Zealand and Rotliegend Germany Shown in Figure. 1.Andesite has an effective porosity of 17±2 % and Sandstone of 14 ± 2% measured using a GeoPyc pycnometer (Micromeritics Instrument Corporation Norcross, GA, USA). Andesite has a porphyritic texture with large plagioclase crystals (up to 3 mm in diameter), pyroxene in a cryptocrystalline matrix, and isolated vesicles up to 6 mm in diameter (Chauhan et al., 2016). Whereas, Rotligend Sandstone had different grain size (between 0.5 to 5 mm) of fine sand and gravel, with monocrystalline quartz 26%, poly-crystalline quartz up to 35% Feldspate 8%, sedimentary volcanic lithoclast grains 9% along with and 13% cement.(Aretz et al ., 2013).

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Figure 1. Top panel shows the rock sample Andesite and Sandstone which were used for XCT. Middle panel and the bottom panel shows the raw images and histogram plots of the raw image of the respective samples. The mineral composition of Andesite and Sandstone was determined by thin sections.

The samples were imaged using a high resolution XCT scanner (Chauhan et al 2016), applying X-ray energy of 110 keV and using a pre-filter of 0.3 copper. During the reconstruction of the projections no noise filter was used. The projections were Radon-transformed in sinograms, thereafter converted through back-projection into tomograms. These stacked tomograms resulted in a 16-bit 3D imagery, with a resulting voxel resolution of 13 µm and 21 µm for Andesite and Sandstone respectively.Andesite required no beam hardening correction (BHC), whereas BHC for Sandstone was done using based on regression analysis using 2D paraboloid fitting. Finally, the tomograms are saved in raw format

Figure 2. Schematic illustration of our proposed method (Fig.2 has been modified after Chauhan et al., 2016).

3.1 Unsupervised techniques 3

MACHINE LEARNING

The graphical user interface (GUI) uses machine learning (ML) algorithms to map pixels of similar values in to respective classes. The ML algorithms implemented fall in the catogories of unsupervised, supervised and ensemble classifiers. Figure. 2. illustrates the processing scheme implemented in the GUI. The image pre-processing was done according to Chauhan et al. (2016).

In the unsupervised technique K-means (MacQueen 1967), Fuzzy C-means (FCM) (Dunn 1973) and selforganized Maps (SOM) (Kohonen 1990) were used for segmentation pore, mineral and matrix phases. The unsupervised algorithms were configured to perform segmentation of three to seven classes. These classes in one-dimensional feature space are the nonoverlapping segments of pixel bins in a histogram. Filter based feature vector selection (Euclidian and Manhattan distance function) were used to initialize

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centroids for K-means, FCM and SOM. In the case of FCM different degree of membership values [1.10 to 1.85] were tested to ‘loosely’ or ‘tightly’ segregate pixel values between mineral and matirx phase. grid topology was chosen in the case of SOM. 3.2

Supervised techniques

In the supervised category feed forward artificial neural Network (FFANN) (Jain et al., 1999) and least square support vector machine (LS-SVM) (Suykens and Vandewalle. 1999) were used to classify pore, mineral and matrix phases (Chauhan et al., 2016). The supervised algorithms rely on a classification model which has to be trained using example set of data that represent each class. In the case FFANN the classification model was trained using segmented dataset from K-means, FCM, and SOM. For LS-SVM a training data set was created, which contained range of pixel values which best represented pore, mineral, matrix and noise regions, these pixel ranges where further labelled in to different classes, which ranged from one to seven. For FFANN and LS-SVM the models were tuned using ten-fold cross-validation function (repeated training and testing) and misclassification rate was determined using mean square root error (MSE) in the case of FFANN. Once the classification model reached an optimal performance threshold it was tested on rest of the XCT slices. 3.3

Ensemble classifier techniques

In the supervised category feed forward artificial neural Network (FFANN) (Jain et al., 1999) and least square support vector machine (LS-SVM) (Suykens and Vandewalle. 1999) were used to classify pore, mineral and matrix phases (Chauhan et al., 2016). The supervised algorithm relies on a classification model which has to be trained using example set of data that represent each class. In the case FFANN the classification model was trained using segmented dataset from K-means, FCM, and SOM. For LS-SVM a training data set was created, which contained range of pixel values which best represented pore, mineral, matrix and noise regions, these pixel ranges where further labelled in to different classes, which ranged from one to seven. For FFANN and LS-SVM the models were tuned using ten-fold cross-validation function (repeated training and testing) and misclassification rate was determined using mean square root error (MSE) in the case of FFANN. Once the classification model reached an optimal performance threshold it was tested on rest of the XCT slices. 3.4

Ensemble classifier techniques

In the ensemble classifier technique RUSBoost and Bragtree algorithms are used (Seif-fert et al., 2008; Breiman, 1996) to classify pore, mineral and matrix phases (Chauhan et al., 2016). In general ensamble classifiers is a ‘bootstrap aggregation’ of different

weak classfiers. The main difference between Bragging and RUSBoost is the way they train their weak classifiers. Bragtree in an iterative scheme, train its classifiers with randomly chosen samples from the training data set, in the second step collects the misclassified instances and retrains its classifiers until the misclassification error is minimized (Chau-han et al 2016). Whereas, RUSBoost sequentially trains its classifiers using the whole training later, essentially focusing on retraining inaccurate classifiers with the large data set until its misclassification error is minimized. The ensemble classifiers where trained using same feature vector (FV) used for LS-SVM, with a minimum leaf size of five and learning rate of 0.1. 4

FEATURE REDUCTION

In a practical rock CT segmentation/classification task a set of apriori information in the form of most useful pixel values is given to ML algorithms for segmentation or training the classification model. This dataset containing apriori information is termed as feature vectors (FV). For unsupervised K-means, FCM, SOM a set of ten XCT images were used to develop the FV. For FFANN five images out of ten were used to train the net-work and LSSVM and ensemble based classifiers a set pixel values which best represented the pore, mineral, matrix and noise regions were used a feature vectors. The unsupervised m ML techniques were tested on ten slices of XCT data 31,577,290 pixels. FFANN was trained using 15,788,645 feature vectors and tested on 31,57,290 pixels. For LS-SVM bragging and boosting the classification model was trained using 2,007 feature vectors and tested on unknown data sample of 31,57,290 pixels. 5

PERFORMANCE AND ACCURACY

Computational performance was measured in terms of the segmentation and classification speed of the ML algorithms shown in table 2. Test were performed on Windows Server 2008 R2 Standard 64-bit Operating System, with two processor Intel(R) Xenon (R), CPU: E645 2.40 GHz and Installed memory (RAM) of 48.0 GB. For unsupervised techniques accuracy or cluster validation was performed to identify ideal class (es), representing the ‘best’ porosity values and to compare the clustering approaches. External validation measures ‘Purity’ and ‘Entropy’ was performed on all the pixels corresponding to the classes three to seven. The Purity and Entropy measure the ability of the clustering method to recover the know classes, despite number of classes are different from number of segementable classes (Jain et al., 1999). Purity is a real number between [0,1], larger the purity values, so better is the clustering method. Conversely, the lower the Entropy value better is the clustering performance. In the case of FFANN, an objective method to determine the classification criterial is by calculating the mean square root error (MSE) between the output and the targets. Lower the MSE value better is

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the classification, zero corresponds to no misclassification. For LS-SVM receiver operation characteristic (ROC) curve was plotted to compute the accuracy, ROC curve give the quality of the classification model. It shows a tradeoff between the sensitivity of the classification model; with respect to the specificity with which it can classify unknown data set. The area under Table 1. Computation time for processing ten slices

K-means FCM SOM FFANN(traning using K-means) FFANN(traning using FCM) LS-SVM Bragging Boosting

Andesite

Sandstone

Musli

00:15:35 00:29:19 01:07:06 08:58:18

00:12:04 00:56:03 17:35:08

0:10:59 00:42:21 01:11:23

06:35:43 63:29:35 05:57:05 07:47:05

6

RESULTS AND ANALYSIS

6.1 Esitmated porosity and pore size distribution

CPU: Time (hrs:min:sec) Machine learning Techniques

the ROC curve represents the accuracy of the classification model. The area of 1 represents a prefect classification; an area of 0.5 represents worthless classification (Khan et al., 2016). In case of Bragging and Boosting misclassification cost of the weak classifiers gave an estimate of the this was performed using Kfold cross-validation technique.

The porosities was determined from the stack of ten XCT slices for three to seven classes using different ML techniques are shown in the left panel of the Figure 3 and the segmented images are shown in Figure 4. The estimated porosity is the ratio between the pore phase voxels and entire sample volume multiplied by 100. In case of Sandstone and Musli estimated porosity was determined using unsupervised techniques whereas for Andesite all the ML techniques were used. In general, the porosity using unsupervised ML techniques agree well with each other for all the three samples. For Andesite, Sandstone and Musli, the

Figure 3. The right panel shows relative porosity using ma-chine learning algorithms for different rock samples. Middle panel shows the volume fraction of different phases quantified using machine learning techniques and the right panel show the pore size distribution of different sample using watershed technique.

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averaged estimated porosity sum over all classes is 15.8 ± 2.5%, 14.8 ± 8.8% and 50.9 ± 13.3% respectively. This is in good agreement to the experimental porosity values obtained for Andesite and Sandstone using GeoPycpynometer. The large standard deviation in the case of Sandstone and Musli is caused by FCM segmentation scheme. When the membership function is tightly constrained [1.10, 1.35] the segregation between pore phase voxels and pore throat voxels is underestimated contributing to the increase in porosity. Conversely, when membership function loosely constrained [1.60, 1.85] pore throat and micro pores are segmented as matrix phases resulting in decrease in porosity and increase in matrix phase, which is clearly visible in volume fraction plot of Sandstone and Musli in the middle panel. The low standard deviation in the estimated porosity values of Andesite is due to the absence of micro porosity and interconnected pores. The pore, mineral and matrix phases are distinct from each other therefore the ML techniques have less difficult in segmentation and classification Pore size distribution (PSD) of Andesite, Sandstone and Muli was computed using the method suggested by Rabbani et al., (2014). The segmented gray scale images where first converted to binary images using thresholding technique. Morphological and filtering operations were performed based on the complexity of the segmented images. Distance transform to convert the bright area into catchment basin and later watershed transformation was performed to segment the pore boundaries. The bottom panel in the Figure 3. Show the PSD and average pore radius of Andesite, Sandstone and Musli from K-means segmented images. 6.2 Performance and accuracy The performance was evaluated based on processing time, where, K-means was the fastest and LS-SVM the slowest. Accuracy was computed for Andesite sample only shown in Figure 5. Entropy values of unsupervised techniques, means square root error (MSE) and receiver operational characteristics (ROC) of supervised techniques (FFANN and LS-SVM respectively) are shown in figure.5. Lowest entropy values are shown by K-means and SOM for classes three and four. This agrees well with the histogram plot in figure 1. Therefore, the porosity values obtained from class three and four are best representative porosity values of Andesite. In the case of FFANN the misclassification rate can be estimated by MSE values. The lowest MSE value implies better is the classification accuracy. FFANN was trained using segmented image of K-means and FCM and then was tested on raw images of Andesite sample. The best classification rate was obtained when FFANN was trained with Kmeans (0.02; for class three) and worst when trained using FCM (1.35; for class seven). ROC values for LS-SVM show that, LS-SVM is able to classify pore phases and matrix with 100% accuracy. Whereas, it is able to differentiate between mineral and matrix phase up to 70%.

Figure 4. The top, middle and last panel shows the 2D segmented images and volume rendered plot of respective samples using unsupervised networks (Andesite figure has been modified after Chauhan et al 2016).

7

CONCLUSIONS

We propose a software tool to visualize and analyses 3D high resolution x-ray computer tomographic (XCT) rock images. The software tool is based on unsupervised, supervised and ensemble machine learning (ML) techniques. In this study we have evaluated the performance and accuracies of the ML techniques to compute relative porosity and pore size distribution in Sandstone (inter connected pores), Musli (micro porosity) and Andesite (alterated minerals) rock samples. The relative porosity values of 15.8 ± 2.5%, 14.8 ± 8.8% and 50.9 ± 13.3% for Andesite, Sandstone and Musli are in very good agreement with the experimental values of 17 ± 2 and 14 ± 2 obtained using GeoPycpynometer.

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Figure 5. top left show the entropy values obtained for Andesite sample segmented using unsupervised techniques. Top right show mean square root error obtained for Andesite sample classified using feed forward artificial neural network (FFANN). The FFANN was trained using k-means, Fuzzy C-means with membership function [1.10, 1.85]. The bottom panel shows the receiver operational characteristics of LS-SVM for classified class four.

In terms of computational time, K-means outperforms all the other ML techniques. Fuzzy c.means can distinguish well between pore and pore-throat boundaries- when the membership function is loosely constrained between 1.60–1.85. Unsupervised ML techniques perform well with filter based feature extraction techniques. We found that different tuning parameters (such as different FCM membership criteria and different SOM topologies and distance functions) need to be tested for the unsupervised techniques. A SOM topology “gridtop” layout (neurons arranged in a grid format), and a SOM Manhattan distant function (sum of the absolute difference) gave consistent results and FCM membership function between [1.35–1.85] gave consistent results. In the case of supervised techniques feed forward neural networks when trained with K-means feature vectors contributed to less misclassification error of 0.16 compared to using FCM feature vectors; which gave a misclassification error of 0.36. The LS-SVM, bragging, and boosting, are driven by feature vectors that are manually selected, and performed extremely well despite a small subset of feature vectors where chossen to train the classification model. But in terms of computational time LS-SVM performed the worst.

REFERENCES Aretz, A., Bär, K., Götz, A. E., & Sass, I. (2015). Outcrop analogue study of Permocarboniferous geothermal sandstone reservoir formations (northern Upper Rhine Graben, Germany): impact of mineral content, depositional environment and diagenesis on petrophysical properties. International Journal of Earth Sciences, 1–22. Breiman, L. (1996). Bagging predictors. Machine learning, 24(2), 123–140. Chauhan, S., Rühaak, W., Khan, F., Enzmann, F., Mielke, P., Kersten, M., & Sass, I. (2016). Processing of rock core microtomography images: Using seven different machine learning algorithms. Computers & Geosciences, 86, 120– 128 Dunn, J. C. (1973). A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters. Journal of Cybernetics, 3, 32–57. Jain, A. K., Murty, M. N., Flynn, P. J. (1999). Data clustering: a review. ACM computing surveys, 31(3), 264–323. Kohonen, T. (1990). The self-organizing map. Proceedings of the IEEE, 78(9), 1464–1480. MacQueen, J. (Ed.). (1967). Some Methods for classification and Analysis of Multivariate Observations. University of California Press. Suykens, J. A., Vandewalle, J. (1999). Least Squares Support Vector Machine Classifiers. Neural Pro-cessing Letters, 9(3), 293–300.

ACKNOWLEDGEMENTS The project was funded by the Federal Ministry of Education and Research (grant no. 03SX381H). The sole responsibility for the contents lies with the authors

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Predicting deformation of MHBS during hydrate dissociation using a state-dependent critical state model J. Shen, C.F. Chiu, G.H. Lei & J. Xu Key Laboratory of Geomechanics and Embankment Engineering of the Ministry of Education, Hohai University, China

C.W.W. Ng Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, HKSAR, China

ABSTRACT: Methane Hydrate-Bearing Sand (MHBS) is a natural soil deposit containing methane hydrate in its pores, which occurs in abundance in deep water marine sediments and permafrost regions. Submarine landslides may be induced by methane hydrate extraction in deep water. Thus, it is crucial to evaluate the mechanical behaviour of MHBS during hydrate dissociation. In this paper, a recently developed state-dependent critical state model for MHBS was further extended to predict the effect of hydrate dissociation on volume change and axial deformation of MHBS. In the formulation, the volume change of MHBS was derived as a combined action of the change in stress, hydrate saturation and temperature. However, the axial deformation is only affected by the change in stress and hydrate saturation. The proposed model was used to predict the laboratory hydrate dissociation tests induced by the thermal recovery method reported in Hyodo et al. (2013). It is found that despite some discrepancies the model predictions can capture some key deformation features of MHBS during hydrate dissociation. In particular, shear failure of MHBS can be predicted for specimen subjected to a high shear stress level.

1

INTRODUCTION

Methane Hydrate-Bearing Sand (MHBS) is a natural soil deposit containing methane hydrate in its pores, which occurs in abundance in deep water marine sediments and permafrost regions. MHBS is considered as a potential energy source for the future (Kvenvolden 1999). Depressurisation and thermal recovery are the two most feasible methods to extract methane from MHBS resulting in hydrate dissociation. Past studies (Masui et al. 2005, Miyazaki et al. 2011, Hyodo et al. 2013, Clayton et al. 2010) have shown that both the strength and stiffness of MHBS are greater than those of clean sand because hydrate may either fill the pores or form part of sand skeleton, as well as cement sand grains at inter-granular contacts. As the strength and stiffness enhancement of hydrate vanish during its dissociation in methane extraction, significant deformation of MHBS may occur leading to submarine landslide and seabed subsidence (Mienert et al. 2005, Nixon & Grozic 2007). Thus, it is crucial to evaluate the deformation of MHBS during hydrate dissociation in deep water methane extraction. A state-dependent critical state model has recently developed for MHBS (Shen et al. 2016). It has been

demonstrated that the model can adequately capture the stress-strain and volume change behaviours of MHBS over a wide range of hydrate saturations, confining pressures and densities using a unified set of parameters. In this paper, the model is further extended to predict the effect of hydrate dissociation on mechanical behaviour of MHBS. 2 2.1

MODEL FORMULATION State-dependent critical state model for MHBS

The state-dependent critical state model is proposed under the frameworks of elasto-plasticity, critical state and state-dependent dilatancy. The yield criterion for MHBS in the mean effective stress (p′) – deviatoric stress (q) space (illustrated in Figure 1) is presented as follows:

where η∗ is the stress ratio at yielding, defined as η∗ = q/(p′ + pb ) and pb is a bonding strength parameter that quantifies the degree of hydrate cementing at the inter-granular contacts.

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defined as ψ(Sh ) = e − ec (Sh ), e and ec (Sh ) are the current void ratio and void ratio at the critical state, respectively for a given confining pressure and Sh , d0 , m and mb are three model parameters. According to the studies of cemented sand (Abdulla and Kiousis, 1997), the initial bonding strength pb0 of MHBS is assumed to be the following power function of Sh :

Figure 1. Yield surface for MHBS in the p′ − q space.

Based on the theory of plasticity, the incremental stress-strain relationships in the p′ − q space are expressed as follows:

where α and β are two positive model parameters. Considering the degradation of hydrate cementing with respect to the deformation (as shown in Figure 1), a simple linear relation between the logarithmic of degradation rate of the bonding strength and the increment in the plastic shear strain is assumed as follows:

where kd is a positive model parameter.

where K and G are the elastic bulk and shear moduli of MHBS, respectively, dεev and dεeq are elastic volumetric and shear strain increments, respectively, Kp is the plastic hardening modulus, and D is the dilatancy p
p p p defined as the ratio dεv dεq (dεv and dεq are plastic volumetric and shear strain increments, respectively). According to the resonant column test results for MHBS reported in Clayton et al. (2010), the elastic shear modulus of MHBS is assumed linearly related to hydrate saturation Sh , expressed as follows

where G0 and ξ are two positive model parameters, e is void ratio and pa is the atmospheric pressure. Based on elasticity theory, the elastic bulk modulus K is equal to

where ν is the Poisson’s ratio, which is assumed to be independent of density, pressure and hydrate saturation in the model. It is evident that D of MHBS depends on both pressure and density (Hyodo et al. 2013). The following state-dependent dilatancy equation modified from Li and Dafalias (2000) is proposed:

where M (Sh ) is the critical stress ratio for MHBS for a given Sh ; ψ(Sh ) is the state parameter for MHBS,

2.2 Constitutive relations considering hydrate dissociation Klar et al. (2010) suggested that in the natural environment methane hydrate is often formed in the sand deposit after it has been consolidated to a given in-situ stresses (p′0 , q0 ). They further postulated that these insitu stresses should be considered in the stress-strain formulations of MHBS. The formulations in the p′ − q stress space can be expressed as follows:

In the derivation of stress, Klar et al. (2013) suggested that the thermo-mechanical effect should be taken into account because of the possible temperature change involved in hydrate dissociation. It is assumed that temperature change will only result in elastic volume change, and thus only mean effective stress is influenced by temperature change. This is approximately true for MHBS because experimental observations (Graham et al. 2004) showed that no significant effects of temperature were encountered in either isotropic compression or triaxial shear for sand. Under this assumption, the incremental form of Eqs. (9) and (10) can be written as

where T is temperature. It can be seen that the change in stress can be caused by change in stiffness, strain and temperature.

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The first term on the right hand side of Eq. (11) shows the change in mean effective stress resulted from the change in elastic bulk modulus, which could be caused by hydrate dissociation. As the elastic bulk modulus is a function of Sh , this term can be further expanded as follows:

The following expression is obtained by substituting Eqs. (13), (17) and (18) into Eq. (11):

The second term on the right hand side of Eq. (11) is the conventional incremental stress-strain relationship. Combining Eq. (2), this term can be further expanded as follows:

It can be seen that not only the effective stress increments (dp′ , dq) but also the internal bonding strength increment dpb are involved in the calculation of plastic volumetric strain. According to Eqs. (7) and (8), pb is a function of hydrate saturation and plastic shear strain. Considering hydrate dissociation, by combining Eqs. (7) and (8), the incremental form of bonding strength pb can be rewritten as

Substituting Eq. (15) into Eq. (3) yields

Similarly, Eq. (12) can be rewritten as

Eqs. (19) and (20) show that the deformation of MHBS can be caused by three factors: effective stress, hydrate saturation and temperature. During hydrate dissociation, hydrate saturation decreases, coupling with the increase in temperature and effective stress for thermal recovery and depressurisation methods, respectively. Therefore, the above two equations give the extended constitutive relations of MHBS considering hydrate dissociation. When the changes of the three influencing factors have been known, the deformation of MHBS during hydrate dissociation can be predicted. 3

Combining Eqs. (16) and (2), Eq. (14) can be rewritten as

The third term on the right hand side of Eq. (11)represents the influence of thermal effect on stress change. The elastic volume change of MHBS under thermal effect is assumed because of the expansion of sand and hydrate grains with the increase of temperature. This term can be given by

where βs and βh are thermal expansion coefficients of sand and hydrate, respectively.

NUMERICAL PREDICTION

The hydrate dissociation test results reported in Hyodo et al. (2013) were used to verify the extended constitutive relations of MHBS. In Hyodo’s experiments, MHBS were synthesised by injecting pressurised methane gas into unsaturated sand specimens. Then, consolidated drained triaxial tests were conducted on three MHBS specimens. All specimens were first isotropically compressed to an effective confining pressure of 5 MPa. After consolidation three different shear stresses were applied as illustrated in Figure 2. In Case 1 no shear stress was applied. In Cases 2 and 3, initial shear stress of 8 and 12 MPa were applied under drained condition, respectively. After shearing to different stress levels, hydrate dissociation was commenced under drained condition using thermal recovery method. The temperature was gradually increased from 5◦ to 20◦ , as shown in Figure 3. The axial and volumetric strains of the specimens were measured. The released methane gas was collected to calculate the change of hydrate saturation with elapsed time as shown in Figure 4. When using thermal recovery method to extract methane gas from MHBS, both the effective stress

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Table 1. Model parameters. Parameter

Symbol

Value

Elastic moduli

G0 ν ξ M eŴ λc A B a b h1 h2 n α(MPa) β kd d0 m mb βs (K −1 ) βh (K −1 )

300 0.05 1200 1.18 1.116 0.129 0.35 1.4 0.6 2.0 1.98 2.19 0.8 0.7 1.6 8 1.6 1.3 0.04 1.77 × 10−6 4.6 × 10−4

Critical state

Hardening rule Figure 2. Loading condition for three different cases (test data from Hyodo et al. 2013).

and temperature are under control. Since the effective stress and temperature has been determined, the ‘measured’ change of hydrate saturation during tests was treated as an input in our procedures to calculate the deformation of the specimens. Table 1 summarises the model parameters used in the numerical prediction of hydrate dissociation tests. Shen et al. (2016) presented the procedures to calibrate the first nineteen model parameters based on the triaxial compression test results reported in Hyodo et al. (2013). For the last two thermal expansion coefficients (βs and βh ), the values reported in the coupled numerical analysis for MHBS by Klar et al. (2013) were adopted. For the sake of simplicity, the following piecewise linear function was used to represent the variation of temperature with time during the hydrate dissociation tests as shown in Figure 3:

where t is time in hours. Likewise, as shown in Figure 4, the measured change of hydrate saturation with elasped time was also best-fitted by the following piecewise linear function:

Bonding Debonding Dilatancy Temperature

Figure 3. Variation of temperature with elapsed time (test data from Hyodo et al. 2013).

An alternative approach to predict the dissociation rate of methane hydrate is given by the following KimBishnoi equation (Kim et al. 1987): Figure 4. Variation of hydrate saturation with elapsed time (test data from Hyodo et al. 2013).

where DH is the dissociation parameter, NH is the moles of hydrate in a given volume V , NH 0 is the

moles of hydrate in the initial state, PF is the average pore pressure and Peq is an equilibrium pressure at temperatre T , defined as follows: Peq = exp (39.13 − −8533.8/T ).

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used as an input in the calculation of the deformation caused by hydrate dissociation. Figure 5 shows the predicted and measured results of hydrate dissociation tests. Through comparisons it can be found that the predictions can well describe the trend of the deformation process for all three cases. In Case 1 (no shear stress) both the measured and predicted deformations of MHBS are negligible, implying little disturbance on the sand skeleton for MHBS due to hydrate dissociation. In Case 2, the deformation of MHBS is negligible at the beginning of hydrate dissociation. As the hydrate saturation decreases below a threshold value, the deformation increases substantially. Such deformation characteristics can be well captured by the predicted results. In Case 3 (the highest applied shear stress) shear failure was observed during hydrate dissociation. It should be noted that the strength of MHBS is controlled by the hydrate saturation. When the hydrate saturation reduces to a certain value, with which the strength of MHBS is smaller than the applied shear stress, the specimen will fail. 4

Figure 5. Predicted and measured variation of axial and volumetric strains with elapsed time (test data from Hyodo et al. 2013).

The dissociation rate expressed by Eq. (23) can be written in terms of hydrate saturation as follows:

According to Eq. (24), when thermal recovery method is used to induce hydrate dissociation, temperature is the unique variable controlling the dissociation rate. Thus, the change of hydrate saturation induced by temperature recovery method can be estimated by combining Eqs. (21) and (24). The suggested value of DH for methane hydrate is 5.85 × 109 . The estimated change of hydrate saturation is shown in Figure 4. It can be seen that the estimated rate of hydrate saturation change using the suggested value is substantially faster than the measured results. It is found that the estimated change of hydrate saturation with time is consistent with the measurements by decreasing DH two orders of magnitude, i.e., 5.85 × 107 . Several reasons may contribute to the discrepancy, such as the inhibiting effect of soil grains on the hydrate dissociation, as well as the measurement delay due to the low discharge capacity of the drainage line. To avoid the above uncertainties, in this study the best-fit lines of measurements using Eq. (22) were

CONCLUSIONS

In this paper, a state-dependent critical state model for MHBS developed by Shen et al. (2016) was extended to predict the effects of hydrate dissociation on mechanical behaviour of MHBS. In the formulation, the volume change of MHBS is derived as a combined action of the change in stress, hydrate saturation and temperature. However, the shear strain is only affected by the change in stress and hydrate saturation. The extended constitutive relations were used to predict the hydrate dissociation tests reported in Hyodo et al. (2013). The model parameters were calibrated based on the triaxial compression tests. It is demonstrated that despite some discrepancies, the predictions can capture the key deformation features of MHBS during hydrate dissociation. In particular, shear failure of MHBS can be predicted under certain high shear stress level. ACKNOWLEDGEMENTS The research is financially supported by GRF 617213 and M-HKUST603/13 provided by Research Grants Council (RGC) of HKSAR and FP204 by HKUST. Grant B13024 by the 111 Project of China, grants 51578213, 51308190 and 41530637 by the National Natural Science Foundation of China, grants 2015B06014 and 2015B25914 by the Fundamental Research Funds for the Central Universities of China are also acknowledged. REFERENCES Abdulla, A.A. & Kiousis, P.D. 1997. Behavior of cemented sands-I. Testing. International Journal for Numerical & Analytical Methods in Geomechanics 21(8): 533–47.

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Clayton, C.R.I. Priest, J.A. & Rees, E.V.L. 2010. The effects of hydrate cement on the stiffness of some sands. Geotechnique 60(6): 435–45. Graham, J. Alfaro, M. & Ferris, J. 2004. Compression a strength of dense sand at high pressures and elevated temperatures. Canadian Geotechnical Journal 41(6): 1206–1212. Hyodo, M. Yoneda, J. Yoshimoto, N. & Nakata, Y. 2013. Mechanical and dissociation properties of methane hydrate-bearing sand in deep seabed. Soils and Foundations 53(2): 299–314. Kim, H.C. Bishnoi, P.R. Heidemann, R.A. & Rizvi, S.S.H. 1987. Kinetics of methane hydrate decomposition. Chemical Engineering Science 42(7):1645–53. Klar, A. Soga, K. & Ng, M.Y.A. 2010. Coupled deformation– flow analysis for methane hydrate extraction. Geotechnique 60(10):765–76. Klar, A. Uchida, S. Soga, K. & Yamamoto, K. 2013. Explicitly coupled thermal flow mechanical formulation for gas-hydrate sediments. Spe Journal 18(2):196–206. Kvenvolden, K.A. 1999. Potential effects of gas hydrate on human welfare. Proceedings of the National Academy of Sciences of the United States of America 96(7): 3420–6. Li, X.S. & Dafalias, Y.F. 2000. Dilatancy for cohesionless soils. Geotechnique 50(4): 449–60.

Masui, A. Haneda, H. Ogata, Y. & Aoki, K. 2005. Effects of methane hydrate formation on shear strength of synthetic methane hydrate sediments. In: Proceedings of the 15th International Offshore and Polar Engineering Conference p. 364–69. Mienert, J. Vanneste, M. Bünz, S. Andreassen, K. Haflidason, H. & Sejrup H.P. 2005. Ocean warming and gas hydrate stability on the mid-Norwegian margin at the Storegga Slide. Marine and Petroleum Geology 22(1): 233–44. Miyazaki, K. Masui, A. Sakamoto, Y. Aoki, K. Tenma, N. & Yamaguchi, T. 2011. Triaxial compressive properties of artificial methane-hydrate-bearing sediment. Journal of Geophysical Research 116(B6). Nixon, M.F. & Grozic, J.L.H. 2007. Submarine slope failure due to gas hydrate dissociation: a preliminary quantification. Canadian Geotechnical Journal 44(3): 314–25. Shen, J. Chiu, C.F. Ng, C.W.W. Lei, G.H. & Xu, J. 2016. A state-dependent critical state model for methane hydratebearing sand. Computers and Geotechnics 75:1–11. Uchida, S. Soga, K. & Yamamoto, K. 2012. Critical state soil constitutive model for methane hydrate soil. Journal of Geophysical Research 117(B3).

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Composite model to reproduce the mechanical behaviour of Methane Hydrate Bearing Sediments M. De La Fuente Geology & Geophysics Department, National Oceanography Centre (University of Southampton and Natural Environment Research Council), Southampton, UK

J. Vaunat Department of Civil and Environmental Engineering, Universitat Politècnica de Catalunya, Barcelona, Spain

H. Marín-Moreno National Oceanography Centre, European Way, Southampton, UK

ABSTRACT: This paper describes the fundamental hypothesis and the formulation of a new constitutive model to cope with the mechanical behaviour of methane hydrate-bearing sediments. The model is based on a composite approach that defines the mechanical response of mineral skeleton and hydrate bond network independently. The proposed model represents the transitional behaviour of MHBS by coupling two independent constitutive models under certain strain compatibility conditions and mass and energy considerations. CASM elasto-plastic critical state model has been chosen to describe the matrix response and the bonding structure follows a damage model. In order to overcome the technical challenges of natural gas production and the geotechnical problems related with its complex rheological response, the constitutive model simulates the global stress-strain response of the composite medium and allows to assess methane hydrate dissociation on the basis of the stress state and temperature prevailing locally within the hydrate component.

1

INTRODUCTION

Gas hydrates are ice-like crystalline compounds composed of low molecular weight gases trapped in a lattice of hydrogen-bonded water molecules (Sloan 1998). Current estimates indicate that gas hydrates trap more than half of the world’s total organic carbon mass and twice as much as all other fossil fuels combined (Kvenvolden, 1993), turning out to be an attractive potential future energy resource (Collett, 2002; Dallimore & Collett, 2005; Ruppel, 2007). Methane hydrate-bearing sediments (MHBS) are natural deposits that host methane hydrate inside its pore space. Methane hydrates are the most common occurring gas hydrate in nature that form under moderately high pressure and low temperature conditions. Its naturally occurrence is primarily found in permafrost regions onshore and in ocean-bottom sediments at many continental margins and slopes (Collett, 2002; Kvenvolden, 1999). One of the main challenges in gas hydrate prospecting and deposit characterization is obtaining the geomechanical properties and controlling the stability of the well during production (Moridis, Collett, Pooladi-Darvish, et al., 2011). MHBS tend to exhibit greater stiffness, strength and dilatancy due to the

presence of hydrate growing in the pores as a structuring element (e.g., Soga et al. (2006) and Waite et al. (2009)). However, it has been shown that this effect disappears when the sediment is excessively compressed or the bonds are destroyed due to shearing (Uchida et al., 2012). Furthermore, recent experimental results show that the mechanical behavior of MHBS is also strongly controlled by sediment type, stress level, hydrate morphology, and sediment history, as well as highly dependent on thermo, hydraulic and geo-chemical coupled interactions (e.g., Clayton et al., 2010; Priest et al., 2009; Sanchez et al., 2014). This paper describes a new constitutive model, inspired in frozen soils behavior, specially developed to analyze sandy methane hydrate reservoirs as these may be the first target for production in the near future (Boswell & Collet, 2006). In this work and from a soil mechanics perspective, MHBS will be understood as a complex multi-phase bonded geomaterial characterized by a highly non-linear, irreversible and path-dependent response to applied loads. The model is based on a composite approach that allows defining the mechanical response of the mineral skeleton and hydrate bond network independently and includes the effect of hydrate morphology on the composite response.

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where:

Figure 1. Schematic arrangement considered in the MHBS composite medium model and graphical definition of the volumetric variables.

2 2.1

METHANE HYDRATE BEARING SEDIMENT COMPOSITE CONSTITUTIVE MODEL Conceptual framework

In this model, MHBS are considered as a composite medium made of a sandy matrix interlocked by a homogeneously distributed network of hydrate bonds. The soil matrix is associated to the characteristics of the original pedologic formation, and its behavior is represented by a typical elastoplastic soil model (Yu, 1998). The bonding hydrate network is modeled by an elastic, suction and temperature dependent damage law, typical of quasi-brittle materials such as ice (Carol et al. 2001). 2.1.1 Topologic considerations In a reference volume, the following volumetric variables may be defined as (Fig. 1). Vt Total volume Vsm Solid volume of matrix skeleton Vb Solid volume of bond material Vm Volume of macropores (pore space between matrix grains) Vv Volume of available porosity (open voids available for fluid transfer) where the total volume is given by:

with the volume of solid phases expressed as:

and the volume of macropores as:

Equation 5 gives the restriction on volumetric strains and illustrates that, in a composite medium, the external volumetric strain (εext vol ) is not equal to the change in porosity (εint vol ) because of the bond compressibility (Cb εbvol ). 2.1.2 Strain partition Compatibility between external and local strains is derived from the conservation of volume defined by Pinyol et al. (2007). They propose a coupling coefficient χb that relates the volumetric response of the bond with the composite volumetric response and it is defined as:

Following this strain partition the external strain increment applied to the MHBS can be rewritten from the equation 5 as:

When χb = 0, bonds are not considered in the loading framework and the behaviour of the composite material recovers that of a sandy soil. However, when χb increases, bond behaviour starts to dominate the composite mechanical response, and for high χb , it behaves like a quasi-brittle material. 2.2

Conventionally, the application of an external compressive volumetric strain creates a decrease on the available pore space and on bond volume, whose changes are given by:

Matrix behaviour

The hydrate resource pyramid (Boswell & Collet, 2006) clearly illustrates that marine sand reservoirs are the major target for long-term development of gas hydrates as a future energy supply. Consequently, an extension of the CASM (Clay and Sand model; Yu, 1998) for unsaturated soils (González, 2011) has been choose as the constitutive model to describe the matrix response.

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preconsolidation pressure which acts as the hardeningsoftening parameter controlling the size of the yield surface. 2.2.2 Elastic behaviour The behaviour inside the yield surface is assumed to be isotropic and elastic. The elastic stress-strain relationship is described based on the Bishop effective stress concept (Bishop, 1959) where the bulk modulus K incorporates the effect of suction on the global volumetric elastic strain as:

Figure 2. CASM yield surfaces normalized by preconsolidation pressure. For a fixed spacing ratio r variations in n value can display local peaks before approaching the critical state condition. After González (2011).

CASM model is a unified critical state model based on the critical state theory and is formulated in terms of the state parameter concept (ξ) introduced by Been & Jefferies (1985). Its election as a matrix constitutive model is due to its simplicity and flexibility in describing the shape of the yield surface as well as its proven ability to predict the mechanical behaviour of reconstituted clays and specially sands. A total of seven model parameters are needed to define CASM, five of which are the same as those in the standard Cam-Clay model, the most popular model used to represent the mechanical behaviour of MHBS (e.g., Uchida 2012). The two extra model parameters are denoted by n and r, where n is used to specify the shape of the yield surface and r is a spacing ratio introduced to control the point of intersection of the critical state line and the yield surface. Figure 2 shows that the intersection point between the critical state line and the yield surface in the CASM model does not necessarily occur at the maximum deviatoric stress (as happens in the original and modified Cam-Clay models). This reproduces an important feature observed in sands in which the deviatoric stress often reaches a local peak before approaching the critical state condition (González, 2011). 2.2.1 Yield function The original CASM model is extended to establish a suction dependency of the preconsolidation pressure and the hardening law following the proposal by Alonso et al. (1990) for the Barcelona Basic Model. In the triaxial stress space the CASM yield function is defined by equation 14:

where q is the deviatoric stress, p is the mean net stress, ps is a tensile strength due to suction, M is the slope of the critical state line in the q-p space, and p′0 is the

where e is the macroscopic void ratio, κ is the slope of the isotropic swelling line (in υ − ln p′ space), Sh is the hydrate saturation and dp∗ represents the increment in pressure due to mean stress (p) and suction (s) variations. 2.2.3 Hardening parameter and flow rule On the basis that the yield surface located at zero suction defines the hardening variable p′0 , an isotropic volumetric hardening-softening law controlled by the plastic volumetric strains is assumed and given by:

where λ∗0 = λ0 /(1 + e) and κ∗ = κ/(1 + e) are the modified slope of the saturated virgin consolidation line and the unloading-reloading line, respectively. The CASM plastic potential is integrated from the stress-dilatancy relationship proposed by Rowe, (1962) and it is defined as:

where ϕ is a size parameter controlling the size of the plastic potential which passes through the current stress state. 2.3 Hydrate behaviour MHBS are highly compacted-stable sediments that behave as a bonded soil with hydrate acting as bonding agent (e.g. Masui et al., 2005, Yun et al., 2007, Miyazaki, K. et al., 2008). However, once the hydrate dissociates due to a decrease in pressure and/or increase in temperature, or is damaged by a mechanical strain, the bonded structure disappears and the soil may behave as unconsolidated material (Brugada et al., 2010). Accordingly, our composite model simulates the hydrate bond behaviour by a scalar damage model proposed by Carol et al. (2001) that allows to represent the medium destructuralization.

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The damage model is based on thermodynamical principles that prevent any energy dissipation during load cycles. Besides, it assumes a linear elastic response for the bond in an undamaged state, with the shear and bulk moduli decreasing progressively during loading as micro-cracks develop inside the material. The damage model is defined as:

where Kb0 and Gb0 are the bulk and shear moduli of the hydrate bond in an intact state, and Kb and Gb the same moduli for a damage level given by parameter D which is equal to the ratio of fissured bond area over whole bond area. As proposed by Carol et al. (2001), an alternative damage variable is used:

Figure 3. Pore-scale distribution of methane hydrate: a Pore-Filling, b Load-bearing, c Cementation. After (Brugada et al., 2010).

where dbσ is given by: This variable can be simply related to the degradation of bond Young modulus by the following expression:

where E0 and E are the undamaged and damaged bond Young’s moduli, respectively. The evolution of L is also linked in the model with the increments of energy stored in the bonds per unit of volume through several damage evolution laws and allows to update the elastic modules for a given damage:

2.4

Coupling

Since hydrate bonds and soil matrix are endowed with their own independent behaviour, local strains and stresses have to be defined for each component. Local strains are compatible with the external strains by the strain partition presented in equation (9). The stress partition is obtained by stating that the virtual work done by the medium under any compatible external strain increment is equal to the sum of the works performed by the matrix and the bonds. Defining σ ext , σ M and σ b as the stresses acting on the medium, matrix and bonds, respectively, and assuming that (i) the incremental external strain dεext vol is associated to the matrix stress σ M through the constitutive law of the soil matrix and (ii) the incremental strain of the bond dεbvol is associated to the bond stress σ b through the constitutive law of the hydrates, the following equations are obtained:

Equation (28) shows the constitutive law of the composite medium, where χb is assumed to depend only on the bond damage variable L by:

where χb0 is the value of χb in the intact state (L = 0). This dependency indicates that part of the load carried by the bond in a given state is transferred to the soil matrix when bonds degrade. 2.4.1 Effect of hydrate morphology in composite behaviour Recent works (e.g, Waite et al., 2009;Yun et al., 2007), provide evidences that the type of sediment, confining stress applied, hydrate saturation and hydrate morphology govern the load-deformation response of MHBS. Specifically, the effect of hydrate habit on seismic wave velocity, attenuation and small strain stiffness has been reported extensively (e.g, Waite et al., 2009; Best et al., 2013). However the understanding on how hydrate habit influences the intermediate and large strain behavior, and the failure condition is still limited. Three main hydrate habits or growth patterns are commonly described in the literature (Fig. 3): pore filling, load-bearing and cementation. Pore-filling hydrate (Fig. 3a) nucleates and grows freely in the pore space, without bridging particles together and affecting essentially the pore fluid bulk stiffness and fluid conduction properties (Ecker et al., 1998; Helgerud et al., 1999). This habit likely evolves to load-bearing hydrate (Fig. 3b) by pore invasion leading to hydrate saturation (Sh ) values that exceeds 25%–40% (Berge, 1999; Yun et al., 2005, 2007). This hydrate pattern bridges nearby grains and contributes to the mechanical stability of the granular skeleton

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stress ph0 at hydrate formation time. This reference value can be obtained from the equilibrium of the chemical potentials between liquid and hydrate phases existing in the sediment pore space by the Clausius– Clapeyron equation (equation 30). Following the work for frozen soils presented by Nishimura et al. (2009), the thermodynamic equilibrium that needs to be satisfied by the hydrate pressure (ph0 , which is assumed equal to ice pressure due to its chemical similarities), methane-saturated water pressure (pw ) and temprature (T ) is given by:

Figure 4. Stress–strain results from drained triaxial tests on Toyoura sand observed by Masui et al. (2005).

where l is the specific latent heat of hydrate fusion and ρ (=1/v) is the mass density of each phase. b) Pore-filling hydrate is considered as a densifier compound, not involved on the load supporting framework. Its effect over the composite strength is only considered by the suction generated on hydrate-water interface (ph0 − pw ). c) An approximately linear evolution of the hardening parameter value (p∗0 ) with hydrate saturation for load-bearing and cementing hydrate habits (Fig. 5). 3

Figure 5. Hardening effect of each hydrate habit on the matrix preconsolidation pressure (p′0 ).

by becoming part of the load-bearing framework. Finally, cementing hydrates (Fig. 3c) nucleate at soil grain contacts and act as a bonding agent that significantly increases the sediment shear and bulk moduli (Helgerud, M. B., J. Dvorkin, A. Nur, A. Sakai 1999). Experimental results obtained from drained triaxial compression tests performed on synthetic hydrate sands (Fig. 4) show how the hydrate habit exerts a strong control on the macroscale mechanical properties of the sediment. Figure 4 clearly shows that cementing samples exhibit a greater enhancement in stiffness, strength and dilatancy than the load-bearing or pore filling cases. To reproduce the effect caused by the different hydrate habits on the composite mechanical properties, the model assumes three initial hypotheses. a) The hydrate is considered formed once the matrix is stressed, taking as a reference zero state the initial

CONSTITUTIVE MODEL FLOW CHART

Figure 6 outlines the flow chart followed to compute the stress increment from the strain increment applied to the composite model. For the sake of clarity, the ideal case of infinitesimal increments is considered. When dealing with discrete increments, the tangent relaM tionships indicated in the flow chart dσijM = Dijkl dεM kl b b b and dσij = Dijkl dεkl should be replaced by convenient iterative procedures. The first step consists in calculating the increment of hydrate strain dεbkl from the increment of external strain dεext vol , and the current value of χb and bond concentration Cb . The increment of hydrate stress dσijb is obtained by integration of the damage model and arises as the product of the damaged hydrate secant elastic stiffness matrix Db with dεbkl . The total hydrate stress is then updated by adding the stress increment dσijb to the previous value. Using the mean value of the pressure and the temperature prevailing locally within the hydrate component (ph , T), the condition for possible methane hydrate dissociation can then be assessed. However, the bond-damage model is restricted to the pore-filling hydrate habit until the hydrate saturation reaches values close to 35% and hydrate passes to form part of the load supporting framework. Secondly, the change in matrix stress is assessed by applying the elastoplastic model CASM to the matrix M strain increment dσijM = Dijkl dεM kl . The effect of suction generated by water-hydrate interfaces is taken into account similarly to the proposal by González (2011). Finally, the total stresses of the composite medium (equation 28) are obtained from the updated hydrate

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effectives stress acting over the matrix skeleton by introducing the role of the suction generated at the hydrate-water interface. The framework developed in this paper requires further validation by comparison with experimental and field data. In this perspective, the model is now being implemented into the 3D finite element code Code_Bright with the objective to model field problems involving MHBS, including the assessment of the stability of offshore infrastructures, cables and pipelines sitting on these sediments.

REFERENCES

Figure 6. Flow chart for numerical algorithm.

and matrix stress. The constitutive law defined in this way is able to recover a pure soil behaviour for null hydrate concentration (Cb = 0) or when total damage of the bonding network occurs (χb = 0). 4

SUMMARY

The experimental study of MHBS has been hampered by sampling difficulties related with depressurization and thermal changes during core extraction and the low solubility of methane in water in laboratory testing (Sanchez et al., 2014). These restrictions and the strong scientific and engineering interest regarding this geomaterial have motivated the development of numerical models to advance our current understanding of their behaviour. In this paper a new composite constitutive model to reproduce the evolving nature of MHBS mechanical properties has been presented. The model results from the integration of two constitutive models, an elastoplastic model for the matrix and a damage model for the bond material, into a common composite framework. Their integration follows imposed internal strain compatibility conditions, and the stress partitioning between the two constituent materials is achieved by means of the virtual work principle. One specificity of the model is to be based on a critical state constitutive law specially developed to cope with the mechanical behavior both clay and sands, instead of the Cam-Clay framework.This will allow for a more precise modelling of sandy reservoirs containing hydrate, which are the major target for near-future development of gas hydrates as an energy supply. Besides, this model considers the non-mechanical effect of pore-filling hydrate in the estimation of the

Alonso, E. E., Gens, A. & Josa, A., 1990. A constitutive model for partially saturated soils. Geotechnique 40, No. 3, 405–430. Been, K. & Jefferies, M.G., 1985. A state parameter for sands. Géotechnique, 35(2), 99–112. Berge, L. I., Jacobsen, K. A., and Solstad, A., 1999. Measured acoustic wave velocities of R11 (CCl3 F) hydrate samples with and without sand as a function of hydrate concentration. Journal of Geophysical Research-Solid Earth, 104(B7), 15415–15424, July (10). Best, A.I., Priest, J. A., Clayton, C.R.I., Rees, E.V.L., 2013. The effect of methane hydrate morphology and water saturation on seismic wave attenuation in sand under shallow sub-seafloor conditions. Earth and Planetary Science Letters, 368, pp. 78–87. Bishop,A.W., 1959. The Principle of Effective Stress. Teknisk Ukeblad 39 (October): 859–863. Boswell, R. and Collett T.S., 2006. The gas hydrates resource pyramid: Fire inthe ice: Methane hydrate newsletter, Fall issue, pp. 5–7. Brugada, J., Cheng,YP., Soga, K., Santamarina, J., 2010. Discrete element modelling of geomechanical behaviour of methane hydrate soils with pore-filling hydrate distribution. Granular Matter, 12(5), pp. 517–525. Carol, I., Rizzi, E. & Willam, K., 2001. On the formulation of anisotropic elastic degradation. I. Theory based on a pseudologarithmic damage tensor rate. Int. J. Solids Struct. 38, No. 4, 91–518. Clayton, C.R.I., Priest, J.A., Rees, E.V., 2010. The effects of hydrate cement on the stiffness of some sands. Géotechnique, 60(6), pp. 435–445. Collett, T.S., 2002. Energy resource potential of natural gas hydrates, AAPG Bull., 86(11), 1971–1992. Dallimore, S. R., and Collett, T.S., 2005. Summary and implications of the Mallik 2002 gas hydrate production research well program, in Scientific Results From the Mallik 2002 Gas Hydrate Production Research Well Program, Mackenzie Delta, Northwest Territories, Canada, vol. 585. Geological Survey of Canada Bulletin 585. González, N., 2011. Development of a family of constitutive models for geotechnical applications. (May), pp. 47–84. Helgerud, M. B., J. Dvorkin, A. Nur, A. Sakai, and T.C., 1999. Elastic-wave velocity in marine sediments with gas hydrates: Effective medium modeling, Geophys. Res. Lett., 26, 2021–2024. Kvenvolden, K.A., 1993. Gas hydrates—geological perspective and global change. Reviews of Geophysics, 31(2), p. 173. Available at: http://doi.wiley.com/10.1029/93RG 00268. Kvenvolden, K.A., 1999. Potential effects of gas hydrate on human welfare. Proceedings of the National Academy

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of Sciences of the United States of America, 96(7), pp. 3420–3426. Masui, A., H. Haneda,Y. Ogata, and K.A., 2005. The effect of saturation degree of methane hydrate on the shear strength of syn- thetic methane hydrate sediments, Proceedings of the 5th International Conference on Gas Hydrates, Trondheim, Norway, vol. 2037, pp. 657–663. Miyazaki, K., A. Masui, H. Haneda, Y. Ogata, K. Aoki, and T.Y., 2008. Variable-compliance-type constitutive model for methane hydrate bearing sediment, paper presented at 6th International Conference on Gas Hydrates, Univ. B. C., Vancouver, B. C., Canada. Moridis G.J, Collett T.S, Pooladi-Darvish M, Hancock S, Santamarina J, Boswell R, Kneafsey T, Rutqvist J, Kovalsky M, Reagan M.T, Sloan E.D, Sum A.K, K.C., 2011. Challenges, Uncertainties and Issues Facing Gas Production From Gas Hydrate Deposits. SPE Res Eval Eng 14(1):76–112, (March 2010). Nishimura, S., Gens, A., Jardine, R., J. Olivella, S., 2009. THM-coupled finite element analysis of frozen soil: formulation and application. Géotechnique, 59(3), pp. 159–171. Pinyol, N., Alonso, E.E. & Vaunat, J., 2007. A constitutive model for soft clayey rocks that includes weathering effects. Géotechnique, 57(2), pp. 137–151. Priest, J.A., Rees, E.V.L., Clayton, C.R.I., 2009. Influence of gas hydrate morphology on the seismic velocities of sands, J. Geophys. Res., 114, B11205. Rowe, P.W., 1962. The stress-dilatancy relation for static equilibrium of an assembly of particles in contact. Proc. Roy. Soc., 267, 500–527.

Ruppel, C., 2007. Tapping methane hydrates for unconventional natural gas. , Elements, 3, 193–199, doi:10.2113/ gselements. 3.3.193., pp. 1–19. Sanchez, M.J., Gai, X., Shastri, A., Santamarina, J.C., 2014. Coupled THCM Modeling of Gas Hydrate Bearing Sediments. American Geophysical Union, Fall Meeting 2014, abstract #B11B-0020. Sloan, E.D., 1998. Clathrate Hydrates of Natural Gases 2nd ed., New York. Soga, K., S. L. Lee, M.Y.A. Ng, andA.K., 2006. Characterisation and engineering properties of methane hydrate soils, in Characterization and Engineering Properties of Natural Soils, vol. 4, edited by K. Soga et al., pp. 2591–2642, Taylor and Francis, London, U.K. Uchida, S., Soga, K. & Yamamoto, K., 2012. Critical state soil constitutive model for methane hydrate soil. Journal of Geophysical Research: Solid Earth, 117(B3). Waite, W.F. et al., 2009. Physical Properties of HydrateBearing Sediments. Change, 47(2008), pp. 1–38. Yu, H.S., 1998. CASM: a unified state parameter model for clay and sand. International Journal for Numerical and Analytical Methods in Geomechanics, 22(8), pp. 621–653. Yun, T. S., F. M. Francisca, J. C. Santamarina, and C.R., 2005. Compressional and shear wave velocities in uncemented sediment containing gas hydrate, Geophys. Res. Lett., 32, L10609. Yun, T.S., Santamarina, J.C. & Ruppel, C., 2007. Mechanical properties of sand, silt, and clay containing tetrahydrofuran hydrate. Journal of Geophysical Research, 112(B4), p. B04106.

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Shallow geothermal systems – geophysical support for geothermal planning maps R. Kirsch, A. Wolf, K. Baezner & C. Thomsen LLUR Geological Survey of Schleswig-Holstein, Flintbek, Germany

H. Wiederhold LIAG Leibniz Institute of Applied Geophysics, Hannover, Germany

ABSTRACT: Shallow geothermal energy using ground heat exchangers is an effective technique to produce heat from (renewable) electrical energy. The geological surveys are concerned with ground heat exchangers mainly due to two reasons: a) efficiency of the geothermal system, b) groundwater protection: ground heat exchanger can penetrate groundwater protective layers leading to pathways for potentially contaminated surface waters into the aquifer. Underground information, especially on thermal conductivity, is required for the proper design of the Ground Heat Exchangers (GHE). Therefore, plannig maps showing the effective thermal conductivity or the specific thermal power of the ground for defined GHE lengths are provided by the geological surveys. These maps are based on drilling results. In areas with low coverage of drillings geophysical data can be used to fill the data gaps. An approach to use geotechnical techniques for an assessment of thermal conductivities is demonstrated and discussed for an area in Northern Schleswig-Holstein.

1 TECHNIQUES OF SHALLOW GEOTHERMAL ENERGY USE Shallow geothermal energy using ground heat exchangers is an effective technique to convert electrical energy to heat, about 4 times more effective than conventional power to heat techniques.

Main components of this heating system are a heatpump and ground heat exchangers (boreholes containing 1 or 2 U-shaped plastic tubes filled with heat transfer fluid (water and antifreeze), Fig. 1). To provide a good thermal contact from the ground to the plastic tubes and to avoid the formation of pathways

Figure 1. Left: base components of a shallow geothermal heating system, right: schematic view of a heat pump (A, B see text).

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for contaminated surface water to the groundwater the borehole is grouted with special cement. The heat transfer fluid is circulating through the plastic tube in the borehole and through the heat exchanger of the heat pump. In the heat exchanger thermal energy is passing from the transfer fluid to the internal cycle of the heatpump, therefore the temperature of the transfer fluid is reduced by 3–5 K and can fall below 0◦ C. When the cooled transfer fluid is flowing again through the plastic tubes, thermal energy is passing from the ground to the transfer fluid and the temperature recovers (Bernier 2006).

2

Figure 2. Mean temperature of the heat transfer fluid related to the thermal conductivity of the underground (length of deep ground heat exchanger 100 m, annual heat load 16.200 MWh, borehole cementation with high thermal conductivity).

DESIGN OF GROUND HEAT EXCHANGERS – ENERGY EFFICIENCY AND GROUNDWATER PROTECTION

Ground heat exchangers are designed to fulfill two demands: energy efficiency of the heat pump and groundwater protection (LLUR 2011). The efficiency of the heat pump is quantified by the coefficient of performance (COP), defined by the ratio of the thermal power provided by the heat pump and the electrical power required to drive the heat pump. Since the production of electrical power is still an important source of CO2 emissions, a COP of at least 4 is necessary to be competitive with a heating system based on natural gas in the context of CO2 reduction. The COP depends on the difference between the temperature of the transfer fluid entering the heat exchanger of the heat pump (e.g. 5◦ C) and the temperature of the heating system (e.g. 30◦ C). Therefore, to enable a high efficiency of the heat pump the temperature of the transfer fluid should be as high as possible at the entrance of the heat pump (see Fig. 1). However, the balance between heat extraction and recovery of the temperature field in the surrounding of the ground heat exchangers during the warm seasons must be considered when ground heat exchangers are planned. For the protection of groundwater resources the formation of pathways for contaminated surface water must be excluded when groundwater protecting layers (till or clay) were penetrated by the drillings for the ground heat exchangers. The borehole must be filled and sealed with cement after the plastic tubes are installed. However, the reliance of the cement against freezing and thawing is not secured. Laboratory experiments showed that cracks leading to enhanced hydraulic conductivity of the cement can be formed after repeated freezing – thawing cycles. Therefore, freezing of the cement must be avoided and the temperature of the heat transfer fluid should not be lower than –3◦ C when leaving the heat pump. So, properly designed ground heat exchangers must assure that the two temperature requirements of the transfer fluid are fulfilled: a) sufficient temperature at the entrance of the heatpump (A in Fig. 1) to enable a high COP of the heat pump, b) temperature should not fall below –3◦ C when leaving the heat pump (B in Fig. 1) to avoid freezing of the cementation.

The key underground parameter for the design of ground heat exchangers is the thermal conductivity (Dietlefsen et al. 2013). Figure 2 shows the mean temperature of the transfer fluid related to the thermal conductivity of the underground (results are modelled using the computer program Earth Energy Designer). For the planning of ground heat exchanger maps showing the thermal conductivity of the underground are required.

3 THERMAL AND ELECTRICAL CHARACTERISTICS OF UNCONSOLIDATED SEDIMENTS The thermal conductivity is defined by the heat flow through the underground material driven by the temperature gradient. For unconsolidated sediments the thermal conductivity is mainly governed by the porosity because the thermal conductivity of the pore fillings air (0.05 W/mK) or water (0.5 W/mK) are low compared with the thermal conductivity of the mineral grains. Average values of thermal conductivites for water saturated material are: sand: 2.4 W/mK till: 2.4 W/mK clay: 1.5 W/mK. The thermal conductivity of dry/unsaturated sand is low, about 0.8 W/mK. For till and clay we assume that both materials contain bound water even above the groundwater table and so the thermal conductivity of unsaturated clayey material is higher than the thermal conductivity of unsaturated sand. So, thermal conductivities of 1.7 W/mK for unsaturated till and 1.0 W/mK for unsaturated clay were postulated. The definition of the electrical conductivity of underground material is similar to the definition of thermal conductivity: by the electrical current density driven by an electrical potential gradient. Commonly, the reciprocal of the electrical conductivity, the specific electrical resistivity in ohm x meter (
m) is used

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Figure 4. Detail of the geothermal planning map based on drilling results showing the mean thermal conductivity of the 100 m depth range.

Figure 3. Airborne electromagnetic mapping system SkyTEM.

for the characterisation of the underground material. Typical values of specific electrical resistivities for water saturated material are: sand: 80–200
m, till: 40–60
m clay: below 30
m. Clayey layers with low thermal conductivities are clearly separated from sand and till layers with high thermal conductivities by low specific electrical resistivities. Therefore, the specific electrical resistivity of the underground can be used for an assessment of the thermal conductivity. A number of geophysical techniques can be applied for the mapping of the electrical resistivity structure of the underground. Conventional 1D and 2D geoelectrical measurements use electrodes to inject a current into the ground and to measure the resulting electrical potential at the surface. Data inversion reveals the 1D or 2D resistivity-depth structure. Electromagnetic techniques make use of eddy currents in the underground induced by time variable magnetic fields to obtain the resistivity structure of the underground. No direct contact to the soil is necessary, so electromagnetic can be used as an airborne technique (HEM, SkyTEM) for the mapping of large areas (Fig. 3). Increasing areas of the lowlands in the

Figure 5. Distribution of drillings used for the geothermal planning map.

Netherlands, Germany and Denmark are covered by airborne electromagnetic surveys.

4

GEOTHERMAL PLANNING MAPS

Geothermal planning maps are launched by the Geological Surveys to give a quick overview of the underground conditions as an aid for the design of ground heat exchangers. Commonly these maps display the specific thermal power (W/m) following the technical guideline VDI 4640 (2001) for different depth ranges, e.g., down to 50 m or 100 m below ground.

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Figure 6. Assessment of thermal conductivities based on SkyTEM resistivity results: from top to bottom: location of the flight line, resistivity distribution below the flight line, resistivity-depth distribution for a selected location (7,500 m along the flightline), allocation of thermal resistivities of the resolved layers, calculated effective thermal conductivity for this location for the depth range down to 100 m.

A new set of geothermal planning maps for Schleswig-Holstein show the thermal conductivity for different depth ranges because this ground property is required for thermal simulation programs like, e.g., Earth Energy Designer (Hellström 1991, Hellström & Sanner 2000). This map is based on drilling results. For each drilling, the weighted mean thermal conductivity is calculated from the layer sequence and the above mentioned tabular values of thermal conductivities for the saturated and the unsaturated zone. The saturated and the unsaturated thermal conductivities are interpolated and, using the depth to groundwater head, thermal conductivities for different depth ranges are calculated and displayed in maps (Fig. 4). A total of 28,742 drillings are used for these maps, of which 4,069 drillings are exceeding 100 m depth penetration. Although a large number of drillings is used for the maps, the distribution of drillings is irregular

Figure 7. Detail of the geothermal planning map showing the effective thermal conductivity for the 50 m depth range. Top: location map with boreholes and SkyTEM sounding points, middle: map based on drilling results alone, bottom: map including additional data points from the SkyTEM survey.

(Fig. 5). Especially in the northern and western part of Schleswig-Holstein data gaps are obvious. 5

CLOSING DATA GAPS WITH RESISTIVITY TECHNIQUES

As shown before, the specific electrical resistivity is closely related to the thermal conductivity. For an area

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at the North Sea coast in Northern Schleswig-Holstein with low drilling density the data base is improved by resistivity data from a SkyTEM survey. The conversion of resistivity data to thermal conductivities is shown in Fig. 6. Data inversion of SkyTEM measurements leads to a sequence of 1D resistivity-depth distributions along the flight line. This resistivity-depth distribution reflects the layer sequence of the underground. In Fig. 6 the 2 low resistivity layers (12.4 and 4.6
m) are geologically interpreted as clay, while the top layer with a specific electrical resistivity of 53.6
m is interpreted as saturated sand. Using the above-quoted thermal conductivities for sand and clay an effective thermal conductivity down to 100 m for this location can be calculated to 1.9 W/mK. The uppermost (unsaturated) layer is not sufficiently resolved by SkyTEM measurements, this can be compensated by additional electrical Schlumberger soundings at those locations. An example from an area in Northern SchleswigHolstein is shown in Fig. 7. Here data from a SkyTEM survey in the German – Danish border region flown in cooperation with LIAG in the scope of the INTERREG project CLIWAT (CLIWAT working group 2011) were used to produce additional sampling points for the thermal conductivity map. The use of SkyTEM data points leads to a more detailed picture and an enhanced reliability of the thermal conductivity map. 6

CONCLUSIONS

is attributed, then the effective thermal conductivity of this site is calculated by the weighted mean of the thermal conductivities of the layers down to a defined depth, e.g. 50 m or 100 m. If the drilling density is poor, the layer sequence of resistivity measurements (VES or airborne EM) can be used to complement the data base. This is demonstrated for a selected location in Northern Schleswig-Holstein where the SkyTEM results were weighted equally to the drilling results. REFERENCES Bernier, M.A. 2006. Closed-Loop Ground-Coupled Heat Pump Systems. ASHARE Journal: 13–19. CLIWAT working group 2011. Groundwater in a future climate – the CLIWAT handbook. Central Denmark Region, Vejle. Ditlefsen, C., Vangkilde-Pedersen, T., Sørensen, I., Bjørn, H., Lajer Højberg, A., Møller, I. 2013. GeoEnergy – a national shallow geothermal research project. Proceedings European Geothermal Congress 2013, Pisa, Italy. Hellström, G. 1991. Ground heat storage – Thermal Analyses of Duct StorageSystems. University of Lund, Sweden. Hellström, G., Sanner B 2000. Earth Energy Designer – users manual. LLUR 2011. Leitfaden zur geothermischen Nutzung des oberflächennahen Untergrundes. Landesamt für Landwirtschaft, Umwelt und ländliche Räume SchleswigHolstein, Geologischer Dienst, Flintbek. VDI 4640 2001. Thermische Nutzung des UntergrundesErdgekoppelte Wärmepumpenanlagen, Teil 1. Verein Deutscher Ingenieure, Düsseldorf.

For geothermal planning maps showing the lateral distribution of thermal conductivities in the underground a sufficient data base is required. Normally these maps are based on drilling results. To each layer reached by the drilling a material specific thermal conductivity

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Validation of a numerical model for the design of borehole heat exchangers in the presence of groundwater flow J. Van Steenwinkel, D. Simpson, M. Degros & W. Vienne AGT – Advanced Groundwater Techniques, Aartselaar, Belgium IFTech Belgium

G. Van Lysebetten WTCB – Scientific and Technical Centre for the Construction Industry, Brussels, Belgium

M. Müller-Petke LIAG – Leibniz Institute for Applied Geophysics, Hannover, Germany

ABSTRACT: Groundwater flow is often disregarded in the design of Borehole Heat Exchangers. Without groundwater flow, the transport of heat from the carrier fluid to the surrounding ground happens through conduction, which is a relatively slow process. The temperature distribution around the loop is axially symmetric, assuming horizontally homogeneous layers. In the presence of groundwater flow, the thermal energy is carried away by advection. The goal of this research was to validate a finite-difference numerical model with a controlled field experiment, in order to develop a design strategy for borehole heat exchangers in the presence of groundwater flow. A test field was installed in the north-east of Belgium in order to create a controlled field experiment with an induced groundwater flow. A single Borehole Heat Exchanger (double-U pipe) was installed down to 50 m depth. A pumping well was drilled at 5 m distance and 6 piezometer wells were installed in two orthogonal directions at different distances from the pumping well. The Borehole Heat Exchanger was equipped with a fibre optic cable inside and outside the loop, to measure the temperature distribution in depth. First, a pumping test was carried out in order to deduct the hydraulic parameters of the formation. Second, a thermal response test was carried out to determine the thermal parameters. Finally, a second thermal response test was conducted while pumping the well, to measure the effect of the groundwater flow. A finite-difference model was constructed with MODFLOW2000 and MT3DMS, in order to simulate the groundwater flow and heat transport, respectively. The field measurements could be accurately simulated with the numerical model, with minor adjustments of the model parameters. Therefore, the model looks a promising tool for the design of borehole heat exchangers in the presence of groundwater flow. 1

INTRODUCTION

Groundwater flow is often disregarded in the design of Borehole Heat Exchangers. Without groundwater flow, the transport of heat from the carrier fluid to the surrounding ground happens through conduction, which is a relatively slow process. The temperature distribution around the loop is axially symmetric, assuming horizontally homogeneous layers. In the presence of groundwater flow, the thermal energy is carried away by advection creating an asymmetric heat plume downstream of the BHE. Recently, there has been an increased interest in the effect of groundwater flow in the design of Borehole Heat Exchangers. Both analytic, such as the moving finite line source model (Carslaw & Jaeger, 1959), and numerical models (finite-element or finite difference, Capozza & Zarrella, 2013; Gehlin & Hellström, 2003; Bauer, 2009) were used to simulate the influence of groundwater flow. The models can be validated against existing BHE-fields (Bauer et al., 2012) or in

controlled field experiments where both the groundwater flow and the thermal transport are well known. Controlled field experiments are not often used, since it is quite costly to install. However, they have the advantage to eliminate a lot of variables that influence the flow and heat transport, enabling to benchmark numerical models in a rigorous manner. The goal of this research was to validate a finitedifference numerical model with a controlled field experiment, in order to develop a design strategy for borehole heat exchangers in the presence of a groundwater flow. 2

EXPERIMENTAL SITE SETUP AND MEASUREMENTS

The experiments carried out on the site had the following objectives:

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•

Determine the local hydrogeology with borehole descriptions and logging.

Estimate the hydraulic parameters with a pumping test and flow test. • Estimate the thermal transport parameters based on a thermal response test, once without and once with an induced groundwater flow by pumping. • Monitor the temperature distribution during the tests to validate the numerical model. •

2.1

Local hydrogeology

An experimental site was selected near the village Hechtel-Eksel in the north-east of Belgium, based on the following criteria: Presence of a sufficiently thick aquifer, with a high transmissivity to allow a significant groundwater flow. Preferably a confined aquifer to simplify the analysis. • Sufficiently distant from existing abstraction wells, rivers or other boundary conditions that could locally disturb the groundwater flow. •

The local hydrogeology was determined from borehole drill cuttings description and geophysical borehole logging: •

AQUIFER 1: phreatic: ◦ 0–1 mbgl: coarse sand (Quaternary); ◦ 1–7 mbgl: fine sand, Formation of Kasterlee (Tertiary);

•

AQUITARD 1: ◦ 7–13.5 mbgl: clay layers intercalated with fine sand, rich in glauconite, Formation of Kasterlee and Diest (Tertiary);

•

AQUIFER 2a: confined, Miocene aquifer system: ◦ 13.5–24.5 mbgl: fine sand with thin clay lenses, rich in glauconite, Formation of Diest (Tertiary);

•

AQUITARD 2: ◦ 24.5–26.5 mbgl: clay layer, Formation of Diest (Tertiary);

•

(Figure 1). The boreholes were drilled with the reverse rotary flush method. A borehole heat exchanger was installed at 5 m from the pumping well down to 50 m depth. The pumping well was screened in Aquifer 2 between 13.5 and 50 mbgl. The piezometer wells each contained multiple piezometer screens at different depths (Figure 2). Piezometer PZ1 had a screen at 75 m depth (below the base of the pumping filter), to be able to estimate the vertical hydraulic conductivity of Aquifer 2. Before pumping, the groundwater levels were measured in the piezometers to determine the natural gradient of the groundwater flow. The gradient in aquifer 2 was equal to 0.36%. A pumping test was carried out, by first conducting a step-drawdown test with four steps of one hour and then continuing the fourth step for 18 hours. The discharges were increased in steps of 7-12-16-21 m3 /h. The drawdowns in all the piezometers were recorded with automatic pressure sensors. The time-drawdown curves were fitted with the multi-layer aquifer modelling software MLU (http://microfem.nl/), of which the following hydraulic parameters were obtained: • •

AQUIFER 2b: confined, Miocene aquifer system: ◦ 26.5–205 mbgl: fine sand with thin clay lenses, rich in glauconite, Formations of Diest and Bolderberg (Tertiary);

•

Figure 1. Horizontal position of the pumping well (PW) and piezometer wells (PZ) on an aerial photo. BHE indicates the position of the borehole heat exchanger.

AQUITARD 3: ◦ 205–280 mbgl: stiff clay, Formation of Rupel (Tertiary).

The Miocene aquifer system is well known and has a regional average, horizontal hydraulic conductivity of 12 m/d (VMM, 2008). 2.2

Pumping test and flow test

A pumping well was installed and 6 piezometer wells along two perpendicular transects at different distances between 5 and 40 m from the pumping well

Aquifer 2: Kh/Kv = 3.9/0.77 m/d; Ss = 9.0E-6 1/m. Aquitard 1: Kv = 0.012 m/d.

Apart from the pumping test, a flow test was conducted with a propeller flow logger while pumping at a constant discharge of 21 m3 /h. The flow test indicated a very even distribution of the transmissivity over the whole thickness of the screened section of Aquifer 2.

2.3 Thermal response tests (TRT) Two thermal response tests were carried out, a first one without and a second one with an induced groundwater flow by pumping in the pumping well. The first test was used to determine the parameters governing the conductive transport, being the thermal conductivity and borehole heat resistance. The second test was used to add the advective process to the conductive transport.

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Figure 2. Schematic vertical section along transect PW-PZ6, indicating the depth of the pumping well screen and piezometer screens below ground level and the hydrogeological layers.

The borehole heat exchanger was installed in a borehole of 130 mm diameter, drilled with a rotary flush drilling rig. A PE, double U-pipe was installed in the borehole. Alongside the U-pipes, a U-shaped, fibre optic cable was installed to be able to measure a complete temperature profile (Figure 3). The annular spacing was filled up with a thermal grout (ThermoCem plus of Heidelberg Cement, λ = 2.0 W/(m.◦ K)). A second fibre optic cable was installed inside one of the U-pipes in order to measure the heat-carrier fluid temperature inside the pipe at regular depths. The fibre optic cables were connected to a measuring unit (GeoDTS of AP sensing, Germany) to read and record the temperature depth profiles in time. Both thermal response tests were carried out with an in-house built unit (IFTech, Belgium), which consists of: • • • •

a heater to add heat to the heat-carrier fluid, circulation pumps, pressure control, sensors to measure incoming and outgoing temperatures, flow and energy.

The system is regulated such that the heat carrier fluid circulates with a constant discharge through the pipes while a constant power is added to fluid. This results in a constant temperature difference (deltaT) between ingoing and outflowing fluid. The TRT’s were carried out with the following settings: Circulation discharge: 0.92 m3 /h. Power injected: 4.23 kW or 84.6 W/m borehole length. • Duration 5.79 days (TRT without flow) and 18.72 days (TRT with flow).

• •

During the second TRT, a groundwater flow was induced by pumping the pumping well. The pumping discharge was increased in three steps as follows: • • • •

0–2.71 days: no pumping, start TRT heating; 2.71–6.72 days: Q = 0.93 m3 /h, TRT heating; 6.72–10.05 days: Q = 2.91 m3 /h, TRT heating; 10.05–18.72 days: Q = 8.63 m3 /h, no heating.

Figure 3. installation of the fibre optic cables alongside (black) and inside (red) the heat carrier pipes, which are connected to the TRT-unit in the back.

Before the last step, the TRT-test was stopped, in order to measure the recovery of the temperatures. Based on the temperature differences between ingoing and outgoing fluid temperatures, the bulk thermal conductivity and borehole heat resistance were calculated with the classical TRT analysis based on the line-source theory at 2.85 W/(m.◦ K) and 0.07 m.◦ K/W. These are acceptable values for a typical BHE in a saturated sand. 3

NUMERICAL SIMULATION OF THE TRT TESTS

3.1

Design of the numerical model

A finite-difference numerical model was constructed to simulate both the groundwater flow and heat transport. The open-source package Modflow2000 (USGS) was used for the flow calculations and MT3DMSv5.3 (University of Alabama, US) for the heat transport, applying the mass-heat transport analogy (Langevin et al., 2008). According to this analogy, mass is equivalent to thermal energy and mass concentration to groundwater temperature. The same mass transport processes of diffusion, dispersion, advection and retardation can be applied to heat transport modelling. The finite-difference grid was composed as follows: •

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Horizontal extension: 4 × 4 km. The model needs to be this large to avoid that the drawdown of the pumping well reaches the borders of the model.

Horizontal cell dimensions: 100 × 100 m at the border, refined to 20 × 20 cm around the well field and to 2.32 × 2.32 cm at the borehole heat exchanger. The first refinement serves to accurately simulate the groundwater pressures and temperatures and the second refinement is to simulate the borehole fluid flow through the pipe. The inner surface of the pipe corresponds to surface of the finest cell. • Number of layers: 13, partly to capture the hydrogeological layers and partly to simulate the bottom of the borehole heat exchanger.

•

The pumping well was inserted as a constant flux boundary condition. The flow of the heat-carrier fluid through the borehole heat exchanger was numerically reproduced by attributing a high vertical hydraulic conductivity inside the pipes and a zone of very low hydraulic conductivity around the pipes. The heat-carrier fluid was circulated in the model by introducing a constant flux boundary condition (Well-package in Modflow) at the top of the model. The temperature of the outflowing fluid was accepted as temperature for the inflowing fluid, a feature which is incorporated in the latest MT3DMS version (Zheng, 2010). A constant heat flux was introduced with the mass-loading option of the Well-package, just after the ingoing constant flux boundary condition. Both the top and bottom of the model were assumed to be no-flux boundary conditions, both for groundwater flow and heat transport. The hydraulic properties were derived from the pumping test, while the thermal properties were estimated based on the TRT without groundwater flow and literature values as initial estimates. The parameters thermal conductivity, total porosity and heat capacity of the solid matrix were varied until a best, visual match was obtained between measured and modelled temperatures: • • • • •

Initial temperature of the groundwater and solid matrix: 11.5◦ C. Bulk thermal conductivity KT_bulk = 2.75 W/(m.◦ K). Total porosity θ = 0.2 m3 /m3 . Heat capacity of the dry solid matrix Cp_solid = 824 J/(kg.◦ C) Dry bulk density of the solid matrix ρb = 1590 kg/m3 .

Figure 4. Temperature evolution of the heat carrier fluid during the two TRT-tests, at 33 m depth below ground surface: measured data and modelled values for ingoing and outcoming pipes.

Figure 5. Measured and simulated heat carrier fluid temperatures at different depths and times.

3.2 Simulation of the TRT tests The two TRT-tests were simulated one after the other, as in the real situation. The best match between measured and modelled temperatures is shown in Figure 4 and Figure 5. The fibre optic measurements allow to evaluate the temperature profiles in depth and time. The general evolution of the heat carrier fluid temperatures was reproduced well. The decline in temperatures due to the advective groundwater flow in the second TRT-test was modelled similar in magnitude and shape as the measured data. However, the simulated, absolute values of the temperatures of the second TRT-test were lower than the measured values. The second TRT-test

had the same heat input as the first, so it is not clear yet why the temperatures rise higher than in the first TRT-test. One hypothesis is the increased air temperature during the second test, which was not taken into account. Diurnal fluctuations in the measured temperatures at shallow depths indicates there is an influence of air temperature on the carrier fluid temperatures. Furthermore, the recovery after the second TRT-test is slower than the measured data. These differences are still being investigated.

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REFERENCES

CONCLUSIONS

The influence of advection on the thermal transport around a BHE was successfully induced by pumping in a nearby groundwater well. The strong advection provoked a significant decrease in temperature in the BHE carrier fluid as most of the heat is exported rapidly. The effect of the advection could be well reproduced with a finite-difference, numerical groundwater model. Some issues still need to be investigated, such as the influence of air temperature variation on the BHE, the vertical distribution of thermal conductivities and the effect of different numerical discretization schemes. ACKNOWLEDGEMENTS This research was funded by the Flemish Government, Department of Environment, Nature and Energy (LNE). The authors wish to thank Benvitec and its subsidiary Kempische Metaalwerken for their cooperation and access to the experimental site. Also special thanks to drilling company Verheyden Putboringen for their cooperation in the drilling and installation of the borehole heat exchangers.

Bauer, D., Heidemann, W., Müller-Steinhagen, H., Diersch, H.-J.G. 2009. Modelling and simulation of groundwater influence on borehole thermal energy stores. Proceedings Effstock – 11th International Conference on Energy Storage, Stockhom, Sweden, 2009. Bauer, D., Heidemann, W., Drück, H., 2012. Validation of groundwater flow and transport modeling tool for borehole thermal energy stores based on FEFLOW. Innostock 2012 – The 12th International Conference on Energy Storage, Lleida, Spain. Carslaw H.S., Jaeger J.C. 1959. Conduction of heat in solids. Claremore Press, Oxford. Gehlin, S.E.A., Hellström, G., Influence of thermal response test by groundwater flow in vertical fractures in hard rock. Renewable Energy 28, 2221–2238. Langevin, C.D., Thorne, D.T., Jr., Dausman, A.M., Sukop, M.C., Guo, Weixing 2008. SEAWAT Version 4: A Computer Program for Simulation of Multi-Species Solute and Heat Transport: U.S. Geological Survey Techniques and Methods Book 6, Chapter A22, 39 p. VMM, 2008. Grondwater in Vlaanderen: Het Centraal Kempisch Systeem. Vlaamse Milieumaatschappij. Aalst. 110 p. Zheng, C. 2010. MT3DMS v5.3 a modular three-dimensional multispecies transport model for simulation of advection, dispersion and chemical reactions of contaminants in groundwater systems – Supplemental user’s guide. University of Alabama, 56 p.

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Fiber-optic temperature measurements in closed-loop geothermal systems: A case study in heterogeneous bedrock G. Radioti, S. Delvoie, K. Sartor, F. Nguyen & R. Charlier University of Liege, Liege, Belgium

ABSTRACT: In order to study the behaviour of shallow closed-loop geothermal systems, four borehole heat exchangers equipped with fiber optics were installed on the campus of the University of Liege (Liege, Belgium) over a surface area of 32 m2 . This paper presents continuous, high-resolution temperature profiles measured along the boreholes length at different phases: at the undisturbed state, during hardening of the grouting material, during the recovery phase of a Distributed Thermal Response Test (DTRT) and during a DTRT of a long duration (7 months). The undisturbed ground temperature is affected by the heat loss from ground structures located close to the boreholes, as also indicated by a 3D numerical model. Temperature profiles during hardening of the grouting material indicate extended fractured zones in the rock mass. Temperature measurements during the recovery phase can be correlated to rock layers with different mineral content. The results are in good agreement with those of the borehole televiewer logging method. The long duration DTRT allow us to follow the thermal plume in the heterogeneous rock mass. Moreover the effect of the duration of the test to the calculated mean thermal conductivity and borehole thermal resistance is investigated. The presented analysis could provide information on bedrock heterogeneity, on the anisotropic thermal behaviour of the rock mass and on the ground temperature variations due to heat loss from ground structures. These information could significantly contribute to the long-term behaviour prediction of the geothermal system and the geothermal reservoir potential.

1

INRODUCTION

In order to study the behaviour of closed-loop geothermal systems in heterogeneous bedrock, four Borehole Heat Exchangers (BHEs), namely B1 to B4, were installed on the campus of the University of Liege (Liege, Belgium) over a surface area of 32 m2 (Radioti et al. 2013). The four BHEs, equipped with doubleU geothermal pipes of 100 m long are located at a distance of approximately 15 m to a building (SEGI) and 6.6 m to an underground structure (feeder pipe) (Fig. 1). After drilling the boreholes, a borehole televiewer was lowered inside the four boreholes. A detailed bedrock characterisation was conducted based on acoustic borehole imaging data, gamma-ray logging data and cuttings observation (Radioti et al. 2015a).

Figure 1. Site location on the campus of the University of Liege (Liege, Belgium).

The site geology is characterised by deposits of sand and gravel until a depth of approximately 8 m. The bedrock follows which consists mainly of siltstone and shale interbedded with sandstone. Fractured zones are detected in the rock mass mainly until a depth of 35 m. The mean layer dip angle is approximately 45◦ SE. Moreover, azimuth and deviation were measured by magnetometers and inclinometers (Monier-Williams et al. 2009). Based on these data, the horizontal distance through depth between B2 and the other three boreholes was estimated and presented in Figure 2. B1 and B2 are characterised by roughly the same lithostratigraphy, which is observed at different depths in B3 and B4, due to the layer dip angle orientation. The distance through depth between B1 and B2 oscillates around 4.1 m. The distance between B2 and B3 or B4 decreases through depth, becoming almost the half at the bottom of the boreholes. During the installation of the geothermal pipes, fiber optic cables were attached along the pipe loops. Fiber optics allows us to obtain continous, highresolution temperature profiles along the pipes length by applying the DTS technique (Hermans et al. 2014). This technique is based on Raman optical time domain reflectometry. The fiber ends are connected to the DTS instrument, which injects a laser pulse. The light travels into the optical fiber and is scattered and reemitted from the observed point. The backscattered light is spread across a range of wavelengths.

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Figure 2. Horizontal distance between B2 and the other three boreholes.

The Raman backscatter signal is temperature sensitive. The temperature along the fiber is determined by the intensity of Raman Stokes and anti-Stokes signals. The position of the temperature reading is determined by the arrival time of the reemitted light pulse. The temperature resolution (standard deviation) of the DTS instrument used in this study is in the order of 0.05◦ C. Temperature was recorded every 20 cm (sampling interval) with a spatial resolution of 2 m. Spatial resolution determines the slope width of a measured temperature change and is an important parameter for the temperature accuracy of local hotspots. If the width of the hotspot is lower than the spatial resolution, the measured temperature is reduced by approximately the ratio of hotspot width to spatial resolution (Hoffman et al. 2007). The boreholes were backfilled with the following grouting materials: B1 and B3 with a silica sand-based commercial material (Geosolid, λ = 2.35 W/mK), B2 with a bentonite-based commercial material (Füllbinder, λ = 0.95 W/mK) and B4 with a homemade admixture with graphite (λ = 2.5 W/mK) (Erol & François 2014). Temperature was measured at the undisturbed state, during hardening of the grouting material and during Distributed Thermal Response Tests (DTRT) (Fujii et al. 2006) conducted in situ in the four BHEs. At each depth position two temperature measurements were available, since the fiber optic cables were attached in a loop along the pipes. The temperature profiles presented hereafter correspond to the average of the these two measurements.

2

UNDISTURBED GROUND TEMPERATURE

Temperature was measured at the undisturbed state several times in a period of 2 years (Fig. 3). The first

Figure 3. Undisturbed ground temperature measured by fiber optics in B2.

approximately 18 m correspond to the thermally unstable zone, where ground temperature is influenced by the air temperature. Below 18 m, measured temperatures appear invariant to time in the two-years period and the temperature decreases through depth at a mean rate of approximately 0.25◦ C/10 m, opposite to the geothermal gradient effect. A 3D numerical model was developed, by using the finite element code LAGAMINE (Charlier et al. 2001, Collin et al. 2002), to investigate if the measured ground temperature profiles could be a result of the heating of the ground due to structures heat loss into the subsurface (Radioti et al. 2015b). This model takes into account the heat loss through the basement of the SEGI building and through the shell of the feeder pipe. The feeder is simulated with a surface heating element. The heat loss (150 W/m length) is calculated based on temperature measurements inside the feeder pipes (Sartor et al. 2014). The heat loss through the foundations of the SEGI building is simulated by imposing a constant temperature through time (17.7◦ C) at the whole building surface, as measured by temperature data loggers at the basement of the building. The initial ground temperature (before the presence of engineering structures, in 1970) is calculated analytically based on air temperature data and on the ground thermal properties (Tinti 2012). The air temperature parameters used in this calculation are based on statistical data for the Sart-Tilman area for a period of 20 years (climate-data.org) and the mean ground thermal conductivity on Thermal Response Tests (TRTs) conducted in situ in the four boreholes. In this model the simplified assumptions are made that at bare ground the temperature is constant through time, equal to the average annual air temperature, and

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Figure 4. Numerical results of ground temperature at the location of the boreholes.

that the ground surface under the pavement can be simulated by a no-heat-flux boundary condition. The numerical results of the ground temperature are presented in Figure 4.The geothermal gradient effect is evident in the temperature profile for the year 1970, which corresponds to the ground temperature before the presence of engineering structures. The heating of the ground, due to the feeder and the SEGI building operation, modifies the temperature gradient at the boreholes location until a depth of 100 m after 20 years (1990). The heating effect becomes progressively evident at greater depth, reaching a depth of 130 m after 45 years (2015). Moreover, the numerical results for the first 100 m are in good agreement with the temperature profiles measured by the fiber optics for the measurement period (2013–2015). Figures 5 shows the temperature profiles in 2014 measured by the fiber optics in the four boreholes. The temperature profiles in B2, B3 and B4 coincide with each other and display a higher temperature in the first 20 m compared to B1. This could be attributed to the distance of each borehole from the feeder pipe, which is located at an average depth of 2.5 m. Given that B2, B3 and B4 are 4 m closer to the feeder pipe than B1, the heat loss effect from the feeder pipe will be more enhanced in theese three boreholes. This effect is also observed in the numerical analysis results presented in Figure 6. 3

DURING HARDENING OF THE GROUTING MATERIAL

Figure 7 shows the temperature profile measured one day after injecting the grouting material in B4. Heat is generated during the first hours of hardening of

Figure 5. Temperature profiles measured by the fiber optics in the four boreholes in 2014.

Figure 6. Numerical results of ground temperature at the location of the four boreholes for the year 2014.

the grouting material, which results in a temperature increase along the borehole length. In the following days temperature retrieves its initial undisturbed profile. In the first 18 m temperature is influenced by the air temperature. Below 18 m, the profile during hardening of the grouting material is characterised by a local maxima, of a significantly increased temperature value, at 29 m. This location corresponds to an extended fractured zone, more than one meter thick, based on the borehole televiewer data analysis.

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Figure 7. Temperature profiles at the undisturbed state and during hardening of the grouting material in B4.

The local maxima could be attributed to a local larger quantity of grouting material and/or local lower thermal diffusivity due to gathering of fractures. A local maxima is also observed in the profile of B1, at a depth corresponding to the center of an extended fractured zone (Radioti et al. 2015a). Random large fractures (more than 10 cm wide) or smaller fractures (of an opening between 5 and 10 cm) cannot be identified in the profiles during hardening of the groutting material in this case-study This could be attributed to the width of hotspots corresponding to random fractures, which is lower than the spatial resolution (2 m) and sampling interval (20 cm).

4

DURING THE RECOVERY PHASE OF A DTRT

Figure 8 (right) presents the naturally occurring gamma radiation data (moving average of 2 m) for B3, which were measured to characterise the clay content of the rock formation. High gamma-ray values indicate shale/siltstone layers while low gamma-ray values indicate sandstone/siltstone layers. Figure 8 (left) presents the temperature difference between a recovery profile (after 4h of recovery) and the undisturbed temperature profile for B3. Local peaks in this profile indicate an uneven heat transfer rate through depth. It is observed that temperature local minima correspond to gamma-ray local minima, indicating sandstone/siltstone layers, while temperature local maxima to gamma-ray local maxima, indicating shale/siltstone layers. The higher thermal diffusivity of

Figure 8. Temperature difference after 4h of recovery and natural gamma radioactivity data for B3.

sandstone/siltstone is evident in the in-situ measurements despite the relatively small thickness of these layers. Sandstone/siltstone layers thinner than 1.2 m are not always detectable in the recovery profile. The width of hotspots corresponding to these layers is lower than the measurements spatial resolution (2 m) and the sampling interval (20 cm). Even if these hotspots were included in the measurement points, the measured temperature could be significantly reduced, and hence be undetectable in the temperature profile. 5

DURING THE HEATING PHASE OF A LONG-DURATION DTRT

A TRT of a heating phase of 7 months was conducted in B2. During this test, temperature is measured at the pipe inlet and outlet in B2, as well as by the fiber optics in the four boreholes. These measurements allow to investigate the behaviour of the BHE in B2 through time and to follow the thermal plume in the heterogeneous rock mass. 5.1 Mean ground thermal conductivity and mean borehole thermal resistance The mean thermal conductivity of the surrounding ground and the mean borehole thermal resistance were calculated based on the pipe inlet and outlet temperature data in B2. The Infinite Line Source model (Carslaw & Jaeger 1959) was used for this calculation and the forward regression technique was applied (Tinti 2012). In this technique a start time point is chosen and the end time point increases gradually. During

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Table 1. Mean ground thermal conductivity and mean borehole thermal resistance for the four BHEs. λ∗grout

Rb

λground

BHE (grouting)

W/mK

Km/W

W/mK

B1 (Geosolid) B2 (Füllbinder) B3 (Geosolid) B4 (Hom. admixture)

2.35 0.95 2.35 2.46

0.079 0.095 0.078 0.080

2.94 2.71 3.09 2.80

* Erol & François 2014.

Figure 9. Mean ground thermal conductivity through time for the first 3 months of the heating phase in B2.

Table 1 presents ground thermal conductivity and borehole thermal resistance results, based on TRTs of a duration of 7 days conducted in the four BHEs. The average ground thermal conductivity is 2.88 ± 0.16 W/mK. The Geosolid admixture and the homemade admixture with graphite display approximately the same thermal conductivity and the corresponding BHEs are characterised by a borehole thermal resistance in the order of 0.08 Km/W. The Füllbinder admixture (B2) has a lower thermal conductivity and the corresponding thermal resistance is 19% higher than the other three BHEs. Though the borehole thermal resistance in B2 decreases with time for a longer duration of the heating phase, as presented previously in Figure 10. 5.2 Temperature evolution in the rock mass

Figure 10. Mean borehole thermal resistance through time for the first 3 months of the heating phase in B2.

the first few hours of the test, the temperature evolution is mainly controlled by the borehole filling and is not representative of the surrounding rock thermal properties (Sanner et al. 2005). A start time point of 10 h was chosen for this analysis, based on optical crosschecking of the measured data. Thermal conductivity and borehole thermal resistance were also evaluated for data in limited time windows. Figures 9 shows the calculated mean thermal conductivity for the first three months of the test. The obtained thermal conductivity values range from 2.66 W/mK to 3.06 W/mK (difference less than 15%) based on the two techniques for the period of 3 months. Figures 10 shows the calculated mean borehole thermal resistance for the first three months of the test. The borehole thermal resistance ranges from 0.093 Km/W to 0.11 Km/W for the first 20 days. Between 20 days and 30 days the thermal resistance decreases of 17% and it converges around a value of 0.085 Km/W for the rest of the time period.

Figure 11 displays the temperature increase through time in the four boreholes. Data for B2 correspond to the mean temperature of the pipe inlet and outlet. Data for the other three boreholes correspond to the depth-average temperature measured by the fiber optics. Temperature starts to increase after approximately 5 days in B3, 10 days in B1 and 16 days in B4. Temperature increases at a higher rate in B3 than the other two boreholes, since this borehole has the smallest distance to B2. Likewise, the lowest increase rate is observed in B4 which is located at the greatest distance to B2. These measurements illustrate the effect of the distance to the heating source on the temperature evolution in the rock mass. Figure 12 shows temperature measured in B3 during the heating phase of the DTRT in B2. The first approximately 18 m are influenced by the air temperature. Temperature starts to increase at the lower part of the borehole, since this part has a smaller distance to B2 than the upper part and is characterised by thick sandstone layers. Figure 13 shows the temperature increase evolution at a depth location of 77.2 m, which corresponds to a local maxima in the temperature profile, and at a depth location of 82.8 m, which corresponds to a local minima of the temperature profile. These locations have approximately the same distance to B2. The temperature difference between the two profiles increases with time, reaching an order of magnitude of 0.3◦ C after 90

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Figure 13. Temperature increase evolution at certain depths in B3.

Figure 11. Temperature evolution in the four BHEs (B2: mean of pipe inlet and outlet temperature – B1,B3,B4: depth-average temperature by fiber optics).

Figure 14. Temperature difference after 78 days of heating and natural gamma radioactivity data for B3.

Figure 12. Temperature profiles in B3 during the heating phase of the DTRT in B2.

days. This indicates a higher heat transfer rate at the location of the local maxima, compared to the one of the local minima. Figure 14 presents the temperature difference between the temperature profile after 78 days and the

undisturbed temperature profile (left), together with the gamma-ray data for B3. It is observed that the local maxima at 77.2 m depth corresponds to the top of a sandstone/siltstone layer and the local minima at 82.8 m depth to the top of a shale/siltstone layer. B3 is characterised by the same lithostratigraphy with B2 but at a lower depth, due to the layer dip angle orientation (45◦ SE). The measured profiles could be the result of the heat diffusion due to the uneven heat transfer rate along the direction of the different layers, which are characterised by a dip angle of 45◦ SE.

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6

CONCLUSIONS

This study presents the analysis of temperature profiles measured by fiber optics in four BHEs in an heterogenous bedrock. The undisturbed ground temperature profiles are characterised by a negative temperature gradient. These profiles can be the result of the heating of the ground by structures located close to the boreholes, as verified also by the 3D numerical model. Temperature profiles during hardening of the grouting material allow to locate extended fracture zones, more than one meter in this specific case. Based on temperature measurements during the recovery phase of a DTRT layers with different mineral content can be detected since they display a different thermal behaviour. The results are in good agreement with those of the borehole televiewer logging method Layers thinner than 1.2 m or random fractures cannot be identified by this procedure in this case-study. The resolution of the applied procedure is limited by the measurement parameters, spatial resolution and sampling interval. The influence of the duration of a TRT to the mean ground thermal conductivity and mean borehole thermal resistance is also investigated. In this case-study, thermal conductivity varies less than 15% for a heating period of 3 months, based on temperature data of the pipe inlet and outlet. The mean borehole thermal resistance decreases of 17% after the first 30 days of the test. Moreover, the BHE with lower grouting thermal conductivity displays a higher borehole thermal resistance. Measuring the temperature in all the boreholes during the long-duration TRT allows to follow the thermal plume in the heterogenous rock mass. The effect of the distance to the heating source and the effect of the rock heterogeneity are displayed in theese measurements. Given the increasing number of closed-loop geothermal systems and the wide application of TRTs, it would be of interest to measure the temperature along the BHE length at the undisturbed state, during hardening of the grouting material and during the recovery phase. Alternatively to fiber optic cables, temperature through depth can be measured by lowering down a temperature sensor into the geothermal pipe. Analysing theese profiles could give valuable information about the rock heterogeneity, the influence of the surrounding structures to the ground temperature field, as well as about the rock geothermal reservoir potential. These information could be included in an advanced numerical model, to predict the long-term behaviour of closed-loop geothermal systems and to optimise their efficiency.

Charlier, R., Radu, J.-P. and Collin, F. (2001). Numerical mod elling of coupled transient phenomena. Revue Française de Génie Civil, 5(6), 719–741. Climate-data.org. Climate data for cities worldwide. Last ac cessed 15-10-2015, http://en.climate-data.org/ Collin, F., Li, X.L., Radu, J.-P. and Charlier, R. (2002). Ther mo-hydro-mechanical coupling in clay barriers. Engineering Geology, 64, 179–193. Erol, S. and François, B. (2014). Efficiency of various grouting materials for borehole heat exchangers. Appl. Therm. Eng., 70, 788–799. Fujii, H., Okubo, H., and Itoi, R. (2006). Thermal Response Tests Using Optical Fiber Thermometers. GRC Transac tions, 30, 545–551. Hermans, T., Nguyen, F., Robert, T. and Revil, A. (2014). Ge ophysical methods for monitoring temperature changes in shallow low enthalpy geothermal systems. Energies, 7 (8), 5083–5118. Hoffmann, L., Müller, M. S., Krämer, S., Giebel, M., Schwotzer, G. and Wieduwilt, T. (2007). Applications of Fibre Optic Temperature Measurement. Proc. Estonian Acad. Sci. Eng., 13 (4), 363–378. Monier-Williams, M.E., Davis, R.K., Paillet, F.L., Turpening, R.M., Sol, S.J.Y and Schneider, G.W. (2009). Review of Borehole Based Geophysical Site Evaluation Tools and Techniques (Rep. NWMO TR-2009-25). Retrieved from Nuclear Waste Management Organization website: http://www.nwmo.ca/uploads_managed/MediaFiles/ 1770_n wmotr-2009-25boreholebasedgeophysicaltools_ r0d.pdf Radioti, G., Charlier, R., Nguyen, F. and Radu, J.-P. (2013). Thermal Response Test in Borehole Heat Exchangers Equipped with Fiber Optics. In: Proceedings, International Workshop on Geomechanics and Energy: The Ground as Energy Source and Storage. EAGE, Lausanne, Switzerland, 96–100. Radioti, G., Delvoie, S., Radu, J.-P., Nguyen, F. and Charlier, R. (2015a). Fractured bedrock investigation by using highresolution borehole images and the Distributed Temperature Sensing technique. In: ISRM Congress 2015 Proceedings – Int’l Symposium on Rock Mechanics, ISRM, Montreal, Can ada. Radioti, G., Delvoie, S., Sartor, K., Nguyen, F. and Charlier, R. (2015b). Fiber-optic temperature profiles analysis for closed-loop geothermal systems: a case study. In: Proceed ings, Second EAGE Workshop on Geomechanics and Ener gy:The Ground as Energy Source and Storage. EAGE, Cel le, Germany. Sanner, B., Hellström, G., Spitler, J., and Gehlin, S. (2005). Thermal Response Test – Current Status and World-Wide Application. Proceedings World Geothermal Congress 2005, 24–29. Sartor, K., Quoilin, S. and Dewallef, P. (2014). Simulation and optimization of a CHP biomass plant and district heating network. Appied Energy, 130, 474–483. Tinti, F. (2012). The probabilistic characterization of under ground as a tool for the optimization of integrated design of shallow geothermal systems (Doctoral dissertation). Univer sity of Bologna, Italy.

REFERENCES Carslaw, H.S., and Jaeger, J.C. (1959).Conduction of Heat in Solids, second edition. New York: Oxford University Press.

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Temperature distribution in the vicinity of a borehole heat exchanger for intermittent heat extraction: An analytical solution S. Erol & B. François Building, Architecture and Town Planning Department (BATir), Université Libre de Bruxelles, Brussels, Belgium

ABSTRACT: Existing analytical solutions for thermal analysis of closed-loop ground heat exchangers systems evaluate temperature change in the heat carrier-fluid and the surrounding ground in the production period of Borehole Heat Exchangers (BHE) only if a continuous heat load is assigned. In the present study, we solve analytically the heat conduction/advection/dispersion equation in porous media, for intermittent heat extraction. We convolute rectangular function or pulses in time domain both for single and multi-BHEs field. The solution includes non-symmetric configurations around the BHEs by considering anisotropic features induced by groundwater convection or intrinsic anisotropy of thermal conductivity. Thermal dispersivity linked to the ground water flow is also considered. The validity of the analytical model is checked through the comparison with results obtained from numerical finite element code. The comparison results agree well with numerical results both for conduction and advection dominated heat transfer systems, and analytical solutions provide significantly shorter runtime compared to numerical simulations. The developed tool allows also to investigate the recovery aspects and the sustainability of closed-loop ground heat exchangers systems in terms of temperature and the energy deficit of the ground.

1

INTRODUCTION

The Ground Source Heat Pump (GSHP) system technologies are the most often application of the shallow geothermal energy use and primarily reduce the energy consumption for the space heating and cooling supplied from the conventional systems. In order to evaluate the necessary drilling depth of a borehole heat exchanger and the regulation of the heat input, the specific heat extraction rate should be optimized regarding the characteristics of the hydrogeological conditions for the long term operational effects in the fields. This is particularly the case for multi-BHEs that may affect significantly the ground temperature on a relatively large area. After an operation period of BHEs, the ground needs time to recover from the temperature drop to sustain the performance of the system in the long-term run (e.g. 30 years) (Signorelli 2004; Rybach and Eugster 2010). In order to investigate an operation both with the heat extraction and the subsequent recovery periods of BHEs, including the groundwater flow dispersion in a porous medium and the axisymmetric heat transfer along the BHE, the 3D numerical simulation tools undergo a large computational effort and require long execution time. On the other hand, most of the analytical solutions described in literature consider a constant continuous heat extraction/injection in time merely for a single BHE (Eskilson 1987; Zeng et al. 2002; Sutton

et al. 2003; Diao et al. 2004; Marcotte et al. 2010; Man et al. 2010; Molina et al. 2011). Until now, intermittent heat extraction can be taken into account through simplified assumptions (Eskilson 1987; Hellström 1991; Claesson and Eskilson 1988). The objective of this study is to develop an analytical solution to evaluate temperature change in the ground both for single and multi-BHEs that considers intermittent heat extraction, thermal conduction, advection and dispersion. This new analytical solution may further help to investigate the regulatory issues such as the recovery of groundwater temperature after the use of GSHP systems, and also can be used in TRT operations for predicting the ground thermal properties (Erol et al., 2015). We start from the Green’s function which is the solution of heat conduction/advection/dispersion equation in porous media and apply an analytical convolution of that function with a rectangular function or pulses, which have different period length and pulse height. The evolution of the mean fluid temperature of the carrying fluid to maintain a constant heat extraction rate is evaluated along the time. Temperature evaluation in the surrounding ground is also deduced. The developed equation is verified with the finite element method software COMSOL Multiphysics. Furthermore, the energy balance of the ground is investigated with the analytical solution during 30 years of production period, and the subsequent energy recovery of the ground after the system is shutdown.

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2 ANALYTICAL DEVELOPMENT 2.1

Single BHE

In geothermal literature, the existing finite and cylindrical analytical solutions with a constant heat load may provide satisfactory estimation of ground thermal parameters to design closed-loop ground heat exchangers systems (Deerman and Kavanaugh 1991; Kavanaugh and Rafferty 2014; Gehlin 2002). In a real case, the systems can be operated with various periods in a given time for different heat extraction/injection rates, instead of a continuous operation as assumed in most of other previously presented analytical methods. Some authors evaluated the temperature change for TRT operation in the vicinity of a single BHE or BHEs field with an analytical solution by using multiple load aggregation algorithms (Yavuzturk 1999; Bernier et al. 2004; Marcotte and Pasquier 2008; Lamarche 2009; Michopoulos and Kyriakis 2009; Michopoulos and Kyriakis 2010). However, some of those approaches may not be appropriate in all cases to evaluate the accurate temperature change in the ground due to neglecting the axial effect, considering only single BHE or not taking into account groundwater flow. In particular when Darcy’s velocity in porous media is considered, the thermal dispersion coefficients must be taken into account, because thermal dispersion has a large impact on the distribution of the temperature plume around BHE, for Darcy’s velocity larger than ×10−8 m/s (Molina et al. 2011). The governing equation of the heat advection/dispersion in porous media is given as follows:

in which uw,x is the Darcy’s velocity on the x-direction, s is a volumetric heat source, and ρm cm is the volumetric heat capacity of the medium, which can be calculated as the weighted arithmetic mean of the solids ρs cs and volumetric heat capacity of water ρw cw (de Marsily 1986):

The solution of the partial differential equation for heat transfer in porous media (Eq. 1) is obtained from the Green’s function G of a pulse point source QP at the given point coordinates (x′ , y′ , z ′ ) and time t = 0 (Metzger 2002):

In order to take into account the axial effect and the groundwater flow, this solution can be applied for the response of a constant line-source with finite length H along the vertical z direction with a pulse heat extraction after applying moving source theory (Carslaw and Jaeger 1959) by integrating Eq. 5 along the z-axis (Diao et al. 2004):

where QL is a pulse heat input per meter depth and vT is thermal transport velocity that can be calculated as follows (Molina et al. 2011):

In order to simplify Eq. 6, the exponential function can be integrated by using u-substitution method:

The components of effective longitudinal and transverse thermal conductivities are defined on the directions of x, y and z as follows (Hopmans et al. 2002):

where λm is the bulk thermal conductivity of porous medium in the absence of groundwater flow, ̟l and ̟t are the longitudinal and transverse dispersivities, respectively.The thermal dispersion is a linear function of groundwater flow and relates to the anisotropy of the velocity field (Molina et al. 2011; Sauty et al. 1982).

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The limits of u-value becomes:

Substituting Eq. 10 and Eq. 11 into Eq. 8, allows to re-write the equation as:

To apply an intermittent injection or extraction of heat in time domain, we convolute analytically Eq. 15 with a single or a series of different rectangular pulses referring to the duration of operations in time. For instance, f (x, y, z, t) function is convoluted with a rectangular heat flow rate function qL (t) defined as follows:

in which T is the period of heat extraction. qL is the heat flow rate taken as independent of the depth in our simulations. The convolution of qL and f function is written as follows:

The integration of exponential function f = exp(−u2 ) can be expressed with error function:

By taking the integration of exponential function, therefore, Eq. 12 reduces to:

For the analytical evaluation of the convolution integral equation, we discretize both qL and f functions with a differential of t. So, the convolution as a sum of impulse responses at coordinates (x, y, z) is given as:

where n denote the time span, i t is the time delay of each unit impulse, and the delayed and shifted impulse response becomes qL (i t)f (t-i t) t. By using the same method, it is possible to convolute f function with rectangular pulses which have different pulse height and length in given identical time span of f function. Thus, recovery period of the ground can be investigated after a production of a single BHE and the numerical computational effort will be decreased. 2.2

Multi-BHEs

In case of multi-BHEs, analytical solution Eq. 15 can be solved in a sum function (Eq. 19) depending on the grid coordinates of each line heat source as illustrated in Figure 1. with simplification, Eq. 14 can be expressed with the error functions as follows:

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Figure 1. Illustration of multi-BHEs geometry demonstrating the grid coordinates.

in which s represents the number of BHEs. We consider the impact of groundwater flow on each BHE at x direction by taking into account thermal transport velocity vT . The sum C(x, y, z, t) can be convoluted as described in the previous Section 2.1 to apply intermittent heat extraction as follows:

3 VALIDATION The developed analytical solutions (Eq. 18 and Eq. 20), for intermittent heat extraction, are verified with 3D numerical models. For the verification, numerical model setup, initial and boundary conditions of the model, input parameters and comparison of the numerical and the analytical solution results are presented in the following. 3.1

Figure 2. Load profile of heat extraction. Table 1. Common initial input parameters for the model domain of single and multi-BHEs field. Parameters

Value

Initial temperature ◦ C (To ) Bulk thermal conductivity of porous medium W m−1 K−1 (λm ) Effective thermal conductivity in the longitudinal direction W m−1 K−1 (λx ) Effective thermal conductivity in the transverse direction W m−1 K−1 (λy = λz ) Volumetric heat capacity MJ m−3 K−1 (ρm cm ) Groundwater flow / discharge m s−1 (uw,x ) Longitudinal thermal dispersion coefficient (̟ l ) Transverse thermal dispersion coefficient (̟ t )

0 2.4a 6.6b 2.82b 2.8a 1 × 10−6c 1d 0.1d

a

Representative values taken from (VDI-Richtlinie 2000). Calculated values according to Eq. 3 and 4. c Assigned only for the models in which heat advection/dispersion is considered. d Values taken from (Hecht-Méndez et al. 2013) to calculate effective thermal conductivities. b

Numerical model setup

In order to validate the analytical solution developed above, simple cases for single and multi-BHEs have been considered through numerical models using COMSOL Multiphysics software. The common numerical characteristics are described here for both single and multi-BHEs field models. The study is carried out by a 3D homogeneous model domain and BHE is represented with the line heat source(s) (W m−1 ). A model domain of 40 m × 40 m in the horizontal direction and 60 m in the vertical direction is set for the simulation. The length of line heat source is 50 m for each. The mesh is generated using uniform tetrahedral elements. The coordinates of single and multi-lines heat sources are shown in Figure 3. In order to get a better resolution of the temperature variations around the line source, close to it the mesh is further refined along the length of line source and also along the line on which the observation point are placed (at the depth of 25 m).

As the boundary conditions, the load profile of heat extraction with three different extraction periods can be seen in Figure 2. The simulation time is restricted to 160 days. The top of the model surface temperature is fixed to 0◦ C, as well as identically assigned initial temperature, to observe the relative temperature change in the subsurface. Initial input parameters are given in Table 1. Thermal dispersion is taken into account leading to anisotropic thermal conductivity of the medium, as described by Eq. 3 and 4. The number of elements changes depending on the model of single or multi-lines heat sources (Table 2). For the simulations, the basic heat transfer module of COMSOL Multiphysics, which uses Fourier’s law, is used, and the groundwater flow is imposed through a homogeneous velocity field. The Backward Euler (Crank-Nicolson Scheme) time marching method with RMS error tolerance of 10−3 is applied and the maximum time step interval set to 86400 s due to better

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approximately 1500 times smaller than the runtime of numerical models. Note that, for the analytical solution, the computation time depends on the number of observation point. It has the advantage that it can reduce the calculation time as a function of the amount of required information.

Table 2. Summary of the model setup for verification. Parameter

Value

Type of problem Numerical method for heat transfer Simulation time Number of elements solved for single BHE model/multi-BHEs model Solver type

3D Standard Galerkin-FEM 160 days 834,679/1,975,633

3.3 Multi-BHEs Flexible Generalized Minimal Residual method

Table 3. Comparison the execution times and time steps for single BHE.

Model

Number of time stepa Runtime (Total simulation) [s] a

Analytical solution (Eq. 18) 2562 Numerical model 1 162 no groundwater flow Numerical model 2 162 with groundwater flow of 1 × 10−6 m/s

9b /13c 15986

Eq. 20 is solved on MATLAB and compared with the numerical results. According to the results, again the analytical method solution agrees with numerical results both with (Figure 6) and without the groundwater flow (Figure 7). The small discrepancy between the results of advection/dispersion case can be accounted for the mesh discretization of the numerical simulation. Comparison of Figure 6 and Figure 7 shows that the maximum temperature decrease in the ground is substantially reduced by the groundwater flow (from –12 K to –8 K in the simulated case).

16974

4

a

Hardware specifications: Intel, 4 core i-5 3.10 GHz, RAM: 16 GB. b Calculation for 5 observation points. c Calculation for 7 observation points (Figure 4 and Figure 5).

SUSTAINABILITY AND RECOVERY ASPECTS

The objective of this section is to evaluate the longterm sustainability of the system and the energy deficit of the ground by comparing the temperature distribution in the vicinity of a BHE and the heat fluxes.

robustness. Table 2 provides a summary of the model setups. For verification plots, temperature changes are observed in time on the x direction of the coordinate system (Figure 3). 3.2

Single BHE

The Eq. 18 is solved on MATLAB and compared with the numerical results. According to the results, the analytical method solution agrees well with numerical results both under conduction (Figure 4) and advection/dispersion dominated heat transfer systems (Figure 5). Comparing the results of temperature difference between conduction and advection/dispersion heat transfer systems, the impact of the groundwater flow/dispersion appears clearly. The first heat extraction phase generates larger temperature decrease in the point located in the x-direction when groundwater flow and dispersion are considered. However, the recovery phase is accelerated due to water flow. Consequently, the subsequent heat extraction induces lower temperature change in the ground close to the BHE. Also, with time, temperature is impacted at larger distance in the direction of the water flow when the groundwater flow and the dispersion are considered (at 10 m, T = 0.8 K with water flow vs T = 0.2 K without water flow). The significant advantage of analytical method can be seen in Table 3. The execution time of Eq. 18 is

Figure 3. Illustration of temperature observation points on the x direction: a) for single BHE b) for multi-BHEs field. Groundwater flow is set on the x direction.

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Figure 4. Comparison of numerical and analytical solution results at the depth of 25 m for single line heat source without groundwater flow. Induced by the load profile of Figure 2.

Figure 5. Comparison of numerical and analytical solution results at the depth of 25 m for single line heat source. Under groundwater flow of 1 × 10−6 m/s on the x-axis direction. Induced by the load profile of Figure 2.

Figure 6. Comparison of numerical and analytical solution results at the depth of 25 m for multi-BHEs field without groundwater flow.

The study is carried out with the developed analytical solution on MATLAB. The scenario contains a production period of 30 years, and a subsequent recovery phase, which is identical duration as the production period. A constant continuous heat extraction of 10.27 W m−1 is applied along 30 years operation period (the total amount of heat extraction 9000 kWh per year = 50 W m−1 × 100 m × 1800 h is distributed hourly for a single BHE with a length of 100 m). The bulk thermal conductivity of the ground is λm = 1.5 W m−1 K−1 , and the bulk volumetric heat

Figure 7. Comparison of numerical and analytical solution results at the depth of 25 m for multi-BHEs field under groundwater flow of 1 × 10−6 m/s on the x-axis direction.

capacity is 2.5 MJ m−3 K−1 . The thermal properties of the ground are set as an average value of soils, which can be seen in shallow subsurface such as clay or silica-sand, and the groundwater flow is not considered. In Figure 8, the relative temperature change results are plotted (e.g. the temperature difference between plume temperature ensuing from the operation and initial ground temperature) during the production and the subsequent recovery phase of the ground. The results show that even at 10 m distance from the BHE, the mean temperature decrease is nearly 0.3 K after 30 years of the ground temperature recovery. Moreover, the bulk energy deficit of the ground demonstrated in Figure 9 is calculated based on the volume integration method respect to the temperature change. During the production period, the Eq. 20 accounts for the balance between the energy extraction and the lateral heat flux in the ground and during the recovery period only the lateral heat flux in the ground is considered. The bulk energy deficit in the ground can be calculated in axisymmetric conditions as follows:

in which H is the length of the BHE and we assume that the energy deficit is identical along the length, T is the temperature change respect to time interval t, dR is the radial distance interval, and R is the radial distance. Compared to the evaluation of the recovery phase respect to the temperature gradient (Figure 8) and regarding to the energy balance in the ground (Figure 9), it can be seen that the justification based on the local change of the ground temperature does not provide a straight insight compared to the replenishment of the bulk ground energy deficit Actually, the fast decline of the temperature deficit after the shutdown of the system is not translated by such a rapid drop of

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Figure 8. Temperature probe of the scenario. Temperature probes at the depth of 50 m from surface.

plume is obtained due to advection and dispersion processes induced by the groundwater movement. The new approach provides significantly shorter computation time compared to numerical simulation to obtain the temperature results of a long-term production of GSHP systems and subsequent recovery period. The consideration of the temperature change in the vicinity of a BHE does not give the direct insight in the replenishment of the bulk ground energy deficit. By taking into account the bulk vertical and the lateral heat fluxes around the BHEs, the evaluation of the energy recovery may be more realistic. As a perspective, our analytical model can serve as a tool to predict the ground thermal evaluation around the BHEs during the heat extraction/injection operations and in the subsequent recovery phase after the GSHP system is shutdown. However, the limitations of the model is that we did not take into account the top surface and the bottom heat fluxes which may accelerate the recovery process in long-term, and the performance of the GSHP system may increase more than we estimated here. ACKNOWLEDGEMENT

Figure 9. The bulk ground energy deficit of Scenario 4, basalt.

energy deficit. The total amount of extracted energy by the BHE over the production period is around 9.72 × 1011 Joule (=10.27 W m−1 × 100 m × 30 years ×3.15 × 107 s/year) and the net energy deficit in the ground after this 30 years of the production period is around 2.7 × 1011 Joule, which means that approximately 70% of the energy already recovered during the production period by the ground lateral heat fluxes (see Figure 9). After subsequent 30 years of recovery, nearly 98 % of the extracted heat is recovered. In the near-field, the consideration of the temperature change is plausible to know if the local temperature drops to the freezing point of the groundwater, but the bulk energy deficit gives more global information about the energy recovery of the ground.

5

CONCLUSION

Analytical solutions of GSHP systems are preferable to have a better comprehension about the heat transfer system of the ground. Starting from the Green’s function, which is a solution of the conduction/advection/dispersion heat transfer in porous media, we deduced an analytical solution that provides temperature distribution around single and multiBHEs for intermittent heat extraction or storage. Axial effect and groundwater flow are considered. The proposed analytical solutions are validated with numerical code. Non-symmetric distribution of temperature

The financial support from Walloon Region in Belgium is profoundly acknowledged (Grand: 1117492 – GeoTherWal – Programme ERable (E24+)). REFERENCES Bernier, M.A., Labib D.P.R & Pine P. 2004. “A Multiple Load Aggregation Algorithm for Annual Hourly Simulations of GCHP Systems”, HVAC & R Res. 10 (4): 471–488. Carslaw, H.S., &. Jaeger J.C. 1959. Conduction of Heat in Solids, Second Edition. US-NY: Oxford University Press. Claesson, J & Eskilson P. 1988. “Conductive Heat Extraction to a Deep Borehole: Thermal Analyses and Dimensioning Rules.” Energy 13 (6): 509–527. Deerman, D.J. & Kavanaugh P.S. 1991. “Simulation of Vertical U-Tube Ground – Coupled Heat Pump Systems Using the Cylindrical Heat Source Solution.” ASHRAE Transactions 97 (1): 287–295. Diao, N., Li Q., & Fang Z. 2004. “Heat Transfer in Ground Heat Exchangers with Groundwater Advection.” Int. J. of Therm. Sci. 43 (14): 1203–1211. Erol S., Hashemi M.A. & François B. (2015). Analytical solution of discontinuous heat extraction for sustainability and recovery aspects of borehole heat exchangers. Int. J. of Thermal Sciences, 88, pp. 47–50. Eskilson, P. 1987. “PhD Thesis: Thermal Analysis of Heat Extraction Boreholes.”, Lund: University of Lund. Gehlin, S. 2002. “PhD. Thesis: Thermal Response Test.”, Luleå: Luleå University of Technology. Hecht-Méndez, J., De Paly M., Beck M. & Bayer P. 2013. “Optimization of Energy Extraction for Vertical ClosedLoop Geothermal Systems Considering Groundwater Flow.” Energy Convers. and Manag. 66: 1–10. Hellström, G. 1991. “Ph.D. Thesis: Ground Heat Storage Thermal Analyses of Duct Storage Systems, I. Theory.” Lund: University of Lund. Hopmans, J.W., Šimunek J. & Bristow K.L. 2002. “Indirect Estimation of Soil Thermal Properties and Water Flux

519

Using Heat Pulse Probe Measurements: Geometry and Dispersion Effects.” Water Resour. Res. 38 (1): 7–14. Kavanaugh, S. P., & Rafferty K. 2014. Geothermal Heating and Cooling: Design of Ground-Source Heat Pump Systems. ASHRAE. Atlanta, US–GA. Lamarche, L. 2009. “A Fast Algorithm for the Hourly Simulations of Ground-Source Heat Pumps Using Arbitrary Response Factors.” Renew. Energy 34 (10): 2252–2258. Man, Y., Yang H., Diao N., Liu J. & Fang Z. 2010. “A New Model and Analytical Solutions for Borehole and Pile Ground Heat Exchangers.” Int. J. Heat Mass Transf. 53 (13–14): 2593–2601. Marcotte, D., Pasquier P., Sheriff F., & Bernier M. 2010. “The Importance of Axial Effects for Borehole Design of Geothermal Heat-Pump Systems.” Renew. Energy 35 (4): 763–770. Marcotte, D., and Pasquier P. 2008. “Fast Fluid and Ground Temperature Computation for Geothermal GroundLoop Heat Exchanger Systems.” Geothermics 37 (6): 651–665. Metzger, T. 2002. “PhD Thesis (in French): Dispersion Thermique En Milieux Poreux: Caractérisation Expérimentale Par Technique Inverse.”, Nancy, Institut national polytechnique de Lorraine (INPL). Michopoulos, A., & Kyriakis N. 2009. “A New Energy Analysis Tool for Ground Source Heat Pump Systems.” Energy and Buildings 41 (9): 937–941. Michopoulos, A., & Kyriakis N. 2010. “The Influence of a Vertical Ground Heat Exchanger Length on the Electricity Consumption of the Heat Pumps.” Renew. Energy 35 (7): 1403–1407. Molina-Giraldo, N., Bayer P., & Blum P.. 2011. “Evaluating the Influence of Thermal Dispersion on Temperature Plumes from Geothermal Systems Using Analytical Solutions.” Int. J. of Therm. Sci. 50 (7): 1223–1231.

Molina-Giraldo, N., Blum P., Zhu K., Bayer P., & Fang Z. 2011. “A Moving Finite Line Source Model to Simulate Borehole Heat Exchangers with GroundwaterAdvection.” Int. J. of Therm. Sci. 50 (14): 2506–2513. Rybach, L., & Eugster W.J.. 2010. “Sustainability Aspects of Geothermal Heat Pump Operation, with Experience from Switzerland.” Geothermics 39 (4): 365–369. Sauty, J. P., Gringarten A.C., Fabris H., Thiery D., Menjoz A., & Landel P.A. 1982. “Sensible Energy Storage in Aquifers: 2. Field Experiments and Comparison with Theoretical Results.” Water Resour. Res. 18 (2): 253–265. Signorelli, S. 2004. “PhD Thesis: Geoscientific Investigations for the Use of Shallow Low Enthalpy Systems.”, Zurich: Swiss Federal Institute of Technology. Sutton, M. G., Nutter D.W., & Couvillion R.J.. 2003. “A Ground Resistance for Vertical Bore Heat Exchangers With Groundwater Flow.” J. of Energy Resour. Technol. 125 (3): 183. VDI-Richtlinie. 2000. “Thermal Use of the Underground – Fundamentals, Approvals and Environmental Aspects, VDI 4640 Blatt 1.” Düsseldorf: Verain Deutscher Ingenieure, VDI-Verlag. Yavuzturk, C. 1999. “PhD Thesis: Modeling of Vertical Ground Loop Heat Exchangers for Ground Source Heat Pump Sytems.” US-OK: Oklahoma State University. Zeng, H. Y., N.R. Diao, & Fang Z.H.. 2002. “A Finite Line-Source Model for Boreholes in Geothermal Heat Exchangers.” Heat Transfer Asian Research 31 (7): 558–567.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Use underground reservoir in Taipei basin as cooling source for air conditioners H.J. Liao Department of Civil and Construction and Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan

Chihping Kuo Department and Institute of Civil Engineering and Environmental Informatics, Minghsin University of Science and Technology, Hsinchu, Taiwan

ABSTRACT: To use the underground reservoir in Taipei basin as the cooling source for air conditioners, a full scale test was carried out in the campus of NTUST to cool down a 15 RT (Refrigeration Tons) air conditioner. Two types of circulating water system were adopted: one is open system; the other is closed system. The open system pumps up groundwater directly from the underground reservoir. It offers a constant temperature cooling source for air conditioners (AC units). After doing heat exchange with AC units, the heated groundwater is discharged back to the reservoir through an open well. Test results showed that the open system has a high cooling capacity and was capable of keeping a 15 RT AC unit running continuously. Since no groundwater was pumped out from the reservoir, ground subsidence was no concern for the open system. In comparison, the closed system discharges the exhaust heat from the AC units through a closed loop pipe which is submerged in the groundwater inside a well. The heat is transmitted to the underground reservoir by means of the circulating water in the pipe loop. However, the heat transmission rate of the water saturated ground is limited and it was unable to dissipate all the exhaust heat from the 15 RT AC unit. As a result, the heat quickly built up around the pipe loop. The AC unit was shut down after running for only a few hours due to overheat. Obviously, the cooling capacity of the closed system is much lower than that of the same well system used by the open system. The groundwater pumping rate of the open system could also be adjusted using a PLC unit based on the actual cooling need of AC unit to further cut down the running cost of water circulation. Numerical simulation also confirms that the heat exchange rate of the closed system is much lower than the open system even though the flow rate of groundwater is capable to carry the same amount of heat away. 1 1.1

INTRODUCTION

accumulated in the basin where Taipei city locates. As a result, the air temperature is increased and makes the heat island effect more serious (Hsieh et al. 2007).

Geographical and climatic conditions

Taipei Basin, located in the northernTaiwan and in subtropical area, covers approximately an area of 243 km2 with the average elevation about 20 m above sea level. It is surrounded by Datun volcanoes in the north; by Linkou tableland in the west; and by hills and mountains in the east and the south. Several major rivers meander through the Taipei basin, namely Tanshui river, Keelung river, Xindian river and Dahan river. Taipei city locates right in the Taipei basin. The weather in summer is hot and humid. Over the past decades, the mean daily surface temperature of Taipei city had been rising from 28.0◦ C in 1960 to 29.5◦ C in 2005 (Chen et al. 2007). In addition, the number of days with temperature above 35◦ C is increased also. Air-conditioners have become a necessity to cool down the indoors temperature in summer. Among the air conditioners used, a large majority are air-cooled type. In other words, most of the heat exhausted from air-conditioners is discharged to the open air and

1.2

Geological and groundwater conditions

Generally, sediments deposited from different rivers are various: soft clays deposited from Keelung river; gravels deposited from Xindian river; and sandy layers deposited from Dahan river. Basically, the sandy and clayey deposits in Taipei basin are underlaid by gravel deposit. The thickness of gravel stratum increases gradually from Xindian in the southeast to Tansui in the northwest (Figure 1). As estimated by Chen (2005), there is about 68.4 billion m3 of groundwater stored in the gravel stratum of Taipei basin. Kuo and Liao (2011) studied the directions and quantities of the groundwater flow in the gravel stratum using the numerical software MODFLOW. The direction of groundwater flow was indicated by the vectors in Figure 2. The average quantity of water budget is about 3.5 × 104 3 /day (cmd) for

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Figure 1. Schematic diagram of the basin profile.

Figure 3. Closed type and open type cooling water circulation.

Figure 2. Schematic diagram of the basin profile.

the entire basin. The value of water budget in the study area can be converted into the groundwater flux, i.e., groundwater velocity, of 13.0 cm/day. The measured temperature of the groundwater changes from 24◦ C in winter to 26◦ C in summer.

The feasibility of using open system in Chingmei gravel stratum has been verified through a field pumping and recharging test and a numerical simulation (Kuo and Liao 2012). These results were adopted and implemented to the full scale groundwater circulation test in a power transform station in the campus of National Taiwan University of Science and Technology (NTUST). Both open type and closed type systems (Figure 3) were studied in full scale and the test results are presented in this paper. 2

HYDROLOGICAL CONDITIONS IN NTUST

1.3 The alternative method

2.1 Location

Since the groundwater resource is rich in the basin, an alternative method for the cooling of AC units is proposed here. To mitigate the above mentioned heat island problem, the exhaust heat from the AC units can be discharged to the underground reservoir in the gravel stratum underlying Taipei city by means of circulating groundwater/water system. Two types of groundwater cooling system, namely the open system and the closed system, can be used. The open system consists of a group of integrated deep wells which pump up cool groundwater and provide a steady cooling source for ACs. After doing heat exchange with the ACs, the heated water was discharged back to the reservoir. During the circulation process, underground reservoir only acts as a heat sink. All the groundwater being pumped up is recharged back to the underground reservoir immediately. So, no pumping induced ground subsidence is expected. In comparison, the closed system brings the heat from AC units down to the underground reservoir through the circulating water in a closed loop pipe. No groundwater is pumped up or discharged in the closed system.

NTUST locates at the southeast side of Taipei basin.As shown in figure 2, flowing direction of groundwater is generally from south to north at the NTUST site. 2.2 Underground soils profile and flowing of groundwater As shown in figure 4, the gravel stratum underneath the NTUST site was located 39∼60 m below ground surface. Inside the gravel stratum, there was a varve clay layer (Wuku layer) of 4 m thick (GL −46∼ −50 m) dividing the gravel layer into upper layer (Chingmei stratum) and lower layer (Banciao stratum). The groundwater levels of the upper and lower layers were located at GL −12.5 m and GL −10 m respectively during the period of testing. Pumping test were performed to estimate the transmissive parameter (T) and it was about equal to 0.0003 m2 /sec. As shown in Figure 2, the direction of groundwater flow were measured and matched the results from numerical simulation. Its velocity also measured and is equal to 0.005 m/sec.The temperature of the groundwater is about 23.5◦ C.

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to get the cool from the groundwater without letting the groundwater flow into the air conditioner. The PHE consisted of 17 heat exchange plates with the heat exchange area of 1.92 m2 . The heat load of this PHE unit was ∼80 kW. It was more than the nominal heat exchange needed for this 15 RT air conditioner (cooling capacity = 24 kWh). Inside the PHE unit, the heated water from AC was separated from the cool groundwater coming from the well by corrugated stainless steel plates. As the heated water flowing through the PHE unit, it exchanges heat with cool groundwater inside the PHE. After that, the exhaust heat from AC was brought down to the gravel stratum by the circulating water. Two types of circulation system were tested here: open system circulates groundwater between aquifer and PHE via wells; closed type circulation system circulates cooling water in a closed loop pipe installed in the wells. 4.2

Figure 4. Aquifer layers under the NTUST test site.

3

METHODOLOGY

Both full-scale tests and numerical simulation of closed type and open type cooling water circulation were performed and compared in this study.

4 4.1

FIELD TEST AT NTUST SITE Heat generating and exchanging devices

The power transform station in NTUST covers a floor area of 124 m2 . Without air conditioning (ie., with only natural air ventilation), the typical indoor temperature rise in the station room was about 5◦ C over a 24 hour period in summer. To control the room temperature, a 15 RT (Refrigeration Tons) water-cooled air conditioner was installed. The air conditioner had a nominal cooling capacity of 82000 BTU/hr (=24 kWh). It equipped with two scroll type compressors. The nominal power consumption of the compressor was 11A each at full load (=22A when both compressors are operating). The compressors operated in two modes: one compressor running and both compressors running. The nominal cooling water needed for this air conditioner was 196 liter/min and the nominal operation temperature of the cooling water was 37◦ C out from and 30∼32◦ C into the air conditioner. Any increase in the temperature of cooling water will decrease the cooling efficiency of the compressor. Because the manufacturer of air conditioner did not recommend using untreated groundwater to cool down the compressors directly. A plate heat exchanger (PHE) unit was used here acting as a buffer unit

Open system

Two PVC standing pipes with a diameter of 254 mm were installed in the well. One had openings at GL −42∼−47 m (the upper well); the other had openings at GL −51∼−58 m (the lower well) (Figure 5). Upper well works as the pumping well while lower well works as the discharging well. A submergible pump of 5 hp (horse power) was installed at 36.5 m below ground surface in the upper well to pump up groundwater for the PHE unit. A rise pipe of 13 mm diameter was connected to the submergible pump. The rate of groundwater pumped up from the well was controlled by the programmable logic controller (PLC) and a rotation speed adjustable pump. The pumping rate was adjusted based on the measured temperature of the cooling water used to cool down the compressors of AC. If the measured temperature was too high, the pumping rate was increased to pump up more cool water. The flow rate of circulating water was measured with a GF Signet paddle-wheel flow sensor. The readings from the flow sensor were sent to the PLC to adjust the flow rate from the well. The water level in the well was measured with vibration wire type pressure transducers. The electricity consumption of AC and submergible pump was measured using the electrical Watt meter. Figure 6 shows the measured temperatures from various thermometers during a full day running period of the air conditioner. The groundwater pumped up from the gravel stratum maintained a constant temperature of 23.5◦ C. The indoors temperature of the power transform station was maintained at a constant value of 17.5±0.5◦ C despite the outdoors temperature varying from 20◦ C in the early morning to around 30◦ C at noon. The air temperature measured at the air outlet of AC varied from 12.5 to 16.5◦ C. Occasionally (say, 10 times over a 24-hour period), the air temperature from AC dropped to 7∼8◦ C. It is an indication that AC was in the mode of both compressors running. However, the time period for both compressors running was very short. For most of the time, only one compressor was

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Figure 6. Temperatures measured from different sensors during a full day operation.

Figure 5. Aquifer layers under NTUST campus.

running. In other words, the AC was able to operate in an energy efficient mode under this open groundwater circulation system and consumed less electricity. Figure 6 also shows that the cooling water temperature on the AC side of the plate heat exchanger (PHE) varies from 32∼33◦ C (to AC) to 33∼34◦ C (from AC). It indicates that the compressors of AC were operating at a temperature of about 33◦ C compared with the nominal operating temperature of around 37◦ C when used with cooling tower system. Meanwhile, the temperature of circulating groundwater to the PHE unit on the well side maintained a steady 23.5◦ C (from the well). The flow rate of the circulating groundwater was controlled by the PLC unit. Although the flow rate jumped up and down between 50 and 200 liter/min in Figure 6, the accumulated flow volume provided to the PHE unit was steady. Compared with the nominal flow rate (=196 liter/min) required when a cooling tower is used, the accumulated flow volume of circulating groundwater was much lower than that of cooling tower [∼120000 liters vs. 282240 liters per day (=1440 min * 196l pm)]. It indicates that 23.5◦ C groundwater is capable to keep a 15RT air conditioner running for a full day using only about 40% of cooling water compared with that of cooling tower.

Figure 7. Schematic diagram of closed circulating water system for AC.

4.3 Closed system Unlike the open system, no groundwater is pumped up from the gravel stratum in the closed system to cool down the AC. Instead, water circulating in the closed system is in a closed pipe (Figure 7). It exchanges the heat with the surrounding groundwater through the outer wall of a double pipe. As mentioned earlier,

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the test well was divided into upper well and lower well. A 40 m long double pipe with an inner diameter of 10 cm was installed in the upper well; while a 60 m long double pipe with an inner diameter of 12.7 cm was in the lower well. The double pipes in the upper and lower wells were connected in series manner. Seamless steel pipe was used for the outer pipe and a PVC pipe of 5 cm in diameter was used as the inner pipe. PVC pipe was used because it has a better heat isolation property to minimize the heat exchange inside the double pipe. Outside the double pipe, there was a PVC pipe of 20 cm in diameter. It was perforated at the depth of GL −41 to −45 m and GL −52 to −60 m to allow groundwater flow in and out of the PVC pipe easily. The annular space between PVC pipe and well wall was back filled with gravel. Only the submerged length of the double pipe in the well was counted as the effective length for heat exchange between heated circulating water and ground/groundwater. At the time of the experiment, the groundwater water level was at GL −25 m. So the submerged length (the effective length) of the double pipe was about total to 50 m. The schematic diagram for the closed type system is shown in Figure 7. The same PHE unit as the open system was used. A pump with 3 hp and flow rate of 150 liter/min was installed on the well side of the PHE unit to circulate the water in the closed system to and fro the ground. No submergible pump was used in the closed system. The heated water flowing out from the PHE unit was pumped to the PVC inner pipe of the double pipe first and back from the annular space between PVC pipe and outer steel pipe. On its way back to PHE unit, the heated water exchanged the heat with ground/groundwater through the outer steel pipe. The heat load of the PHE unit used here was equal to 70∼79 kW. But the heat exchange capacity of 50 m long submerged pipe was to be determined from this experiment. As shown in Figure 8, the water temperatures on the AC side and the well side of the PHE unit increased quickly when AC was running. Obviously, the heat generated from the AC and the water pump was beyond the heat exchange capacity of this closed circulation system. After running for about 4 hours, the temperature of the cooling water on the AC side of the PHE unit reached about 53◦ C; while the temperature of circulating water on the well side reached about 46◦ C. The AC was shut down automatically to protect the compressor from overheating. After AC shut down, the water circulation pump on the well side stayed running to keep the water in the closed pipe flowing. Under this circumstance, it took 16.5 hours for the water temperature drop back to 30◦ C. But the temperature was unable to drop back to the initial 23.5◦ C (i.e., the initial water temperature when the test started). This was caused by the heat generated from the operating water pump. However, if the water circulation pump was shut down and no more heat contributed to the closed system, the temperature was able to drop back to 23.5◦ C after 24 hours (Figure 9). From the phenomenon observed, it can be concluded that if the generated heat from AC is

Figure 8. Temperature curves and heat exchange curves of AC for the closed system tested here (AC is off but the water circulation pump is on during the cool down period).

Figure 9. Water temperature in and out from the PHE unit (during the cool down period both the AC and water circulation pump were off).

more than the heat exchange capacity of the closed system, the water temperature will keep increasing until the AC automatically shut down for safety reason; otherwise, the water temperature will only increase to a certain value and then remains there. 5

NUMERICAL SIMULATION

Based on the measured local groundwater flow, a heat transport model established from the SHEMAT (Simulator for HEat and MAss Transport, Clauser 2003) program was used to simulate the heat transmission behavior which resulted from two types of circulating water system for AC. 3-D ms consisting of 144 × 142 × 3 cells were used. In the center area (2000 m × 2000 m), each cell represented an area of 1 m × 1 m; outside the center area, each cell represented an area of 10 m × 10 m or 20 m × 20 m depending on the locations. The upper and lower layers were treated as an aquitard, and the middle layer was a confined aquifer. However, SHEMAT can only be used in a layer of constant thickness for the current version. So, a mean value of 30 m was adopted to approximate the thickness of the aquifer. To simulate the flowing groundwater condition in the Chingmei stratum with the SHEMAT program, a line of virtual pumping wells was placed at the effluent boundary of the study area to provide a groundwater flow with velocity = 0.005 m/sec. Meanwhile, a

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line of virtually discharging wells were placed at the inflow boundary. The parameters used in this model were as follows: effective porosity = 0.25 and conductivity = 102 cm/sec (Freeze & Cherry 1979), thermal capacity = 1.875 MJ/m3◦ K and conductivity = 1.308 W/m◦ K (Tindall & Kunkel 1999). 5.1

Open system

A steady recharging well with 200 liter/min and 37◦ C were placed in the central point (1000 m, 1000 m) in the simulated model. The temperature change and distribution is shown in Figure 10. At the first four hours, the heat diffuses mainly radially around the well. The influence of groundwater flow is not significant yet at this stage. After 24 hours, the heat center still keeps diffusing radially around the well but some heat has started to dissipate with the groundwater flow to the downstream. After 168 hours (=1 week), the heat is mainly dissipating along with the groundwater flow. After 240 hours (=10 days), the dissipating heat is carried away mainly by the groundwater flow to the downstream. Very little heat is transmitted laterally to the direction other than the groundwater flow direction. The long-term simulation shows the same distribution pattern. The heat dissipation maintains steadily toward the downstream of groundwater flow. In other words, the exhausted heat discharging from the open system will be carried away by the groundwater flow and will not accumulate around the well. However, due to the limitation of boundary setting, the distribution of exhaust heat extends to a distance of 2 km or more. But it is understood that the exhaust heat from the discharging well will dissipate to the surrounding water body as the heated water flows downstream with groundwater flow. In fact, the numerical results also show that the heat dissipation in vertical direction (depth direction) can be as far as 20 m. So, the heat dissipation distance estimated from the numerical analysis can only be treated as the upper bound cases for the open system. 5.2

Closed system

Closed system means the well will not recharge water into aquifer. Due to the limit of the numerical software, the exhausted heat has to be transferred into equivalent discharging well with steady flow in actual temperature. From Figure 8, the heat generation rate can be estimated to be 0.25 kW/min (=50 kW/200 min). That equals a steady flow with 7.3 liter/min and a 29.5◦ C temperature difference. Therefore, a steady discharging well with 7.3 liter/min and 53◦ C were placed in the central point (1000 m, 1000 m) in the simulated model. Without discharging the water to the reservoir, the diffusion of heat (mainly by heat transmission) is very limited. At the first four hours, the heat diffuses radially and accumulates quickly around the well. Comparing to the open system, the quantity of heat exhausted from this well

Figure 10. 2-D view of simulated short-term to long-term temperature change and distribution for the open system, the axis presents distance in meter.

to aquifer is much less. It means that most of the heat is trapped inside the well and was unable to dissipate to the reservoir. In fact, it took up to 24 hours for the exhaust heat to fully dissipate to restart the closed system again.

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following conclusions can be drawn from the results of this test. 1. The 23.5◦ C groundwater pumped up from the well in the open system can provide a steady cooling source for a 15 RT AC unit running all day long. Using the same well, the heat discharged from the closed system could not keep up with the heat generated from the AC. The water temperature in the closed system kept increasing and caused the AC to shut down due to overheat. The open system can provide a much better cooling capacity to the AC than the closed system 2. The submergible water pump in the open system accounts for a large portion of power consumption. By adjusting the pumping rate using a PLC unit based on the cooling need of AC can reduce the overall power consumption of the system. 3. Due to the slow heat exchange rate between heated water and surrounding ground/groundwater at NTUST campus, the cooling capacity of the closed system is much lower than that of the same well system used by the open system. An optimal operation pattern for a closed system and its matching airconditioners can be established in advance through the temperature curve of circulation water obtained from the field test or numerical analysis. 4. For the open system, the mineral contents of the groundwater may cause scale or contamination problem inside the PHE unit and the circulation pipe. But it has a better heat dissipation capacity. In comparison, water in the closed system has no direct contact with groundwater. No contamination in the pipeline has been experienced over the period of this experiment. REFERENCES

Figure 11. 2-D view of simulated short-term temperature change and distribution for the closed type circulation system, the axis presents distance in meter.

6

CONCLUSIONS AND SUGGESTIONS

A full scale test on two types of cooling water circulation system (open system and closed system) was carried out to cool down a 15 RT (Refrigeration Tons) air conditioner in the campus of NTUST. The

Chen, W.F. 2005.Groundwater in Taiwan. Taipei: Sinobooks. (in Chinese) Chen, T.C., Wang, S.Y., and Yen M.C. 2007. Enhancement of Afternoon Thunderstorm Activity by Urbanization in a Valley: Taipei”, Journal of Applied Meteorology and Climatology, American Meteorological Society, 46, 1324–1340. Clauser, Christoph (Ed.), Numerical Simulation of Reactive Flow in Hot Aquifers, SHEMAT and Processing SHEMAT Freeze, R.A. & Cherry, J.A. 1979. Groundwater. PrenticeHall. Englewood Cliffs NJ. Hsieh, C.M., Aramakia, T, & Hanakia, K. 2007. Estimation of heat rejection based on the air-conditioner use time and its mitigation from buildings in Taipei City. Building and Environment, 42, 3125–3137. Kuo, C.P. & Liao, H.J. 2012. The feasibility of using circulating groundwater as renewable energy sources for air-conditioning in Taipei basin. Renewable Energy 39 (1), 175–182. Tindall, J.A. & Kunkel, J.R. 1999.Unsaturated Zone Hydrology for Scientists and Engineers. Prentice-Hall, London. Tsao,Y.S., Lin, C.N., Tan,Y.C. & Mao, A.S. 1985. Simulation and application of mathematical groundwater model in Taipei Basin. Ministry of Economic Affairs. Taipei. (in Chinese) Wang, C.C. 2007. Heat Exchange Design. Wu-Nan Books Company. (in Chinese)

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Cyclic loading effects on soil-energy pile interaction S. Xiao, M.T. Suleiman & R. Elzeiny Lehigh University, Bethlehem, USA

M.J. Al-Khawaja Qatar University, Doha, Qatar

ABSTRACT: To reduce greenhouse gas emission from space heating and cooling, energy piles have been used in buildings as an alternative renewable energy source for approximate by two decades. However, the effects of cyclic thermal loading, due to the intermittent operation of the heat pump, on the soil-energy pile interaction have not been fully investigated. Energy piles are subjected to cyclic temperature changes that affect the properties of soil-structure (or pile) interface. In addition, the effects of temperature variations produce cyclic expansion and contraction of the pile. To evaluate the effects of radial expansion/contraction cycles, a fully controlled thermal-modified borehole shear test (Thermal-mBST) device was developed at Lehigh University to measure the thermo-mechanical behavior of the soil-energy pile interface. A pair of concrete plates, representing the pile surface, were used. The plates have embedded aluminum small diameter pipes that are connected to a heat pump to control the temperature of the Thermal-mBST. Two linear potentiometers were fixed between the two concrete plates to control/measure the horizontal displacement between the two plates. The testing system is capable of simulating temperature change and cycles, expansion/contraction (displacement) change and cycles, as well as the combination of temperature and expansion/contraction cycles. In this paper, the Thermal-mBST device was utilized to conduct tests with temperature changes (
T) of 0 and +20◦ C at Soil-Concrete Interface (SCI) under initial normal pressure of 41.4 kPa utilizing an aluminum tank filled with silty clay. The tests were performed under heating cycles, expansion cycles, and combined heating and expansion cycles. After applying the cycles, the shearing stage was performed to measure the stress-displacement curves of the soil-pile interface (t-z curves).

1

INTRODUCTION

Shallow geothermal energy, which is one of the promising renewable energy sources, takes advantage of the nearly constant and moderate temperature of the ground to heat and cool buildings. The Ground Source Heat Pump (GSHP) exchanges heat with the ground through a ground heat exchanger.As a development from conventional GSHP systems, energy piles are used to support the superstructure load and also function as ground heat exchangers for heating and cooling of buildings (Brandl 2006). Several published full-scale tests investigated this aspect of energy piles and showed thermally induced deformation and forces in the foundation element (Brandl 2006, Laloui et al. 2006, Bourne-Webb et al. 2009, McCartney & Murphy 2012, Suryatriyastuti et al. 2012 Akrouch et al. 2014 and You et al. 2016). The intermittent operation of the heat pump presents new challenges to foundation engineers, one of which is cyclic thermal loading effects on soil-energy pile interaction. The effects of temperature changes on soilstructure interface properties were investigated by Suleiman & Xiao (2014), Murphy & McCartney (2014), Xiao & Suleiman (2015), and Donna et al.

(2015). Suleiman & Xiao (2014) and Xiao & Suleiman (2015) who utilized Thermal-mBST reported the effects of the monotonic thermal and displacement cycle on soil-concrete interface properties, at temperatures of 2 to 40◦ C. The results showed that expansion/contraction has significant effect on the shear resistance in normally-consolidated unsaturated soil. Murphy & McCartney (2014) performed thermalborehole shear tests in Boulder clay and silty sand considering only the effects of the temperature ranging from 10 to 45◦ C. Short time temperature on the interface did not show major impact on the shape of the normalized T-z curve. Donna et al. (2015) performed soil-concrete interface tests using a modified direct shear device with dry sand and saturated clay in isothermal condition. The testing temperature ranged from 22 to 60◦ C. The results showed that the sand-concrete interface behavior is not affected by the temperature changes at constant normal load nor constant normal stiffness conditions. The tests with clay showed the shear strength increased with increasing temperature due to the effects of temperature on clay deformation. The change of temperature leads to expansion and contraction of the pile altering the normal pressure

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at the soil-pile interface and leading to changes of the soil-pile interface properties (i.e., shaft resistance). Energy pile expands in both axial and radial directions when subjected to heating, and contracts when subjected to cooling. Radial expansion and contraction of energy piles were studied by Suryatriyastuti et al. (2012), Suleiman & Xiao (2014), Xiao & Suleiman (2015), Olgun et al. (2014), and Wang et al. (2015). However, the effects of temperature cycles and expansion/contraction cycles on the soil-pile interface properties have not been fully investigated. In this paper, the Thermal-mBST device was utilized to evaluate the effects of cyclic thermal loading and expansion/contraction cycles on soil and soil-pile interface mechanical properties. 2 TESTING APPARATUS To investigate the effects of temperature and expansion/contraction cycles on the soil-energy pile interface properties, a device with advanced capabilities was used in this research (Figure 1). This device, which is called Thermal-mBST, was developed based on Handy & Fox (1967), Suleiman & Xiao (2014), Murphy & McCartney (2014), and Xiao & Suleiman (2015). Compared to the device used in Xiao & Suleiman (2015), this improved device included the following modifications: (1) the concrete shearing plates were embedded with small diameter aluminum pipes which connect to a heat pump to apply heating and cooling, and insulation was used to reduce the condensation effect on the water content of surrounding soil; (2) thermocouples were installed in the soil and on the surface of the concrete shear plate to measure temperatures at the soil-concrete interface (3) two linear potentiometers were installed between the shear plates to measure the horizontal displacement, and air pressure in the pneumatic piston can be adjusted to control displacements representing the expansion and contraction of energy piles; (4) the testing device was automated, and loads and displacements were fully controlled by a control system during the test. These modifications allow for assigning thermal loading on the concrete shearing plates, measuring the temperature at the soil-concrete interface and temperature distribution in soil, and controlling the horizontal displacement between the plates to simulate the radial expansion and contraction of energy piles. The Thermal-mBST was conducted in the laboratory inside a soil tank with 470 mm in diameter and 610 mm height as shown in Figure 1. The soil borehole at center of the tank where the shear head was placed is 95 mm in diameter. The shear head of the Thermal-mBST includes a pneumatic piston sandwiched between two concrete plates as shown in Figure 1b. Different normal stresses on the soil-concrete interface can be produced by changing the air pressure of the pneumatic piston. The dimensions of the shear plate are 51 by 102 mm. Linear variable differential transformers (LVDTs) were used to measure the vertical movement of the shear head. The pulling force was

Figure 1. Experimental apparatus of the Thermal-mBST: (a) configuration of the step-up; and (b) shear head.

measured by a load cell. A pressure bag was placed on top of the soil to apply 68.9 kPa overburden pressure to consolidate the soil and simulate larger overburden pressure in the soil. 3

SOIL MATERIAL AND PREPARATION

Soil obtained from a construction site in Lehigh Valley, Pennsylvania USA, was used in the Thermal-mBSTs. The soil particle size distribution curve is shown in Figure 2. Using the Unified Soil Classification System (USCS), the soil was classified as silty clay with fines content of 80%. The liquid and plastic limits of the soil were 28% and 22%, respectively. The maximum dry unit weight and optimum moisture content determined using Standard Proctor tests were 17.4 kN/m3 and 14%, respectively. To perform the Thermal-mBST

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Figure 2. Particle size distribution of the soil.

test inside the soil tank, the soil was prepared with a target moisture content of 18%, dry unit weight of 13.7 kN/m3 , and degree of saturation of the soil is 54%. The measured thermal conductivity of the soil at the same moisture content is ∼1.1 W/mK, and the volumetric heat capacity is ∼ 2042 kJ/m3 K. The soil was placed in the tank in 5 layers, each layer was compacted by 25 blows using a steel tamper to achieve the target dry unit weight. A steel tube with a diameter of 95 cm was embedded in the soil along the center of the tank to form a hole through the depth. After compaction, the tube was pulled out to allow for lowering the shear head of the Thermal-mBST inside the created hole. An air bag was placed on top of the soil surface and inflated to apply a vertical pressure of 69 kPa simulating overburden pressure, and the soil was allowed to consolidate for 48 hours. 4 TEST PROCEDURES The shear head was lowered in the hole at the center of the soil tank, a target normal horizontal pressure was applied for 12 hours (consolidation stage). In the test with temperature cycles only, the plates were heated or cooled by circulating fluid with different temperatures. During the heating cycles, one heat pump is used and the heat pump setting temperature is 5 to 8◦ C higher than the target temperature of the soil-concrete interface to account for the heat loss. Once the target temperature of soil-concrete interface is achieved (i.e., 0.5 temperature cycle as shown in Figure 3), the heat pump stops functioning, and the other heat pump starts to cool the temperature of the plates down to the room temperature (i.e. 1 temperature cycle) with the setting temperature of 2◦ C lower than the room temperature. In the displacement cycles only, the control system adjusts the air pressure of the pneumatic piston to change the normal pressure at the soil-concrete interface. The piston pushes the plates outward toward the surrounding soil when the normal pressure is increasing, and the plates move backward when the normal pressure is decreasing. The expansion to target displacement is defined as 0.5 cycle of displacement.

Figure 3. Definition of displacement and temperature cycles.

The normal pressure can be reduced by the controller to make the plates return to its original position which is 1 displacement cycle as shown in Figure 3. The system also can combine the displacement and temperature cycles at the same time by controlling the heat pumps and normal pressure at the soil-concrete interface. To separate the temperature cycles and expansion/contraction cycles effects on the soil-concrete interaction, the Thermal-mBSTs can be conducted with expansion/contraction cycles and temperature cycles separately. After applying the test condition (e.g. displacement cycle), the shearing stage starts. The interface is sheared with a constant shearing rate of 0.05 mm/s which is similar to the conventional borehole shear test (Lutenegger, 1987). Stress vs. displacement relation (t-z curve) can be obtained through the results of the load cell and LVDTs during shearing. 5

RESUSLTS AND ANALYSIS

A reference test was conducted without temperature cycle or displacement cycle (
D = 0,
T = 0) with normal stress of 41.4 kPa. The peak stress of t-z curve for this reference test is 35.8 kPa. The secant shear modulus E50 is 111.6 kPa/mm. 5.1

Effect of temperature change and cycles

Figure 4 shows the t-z curves after 0.5, and 10.5 heating cycles under normal stress of 41.4 kPa. With 0.5 heating cycle (
T = 0.5), two tests were performed, one is continuously heating for 0.5 hour, and the other one is continuously heating for 10.5 hours. For 0.5 hour’s heating test, the peak shear strength decreased by 9% compared to the reference test. This may be attributed to the undrained heating, where the time for the dissipation of thermall-induced excess pore water pressures was not sufficient (Murphy and McCartney,

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Figure 5. Horizontal displacement during the heating cycle with constant normal stress of 41.4 kPa. Figure 4. Heating effects on t-z curves of SCI.

2014). For the 10.5 hours’ heating test, the shearing behavior of the soil-concrete interface showed strainsoftening response. The peak shear strength is almost the same as the reference test. However, the residual shear strength is 15% lower than the reference test. The peak strength increased after 10.5 hours’ heating may be caused by drained heating and increasing suction where the water content deceased from 18% to 14.2% near the soil-concrete interface. After 10.5 heating cycles, the peak shear strength is 10% lower than the reference test, and residual strength is 15% lower than the reference test, which may also be attributed to the process of undrained heating. Figure 5 shows the displacement change between the two shear plates during heating cycles with constant normal stress during each temperature cycle that took one hour. After 10.5 heating cycle, the horizontal distance change between the two plates is 489 µm. The horizontal displacement during the heating cycle indicated a thermal-softening behavior of the soil and thermal-induced settlement. The rate of the thermalsoftening behavior decreases with number of cycles. The horizontal displacement increases with the number of heating cycles in this test. Water migration also was observed in the test. Water contents of 17.4%, 15.8%, and 14.2% were measured after 0.5 hour’s heating, 10.5 hours’ heating, and 10.5 heating cycles, separately. Water migration followed by suction variation in the soil may affect the soil-concrete interface properties (Hamid & Miller 2009). The displacement change of the plates is around 847 µm after 10.5 hours’ continuous heating. Those temperature-induced soil settlement changed the relative density of the soil which may affect soil-concrete interaction (DeJong et al. 2009). Figure 6 shows the temperature distribution at the soil-concrete interface and in the surrounding soil for the 10.5 heating cycles test. As shown in the figure, the temperature distribution is uniform at the beginning (
T = 0) in the soil. The temperature active zone, where the soil experiences temperature changes, is approximately 50 mm for the 0.5 and 1 heating cycles. The temperature active zone increases as the number of

Figure 6. Temperature distribution of the soil during the heating cycles.

heating cycles increases. At the end of the 10.5 heating cycles, the temperature active zone is approximately 75 mm. 5.2 Effect of expansion and cycles Figure 7 shows the effects of expansion cycles on the soil-concrete properties. After applying the expansion cycles, the interface was sheared at the expansion position in the tests with 0.5 and 10.5 expansion cycles. When compared to the reference test (
D = 0,
T = 0), the peak strength has 21.8% increase in the test with 0.5 expansion cycle (
D = 0.5,
T = 0) and 12.3% increase in the test of 10.5 expansion cycles (
D = 10.5,
T = 0). In the 10 expansion cycle test (
D = 10,
T = 0), the interface was sheared when the plates returned back to the initial position, the reduction of the peak strength of the interface is 73.6% compared to the reference test. This may be attributed to the permanent soil deformation occurred during the expansion cycles. Figure 8 shows the relationship between normal stresses and displacement in the test with 10.5 expansion cycles. In this test, the plates expand and return back and forth between the initial and target expansion positions. The corresponding normal stresses at target expansion position decreased with number of cycles which is shown in Figure 8.

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Figure 7. Expansion effects on the t-z curves of SCI.

Figure 9. Combination of expansion and heating effects on t-z curves with INS of 41.4 kPa.

6

Figure 8. Normal stress vs. expansion displacement during the 10.5 expansion cycles.

The initial normal stress was 41.4 kPa which was increased to 49.6 kPa at the expansion position at 0.5 expansion cycle. After 1 expansion cycle, the normal stress was 17.1 kPa which had 38.0% reduction compared to the initial normal stress. The normal stresses were 11.4 and 40.4 kPa after 10 and 10.5 expansion cycles. 5.3

Combined effect of heating and expansion

The effects of temperature and expansion cycles can be combined together using the Thermal-mBST device. Figure 9 shows the t-z curves after 0.5 expansion cycle (
D = 0.5,
T = 0), 0.5 heating cycle (
D = 0,
T = 0.5), and combination of 0.5 expansion and 0.5 heating cycle
D = 0.5 and
T = 0.5). The peak shear strength of the test with
D = 0.5,
T = 0.5 is 40.6 kPa compared to 43.6 kPa of the test with
D = 0.5,
T = 0. During the 0.5 expansion cycle, the normal stress increases as the concrete plates expand. Due to the thermal-softening behavior of the soil in vicinity of the interface during heating, the normal stress is 46.7 kPa when the plates have 120 µm expansion with heating cycle (
D = 0.5,
T = 0.5) compared with the normal stress of 49.5 kPa in the test with
D = 0.5,
T = 0.

CONCLUSION

Shallow geothermal energy, which is one of the promising renewable energy sources, utilizes the nearly constant and moderate temperature of the ground to heat and cool buildings. The ground source heat pump (GSHP) exchanges heat with the ground through a ground heat exchanger. As a development from conventional GSHP systems, energy piles can be used to support the superstructure load and also function as ground heat exchangers for heating and cooling of buildings. The intermittent operation of the heat pump presents new challenges to foundation engineers, one of which is cyclic thermal loading effects on soil-energy pile interface properties. Thermal-mBSTs were conducted to evaluate the expansion/contraction and temperature cycles on the soil-energy pile interaction by directly measuring t-z curves. The results showed that the shear strength decreased when the soil-pile interface was subjected to short-term heating. After 0.5 heating cycle in half hour, the peak strength decreased by 9%. The stress-displacement response of the soil-pile interface showed a peak followed by a reduction of shear resistance when subjected to long-term heating (drained heating) or cycles. In the 10.5 hours’ heating test, the peak strength is almost the same as the reference test, however, the residual strength is 15% lower than the peak strength. The permeant deformations can be caused by both displacement cycles and temperature cycles which lower the normal stress on the soil-pile interface and result in a significant decrease of the shear strength. The soil subjected to a constant normal stress and thermal loads will deform with number of heating cycles. The normally-consolidated soil has significant permanent deformation after the first expansion cycle. REFERENCES Akpinar, M. V., & Benson, C. H. Effect of temperature on shear strength of two geomembrane–geotextile interfaces. Geotextiles and Geomembranes, 23(5): 443–453.

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Akrouch, G., Sanchez, M., & Briaud, J. L. 2014. Thermomechanical behavior of energy piles in high plasticity clays. Acta Geotechnica, 9(3): 399–412. Bourne-Webb, P. J.,Amatya, B., Soga, K.,Amis, T., Davidson, C. & Payne, P. 2009. Energy Pile Test at Lambeth College, London: Geotechnical and Thermodynamic Aspects of Pile Response to Heat Cycles. Géotechnique, 59(3): 237–248. Brandl, H. 2006. Energy Foundations and other Geothermal Ground Structures. Géotechnique, 56 (2): 81–122. DeJong, J. & Westgate, Z. 2009. Role of Initial State, Material Properties, and Confinement Condition on Local and Global Soil-Structure Interface Behavior. J. Geotech. Geoenviron. Eng., 135(11):1646–1660. Di Donna, A. Ferrari, A., & Laloui, L. 2015. Experimental investigations of the soil–concrete interface: physical mechanisms, cyclic mobilization, and behaviour at different temperatures. Canadian Geotechnical Journal, 53: 1–14. Hamid, T.B, and Miller, G.A. 2009. Shear strength of unsaturated soil interfaces. Canadian Geotechnical Journal, 46(5): 595–606. Handy, R. L. & Fox, N. S. 1967. A Soil Borehole Direct Shear Test Device. Highway Research News, Transportation Research Record, 27: 42–51. Karademir, T., & Frost, J. 2011. Elevated Temperature Effects on Geotextile-Geomembrane Interface Strength. Geo-Frontiers 2011: 1023–1033. Laloui, L., Nuth, M., & Vulliet, L. 2006. Experimental and Numerical Investigations of the Behavior of a Heat Exchanger Pile. International Journal for Numerical and Analytical Methods in Geomechanics, 30(8):763–781.

Lutenegger, A. J. 1987. Suggested Method for Performing the Borehole Shear Test. Geotechnical Testing Journal, 10(1): 19–25. McCartney, J.S. & Murphy, K.D. 2012. Strain distributions in full-scale energy foundations. DFI Journal, 6(2): 26–38. Murphy, K., & McCartney, J. 2014. Thermal Borehole Shear Device. Geotechnical Testing Journal, 37(6): 1–16. Olgun, G. Ozudogru, T.Y., & Arson, C. F. 2014. Thermomechanical radial expansion of heat exchanger piles and possible effects on contact pressures at pile–soil interface. Géotechnique Letters, 4(3): 170–178. Suleiman, M. T., & Xiao, S. 2014. Soil-Pile Interaction of Geothermal Deep Foundations. Proceedings of the 27th Central Pennsylvania Geotechnical Conference, Hershey, PA on April 23–25, 2014. Suryatriyastuti, M.E., Mroueh, H., & Burlon, S. 2012. Understanding the temperature-induced mechanical behaviour of energy pile foundations. Renewable and Sustainable Energy Reviews, 16(5): 3344–3354. Xiao, S. & Suleiman, M. T. 2015. Investigation of Thermomechanical Behavior of Soil-Energy Pile Interface Using Modified Borehole Shear Tests. IFCEE 2015, San Antonio, Texas. Xiao, S., Suleiman, T. M. & McCartney, J. S. 2014. Shear Behavior of Silty Soil and Soil-Structure Interface under Temperature Effects. GeoCongress 2014. Atlanta, GA. Feb. 23–26, 2014. You, S., Cheng, X., Guo, H., & Yao, Z. 2016. Experimental study on structural response of CFG energy piles. 2016. Applied Thermal Engineering, 96(5): 640–651.

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Benefits and optimisation of district hybrid ground source heat pump systems O. Mikhaylova The University of Melbourne, Melbourne, Australia

R. Choudhary & K. Soga The University of Cambridge, Cambridge, UK

I.W. Johnston The University of Melbourne, Melbourne, Australia

ABSTRACT: Buildings consume large amounts of energy, largely to satisfy their heating and cooling needs. Since most of this energy is derived from fossil fuels, buildings are responsible for a significant share of the world’s CO2 emissions. Shallow geothermal energy is a promising sustainable source of energy which can potentially satisfy the thermal requirements of buildings not only economically but also with reduced carbon emissions. For high density urban areas, buildings can be connected to district Hybrid Ground Source Heat Pump (HGSHP) systems for heating and cooling purposes. This study discusses the benefits of district over individual HGSHP systems. A methodology for the optimisation of district HGSHP systems is proposed which considers building thermal demand regimes. Such optimisation can reduce the total lifetime costs of heating and cooling, capital investments and payback periods of HGSHP systems. The importance of considering the demand regimes in the optimisation is demonstrated through a case study. The case study shows that an optimised district HGSHP system can have significant financial benefits over individual HGSHP systems and therefore make district systems more attractive to investors.

1

INTRODUCTION

Currently, buildings consume large amounts of fossil fuels for heating and cooling purposes to make them significant CO2 emitters. To reduce emissions, lowcarbon geothermal energy from shallow depths can be supplied to buildings to satisfy their thermal needs. The capital costs of shallow geothermal energy installations, or Ground Source Heat Pump (GSHP) systems, can be high in comparison to traditional heating and cooling systems. Some governments, for example the UK, have introduced incentives to compensate high installation costs of these systems. More research into optimisation of GSHP system is needed to increase their financial attractiveness to potential investors. Previous research into the economics of geothermal systems suggests that hybrids of GSHP and traditional heating and cooling systems (HGSHP systems) can often be more financially beneficial heating and/or cooling options than GSHP only systems (for example, Hackel et al. (2009), Alavy et al. (2013), Nguyen et al. (2014) and Hénault et al. (2015)). In such systems, the GSHPs are sized for a certain portion (or shave factor) of a peak thermal demand α (Alavy et al., 2013). As such, GSHPs provide baseline thermal power up to their installed capacities and the rest is topped-up

by a traditional system, for example, a gas boiler in heating or a cooling tower in cooling. This arrangement allows the expensive Ground Heat Exchangers (GHEs) to provide most of the thermal energy (usually 70–95 % of the annual required energy) while the comparatively cheaper traditional systems to provide the balance of the energy. In highly populated urban areas, buildings are located close to each other, so they can be combined into districts for thermal energy supply purposes. In such cases, the energy would be provided by centralised district systems. Just as occurs with individual HGSHP systems, district HGSHP systems could be more economical when sized to a certain shave factor α. In the design and optimisation of district HGSHP systems, the specific variations of thermal power demand, particularly in time, of different types of buildings needs to be taken into account. This study evaluates likely financial benefits of district over individual HGSHP systems. In particular, the study proposes a methodology to consider thermal demand regimes of individual buildings in the design of district HGSHP systems, so that such systems can be optimised. An example case demonstrates the proposed methodology and the potential advantages of district HGSHP system arrangements.

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2 2.1

METHODOLOGY Building occupancy regimes

Building occupancy is a major factor influencing buildings’ thermal demand regimes or the periods when buildings need thermal power. When buildings are unoccupied, their heating or cooling systems are usually switched off or on set-back mode. When buildings are occupied, their heating or cooling systems are usually switched on and may supply thermal energy to the buildings depending on the current ambient air temperature and other factors (eg. internal gains). Different buildings tend to be occupied at different rates at any given time, albeit there are similarities depending on nature of activities in buildings. For example, residential buildings are likely to be less occupied during daytime and predominantly occupied during nights, whereas commercial buildings are likely to be occupied during office hours and unoccupied for the rest of the time. In this study, two building types were distinguished: a residential building (Type A) and an office building (Type B). The occupancy of a building at a particular point of time is modelled by its probability of presence P(p). The probability of presence is the probability of the building being occupied at a particular point of time. The assumed P(p)’s of the two building types at two distinct time periods (9 am–6 pm and 6 pm–9 am) are shown in Table 1. This is a simplified representation of possible and more complex building occupancy regimes as the purpose here is to illustrate the principles of the proposed HGSHP optimisation methodology.

of tbase = 16◦ C. The baseline temperature determines when heating is needed: if an ambient air temperature is less than the baseline temperature, a building needs heating. The peak heating power demand HDmax occurs at the minimum ambient air temperature tamb_min . In the analysis, both Type A and B buildings were assumed to have the same heating power demands HDdesign,A = HDdesign,B = 10 kW at the average ambient air temperature of the heating design month in London, tdesign = 4.4◦ C (Table 1). The heating demand of the building k at any particular hourly timestep i, when the ambient air temperature is tamb,i , is calculated as

If occupied, a building is assumed to require 100% of heating power estimated for a particular ambient air temperature. If unoccupied, the building is assumed to have a zero power demand. Since, overall, Type A buildings have a greater occupancy than Type B buildings, Type A buildings require more heating energy annually than Type B buildings, all other factors being equal (Table 1). The annual building heating energy is calculated as the sum of the energy required by the building at each hourly timestep i of a year j. Considering P(p)k,i of the building k at the hourly timestep i, the annual heating energy of the building, Ek,j , is

The lifetime heating energy required for the building k can be estimated as

2.2 Building thermal demands considering occupancy regimes The example case was performed for the climatic conditions of London, UK. In this climate, even if cooling is provided to a building, the annual building heating demand tends to be higher than its annual cooling demand. Thus, HGSHP systems are generally sized for heating with GHEs sized for a reduced yearly average ground load (Section 2.3). The HGSHP design methodology is very similar for both heating only and heating dominant cases, so the impact of thermal demand regimes on sizing of HGSHP systems would be the same in these cases. To demonstrate general principles of the proposed optimisation methodology, the buildings are assumed to require heating only. Building heating demand amounts and regimes were assumed to depend on ambient air temperatures and occupancy of buildings. Other factors, such as fractions of heating use and internal temperature set points, can also affect building thermal demands and should be taken into account in detailed analyses. However, to keep the demonstration simple, these additional parameters are not considered. The building heating demands are assumed to be proportional to ambient air temperatures with an assumed baseline ambient air temperature for heating

where Tlife is the life time of the HGSHP system. Similarly, if two building A and B are considered, their annual heating energy at year j, EA + B,j , and lifetime heating energy, EA + B,tot , are

2.3 Sizing GHEs In this study, the ASHRAE design approach is used to size GHEs (Philippe et al., 2010). According to this method, the design length of GHEs is

The descriptions of the parameters in Equation 6 are given in Table 2. The GHE ground thermal load design parameters (qy , qm and qh ) were calculated based on the estimated

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Table 1. Occupancy and thermal demand of the two building types for the example problem. Probability of presence P(p)

Type A (Residential) Type B (Office)

9 am–6 pm

6 pm–9 am

Design heating demand HDdesign , kW

Annual heating energy Ej , kWh

0.5 0.9

0.9 0.1

10 10

37,890 15,340

Table 2. GHE design parameters. Design parameter

Value

Description

qh , kW qm , kW qy , kW Rb , m · K/W R1 0y, m · K/W

Calculated based on assumed building thermal demands, P(p)s, α and COPGSHP 0.111 0.212

R1 m, m · K/W

0.197

R6 h, m · K/W

0.113

Tm , ◦ C Tg , ◦ C Tp , ◦ C

2.3 13.0 0

Peak hourly ground load Monthly ground load Yearly average ground load Effective thermal resistance of the borehole Effective thermal resistance of the ground to 10 years ground load Effective thermal resistance of the ground to one month ground load Effective thermal resistance of the ground to 6 hours ground load Mean GHE fluid temperature Undisturbed ground temperature Temperature penalty

building thermal demands, their P(p)’s, the shave factor of a particular HGSHP configuration α and the coefficient of performance of GSHPs COPGSHP . The rest of the parameters are defined by the ground thermal properties and GHE configurations. For the example case, these parameters are set following the typical values used for vertical borehole GHEs in London and assumed to be the same for all system configurations of the example case (Table 2). The GHEs are assumed to be installed sufficiently apart from each other to not thermally interact (hence, Tp = 0). For a more detailed explanation of the GHE calculation method, Philippe et al. (2010) should be consulted. 2.4

Table 3. Financial comparison assumptions. Parameter

Value

Installation cost of 1 kW of GSHPs, icGSHP , £ Installation cost of 1 kW of gas boiler, icboil , £ Installation cost of 1 m of GHEs, icGHE , £ 1 kWh from electricity, ce , £ 1 kWh from gas, cg , £ COP of GSHPs, COPGSHP COP of gas boiler, COPboil Life time of HGSHP system Tlife , years Discount rate, DR Government incentive rate per 1 kWh of geothermal heat, rRHI , £

240 25 37.5 0.17 0.05 3.5 0.95 20 0.05 0.0884

Financial indicators

Financial comparisons of different heating system arrangements and configurations were performed based on (a) total normalised costs of heating over lifetimes of heating systems and (b) payback periods. The total normalised costs of heating were calculated considering the capital costs of HGSHP systems and the lifetime costs of the heating energy delivered to the building in net present values. The costs of heating systems inside buildings (for example, in-room heating units, internal distribution pipework) and HGSHP maintenance costs were assumed to be the same for all HGSHP configurations and, hence, are not included into the comparisons. The unit costs and other parameters for the financial comparisons are summarised in Table 3.

The capital cost of the particular configuration of a HGSHP system, where the GSHP is sized to a particular α, is calculated as

where CGSHP is the capital cost of the ground source heat pump; CGHE is the capital cost of the GHEs and Cboil is the capital cost of the boiler. These costs are calculated as

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Note that the capital costs of the HGSHP system sized to the same α will be different for buildings A and B as the lengths (and therefore the costs) of GHEs for these buildings are different (see Equation 9). In the calculations of annual heating energy costs, the UK government’s renewable heat incentive (Ofgem, 2016) is taken into account. The incentive compensates high capital investments into GSHP systems and is paid on a prorata basis for each kWh of geothermal energy delivered. The incentives were calculated as for non-domestic (commercial) installations at the rRHI = 0.0884 £/kWh rate paid over the first 20 years of GSHP installation. The annual cost of heating energy at any particular year j, including the renewable heat incentive, is calculated as

where Ch_GSHP,j is the cost of heating energy provided by the GSHPs at the year j; Ch_boil,j is the cost of heating energy provided by the boiler at the year j and RHIj is the renewable heat incentives received at the year j. The annual heating energy provided by GSHPs during year j, EGSHP,j, is a share of the required annual building energy, Ej , and determined by the design shave factor, α. When needed, the boiler tops the heating energy supplied by GSHPs up to the required amount. The annual heating energy provided by the boiler during year j, Eboil,j , is

Considering the coefficients of performance of the equipment, the annual costs of the heating energy in Equation 11 are estimated as

The annual costs of heating energy are converted into net present values to estimate the total lifetime cost of heating as

where the assumed discount rate DR. Note that the discount rate prediction is a complex process and should be performed for a particular project (see examples in Oxera ( 2011)). Here, for demonstration purposes, DR of 5% is assumed as a reasonable value for a low-carbon technology projects (Oxera, 2011). The Equation 16 follows Alavy et al. (2013). Since heating systems with different total lifetime required heating energy will be evaluated, the total lifetime cost of heating Ctot is normalised by the amount of heating energy provided during the lifetime of the

heating system, Etot . Hence, all comparisons are performed on the basis of the total normalised costs of heating in £/MWh which is

The payback period of a particular HGSHP system configuration, PBP, is calculated by dividing initial capital investment by the total annual returns in energy savings as

In PBP calculations, the initial capital investments were taken as the difference in the capital costs of the HGSHP system, Ccap (Equation 7), and a gas-only heating system, Cboil_α = 0 (hence, for a gas heating system, the payback period is zero). The annual returns are quantified as the difference between annual heating energy costs in cases of the HGSHP including renewable heat incentives, Ch,j (Equation 11), and the gas-only heating systems, Ch_α = 0,j , converted into net present values. The payback periods were calculated in years needed to return initial investments. 3

RESULTS

In the case study, individual and district arrangements of HGSHP systems for mixes of two buildings are compared. The following three mixes of Type A and B buildings are evaluated: • • •

“A+A” mix: a Type A + a Type A buildings “B+B” mix: a Type B + a Type B buildings “A+B” mix: a Type A + a Type B buildings

In the individual arrangements, the thermal demands per building are used to size the GHEs. In the district arrangements, the thermal demands of the two buildings are combined before sizing the GHE. Thus, for these two arrangements of a same mix, the qy and qm thermal loads might be different at the same qh . For both individual and district heating system arrangements, the GSHPs are sized for a range of α values from 0 to 100 % with a step of 3 % to cover possible configurations of the HGSHP systems. Financial indicators of the resultant configurations of HGSHP systems are calculated to determine their cost effectiveness. The results of the financial comparisons for the three building mixes are presented in Figure 1. In the figure, total normalised costs of heating TNC in £/MWh (Equation 17) are plotted against capital costs of different heating system configurations, Ccap in £ (Equation 7). In each plot,Ccap along the horizontal axis varies from the cost of a gas-only (the most left point, α = 0) to the cost of GSHP-only (the most right point, α = 100 %) heating systems. The points

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in between represent the hybrid heating system configurations with α increasing from left to right. For each building mix, the minimum value of TNC represents the most financially optimal solution. Key observations from Figure 1 are summarised in Table 4. From Figure 1, if GSHP-only heating is compared with gas-only alternatives, a GSHP-only heating is more economical than a gas-only heating in the “A+A” and the “A+B” mix. However, in the “B+B” mix, a GSHP-only heating is a more expensive option compared to a gas-only heating. In addition, TNC for the gas-only options are the same for both “A+A” and “B+B” mixes while there is a significant difference in TNC between these two mixes for GSHP-only options. Such differences are explained by the principles of GHE sizing. The Type A and B buildings have the same design heating demands (Table 1) which largely determine the required lengths of “expensive” GHEs, and therefore influence the cost. At the same time, annually, less “free” geothermal energy is supplied to Type B buildings compared to Type A buildings due to the differences in their annual heating energy demands (Table 1). Hence, the high capital costs of the GSHP systems are not compensated by the delivered “free” geothermal energy in Type B buildings as much as they are in Type A buildings. In other words, “expensive” GHEs are utilized more efficiently in Type A buildings compared to Type B buildings. In all three building mixes considered, the TNC is at a minimum when the hybrids of a GSHP and a boiler are used for the heating in comparison to the GSHPonly and gas-only systems. In Figure 1, the minimum points at the TNC curves represent the most financially optimum HGSHP configurations which correspond to the GSHPs sized to certain shares of peak power demand HDmax or shave factors α. In the optimum cases of all three building mixes, the district HGSHP systems would ensure lower TNC compared to individual HGSHP systems installed for the same buildings (Figure 1). However, the difference between the optimum district and individual TNC’s are much higher in the “A+B” mix compared to the other two mixes. This is explained by the significant differences in occupancy regimes of Type A and B buildings (Table 1), so that, when combined, these buildings efficiently share GSHP installed capacities, and maximize the utility of GHEs. Note that in all optimum hybrid cases, significant shares of heating energy are provided from sustainable geothermal sources (Table 4) ensuring low CO2 emissions from the buildings. If two buildings with different occupancy rates are connected to a district HGSHP system, the building with a lower overall occupancy rate would benefit more financially from the district arrangement than the building with a higher overall occupancy rate. Indeed, the minimum TNC for residential buildings in the “A+A” mix is the same as the minimum TNC for buildings in the “A+B” mix, 14.6 £/MWh. At the same time, the minimum TNC for office buildings in the “B+B” mix is much higher, 23.1 £/MWh. The minimum TNC in the “A+B” mix is 14.6 £/MWh. Hence, Type B buildings would access a much lower total

Figure 1. Total normalised costs of heating TNC for three building mixes: a) “A+A”, b) “B+B” and c) “A+B”.

normalised cost of heating if they are in the “A+B” mixes compared to when they are in the “B+B” mixes. However, Type A buildings would also benefit from being in the “A+B” mixes, since such districts would

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Table 4. Financial comparison. At optimum configuration Building mix system

Type of HGSHP

α, %

TNC, £/MWh

Share of geothermal energy, %

Ccap , £

“A+A”

Individual District Individual District Individual District sized conventionally District

56 53 33 31 47 47 33

14.6 15.0 25.5 23.1 18.7 15.8 14.6

91.3 91.1 75.5 79.2 86.6 96.1 88.8

20,300 19,600 11,300 10,700 16,600 16,900 13,200

“B+B” “A+B”

allow them to have lower capital costs compared to the “A+A” mixes (£13,200 in comparison to £19,600, see Table 4) while still accessing the same low TNC. Results demonstrate that building thermal demand regimes must be combined when sizing GHEs in order to better optimise district HGSHP systems. Indeed, in the “A+B” mix, the individual HGSHP system would be sized for a shave factor of α = 47 % to achieve the minimum TNC = 18.7 £/MWh (the minimum of the “Individual” curve in Figure 1c). If the district HGSHP system was designed by designing the GHEs as per individual demands, the GSHP would be sized for the same α = 47 % which would result in TNC = 15.8 £/MWh. However, if the thermal demand of the buildings is combined, the GSHPs would be sized for α = 33 % which would reduce the TNC to 14.6 £/MWh (the minimum of the District curve in Figure 1c). In addition, 22 % less of the capital cost would be invested to achieve the minimum TNC, £13,200 in comparison to £16,900 (Table 4). To evaluate risks of investments into HGSHP heating systems, payback periods were calculated. The payback periods were estimated for the optimum configurations of HGSHP systems installed individually and for districts of two buildings as well as for district arrangements when HGSHP systems were sized individually, without combining building thermal demand regimes. The results of the estimation are shown in Figure 2. From the figure, the initial investments into HGSHP systems of Type A (residential) buildings have significantly lower payback periods compared to the initial investments into HGSHP systems of Type B (office) buildings. For example, for the cases of district arrangements, the payback period for the “A+A” mix is 5.8 years whereas the payback period for the “B+B” mix is much higher, 9.3 years. This is explained by higher annual returns in the “A+A” mixes due to the higher annual heating demands for Type A buildings in comparison to Type B buildings for the same design heating demands (Table 1). Among all calculated payback periods presented in Figure 2, the minimum of 5.4 years is expected in the district arrangement of the “A+B” mix. In this mix, both Type A and Type B buildings would benefit from low payback periods as well as from the low capital

Figure 2. Payback periods for optimum HGSHP configurations for three building mixes: “A+A”, “B+B” and “A+B”.

costs and total normalised costs of heating (Table 4). For the individual as well as for district HGSHP systems sized conventionally, without taking into account building thermal demand regimes, the payback period of the “A+B” mix would be higher, 7.6 and 6.8 years respectively. This, again, demonstrates that district HGSHP systems are more economical than individual HGSHP systems especially when the district systems are optimised with building thermal demand regimes. The example case presented investigates some general aspects of the optimisation of district HGSHP systems by considering building thermal demand regimes. More research should be performed to quantify thermal demand regimes of typical building mixes based on factors, additional to building occupancy. These detailed heating demand regimes could be used in comprehensive studies of their effects on optimisation of district HGSHP systems. Based on these studies, optimum building mixes can be suggested, so that the minimum total normalised costs of heating, capital investments and payback periods are achieved. 4

CONCLUSIONS

The paper discusses potential financial benefits of district hybrid ground source heat pump (HGSHP) systems in comparison to individual HGSHP systems.

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A methodology of the financial optimisation of district HGSHP systems was presented where building thermal demand regimes were taken into account to find the optimum share of GSHP systems in the hybrids. An illustrative example demonstrates the economic advantages of district systems for two building mixes and the importance of combining the building thermal demand regimes when district GHEs are designed. It shows that if buildings with significantly different thermal demand regimes were connected to one (district) HGSHP system, they would benefit financially from such a system arrangement. In particular, their total normalised costs of heating and payback periods would be significantly lower in comparison to individual HGSHP systems. In addition, the example shows that for the optimum sizing of district HGSHP systems, the building thermal demand regimes have to be combined when sizing the GHEs. If GHEs in such hybrids were sized conventionally, without taking into account the demand regimes, the resultant total normalised costs of heating and capital costs would be higher than at the optimum sizing. ACKNOWLEDGEMENT The first author would like to acknowledge the financial support provided by an Endeavour Research

Fellowship funded by The Australian Government Department of Education. REFERENCES Alavy M, Nguyen H V, Leong WH, et al. (2013) A methodology and computerized approach for optimizing hybrid ground source heat pump system design. Renewable Energy, 57, 404–412. Hackel S, Nellis G and Klein S (2009) Optimization of Cooling-Dominated Hybrid Ground-Coupled Heat Pump Systems. ASHRAE Transactions, 115(1), 565–580. Hénault B, Pasquier P and Kummert M (2015) Financial optimization and design of hybrid ground-coupled heat pump systems. Applied Thermal Engineering, 93, 72–82. Nguyen H V, Law YLE, Alavy M, et al. (2014) An analysis of the factors affecting hybrid ground-source heat pump installation potential in North America. Applied Energy, 125, 28–38. Ofgem (2016) Non-Domestic RHI Main Guidance. Available from: https://www.ofgem.gov.uk/environmentalprogrammes/non-domestic-renewable-heat-incentive-rhi (accessed 1 February 2016). Oxera (2011) Discount rates for low-carbon and renewable generation technologies. Available from: https://www.the ccc.org.uk/archive/aws/Renewables Review/Oxera low carbon discount rates 180411.pdf (accessed 1 February 2016). Philippe M, Bernier M and Marchio D (2010) Sizing Calculation Spreadsheet Vertical Geothermal Borefields. ASHRAE Journal, 52(7), 20–28.

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Thermo-mechanical finite element analyses of energy walls D. Sterpi & L. Mauri Department of Civil and Environmental Engineering, Politecnico di Milano, Milano, Italy

ABSTRACT: Energy walls are thermo–active diaphragm walls that embed heat exchanger pipes with the purpose to exploit the thermal energy of the subsoil. Their geotechnical and structural performance is related to both thermal and mechanical loads and still needs to be thoroughly investigated. To this purpose, three– dimensional thermo–mechanical finite element analyses allow to highlight the effects of the heat transfer process on the soil temperature field, on the wall and on the soil–structure interaction, in terms of internal actions and earth pressures. The main findings show that the effects of the thermal loads can be considered admissible for the geostructure, in terms of its global stability and structural safety, though they are generally not negligible. Unexpected overstress conditions can occur, such as tensile stresses and out–of–plane effects, whose magnitude depends on the thermal boundary conditions and on the constraint degree of the structure.

1

INTRODUCTION

The energy consumption in Europe is rapidly increasing especially in the sector of buildings, which has surpassed the sectors of industry and transport. Out of the building total energy demand, heating currently accounts for 40% and, moreover, the cooling demand is expected to rise significantly in the next years (International Energy Agency, 2014, Pérez-Lombard et al 2008). The promotion of geothermal energy for building thermal conditioning is therefore crucial to meet the European targets about renewable energy exploitation and greenhouse gas emissions reduction (European Parliament, 2010). In fact, even at low depths or at the near-surface the geothermal energy, directly used as thermal energy, is pervasively available, a characteristic that makes it optimal for local harvesting and diffuse distribution at both single space and district scales (Lund et al. 2011). Energy walls are thermo–active reinforced concrete diaphragm walls designed as soil retaining structures that, similarly to other so called “energy geostructures” (Brandl 2006, Adam & Markiewicz 2009, Amis et al 2010, Laloui & Di Donna 2013, Nicholson et al 2013), embed heat exchanger pipes with the purpose to use the subsoil as a natural reservoir, where heat can be dispersed in the summer season and extracted in the winter season. Although basically limited to the new constructions, this system offers the advantage of using existing components of the structure without requiring additional works, and associated costs, as in the case of the more traditional borehole heat exchanger systems. With the spread of this technology, the issue raised about the behaviour of these structures that, designed to serve a prior structural function, are subjected

to combined thermal and mechanical loads in their ordinary working conditions. The earliest investigation was addressed to the energy piles (Knellwolf et al 2011, Amatya et al 2012, Suryatriyastuti et al 2012), more recently the study broadened to energy tunnels and retaining walls (Xia et al 2012, Barla et al 2016). Monitoring data from instrumented full scale energy piles provided major insights in their thermomechanical behaviour and established important databases for the validation of numerical analyses and the calibration of the relevant parameters (Laloui et al 2006, Bourne–Webb et al 2009). Taking advantage of ideal, controlled and repeatable conditions, also laboratory tests on small scale models helped in identifying the pile response (Kramer et al 2015, Stewart & McCartney 2014). With respect to the energy piles, the field experience with energy walls is newer and still there is some lack of monitoring data about their thermo–mechanical response. Following a preliminary study on the performance of an energy wall, from the perspective of both the geothermal energy exploitation and the short and long term influence on the soil temperatures (Sterpi et al 2014), the research is now addressed to investigate the effects of the heat transfer process on the diaphragm wall and on the soil–structure interaction (Mauri 2015). Three–dimensional finite element analyses allow to get insights into the thermal induced stresses that, ultimately, affect the earth pressure distributions and the wall internal actions, such as axial loads and bending moments. 2

ENERGY PILES AND ENERGY WALLS

All the data collected from the experimental investigations on energy piles, together with the numerical

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and analytical predictions, confirm that the pile-soil interface resistance and the conditions at the pile head and toe, such as the presence of the over-structure or of a stiff substratum, exert constraints on the thermal expansion of the pile when heated, and on the thermal contraction when cooled. These constraints lead to thermal induced stresses that act in addition to the stresses induced by the mechanical loads, and influence the final stress distribution (e.g. Laloui et al 2006, Amatya et al 2012). Moreover, the cyclic nature of the thermal load has raised the question about the possible occurrence of a shaft resistance loss, due to both a progressive degradation of the interface and a reduction of the normal effective stress induced by soil volume contractions (Suryatriyastuti et al 2014). In energy piles, significant changes were eventually observed in the mobilised shaft resistance and in the pile axial load and, although they are not expected to lead to detrimental consequences, they should be taken into consideration at the design stage. Thermal induced stresses develop also in energy walls, but their effects are less predictable than in energy piles. Firstly, the wall has a greater complexity in terms of geometry: the axisymmetric approximation is not applicable and various restraints could act on the wall from structural components as anchors, roof and base slabs, etc. Secondly, the wall is fully embedded in the soil in its lowest part only, and the thermal boundary condition at the side exposed to the excavation could be undefined. In addition, the section area of the energy wall is large enough to host a variety of different suitable layouts of the heat exchanger, with consequent different temperature gradients induced by the heat transfer process. With respect to the energy performance, the heat transfer models developed for axisymmetric structures, such as borehole heat exchangers or energy piles, cannot be straightforwardly extended to energy walls, but specific models have to be developed (Sun et al 2013). The applicability of Thermal Response Tests to energy geostructures, even to piles, is still under investigation (Park et al 2013, Cecinato & Loveridge 2015). Due to difficulties inherent to the problem modelling and to the current exiguity of data from monitored cases, mainly focused on the thermal performance and on the temperature gradients within the structure and the ground (Brandl, 2006, Xia et al 2012), the thermo-mechanical behaviour of energy walls has not yet been fully investigated. The energy wall, as soil retaining structure, is basically subjected to lateral pressures contrasted by its flexural response, a structural behaviour entirely different from the one of piles; yet, the thermal loads will induce mainly an axial expansion/contraction effect similar to the one of piles. However, this effect is generally not uniformly distributed along the wall longitudinal axis. In fact, the distance between the two transversal sections hosting the descending and the ascending portions of the heat exchanger is not negligible and, since the two portions carry the fluid at

different temperatures, the two sections are subjected to different thermal expansions or contractions. Consequently, different transversal sections of the wall will behave differently and will interact, so that three– dimensional effects in the stress–strain distribution are to be expected. In the following, these aspects are discussed with reference to an energy wall, assembled with segments hosting two heat exchanger pipes each. A preliminary FEM thermal analysis of the soil–structure system permits to investigate the cyclic thermal working conditions. The most demanding condition for the wall, corresponding to the highest temperature variations, is then identified and considered as thermal load in a thermo–mechanical analysis. 3 3.1

DESCRIPTION OF THE PROBLEM Geometry

A 10 m high excavation, hosting a three level basement of a four floor residential building, is supported by two facing energy walls, reaching the depth of 15 m. A vertical symmetry plane allows to model only half of the excavation (fig. 1.a). The wall and the basement floor slab have both a thickness of 0.5 m. In these analyses the possible presence of a roof slab and of an over–structure is disregarded. The energy wall is formed by single connected segments of reinforced concrete, each of them is 2.4 m large and embeds two heat exchanger pipes (fig. 1.b), fixed to the reinforcement cage at the sides of the segment, so to keep clear the central part where concrete is cast. Each pipe is made of high-density polyethylene, has a 30 mm diameter and circulates a heat carrier fluid, mixture of water and glycol with antifreeze function. For the sake of computational simplicity, the loops were assumed U-shaped and laid in the longitudinal mid-section of the wall (fig. 1.c), though the results of previous analyses suggested that different layouts would increase the energy efficiency (Sterpi et al. 2014). In the plan section of the wall, a series of parallel symmetry planes can be identified, at a distance of 1.2 m from each other (fig. 1.b).Therefore, the analysis of the problem can be reduced to the three-dimensional analysis of a 1.2 m wide slice corresponding to half of the single segment. 3.2

Materials

The subsoil consists of a saturated, well graded, silty sand, of increasing stiffness with depth, in a hydrostatic regime. Although the silty component yields a not negligible cohesion, the influence of temperature on the soil behaviour was limited to thermal expansion and the hydro-mechanical coupling effects were neglected. The soil mechanical behaviour was assumed isotropic, elastic perfectly plastic, with MohrCoulomb failure criterion and non-associated flow

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Figure 1. (a) Section of the energy wall and the base slab in the (y,z) plane; (b) plan section in the (x,y) plane of a single segment of the energy wall with two embedded U-shaped pipes; (c) 3D sketch with (x,y,z) reference system. The two opposite symmetry planes are 1.2 m apart in the x direction. (units: m). Table 1. Thermo–mechanical properties. E MPa

ν –

c φ kPa ◦

Saturated soil 80–120 0.3 20 Soil–wall interface 80–100 0.3 1 Reinforced concrete 30000 0.2 –

ψ ◦

α 1/◦ C

32 15 10−5 22.6 5 10−5 – – 10−5

Table 2. Physical and thermal properties.

Saturated soil Reinforced concrete Heat carrier fluid

Density kg/m3

Thermal conductivity W/(m◦ C)

Specific heat J/(kg◦ C)

1930 2500 1000

2.2 2.6 0.57

1642 880 4186

rule. The reinforced concrete elements are modelled as homogeneous, isotropic, perfectly elastic, and susceptible to thermal expansion. The presence of a soil-wall interface, with poorer mechanical properties, was also modelled (Table 1). The thermal properties of saturated soil and reinforced concrete (Table 2) were assumed from the weighted arithmetic means of the properties of the single components, the weights being volume fractions for the thermal conductivity and mass fractions for the specific heat capacity (Rees et al., 2000).

Prescribed thermal loading and boundary conditions govern the heat transfer process and the final temperature gradients. In this problem, constant temperatures of 15◦ C at the soil base and 18◦ C at the internal sides of the excavation were assumed. The lateral boundaries and the front and back faces of the domain, as symmetry planes, were given an adiabatic condition. A yearly cyclic thermal condition was prescribed at the ground surface, corresponding to the seasonally varying air temperatures (fig. 2). The thermal loading condition provided by the heat exchanger is in the form of a mass flux having given temperature at the inlet, i.e. the fluid velocity and inlet temperature have to be assigned. A fluid velocity of 0.05 m/s was assumed. It should be also pointed out that, for any given loop layout, one velocity exists that maximises the heat flux and that high velocities in the circuit could lead to local and distributed energy losses that would reduce the energy performance (Sterpi et al. 2014). The inlet temperature was prescribed as time– dependent condition of yearly periodicity (fig. 2), assuming a dual operating mode (heating/cooling). The extreme values of 2◦ C in heating mode and 30◦ C in cooling mode and the extended periods of three summer months and six winter months were chosen in order to analyse the effects of upper and lower limits of actual thermal loads.

4

NUMERICAL MODEL

3.3 Thermal loading and boundary conditions

4.1

The heat transfer occurs by convection within the heat exchanger and by conduction within the concrete wall and the soil, since there is no groundwater flow and radiation can be neglected.

The initial condition of the soil temperature field, T0 (x,t), is the one obtained as steady state solution of a heat transfer analysis in absence of the geothermal system. The steady state solution is characterized

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Heat transfer process and thermal analysis

Figure 2. Seasonal variation of the ground surface temperature (solid line) and fluid inlet temperature in a heating/cooling operating mode (grey areas).

by the same yearly periodicity of the ground surface temperatures. Once the initial temperature condition is set, the thermal analysis can be carried out adding the thermal load applied by the heat exchanger in dual operating mode. With the fluid temperatures and operating periods shown in figure 2, the steady state soil temperature field T(x,t) is reached after a transient phase lasting 2 years. Note that a single operating mode (for instance winter heating mode), in a hydrostatic regime, would induce the transient phase to last longer, due to the lack of thermal energy recharge (in the summer period) and the consequent thermal drift, i.e. a continuous decrease in the soil temperature. Alternate periods of thermal energy injections and extractions, of possibly comparable amounts, limit the thermal drift effect and the steady state solution is reached in a shorter time. The most demanding thermal working conditions for the energy wall over the year are those corresponding to the highest temperature increases and decreases. Focusing on the temperature increases, the highest values are reached at time taug corresponding to the end of August. Then, the temperature variation T(x,taug ) is calculated at each point x, as difference between the initial values T0 (x,taug ) and the values T(x,taug ) resulting from operating the geothermal system. The temperature variation T(x,taug ) is shown in figures 3 and 4 with reference to respectively the soil mass and the energy wall. In particular, figure 3 shows the variation in the temperature field along the wall longitudinal axis, due to the presence of warmer (x = 1.2 m, fig. 3.a) and cooler (x = 0. m, fig. 3.b) sections, thus proving the necessity to perform a three-dimensional analysis. The geothermal system influences the soil temperatures up to a distance of about 4 m from the wall, but the major variations (greater than 2◦ C) are found within 2.5–3 m from it. The highest temperature increase, at the soil-wall interface of the wall deepest part, is about 9.5◦ C.

Figure 3. Contour lines of the highest temperature increase, at time taug : (a) in the warmest section (max value +11.5◦ C) and (b) in the coolest section (max value +9.2◦ C); (min value 0).

Figure 4 shows the temperature gradients within the energy wall, along the vertical and longitudinal directions and in the thickness. The marked influence of the thermal boundary condition at the excavation side is evident from figure 4.b. 4.2 Thermo-mechanical analysis The initial stress-strain state σ 0 (x) − ε0 (x), was obtained simulating the construction process in a conventional mechanical analysis. Then, the temperature variation T(x,taug ), corresponding to the highest temperature increase in the summer period, was applied as thermal load in a thermo-mechanical analysis on the system characterized by initial conditions σ 0 (x) − ε0 (x) − T0 (x,taug ). The associated thermal expansions in the soil and the wall induce thermal strains and stresses that lead to a stress-strain state σ 1 (x) − ε1 (x), that can be compared with the state σ 0 (x) − ε0 (x) to analyse the influence of the geothermal system. With respect to the initial condition, the wall exhibits a negligible variation of vertical displacements

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Figure 5. Axial force in the energy wall under thermo-mechanical loads, at the warmest (x = 1.2 m) and coolest (x = 0.) sections, with respect to the initial condition.

Figure 4. Contour lines of the highest temperature increase at time taug in the energy wall, from the viewpoint of (a) the wall side facing the soil and (b) the wall side facing the excavation (min value 0, max value +11.5◦ C).

and a limited increase of horizontal displacements (+8% at the wall top). The earth lateral pressures increase in the active zone (soil mass side), at the depth of 11–14 m from the ground surface, of about 10%, while in the passive zone (excavation side) the variation is negligible. The thermal induced stresses lead to significant variations in the wall internal actions. Figure 5 shows the axial force distribution within the wall, for the initial condition (solid line) and the conditions reached under thermal loads (dashed lines). As expected, the warmest section, close to the descending portions of the heat exchangers (x = 1.2 m), undergoes an increase in compressive axial load due to restraints that limit its free thermal expansion. These restraints are exerted by the soil, at the wall faces and base, by the thermal condition imposed at the excavation side, and by adjacent sections of the wall itself that are not equally heated. At the same time, the coolest section (x = 0. m) is subjected to a tensile action, exerted by the adjacent heated sections, that eventually results in a positive (tensile) axial force. Note that the thermal condition at the excavation side (0–10 m from the ground surface) exerts a great influence, leading to variations in the axial force

Figure 6. Bending moment in the energy wall under thermo-mechanical loads, at the warmest (x = 1.2 m) and coolest (x = 0.) sections, with respect to the initial condition.

greater than those calculated in the fully embedded part of the wall (10–15 m). The influence of thermal loads reflects also, though not to the same extent, on the wall bending moment distribution, shown in figure 6 with the same notation as in figure 5. The thermal induced stresses lead to minor variations in the upper part of the wall, with positive or slightly negative values in respectively the warmest or the coolest sections, where the initial condition would conversely set a vanishing bending moment. The non-uniformity in the wall structural response along the longitudinal axis (x direction), due to the not

549

uniform distribution of the thermal load T(x,taug ), is therefore confirmed by the various results. The generic transversal section of the wall will undergo internal actions within the limits calculated in sections x = 0 and x = 1.2 m. Unexpected stress states, such as tensile stresses, torsion and out-of-plane effects, result from this non-uniformity.

5

CONCLUSIONS

The thermal analysis of the soil–structure system permitted, first, to investigate the thermal working conditions of the energy wall, subjected to a dual operating mode and to seasonal variations of the atmospheric temperature. The most demanding working conditions were then identified and considered as thermal loads in a thermo–mechanical analysis. The structural response of energy walls is similar to the one observed in energy piles, but while for piles the conventional assumption of axisymmetry is still appropriate, in the analysis and design of walls the conventional plane strain assumption has to be replaced by a three-dimensional scheme. The numerical findings show that the effects of the thermal loads can be considered admissible for the geostructure, in terms of its global stability and structural safety. In fact, they are prominent in the axial direction and therefore mildly affect the structural response of the wall that is mainly based on a flexural behaviour. However, these effects are generally not negligible. The results indicate the development of internal actions that are unusual in ordinary diaphragm walls, such as tensile stresses. The magnitude of these effects depends on the thermal boundary conditions and on the constraint degree of the structure, i.e. on the presence of connected structures. Therefore, the optimal structural design of energy walls should take into account possible situations of unexpected overstress conditions as consequences of the additional thermal loads.

REFERENCES Adam, D. & Markiewicz, R. 2009. Energy from earth-coupled structures, foundations, tunnels and sewers. Géotechnique 59(3), 229–236. Amatya, B.L., Soga, K., Bourne-Webb, P.J., Amis, T. & Laloui, L. 2012. Thermo-mechanical behaviour of energy piles. Géotechnique 62(6), 503–519. Amis, T., Robinson, C.A.W. & Wong, S. 2010. Integrating geothermal loops into the diaphragm walls of the Knights–bridge Palace Hotel project. Proc. 11th Int. Conf. Geotechnical Challenges in Urban Regeneration, London. Barla, M., Di Donna, A. & Perino, A. 2016. Application of energy tunnels to an urban environment. Geothermics 61, 104–113. Bourne-Webb, P.J., Amatya B., Soga, K., Amis, T., Davidson, C. & Payne P. 2009. Energy pile test at Lambeth College, London: geotechnical and thermodynamic aspects

of pile response to heat cycles, Géotechnique, 59(3), 237–248. Brandl, H. 2006. Energy foundations and other thermo-active ground structures. Géotechnique 56(2), 81–122. Cecinato, F. & Loveridge, F. 2015. Influences on the thermal efficiency of energy piles. Energy 82, 1021–1033. European Parliament and Council (2010). Directive 2010/31/ EU of the European Parliament and of the Council of 19 May 2010 on the energy performance of buildings. Official Journal of the European Union, L. 153/13. International Energy Agency (2014). Key World Energy Statistics 2014. OECD/IEA, Paris (www.iea.org). Knellwolf, C., Peron, H. & Laloui, L. 2011. Geotechnical analysis of heat exchanger piles. J. Geotech. Geoenv. Engng. ASCE 137(10), 890–902. Kramer, C.A., Ghasemi–Fare, O. & Basu, P. 2015. Laboratory thermal performance tests on a model heat exchanger pile in sand. Geotech. Geol. Engineering 33, 253–271. Laloui, L. & Di Donna, A. 2013. Energy Geostructures, ISTE and John Wiley & Sons. Laloui, L., Nuth, M. & Vulliet, L. 2006. Experimental and numerical investigations of the behaviour of a heat exchanger pile. Int. J. Numer. Anal. Meth. Geomech. 30(8), 763–781. Lund, J.W., Freeston, D.H. & Boyd, T.L. 2011. Direct application of geothermal energy 2010 worldwide review. Geothermics 40, 159–180. Mauri, L. 2015.A study on energy walls behaviour by thermomechanical numerical analyses (in italian). MS Thesis, Politecnico di Milano, Italy. Nicholson, D. P., Chen, Q., Pillai, A. & Chendorain, M. 2013. Developments in thermal pile and thermal tunnel linings for city scale GSHP systems. Proc. 38th Workshop Geothermal Reservoir Engineering, Stanford University, California, SGP-TR-198. Park, H., Lee, S-R., Yoon, S. & Choi, J-C. 2013. Evaluation of thermal response and performance of PHC energy pile: field experiments and numerical simulation. Applied Energy 103, 12–24. Pérez-Lombard, L., Ortiz, J. & Pout, C. 2008. A review on buildings energy consumption information. Energy & Buildings 40, 394–398. Rees, S.W., Adjali, M.H., Zhou, Z., Davies, M. & Thomas H.R. 2000, Ground heat transfer effects on the thermal performance of earth-contact structures. Renewable Sustainable Energy Rev. 4(3), 213–265 Sterpi, D., Angelotti, A., Corti, D. & Ramus, M. 2014. Numerical analysis of heat transfer in thermo-active diaphragm walls. Proc. 8th NUMGE Conf. (eds. Hicks– Brinkgreve–Rohe), London: Taylor&Francis Group, Vol.2, 1043–1048. Stewart, M.A. & McCartney, J.S. 2014. Centrifuge modeling of soil-structure interaction in energy foundations. ASCE J. Geotech. Geoenviron. Eng. 140(4), 04013044. Sun, M., Xia, C. & Zhang, G. 2013. Heat transfer model and design method for geothermal heat exchange tubes in diaphragm walls. Energy & Buildings 61, 250–259 Suryatriyastuti, M.E., Mroueh, H. & Burlon, S. 2012. Understanding the temperature-induced mechanical behavior of energy pile foundations, Renewable Sustainable Energy Rev. 16, 3344–3354 Suryatriyastuti, M.E., Mroueh, H. & Burlon, S. 2014. A load transfer approach for studying the cyclic behaviour of thermo-active piles, Comp. & Geot. 55, 378–391 Xia, C., Sun, M., Zhang, G., Xiao, S. & Zou, Y. 2012. Experimental study on geothermal heat exchangers buried in diaphragm walls. Energy & Buildings 52, 50–55

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Lessons learned from mechanical monitoring of a thermoactive pile J. Habert & M. El’Mejahed Cerema, Lille, France

J.B. Bernard Ecome, Paris, France

ABSTRACT: This paper deals with a one year-long monitoring a thermo-active pile under a two-storey residential building in Gonesse (France). To fulfil the heating demands of the building, flight auger piles have been installed and equipped with PEHD pipes, allowing the circulation of a cold fluid, which could be heated by the surrounding soil. To apprehend the pile’s behaviour, displacements sensors have been fixed to the reinforcement cage and embedded in concrete, to enable an automatic monitoring of strains and temperatures. On the one hand, it provides elements on strains, temperatures and stress along the pile and caused by real heating demands and circulation of a cold fluid. On the other hand, it also gives access to phenomena relevant for all piles (both thermoactive and standard ones) but currently neglected for the design of structures : significant evolutions of strains and stress in piles caused by the daily variations of outdoor temperature and sunshine can be underlined. The analysis of the measurements hence allows to improve understanding the behaviour of thermoactive but also standard piles.

1

INTRODUCTION

to i) additional displacements, ii) additional structural forces and iii) modified factors of geotechnical safety (pile compressive or tensile capacity).

1.1 A promising method In order to reduce the consumption of fossil energy sources and the energy bill for heating and cooling demands of buildings, energy geostructures constitute an interesting alternative. Integrating heat exchanger elements into geotechnical structures, and especially in piles needed to ensure the baring capacity of the structure, leads to minimized drilling costs, especially in comparison with additional vertical geothermal probes. This technology has been used for almost 30 years in different countries in Europe : Keble College in Oxford-UK on 2001 (Kefford & al., 2010), Dock Midfield Zurich Terminal Airport-Switzerland on 2003 (Pahud & al., 2007), thermoactive embedded walls of metropolitan stations, (Brandl, 2006, Bardoneschi & Bernard, 2014). 1.2 Thermo-Mechanical effects However mechanical effects induce by temperature variations shall be addressed. The injected fluid in the pile, whose temperature comprised between 1◦ C to 35◦ C, I) leads indeed to either contraction (when a cold fluid is injected) or dilation (when a warm fluid is injected) of the pile itself and the surrounding soil, but also ii) potentially modifies the soil strength and stiffness parameters due to thermo-mechanic effects. These phenomena can in a second step lead

1.3

Current practice for thermoactive piles design

Eurocodes and especially Eurocode 7 (EN 1997-1: 2004) don’t address especially thermoactive geostructures. Consequently there is currently neither design standards nor even design method for thermo-active piles. To ensure safety of such structures, contractors have been constructing the buildings on thermoactive piles with empirical consideration or with conservative design by increasing the safety factor for geotechnical resistance (Boënnec, 2009, Knellwolf et al., 2011). However mechanical design of thermoactive piles appears clearly as a two steps problem : on the first step (but most important step of the process thermoactive piles behaviour has to be reproduced. It involved to understand the behaviour of such piles, bases on a wide range of tests, including in situ tests, physical modelling and long term monitoring : the present article deals with a one year-long monitoring thermoactive piles under a building.

2

MONITORED BUILDING DESCRIPTION

Piles of a two storey residential building located in Gonesse (France) have been monitored. Figure 1 shows an overview of the building.

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Figure 1. Overview of the monitored building, on the right side of the picture (source Google Earth).

2.1

Figure 2. Vibrating wire gauge fixed on reinforcing cage.

Building description and energy demands

41 flats have been build, with a global area of 2995 m2 . The overall building presents a peak heating demand of 49 kW, combined with a global heating demand of 10.5 MWh/year. 2.2 Soil conditions and foundation system The building is located on alluvial modern deposits with poor mechanical properties on the first 7 to 9 meters, covering sandy layers (Sables de Beauchamps). To ensure its bearing capacity, pile foundations have been chosen. The average SLS load on each pile is 250 kN. Continuous flight auger piles have been installed, with a 12,00 m length and a diameter comprised between 500 and 600 mm.

Figure 3. Location of monitored piles and strain gauges in each pile.

2.3 Thermoactive piles energetic design Crossing energy demands of the supported buildings and the length of the piles, it has been chosen to only fulfil the heating demands of the building. In the present case, after estimating thermal properties of the surrounding soils, 63 geothermal piles (out of 80 available piles) have been equipped, each with two U-shaped geothermal pipes. 2.4 Monitoring of piles Two piles have been monitored : a first thermoactive 600 mm in diameter pile (P71) , located under the building. A second standard (non thermoactive) 500 mm in diameter pile (P65) located under the edge of the building. To ensure the long term monitoring of piles, two kind of sensors have been installed: – strain sensors, consisting in vibrating-wire gauges, to monitor the vertical strain. These sensors have been fixed to the reinforced cages (as shown on Figure 2), before their embedding in the fresh concrete. C-110 vibrating-wire gauges provided by Telemac have been used,

– temperature sensors, consisting of continuous optic fiber and thermocouples. Due to construction process, it was finally not possible to have access to temperature datas. That’s why only results of the vibrating wire gauges will be presented in this article. However, these gauges also allow a measurement of the temperature. Figure 3 shows The location of the seven gauges initially installed : it has been tried to keep (before embedding in concrete) a constant spacing between the strain sensors and the U-loop PEHD pipes.

3

OBTAINED MEASUREMENTS

The building has been under construction from the beginning of 2012 until middle of 2013. The first measurements have been made in October 2014, a priori just before the second heating cycle. For different reasons it was note possible to have access to measurement of strain of gauges 3 and 7. Measurements have been performed automatically every 5 minutes since 22nd October 2014.

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Figure 4. Typical temperatures measurements.

Figure 6. Characteristic evolving of vertical strains (geothermal pile, z = 7 m).

Figure 5. Temperatures measurements in thermoactive pile.

Figure 7. Overall strain measurements.

3.1 Temperature measurements

expansion factor of the vibrating wire. As thermal expansion factors of the vibrating wire gauges and the pile materials (concretes and steel are very similar, the vertical strain εel v can easily and directly be obtained, using Equation 3.

Figures 4 and 5 show the characteristic evolving of temperature both in thermoactive and standard piles. For the thermoactive pile, the progressive decreasing of temperature can be stated during winter. For the standard pile, the first temperature sensor show important temperature variations, due to his location under the building’s edge. This sensor is indeed affected by the outside temperature. On the contrary, the deeper sensors do not show significant temperature variations. 3.2

Strain measurements

Vertical strain in the pile can be studied through taking into account temperature effects and decomposing the total vertical strain εv in an elastic part εel v and at thermal part εth , as quoted in Equation 1 (Laloui & al, v 1999).

Through measuring the frequency F of vibratingwire gauges at time t, the vertical strain can be obtained using Equation 2, taking into account temperature T .

where K is a gauge factor (for C110 vibrating wire gauges, K = 1.875 10−9 Hz−2 ) and αT the thermal

Figure 6 shows the characteristic evolving of these different strains for the gauge V2 in thermoactive pile. When a cold fluid is injected in a mechanically free pile, the vertical strain would be equal to the thermal strain εth v and traduce contraction. Because of the surrounding soil and supported structure, the (observed) vertical shrinkage εv of the pile which is a limited part of the thermal strain. This phenomena however leads to additional tensile stresses in the pile, equal to Eεel v (where E is the Young modulus of the pile material). During winter positive elastic vertical strain means tensile stress. Figure 7 shows the characteristic evolving of temperature and strains for different sensors both in the thermoactive pile (P71) and the standard pile (P65) (each point is the average measurement during 4 days). Figure 8 shows the same results on a shorter period to ease the analysis (each point is the average measurement during 1 day). For the standard pile, since the temperature remains quite constant, there is no strain caused by temperature changes, and the elastic vertical strain is equal to the vertical strain.

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Figure 8. Strain measurements during the first winter.

Figure 10. Correlation between outside temperature and strains, pile P71, z = 7 m.

Figure 9. Influence of outside temperature, pile P71, z = 7 m.

Figure 11. Influence of time interval between consecutive measurements.

4 4.1

FURTHER ANALYSIS Influence of outside temperature

Figure 9 shows the daily evolution of elastic vertical strain during the 26th and 27th October 2014. The correlation between the pile temperature and the strains hence appears clearly. When the outside temperature increase, the load on the geothermal pile P71 decreases. At the same time, the load on the Standard pile decreases. Moreover the effect of the outside temperature is more important for the shallow sensors than for the deepest ones. It’s supposed that these results are linked to the thermal expansion and contraction of the building itself accompanying outside temperature variations. To better analyse the phenomena, the Figure 10 shows the correlation and the phase angle between outside temperature and strains. Especially in summer, daily evolutions of temperature can lead to additional strain up to 30 µdef. If the short term modulus of deformation of concrete is considered, with an average value of 30000 MPa, a daily variation of vertical stress in pile up to 90 kPa can also be obtained. 4.2

Choosing the right time interval

Figure 11 shows the influence of the chosen time interval between consecutive measurements during 27th October 2014, for pile P71 at z = 7 m.

Figure 12. Strain variations in geothermal pile, z = 7 m.

Hence a 5 minutes interval (as chosen here) might appear quite small and at the same lead to a significant load of datas. However, increasing this interval up to 2 hour will prevent to have access extreme values. Consequently the present study leads us to maintain at least on measurement each hour. 4.3 Influence of geothermal fluid The evolving of the vertical strain is then compared to temperature changes in geothermal pile P71. In a first step, measurements obtained for the thermoactive pile at z = 7 m are plotted in Figure 12 (each point is the average measurement during a 4 days period). Strains hence appear to evolve quite linearly with temperature variations. The same analysis can finally be performed for each strain gauges, and also for

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Moreover, the measurement provides useful information for standard piles located under buildings. The importance of the variations of strains due to outside temperature has indeed been stated. This phenomena highlights the importance of automated measurements to finely understand the behaviour of piles under buildings. The vertical strain monitoring is still functioning and will allow in the future year to better understand the behaviour of thermoactive pile systems. ACKNOWLEDGEMENTS

Figure 13. Strain variations in the two monitored piles.

The work described in this paper forms part of a research project “GECKO” which is supported by a grant from the French National Research Agency (ANR). It is an industrial project with international collaboration, involving companies and research laboratories in civil and energy engineering sector: ECOME, BRGM, Cerema, IFSTTAR, LEMTA, LGCgE-Université Lille 1.

Table 1. Ratio between temperature variations in pile 71 and strain. P71

Pile z (m)

0.5

◦ εel v /T (µdef/ C)

−9.1

P67

7

11.8

6

−10.7

−7.3

4.5

11.8 2.8

REFERENCES gauges installed in the standard pile. Strains variations are presented on Figure 13. This allows to determine the ratio εel v /T. The results for the first winter are presented in Table 1. The previous analysis hence shows that during winter, due to the circulation of a cold fluid, the load on geothermal piles will slightly decrease, quite linearly with temperature variations. Consequently, the mechanical vertical load on standard piles will increase. 4.4

Conclusions

The present paper deals with a long term monitoring of a thermoactive pile but also of a standard piles. Based on different analysis of the strains in two piles under a residential building, different phenomena have been output. During winter, the temperature variation leads to contraction of geothermal piles, and hence a decrease of the compressive vertical stress and of the load at pile head. This phenomena is accompanied by an increase of the load the measurements on narrow standard piles.

Bardoneschi, B. & Bernard, J.B., 2014, Captage géothermique en parois moulées de stations de métro, Xpair.com Bourne-Webb P.J., Amatya B., Soga K., Amis T., Davidson C., Payne P., 2009: Energy pile test at Lambeth College, London: Geotechnical and thermodynamic aspects of pile response to heat cycles, Geotechnique, vol. 59, no. 3, 237–248. Brandl H., Energy foundations and other thermo-active ground structures, Geotechnique, 56 n◦ 2, 81–122. Kefford N, 2010, Case study, long term monitoring of energy piles at Keble College GSHPA Research Seminar., Oxford. ARUP. Pahud, D. & Hubbuch, M., 2007 : Measured thermal performances of the energy pile system of the dock midfield at Zurich Airport, European Geothermal Congress. Knellwolf, C., Peron H., andLaloui L., 2011 : Geotechnical Analysis of Heat Exchanger Piles. Journal of Geotechnical and Geoenvironmental Engineering, 137(10), 890–902. Boënnec, O., 2009 : Piling on the Energy, GeoDrilling International, 25–28. Laloui, L., Moreni, M., Steinmann, G., Vulliet, L., Fromentin, A., Pahud, D. 1999 : Test en conditions réelles du comportement statique d’un pieu soumis à des sollicitations thermo-mécaniques. Report of the Swiss Federal Office of Energy.

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Effect of forced thermal recharging on the thermal behaviour of a field scale geothermal energy pile Mohammed Faizal & Abdelmalek Bouazza Department of Civil Engineering, Monash University, Melbourne, Australia

ABSTRACT: Many applications require ground source heat pumps coupled with energy piles to operate for a given number of hours per day. During the times when the heat pumps are switched off, the ground temperatures normally recover naturally. The ground can be forcefully recharged during the rest periods using solar heaters or cooling towers combined with energy piles. The effect of solar thermal recharging on energy extracted, ground and pile temperatures, and pile thermal strains and stresses are presented in this paper. Forced ground thermal recovery is experimentally investigated and included for 8 hours operation with 16 hours heating and 16 hours operation with 8 hours heating. The longer recharge duration gives higher benefits in terms of energy extracted and ground temperature recoveries with larger thermal loads on the pile. The pile temperatures, thermal strains and stresses undergo cyclic response for both operating modes. 1

INTRODUCTION

Geothermal energy piles are foundation piles used as underground heat exchangers to maintain human thermal comfort in buildings, via the use of a Ground Source Heat Pump (GSHP). The GSHPs may be operational for different intermittent hours per day or may run continuously for 24 hours daily. The ground temperatures during the rest periods of intermittent modes can be forcefully recharged through the use of optimized hybrid systems that utilise solar collectors or cooling towers combined with GSHPs (Wood et al., 2010, Man et al., 2010). Forced thermal recharging improves geothermal energy usage as well as effectively alleviates the heat build-up and provides a balance of ground temperatures around the heat exchanger (Jalaluddin and Miyara, 2012). Unlike borehole heat exchangers, the dimensions and spacing of energy piles are restricted by the superstructure design. Hybrid systems are therefore a feasible option to improve energy usage from energy piles and preventing ground thermal imbalances in a given building footprint. It thus becomes important to study the ground temperatures and pile thermal behaviour to identify any potential limitations as a result of forced thermal ground recharge. Intermittent operating modes of borehole heat exchangers with forced ground recharge have shown that improvement in ground temperatures and performance of the GSHP is more effective compared to natural ground recovery (Dai et al., 2015, Wang et al., 2010, Wang et al., 2012, Man et al., 2010). The few studies on energy piles with ground solar thermal recharge have also shown to oppose the ground temperature reduction and improve performance of the GSHPs (Wood et al., 2010, Wood, 2011). At present,

the thermal strain and stress distribution in field scale energy piles has mostly been studied for continuous operating modes (Laloui et al., 2006, Bourne-Webb et al., 2009, Murphy et al., 2014, Murphy and McCartney, 2014, McCartney and Murphy, 2012, Akrouch et al., 2014, Wang et al., 2015, Mimouni, 2014). The thermal behaviour of energy piles for intermittent operation with forced ground thermal recharge remains yet to be studied. The objective of this paper is thus to experimentally investigate the influence of forced ground thermal recharging for two operation modes of a field scale energy pile. The forced thermal recharging is done during the non-operating times of the cooling unit, simulating a solar hybrid GSHP system for a scheduled intermittent mode of operation. The recharging hot water temperature is maximized to study the effects of extreme operating conditions.

2

PILE INSTRUMENTATION AND EXPERIMENTAL PROCEDURE

Two operating modes were experimentally investigated on a field scale energy pile located at Monash University, Australia (Wang et al., 2015, Singh et al., 2015), one mode with 8 hours of daily cooling followed by 16 hours of heating (8C16H mode) and the other mode was 16 hours of daily cooling followed by 8 hours of heating (16C8H mode). Six days (128 hours) of results are assessed for each mode. Only six days of data are presented due to site constraints in the 8C16H mode. The results of the 16C8H mode are adapted from recent studies reported by (Faizal et al., 2015). In these experiments, the hot water is circulated

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in the same loops as the cold water immediately after switching off the chiller. A United Refrigeration chiller with a tank volume of approximately 35 litres was used to circulate cold water. A GeoCube TRT unit with a tank volume of approximately 4 litres was used to circulate hot water in the pile, at flowrates of 15 and 13.5 litres/per min, respectively. A GPI TM075 water flowmeter mounted on the inlet to pile pipe recorded the water flowrates. The chiller and the heater were connected to the pile inlet and outlets using insulated HDPE pipes, with an approximate length of 15 m. The water temperature in the chiller and heater tanks were manually controlled using bypass valves, before the water was released into the pile (Fig. 1). The purpose of regulating the temperatures at the beginning of each thermal cycle was to study the pile thermal behaviour under extreme operating conditions. The hot water in the pipe loops from the heating cycles got mixed and increased the cold water temperatures in the cooling cycle for both modes. This change in temperatures is expected practically in alternating heating/cooling applications of hybrid systems (Dai et al., 2015). Also, the elevated temperatures of the ground from the heating cycle contributed to the increase of the cold water temperature in the chiller tank during the cooling cycle. Similarly, the hot water temperature was affected by the cold water in the loops when released into the pile immediately after the cooling cycle. Hence flow in the pile was stopped multiple times by shutting the inlet and outlet valves of the cooling/heating unit and using the bypass valves to control the water temperature before releasing it into the pile. Since it was desired to have a continuous flow in the pile, the stoppage times were minimized as much as possible. Due to extreme high temperatures from the heating cycle in the 8C16H mode (as high as 70◦ C), the compressor of the chilling unit would overload and was stopped to cool down. Hence, the effective cooling and heating periods are approximately 15.5–16 hours for the 16C8H mode and between 4–7 hours in the 8C16H mode. Figure 2 shows a schematic of the instrumented bored pile used for this study. This pile (0.6 m diameter with a depth of 16.1 m), which was installed in December 2010, was specifically designed to study the changes in the shaft capacity of pile after heating and cooling operations (Wang et al., 2015), and thus is slightly different from a conventional pile. There were two OsterbergCell (O-Cell) load testing systems installed at approximately 10 m and 14 m below ground level, dividing the pile into three sections: the 10 m upper section, the 4 m middle section, and the lower 1 m section. Three standard HDPE pipe loops, with outer diameter of 25 mm and inner diameter of 20 mm were attached to the reinforcement pile cage. The pipes were installed 50 mm from the edge of the pile and to the top of the lower O-Cell (LOC), to a depth of 14.2 m. The spacing between the loops was about 175 mm. Embedment and sister bar vibrating wire strain gauges were installed at different depths along the axis

Figure 1. Chiller and heater connection to the pile.

of the pile (Fig. 2). Type K thermocouples recorded atmospheric temperatures, inlet and outlet water temperatures at the pile head, and ground temperatures at eight depths in two boreholes located at radial distances of 0.5 m and 2 m from the pile edge. The data from the thermocouples were logged using Pico Technology’s USB-TC08 data logger, whereas data from the strain gauges were logged using DataTaker’s DT80G and CEM20 data loggers. For the purpose of this study, the temperatures and thermal strains observed from the axial strain gauges on the upper and middle pile sections are considered, at depths of 5.4 m and 8.2 m, and 11.6 m and 13.3 m, respectively. The soil profile at the test site consisted of sands and fine to coarse to very dense clayey sands, also summarized in Fig. 2 (Yu et al., 2015, Barry-Macaulay et al., 2013). The top end of the pile was not restrained and the pile head was exposed to the atmosphere. The undisturbed ground temperatures for the year 2013 recorded at this site showed that surface temperature fluctuations were felt up to 6 m depth (Yu et al., 2014). The thermal strains, εT , induced in the concrete were calculated as:

where fi is the resonant frequencies of the strain gauges at time i, fo is the reference resonant frequency, GB is the calibration factor (G is gauge factor and B is batch factor), Ti is the temperature of the strain gauges at time i, To is the reference temperature, and αs is the thermal expansion of the steel wire. The free or unrestrained thermal strains, εT ,free , of each gauge were calculated as (Murphy et al., 2014, Murphy and McCartney, 2014):

where αc is the coefficient of linear thermal expansion of concrete and T is the change in temperature of concrete. The thermal expansion coefficient of concrete depends on the constituents of the mix, and can

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Figure 3. Atmospheric temperatures for the two modes recorded during experimentation.

Figure 2. (a) Schematic of the instrumented energy pile (LOC: lower O-cell, UOC: upper O-cell, Emb: embedment strain gauges, Sis: sister bar strain gauges) (Adapted from (Wang et al., 2015).

be as high as 14.5 µε/◦ C, while that of steel reinforcements ranges from 11.9 to 13 µε/◦ C (McCartney et al., 2010, Stewart and McCartney, 2014). Thermally induced stresses, σT , were calculated from the difference between the measured thermal strains and the free thermal strains from the gauges as (Murphy and McCartney, 2014, Murphy et al., 2014):

where E is the Young’s modulus of the pile concrete (taken as 30 GPa). In the present study, cooling is taken as compressive, giving negative thermal strains. The difference in the water temperatures at inlet and outlet of the pile is used to calculate the energy ˙ as: extracted or rejected, Q,

where ρ is density, V˙ is volume flowrate, and Cp is the specific heat capacity of water, Tf ,out − Tf ,in is the temperature difference between inlet and outlet water at pile head, and L is the length of the pile (14.2 m since the HDPE pipes only extended up to this depth in the pile). 3

RESULTS AND DISCUSSIONS

The atmospheric temperatures recorded at the test site for the two operating modes during the experimentation period (128 hours, 6 days) are shown in Fig. 3.

They ranged between 21– 35◦ C for 8C16H mode and 16–37◦ C for 16C8H mode. Figures 4a and 4b show the fluid inlet, outlet, and change in fluid temperatures of the 8C16H and 16C8H modes, respectively, presented after the target inlet temperatures were achieved using the bypass valves, as discussed in section 2. The lowest initial inlet cold water temperature achieved in the 8C16H mode for cooling operation was approximately 20–28◦ C (Fig. 4b), outlet temperatures ranged between 16◦ C to 34◦ C, and difference between inlet and outlet between 4◦ C to 6◦ C for all cooling cycles. The inlet hot water temperature for the heating cycle of 8C16H mode was initially 40◦ C (Fig. 4b) and went as high as 70◦ C in the heating cycle. The outlet temperatures ranged from 35◦ C to 62◦ C and the difference between the outlet and inlet hot fluid temperatures was almost a constant of 9◦ C. The lowest initial inlet cold water temperature achieved in the 16C8H mode for cooling operation was approximately 16◦ C (Fig. 4a), outlet temperatures ranged between 11◦ C to 21◦ C, and difference between inlet and outlet between 3◦ C to 5◦ C for all cooling cycles. The inlet hot water temperature for the heating cycle of 16C8H mode was initially between 30◦ C–33◦ C and went as high as 55◦ C in the heating cycle. The outlet temperatures ranged from 25◦ C to 45◦ C and the difference between the outlet and inlet hot fluid temperatures was almost a constant of 9◦ C. The difference between the outlet and inlet hot fluid temperatures was almost constant for both modes, possibly due to the low volume capacity of the heating unit and powerful electrical heaters which rapidly heated the returning fluid from the pile before re-circulating it to the inlet. Hence a constant amount of thermal energy was injected into the ground daily during the forced thermal recharging period (Fig. 7). It should be noted that the heating cycle temperatures are maximized to investigate extreme operating conditions. Figures 5 and 6 show the ground temperatures for both modes at radial distances R = 0.5 m and R = 2 m from the pile edge. The ground temperatures at 2 m and 4 m depths were affected by atmospheric temperatures. There was no change in ground temperatures at 16 m

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Figure 4. Fluid temperatures a) 8C16H mode and b) 16C8H mode (Note: the vertical axis scales are different).

depth for both modes since the pipe loops in the pile were only installed up to 14.2 m depth. The daily ground temperature recovery are more evident in the 8C16H mode at R = 0.5 m due to longer recharging time and higher inlet temperatures which considerably increased the ground temperature compared to the 16C8H mode. Optimized hybrid systems in actual operating conditions with design control strategies will have better balance of ground temperatures (Man et al., 2010). The ground temperature increase at R = 0.5 m in the 8C16H mode at end of experiments was approximately 10◦ C and 3◦ C in the 16C8H mode, with reference to initial temperature for a depth of 12 m (Fig. 5c) The ground temperature changes were almost negligible at R = 2 m for both modes. This leads to the conclusion that forced thermal recharging (even under extreme operating conditions) may not have any potential thermal interactions with other nearby energy piles in long-term actual building operations. Further studies with longer operation times will give more insight into ground temperature response at different radial distances. Figure 7 compares the average energies extracted and injected for the two modes, where energy extracted

is positive and energy injected is negative. The energy injected in both modes is almost constant at 570– 590 W/m due to almost constant difference between inlet and outlet temperatures (Fig. 4). The 8C16H mode gives almost twice higher heat extraction rates than the 16C8H mode. Compared to the 16C8H mode, the 8C16H mode significantly improves the thermal gradient between the ground and the fluid as a result of higher ground temperatures; therefore more energy is extracted in the cooling cycle of the 8C16H mode. Figures 8a and 8b shows pile temperatures for 8C16H and 16C8H modes, respectively. There is an almost cyclic pile temperature change from approximately 26◦ C to 54◦ C in the 8C16H mode from end of recharge to end of cooling, and from approximately 13◦ C to 34◦ C in the 16C8H mode from end of recharge to end of cooling, for depth of 5.4 m (Fig. 8c). There are differences in 8C16H mode peak temps due to chiller stoppage which resulted from very high temperatures circulating in the chiller tank. The 8C16H mode generally induces higher temperatures in the pile compared to 16C8H mode (Fig. 8c); hence larger thermal strains and stresses are expected for this mode. Pile temperatures of both modes however undergo cyclic operation and return to almost similar values at end of cooling

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Figure 5. Transient ground temperatures at R = 0.5 m. a) 8C16H mode, b) 16C8H mode and c) 12 m depth for both modes.

and recovery cycles for consecutive days. This gives rise to cyclic response of thermally induced strains and stresses in the pile. Due to the discontinuity in the piles created by the presence of the O-cells, the upper 10 m and the middle 4 m sections of the pile were analysed separately. Figures 9a and 9b shows pile temperatures against depth for 8C16H and 16C8H modes, respectively, between 80–120 hours. There are slight differences between peak temperatures at end of cooling and recharging for 8C16H mode due to inconsistency in maintaining the inlet fluid temperatures. The 8C16H mode gave larger temperature difference between depths compared to 16C8H mode due to higher fluid temperatures in the heating cycle (5◦ C for 8C16H

and 2◦ C for 16C8H mode). The difference between recovery and cooled peak temperature is also higher in 8C16H mode due to high heating fluid temperatures (28◦ C for 8C16H and 22◦ C for 16C8H mode for depth of 5.4 m). Figures 10a and 10b show the pile axial thermal strains for 8C16H and 16C8H modes, respectively, calculated using equation 1 and zeroed at beginning of experiments. The lowest observed thermal strains, and hence the most restricted, is observed at 5.4 m depth for both modes. The peak thermal strains at end of cooling/recovery for both modes return to similar values for daily thermal cycles. It appears that the soil surrounding the pile did not affect or limit the thermal strain behaviour as a result of soil-structure interaction,

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Figure 6. Transient ground temperatures at R = 2 m. a) 8C16H mode and b) 16C8H modes.

Figure 7. Daily average energy extracted/injected for both modes.

for the present case. A further study of forced thermal recharging on effects of soil properties and pile settlement would give more insight into the coupled behaviour of pile and soil. There is an almost cyclic change in thermal strains from approximately 110 µε to 300 µε in the 8C16H mode from end of cooling to end of recharge, and from approximately −20 µε to 110 µε◦ C in the 16C8H mode from end of cooling to end of recharge, for a depth of 5.4 m (Figure 10c). The 8C16H mode generally induces higher thermal loads in the pile as a result of higher thermally induced

strains compared to the 16C8H mode (due to higher recharging temperatures and longer recharging time). Even though the 8C16H mode induces higher thermal loads in the pile, the thermal axial strains from the present results however show a cyclic response for daily thermal cycles for both modes. Hence, it is possible that no substantial deformations in the pile and surrounding soil as a result of increased thermal loading are expected due to forced thermal recharging in the present study. Figures 11a and 11b show the axial thermal strains against depth, for 8C16H and 16C8H modes,

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Figure 8. Transient pile temperatures for a) 8C16H mode, b) 16C8H mode and c) at 5.4 m depth for both modes (Note: the vertical axis scales are different).

respectively. The lowest thermal strains were observed at 5.4 m for both modes indicating that the largest constraint was at this location in the upper pile section. There are slight differences between thermal strains at end of cooling and recovery since the pile did not reach thermal equilibrium with the ground as a result of short term operation. The difference between recovery and cooled peak thermal strains is higher in the 8C16H mode due to high heating fluid temperatures (190 µε for 8C16H and 130 µε absolute for 16C8H mode for depth of 5.4 m). Higher inlet temperatures in the heating cycle also lead to higher strain constraints at 5.4 m depth compared to 8.2 m depth. The thermal strains are less restrained at 8.2 m depth due to partial restraint provided by the upper load cell. Due to lower cooling fluid temperature

and longer cooling period, the thermal strains in the 16C8H mode were observed to be negative at end of daily cooling cycles. Figures 12a and 12b show the axial thermal stresses in the pile for 8C16H and 16C8H modes, respectively. The axial thermal stresses are estimated using equation 3. As expected, significant differences in axial thermal stresses are observed between the two modes due to significant differences in pile temperatures and thermal strains. The maximum cyclic thermal stresses in the 8C16H mode at end of cooling and recovery was approximately 0 MPa and 6.5 MPa, respectively, whereas the maximum cyclic thermal stresses after equilibrium in the 16C8H mode at end of cooling and recovery was approximately −1.1 MPa and 3.5 MPa, respectively, at 5.4 m depth (Fig. 12c). The thermal

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Figure 9. Pile temperatures against depth for a) 8C16H mode and b) 16C8H mode (Note: the horizontal axis scales are different).

stresses at end of cooling for 16C8H mode was consistently negative as a result of lower fluid temperature and longer operation time. The response of thermal stresses for both modes is cyclic with minimal differences between peak values at end of cooling and recovery cycles between consecutive days. The results indicate that the induced thermal stresses in energy piles should be stable for forced thermal recharging. Hence no significant effects on the pile performance and surrounding soil deformation are expected as a result of forced thermal recharging. It should be noted that the recharging temperatures in the present studies have been maximized to study the effects of extreme operating conditions. Thermally induced stresses in energy piles in actual operations of hybrid systems will be much lower due to control strategies put in place to activate ground recharging. Figures 13a and 13b show the pile axial thermal stresses against depth for 8C16H and 16C8H modes, respectively. The trends in thermal stresses against

depth are different from previously studied field scale energy piles (Laloui et al., 2006, Bourne-Webb et al., 2009, Murphy et al., 2014, Murphy and McCartney, 2014, McCartney and Murphy, 2012, Akrouch et al., 2014) due to presence of O-cells which divided the pile into sections, and due to less number of gauges. The thermal stresses for both modes are highest at 5.4 m depth at end of both cooling and heating cycles due to the larger restraint on thermal strains compared to other depths. The lowest thermal stresses for both modes are for 8.2 m depth possibly due to partial restraint provided by the upper O-cell which created a discontinuity in the pile. The difference between recovery and cooled peak thermal stresses is higher in the 8C16H mode due to high heating fluid temperatures (6200 kPa for 8C16H and 5000 kPa absolute for 16C8H mode for depth of 5.4 m). Higher inlet temperatures in the heating cycle also lead to higher strain constraints at 5.4 m depth compared to 8.2 m depth.

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Figure 10. Transient thermal strains for a) 8C16H mode, b) 16C8H mode and c) 5.4 m depth for both modes (Note: the vertical axis scales are different).

Figure 11. Axial thermal strains against depth for a) 8C16H mode and b) 16C8H mode (Note: the horizontal axis scales are different).

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Figure 12. Transient axial thermal stresses for a) 8C16H mode, b) 8C16H mode and c) 5.4 m depth for both modes (Note: the vertical axis scales are different).

4

CONCLUDING REMARKS

The objective of this paper was to study the thermal behaviour of a field scale energy pile under forced ground recharge (simulating solar thermal recharge) for 8 hours cooling and 16 hours heating (8C16H), and 16 hours cooling and 8 hours heating (16C8H), respectively. The hot water temperature was maximized for a scheduled recharging during non-operating times of the cooling unit to study the effects of extreme

operating conditions.The following major conclusions are drawn from the results of this study:

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•

The ground temperatures at 2 m radial distance from the pile surface was not affected by high pile emperatures; hence it is possible that no potential thermal interactions between energy piles with 2 m or more spacing in actual building operations are expected due to elevated temperatures from forced thermal recharging.

Figure 13. Axial thermal stresses against depth for a) 8C16H mode and b) 16C8H mode (Note: the horizontal axis scales are different).

Higher recharging temperatures with longer recharging time leads to higher ground temperatures near the pile. • The energy extracted was almost twice in the 8C16H mode compared to 16C8H mode. • The pile temperatures, thermal strains and stresses are higher in the 8C16H mode, but undergo cyclic response for both operating modes; hence it is possible that no significant structural effects are expected from forced thermal recharging for the pile and soil in the current study. •

Intermittent operating modes with controlled forced thermal recharging can be beneficial in terms of energy extraction and ground temperature balance for geothermal energy piles since no significant structural effects are expected. Further studies on conventional piles with optimized hybrid systems will give more insight on coupled thermal behaviour of soil and pile. ACKNOWLEDGEMENTS This research was supported under the Australian Research Council’s Linkage Projects funding scheme

(project number LP120200613) and contributions from Vibropile Pty. Ltd., Golder Associates Pty. Ltd. and GeoExchange Australia Pty. Ltd. Their support is gratefully acknowledged.

REFERENCES Akrouch, G., Sanchez, M. & Briaud, J.L. 2014. Thermomechanical behavior of energy piles in high plasticity clays. Acta Geotechnica, 9, 399–412. Barry-Macaulay, D., Bouazza, A., Singh, R. M., Wang, B. & Ranjith, P. G. 2013. Thermal conductivity of soils and rocks from the Melbourne (Australia) region. Engineering Geology, 164, 131–138. Bourne-Webb, P. J., Amatya, B., Soga, K., Amis, T., Davidson, C. & Payne, P. 2009. Energy pile test at Lambeth College, London: geotechnical and thermodynamic aspects of pile response to heat cycles. Geotechnique, 59, 237–248. Dai, L., Li, S., Duanmu, L., Li, X., Shang, Y. & Dong, M. 2015. Experimental performance analysis of a solar assisted ground source heat pump system under different heating operation modes. Applied Thermal Engineering, 75, 325–333.

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Faizal, M., Bouazza, A. & Singh, R. M. 2015. An experimental investigation of the influence of intermittent and continuous operating modes on the thermal behaviour of a full scale geothermal energy pile (Under review). Jalaluddin & Miyara, A. 2012. Thermal performance investigation of several types of vertical ground heat exchangers with different operation mode.AppliedThermal Engineering, 33–34, 167–174. Laloui, L., Nuth, M. & Vulliet, L. 2006. Experimental and numerical investigations of the behaviour of a heat exchanger pile. International Journal for Numerical and Analytical Methods in Geomechanics, 30, 763–781. Man, Y., Yang, H. & Wang, J. 2010. Study on hybrid ground-coupled heat pump system for air-conditioning in hot-weather areas like Hong Kong. Applied Energy, 87, 2826–2833. McCartney, J. S. & Murphy, K. D. 2012. Strain distributions in full-scale energy foundations. DFI Journal: The Journal of the Deep Foundations Institute, 6, 26–38. McCartney, J. S., Rosenberg, J. E. & Sultanova, A. 2010. Engineering performance of thermo-active foundations. GeoTrends. Mimouni, T. 2014. Thermomechanical characterization of energy geostructures with emphasis on energy piles. PhD thesis, École Polytechnique Fédérale de Lausanne. Murphy, K. D. & McCartney, J. 2014. Seasonal response of energy foundations during building operation. Geotechnical and Geological Engineering, 1–14. Murphy, K. D., McCartney, J. S. & Henry, K. S. 2014. Evaluation of thermo-mechanical and thermal behavior of full-scale energy foundations. Acta Geotechnica, 1–17. Singh, R., Bouazza, A. & Wang, B. 2015. Near-field ground thermal response to heating of a geothermal energy pile: observations from a field test. Soils and Foundations.

Stewart, M. A. & McCartney, J. S. 2014. Centrifuge modeling of soil-structure interaction in energy foundations. Journal of Geotechnical and Geoenvironmental Engineering, 140, 04013044. Wang, B., Bouazza, A., Singh, R., Haberfield, C., BarryMacaulay, D. & Baycan, S. 2015. Posttemperature effects on shaft capacity of a full-scale geothermal energy pile. Journal of Geotechnical and Geoenvironmental Engineering, 0, 04014125. Wang, E., Fung, A. S., Qi, C. & Leong, W. H. 2012. Performance prediction of a hybrid solar ground-source heat pump system. Energy and Buildings, 47, 600–611. Wang, X., Zheng, M., Zhang, W., Zhang, S. & Yang, T. 2010. Experimental study of a solar-assisted ground-coupled heat pump system with solar seasonal thermal storage in severe cold areas. Energy and Buildings, 42, 2104–2110. Wood, C. 2011. Energy piles for residential installations and other low rise buildings. Ground source live sustainable heating & cooling. Peterborough. Wood, C. J., Liu, H. & Riffat, S. B. 2010. Comparison of a modelled and field tested piled ground heat exchanger system for a residential building and the simulated effect of assisted ground heat recharge. International Journal of Low-Carbon Technologies, 5, 137–143. Yu, K. L., Singh, R. M., Bouazza, A. & Bui, H. H. 2014. Evaluation of soil thermal properties through numerical simulations of a heating test on a geothermal energy pile. Proceedings of the 7th International Congress on Environmental Geotechnics. Yu, K. L., Singh, R. M., Bouazza, A. & Bui, H. H. 2015. Determining soil thermal conductivity through numerical simulation of a heating test on a heat exchanger pile. Geotechnical and Geological Engineering, 33, 239–252.

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Numerical investigation of the mechanical behaviour of single energy piles and energy pile groups C. Tsetoulidis, A. Naskos & K. Georgiadis Aristotle University of Thessaloniki, Thessaloniki, Greece

ABSTRACT: The effect of thermal loading on the mechanical behaviour of single energy piles and energy piles in pile groups is investigated. Finite element analyses are presented, in which both thermal and mechanical loads are applied to the piles. The numerical modelling procedure is first validated against a documented in the literature full-scale experiment. Subsequently, two numerical investigations are presented. In the first investigation, the effect of thermal loading on the axial response of single piles is examined. The second numerical investigation involves axially loaded 3 × 3 pile groups with a rigid cap, in which either the centre pile or all piles of the group are thermo-active. It is shown that the effect of thermal loading on the axial pile forces is significant and depends on the number of piles that are thermally active in the pile group and on the relative values of the coefficient of thermal expansion of the pile and the ground. 1

INTRODUCTION

One of the most unexploited sources of renewable energy in our days, that escapes the boundaries of classical geothermal applications, is the use of the almost constant temperature of the ground in the superficial layers of the earth’s crust (Brandl, 2006). Up until recently, the few attempts that had been made to harvest this form of energy were mostly focused on “energy wells” or “energy boreholes” acting as heat exchangers. However, based on this idea, over the last three decades, this technique has also been implemented on foundation elements with significant environmental and economic results. The most common type of such a foundation element in practice is the energy pile (e.g. “Dock Midfield” station of the airport in Zurich, Norddeutsche Landesbank in Hamburg, The School Center in Berlin, etc.). Nonetheless, despite the applications that have taken place so far, there is still a lot of uncertainty on the issue of the mechanical behaviour of such elements, due to the considerable thermal loading that is applied on top of the mechanical loading of the piles. Investigations on the thermo-mechanical behaviour of energy piles that involve thermal pile tests or monitoring, have been conducted in Bad Schallerbach, Austria (Brandl, 1998 & 2006), Frankfurt am Main, Germany (Ennigkeit & Katzenbach, 2001), Lausanne, Switzerland (Laloui et al., 2006) and London, UK (Amis et al., 2008 and Bourne-Webb et al., 2009). Fundamental theoretical models have been proposed to describe the mechanical behaviour of energy piles (e.g. Bourne-Webb et al., 2011 and Amatya et al., 2012), which incorporate some critical basic aspects. However, they are based on limited data and several assumptions and therefore, there appears to be room

for improvement. Recently, numerical investigations have been published that investigate aspects of the behaviour of energy piles (e.g. Ozudogru et al., 2014, Salciarini et al., 2014, Bourne-Webb et al., 2015, Di Donna et al., 2016). This paper presents such a numerical study using finite element analysis conducted in order to investigate the behaviour of single energy piles and energy pile groups under axial loading. 2

FINITE ELEMENT ANALYSES

The numerical analyses presented in this paper were performed with the finite element program ABAQUS. Two finite element meshes were used in the analyses; one for the single pile analyses and one for the 3 × 3 pile group analyses. The pile dimensions and soil stratigraphy of the Lambeth College, London energy pile test (Amis et al., 2008 and Bourne-Webb et al., 2009) were used. Therefore, in all cases considered, the pile(s) had a length of L = 23 m and a diameter of D = 0.6 m, while the stratigraphy consisted of a top 1.5 m thick Made Ground layer, overlaying a 4 m thick layer of Terrace Deposits, which is underlain by a deep London Clay layer. The same centre-to-centre pile spacing of 1.8 m (3 pile diameters) was considered in all pile group analyses. The soil behaviour was modelled as linear elasticperfectly plastic with a Mohr-Coulomb failure criterion and a Drucker-Prager plastic potential surface. The mechanical material properties of the ground layers are presented in Table 1. Typical thermal properties were selected for the materials and are shown in Table 2. The piles were modelled as linear elastic with Young’s modulus Ep = 2.9 · 107 kPa, Poisson’s ratio

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Table 1. Mechanical properties of soil layers. Layer

E MPa

v –

φ′ ◦

c′ or su γ kPa kN/m3

Made Ground 20 0.2 20 0 19 Terrace 20 0.2 30 0 19 Deposits London Clay 800 · su 0.49 0 70+7z 20 E: Young’s modulus, v: Poisson’s ratio, φ: angle of shearing resistance, c: effective cohesion, su : undrained shear strength, γ: bulk unit weight. Table 2. Thermal properties of soil layers. Layer

λ W/m/K

C J/kg/K

α m/m/K

Made Ground Terrace Deposits London Clay

2 2 1.5

1200 1200 1000

5.6 · 10−6 5.6 · 10−6 10 · 10−6

Figure 2. Finite element mesh for the pile group analyses.

λ: thermal conductivity, C: heat capacity, α: coefficient of thermal expansion.

Figure 1. Finite element mesh for the single pile analyses.

vp = 0.1, unit weight γ = 25 kN/m3 , thermal conductivity λp = 1.7 W/m/K, heat capacity Cp = 960 J/kg/K and coefficient of thermal expansion αp = 8.5 · 10−6 m/m/K. The pile soil interface was modelled as frictional with a friction angle equal to the angle of shearing resistance of the adjacent soil, for the top layers, and equal to 28◦ for the London Clay layer. A maximum (cut-off) shear stress equal to a · su was specified for the part of the interface in the London Clay layer, where a is the adhesion factor. The adhesion factor was calculated according to Kulhawy (1991). The finite element mesh used for the single pile analyses is shown in Figure 1, while the mesh used for the pile group analyses is shown in Figure 2. Both meshes have a diameter of 48 m (80 × D) and a height of 35 m (1.4 × L). Second order hexahedral elements were used for the pile(s) and for a cylindrical region around the pile or pile group. This region had a diameter of 3 m in the mesh used for the single pile analyses

and 12 m in the mesh used for the pile group analyses. First order hexahedral elements were used for the rest of the mesh. In total, the finite element mesh for the single pile analyses (Fig. 1) consisted of 31382 elements, while that for the pile group analyses consisted of 92274 elements. The vertical boundaries of both meshes were fixed in the normal direction, while the bottom boundary was fixed in all directions. A constant temperature field of 18◦ C was prescribed for all elements of the meshes at the beginning of each analysis and the same temperature was prescribed as a boundary condition at all boundaries throughout the analyses. Thermal loading was modelled in separate transient heat transfer analyses in which temperature variations were prescribed to the pile elements. The calculated temperature fields for each time increment of the heat transfer analysis, were then imposed on the same time steps of the mechanical FE analyses in order to obtain the mechanical response to the temperature changes. The numerical procedure adopted in this study was validated by simulating the Lambeth College thermal pile test in London presented by Bourne-Webb et al. (2009). In this test, a single pile was subjected to a cooling and a heating stage under constant working load. The test procedure was simulated numerically using the finite element mesh of Figure 1 and the numerical procedure described above and the calculated pile head settlements were compared to the measurements reported in Bourne-Webb et al. (2009). A relatively good agreement between the numerical results and the measurements was observed; the differences between the computed and experimental pile head settlements were 1%, 2% and 15%, at the end of the mechanical loading (1200 kN working load), cooling (T = −18◦ C) and heating (T = +28◦ C), respectively. 3 3.1

SINGLE ENERGY PILE Overview of analyses

The mechanical behaviour of an axially loaded single energy pile is first investigated. Thermal loading

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cycles of cooling and heating are applied to the pile at different constant axial working loads. For reasons of comparison, the cooling and heating cycles that are applied are the same as those in the simulated experiment at Lambeth College. The effect of thermal loading on the axial bearing capacity is first investigated, by simulating pile loading to failure at different applied temperatures. The interface shear stress and axial load distributions at different mechanical and thermal loads are then examined, by simulating cooling and heating cycles under constant axial working loads. Finally, the pile settlements are discussed. 3.2

Effect of thermal loading on the pile axial bearing capacity

Three loading cases are examined: (i) axial pile loading to failure with no thermal load, (ii) application of a 1200 kN axial load at the pile head followed by cooling of the pile to 0◦ C at constant pile head axial load and finally loading of the pile to failure under constant temperature, and (iii) application of a 1200 kN axial load at the pile head, heating of the pile to 30◦ C at constant pile head axial load and finally loading of the pile to failure under constant temperature. The calculated ultimate loads were 4785 kN, 4641 kN and 4847 kN for cases (i), (ii) and (iii), respectively.The load-displacement curves for the three cases are shown in Figure 3. It can be observed that, as expected, the bearing capacity of the pile does not change significantly due to the thermal load (approximately 3% in cooling and 1.3% in heating). The small decrease due to cooling and increase due to heating can be attributed to the material contraction or expansion due to cooling or heating, respectively. During the cooling stage, the pile and soil contract, which causes the normal stresses on the pile interface to decrease and consequently the interface shear strength to also decrease. Similarly, heating of the pile and soil results in expansion and increase of the normal interface stresses and interface shear strength. Obviously, this decrease or increase of the interface shear strength leads to the respective decrease or increase of the axial bearing capacity due to cooling or heating that is seen in Figure 3. Furthermore, it is also worth mentioning that a greater vertical displacement is required to mobilise the full axial pile resistance during cooling than during heating. This occurs due to the pile contraction due to cooling that is added to the pile settlement due to the mechanical load. The reverse mechanism takes place in the heating stage. 3.3 Effect of thermal loading on the pile axial force distribution Four different pile-head axial load cases are considered (the pile self-weight is applied in all cases): zero, 1200 kN, 2400 kN and 3600 kN. For all four loads, the same three cases of thermal loading (under constant pile head mechanical load) as above are examined: no thermal loading, cooling to 0◦ C and heating to 30◦ C.

Figure 3.

Axial load-settlement curves.

Figure 4. Axial force distributions with depth.

The results of the analyses indicate that heating and cooling significantly affect the magnitude and distribution of the axial stresses along an energy pile. Figure 4 presents the axial force variation with depth for the twelve cases analysed. Differences of up to 670 kN in the axial force can be observed between the mechanically loaded and the thermally loaded pile cases. It can be seen in Figure 4 that heating causes the axial loads to increase along the whole length of the pile. This increase is clearly caused by the pile axial thermal expansion. This expansion is restrained at the base and also by the interface shear stresses, which lead to the observed increase in the axial forces. On the other hand, as illustrated in the same figure, the effect of cooling on the axial pile forces depends on the applied mechanical load at the pile head. At zero or low axial pile head loads, the axial forces, as anticipated, decrease due to the pile contraction and

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Table 3. Calculated pile settlements (mm). Axial pile head load

Mechanical only loading

End of cooling cycle

End of heating cycle

No load 1200 kN 2400 kN 3600 kN At failure

+0.2 +2.2 +5.2 +9 +12.3

+2.7 +5.3 +8.5 +12.2 +15.9

−0.95 +1.6 +4.7 +8.6 +11.8

3.4 Pile settlements

Figure 5. Interface shear stress distributions with depth for no thermal loading and after cooling.

the resulting interface shear stress changes. However, an increase in the axial forces over the whole length of the pile is observed for the case of a large pile head load of 3600 kN. At the intermediate pile head load of 2400 kN a reversal in the behaviour is observed at mid-length of the pile. The axial forces increase in the upper half of the pile and decrease in the lower part. This unexpected response of the pile at cooling can be attributed to the pile–soil interface behaviour, and specifically, as explained in more detail below, to the reduction in the interface shear strength due to cooling. As the applied pile head load increases the interface shear stresses also increase. When the applied load is small the interface stresses are much smaller than the interface shear strength. However, as the applied load becomes larger, the interface shear strength is mobilized. Initially, this occurs only in the upper part of the pile, but as the pile head load increases larger parts of the pile interface are mobilized. As seen in Figure 5, the interface shear strength under mechanical only loading is mobilised in the top 12 m and 7.5 m for pile head loads of 3600 kN and 2400 kN, respectively. In contrast, no shear strength mobilization is evident for zero applied load and for 1200 kN applied load. Cooling, generally tends to cause an increase in the interface shear stresses in the upper part of the pile and a decrease in the lower pile. This is due to the coolinginduced contraction and is observed clearly for the self-weight only case in Figure 5. At large pile head loads, however, where the maximum shear stress has already been reached in part of the pile due to mechanical loading, this shear stress increase in the upper part of the pile is not possible. Moreover, because of the decrease in the shear strength due to cooling (which was discussed above), the shear stresses in this part of the pile are in fact forced to decrease. This has an effect similar to heating and leads to the observed increase in the axial forces (Figure 4).

The calculated pile settlements at the end of the initial pile head axial loading, the end of cooling to 0◦ C and the end of heating to 30◦ C are presented in Table 3 for zero axial load (the pile is loaded with only its self-weight), 1200 kN, 2400 kN and 3600 kN. It can be seen in Table 3 that, as expected, cooling of the pile causes further settlement of the pile, which varies between 2.5 mm and 3.6 mm for the different pile head load levels. The opposite effect is observed during heating, where an upward movement of the pile between 3.6 mm and 4.1 mm is observed. While the magnitude of the calculated displacements is small, the percentage increase or decrease of the settlement due to cooling or heating, respectively, is significant. Settlement changes due to thermal loading can be greater than the initial settlement due to the axial pile head load. For an axial load of 1200 kN an increase of 141% is calculated during cooling and a decrease of 168% is calculated during heating. The respective percentage differences for 2400 kN applied pile head load are 63% and 73%. 4

ENERGY PILES IN A PILE GROUP

4.1 Overview of analyses In the second part of this study, the behaviour of pile groups in which one or all of the piles are thermoactive was investigated. A 9-pile group was considered in a square 3 × 3 grid with a 3 pile diameter centreto-centre spacing (= 0.6 m × 3 = 1.8 m spacing). All the piles of the group were connected with a rigid pile cap. The same phases of cooling and heating, as in the single pile investigation, were applied. However, two separate cases were analysed. In the first case, the whole group was composed of thermo-active piles and in the second, only the centre pile was thermoactive. In the following paragraphs, the axial force distributions along the pile length for the centre, a corner and a side pile of the 3 × 3 pile group, are presented and discussed. The pile group settlements are also considered. 4.2 Thermo-active pile group The case in which all the piles of the 3 × 3 pile group are thermo-active is first presented. The pile group

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Figure 6. Thermo-active pile group: Axial force distributions with depth for the centre pile, a corner pile and a side pile of the pile group.

self-weight was first activated and then a 7200 kN vertical load was applied at the centre of the pile cap. Following the load application, all the piles were subjected to a cooling cycle (cooling from 18◦ C to 0◦ C) and then a heating cycle (heating to 30◦ C). The axial force distributions for the centre pile, a side pile and a corner pile, obtained from the numerical analyses, are presented in Figure 6. A first interesting finding, which can be seen in this figure, is that in the case of cooling a significant increase of the axial forces is observed throughout the whole length of all the piles. This is in contrast with the response of the single energy pile discussed above, in which the pilesoil interface shear stress changes generated by the pile contraction due to cooling caused a decrease of the pile axial forces. The reason for the observed increase in the pile axial forces during cooling lies mostly in the thermal dilation coefficient α of the London Clay, which is greater than that of the pile. Because of this, the greater part of the soil (the London Clay layer) contracts more than the pile for the same temperature increment. As illustrated in Figure 7a, in the case of a single pile, only a small region around the pile is affected by the temperature reduction in the pile and the average temperature change in this region is much smaller than that of the pile. In contrast, in the case of a pile group in which all piles are thermo-active (Figure 7b), a large volume of soil that contains the whole pile group undergoes approximately the same temperature reduction as that of the piles. Consequently, although the piles obviously contract during cooling, they contract less than the ground, leading to interface shear stress changes that increase the pile axial forces. Interestingly, the axial forces also increase in all piles during heating, despite the fact that the London Clay layer can potentially dilate more than the pile.

Figure 7. Temperature fields at the end of cooling: (a) single energy pile, (b) thermo-active pile group.

This can be attributed to the end restraints imposed on the piles at the pile bases and the pile cap and also on the restraint imposed on the ground surface by the pile cap. These effects counteract the tendency of the piles to contract compared to the soil, and leads to an increase of the pile axial forces along the whole length of all the piles. This increase is smaller than that during cooling in the part of the piles that is situated in the London Clay layer. It can also be observed in Figure 6 that while cooling has no effect on the loads carried by each pile of the pile group (the axial forces at the pile heads remain unchanged), heating causes a redistribution of the axial loads. The pile head load increases at the centre pile and the four side piles and decreases at the four corner piles. 4.3 Thermo-active centre pile in pile group The similar procedure as above was followed. The pile group was loaded with 7200 kN and then a cooling and a thermal cycle were applied only to the centre pile. It is evident from Figure 8 that the behavior of the pile group is significantly different in the case of one thermo-active pile compared to the case in which all piles are thermo-active (discussed above). In this case, as expected, heating and cooling have the most significant effect on the axial forces of the centre pile. Much smaller axial force changes are observed in the other piles of the group. These force changes are of opposite sign to the force changes of the centre pile, which indicates that the behaviour of the rest of the piles of the pile group is similar to that of reaction piles. During cooling, the centre pile axial compressive forces decrease remarkably, to the point that they become tensile along almost the entire length of the pile. The reason for this decrease is that as the centre

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Table 4. Calculated pile group settlements (mm).

All piles thermo-active Only centre pile thermo-active

Figure 8. Thermo-active centre pile in pile group: Axial force distributions with depth for the centre pile, a corner pile and a side pile of the pile group.

pile is cooled, it tends to contract, however, movement is restricted at the pile cap, while contraction is also restricted by the resisting side friction. As a result, tensile axial stresses develop along its length. In contrast with the fully thermo-active pile group, in this case, the temperature field of the model resembles more that of a single energy pile, with a much smaller area of soil where the temperature changes decidedly. As a result, the overall pile contraction is greater than the contraction of the ground. In the heating phase, the centre pile axial compressive forces increase significantly. The reverse behaviour to that of the cooling stage is observed. As the pile tends to expand, the interface side friction, and the base and the cap restraints, prevent its deformation and consequently generate further compressive axial stresses along the pile length. As mentioned above, opposite sign axial force changes to those of the centre pile are observed in the rest of the piles of the group. Their axial forces increase when the centre pile is cooled and decrease when the centre pile is heated. This is essentially a redistribution of pile head loads within the pile group. The rest of the piles in the group are largely unaffected by the temperature changes around the centre pile and simply react to the axial load applied to the pile cap by the centre pile during each thermal load phase.

4.4

Pile group settlements

The calculated pile settlements at the end of the initial pile group axial loading, the end of cooling to 0◦ C and the end of heating to 30◦ C are presented in Table 4 for the case in which all piles of the group are thermoactive and the case in which only the centre pile is thermo-active.

Mechanical only loading

End of cooling cycle

End of heating cycle

+2.6

+7.6

+3.9

+2.6

+3.6

+2.9

As expected, the impact of cooling or heating is much more significant when all piles are thermoactive. A further settlement of 4 mm (154% increase) is computed during cooling of all piles of the group, compared to 1 mm (38% increase) when only the centre pile is cooled. It is also interesting to observe that the extra settlement induced by cooling the pile(s) is not reversed during heating. In fact at the end of heating, the final settlement is always greater than the initial settlement of 2.6 mm. This indicates that significant plastic deformation occurs during cooling. 5

CONCLUSIONS

An investigation of the mechanical behaviour of energy piles and energy pile groups with the use of finite elements analysis was presented. The behaviour of single energy piles subjected to cooling and heating cycles under different constant axial pile head loads was first examined. It was found that heating and cooling have a small effect on the pile axial bearing capacity. The small changes in the bearing capacity can be attributed to the increase or decrease of the normal stresses acting on the pile-soil interface during heating or cooling, respectively. It was also shown that thermal loading cycles have a significant effect on the axial forces and their distribution along the pile length. Heating of the pile increased the axial forces along its entire length. The response to cooling was found to depend on the level of shear strength mobilisation at the pile-soil interface and consequently on the applied axial load at the pile head. For low pile loads cooling caused a decrease of the axial forces. However, for higher pile axial loads, an increase of the compressive forces was observed in part of the pile and for very high loads along the entire length of the pile. In the second part of the study, the behaviour of a 3 × 3 energy pile group was examined. Analyses were performed in which either all piles of the pile group or only the centre pile of the pile group were thermoactive. A significant increase in the axial compressive forces of the piles both in the cooling and in the heating phases was observed when all piles were modelled as thermo-active. This increase in the cooling phase can be attributed to the fact that the London Clay was

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assumed to have a higher coefficient of thermal expansion than the pile concrete and to the much higher temperature changes in the ground, compared to those computed for a single pile. The axial compressive forces also increased during heating, because of the imposed end constraints. When only the centre pile was modelled as thermoactive, very large decreases or increases of the axial forces in the centre pile were found for cooling and heating, respectively. The decrease of the axial forces during cooling were so large that the greater part of the pile went into tension. The rest of the piles of the group were much less affected.

REFERENCES Amatya, B.L., Soga, K., Bourne-Webb, P.J., Amis, T. & Laloui, L. 2012. Thermo-mechanical behaviour of energy piles. Géotechnique 62(6): 503–519. Amis, T., Bourne-Webb, P., Davidson, C., Amatya, B. & Soga, K. 2008. The effects of heating and cooling energy piles under working load at Lambeth College, UK. Proceedings of the 33rd Annual and 11th International Conference of the Deep Foundations Institute, New York, USA. Bourne-Webb, P.J., Amatya, B.L., Soga, K., Amis, T., Davidson, C. & Payne, P. 2009. Energy pile test at Lambeth College, London: Geotechnical and thermodynamic aspects of pile response to heat cycles. Géotechnique 59(3): 237–248. Bourne-Webb, P.J., Amatya, B.L. & Soga, K. 2011. A framework for understanding energy pile behavior. Proceedings of the Institution of Civil Engineers – Geotechnical Engineering 166(2): 170–177.

Bourne-Webb, P.J., Bodas Freitas, T.M., Freitas Assuncao, R.M. 2015. Soil–pile thermal interactions in energy foundations. Géotechnique 66(2): 167–171. Brandl, H. 1998. Energy piles and diaphragm walls for heat transfer from and into the ground. Proceedings of the 3rd International Geotechnical Seminar, Deep Foundations on Bored and Auger Piles (BAP III), University of Ghent, Belgium, vol. 1, pp. 37–60. Brandl, H. 2006. Energy foundations and other thermo-active ground structures. Géotechnique 56(2): 81–122. Di Donna, A., Rotta Loria, A.F. & Laloui, L. 2016. Numerical study of the response of a group of energy piles under different combinations of thermo-mechanical loads. Computers and Geotechnics 72: 126–142. Ennigkeit, A., Katzenbach, R. 2001. The double use of piles as foundation and heat exchanging elements. Proceedings of XVth International Conference on Soil Mechanics and Geotechnical Engineering (ICSMGE), Istanbul Turkey, 27–31 August 2001, Vol. 2, pp. 893–896. Kulhawy, F.H. _1991. Drilled shaft foundations. Foundation engineering handbook, Chapman and Hill, New York. Laloui, L., Nuth, M. & Vulliet, L. 2006. Experimental and numerical investigations of the behaviour of a heat exchanger pile. Int. J. Numer. Analyt. Methods Geomech. 30(8): 763–781. Ozudogru, T.Y., Olgun, C.G. & Arson, C.F. 2015. Analysis of Friction Induced Thermo-Mechanical Stresses on a Heat Exchanger Pile in Isothermal Soil. Geotechnical and Geological Engineering 33(2): 357–371. Salciarini, D., Ronchi, F., Cattoni, E. & Tamagnini C. 2015. Thermomechanical Effects Induced by Energy Piles Operation in a Small Piled Raft. Int. J. Geomech. 15(2).

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Thermo-mechanical behavior of small-scale energy pile in dry sand V.T. Nguyen Universite Paris-Est, Laboratoire Navier (UMR CNRS 8205), France Hanoi University of Mining and Geology, Vietnam

A.M. Tang & J.M. Pereira Universite Paris-Est, Laboratoire Navier (UMR CNRS 8205), France

ABSTRACT: A small-scale energy pile has been developed in laboratory to study its thermo-mechanical behaviour under thermal cycles. A model pile (20 mm external diameter) of ultimate axial load capacity of 500 N was installed in dry sand. During the experiment, the pile was initially loaded with a series of axial load, which range from 0 N to 300 N, with an increment of 50 N. For each step of axial loading, a thermal cycle was applied immediately after the pile head settlement due to axial loading had stabilised. The pile behaviour is discussed in terms of cumulative thermal settlement, effect of creep during thermo-mechanical loading stage and also the change of mobilized friction along the pile wall through the analysis of the evaluation of axial force profiles along the thermo-mechanical loading stages.

1

INTRODUCTION

Energy piles, or heat exchanger piles, have a dual function: providing support for overhead structures as a conventional pile foundation and exchanging heat with the ground for purpose of heating and/or cooling the building. Energy piles have been used in some European countries during the last two decades. This technique has gained encouraging efficiencies in the use of renewable energy in modern cities and contributed to the reduction of CO2 emission Brandl 1998; Brandl 2006, Laloui et al. 2006, Adam & Markiewicz 2009, Pahud & Hubbuch 2007). However, experiences and installation are not homogeneous across countries due to the lack of design standards, including rules defining geotechnical design of energy piles. Many studies have been performed to investigate on the thermo-mechanical behaviour of energy piles (Laloui et al. 1999, Bourne-Webb et al. 2009, Lam et al. 2009, Laloui 2011, McCartney & Rosenberg 2011, Amatya et al. 2012, Kalantidou et al. 2012, Yavari et al. 2013, Murphy et al. 2014, Ng et al. 2014, Suryatriyastuti et al. 2013, Di Donna & Laloui 2014, Yavari et al. 2014, Wang et al. 2014, Saggu & Chakraborty 2014, Akrouch et al. 2014, Goode et al. 2014, Stewart & Mccartney 2014, Mimouni & Laloui 2015, Wang et al. 2016). The results evidenced the effects of temperature change on the pile-soil interaction and the mobilized resistance of piles.

The present paper focuses on experiments on a small-scale pile in laboratory to study its thermomechanical behaviour under thermal cycles.

2

EXPERIMENTAL METHOD

2.1 Experiment setup A pile model of 20 mm external diameter and 600 mm length was installed in a dry sand sample of 548 mm inner diameter and 900 mm height (Figures 1 & 2). The pile model is an aluminum tube with an internal diameter of 18 mm and sealed at the bottom. The pile surface was coated with sand to simulate the roughness of the pile. The sand used in this study (Fontainebleau sand) has the following physical properties: particle density ρs = 2.67 Mg/m3 ; maximal void ratio emax = 0.94; minimal void ratio emin = 0.54; and median grain size D50 = 0.23 mm. Installation process began with the compaction of the first two layers of 100 mm thickness, then two layers of 50 mm beneath the pile toe. Pile was then placed in its position inside the soil container and was fixed by a steel bar that was blocked on the above surface of soil container. Finally, the other sand layers of 100 mm were compacted around the pile. The soil was compacted manually by using a wooden tamper, at a unit weight of 15.1 kN/m3 .

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Figure 2. View of the experimental setup.

Figure 1. Pile model and sensors distribution profile.

During the compaction, three temperature sensors and two pressure gauges were installed as showed in Figure 1. The two pressure sensors (P12 & P20) were located at 50 mm below the pile toe. P12 measures the total horizontal pressure and P20 measures the total vertical pressure of soil. The three soil temperature sensors (S5, S6 & S7) are placed at the same level (300 mm below the soil surface) and at three distances from the pile axis, 20, 40 and 80 mm, respectively. To measure the pile axial strain, five strain gauges were distributed along the pile length. Three displacement transducers (LVDT) were used to measure the pile head displacement, and a load cell is placed at the pile top to record the pile head load. By using a water tank placed above the pile head, the pile head load is controlled by the water level in the tank. A metallic U-tube, connected to a temperaturecontrolled bath, is placed inside the pile tube for heating and cooling the pile. The soil container was thermally isolated to avoid heat exchange with the ambient air. A similar pile model could be found in the studies of Kalantidou et al. (2012) and Yavari et al. (2014a). 2.2 Test program In this study, four experiments have been performed. After each experiment, the pile model was reinstalled

according to the process described above. Two experiments T1 and T2 were performed to investigate the load-displacement curve of the pile under mechanical loading. The test procedure follows The French standard NF P 94-150-1 (1999) (Figure 3). In the preparation step, the pile was firstly loaded to 0.1Qmax for 15 minutes and then unloaded to remove the disturbed settlement component due to soil compaction related to the pile installation process (Qmax is the ultimate load which induced 10%D settlement of pile head, D being the external diameter of pile). In the experiment, the pile was loaded in steps and subjected to two loading cycles to obtain a load-displacement relationship. The loading paths of the thermo-mechanical experiments (T3 and T4) are shown in Figure 4. For test T3, after the installation, the pile was first heated from 20◦ to 21◦ C for 60 min and then cooled to 19◦ C for 60 min. The second thermal cycle was repeated using the same procedure as for the first cycle, after a recovery period allowing returning to the initial thermal condition. The total duration of the two cycles equals to 6 hours. Once the temperature reached the initial value (20◦ C), the pile head load was increased to 100 N. When the settlement stabilized (after 60 min), two thermal cycles similar to the previous ones were applied. By doing so, the pile will be loaded to 300 N. For test T4, pile was first heated from 20◦ to 21◦ C for 120 min and then cooled to 19◦ C for 120 min without head load, after a recovery period allowing to return to initial temperature. The total duration of one cycle equals to 8 hours. Once the temperature reached the initial value (20◦ C), the pile was loaded to 100 N, when the settlement reached stabilization (after 120 min), one thermal cycle similar to the previous ones was applied. Then, at the end of thermal cycle, the pile was unloaded for overnight. The next day, pile was loaded again to 150 N for 120 min, then a thermal cycle was applied to the pile. Similar loading processes will be applied until the loading step of 300 N.

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Figure 3. Mechanical loading experiments (Test T1 & T2).

3 3.1

RESULTS AND DISCUSSION Mechanical behavior

In this section, the effects of mechanical loading phase on the pile behaviou will be discussed.At first, effect of time on pile settlement was evaluated over a period of 60 minutes according to the French Recommendation NF P 94-150-1 (1999). In each constant loading step, the pile settled immediately and then the settlement continues over time but with a lower rate. In the experiment, the results were recorded continuously with an interval of 1 minute. Figure 5 shows the time evolution of pile head settlement in logarithmic scale over a 60 minutes period for test T1. It can be seen that, after only a few minutes of loading, the pile settled at a lower rate with a linear trend. Therefore, creep rate of pile in each loading step could be evaluated by the slope of the curve settlement-time in log scale. Following the French Recommendation NF P 94-150-1 (1999), under each constant loading, creep of pile can be measured by the following index:

where αn = creep rate; n = step number; S60 = settlement of pile head at time t = 60 minutes; S10 = settlement of pile head at time t = 10 minutes. Figure 6 shows creep rate results of the four tests. The settlement obtained in the four tests is illustrated by the load-settlement curve in Figure 7. The pile head settlement value of each loading step in T3 is determined after one hour of mechanical load and it includes the settlement caused by thermal loading of pile in previous loading steps. For test T4, pile head settlement was measured after 1 hour of each mechanical

Figure 4. Thermo-mechanical loading of T3(a) and T4(b).

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Figure 8. Axial force profile for test T3.

Figure 5. Settlement under constant mechanical load versus logarithm of time (test T1).

Figure 6. Creep behaviour of pile.

load step and plus the irreversible settlement of the previous loading steps. From the load-settlement curve, the ultimate bearing capacity of pile (corresponding to a normalised settlement of 10% of pile diameter) can be approximately estimated at 500 N. In addition, the results of the four tests show a good repeatability of the applied procedure. Although experiments T3 and T4 comprised coupled thermo-mechanical load, the results in Figure 7 showed a similar load-settlement curve for all four tests. This result implies that the contribution of thermal cycles in each step of loading to cumulative displacement of pile is negligible when compared to that of mechanical loading. The axial deformations that were recorded from the strains gauges were used to measure axial force of along the pile. Figure 8 shows a result of axial force distribution along the pile length obtained at the end of each loading step. Axial load of pile at levels of 100, 200, 300, 400 and 500 mm from the surface were derived from the gauges G5, G4, G3, G2 and G1 respectively. Axial load value on the surface is used directly from the load cell. This result indicates that most of pile head load is transmitted to the soil via mobilized friction on the pile shaft, while a small amount of head load is transmitted into the soil through the pile toe. This latter value could be estimated by extrapolation from the last two measured forces at G1 and G2. This value is about 20% of the head load. It can be said that the mobilized friction on the pile shaft is significant, and that the mobilized resistance of the pile depends mainly on skin friction. 3.2 Thermo-mechanical behavior of pile under constant mechanical loading

Figure 7. Load-displacement curve.

Figure 9 shows temperature as measured at various locations in the soil and pile. After 1 hour of heating or cooling, temperature change of pile seems to be stable. Soil temperature change is non-significant. This is due to the small thermal loading applied to the pile, about ±1◦ C. However, after each heating and cooling cycle, cumulative settlement of pile continues to

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Figure 9. Temperature and settlement versus time at 100 N loading step (test T3).

Figure 11. Pile head settlement in T4. (a) axial loading equal to 0 N; (b) 100 N; (c) 150 N; (d) 200 N; (e) 250 N and (f) 300 N.

Figure 10. Pile head settlement in T3. (a) axial loading equal to 0 N; (b) 100 N; (c) 150 N; (d) 200 N; (e) 250 N and (f) 300 N.

increase. Settlement of pile in cooling phase is significant, but in the heating phase the pile head heave is almost negligible. At the end of each thermal loading step, the settlement of pile tends to increase when the temperature of pile reached stable value. Figure 10 and 11 represent incremental settlement of pile during heating-cooling cycles. Accordingly, the initial point corresponding to the start of each thermal cycle is set to zero displacement. The final point corresponds to the end of thermal cycles. It was observed that the pile behavior during the thermal cycle phase depends on the mechanical load applied to the pile. When the mechanical loading was null (0 N), the displacement of the pile head was the same as the pile’s thermal expansion curve, which expresses the deformation of a pile restrained at its toe but free in other direction under a temperature change (Figure 10a, 11a). During the following loading steps, the pile settlement during cooling phase was not compensated by heave during heating so that permanent and cumulating settlement was observed. In test T3 (Figure 10), the slope of the settlement curve under the first cooling phase is the same as in the second cooling phase. It is also similar to the slope of the pile

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Figure 12. Axial force along the pile length in test T3

thermal expansion curve. It can be said that, the settlement of pile of two cooling phase increases linearly with temperature reduction. In case of Figure 10d, the irreversible settlement at the end of second cooling phase continues to increase after the temperature has stabilized. Pile uplift in heating phase was observed only in case of Figure 10b, c, but very small. In test T4, time of heating/cooling phase is twice as large as the one of heating/cooling phase in T3, and the displacement result is quite similar to the T3. However, in the case of Figure 11d, e, f the settlement increases rapidly at the beginning of cooling phase, and then at the end of cooling phase it continues to increase after the temperature has stabilized. This could be explained by the effect of creep behaviour, it means the settlement of pile would include thermal contraction and creep settlement. The effect of temperature cycles on the pile head displacement is quite small, about 0.2% when the pile worked under a specified load. Axial force measured during test T3 is shown in Figure 12. As it can be seen in the first step in which pile was heated and cooled without axial loading, the effect of cyclic loading on the axial force along the pile length does not a clear trend. Axial force increases during cooling phase and during the heating this value does not seem to change from the previous state. However, during the following steps the effect of thermal cycles was quite clear, with an increase during heating, and a decrease during cooling. This result can be seen as reasonable for this floating pile, which transmits most of head load to the soil through skin friction. Actually, this phenomenon is similar to the experimental results on the full-scale energy pile model of Bourne-Webb et al. (2009), Laloui (2011). The influence of thermal cycle on the evolution of axial force can be seen more clearly at the middle of the pile length, while at the pile base this influence seems insignificant. A similar result was obtained in experiment T4.

Figure 13. Decoupling thermal and mechanical effects on pile head displacement.

Another aspect was also examined in this study: the effect of thermal cycles and the effect of creep on the pile displacement during thermo-mechanical loading stages. The thermal settlement in each test is obtained by removing the mechanical settlement of the pile under the corresponding load. The result in Figure 5 shows that the effect of time in log scale on the pile settlement is linear when pile worked under a constant head load. For this reason the mechanical settlement during each loading step in the thermo-mechanical period can be derived from the creep rate. Finally, from the results in Figure 10 and 11, the cumulative settlement of the pile could be measured to decouple the thermal and mechanical effects, as shown in Figure 13. Although the creep value in T3 and T4 increases as the pile head load increases, this relationship is not linear. The creep rate increased insignificantly when pile worked under small head load, while under higher head load the creep rate increased significantly. It should be noted that, the settlement of pile caused by creep behaviour increases with time, the duration of a cycle loading of test T4 is longer than that of test T3, so that

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after one cycle loading a greater settlement obtained in test T4. The irreversible settlement related to thermal cycles was larger than the effect of creep during thermo-mechanical loading stage. However, the evolution of cumulated thermal settlement with the loading steps does not show a clear trend. Although the thermal settlement of pile is very small compared to the safety limit (10%D) more work is needed to confirm the effect of many cycles of loading on the behavior of energy pile in the long term. 4

CONCLUSIONS

This paper presents an experimental study of the behavior of small-scale energy pile in dry sand. Four tests focused on the influence of thermal cycles on the thermo-mechanical behavior of pile. The following conclusions can be drawn: – The maximum thermal cumulating settlement of pile head is very small: about 0.25%D. – The axial force along the pile increases in heating phase and decreases in cooling phase, and the most obvious change was found near the middle of pile length. This phenomenon is compatible with the case of a floating pile which transmits the head load to the ground through the skin friction. – The irreversible settlement related to thermal cycles was larger than the effect of creep during thermomechanical loading stage, and depends on the mechanical load applied to the pile. REFERENCES Adam, D. & Markiewicz, R., 2009. Energy from earthcoupled structures, foundations, tunnels and sewers. Géotechnique, 59(3), pp. 229–236. Akrouch, G.A., Sánchez, M. & Briaud, J.-L., 2014. Thermomechanical behavior of energy piles in high plasticity clays. Acta Geotechnica, 9(3), pp. 399–412. Amatya, B.L. et al., 2012. Thermo-mechanical behaviour of energy piles. Geotechnique, 62(6), pp. 503–519. Bourne-Webb, P.J. et al., 2009. Energy pile test at Lambeth College, London: geotechnical and thermodynamic aspects of pile response to heat cycles. Géotechnique, 59(3), pp. 237–248. Brandl, H., 2006. Energy foundations and other thermoactive ground structures. Géotechnique, 56(2), pp. 81– 122. Brandl, H., 1998. Energy piles for heating and cooling of buildings. In 7th International confrence exihibition Piling and deep foundations. Vienna, pp. 341–346. Di Donna, A. & Laloui, L., 2014. Numerical analysis of the geotechnical behaviour of energy piles. Goode, J.C., Zhang, M. & Mccartney, J.S., 2014. Centrifuge modelling of energy foundations in sand. In The 8th international conference on Physical modelling in Geomechanics (ICPMG2014). Perth, Australia, pp. 729–735.

Kalantidou, A. et al., 2012. Preliminary study on the mechanical behaviour of heat exchanger pile in physical model. Géotechnique, 62(11), pp.1047–1051. Laloui et al., 1999. In-situ thermo-mechanical load test on a heat exchanger pile. In 4th International confrence on Deep foundation practice. Singapore, pp. 273–279. Laloui, L., 2011. In Situ Testing of a Heat Exchanger Pile. Geo-Frontiers 2011 – Advances in Geotechnical Engineering. ASCE, pp.410–419. Laloui, L., Nuth, M. & Vulliet, L., 2006. Experimental and numerical investigations of the behaviour of a heat exchanger pile. International Journal for Numerical and Analytical Methods in Geomechanics, 30(8), pp.763–781. Lam, S.Y. et al., 2009. Centrifuge and numerical modeling of axial load effects on piles in consolidating ground. Canadian Geotechnical Journal, 46(1), pp.10–24. McCartney, J.S. & Rosenberg, J.E., 2011. Impact of Heat Exchange on Side Shear in Thermo-Active Foundations. Geo-Frontiers 2011 © ASCE 2011, pp.488–498. Mimouni, T. & Laloui, L., 2015. Behaviour of a group of energy piles. , 17(May), pp.1–17. Murphy, K.D., McCartney, J.S. & Henry, K.S., 2014. Evaluation of thermo-mechanical and thermal behavior of full-scale energy foundations. Acta Geotechnica, 10(2), pp.179–195. NF P 94-150-1, 1999. Essai statique de pieu isolé sous un effort axial., pp.1–28. Ng, C.W.W. et al., 2014. Centrifuge modelling of energy piles subjected to heating and cooling cycles in clay. Géotechnique Letters, 4(October–December), pp.310–316. Pahud, D. & Hubbuch, M., 2007. Measured Thermal Performances of the Energy Pile System of the Dock Midfield at Zürich Airport. In Procedding European Geothermal Congress 2007. Unterhaching, Germany, pp. 1–7. Saggu, R. & Chakraborty, T., 2014. Cyclic ThermoMechanical Analysis of Energy Piles in Sand. Geotechnical and Geological Engineering, 33(2), pp.321–342. Stewart, M.A. & Mccartney, J.S., 2014. Centrifuge Modeling of Soil-Structure Interaction in Energy Foundations. Journal of Geotechnical and Geoenvironmental Engineering, 140(4), pp.1–11. Suryatriyastuti, M.E., Mroueh, H. & Burlon, S., 2013. A load transfer approach for studying the cyclic behavior of thermo-active piles. Computers and Geotechnics, 55, pp.378–391. Wang, B. et al., 2014. Posttemperature Effects on Shaft Capacity of a Full-Scale Geothermal Energy Pile. Journal of Geotechnical and Geoenvironmental Engineering, pp.1–12. Wang, C. et al., 2016. Model tests of energy piles with and without a vertical load. Environmental Geotechnics, pp.1–11. Yavari, N. et al., 2014. Experimental study on the mechanical behaviour of a heat exchanger pile using physical modelling. Acta Geotechnica, pp.385–398. Yavari, N. et al., 2013. A simple method for numerical modelling of mechanical behaviour of an energy pile. Geotechnique letters, pp.1–6.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Long term monitoring of CFA energy pile schemes in the UK F.A. Loveridge & W. Powrie University of Southampton, Southampton, UK

T. Amis GI Energy, UK

M. Wischy & J. Kiauk Siemens

ABSTRACT: Energy pile schemes involve the use of structural foundations as heat exchangers in a ground source heat pump system. Such schemes are attractive, as they reduce energy consumption compared with traditional building heating and cooling systems. As energy prices increase and governments introduce subsidies they are also proving increasingly economically attractive. Additionally, energy piles can contribute to reducing the carbon dioxide emissions associated with a development. However, this approach to heating and cooling building remains relatively novel and the lack of published long term performance data remains a barrier to further implementation. Two issues remain to be addressed by long term monitoring. First, the need for a database of operational energy piles schemes were the energy performance is proven over many years. Secondly, availability of long term datasets of pile thermal behavior that can be used to validate design approaches and tools and hence encourage less conservative design practices. This paper presents the initial results from a study aimed at tackling these issues through long term instrumentation and monitoring of two energy pile schemes in the United Kingdom. 1

INTRODUCTION

Energy pile schemes involve the use of structural foundations as heat exchangers in a ground source heat pump system. Such schemes are attractive, as they reduce energy consumption compared with traditional building heating and cooling systems.As energy prices increase and governments introduce subsidies they are also proving increasingly economically attractive. Additionally, energy piles can contribute to reducing the carbon dioxide emissions associated with a development. Energy piles have been in operation in Europe since the 1980’s (Brandl, 2006). Some notable case studies include Zurich Airport (Pahud & Hubbach, 2007), One New Change in London (Amis & Loveridge, 2014) and Keble College Oxford (Suckling & Smith, 2002, Nicholson et al, 2014). However, despite an increase in constructed cases in recent years, relatively little performance data are available, especially for the long term (Bourne-Webb, 2013). This holds back validation of thermal design approaches, and limits the value of demonstration projects. Since 2011, the University of Southampton and GI Energy have been working in partnership to develop monitoring sites for energy pile schemes. The project has seen the instrumentation of energy piles beneath two buildings in the United Kingdom. Temperature sensors installed in the foundations are combined with

data from building energy management systems to provide the opportunity to assess both the whole system performance and the pile thermal behaviour. The latter is particularly important for understanding modelling and design approaches and their application to energy piles. This paper provides details of the two monitoring sites and some initial results from the schemes so far. Lessons learnt from both the installation of instrumentation and the resulting data are also considered. 2 THE CRYSTAL, EAST LONDON The first scheme to be instrumented was Siemens’ landmark sustainable building in East London, known as The Crystal (Figure 1). The Crystal is a multi-use development and contains an interactive exhibition of sustainable technologies as well as office space and conference facilities. It has been designed to be an allelectric building and utilises solar thermal and ground source heat pumps to generate all the thermal energy needed by the development. Photovoltaics also generate electricity to reduce reliance on a more carbon intensive national supply. The source side of the ground source heat pump system comprises 160 pile heat exchangers and a field of 36 deep boreholes. The piles are 600 mm, 750 mm or 1200 mm in diameter and were constructed using

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Table 1. Ground conditions at the Crystal. Strata

Description

Depth

Made Ground

Fine to coarse brick and concrete gravel; soft to firm black sandy gravelly clay Very soft clayey silt, sandy clay and peat Medium dense silty fine to coarse sand and fine to coarse gravel (mainly flint) Stiff thinly laminated fissured silty clay with silt partings Silty fine sand and fissured silty clay Very dense, slightly silty fine sand Medium density (Grade B3) chalk

3.3 m

Figure 1. The Crystal building in East London.

Alluvium

contiguous flight auger (CFA) techniques to approximately 21m depth. Each pile incorporates a pair of High Density Polyethylene (HDPE) U-pipes, which were inserted into the centre of the pile after the pile cage had been plunged into the concrete. The U-pipes were then connected together in series and usually joined into a single circuit with a neighbouring pile, before the pipework continued to the manifold chamber and then on via larger header pipes to the plant room for connection to the heat pumps. Each borehole is 150 m deep and contains a single HDPE U-pipe. Backfill material is gravel through the permeable strata encountered in the lower two thirds of the hole and grout over the upper third (refer to Section 2.1 below for geological information). The Crystal has been operational since 2012, but it has taken several years for some of the relevant building monitoring data to come on stream. Hence it is only now that initial interpretation of these data can commence.

River Terrace Deposits

2.1

Lambeth Group Thanet Sands Chalk

Pile and borehole instrumentation

One 1200 mm diameter pile near the north east corner of the building was selected for monitoring. The pile was equipped with five thermistor strings. One of these was attached to the central bundle of four pipes (two U-tubes), themselves inserted into the pile attached to a 40 mm steel bar for stiffness. The U-pipes, the steel bar and the thermistor strings were installed to a depth of 20 m within the pile. The other four thermistor strings were attached at equal spacings around the circumference of the steel reinforcing cage (Table 2). As the pile cage only extends to 8.5 m below the pile cut off level it was not possible to extend the outer thermistor strings over the full 21 m pile depth. Thermistor strings were also installed in one of the borehole heat exchangers and two additional monitoring boreholes (Loveridge et al., 2013). However,

11.2 m 23.5 m 43.3 m 56.1 m >150 m

Table 2. Depths of thermistors installed within the instrumented pile at The Crystal. Depth Below Pile Cut Off Level (m) Thermistor Level

Central String

Outer Strings

1 2 3 4 5 6

0.7 3.6 7.1 11.1 15.1 19.1

0.75 3.25 6.6 – – –

Ground conditions

The site is underlain by a sequence of London Basin deposits. The piles are founded in the London Clay, but also pass through a significant thickness of superficial and man-made deposits (Table 1). The boreholes continue through the full sequence of strata and are installed for approximately two thirds of their length in the aquifer formed by the Chalk and the overlying Thanet Sands. As the site is located near to the confluence of the Thames and the River Lea in east London, the groundwater table is close to the ground surface, at the base of the Made Ground. 2.2

London Clay

6.3 m

damage occurred to buried cabling during construction which unfortunately meant that data access to these instruments was lost and could not be re-established. All instrumentation was wired into a datalogging system located in the energy centre building adjacent to The Crystal. The logger can be accessed remotely to allow monitoring of the system from offsite. Temperature data have been collected since the summer of 2012.

2.3 Building monitoring The Crystal is equipped with a comprehensive building energy management system (BEMS). Three heat meters record the heating and cooling energy delivered to the building. Two more heat meters record the amount of heat exchanged with the ground, one for the pile ground loop circuit and one for the borehole ground loop circuit. These data have been available since the spring of 2013, except the heat meter for the borehole ground loop which was not communicating correctly with the BEMS until 2015. Additionally, the ground loop heat meters require further adjustment to differentiate between the direction of heat transfer to (or from) the ground.

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Figure 3. Average operational pile temperatures since 2012 (data gap in the autumn of 2015 due to data logger malfunction).

Figure 2. Undisturbed ground temperatures at The Crystal site.

A further heat meter was installed by the University of Southampton on the pipe circuit for the instrumented energy pile during construction. However, this meter has also had substantial communication difficulties with the logging equipment and no data are available from this meter at the present time. 2.4

Results

Initial results from the pile monitoring during and immediately following construction are included in Loveridge & Powrie (2013a). These data, along with further measurements from a thermal response test carried out in an instrumented borehole at the site (Loveridge et al., 2013), show that the undisturbed ground temperature is approximately 12.8◦ C over the depth range relevant to the energy piles (refer to Figure 2). For the purposes of initial analysis of performance, pile temperatures can be taken as approximately constant with depth. Consequently, average operational pile temperatures for the string attached to the pipes and those installed on the reinforcing cage are presented in Figure 3. Using averages removes local variations due to any asymmetric installation of the pile cage and central pipes and allows the overall trends to be identified. However, it does obscure axial effects, which are potentially important, but are outside the scope of this paper. The data show large fluctuations in temperature at the centre of the pile, from approximately 7◦ C to 26◦ C. However, the temperature range at the steel cage, nearer the edge of pile, is much less, approximately 10◦ C to 18◦ C. It can also be seen that there is an overall rise in the temperature of the pile over the three

Figure 4. Energy demand of The Crystal during 2014 and 2015. Winter months taken as January to April and November to December; summer months taken as May to October.

years of monitoring. In the summer of 2015 the average temperature of the thermistors installed on the pile cage was approximately two degrees warmer than at the start of monitoring in summer 2012, when it was close to the undisturbed condition (Figure 2). The rise in pile temperature is likely to represent a net transfer of heat from the building to the ground during the first three years of operation. However, when the overall thermal energy demand of The Crystal is analysed, the heating and cooling profile is close to balanced (Figure 4), with annual demand approximately 550 MWh per year each for both heating and cooling. On the other hand, the instantaneous rate of energy demand does differ between heating and cooling (Figure 5). The maximum power demand in heating is 399 kW, while in cooling it is 572 kW. This may be the cause of the net heat injection to the ground. Another factor that cannot be assessed yet is the relative contribution of the piles and boreholes to the heating and cooling demand. For example, the piles could be taking a different heating/cooling ratio compared to the borehole field. Finally, the weather during the period of assessment must be considered to place any trends in context. Table 3 shows that during the last four years temperatures in the UK have been warmer that the long term average by several degrees. This may also have affected the rise in temperature seen within the instrumented pile during this period by triggering a higher than normal cooling demand. Global coefficient of performance (COP) data for the ground source heat pump system at The Crystal can be taken as an initial indicator of the energy

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Figure 5. Heating and cooling power required at The Crystal since summer 2013. Table 3. UK mean annual temperature anomalies compared with 1961 to 1990 long term average. Year

Temperature Anomaly (◦ C)

2015 2014 2013 2012

+0.9 +1.6 +0.5 +0.4

efficieny of the system. Current data suggest COPs between 2.5 and 3.0 depending on the time of year. However, the operational control system is still being optimized, hence these values are expected to increase in the future. 3

22 STATION ROAD, CAMBRIDGE

22 Station Road (Figure 6) is the new building for Mott MacDonald and Birketts in Cambridge. It forms part of the extensive redevelopment of the zone around Cambridge Station known as CB1. The building comprises a basement carpark and a further six floors of office space. The building is founded on 81 CFA piles of 450 mm diameter and 68 CFA piles of 600 mm diameter. Pile lengths are between 20 m and 25 m. Each pile is equipped with a single polyethylene pipe U-loop. As at The Crystal, the pipes were plunged into the centre of the pile following insertion of the steel reinforcing cage. In this case the pipes were attached to a 32 mm diameter steel bar for weight and stiffness. The U-loop pipes from individual energy piles were connected together to form a series circuit with the pipes from adjacent piles. Each circuit contains between four and six piles and is connected to the header pipes at the manifold located in the building basement. The header pipes then run to the upper floor of the building, where the heat pumps and other plant are located. 3.1

Figure 6. Artist’s impression of the completed building at 22 Station Road (source: http://www.cb1cambridge.eu/ 22-station-road).

Clay. Boreholes from the site describe the Gault as initially a firm to stiff slightly sandy slightly silty calcareous CLAY to approximately 6.5 m below pile cut off level. Beneath this the Gault becomes a stiff to very stiff laminated and fissured calcareous CLAY. The groundwater table at the site is relatively high, with water strikes during borehole drilling rising to approximately 2 m below pile cut-off level. 3.2 Instrumentation A balanced circuit of up to six piles of 600 mm diameter energy piles, each 20 m long, was instrumented using thermistor strings. Each of the six piles was equipped with two four-thermistor strings attached to the U-loop pipes and four two-thermistor strings attached to four of the six main bars on the reinforcement cage (Figures 7 & 8). Table 4 gives a summary of the thermistor levels. As at The Crystal the steel reinforcing cage did not extend the full depth of the pile. Therefore fewer thermistor levels were installed on the steel cage compared with the central pipes. Heat meters were installed by GI Energy on the six-pile circuit where it reached the manifold in the basement, to enable further monitoring of the performance of the ground energy system as a whole and to record: • • • • •

Ground conditions

The ground conditions at the site are Made Ground, overlying River Terrace Deposits and Gault Clay. Owing to the construction of a new basement and the lowering of the original ground level, the piles were constructed over their full length through the Gault

Thermal Energy Power (kW) Cumulative Thermal Energy delivered (kWh) Flow Rate (L/sec) Flow Temperature (◦ C) Return Temperature (◦ C)

All the GI Energy monitoring points and the University of Southampton thermistor strings were connected via remote panels to the same monitoring system to

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Figure 7. Detail of thermistor strings installed on the steel cage at 22 Station Road.

Figure 8. Schematic arrangement of thermistor strings within the instrumented piles at 22 Station Road. Figure 9. Temperatures within the six instrumented piles at 22 Station Road at three dates during construction.

Table 4. Depths of thermistors installed within the piles at 22 Station Road. Thermistor Level 1 2 3 4

Height Above Pile Toe (m) Central Strings

Outer Strings

17.5–18.0 13.5–14.0 7.5–8.0 1.5–2.0

17.5–18.0 13.5–14.0 7.5–8.0 1.5–2.0

allow web-based desktop reading of the data from any location. 3.3

Initial data

The remote monitoring system is not yet available as final commissioning of the system is ongoing. However, spot readings from the thermistors were taken at various points during construction (Figure 9).The piles were cast during April 2014, with the slab construction

proceeding the following month. By September 2014 the instrument cables and polyethylene pipes were all routed to the manifold located in the basement and the building was being constructed around this. Subsequent readings were taken in the autumn of 2015 as the cables were wired into the remote panels. By this time the structure was largely complete, although fit-out and commissioning work continued throughout the remainder of the year. Spot readings from the thermistor strings at three points during construction of the building are shown in Figure 9. Shortly after construction of the piles (May 2014) there was an elevated temperature of 14◦ C to 16◦ C in the lower part of the piles, probably reflecting the residual heat of hydration of the concrete. At the top of the piles the temperature readings were reduced, reflecting the time of year (late spring to early summer) when summer air temperatures had not yet had a chance to be reflected in the near surface layers.

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By September 2014 the upper part of the piles have increased in temperature as the average air temperature also increased over the summer, but the values recorded in the lower part of the pile have reduced as the heat of hydration in the pile dissipates. The following spring, in April 2015, when it can be assumed that the heat of hydration has fully dissipated, the temperature near the base of the piles was around 13◦ C. This can be taken as representative of undisturbed conditions. Lower temperatures were recorded near the ground surface, reflecting the cooler air temperatures in the preceding winter period.

4

DISCUSSION

4.1 Lessons learnt from installations The Crystal instrumentation was arranged very close to construction which left few options for optimising the thermistor arrangements within the framework of the thermal design of the system. By contrast, involvement with the development of the new building at 22 Station Road commenced much earlier in the project cycle. This allowed greater planning time and as a result the entire six pile circuit was instrumented rather than just one of the piles within a circuit as at the Crystal.This additional planning also allowed integration of the pile and building monitoring systems into a single remote access arrangement. Both case studies illustrate the need to allow sufficient redundancy within any instrumentation scheme implemented within the framework of a live construction project. In only instrumenting one pile at the Crystal, it was fortunate that most of the thermistors have remained fully functional for over three years. However, unfortunately, access to the borehole heat exchanger instrumentation was lost due to cable breaks, caused by construction which were subsequently buried before they could be located and rectified. Having six piles instrumented at Station Road has meant the significance of some instrument losses during pile breakout has been reduced. A further lesson regarding redundancy learnt from the Crystal and applied to Station Road was the inclusion of two strings attached to the central pipes installed within each pile. One advantage of the building arrangement at the Station Road site is that the manifold is located within the basement of the building, making it potentially much more accessible in the future. The corresponding manifold at The Crystal is contained within a deep manhole in the grounds of the building. While this is accessible, additional health and safety considerations of the deep manhole make maintaining instrumentation in this area (the heat meter and a logger remote panel) more challenging. At both sites it would have been beneficial to have included in-ground instrumentation to provide additional temperature data beyond those measured within the piles. Despite the additional planning time

Figure 10. Hourly cooling demand at the Crystal during two days in July 2015.

available at Station Road, it just would not have been possible within a tight construction programme on a very constricted site to bring in additional plant to achieve this goal. Consequently this additional information remains recommended for future monitoring sites where possible. 4.2 Key observations from operation The building at 22 Station Road has yet to experience an operational period. However, operational data are now available for a number of years at The Crystal, although not all of the building monitoring equipment has been online for the entire duration. Nonetheless some interesting observations can be drawn out. As shown in Section 2.4 above, despite a nominally balanced energy requirement it is possible for the peak power requirements to be uneven. This may be responsible for the gradual increase in the pile temperatures over the last three years, however, other factors may also be relevant and additional data are required to analyse these. Nonetheless, the observation still demonstrates an important point with regard to the design of ground source heat pump systems. The data show how lumped demand can be misleading when real demand varies over short timescales. This is illustrated in Figure 10, which shows some detail from Figure 5 during two days in July 2015. Consequently, design of complex ground source heat pump systems should be carried out using hourly energy demand data (kWh per hour) – effectively instantaneous power. Differences in predicted system capacities when using longer duration rather than hourly demand data has recently been highlighted by Zhang (2016), who used hourly, monthly and yearly demand data for a Westminster wide district heating study and compared the results. In this case the use of monthly or yearly demand data was found to be non-conservative in terms of estimating the proportion of the city that could be included within the district heating scheme. The difference in predicted capacity between using monthly or yearly data and using hourly data was between 10% and 15%. The second important observation from The Crystal data is the extent of the temperature gradient across the instrumented pile. This varies throughout the year (Figure 11) and reaches a peak value of approximately

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Figure 11. Temperature difference between the thermistor strings installed on the pile cage and those on the central U-pipes. Positive difference indicates a cooler pile centre and hence heat extraction from the pile and ground.

However, sometimes the apparent resistance value is smaller than this and often the value is larger. The larger values reflect periods when the thermal load is reducing so that the temperature close to the pipes is falling more quickly than at the pile edge. In these cases as the power drops, the temperature difference also drops but not as rapidly. This causes the apparent increase in resistance. The implications of the absence of a thermal steady state within the pile are described by Loveridge & Powrie (2013b). Assuming a steady state where none is present can lead to the over-estimation of the temperature changes that will occur within the pile and the ground. This means that the true capacity of the associated ground source heat pump system will be underestimated during design.

5

Figure 12. Apparent thermal resistance of the pile between the pipes and the steel cage, calculated for two days in July 2015.

8 degrees. Peak values typically occur at times of peak demand. The additional superimposed variability is a reflection of two factors, first the variable thermal load (Figure 5 & Figure 10) and secondly the fact that the pile is not at a thermal steady state as assumed by many design approaches. The thermal load and pile temperature data can be used to quantify the degree of steady state within the pile. For clarity, considering only the same two days in July (Figure 10), Figure 12 shows corresponding changes in apparent thermal resistance. Thermal resistance is the ratio of the thermal power applied to the pile and the temperature difference across the pile. In this instance it has been calculated using the pile temperature sensors and hence is not the full pile resistance, just the resistance between the outside of the pipes and the pile cage. In this case the term “apparent” thermal resistance has been used since strictly speaking resistance is a steady state concept and within this large diameter pile a steady state will not be present. Nonetheless, consideration of the changes in values of apparent resistance allows some interesting observations to be made. The results show that the calculated apparent resistance in the pile concrete is far from constant (as would be the case if there was a thermal steady state). When there is a sustained period of heat injection (Figure 10) the apparent resistance stabilises at approximately to 0.1 mK/W, and this could be close to a steady state value. Certainly it is not an unreasonable value for a pile of this size and type (e.g. SIA, 2005).

SUMMARY

This paper presents initial results from two energy pile monitoring schemes in the UK. Such schemes are essential to allow better understanding of the long term benefits of using energy piles with ground source heat pump schemes and also to allow verification of appropriate and rigorous design approaches. Initial data from the first scheme are showing the importance of understanding the nature of the applied thermal loads for such systems. This is in terms of both the overall seasonal energy balance and the short term variation in demand. The short term variation in demand also contributes to the variable temperature observed within the pile. This causes fluctuation in the temperature difference across the pile and hence also the dynamic thermal resistance. Such transient behavior must be accounted for in design to prevent under-estimation of the ground source heat pump system capacity.

ACKNOWLEDGEMENTS Installation and maintenance of field instrumentation is time consuming and requires complete support from the contractors and designers involved in the schemes. At The Crystal, in addition to full support from Siemens, we are extremely grateful for assistance and cooperation from Balfour Beatty Ground Engineering, Arup, Foundation Developments Limited and IGS. At 22 Station Road we were supported by Mott MacDonald, Central Piling and Wates. The fieldwork presented in this paper was funded by the Engineering and Physical Sciences Research Council (research grant number EP/H049010/1) and was further supported by Mott MacDonald, Cementation Skanska, GolderAssociations & WJ Groundwater. The lead author is additionally funded by the Royal Academy of Engineering, with support from Mott MacDonald,Arup, Cementation Skanska, WJ Groundwater, GI Energy, Neo-Energy, Mimer Energy and the British Geological Survey.

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REFERENCES Amis, T. & Loveridge, F. (2014) Energy piles and other thermal foundations for GSHP – Developments in UK practice and research, The REHVA European HVAC Journal, January, 2014, 32–35. Bourne-Webb, P. (2013) Observed response of energy geostructures, In: Laloui & Di Donna (Eds), Energy Geostructures, Wiley, London. pp. 45–77. Brandl, H. (2006) Energy foundations and other thermo active ground structures, Geotechnique, 56 (2), 81–122. Loveridge, F. & Powrie, W. (2013a) Performance of Piled Foundations Used as Heat Exchangers, In: Proceedings of the 18th International Conference for Soil Mechanics and Geotechnical Engineering, Paris, France, September 2–5, 2013. Loveridge, F. & Powrie, W. (2013b) Temperature response functions (G-functions) for single pile heat exchangers, Energy, 57, 554–564. Loveridge, F., Holmes, G., Powrie, W. & Roberts, T. (2013) Thermal response testing through the Chalk aquifer, Proceedings of the Institution of Civil Engineers Geotechnical Engineering, 166 (2), 197–210. Met Office (2016) Climate summaries [online http://www.met office.gov.uk/climate/uk/summaries; accessed 21st January 2016].

Nicholson, D., Smith, P., Bowers, G. A., Cuceoglu, F., Olgun, C. G., McCartney, J. S., Henry, K., Meyer, L. L. & Loveridge, F. A. (2014a) Environmental impact calculations, life cycle cost analysis, DFI Journal, 8 (2), 130–146. Pahud, D. & Hubbach, M. (2007) Measured Thermal Performances of the Energy Pile System of the Dock Midfield at Zürich Airport, Proceedings European Geothermal Congress 2007, Unterhaching, Germany, 30 May–1 June 2007. SIA (2005) Utilisation de la chaleur du sol par des ouvrages de fondation et de soutenement en beton, Guide pour la conception, la realisation et la maintenance, Swiss Society of Engineers and Architects, Documentation D 0190. (In French). Suckling, T. P. & Smith, P. E. H. (2002) Environmentally Friendly Geothermal Piles At Keble College, Oxford, UK. In: Proceedings of the Ninth International Conference on Piling and Deep Foundations, 2002, Nice, France. Deep Foundations Institute, New Jersey, USA. Zhang, Y. (2016) Application Potential of Shallow Geothermal Energy at City Scale. PhD Thesis, Department of Engineering, University of Cambridge.

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Numerical analysis of thermal cycling during a multi-stage energy pile thermal response test F. Cecinato & R. Piglialepre University of Trento, Trento, Italy

F.A. Loveridge University of Southampton, Southampton, UK

D. Nicholson Arup, London, UK

ABSTRACT: Energy piles are emerging as convenient alternative to the more traditional Borehole Heat Exchangers (BHEs) to provide heating/cooling to buildings, as they remove the need for special purpose excavations and can accommodate more pipes, thus enhancing energy performance. However, their different aspect ratio compared to BHEs requires different modelling tools and dedicated thermal response testing, to achieve adequate thermal design. In this work, the results of an extended multi-stage Thermal Response Test (TRT) carried out on a single energy pile installed in London Clay are presented in terms of both fluid temperature data and concrete temperature, measured by vibrating wire strain gauges and optic fibre sensors. The results are then explored in detail by means of a finite element numerical code, able to account for both convective heat exchange in the fluid, between the fluid and the solids and transient heat diffusion in the concrete and the ground. Analysis of the TRT field data shows that during the later stages of the test there is clear evidence of cyclic changes in performance. Investigation of these effects using the numerical model raises the possibility that there could be some alteration of the properties of the soil-pile contact during the test. Hypotheses for the observed behaviour are tentatively put forward and discussed with work recommended to further investigate the percieved phenomena. 1

INTRODUCTION

Energy piles, serving the double function of foundations and heat exchangers, have been proposed as a convenient alternative to borehole heat exchangers, as they remove the requirement to make expensive special purpose excavations. Furthermore, their comparatively larger diameter means they can be expected to have a greater energy capacity per drilled metre (Bozis et al., 2011). Approaches to the thermal design of energy piles tend to be based on analytical (or empirical) methods developed for borehole ground heat exchangers. Such methods assume that the dominant thermal process in the ground is conduction and use analytical solutions to the diffusion equation to relate predicted temperature changes in the ground and the pile to the input of thermal loads in the form of the heating and cooling demand of the building. Typically transient solutions are applied to determine the temperature changes in the ground (e.g Eskilson, 1987, Claesson & Javed, 2011), while steady state solutions based on thermal resistance are used for the borehole or pile itself (e.g. Lamarche et al., 2010). In all these approaches it is assumed that the soil and the concrete that forms the

pile are homogeneous and isotropic and that their thermal properties are constant and independent of temperature. Thermal response testing is an in situ technique to determine the thermal properties of the ground and the thermal resistance of a borehole heat exchanger. It has also been applied to piles, although there are difficulties with doing so for larger diameter piles (Loveridge et al., 2014a). The same analysis methods and assumptions that are used for thermal design can be applied to the interpretation of thermal response tests, although in practice usually the simplest of analytical models, the line source, is adopted. This means that provision of reliable thermal design parameters is also dependent on the assumptions of homogeneous and isotropic conditions with temperature independent behaviour. This paper will report on the case study of an extended thermal response test of a small diameter energy pile, which shows some indication that cyclic thermal performance could indicate temperature dependent behavior. The test results are explored by a combination of field data (Section 3) and numerical simulation (Section 4), before the relevance and significance of the findings are discussed and tentative conclusions drawn (Section 5). Before describing

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this work the paper first presents a brief introduction to thermal response testing (Section 2). 2 THERMAL RESPONSE TESTING Thermal Response Testing (TRT) is an in situ investigation technique developed for borehole heat exchangers and subsequently extended for use with some energy piles. The test aims to determine the thermal conductivity of the ground and the thermal resistance of the heat exchanger to provide input parameters for thermal design. In a typical test the ground heat exchanger is connected, via its heat transfer pipes, to a number of heaters and a circulation pump. Circulation of the heated fluid through the borehole or pile allows heat to be injected to the ground at constant rate. The temperature change of the inlet and outlet fluid are monitored throughout the test and the results used with an analytical solution to the diffusion equation to calculate the ground thermal conductivity and heat exchanger thermal resistance. As a minimum, tests include a heat injection stage, but additional information can also be gained by continuing to circulate the fluid and monitor its temperature once the heaters have been switches off, i.e. during a recovery stage. There are several international and national guidelines for the test to encourage high quality testing and interpretation (Sanner et al, 2005; IGSHPA, 2007; GSHPA, 2011). However, it must be recognised that the accuracy of the test depends on how well the real in situ conditions reflect the assumptions that are inherent in the analytical methods used in interpretation. Well conducted tests carried out in boreholes in reasonably consistent ground conditions can be expected to achieve an accuracy of around 10% (Witte, 2013, Spitler & Gehlin, 2015). However, non-uniform ground conditions can result in more significant errors developing (Signorelli et al, 2006).

Ten days after grouting the pile, a multi-stage thermal response test was carried out. Unusually the test comprised a number of different phases (Figure 1) which were designed to allow investigation of the thermo-mechanical response of the pile (Ouyang, 2014). After an initial circulation phase, a heat injection test (Stage 2) and recovery period (Stage 3) was followed by a heat extraction test (Stage 4) and recovery period (Stage 5). Cyclic testing was then commenced comprising two heat injection phases (Stages 6 and 8) separated by heat extraction phases (Stages 7 and 9). Each test stage followed directly from the preceding phase and measurements were maintained throughout, except for a 4 day period in Stage 6 when repairs were being carried out to a faulty heating unit. Consequently the heat injection of Stage 6 is only seen at the latter part of this time period and there is an extended period of no recorded applied power prior to then (Figure 1). However, during the period when the power was not recorded, some heat was rejected to the system, as is shown by the concrete temperature data (refer to Figure 3 and Section 3.2).

3

3.1 Instrumentation & monitoring

CASE STUDY

The thermal response test described in this study was carried out on a 300 mm diameter and 26.8 m length test pile constructed at a London development site (Loveridge et al., 2014b). Beneath an initial concrete slab, the pile was constructed through water saturated London Clay over its entire length. The stratum was described as firm to stiff grey clay and contained some layers of claystones. A single U-loop of heat transfer pipe was installed in the hole to 26 m depth and backfilled with hard pile cementitious grout. The pipes were made from high performance polyethylene material with an external diameter of 32 mm and a wall thickness of 2.9 mm. The pipes were installed separated by rigid spacers ensuring an even separation of the pipes and a centre to centre spacing between the two legs of the U-tube of around 135 mm. The spacers also served as a housing to mount numerous sensors which are described in Section 3.1 below.

Figure 1. The multi-stage thermal response testing, showing heating power input at each stage.

The inlet and outlet heat exchanger fluid temperature Tin and Tout were measured throughout the test, except at the start of Stage 6 when the heating equipment was faulty. Moreover, the evolution of temperature within the concrete Tc during the TRT was measured in two ways, namely (i) at four locations along the pile depth, by means of temperature sensors associated with Vibrating Wire Strain Gauges (VWSG), and (ii) continuously along the pile depth by means of Optic Fibre Sensors (OFS) placed at four positions (Figure 2). Strain was also measured by both the VWSG and the OFS cables, however, consideration of this data is not within the scope of this study. Full description of these data and their interpretation are contained within Ouyang (2014). 3.2 Results The resulting fluid temperatures at the inlet and outlet in response to the applied cycles of heating (Figure 1)

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Figure 3. Fluid and VWSG average concrete temperature (at pile mid-height) data throughout the test.

Figure 2. Location of the temperature sensors within the pile cross section.

are shown in Figure 3. The temperature increases in response to heat injection and reduces in response to heat extraction. It can also be seen that there is a bigger difference between the inlet and outlet temperatures when the applied heating power is greater. Figure 3 also shows as an example the average temperatures recorded by the VWSGs at pile mid-height, which are seen to have reduced amplitudes of variation to the fluid temperatures due to their greater offset from the pipes. It can be also noticed in Figure 3 that during the second part of stage 5 and the first part of stage 6 the concrete temperature varies unexpectedly, in a way that suggests heat extraction, although this is neither reflected from the fluid temperatures nor from the applied power (Figure 1). A similar pattern is seen in the OFS data, including on those OFS cables located on the heat transfer pipes (Figure 2). This discrepancy is the likely result of the heating system malfunctioning in that period, leading us to presume that fluid temperature measurements are not reliable during stage 5 and the beginning of stage 6. Temperature measurements were also available from within the concrete from the OFS placed at approximately the same distance from the pipes. It emerged that overall, the VWSG measurements are more stable and consistent compared to OFS measurements, which appear more wavy. After applying a moving average filter to the latter data, comparison of the two types of measurements showed adequate consistency. As an example, in Figure 4 VWSG and OFS data are plotted versus depth for an instant at the end of stage 6. It can be noticed that the two different OFS datasets tend to overlap in correspondence with the locations of spacers. This could indicate that the OFS cables were not perfectly straight along the pile; hence

Figure 4. Comparison between OFS and VWSG temperature measurements after application of moving average filter to OFS data. The horizontal dotted lines denote the approximate locations of spacers.

a certain degree of oscillation of OFS temperature measurements might have reflected the variable distance of the cables from the pipes (i.e. changes of position in different cross-sections along the pile). 4

NUMERICAL SIMULATION

4.1 Model description The numerical model (Cecinato and Loveridge 2015, Cecinato et al. 2015) aims at realistically reproducing the main processes behind the heat transfer phenomena taking place in geothermal structures, namely thermal convection between the fluid and the pipe wall, thermal conduction in the grout/concrete, and thermal conduction in the ground. Convective heat transfer in the pore water is not considered. Hence, while the model is always applicable to low-permeability or dry geomaterials, it can only be applied to high-permeability watersaturated materials if the groundwater at a specific site is known to be static. The transient heat convection-diffusion problem for energy piles was solved using the Finite Element (FE) code ABAQUS to integrate 3D transient conduction through the solids, complemented by writing bespoke

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Table 1. Material properties used in the simulation. Material

Parameters

Fluid

Density Kinematic viscosity Specific heat capacity Mass flowrate Thermal conductivity Prandtl number Concrete Density Specific heat capacity Thermal conductivity Pipes Thermal conductivity London Clay Density Specific heat capacity Thermal conductivity

Values

Units

1000 1.00E–06 4200 0.108 0.6 7 2210 1050 2.8 0.385 1900 1820 2.3

kg/m3 m2 /s J/(kg K) kg/s W/mK kg/m3 J/(kg K) W/mK W/mK kg/m3 J/(kg K) W/mK

in the numerical model as a half domain exploiting symmetry (Figure 5). Validation of the model has been previously undertaken using fluid data from Stages 2 to 5 of the case study described above (Cecinato and Loveridge 2015, Cecinato et al. 2015). The physical and thermal properties of the materials involved are given in Table 1. Figure 5. FE mesh representing the pipes (schematised in 1D as a line of nodes), the pile and surrounding ground, with temperature contours. Only half of the domain is considered, to save computational time exploiting symmetry.

user subroutines to model the convective heat transfer at the fluid/solid interface and the temperature changes in the fluid along the pipe, represented within the FE mesh as lines of nodes, where the heat exchange resulting from convection-diffusion in the pipes is concentrated. The 3D nature of the pipes (i.e. the relevant diameter, in addition to length) is properly accounted for via the user subroutines, by multiplying the heat flux corresponding to each pipe node by the corresponding lateral surface area of each pipe segment. To minimise computational time, while controlling the element aspect ratio and node spacing at key locations to warrant accuracy of heat exchange calculations, the 3D FE mesh was created manually in an axisymmetric fashion using 6-node linear triangular prism and 8-node linear brick diffusive heat transfer elements (Figure 5). The spacing of the nodes representing the ground was progressively increased towards the outer boundary, while the mesh was refined in the exchanger pipe and surrounding pile areas. The size of the domain was determined by numerical experimentation to be much larger than the area actually affected by heat transfer over the time range explored in this study. To simulate the TRT case study, the inlet fluid temperature was prescribed as a function of time, as a boundary condition for the analysis. At zero heat flux an initial equilibrium temperature for both the fluid and the concrete/ground conditions was specified. The TRT geometry was reproduced in detail

4.2 Model development Although in previous validation of the model it was shown to perform well in reproducing the thermal behaviour of the test pile, subsequent work had shown that the inherent simplification of representing the pipes as 1D lines of nodes in the FE mesh might lead to less accurate calculations when pipes are placed very close together (Loveridge and Cecinato, 2016). To investigate this potential effect, the numerical model was modified by changing both the FE mesh and the user subroutines, to represent the exchanger pipes in 3D. The scheme adopted involves representing each pipe in the pile cross-section with a set of nodes (2, 4 or 8) distributed along the pipe’s circumference, so that each node represents a part of the total pipe surface involved in the heat flux (Figure 6). On the other hand, in the original model a single node represents the whole pipe surface in a pile cross-section. The modified model was then used to run the same TRT simulations from Stage 2 to Stage 5, showing a significant improvement in the RMSE comparing the simulated and measured outlet fluid temperature. For example, for Stage 2, Table 2 shows the general decrease in RMSE, and hence increase in fit, as the number of pipe nodes is increased. This suggests an increase in the accuracy of the simulation due to a more realistic representation of the heat flux spatial distribution across the pipes. Additionally, more symmetrical temperature contours further suggest a progressive improvement in the representative of the heat fluxes (Figure 6). 4.3 Simulation of case study The model was now used to reproduce the entire temperature history of the TRT case study over all stages

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Figure 7. Comparison of measured and simulated outlet fluid temperature during the TRT.

Figure 6. FE mesh representing a cross-section of the pipes area with temperature contours during heat injection, for half of the domain. The model was developed by representing each pipe in the pile cross-section with a set of (a) 2, (b) 4 or (c) 8 nodes instead of a single node as originally proposed (Figure 5). Table 2. Improved model fit (Stage 2) when using increased number of nodes to represent the fluid pipes. No. Nodes

1

2

4

8

RMSE

0.240

0.202

0.169

0.196

Figure 8. Comparison of measured and simulated outlet fluid temperature during the TRT, enlargement of later stages 6–9.

of the test, using the 4 node 3D representation of pipes. This provided an appropriate balance between set up and computational time expended and the output accuracy. The field measured fluid temperature was used as specified boundary condition and both the evolution of the outlet fluid temperature (Tout ) and the concrete temperate (Tc ) were used to assess fit of the model. Based on the assessment of the OFS field data given in Section 3.2, only the VWSG data were used to assess Tc . In Figure 7 the simulated and measured outlet fluid temperature are reported for comparison, for all of the TRT stages, leaving out the second part of stage 5 and the early part of stage 6 (due to the above mentioned problems in that part of the TRT with measurements reliability). The numerical simulation effectively reproduces the field measurements for all considered stages of the TRT, however, it could be noticed that it does not approximate all stages with the same accuracy. In particular, the cyclic testing stages (6 to 9) appear to be reproduced less precisely, as can be seen in an enlargement of these stages (Figure 8). To evaluate further the accuracy of the simulation, the root mean square error (RMSE) of the residuals was calculated, resulting in the values given in Table 3. A tendency for the simulation accuracy to worsen (i) for heat extraction phases (4, 7 and 9) and

Table 3. Model fit for the different test stages. Stage RMSE Stage RMSE

2 0.169 6 (2nd part) 0.588

3 0.205 7 0.993

4 0.504 8 0.231

5 N/A 9 1.598

(ii) generally at later TRT stages is observed, with special regard to the heat extraction phases during thermal cycling. A similar effect was observed by Loveridge et al. (2014b) when fitting analytical solutions to the same data. Those authors observed particular misfit of the analytical models in the last four stages of the test. It was suggested that this effect could be the results of the pile thermal resistance may not be constant. It was hypothesised that this could be due to increased contact resistance at the pile-soil boundary when the pile is cooled. However, the authors also showed that this hypothesis could not explain all the observed behaviours of the pile during the test. In Figure 9 the VWSG-measured and simulated (using the original 1D pipe scheme, to save computational time yet providing adequate accuracy) concrete temperature values are reported, as an example, at pile mid-height (13.8m depth) throughout the TRT. Simulation #1 was obtained using the measured inlet fluid temperature as boundary condition, and it can

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Figure 9. Comparison of measured and simulated concrete temperature during the TRT. Simulation #1 is obtained using the measured Tout as boundary condition while Simulation #2 is obtained with a corrected input during stages 5 and 6.

be seen that data are not adequately reproduced during stages 5 and 6, during which the fluid temperature measurements have been considered unreliable due a temporary system breakdown. To be able to reproduce the evolution of Tc , the temperature input Tin was modified during those stages generating a synthetic temperature history, by means of numerical back-analysis (Piglialepre 2016). This modified Tin was used to run Simulation #2, which can adequately reproduce Tc also during stages 5 and 6. The modified Tin has a negligible effect on the subsequent stages due to sufficient recovery time prior to the start of heat injection in Stage 6. In general, the measured concrete temperature evolution is now correctly reproduced using Simulation #2 with synthetic input for Stages 5 and 6 (Figure 8). However a worse fit during the last stages is still observed in both simualtions, with special reference to heat extraction stage 7 (field data were not available for stage 9). This is consistent with what has been observed above for the outlet fluid temperature. 4.4

Cyclic effects

A sensitivity study was carried out to preliminarily investigate the possible reasons for the particular mismatch between the outlet temperature simulations and data during heat extraction stages 7 and 9. The fact that during those stages less heat than predicted is extracted may suggest that, by virtue of differential contraction between concrete and soil within the elastic regime and/or due to possible thermo-plastic effects in the soil upon thermal cycling, contact at the pile-soil interface might be reduced. This in turn could affect the lateral bearing capacity of the pile. As a first-attempt analysis, the thermo-mechanical pile-soil interaction was not modelled numerically (the FE analysis was kept purely thermal), but its possible effect was accounted for by changing the thermal properties of a thin layer of solid elements (i.e. a 1 cm thick ring) in contact with the pile. Possible reduction of contact between pile and soil was simulated by setting

Figure 10. Comparison of measured and simulated outlet fluid temperature during stage 7.

Figure 11. Comparison of measured and simulated outlet fluid temperature during stage 9. Table 4. Model fit for test stages 7 and 9 obtained with the original settings and with the altered interface settings. Stage

7

9

RMSE (original model) RMSE (altered interface)

0.993 0.844

1.598 0.703

for this layer values of density, thermal conductivity and specific heat equal to those of air. A comparison of simulations of Tout obtained with these settings and measurements for stages 7 and 9 is shown in Figures 10 and 11 respectively. In Table 4 the model fit in terms of RMSE is reported for stages 7 and 9 compared to values obtained with the original simulation (cf. Section 4.3). It can be seen that model simulations now can better reproduce field data, especially regarding stage 9, representing the second thermal loading-unloading cycle. This result corroborates the conjecture that pile-soil contact might have been reduced during stages 7 and 9, although further numerical analysis accounting for thermo-mechanical couplings would be needed to adequately support this hypothesis. 5

DISCUSSION & CONCLUSIONS

In this work, a recently proposed FE numerical model to interpret the thermal behaviour of energy piles was

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further developed and validated against field data from a multi-stage thermal response test. Numerical developments, consisting in providing a 3D representation of pipes (instead of the original 1D schematisation), led to significant improvements in the model accuracy. The comparison of simulations and field data throughout the multi-stage TRT, both in terms of outlet fluid and concrete temperature, highlighted that the simulations provide a very good fit in the early TRT stages, and a worse fit at later stages. In particular, the model accuracy appears to worsen in correspondence with the heat extraction phases. This suggests the presence of cyclic effects in the case study at hand. A similar effect was observed by Loveridge et al. (2014b) when fitting analytical solutions to the same data, and by Ouyang (2014) when assessing the effect of pilesoil interaction in the thermal exchange process of the same TRT. To further investigate cyclic effects, a sensitivity study was carried out by tentatively changing the thermo-physical properties at the soil-pile interface during the last heat extraction phases (stages 7 and 9), to reproduce in a simplified manner the possible formation of an air gap, due to thermally induced (differential) contraction of the pile and soil material. This resulted in an improved fit of outlet temperature data (with special regard to Stage 9, i.e. the last heat extraction cycle), suggesting that a reduction of pile-soil contact may have been possible in this case. However, this mechanism is not proven and should be corroborated by further investigation accounting for thermo-mechanical couplings in a more rigorous manner. However, care must also be taken in extrapolating this case to general practice for two reasons. Firstly, the pile was not subject to mechanical load during the TRT. As highlighted by Ouyang (2014), the mechanical load would allow the pile to form a better interface with the soil prior to thermal loading, thus preventing the free contraction of the pile in the cooling cycle. Ouyang (2014) also suggest that the interface effects of “weak interaction” could result from the unusually large size of the plastic spacers or the short time delay between pile grouting and testing of the piles. The former could lead to differential thermal expansion effects within the pile, while the latter could have resulted in the grout not having cured completely, hence having different physical characteristics compared with a working pile. Nonetheless, the possible thermally induced weakening of pile-soil contact is worth additional analysis considering the thermo-mechanical couplings relevant to the suggested mechanisms. This will help to understand whether or not there is a real risk of changing pile-soil interface conditions in operational scenarios. ACKNOWLEDGEMENTS Francesco Cecinato acknowledges financial support from European Union FP7 project under contract num ber PIAPP-GA-2013-609758-HOTBRICKS.

Fleur Loveridge is funded by the Royal Academy of Engineering under their Research Fellow scheme.

REFERENCES Eskilson, P. 1987. Thermal analysis of heat extraction boreholes. Doctoral Thesis, Department of Mathematical Physics, University of Lund, Sweden (http://www.building physics.com/Eskilson1987.pdf). Bozis, D., Papakostas, K., & Kyriakis, N. 2011. On the evaluation of design parameters effects on the heat transfer efficiency of energy piles, Energy and Buildings, 43 (4), 1020–1029. Cecinato, F. & Loveridge, F. A. 2015. Influences on the thermal efficiency of energy piles. Energy, 82, 1021– 1033. Cecinato, F., Loveridge, F., Gajo, A. & Powrie, W. 2015. A new modelling approach for piled and other ground heat exchanger applications. In, XVI European Conference for Soil Mechanics and Geotechnical Engineering, Edinburgh, GB, 13–17 Sep 2015. 6 pp. GSHPA 2011. Closed-loop Vertical Borehole Design, Installation & Materials Standards Issue 1.0, September 2011. Ground Source Heat Pump Association, Milton Keynes, UK. IGSHPA 2007. Closed-loop/geothermal heat pump systems: Design and installation standards, International Ground Source Heat Pump Association/Oklahoma State University. Javed, S. & Claesson, J. 2011. New analytical and numerical solutions for the short-term analysis of vertical ground heat exchangers. ASHRAE Transactions, 117(1): 3–12. Lamarche, L., Kajl, S. & Beauchamp, B. 2010. A review of methods to evaluate borehole thermal resistance in geothermal heat pump systems. Geothermics, 39, 187–200. Loveridge, F. A. & Cecinato, F. 2016. Thermal performance of thermo-active CFA piles. Environmental Geotechnics, doi: 10.1680/jenge.15.00023. Loveridge, F.A., Brettmann, T., Olgun, C.G. & Powrie, W. 2014a. Assessing the applicability of thermal response testing to energy piles. In, Global Perspectives on the Sustainable Execution of Foundations Works, Stockholm, SE, 21–23 May 2014. 10 pp. Loveridge, F.A., Powrie, W. & Nicholson, D. 2014b. Comparison of two different models for pile thermal response test interpretation. Acta Geotechnica, 9 (3), 367–384. Ouyang, Y. 2014. Geotechnical behaviour of energy piles. PhD thesis, University of Cambridge, UK. Piglialepre, R. 2016. Analisi numerica del funzionamento di un palo geotermico. MSc thesis, University of Trento, Italy. Sanner, B., Hellstrom, G., Spitler, J. & Gehlin S. E. A. 2005. Thermal Response Test – Current Status and WorldWide Application, In: Proceedings World Geothermal Congress, 24–29th April 2005 Antalya, Turkey. International Geothermal Association. Signorelli, S., Bassetti, S., Pahud, D. & Kohl, T. 2007. Numerical evaluation of thermal response tests. Geothermics, 36, 141–166. Spitler, J. D. & Gehlin, S. E. A. 2015. Thermal response testing for ground source heat pump systems – An historical review. Renewable and sustainable energy reviews, 50, 1125–1137. Witte, H. J. L. 2013. Error analysis of thermal response tests. Energy, 109, 302–311.

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An investigation of the potential thermal energy of geothermal tunnels with focus on a case study in Stuttgart, Germany P. Buhmann, B. Westrich & C. Moormann Institute of Geotechnical Engineering, University of Stuttgart, Germany

A. Bidarmaghz & G. Narsilio Department of Infrastructure Engineering, The University of Melbourne, Australia

ABSTRACT: Shallow surface geothermal energy is an essential contribution to the base load of heating energy. The thermal activation of tunnels is an interesting alternative and an economically appropriate supplement of the present hybrid systems in the field of ground engineering. An essential difference between the tunnel absorber and structures such as activated piles and diaphragm wall elements is the use of heat fluxes from the earth, as well as from the inside of the tunnel. Due to this circumstance, the tunnel absorber is assigned to the group of the duo hybrid systems. The tunnel air temperature is essential for the heat flux inside the tunnel. Stuttgart Fasanenhof and Jenbach are two geothermal tunnel plants which have been delivering dependable measurement data of the subsoil temperature, the tunnel lining temperature and the tunnel air temperature since 2011. Based on the selected operation modes and case studies, the measurement results are analyzed and discussed. In addition, the possible geothermal potential of a geothermal tunnel plant is introduced.

1

GENERAL

In Germany, approximately 12% of the primary power demand is covered by renewable energy (Nieder et al., 2015). In the heating sector, biomass accounts for 87.7%, solar thermal energy accounts for 5%, while geothermal energy accounts for only 7.3%. The development of solar thermal energy shows a steadily rising trend. This expansion stagnates the development of classical geothermal energy absorber systems. In 2014, the total volume of investment in renewable energy in Germany amounted to 18.9 billion euros. Approximately 5% of this amount was used in the area of geothermal energy, for both shallow and deep geothermal energy. Shallow geothermal energy reaches a depth of up to 400 m below the surface. With a geothermal gradient of about 3◦ C/100 m, temperatures can reach 25◦ C; nevertheless, the temperature often lies between 10– 15◦ C in the above locations. For the climate control of buildings, the necessary temperature rise is achieved by the application of a heat pump. A classic absorber system in the field of shallow surface geothermal energy is the borehole heat exchanger. Current studies show (Eicker and Thumm, 2012) that the projected withdrawal lines in this absorber technology is often not achieved. In addition, the cost of manufacturing the deep-drilling makes heat production unprofitable. An alternative to the classic absorber systems of the shallow geothermal energy is the activation of

earth-facing concrete structures in the field of building construction and civil engineering. For decades, the thermal activation of structures of ground engineering such as piles (Knapp, 1992) and diaphragm walls (Brandl, 2013) has reached an economically effective level. Heat fluxes are used with systems like borehole heat exchangers, between the absorber element (borehole heat exchanger, thermally activated foundation structure) and the surrounding subsoil, for the extraction of energy.A logical advancement is the thermal activation of tubular components in the subsoil like infrastructure tunnels, sewers and other related components. The heat exchanger for these constructions is situated inside the load bearing concrete shell. With the activation of sewers, a combination with absorbers situated on the channel bottom is also possible. Besides, the large earth facing surface of these components are activated in contrast to classical geothermal energy absorbers; not only the heat flux from the absorber to the earth is active, but the heat flux between the absorber and the inside of the tunnel of the thermally activated tube is also active. The geothermal potential and possible specific extraction capacities of this new technology stand in a context of different influences, which are to be considered during the design as well as the operation of the plant (Fig. 1). At present, 6 tunnels have been equipped with absorber systems world-wide (Frodl et al., 2010; Islam et al., 2006; Markiewicz, 2004; Zhang et al., 2013),

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Figure 1. Actions and interactions on tunnel geothermal plant.

Figure 2. Subsoil conditions.

providing heating and cooling energy for very different applications. 2

EXPERIMENTAL PLANTS

Two basically different experimental plants were available to the authors for this research activity. They include the Stuttgart Fasanenhof tunnel (Germany), an approximately 380m long shallowly lying suburban railway tunnel, as well as the 3470m long railway Jenbach tunnel (Austria) running in the valley Inn. The tunnels differ in their geometrical dimension, their use, their geothermal absorber equipment as well as their geological and hydrogeological conditions (Fig. 2). In the Jenbach tunnel, which is situated in the high hydraulically permeable “Innschotter” (gravel layers of the river Inn), the heat transport in the porous media subsoil is mainly driven by convection, while at the Stuttgart Fasanenhof tunnel, the heat transport occurs in the solid rock primarily based on conduction. The Stuttgart Fasanenhof tunnel is operated as a pure test plant with given load scenarios, while the Jenbach tunnel serves a neighboring contractor’s yard for climate control, covering a real user’s behavior.

Figure 3. Absorber system tunnel stuttgart fasanenhof.

The following explanations consider only the Stuttgart Fasanenhof tunnel. At the Stuttgart Fasanenhof tunnel, two separate tunnel blocks of 10.0m each were equipped with absorber technology. Therefore, meandering conduits in which an absorber liquid circulates, beginning from the tunnel ridge up to the escape in the tunnel walls (Fig. 3) were fastened to the outside lining of the tunnel by means of so-called splints. The whole conduit length per activated block amounts to 400m. The running after built-in inner tunnel lining protects the conduit system against damages. An intensive measuring equipment carries out the supervision of the tunnel air and tunnel lining temperature with the aid of a total of 140 measuring transducers. To capture the development of the subsoil temperature, vertical and horizontal measuring probes were installed in the area of the ridge and the elms of the tunnel at discreet points; the development of the subsoil temperature was measured. Further, the inlet (ϑin ) as well as the outlet temperature (ϑout ) of the primary circuit of the absorber system were mea˙ was also measured. sured. The volume flow rate (V) With these data, it is possible to calculate the over˙ by using the following all extracted heat flux (Q) equation:

Also, it is possible to calculate the heat fluxe densities from the absorber to the subsoil as well as from the absorber to the interior of the tunnel by using the following equation:

At the Stuttgart Fasanenhof tunnel, from 2011 till now, numerous load scenarios were tested and evaluated. At this point, the interval operation mode from 2011/12 is introduced. Figure 4 shows the interval operation mode for a period of 7 days. For the simulation of the interval operation mode, the volume flow rate (approx. 500 l/h) of an operation

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Figure 4. Intervall heating mode 2011/2012.

of 2 months duration is held steady and the inlet temperature of the primary circuit is regulated for 8 h each day to approximately 0.5◦ C. During the remaining 16 hours, the inlet temperature of the primary circuit is influenced by the tunnel climate, the subsoil temperature and the connected operation room. A steadily rising tunnel air temperature which follows the outside air temperature of the tunnel is observed. During the day time, a heat extraction rate of 20 W/m2 is achieved. This heat extraction rate does not influence the subsoil temperature development significantly. In the summer of 2016, the Stuttgart Fasanenhof tunnel will be driven with a realistic chill demand profile for the first time. This investigation offers an essential contribution to the quantification of possible heat extraction capacities. 3

REFERENCE LOAD PROFILES

The geothermal potential as well as the attainable heat extraction rate of a geothermal tunnel plant strongly depend on the energy demand profile. In the case of an energy extraction rate taken from the absorber higher than the heat fluxes from the subsoil to the absorber, together with the heat fluxes from the interior of the tunnel to the absorber, there will be decreasing geothermal potential over the time of operation, considering a constant absorber temperature. Consequently the assessment of the geothermal potential depends, beside the geological and hydrogeological conditions, substantially on the operation modes of the geothermal tunnel plant. If no object-related heating or chilling demand profiles are known, e.g. from comparative objects or preliminary numerical studies, suitable simplistic demand profiles must be generated for an energetic evaluation of a geothermal tunnel plant. This occurs on the base (Verein Deutscher Ingenieure, 2008) and the test reference years of the German weather service (Bundesamtes für Bauwesen und Raumordnung, 2014). Fig. 5 shows the generated thermal energy demand for heating and hot water of a representative

Figure 5. Thermal energy demand profiles for heating (continous line) and hot water (dotted line).

Figure 6. Numerical simulation model; dimensions: height: 50 m, width: 121 m; 37.000 three node elements.

single-family dwelling of the Swabian-Franconian terraced countryside and foothills of the Alps for January and May. Seasonally, daily as well as hourly, a very different thermal energy demand can be seen. If the shown demand scenarios can be run by the operation of the geothermal-heat pump-absorber system, the geothermal tunnel plant gains the possibility of a thermal regeneration. For a geothermal absorber system that is particularly influenced by conductive heat transport, like the Stuttgart Fasanenhof tunnel, this has an essential meaning. 4

CASE STUDY

Within the scope of a case study, the Stuttgart Fasanenhof tunnel was analyzed for an exemplary heating energy demand of a single-family dwelling. The simulations are based on one (Schneider, 2013) validated and calibrated numerical 2D-model, which was calculated using the software FeFlow 6.1. Basically, it is possible to consider the energy demand as a 2nd kind of boundary condition in the area of the existing heat exchanger between the inner and outer tunnel lining. However, this boundary condition

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Figure 8. Tunnel air temperature and surface temperature outside tunnel; heat flux density in the area of the absorber.

like infrastructure tunnels, sewers and other related components. Two experimental geothermal tunnel plants offer the possibility to investigate the interaction among the tunnel air, the absorber system and the surrounding subsoil. This forms the basis for validating numerical simulation models. The heat extraction capacity of a geothermal tunnel plant is highly influenced by the energy demand profile the plant is operated with as well as the subsoil and tunnel air conditions. Extractions rates for short shallow laying suburban railway tunnels can be assumed to be 50 W/m2 for long term heating modes. Figure 7. Temperature field around the tunnel a) after a cooling period, b) after a regeneration period [◦ C].

ACKNOWLEDGEMENTS may be taken into account in the subsoil temperatures, which lie beyond the juridically limiting values. The extracted heat flux by time would to be adapted to the development of the subsoil temperatures. This form of the iteration is currently not available. Hence, for the case study, a minimally allowed absorber temperature was prescibed on the system for the heating mode by 0◦ C. Fig. 7 shows the temperature field around the tunnel after the heating mode, a), as well as the regeneration time, b). Consequently, the so ascertained maximum geothermal potential of the geothermal tunnel plant describes the maximum heat flux density (˙q) per 1 square meter of the absorber surface for the analyzed energy demand profile for a single-family dwelling. Considering a monovalent operation for the analyzed single-family dwelling, a maximum heat flux density of 50 W/m2 can be the base for dimensioning the heating system (Fig. 8). 5

CONCLUSIONS

The actual developments in the geothermal market require a lowering of the heat production cost, so that geothermal energy can compete with other renewable energy sources in future. The thermal activation of earth-facing concrete structures in the field of building construction and civil engineering is a first step in this direction. A logical advancement is the thermal activation of tubular components in the subsoil

The authors would like to thank the German Federal Ministry for Economic Affairs and Energy for financial support; they would like to thank the Stuttgarter Strassenbahn AG and Ed. Züblin AG for financial and technical support for carrying out the described large-scale pilot projects. REFERENCES Brandl, H. (2013), “Thermo-active Ground-Source Structures for Heating and Cooling”, Procedia Engineering, Vol. 57, pp. 9–18. Bundesamtes für Bauwesen und Raumordnung (BBR) (2014), Testreferenzjahre von Deutschland für mittlere, extreme und zukünftige Witterungsverhältnisse, Offenbach. Eicker, U. and Thumm, F. (2012), “Energieeffizienz und Wirtschaftlichkeit oberflächennaher Geothermie für das Heizen und Kühlen von Nichtwohngebäuden”, Bauphysik, Vol. 34 No. 1, pp. 11–18. Frodl, S., Franzius, J.N. and Bartl, T. (2010), “Design and construction of the geothermal tunnel system in Jenbach – Planung und Bau der Tunnelgeothermieanlage in Jenbach”, Geomechanics and Tunnelling, Vol. 3 No. 5, pp. 658–668. Islam, M.S., Fukuhara, T., Watanabe, H. and Nakamura, A. (2006), “Horizontal U-Tube Road Heating System using Ground Tunnel Heat”, Journal of Snow Engineering of Japan, Vol. 22 No. 3, pp. 229–234. Knapp, C. (1992), “Energiepfähle: Ein interessantes System zur Energiegewinnung”, Wohnen, 1992, pp. 6–7, available at: http://dx.doi.org/10.5169/seals-105919.

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Markiewicz, R. (2004), “Numerische und experimentelle Untersuchungen zur Nutzung von geothermischer Energie mittels erdberührter Bauteile und Neuentwicklungen für den Tunnelbau”, Institut für Grundbau und Bodenmechanik, Technischen Universität Wien, Wien, 09/2004. Nieder, T., Bickel, P. and Musiol, F. (2015), Entwicklung der erneuerbaren Energien in Deutschland im Jahr 2014: Grafiken und Diagramme unter Verwendung aktueller Datender Arbeitsgruppe Erneuerbare Energien-Statistik (AGEE-Stat),Stand Dezember 2015, Stuttgart. Schneider, M. (2013), “Zur energetischen Nutzung von Tunnelbauwerken – Messungen und numerische Berechnungen am Beispiel Fasanenhof ”, Mitteilung 68 des

Instituts für Geotechnik der Universität Stuttgart, Institut für Geotechnik, Universität Stuttgart, Stuttgart, 2013. Verein Deutscher Ingenieure (2008), Referenzlastprofile von Ein- und Mehrfamilienhäusern für den Einsatz von KWKAnlagen No. VDI 4655, Beuth Verlag GmbH, Berlin. Zhang, G., Xia, C., Sun, M., Zou, Y. and Xiao, S. (2013), “A new model and analytical solution for the heat conduction of tunnel lining ground heat exchangers”, Cold Regions Science and Technology, Vol. 88 No. 0, pp. 59–66.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Probabilistic analysis of a rock salt cavern with application to energy storage systems, using subset simulation methodology E. Mahmoudi, K. Khaledi, D. König & T. Schanz Chair of Soil and Rock Mechanics, Ruhr-Universität Bochum, Germany

ABSTRACT: This paper presents an efficient approach to evaluate failure probability in geotechnical structures dealing with rare failure events. Subset simulation is an appropriate method to substitute Monte Carlo simulationbased approaches while it decreases computational costs of reliability analyses. This methodology combines the idea of dividing a failure region into a sequence of nested failure regions and Markov chain Monte Carlo sampling methodology. To accomplish this, a modified Metropolis-Hastings method is utilized to generate a chain of random samples in intermediate failure regions from existing samples. Furthermore, subset simulation is employed to evaluate the failure probability of an underground energy storage system. The surplus baseload of the produced electrical energy by renewable resources can be converted to compressed air and stored in rock salt caverns. The validation of the integrity and stability of these caverns is a prerequisite in the geotechnical design process of them. The present study provides a reliability-based analysis of a typical renewable energy storage cavern in rock salt. An elasto-viscoplastic creep constitutive model is applied to a finite element numerical model of rock salt cavern to assess its behavior. The constitutive parameters are represented as random variables with predefined PDF, mean, and standard deviation. The occurrence of dilation is considered as the mechanical failure criteria of the system. Subset simulation is further validated by a comparison with a Monte Carlo simulation-based analysis.

1

INTRODUCTION

Due to the fact that the uncertainties in the rock and soil medium properties are unavoidable, a reliable design procedure in geotechnical engineering issues can not rely merely on deterministic approaches. Besides the inherent randomness involved in some unpredictable natural process, sources of uncertainties in modeling of physical phenomena may be classified into two major categories: Aleatoric: this type of uncertainties may arise when the estimation of the parameters and their statistical measures are inaccurate. Also called as statistical errors may be mostly due to the lack of available data and assigning inappropriate statistical features to the input variables. • Epistemic: the second type of errors in imperfect modeling correspond to the inaccuracies of modeling and simulation. A mathematical equation which idealizes natural phenomena in the framework of constitutive model, idealized boundary conditions and geometry, or even ignoring some interaction may be origins of these systematic errors. •

Thereupon, in addition to an adequately accurate computational model, the stochastic analyzes approaches are needed as well. In other words, carrying out probabilistic analyzes, as substantial tools which consider

these uncertainties and evaluate the effect of them on system predictions seems essential. Reliability analysis assesses the uncertainty effects and their mitigation in the final design which leads to risk-informed decisions. Nowadays, numerical simulations are designed with increasing complexity and higher expectation for their reliable predictions. Subsequently, involved failure events in such sophisticated designs are intended to be rare, which makes its assessment by classical methods, computationally prohibitive. Setting up and solving a reliability-based analysis problem is usually conducted by Monte Carlo Simulation (MCS) methods. However, in case of rare failure events, the MCS-based method needs a large number of system evaluations, which drastically increases the computational burden, especially for complex models. To overcome this drawback, subset simulation method is employed to decrease the required number of model executions. In this approach, a small failure probability is broken down into a series of larger conditional probabilities of some chosen intermediate failure events. The efficiency of subset simulation approach is shown in this paper by probabilistic analysis of the stability of a rock salt storage for renewable energy. Besides all advantages of producing energy from renewable resources, their production profile may not

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be compatible with the consumption profile, which can question their functionality. Storing pressurized gas, compressed by surplus of the produced electrical renewable-based energy, in rock salt cavities can overcome this disadvantage. Rock salt formation has proper features, as negligible permeability, high compressive strength, as well as healing properties. Although an underground storage plant is generally safer and more stable than same facilities on the ground, a poorly designed or operated plant may cause major accidents (Berést and Brouard 2003). Therefore, the stability of a rock salt cavity in an underground storing plant are the most important issues in their geomechanical design process. In order to investigate how reliable the safety of a rock salt cavity is, a no dilation criterion is defined. Exceeding this criterion may cause initiation of cracks in the rock salt which leads to failure in the cavern’s sealing. In this regard, a finite element numerical simulation of a rock salt cavern, based on an elasto-viscoplastic creep constitutive model is conducted to predict the behavior of surrounding rock salt. The prediction of the rock salt cavity behavior in the computational model relies mainly on the governing constitutive model. Therefore, the mechanical properties of rock salt media play a key role in the numerical design, but determining their values is based on rare test data sets. Moreover, the natural variability of rock salt in the field, accessibility, difficulties to run in-situ experiments, and lack of adequate experimental set ups for conducting full-scale tests result in significant levels of uncertainties. Therefore, utilizing probabilistic approaches developed in Wang (2011), Mollon et al. (2013) and Phoon & Ching (2014) seems a necessity. In this context, the contributed parameters of the governing constitutive model are considered as random variables with predefined statistical measures. This study describes the methodology of conducting subset simulation in Sec 2. A modified and efficient version of Metropolis-Hastings method is also presented in this section. After a brief description of the numerical simulation model of a rock salt cavern in Sec. 3, the employed constitutive model and the statistical measures of governing input variables are introduced. Sec. 3 follows with presenting the results of conducting subset simulation. The article is ended with conclusions in Sec. 4. 2 2.1

METHODOLOGY Reliability analysis

Reliability analysis evaluates the likelihood of contravening the system stability or functionality criteria. In reliability analysis, the space of the system response is divided into failure and safe regions (Tang et al. 1976). These regions are separated by the limit state surface, Gx = 0. With a given performance function Gx , the failure event is defined as

Subsequently, the failure probability is computed by

where fX (x)dx is the joint probability density function of X (the vector of variables). In order to solve the integral in Eq. 2, many mathematical techniques have been proposed in the literature. These methods can be classified into two main categories on the basis of their underlying approaches, namely analytical approximation (e.g., direct integration method, Gaussian approximation, perturbation, first/second – order reliability or Taylor series methods) and stochastic (e.g., importance sampling and MCS-based). For more details about these methodologies, see Ang & Tang (2007) and Au & Wang (2014). Nevertheless, despite the employed mathematical approach i.e., deterministic or stochastic, the involved computational effort grows drastically when the failure event corresponds with small probability.

2.2

Subset simulation approach

Direct Monte Carlo which uses statistical averaging over random samples generated from the probability density function of the parameters to evaluate PF , is a well-known and robust procedure to address every complex model. It is employed widely in the geotechnical field to conduct reliability analyzes, (Tang et al. 1976, Phoon and Ching 2014, Miro et al. 2015). However, since the number of the numerical simulation runs required to achieve a given probability of failure (pF ) is proportional to 1/pF , for a small probability failure a huge number of numerical simulations is needed. Subset simulation is an advanced MCS method that combines conditional probability and Markov chain Monte Carlo (MCMC) method to calculate small values of probabilities by a few number of the deterministic model executions. This methodology was developed by Au & Beck (2001). Subset simulation method is based on a simple idea that the failure probability of a rare event can be represented as the products of a number of more likely conditional failure probabilities. Different steps of conducting subset simulation method, presented by Au & Wang (2014), are illustrated in Fig. 1. Consider a failure event F defined by the condition Gx ≤ 0, where Gx is the performance function, and let s1 , . . . , sm , . . . , sZ be a sample of Z realizations of a vector s, where s is composed of K random variables. In the subset simulation method, the space of uncertain parameters is divided into l levels with an equal number of Zs realizations (s1 , . . . , sm , . . . , sZs ) in each level. A sequence of nested failure regions F1 , . . . , Fj , . . . , Fl of decreasing size are defined where F1 ⊃ . . . ⊃ Fj ⊃ . . . ⊃ Fl = F. An intermediate failure region, Fj can be defined by G < yj , where yj is an intermediate failure threshold whose value is larger than zero. Thus, there is a decreasing sequence

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Figure 2. Flowchart of modified metropolis-hastings sampling method.

value of the prescribed value of nth component in the ascending order, Figure 1. Flowchart of subset simulation method.

of positive failure thresholds y1 , . . . , yj , . . . , yl corresponding to F1 , . . . , Fj , . . . , Fl , respectively. It should be noted that, y1 > . . . > yj > . . . > yl = 0. An intermediate level, j contains a safe region and a failure region defined with respect to a given failure threshold yj . The failure probability corresponding to the intermediate level of j is calculated by

here IFj (sm ) is a non-negative scalar function, which is equal to one if the system output, related to the vector of sm , is located in the failure region with respect to Fj , otherwise IFj (sm ) = 0. The first Zs realizations are generated using MCS methodology according to a target PDF. In order to compute the failure probability in this study, a same prescribed conditional failure probability P(Fj+1 |Fj ) is considered for all levels and yj in each level is evaluated, separately. In the following, the value of performance functions for each sample are calculated and sorted in an ascending order. Subsequently, the ratio between the number of realizations for which G < yj and the number of samples Zs is equal to the prescribed value of the conditional failure probability, yj will be the intermediate threshold (Ahmed and Soubra 2012). In other words, yj is equal to the

In the next step, the parameter sets corresponding to those Zs × P(Fj+1 |Fj ) realizations, which are located in the failure zone of Fj , are used as seeds in MCMC analysis. Seeds generate Zs new samples for the next level of subset simulation. This procedure to generate new levels of intermediate failure regions is repeated up to reaching yj ≤ 0. The failure probability of the failure region F, denoted as PF , is calculated from the sequence of conditional failure probabilities

where l is the number of levels required to reach the limit state surface. 2.2.1 Modified metropolis-hastings Markov chain Monte Carlo methodology generates efficient random samples according to an arbitrarily given probability distribution. This method has been utilized in statistical estimation problems, like Bayesian system identification or rare events simulations. One of the well-known algorithms to carry out MCMC methodology is Metropolis-Hastings (Metropolis et al. 1953, Hastings 1970). This algorithm proceeds by generating new sequences of the

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Markov chain from a proposal distribution conditional (q(.|x(h) )) on the current samples x(h) . Then, it accepts or rejects these new samples with a certain acceptance probability which is based on the current and the proposed state. Fig. 2 shows the steps of a modified Metropolis-Hastings algorithm, proposed by Santoso et al. (2011). In order to obtain the next sample x(h+1) from x(h) , a candidate sample x(∗) from a proposal PDF is generated, firstly. Then, B factor is calculated,

3.2 Material model Since the stress-strain response of rock salt is governed by its mechanical properties, the numerical analysis should be based on an appropriate constitutive model. In this paper, an elasto-viscoplastic creep model is employed to describe the time-dependent behavior of rock salt considering dilatation and creep behavior. Under the small strain assumptions, the total strain rate is defined using the equation below,

If B ≤ 1, then x(h+1) = x(∗) , otherwise the first step is repeated to generate a new candidate. Afterward, G(x(h+1) ), i.e., the performance function for x(h+1) is evaluated. In case G(x(h+1) ) < yj , which means x(h+1) is located in Fj domain, x(∗) is accepted as the new sample. Otherwise, x(∗) is rejected and x(h+1) = x(h) . According to the suggestion made by Santoso et al. (2011), in this study, the target probability distribution is assumed to be Gaussian and the proposal PDF was chosen to be uniform.

The elastic strain rate, ε˙ el is defined using the generalized Hooke’s law. The viscoplastic component of strain rate, ε˙ vp is described by utilizing a nonassociated flow rule, which has been developed by Desai & Varadarajan (1987) based on the viscoplastic model of Perzyna (1966). The creep strain rate, ε˙ cr ij which represents the steady state creep behaviour of the rock salt is defined on the basis of the viscosity of Maxwell model (stress-dependent) which controls the steady state strain rate of the model (Heusermann et al. 2003).This constitutive model is developed by the authors and explained in detail in a companion paper.

3

3.3 Random variables

3.1

EXAMPLE ANALYSIS Deterministic numerical model

Figure 3 shows a typical geological profile of a rock salt strata where a storage cavern may be excavated. The rock mass is idealized by dividing it into two homogeneous layers, i.e. rock salt and cap rock. In this work, the depth of cavern’s roof is assumed to be equal to 800 m. The non-saline material above the rock salt formation, i.e. cap rock with a specific weight of γcr = 21 KN/m3 , simulated as a uniform load at the top of the rock salt column. The shape of the cavity after excavation is considered as a cylinder with a height of 233 m and a diameter of 75 m. Fig. 3 illustrates the geometry, boundary conditions and discretized finite element mesh of this cavern. More details about this simulation are presented by the authors in (Khaledi et al. 2016). In order to model the solution mining procedure, the whole excavation and debrining process are simplified by reducing the internal pressure of cavern in a time duration about three and a half years. To accomplish this, the geostatic stress, which is assumed to be initial stress condition, is reduced gradually to the maximum internal pressure of the cavern. The stored gas is also simulated by applying the equivalent internal pressure to the cavern’s boundary. The operation protocol is assumed to be cyclic (one cycle per day). Hence, the internal pressure of the cavity after excavation is set to 10 MPa, afterward it decreased to 7 MPa during 12 hours, and then it is kept constant for 12 hours. The cyclic loading simulation is followed by raising the internal pressure gradually to 10 MPa within 12 hours time interval. In this study, 100 cycles of charging/discharging the cavern are simulated.

In order to conduct reliability analysis, the statistical measures of the relevant uncertainties should be identified for each input parameter. The uncertain input variables are characterized by their statistical moments, e.g., the mean value and standard deviation, besides their relevant probability density functions. Based on the results of a conducted and documented sensitivity analysis by the authors in a companion paper, six mentioned parameters in the Table 1 have the most influence on the outputs variability. All the regarded uncertain parameters are assumed to vary between upper and lower bounds according to their statistical measures. The minimum and maximum values of the uncertain parameters are chosen based on former experiences (Hansen et al. 1984, Desai and Zhang 1987, Sane et al. 2008, Guo et al. 2012, Heusermann et al. 2003) and engineering judgment. It should be noted that the probability distribution of the input variables is assumed to be in accordance with a Gaussian distribution, the most common distribution encountered in engineering applications. 3.4 Failure criteria The deviatoric stress, which can be induced by different internal pressures and in-situ stresses of the rock around the cavities, leads to creep deformation and dilatant behavior, as well (Cristescu & Hunsche 1998). Because of dilatation, the mechanical properties of the host rock can change drastically, which may initiate micro cracks. In some cases, a micro crack network can provide possible path ways for the stored product in the cavity to mitigate out. Therefore, the dilatant zone in the rock surrounding the cavern should be avoided.

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Figure 3. Representative stratigraphy of salt deposit (a), geometry and boundary conditions of the salt cavern model (b). Table 1. Statistical characteristics of material parameters. Parameter

Description

Dimension

Boundaries

COV (%)

E N a1 γ η η∗M

Elastic modulus Flow exponent Hardening parameter Ultimate parameter Hardening parameter Maxwell coefficient

MPa [-] [-] [-] [-] MPa s

[19000 , 25000] [2.4 , 3.5] [0.3e−4 , 0.35e−3] [0.085 , 0.11] [0.7 , 0.9] [1e12 , 3e12]

10 5 5 5 5 10

The mathematical formulation of dilatancy boundary which determines the dilatancy domain in the stress space entitled as compression/dilatancy (C/D) boundary. Those loading conditions leading the stress state to locate above the C/D line (namely dilatant zone) is regarded as unsafe states, thereupon the C/D line is considered as the failure criterion. Over the years, various constitutive models based on various empirical investigations or different rheological models, define slightly different C/D boundaries (Mahmoudi et al. 2015). In this study, Desai dilatancy boundary (Desai and Zhang 1987) is employed. To investigate the occurrence of dilatancy around the cavern, the second variant of the stress state of the surrounding rock salt is evaluated to define a quantity as degree of utilization (DoU ), based on Bond & Harris (2008) and DIN 1054:2003-01,

√ J2 is the value of the second invariant of deviatoric stress. If DoU , transcended one it corresponds to accordance of dilatancy around the cavern. As previously mentioned, the model response space is separated through the limit state surface, into safe and failure regions. In this study Gx , the performance function, is related to no dilation failure criterion. Based on that, the following function is defined,

In Eq. 9, Gs is the performance function related to the degree of utilization against dilatation, the subscripts u and s indicate ultimate resistance and calculated values of the system, respectively. 3.5


here, J2dil indicates the distance of the CC/D boundary from the isotropic condition in π-plane and

Results

In the following, results of conducting subset simulation method to evaluate the failure probability of the above mentioned rock salt cavern are presented. Firstly, the required number of model evaluations in each level is determined. Afterward, a comparative

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Figure 4. Coefficient of variation of failure probability versus the number of samples generated per level.

study is conducted in order to verify the obtained outcomes by subset simulation. 3.5.1 Sufficient number of model evaluation As we consider the intermediate failure P(Fj+1 |Fj ) amount in all intermediate levels to be the same, the corresponding intermediate thresholds depend on the generated conditional samples and vary in different runs. To ensure that the variations in the sample sets make no significant differences in the obtained value of PF , the coefficient of variation of the probability failure value (denoted as COVPF ) can be a proper measure of how accurate is the conducted analysis. For more details about the procedure of evaluating COVPF , see Au and Beck (2001). In order to obtain the optimal number of required sample sizes, different Zs are applied to calculate the probability of failure, and for each case, the COVPF is computed. Fig. 4 represents the considered number of realizations in each level of subset simulation versus its corresponding COVPF . It demonstrates the dependency of the coefficient of variation of PF on the number of samples. Based on this figure, raising Zs from 1000 to 4000 makes no important change in the COVPF , thereupon, the number of samples per level in the present study is chosen to be equal to 1000. 3.5.2 Validation by comparing with MCS method The efficiency of subset simulation methodology is examined by comparing its results with the estimated PF s using an MCS-based analysis. The failure probability of the rock salt cavern’s vicinity, considering no-dilation criteria, is calculated by conducting both methodologies. The comparison here is conducted for a point located on the bottom of the cavern, and the failure probability is computed against several prescribed DoUu . Fig. 5 illustrates the obtained results, where in the MCS-based approach 100,000 samples are used. In subset simulation method the corresponding PF is estimated by generating samples through three levels of

Figure 5. Comparison between the obtained PF computed by applying MCS and subset simulation on the bottom of cavern.

intermediate failure probabilities. Thereupon, the final PF s are calculated by subset simulation using 3,000 realizations. These results show that, although the computational burden required in subset simulation approach is significantly less compared to MCS, the differences between the obtained PF s are negligible.

4

CONCLUSIONS

This paper presents a computationally affordable reliability analysis method, called as subset simulation. Subset simulation can address small probabilities encountered in the practical reliability assessment of complex systems which calculating them with classical MCS-based methods is computationally expensive. A modified Metropolis-Hasting approach is employed to generate adaptive samples in a sequences of failure regions. Moreover, reliability-based analysis is conducted on a typical renewable energy storage cavern in rock salt. In this regards, constitutive parameters are represented as random variables and the probability of failure in the stability of system is evaluated considering no dilation criterion. Afterward, the efficiency and accuracy of subset simulation was justified by conducting a comparative calculation. It should be noted that this case study is a synthetic one, nevertheless, the proposed method can be applied analogously to realistic problems. REFERENCES Ahmed, A. & A.-H. Soubra (2012). Extension of subset simulation approach for uncertainty propagation and global sensitivity analysis. Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 6(3), 162 – 176.

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Ang, A. H.-S. & W. H. Tang (2007). Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering, 2nd Edition. John Wiley & Sons Ltd. Au, S.-K. & J. L. Beck (2001). Estimation of small failure probabilities in high dimensions by subset simulation. Probabilistic Engineering Mechanics 16, 263–277. Au, S.-K. & Y. Wang (2014). Engineering risk assessment with subset simulation. John Wiley & Sons Ltd. Berést, P. & B. Brouard (2003). Safety of salt caverns used for underground storage. Oil & Gas Science and Technology 58, 361–384. Bond, A. & A. Harris (2008). Decoding Eurocode 7. Taylor & Francis. Cristescu, N. & U. Hunsche (1998). Time Effects in Rock Mechanics. John Wiley & Sons Ltd. Desai, C. & A. Varadarajan (1987). A constitutive model for quasi-static behavior of rock salt. J. Geophys. Res 92, 445– 456. Desai, C. & D. Zhang (1987). Viscoplastic model for geologic material with generalized flow rule. Int. J. numer. Anal. Met 11, 603–627. Guo, Y., C. Yang, & H. Mao (2012). Mechanical properties of jintan rock salt undercomplex stress paths. Int. J. Rock. Mech. Min 56, 54–61. Hansen, F. D., K. D. Mellegard, & P. E. Senseny (1984). Elasticity and strength of ten natural rock salts. In H. R. J. Hardy and M. Langer (Eds.), The Mechanical Behavior of Salt,Proc. of the First Conferenc, pp. 53–70. Hastings, W. K. (1970). Monte carlo sampling methods using markov chains and their applications. Biometrika 57, 97–109. Heusermann, S., O. Rolfs, & U. Schmidt (2003). Nonlinear finite element analysis of solution mined storage caverns in rock salt using the lubby2 constitutive model. Computers and structures journal 81, 629–638. Khaledi, K., E. Mahmoudi, M. Datcheva, D. König, & T. Schanz (2016). Sensitivity analysis and parameter identification of a time dependent constitutive model for rock

salt. Journal of Computational and Applied Mathematics 293, 128–138. Mahmoudi, E., K. Khaledi, D. König, & T. Schanz (2015). Numerical simulation of deep and shallow energy storage systems in rock salt. In T. Schanz and A. Hettler (Eds.), Aktuelle Forschung in der Bodenmechanik 2015, pp. 69–83. Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, & E. Teller (1953). Equation of state calculations by fast computing machines. The Journal of Chemical Physics 21, 1087–1092. Miro, S., M. König, D. Hartmann, & T. Schanz (2015). A probabilistic analysis of subsoil parameters uncertainty impacts on tunnel-induced ground movements with a back-analysis study. Computers and Geotechnics 68, 38–53. Mollon, G., D. Dias, & A.-H. Soubra (2013). Range of the safe retaining pressures of a pressurized tunnel face by a probabilistic approach. Journal of Geotechnical and Geoenvironmental Engineering 139, 1954–1967. Perzyna, P. (1966). Fundamental problems in viscoplasticity. Rec. Adv. Appl. Mech 9, 243–377. Phoon, K.-K. & J. Ching (2014). Risk and Reliability in Geotechnical Engineering. CRC Press. Sane, S., C. Desai, J. Jenson, D. Contractor, A. Carlson, & P. Clark (2008). Disturbed state constitutive modeling of two pleistocene tills. Quaternary Science Reviews 27, 267–283. Santoso, A., K. Phoon, & S. Quek (2011). Modified metropolishastings algorithm with reduced chain correlation for efficient subset simulation. Probabilistic Engineering Mechanics 26, 331–341. Tang, W. H., M. S. Yucemen, & A. H. S. Ang (1976). Probability based short-term design of slope. Canadian Geotechnical Journal 13, 201–215. Wang, Y. (2011). Reliability based design of spread soundations by monte carlo simulations. Geotechnics 61, 677–685.

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Effect of degree of saturation on thermal conductivity of CLSM used for a horizontal ground coupled heat pump system T.M. Do, Y.S. Kim, C.H. Lee & M.Q. Dang Department of Civil and Environmental Engineering, Chonnam National University, South Korea

ABSTRACT: The aim of this paper is to investigate the effect of degree of saturation on thermal conductivity of coal ash based CLSM for an use as backfill material of a Horizontal Ground Coupled Heat Pump system (HGCHP). Initially, a family of coal ash based CLSM mixtures with a variable range of water to binder (W/B) and water to solid (W/S) ratios, different kinds of binders (e.g., cement and Cementless Binder (CB)) were systematically tested in accordance with applicable ASTM Standards to determine general properties of CLSM including bleeding, flowability, fresh unit weight, initial setting time, and unconfined compressive strength. Subsequently, thermal conductivity was measured by using thermal needle probe conforming ASTM D 5334 at various degrees of saturation of CLSM specimens.As a result, the general engineering properties of coal ash based CLSM satisfied the specification of ACI 229R. In addition, a sensitive relationship between degree of saturation and thermal conductivity of prepared CLSM mixtures was achieved, the higher the degree of saturation, the higher the thermal conductivity. This finding is very important when determining a proper thermal conductivity with respect to various degrees of saturation to play a significant role in achieving optimum performance and full potential toward the use of the given CLSM mixtures as a backfill for trenches of HGCHP. Finally, a thermal conductivity prediction equation was proposed as a function of degree of saturation, thermal conductivity under fully saturated and dry states.

1

INTRODUCTION

Based on the standpoint that the warm earth and groundwater below the surface provides a free renewable source of energy year-round to heat and cool an average suburban residential home, Ground-Source Heat Pump (GSHP) systems, transforming this Earth Energy into useful energy to heat and cool buildings, have progressively been evolved in Korea. Significant energy savings can be achieved through the use of GSHPs in place of conventional air-conditioning systems and air-source heat pumps. In general, GSHP systems exchange heat with the ground, often by means of GCHP that use the ground as a heat source and sink, either with vertical or horizontal ground heat exchangers. In these systems, a backfill material is used to fill up as well as provide heat transfer medium between heat exchanger and surrounding ground (e.g., soils or rocks) and also control groundwater movement to prevent contamination of water supply. For that purpose, it is ideal to apply Controlled Low Strength Material (CLSM) as a backfill material to oppose the use of conventional grouts. Meanwhile, with a generation of 3,245 MW thermal power plants every year, large quantities of coal ashes are being produced during incineration and stored at Honam area in Korea. The disposal of these wastes will be a big challenge in the near future for Korea to decrease harmful environmental effects. Interestingly, CLSM can use

these coal ashes as their mixture components. The American Concrete Institute (ACI) defines a CLSM as a self-leveling, self-compacting, and cementitious material primarily used to replace conventional backfill soil and structural fillings that result in unconfined compressive strengths of 1,200 psi (8.3 MPa) or less (ACI 229R, 1999). CLSM should not be considered as a type of low-strength concrete, but rather as a structural backfill. CLSM is known by many different names such as flowable fill, controlled density fill, unshrinkable fill, flowable mortar, soil-cement slurry, and plastic soil-cement. There are various inherent advantages of using CLSM instead of compacted fill in these applications. These benefits include reduced labor and equipment costs (due to self-leveling properties and no need for compaction), faster construction, and the ability to place material in confined spaces (ACI 229R, 1999). If future excavation is anticipated, the maximum long-term compressive strength should generally be less than 2.1 MPa (i.e., general fill) (ACI 229R, 1999). It is advantageous due to the relatively low strength itself of CLSM. Another advantage of CLSM is that it possibly contains by-product materials, thereby reducing the demand on landfills, where these materials may otherwise be deposited and contributing towards the sustainable development (Razak et al., 2009). During the past decade, several successful applications of coal ashes in CLSM have been reported (Gabr and Bowders, 2002; Lee et al., 2013; Katz

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and Kovler, 2004). Other industrial by-products have been used in CLSM production such as foundry sand (Siddique and Noumowe, 2008) blast furnace slag (Muhmood et al., 2009) and others. The most common ones of these studies are the ones that consider the recycled and by-product materials as ingredients for a production of CLSM. However, thermal conductivity of CLSM under various degrees of saturation has never been closely evaluated in the literature. In addition, from a standpoint of economics and sustainable development, it has been a trend of CLSM production without using cement since the production of Portland cement not only consumes limestone, clay, coal, and electricity, but also releases waste gases such as CO2 , SO3 , and NOx . In Korea, cementless binder (CB) which is manufactured with granulated blast-furnace slag and other alkali activators is a new alternative material to cement for the production of CLSM (Mun et al., 2007). The reactions of pozzolanic materials (e.g., fly ash and ponded ash in CLSM mixture) and slag coupled with some activators in CB are believed to help in hardening and strength development of CLSM. Since the HGCHP is often less expensive to install than the vertical one, but requires a larger land area, it can be preferably used in Honam area for residential and small commercial buildings. In this study, CLSM made with coal ashes and cementless binder was considered to be used as a backfill material for the HGCHP. Moreover, due to the fact that direct measurement thermal conductivity of this material under various degrees of saturation is practically impossible, the evaluation of effect of degree of saturation on thermal conductivity of CLSM plays a key role to the efficiency maintenance of the HGCHP systems. 2

EXPERIMENTAL STUDY

2.1 Materials Conventional CLSM mixtures usually consist of water, Portland cement, fly ash and aggregates (ACI 229R 1999). Fine aggregate is considered as a material with particles in a size range from 4.75 mm (No. 4 sieve) to 0.075 mm (No. 200 sieve), commonly up to 80– 85% (ACI 229R, 1999). In the present study, ponded ash originated from cogeneration plants in Honam area was used as a fine aggregate in a production of CLSM. Ponded ash was first dried in an oven at 105◦ C until constant mass, and then sieved through a 9.52 mm size sieve to eliminate unnecessary large particles and approach the particle size of natural fine aggregates. The physical properties of ponded ash are detailed in Table 1. The particle size distribution curve of ponded ash is shown in Fig. 1. Ponded ash was classified as a poorly graded sand (SP) based on Unified Soil Classification System (USCS) (ATSM D2487 2004) with the classification parameters of Cu (20.25), Cc (0.94). The fineness modulus of ponded ash was 3.37. In addition to fine aggregate, other ingredients such as cement, supplementary cementitious materials and water are

Figure 1. Particle size distribution of ponded ash. Table 1. Physical properties of ponded ash. Properties

Ponded ash

Maximum dry density (kg/m3 ) Optimum Moisture Content (OMC) (%) Natural water content (%) Specific gravity Water absorption (%) Fineness modulus Particles 50 Hz). Based on the observations in Bantaki tunnel, Sakurai (2014) and Uenishi (2012) recommended that more attention be given to detection of such very high frequency waves and to account for them during seismic analyses of structures. The 1995 Kobe earthquake did have a very strong vertical component compared to other earthquakes observed previously in the area as shown in Figure 12 and Figure 13. Figure 12 shows the horizontal and vertical components of acceleration time history recorded at Kobe University (PEER, 2015). The average shear wave velocity for the top 30 m at the site is > 1000 m/s, so site amplification effects appear to be negligible. Figure 13 shows the amplitude spectrum for the horizontal and vertical components, showing high energy content up to 10 Hz in vertical component. While it is possible that very high frequency waves (50 Hz) were generated by a smaller event in the fractured region in close proximity to the tunnel; triggered by the incoming ground motion from the main event; the authors are skeptical that these very high frequency

Figure 13. Amplitude spectra for the acceleration vs time histories from the 1995 Kobe earthquake recorded at Kobe University. The horizontal component is shown on the top and the vertical component on the bottom.

components originated from the main event and travelled more than 30 km (the distance of Bantaki tunnel from epicenter) without significant attenuation. The analyses by Uenishi (2012), which relates the amplification in hoop stress at the spring line of the support (i.e. the dynamic hoop stress at the spring line normalized by the stress amplitude of the incoming wave) as a function of (λ/a), [i.e. wavelength of the incoming wave normalized by tunnel radius] indicates that P-waves with λ/a = 50 result in a higher stress amplification at the spring line than λ/a = 10. For an inner radius of 4 m and P-wave velocity of 2000 m/s, λ/a = 50 corresponds to a frequency of 10 Hz, which was indeed observed in the vertical component of the incoming motion.

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The higher frequency (50 Hz) P-waves were used to explain the damage to the base slab only. Uenishi (2012) used radial particle velocity induced by the P-waves and compared the difference in peak velocity at the crown and invert of the tunnel – with significant difference indicative of base slab damage. However, this is not the right criterion and contradicts the evidence that damage was observed only to the base slab, while both the invert and the crown remained undamaged. In fact, significant vertical acceleration (even low frequency) in the downward direction would detach the slab from the liner (because the liner is constrained to move with the rock but the slab is not) and very high frequencies (50 Hz) are not needed to explain the damage observed. A simple 2D numerical simulation has been carried out using FLAC (Itasca, 2011) to evaluate the dynamic hoop stresses introduced by the vertical component of the recorded ground motion. The model consists of the 10 m diameter tunnel with a liner thickness of 0.65 m and an overburden of 200 m. The rock is assumed to have a P-wave velocity of 2000 m/s, and a stiffness of 40 GPa is used for the concrete liner. The vertical component of ground motion is divided by a factor of two to estimate the incoming motion (upward traveling wave) which is applied at the base of the model. The maximum hoop stress resulting from the axial forces along the liner is monitored and presented as a function of angle as shown in Figure 14. The results indicate that compressive stresses, up to 4.3 MPa, were generated at the spring line due to the dynamic shaking. These stresses are in addition to those from the static loading of the liner. Keeping in mind that the unconfined compressive strength of concrete is around 25-30 MPa, the seismically induced stresses due to this vertical component are very high, even without accounting for any energy in the very high frequency domain. The compressive stresses from dynamic loading calculated above do not account for other amplification mechanisms. The most important is the amplification of ground motions due to topographic effects and presence of discontinuities and stiffness contrast. A numerical simulation to evaluate this effect is carried out as shown in Figure 15. The surrounding rock mass (granite) is assumed to have a P-wave velocity of 4000 m/s and S-wave velocity of 2000 m/s whereas the fractured region has a P-wave velocity of 2000 m/s and S-wave velocity of 1000 m/s. Both horizontal and vertical components of ground motion are applied at the base of the model and amplification factors for peak velocity are calculated along the entire region for both horizontal (Figure 16) and vertical (Figure 17) components. Note that for level ground with uniform properties, an amplification factor of 2 at the surface is expected due to free surface amplification as discussed earlier in this paper. Factors greater than two observed here are a result of (a) topographic amplification as the hill geometry tends to focus the incoming seismic energy, resulting in amplification of the motion; (b) the presence of the

Figure 14. Numerical model showing the tunnel and liner (top) and seismic motion induced maximum hoop stresses as a function of location (bottom).

Figure 15. Numerical model for the Bantaki tunnel site showing the fractured region, tunnel alignment and location of the observed failure.

fractured region tends to trap the seismic waves. The results show that while the horizontal component is not affected much by the fractured region, high amplification of the vertical component is observed in the fractured region, with amplification factors as high as 2.5 observed close to the failure location (marked on the plots). For comparison, an amplification factor of 1.7 was observed at the tunnel location for level ground and no stiffness contrast used in the analyses to calculate the compressive stresses in the liner. This additional amplification of the vertical component would lead to even higher dynamically induced compressive stresses in the liner and combined with higher dynamic stress amplification observed for the liner in fractured (lower stiffness) rock compared to good quality (high stiffness) rock by Uenishi (2012), would explain the failure observed at the spring line only along the portion of the tunnel in the fractured region. The above example shows that it is important to avoid such regions of fractured rock resulting in stiffness contrast especially in hill type geometries

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groundwater level and/or low permeability rock are also valuable attributes of a site – to minimize pumping requirements for the facility. 6

Figure 16. Amplification factors for peak ground velocity (m/s) in the horizontal direction. The Bantaki tunnel alignment and the failure location are also shown.

Figure 17. Amplification factors for peak ground velocity (m/s) in vertical direction. The alignment for Bantaki tunnel and failure location are also shown.

when seating underground nuclear reactors, as these conditions increase the potential for damage during a seismic event. However, it should be noted that, despite such strong shaking and unfavorable geological and topographic conditions, the damage observed in the Bantaki tunnel was still much smaller than the damage observed in the above-ground structures during the 1995 Kobe earthquake. This reinforces the point that underground structures in rock are safer than aboveground structures during earthquakes. Furthermore, the example illustrates how numerical analyses can aid in the selection of site locations for UNPPs by identifying potentially problematic regions through consideration of the site geology and material properties. 5

SOME GENERAL CONSIDERATIONS RE SITING OF UNDERGROUND NUCLEAR POWER PLANTS

For situations where it is necessary to locate underground nuclear power plants close to the ocean, it is preferable that the surface access to the plant be at an elevation of the order of 50m or more, and that this access be equipped with bulkheads that can be activated rapidly in the event of a major earthquake. The underground plant should be located in competent rock. A main advantage of the underground location is the ability to reduce inertial loading of the reactor by lateral support and embedment. This can be accomplished at any depth in the rock, indicating that the reactor can be as shallow as considered desirable, provided there is a minimum cover of 25 m below surface-in order to meet containment requirements comparable to a typical surface design. A low

CONCLUSIONS

Underground location has significant safety benefits compared to surface placement for a variety of commercial and industrial applications. This paper focuses on the benefits of underground siting of nuclear power plants, with emphasis on protection from earthquakes.Although the most established source of ‘green energy’, public opposition to use of nuclear power has intensified, especially in seismically active regions of the world, as a result of the very serious accident at Fukushima, Japan, in 2011 resulting from the major earthquake (Mw = 6.6) and associated tsunami. Several underground nuclear plants have been constructed and operated, but there is no known record of such a plant having been subject to a damaging earthquake. There is evidence that shallow underground structures e.g. subway transit systems, perform significantly better than surface facilities during severe earthquakes. Numerical modeling techniques are now available that can provide valuable assessments of the dynamic response of underground facilities (e.g. mines, nuclear waste repositories.) and can provide valuable insights on the influence of local topography and geology in siting considerations. Although the numerical analyses carried out in this paper are highly simplified, they serve to illustrate the benefits of the location and provide an instructive qualitative comparison of different underground configurations. It is seen that peak ground accelerations are reduced compared to those at the ground surface. Unlike surface facilities, excavations are not free-standing structures, and so experience lower inertial forces. Reactors – especially modular units- can be laterally supported to the wall of the excavation or embedded in concrete, reducing forces and bending moments considerably, resulting in a robust seismic design. More detailed and sophisticated numerical modeling efforts can be conducted to better quantify these advantages for specific underground locations and designs. REFERENCES Damjanac. B, Board M., Lin M., Kicker D. & Leem J. 2007. Mechanical degradation of emplacement drifts at Yucca Mountain – A modeling case study. Part II: Lithophysal rock. Int. J. Rock Mech. & Mining Sci., 44: 368–399 Duffaut, P. and Vaskou, P. 2014. Geological and Geographical Criteria for Underground Siting of Nuclear Reactors, 8th Asian Rock Mech. Symp. Sapporo, Japan Giraud, K. M., Kunze J F., Mahar J. M. & Myers C.W. 2009. Cost Advantages of Large Underground Nuclear Power Parks, American Nuclear Society, Annual Meeting, Atlanta, GA, June 14–18, 2009.

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Itasca Consulting Group, Inc. 2011. FLAC (Fast Lagrangian Analysis of Continua), Version 7.0. Minneapolis: Itasca. Kolsky, H. 1963. Stress Waves in Solids. Dover (New York) 213p. (See p.89) Lin. M, Kicker D., Damjanac B. & Karakozian M. 2007. Mechanical degradation of emplacement drifts at Yucca Mountain – A modeling case study. Part I: Nonlithophysal rock. Int. J. Rock Mech. & Mining Sci., 44: 351–367. Giraud, K. M., Kunze J F., Mahar J. M. & Myers C.W. 2009. Cost Advantages of Large Underground Nuclear Power Parks, American Nuclear Society, Annual Meeting, Atlanta, GA, June 14–18, 2009. Myers,W. and Elkins N. 2004. Siting Nuclear Power Plants Underground: Old Idea, New Circumstances, Nuclear News, 47(3): 33–38. Myers, C.W. & Mahar J.M. 2011. Underground Siting of Small Modular Reactors: Rationale, Concepts, and Applications. ASME Small Modular Reactor Symposium September 28–30, 2011 Washington, DC. USA Neretnieks, I. 1980. Safety Tunnel for Core Melting In Nuclear Power Plants Underground Space, Pergamon, Oxford. 1: 179–180 [See also Neretnieks, I. and Nykvist B. 1978. Nägra möjligheter till konsekvenslindring vid härdsmältning; Some possibilities to decrease the consequences of a core melt; written in Swedish; Dept. of Chemical Engineering. Royal Institute of Technology, Stockholm.] Pacific Earthquake Engineering Research Center. 2015 PEER Ground Motion Database http://ngawest2.berkeley. edu/ Ragheb, M. 2015. Inherently Safe Reactor Designs. Univ. Illinois, Urbana–Champaign, USA Sakharov Andrei. 1990. Memoirs, Random House, USA 773p. Quoted in W. Myers and N. Elkins. 2004. Underground Nuclear Parks and the Continental SuperGrid (Los Alamos Nat’l Lab.) SuperGrid 2 Conference, University of Illinois at Urbana-Champaign, Oct. 25–27, 2004. [A similar opinion by Edward Teller is also quoted.]

Sakurai, S. 2014. Case Studies on the Dynamic Behavior of Tunnels Caused by Hyogoken–Nanbu Earthquake, Whose Epicenter was Very Close to the Tunnels. Proc. 8th Asian Rock Mechanics Symposium ARMS8 14–16 October 2014, Sapporo, Japan. Socolow, R. & Glaser A. 2009. Balancing risks: nuclear energy & climate change; Daedalus, Amer. Acad. Arts & Sci. Fall 2009, 138(4): 31–44. Uenishi, K. 2012. Elastodynamic Analysis of Underground Structural Failures Induced by Seismic Body Waves J. Appl. Mech 79(3), 031014 (Apr 05, 2012) Watson, M.B., Kammer.W.A. 1972. Underground nuclear power plant siting. E.Q.L. Report No.6 Environmental Quality Laboratory, California Institute of Technology, Pasadena, CA. 91109, Sept 1972, 150pp. WEB REFERENCES. WR1. http://www.nei.org/Knowledge-Center/NuclearStatistics/World-Statistics WR2. http://www.nrc.gov/reading-rm/doc-collections/ factsheets/3mile -isle .html Note “the small radioactive releases had no detectable health effects on plant workers or the public.” WR3. https://en.wikipedia.org/wiki/Chernobyl_disaster WR4. https:/ / en.twikipedia.org / wiki / Fukushima _ Daiichi_ nucleardisaster “The earthquake triggered a 13-to-15metre (43 to 49 ft) maximum height tsunami that arrived approximately 50 minutes later.” WR5. http://www.livescience.com/39110-japan-2011-earth quak e-tsunami-facts.html Note; “The tsunami waves reached run-up heights (how far the wave surges inland above sea level) of up to 128 feet (39 meters) at Miyako city and traveled inland as far as 6 miles (10 km) in Sendai.” WR6. http://www.nei.org/News-Media/News/Japan-NuclearUp date WR7. http://thesource.metro.net/2012/08/10/designing-asubwa y-to-withstand-an-earthquake/

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An analytical study of PRACLAY Heater test G.J. Chen European Underground Research Infrastructure For Nuclear Waste Disposal In Clay Environment (EURIDICE), Belgian Nuclear Research Center, Mol, Belgium

L. Yu Institute for Environment, Health, and Safety (EHS), Belgian Nuclear Research Center, Mol, Belgium

Xiang Ling Li European Underground Research Infrastructure For Nuclear Waste Disposal In Clay Environment (EURIDICE), Belgian Nuclear Research Center, Mol, Belgium

ABSTRACT: In the context of a large scale in-situ PRACLAY Heater test which is currently running at the HADES underground research facility (URF) in Mol, Belgium, an analytical solution is developed to study the Thermo-Hydro-Mechanical (THM) responses in the Boom Clay, backfilling sand and supporting liner around the heated PRACLAY gallery. After sufficient verification, the present solution is applied in the PRACLAY Heater test for a predictive reference calculation and a parametric sensitivity study. The new analytical solution proves to be a convenient tool for a good understanding of the resulting coupled THM behaviour and is therefore valuable for the interpretation of measured data in engineering practices and for a rational design of potential radioactive waste repositories.

1

INTRODUCTION

There is a general consensus that geological disposal is considered a possible solution for the long-term management of high-activity, long-lived radioactive waste (NEA, 2008). As a side effect of radioactive decay, a significant amount of heat is released even after several decades of cooling in surface facilities, which makes the host formation undergo significant temperature gradient, induce hydraulic PWP gradient and a change in effective stresses. The large scale PRACLAY Heater test is carried out in the HADES URL in Mol, Belgium with the purpose to simulate the thermal impact generated by heat-emitting high-level waste (HLW) on Boom Clay at a repository-representative configuration (Li et al. 2013, Van Marcke et al. 2013), and to directly gather knowledge of the THM response of the Boom Clay to complex loadings. The PRACLAY Heater test is hosted in the PRACLAY gallery (Figure 1), which has been established in the Boom Clay at 223 m depth. The PRACLAY gallery is a horizontal drift with a length of about 44 m, internal and external diameters of 1.9 and 2.5 m, respectively. A hydraulic seal was installed to separate the heated part (33 m) of the gallery from the nonheated part (10 m). Due to the restrictions of an in situ test compared to the real repository, the PRACLAY Heater test intends to reach the most critical thermal load in terms of maximum temperature as well as temperature gradient within a

Figure 1. Layout of the PRACLAY gallery.

period of time. Therefore, the gallery was backfilled with high-permeability sand which is required to be fully saturated before heating, and a target temperature of 80◦ C is decided at the interface between liner and host Boom Clay in the test for at least 10 years. After the pioneering consolidation theory (Biot 1956 & 1957, Rice and Cleary 1976), there exists a substantial and growing suite of analytical solutions to predict the change in stress and pore pressure induced by a thermal loading in a saturated poroelastic medium (Booker and Savvidou 1984 & 1985, Giraud and Rousset 1995, McTigue 1986, Savvidou and Booker 1989, Wang and Papamichos 1999), and in layered saturated poroelastic media (Small and Booker 1986, Giraud et al. 1998). In the context of PRACLAY Heater test, an analytical solution of the temperature, pore pressure, stress and displacement fields around an infinite-long cylindrical cavity is obtained with a time-dependent heat source applied in the cavity. The cavity is backfilled

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with saturated material, supported by casing or liner and hosted in a low-permeability geological formation. The analytical solution is formulated in Laplace domain, and results in real time space are obtained by numerical inversion. Since this analytical solution considers the plane strain condition, it is more representative for the middle cross-section of PRACLAY Heater test (Figure 1). The new solution is applied in PRACLAY Heater test for a predictive reference calculation, and the results are verified by numerical results obtained from the commercial finite element software COMSOL Multiphysics (COMSOL 2008). An extensive parametric study is performed for PRACLAY Heater test. Numerical analyses are essential in the whole process of PRACLAY Heater test, from test design, construction, predictions, risk analysis to data interpretations. Although numerical simulations based on finite element method play an important role, in parallel, (semi)-analytical solutions are necessary to provide confidence in the results, and further contribute to aspects such as code verification, model validation, process understanding with respect to coupling behaviour, and sensitivity and uncertainty analysis. The solution provided in this study solves the THM coupled problem in a semi-analytical manner, hence with a high computational efficiency. Temperature, pore water pressure, stress and displacement fields can be obtained at any time without the need for time-stepping algorithms which are encountered in numerical approaches. Therefore, analytical solutions are of great value in preliminary designs in which only a limited knowledge of the range of values associated with the material parameters is known (Selvadurai 2007). They can be used at this stage for quick order-of-magnitude estimates, for better understanding the physical phenomena involved, for scoping effects of parameter and boundary condition variabilities. Furthermore, due to the versatility of the solution derived in this paper, its application is not limited to nuclear waste disposal, and it can be applied in diverse areas related to energy geotechnics.

2 2.1

Figure 2. Problem geometry and materials.

conditions. The nature and geometry of the problem defined in Figure 2 indicate that the problem considered here possesses radial symmetry, and a cylindrical co-ordinate system (r, θ) is therefore used. The classic sign convention for poroelasticity is used in this study, in which the tensile stresses and strains are considered positive. 2.2 Balance equations The governing equations for non-isothermal consolidation in a linear poroelastic medium are formulated here in terms of three primary variables: temperature (T), pore water pressure (p) and radial displacement (u). For an infinitesimal element in homogeneous and isotropic, fully saturated porous medium with a connected pore structure, Biot formulations of the linear constitutive equations for an axisymmetric problem are expressed using incremental total stresses and pore water pressure as

SOLUTION FORMULATION Problem description

Consider a cylindrical cavity excavated or drilled in a deep geological formation, the geological formation occupies the region of b ≤ r ≤ ∞, and the cavity is backfilled after the ring-shaped liner/casing is installed in the region of a ≤ r ≤ b (Figure 2). The three materials are assumed to be saturated and behave as poroelastic media. An initially uniform radial stress σr0i , pore water pressure p0i and temperature T0i are assumed, with i = 1, 2, 3 denoting the backfill material, liner/casing and surrounding formation respectively in the rest of this paper. A heat flux F(t) is applied at the interface between the liner/casing and the backfill material. The problem is analyzed under plane strain

where σr , σθ , p and T denote increments of the total radial stress, total circumferential stress, pore water pressure and temperature respectively. They are expressed commonly as σr = σr − σr0i , σθ = σθ − σθ0i , p = p − p0i , T = T − T0i . εv is the volumetric strain equal to ∂u + ur , in which u denotes the radial ∂r displacement; αsi is the volumetric thermal expansion coefficient of the solid skeleton; Kbi is the bulk drained i (1+νi ) modulus of the porous medium, expressed as 2G ; 3(1−2νi ) Gi is the shear modulus and νi is the Poisson’s ratio; ξi is Biot’s coefficient and expressed as ξi = 1 − KKbisi where Ksi is the bulk modulus of the solid particles.

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Mass conservation of a compressible fluid phase yields the continuity equation

where ki is the conventional Darcy hydraulic conductivity of the porous medium; γl is the unit weight of 2 liquid phase; the operator ∇ 2 is expressed as ∂r∂ 2 + 1r ∂r∂ in polar coordinates for an axisymmetric problem; βli is the combined compressibility of the pore fluid and solid phase, also known as storage coefficient, defined as the volume change of the pore fluid per unit volume of porous medium as a result of a unit increase of pore i pressure and expressed as βli = Knlii + ξiK−n , where ni si is the porosity of the porous medium, Kli is the bulk modulus of the liquid phase; βTi is volumetric thermal expansion coefficient of the porous medium and expressed as βTi = ni αli + (ξi − ni )αsi , where αli is the volumetric thermal expansion coefficient of the liquid phase. The thermal balance equation for a heat conduction problem can be uncoupled from hydraulic and mechanical problems when involving low gradients of fluid flow in low-permeability media (Giraud et al. 1998, Wang and Papamichos 1999, among others). Therefore, the thermal diffusion equation can be written as

where ρi , ci and λi are the density, the specific heat and the thermal conductivity of the porous medium, respectively. In conclusion, the problem is characterized by the following 15 independent parameters: (1) Two geometrical parameters: a and b; (2) Heat flux: F(t); (3) 12 constitutive parameters for each material: ρi , ci , λi , ni , ki , Gi , νi , αsi , αli , Ksi , Kli ξi . 2.3

Boundary and initial conditions

The variation of the pore water pressure, stresses and temperature induced by the heating is negligibly small in the far field of the porous medium:

Continuity of the displacement, pore water pressure, stress, temperature, liquid flux and heat flux exists at the interface between the clay and liner (r = b):

Similarly, continuity at the interface between the liner and backfill gives the following conditions (r = a)

Initial radial stress, pore water pressure and temperature for each domain are

2.4 Solution formulation The uncoupled thermal balance equation can be easily solved by applying Laplace transform to Eq. (3). The solution of temperature in Laplace domain is expressed as:

2 where qTi = ρλi ci i s, s is Laplace operator. f˜ (s) is the Laplace transform of
a given function f (t) and is ∞ expressed as f˜ (s) = 0 f (t) e−st dt. I0 and K0 are the modified Bessel functions of order 0. The six unknowns ATi and BTi can be determined considering temperature boundary condition (4c), bounded temperature at r = 0 and the four continuity conditions (5d), (5de), (6d) and 6(e). r θ Substituting equilibrium equation, ∂σ + σr −σ =0 ∂r r into the constitutive equation (1) with a new symbol i) results in ηi defined as (1−ν 1−2νi

A partial differential equation regarding the water pressure can be built by combining Eq. (9) and the continuity equation for the liquid phase Eq. (2). After applying Laplace transform and substituting temperature using the solution already obtained from Eq. (8), water pressure is obtained. General solutions of radial displacement and radial stress are subsequently solved by substituting solutions of temperature and pore water pressure into Eqs. (9) and (1): unknown can be solved by considering the continuity and boundary conditions, together with the bounded values of p and u at r =0. So far, all the solutions are solved in Laplace space. The solutions in the real time domain can be obtained using a numerical inversion scheme by Crump’s algorithm (Crump 1976) which has been successfully applied in previous studies (Chen and Yu 2015, among others).

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Table 1. Main parameters used for the Heater test. Parameters Int. radius of liner Ext. radius of liner Heat flux Bulk density Specific heat Thermal conductivity Porosity Intrinsic permeability Shear modulus Biot coefficient Poisson’s ratio Solid skeleton vol. therm. expan. coeff. Liquid phase vol. therm. expan. coeff. Bulk modulus of liquid phase Bulk modulus of solid particles Initial temperature

Sand

Liner

a

m

0.95

b

m

1.25

ρ c λ

W/m kg/m3 2000 J /kg/K 1466 W /m/K 2.9

Figure 3 2278 948 2.86

n k

m2

0.394 2.34 ×10−11 12 1.0

G ξ ν αs

MPa 1/◦ C

0.1 4.5 ×10−18 17600 0.23 0.25 3.0×10−5

αl

1/◦ C

3.4×10−4

Kl0 MPa

2222

Ks MPa

30000

T0i

◦

C

clay

2000 1434 1.53 0.39 4.5 ×10−19 120 1.0

Figure 3. Heat flux for PRACLAY Heater test.

16 Figure 4. Temperature at liner extrados.

3.3 Verification

3 A PREDICTION FOR PRACLAY HEATER TEST 3.1

Main parameters

The reference parameters for PRACLAY Heater test are listed in Table 1. With a length of 30 m of the heater, there will be a sufficiently long, homogeneous section in the middle part of the gallery, therefore the analytical solution obtained in this study is representative of the middle section. The heat flux shown in Figure 3 is used as the thermal boundary condition at r = a, with a stepwise increasing power during the first 278 days and decreasing for the continuation of the test. The heat flux is a piecewise constant or linear function for which the explicit expression of the Laplace transform exists, and the discretization of the temporal evolution of the heat source term (heat flux) is not necessary. 3.2

Blind prediction

In order to verify the correctness of the present solution, a comparison is made between results from the present analytical solution and those from a commercial software, COMSOL Multiphysics (COMSOL 2008), which is a powerful and widely used finite element code for solving THM coupled problems in geomechanics. The domain considered in the finite element model is a quarter of the geometry shown in Figure 2. The size of the modelled region is 1000 m tall and 1000 m wide with a geometry meshed by 3360 triangular quadratic elements. The temperature, pore pressure and radial stress at the outer boundary of the domain are assumed not to be affected by the heating. Numerical results calculated by both the analytical solution and by COMSOL are compared in Figure 4∼ Figure 6, and the excellent agreement confirms the correctness of the developed analytical solution. 4

Figure 4 gives the time evolution of temperature at lining extrados for 10 years. Figure 5 and Figure 6 give the radial profiles of the temperature change and pore pressure change after heating for 278 days, 3 years and 10.5 years respectively. After heating for more than 10 years, the thermally disturbed radius reaches more than 30 m (see Figure 5), and the hydraulic disturbed radius reaches 50 m (See Figure 6).

SENSITIVITY ANALYSIS FOR PRACLAY HEATER TEST

There are variabilities and uncertainties in material parameters, such as thermal conductivities of the three materials, intrinsic permeability of the liner and the Boom Clay, thermal expansion coefficient of the Boom Clay, etc. Investigating the consequences of parameter variations within their plausible range is valuable for the interpretation of the in situ measured

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Figure 5. Radial profiles of temperature increment.

Figure 7. Effect of Boom Clay thermal conductivity on temperature around PRACLAY gallery.

Figure 6. Radial profiles of PWP increment.

data. In this section, some parameter uncertainties are discussed and their effects on the THM responses in PRACLAY Heater test are studied. 4.1 Thermal conductivity of Boom Clay The Boom Clay is a marine sediment, characterised by a banded structure essentially created by the alternation of silty and clayey beds. The equivalent thermal conductivity of the Boom Clay used in the base case, λBC = 1.53 W/(mK), is the geometric mean of the thermal conductivity in the bedding plane (λBCH = 1.65 W/(mK)) and in the perpendicular direction (λBCV = 1.31 W/(mK)). These two values come from a medium-scale in situ heating test -ATLAS III test- in which in situ temperature measurements were well fitted with a numerical anisotropic model (Chen et al. 2011). In this section, three values for λBC varying between 1.31 and 1.65 (W/(mK)) are tested. With the same heat flux as presented in Figure 3, the induced temperature and its gradient in the Boom Clay becomes higher when using a lower value for λBC as shown in Figure 7. The temperature difference among the three cases is more than 10◦ C. 4.2 Intrinsic permeability of Boom Clay Measurements of intrinsic permeability of the Boom Clay, KBC , by various techniques give quite consistent

Figure 8. Effect of Boom Clay permeability on PWP change around PRACLAY gallery.

values in the order of 10−19 m2 (Chen et al., 2014). In addition to the reference value of 4.5×10−19 m2 , two variants within the range of the measured values in both laboratory and in situ, i.e. 3.0×10−19 m2 and 6.0×10−19 m2 , are evaluated in this section to test the impact of KBC on the system response. Figure 8 presents the radial profiles of pore pressure change around the gallery. A significant impact of the considered range of KBC on pore water pressure change around the gallery can be observed. The maximum pore pressure difference reaches about 0.5 MPa in the gallery between the three cases. 4.3 Young’s modulus of Boom Clay The Young’s modulus of the Boom Clay is considered 300 MPa by many researchers (Bernier et al. 2002 & 2007). Another medium-scale in situ heating test in Boom Clay-ATLAS III (Chen et al. 2011) – indicates that higher Young’s moduli for the Boom Clay in both horizontal (Eh ) and vertical directions (Ev ) (Eh = 1400 MPa and Ev = 700 MPa) are capable of reproducing well the measured pore water pressures. A higher value of 1350 MPa was also obtained from the in situ wave velocities of a seismic test performed in HADES URL (Chen et al. 2011). Therefore, in addition to the reference value of 300 MPa used in the base case, anther variant, i.e. 1000 MPa is evaluated in this section.

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The radial profiles of the pore water pressure change around the gallery after heating for 278 days and 10.5 years respectively are given in Figure 10, and very limited difference among the three cases is observed. 4.5 Saturation degree of pore liquid in backfilling sand

Figure 9. Effect of Boom Clay Young’s modulus on PWP change around PRACLAY gallery.

Figure 10. Effect of Boom Clay thermal expansion coefficient on PWP change around PRACLAY gallery.

The profiles of pore pressure change for the two cases show a considerable impact of the Young’s modulus of the Boom Clay on pore pressure change (see Figure 9).A higher pore pressure will be generated when the clay becomes more rigid, reaching a difference of 1.3 MPa in the gallery between the two cases. 4.4 Thermal expansion coefficient of Boom Clay When the temperature in the saturated Boom Clay increases, the pore water pressure increases because the thermal expansion coefficient of pore water is much higher than that of the solid skeleton. The sensitivity of the thermal expansion coefficient of solid skeleton on the pore pressure is studied in this section. In the reference case, the volumetric thermal expansion coefficient for solid skeleton of the Boom Clay, αs , is taken to be 3×10−5◦ C−1 . Various values of the linear thermal expansion coefficient for the solid skeleton of the Boom Clay ranging from 1.38×10−5◦ C∼4.3×10−5◦ C can be found in the literature (Baldi et al 1988, Cui et al. 2000, Monfared et al. 2012). Therefore, in addition to the base case, two variants for αs , i.e. 6.0×10−5◦ C−1 and 1.2×10−4◦ C−1 , are evaluated to test the impact of αs on the pore water pressure change around the PRACLAY gallery.

After the PRACLAY gallery was backfilled with sand, water was injected into the sand. Although some measures were taken to keep venting the air in the backfilled gallery, there still remains some free air trapped in the water. The compressibility of the liquid significantly depends on the compressibility of the trapped free air. The compressibility of a pore fluid under such circumstances is significantly higher than that of pure water, even with 1% of free air in the fluid. The relationship between the pore fluid compressibility and saturation degree can be approximated as Equation 10 when it is close to full saturation (Fredlund and Rahardjo 1997):

where Kl0 is the bulk modulus of pure water and equal to 2222 MPa (Table 1), Sl is the saturation degree of the pore fluid, Pl0 is the absolute pore liquid pressure, and h is the volumetric solubility coefficient of air which varies slightly with temperature. For simplicity, constant values for Pl0 = 1 MPa and h = 0.02 are assumed. According to Equation 10, the bulk modulus of pore liquid Kl is calculated to be 14.4 MPa, 33.1 MPa and 46.7 MPa respectively for Sl equal to 95%, 99% and 99.9%. When the air is completely dissolved into the water with Sl = 100%, the liquid compressibility drops to the water compressibility abruptly, i.e. Kl = Kl0 . The results in Figure 9 clearly show the effects of sand saturation degree on the pore pressure response. Even when the saturation degree of the sand backfill reaches 99.9% before heating starts, the induced pore pressure in the gallery is still ∼0.3 MPa lower than the case with completely saturated sand backfill. In the case of saturation degree lower than 95%, thermalinduced pore pressure increase in the near field of clay can be higher than that induced in the gallery as indicated in Figure 11. But it should be noticed that in the above analysis, the saturation degree of sand is assumed constant in the test. This is not realistic because the saturation degree of sand will increase with the increase of temperature and pore pressure in the gallery. Therefore the results in this section are only for indicative purpose. 5

CONCLUSION

An analytical solution has been derived for thermohydro-mechanical responses around a cylindrical cavity drilled or excavated in a low-permeability formation when subject to a time-dependent heat flux.

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REFERENCES

Figure 11. Effect of sand saturation degree on PWP change around PRACLAY gallery.

The cavity is considered to be backfilled with a saturated material after the cavity is supported by casing or liner. The solution has been sufficiently verified before it is applied in a large scale in situ PRACLAY Heater test. The solution is used for a predictive calculation of PRACLAY Heater test. The results show that the disturbed zone reaches more than 30 m from the axis of the gallery for temperature and about 50 m for pore water pressure. A parametric study has been carried out for the PRACLAY Heater test by varying some material properties within their plausible range. The results reveal the following conclusions: With the same heat flux, the induced temperature and its gradient in the Boom Clay become higher when using a lower value for λBC . The Boom Clay temperature difference is more than 10◦ C when λBC varying between 1.31 and 1.65 (W/(mK)). The impact of the permeability of the Boom Clay on the pore pressure change around the PRACLAY gallery is significant when varying the intrinsic permeability of the Boom Clay between 3×10−12 m2 ∼6×10−12 m2 with a corresponding pore pressure difference of maximum ∼0.5 MPa in the gallery. A considerable impact of theYoung’s modulus of the Boom Clay is expected. A higher pore water pressure is foreseen in the gallery with a higher stiffness of the clay. Very limited effect of the Boom Clay thermal expansion coefficient on the pore water pressure change is found. The saturation degree of the sand backfill has an important impact on the pore pressure response even when the saturation degree reaches 99.9%. The solution is derived for a backfilled cavity in which up to three materials are involved and it can be easily adapted to problems with fewer materials. The transient fields at any time are obtained in a semianalytical manner. The great flexibility in geometric dimension and the high computational efficiency facilitate its application in preliminary designs of potential repositories for radioactive waste or other applications with coupled THM effects.

Baldi, G. Hueckel, T. & Pellegrini, R. 1988. Thermal volume changes of the mineral–water system in low-porosity clay soils. Canadian Geotechnical Journal 25(4):807–825. Bernier, F. Li, X.L. Verstricht, J. Barnichon, J.D., Labiouse, V. & Bastiaens, W. et al. 2002. CLIPEX: clay instrumentation programme for the extension of an Underground Research Laboratory. Luxembourg: Commission of the European Communities, EUR20619. Bernier, F. Li, X.L. and Bastiaens, W. 2007. Twenty-five years’ geotechnical observation and testing in the Tertiary Boom Clay formation. Géotechnique 57(2): 229–37. Biot, M.A. 1956. Theory of propagation of elastic waves in a fluid saturated porous solid. Journal of Acoust. Soc. Am., 28(2): 168–191. Biot, M.A. & Willis, D.G. 1957. The elastic coefficients of theory of consolidation. Journal of Applied Mechanics 24:594–601. Booker, J.R. Savvidou, C. 1984. Consolidation around a spherical heat source. International Journal of Solids and Structures 20: 1079–1090. Booker, J.R. Savvidou, C. 1985. Consolidation around a point heat source. International Journal for Numerical and Analytical Methods in Geomechanics 9(2): 173–184. Chen, G. Sillen, X. Verstricht, J. Li, X. 2011. ATLAS III in situ heating test in boom clay: Field data, observation and interpretation. Computers and Geotechnics 38(5): 683–696. Chen, G.J. & Yu, L. 2015. Consolidation around a tunnel in a general poroelastic medium under anisotropic initial stress conditions. Computers and Geotechnics 66: 39–52. Chen, G. Maes, T. Vandervoort, F. Sillen, X. Van Marcke, P. Honty, M. 2014. Thermal Impact on Damaged Boom Clay and Opalinus Clay: Permeameter and Isostatic Tests with µCT Scanning. Rock Mechanics and Rock Engineering 47(1): 87–99. COMSOL. Multiphysics software and User’s Guide, version 3.5a. COMSOL AB, Stockholm, Sweden; 2008. Crump, K.S. 1976. Numerical inversion of Laplace transform using a Fourier series approximation. Journal of Association for Computing Machinery 23: 89–96. Cui, Y.J. Sultan, N. & Delage, P. 2000. A thermomechanical model for saturated clays. Canadian Geotechnical Journal 37(3): 607–620. Fredlund, D.G. & Rahardjo, H. 1997. Soil mechanics for unsaturated soils. John Wiley. Giraud, A. & Rousset, G. 1995. Consolidation around a volumic spherical decaying heat source. Journal of Thermal Stresses 18(5): 513–536. Giraud, A. Homand, F. & Rousset, G. 1998. Thermoelastic and thermoplastic response of a double-layer porous space containing a decaying heat source. International Journal for Numerical and Analytical Methods in Geomechanics 22(2): 133–149. Li X.L. Chen G.J., Verstricht, J. Van Marcke, P. Troullinos, I. 2013. The large scale in-situ PRACLAY Heating and Seal tests in URL HADES, Mol, Belgium . Proceedings of the ASME 2013 15th international conference on environmental remediation and radioactive waste management (ICEM2013), Sep 8–12, 2013, Brussels, Belgium. McTigue, D.F. 1986. Thermoelastic Response of FluidSaturated Porous Rock. Journal of Geophysical Research Atmospheres 91(B9): 9533–9542. Monfared, M. Sulem, J. Delage, P. & Mohajerani, M. 2012. On the THM behaviour of a sheared Boom clay sample: Application to the behaviour and sealing properties of the EDZ. Engineering Geology 124(4): 47–58.

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NEA(Nuclear Energy Agency), 2008. Moving forward with geological disposal of radioactive waste: an NEA RWMC collective statement. NEA/RWM (2008) 5/REV2. 12 June 2008, NEA, Paris, Report No. 6433. Rice, J.R. & Cleary, M.P. 1976. Some basic stress-diffusion solutions for fluid saturated elastic porous media with compressible constituents. Rev. Geophys. Space Phys. 14: 227–241. Small, J.C. & Booker, J.R. 1986. The behaviour of layered soil or rock containing a decaying heat source. International Journal for Numerical and Analytical Methods in Geomechanics 10(5): 501–519. Savvidou, C. & Booker, J.R. 1989. Consolidation around a heat source buried deep in a porous thermoelastic medium with anisotropic flow properties. International Journal for Numerical and Analytical Methods in Geomechanics 13(1): 75–90.

Selvadurai, A.P.S. 2007. The analytical method in geomechanics. Appl. Mech. Rev. 60: 87–106. Van Marcke, P. Li, X.L. Bastiaens, W. Verstricht, J. Chen, G.J., Leysen, J. Rypens, J. 2013. The design and installation of the PRACLAY In-Situ Experiment. EURIDICE Report 13–129, Mol, Belgium. Wang, Y. & Papamichos, E. 1999. Thermal effects on fluid flow and hydraulic fracturing from wellbores and cavities in low-permeability formations. International Journal for Numerical and Analytical Methods in Geomechanics 23(15): 1819–1834. Yu, L. Rogiers, B. Gedeon, M. Marivoet, J. De Craen, M. Mallants, D. 2013. A critical review of laboratory and in-situ hydraulic conductivity measurements for the Boom Clay in Belgium. Applied Clay Science 75–76: 1–12.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Experimental study of thermal effects on clay rock for deep disposal of radioactive waste Chun-Liang Zhang Gesellschaft für Anlagen- und Reaktorsicherheit (GRS), Braunschweig, Germany

ABSTRACT: Thermal effects on the Callovo-Oxfordian and Opalinus clay rocks for hosting high-level radioactive waste were comprehensively investigated under repository relevant conditions. Various kinds of laboratory experiments were performed on normally-sized and large hollow cylindrical samples in respects of thermal expansion and contraction, thermally-induced porewater pressure, temperature influences on deformation and strength, thermal impacts on swelling, fracture sealing and permeability. Major findings are presented in this paper. 1

INTRODUCTION

Clay rocks are widely investigated for deep geological disposal of high-level radioactive waste (HLW) due to their favorable properties such as large homogeneous rock mass, stable geological structure, extremely low hydraulic conductivity, swelling and creep capabilities, self-sealing potential of fractures, and especially high sorption capacity for retardation of radionuclides. In France and Switzerland, for instance, the potential repositories will be constructed in the Callovo-Oxfordian and Opalinus argillaceous formations respectively. They will be located at great depths of more than 500 m below the ground surface. HLW canisters will be disposed in horizontal steel-cased boreholes designed in the French concept (Andra, 2005), and/or emplaced in horizontal drifts and backfilled with bentonite in the Swiss concept (Nagra, 2002). The clay host rocks will be impacted by thermal load from heat-emitting HLW. The most concern is whether and how the favorable barrier properties of the clay rocks will be altered during the thermal period over several thousands of years under designed temperatures below 90◦ C. This important issue has been comprehensively investigated at the GRS geo-laboratory during the last decade (Zhang et al., 2004; 2007; 2010; 2013). Various kinds of laboratory experiments were performed on normally-sized and large hollow cylindrical samples under repository relevant conditions: (1) stresses covering the range from the initial lithostatic state to redistributed levels after excavation, (2) hydraulic drained and undrained boundaries, and (3) heating from ambient temperature up to 90–120◦ C and a subsequent cooling phase. The tests on normally-sized samples aimed at characterizing thermal properties, thermal expansion and contraction, thermally-induced porewater pressure, temperature influences on deformation and strength, thermal impacts on swelling, fracture

sealing and permeability, while the large hollow cylinder tests focused on examining thermal impact on the damaged zone around HLW boreholes. Major findings are overviewed in this paper. 2

CHARACTERISTICS OF THE CLAYSTONES

The Callovo-Oxfordian (COX) and Opalinus (OPA) clay rocks have been highly consolidated during the individual geological history over hundreds of millions of years, leading to low porosities of 14–18% and extremely low permeabilities of 10−20 –10−21 m2 (Bock et al., 2010). The studied COX claystone contains 25–55% clay minerals, 20–38% carbonates and 20–30% quartz (Andra, 2005), while the OPA claystone has higher clay contents 58–76%, less carbonates 6–24% and quartz 5–28% (Bossart & Wermeille, 2003). The pore sizes mainly range from nanoscale in between the parallel platelets of the clay particles to micro- and mesoscale between solid particles. The claystone matrix consists of particles with strongly adsorbed interlayer water and strongly to weakly adsorbed water at the external surfaces. Only a small amount of mobile water exists in large pores. Obviously, the neighboring clay particles are not directly connected, but mainly through the bound pore water, which plays a dominant role in coupled ThermoHydro-Mechanical-Chemical (THMC) processes in the clay rocks (Horseman et al., 1996). For the laboratory experiments, a large number of core samples were extracted from the Underground Research Laboratories (URLs) at Bure in France and Mont-Terri in Switzerland. Normal samples were prepared to sizes of diameter/length = 50/100 and 100/200 mm. Large hollow cylinders were prepared to a size of 280 mm diameter and ∼500 mm length with a central borehole of 100 mm diameter. The samples were unavoidably disturbed by coring and preparation,

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Figure 2. Thermal expansion and contraction of a COX sample during heating and cooling.

Figure 1. Setup and THM conditions for triaxial thermal tests on normally-sized samples.

causing desaturation and micro-fissures. In order to minimize effects of the disturbances on the quality of test results, the samples were resaturated and reconsolidated before testing under isostatic loads equal to and even higher than the in situ overburden pressures up to 15–20 MPa. 3 THERMAL TESTS ON NORMAL SAMPLES Thermal tests on normally-sized samples were carried out in triaxial apparatus to examine thermal effects on deformation and strength, porewater pressure, and sealing of fractures. Figure 1 shows a testing setup and the assembly of a sample.The equipment allows a maximum axial and radial load of 50 MPa and a maximum temperature of 200◦ C. Heating is accomplished using an electrical heater positioned in the cell. Axial deformation is recorded by a LVDT deformation transducer mounted inside the cell between the upper and lower loading platens, while a circumferential extensometer chain is installed around the sample at its mid-height to measure lateral deformation. The hydraulic system permits monitoring pore back-pressure at the sample ends and fluid flow through the sample. 3.1 Thermal expansion Thermal expansion behavior of the claystones was determined by heating and cooling the samples under different isostatic stresses and undrained conditions. Strain gauges were attached on the sample surface for measuring local axial and radial strain. Figure 2 shows the strain evolution measured on a COX sample during a heating/cooling cycle at confining stress of 5 MPa. The sample with a high initial saturation degree of 96% was heated by stepwise increasing temperature from 23◦ C to 68◦ C and then cooled down. The measured data show that (a) each temperature increase generates expansion in all directions; (b) the expansion does not change much with time at constant temperatures below 47◦ C and then turns over to a gradual contraction at higher temperatures; and (c) cooling down

Figure 3. Thermal expansion coefficient of a stressed COX sample as a function of temperature.

yields contraction. The contraction at the high temperatures above 56◦ C might be caused by mobilization of the heated porewater into the unsaturated pores and also by possible leakage of the boundary against such high temperatures, allowing release of the porewater and thus leading to consolidation. Based on the data, thermal expansion coefficient can be obtained. Figure 3 illustrates the volumetric expansion coefficients obtained during heating. For a water-saturated porous medium, the thermal expansion is governed by the expansion of the solid grains and the pore water. The thermal expansion coefficient can be approached by

where φ is the porosity, αs , αw and αm are the linear expansion coefficient of the solid grains, the volumetric expansion coefficient of the porewater and the porous medium, respectively. Using αs value of 2.0 · 10−6◦ C−1 for clay minerals (Noynaert, 2000) and αw = 3.4·10−4◦ C−1 for pore water, αm = 6.1 · 10−5◦ C−1 is obtained for the claystone with a porosity of φ = 16.5% at 20◦ C.

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Figure 4. Anisotropy of thermal expansion and contraction of an OPA sample during a heating-cooling cycle without confining load.

Additionally, the data also show an increase of the coefficient with temperature, which may be approached by a linear relation

where T and To are the actual and the reference temperature (20◦ C), respectively, and ω is a factor. Fitting the data yields ω = 1.0 · 10−6◦ C−1 . The sedimentary clay rocks commonly exhibit thermal anisotropy with bedding structure. Figure 4 show the thermal expansion anisotropy of an OPA sample without any confinement. The expansion coefficient (α⊥ ) in direction perpendicular to the bedding plane is about one order of magnitude higher than that (α// ) parallel to the bedding. The significant thermal anisotropy shall reduce when the claystone is subjected to external stresses, under which thermal expansion of the micro-fissures mostly oriented along the bedding planes will be suppressed. 3.2 Thermally-induced porewater pressure The difference in thermal expansion between porewater and solid grains in saturated claystone is the driving force for build-up of over pore pressure in case of heating. Because the very low permeabilities of the claystones do not allow the expanding porewater to disperse adequately, heating will result in an increase in pore pressure. Figure 5 shows an example observed on an OPA sample. The sample was firstly resaturated with synthetic porewater and consolidated at a stress of 15 MPa. Undrained heating from 30◦ C to 60◦ C resulted in an increase in pore pressure from 1 MPa to 8 MPa at inlet and 7 MPa at outlet. The increase of the pressures continued slowly with time. The different responses of the water back-pressures (Pin > Pout ) might be caused by the different reservoirs in volume. The second heating up to 80◦ C yielded a short pressure rising to about 11 MPa. After the peak, the pressures dropped

Figure 5. Thermally-induced porewater pressure (a) and deformation (b) in an OPA sample.

gradually down as unexpected. Similar evolution of the measured water back-pressures appeared at further elevated temperatures of 100 and 120◦ C.The reduction of the pore pressure might be due to some release of the thermally-mobilized porewater from the imperfect sealing of the test boundary against such high temperatures. As consequence of the dissipation of the pore pressure, the effective stress increases and compresses the pore volume. 3.3 Creep at high temperatures Thermal impact on the long-term deformation of the clay rocks was examined in triaxial creep tests under various temperatures and stresses. Figure 6 shows an example of the creep tests on highly watersaturated COX samples at different temperatures of 28◦ C to 110◦ C. The strain-time curves obtained at σ1 /σ3 = 15/0.5 MPa show that: (a) each temperature increase leads to a short-time radial expansion but a slight axial compression; (b) the axial, radial, and volumetric strains (ε1 , ε3 , εv ) increases quite linearly with time at each elevated temperature below 90◦ C, suggesting no or negligible thermal transient creep; (c) at higher temperatures above 90◦ C, the creep slows down; and (d) cooling down results in a short-term radial contraction and small axial strain, but almost no creep any more at each lowered temperature. The creep acceleration at elevated temperatures up to 90◦ C probably results from the reduction of viscosity and friction of bound water-films between solid particles. As mentioned before, the testing system was not absolutely

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Figure 6. Triaxial creep of a COX sample under different temperatures.

in undrained condition against high temperatures, allowing release of the porewater. The amount of the water release was identified up to 2% after testing. As a consequence of the porewater release, the pore structure was consolidated under the applied load, increasing the friction resistance between particles and hence decelerating the creep. The creep of a water-saturated clay rock is mainly governed by slip and rupture of bound water-films between solid particles. Based on the long-term creep experiments on the COX and OPA claystones (Zhang et al., 2007; 2010; 2013; Zhang, 2015), a creep equation has been derived by modification of the Mitchell’s law (1976). The stationary creep rate can be expressed as function of stress and temperature

where ε˙ is the stationary shear creep rate (s−1 ), σd the deviatoric stress (MPa), T the absolute temperature (K), R the universal gas constant (8.31433·10−3 kJmol−1 K−1 ), Q the apparent activation energy (kJmol−1 ), A a parameter in s−1 , and α a parameter in MPa−1 . For the COX claystone, the parameters are established: A = 2.2·10−4 s−1 , α = 0.2 MPa−1 , and Q = 45 kJmol−1 . Figure 7 compares the quantified mathematical model with the measured creep rates as function of deviatoric stress at T = 25◦ C (a) and temperature at different stress states (b). A reasonable agreement can be found. 3.4 Temperature influence on strength Temperature influence on the strength of a claystone is differing from saturated to unsaturated state and from drained to undrained conditions. Figure 8 compares the peak strength values obtained on the COX samples during undrained compression at ambient temperature of 20–30◦ C (black points) and at elevated temperatures of 40–100◦ C (collar points) as well as the strength after drained heating (upper part). It can be seen that the strength curves at the different temperatures are close to each other, indicating that the temperature influence is insignificant. However, in the other tests

Figure 7. Stationary shear creep rate of the water-saturated COX claystone as function of deviatoric stress (a) and temperature (b).

on the water-saturated OPA samples at lateral stresses around 3 MPa, a significant reduction of the strength was observed from 20 MPa at 20◦ C down to 5 MPa at 116◦ C (Zhang et al. 2007). The different conclusions drawn from the COX and OPA claystones have to be examined in the future. Interesting is that the maximum strength was achieved after drained heating at high temperatures of 90◦ C and 150◦ C. This is actually attributed to the release of the thermally-mobilized porewater, which enhances the friction resistance between particles against shearing. This finding implies that the mechanical stability of the host rock surrounding the HLW boreholes and drifts will be enhanced during heating phase. 3.5

Swelling after heating

The clay rock close to HLW will be heated up to the designed maximum temperature of 90◦ C and dried in some degrees. The mineralogical components, particularly the expansive clay minerals, may be altered. This may affect the swelling capability of the claystone and

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Figure 8. Comparison of drained and undrained thermal strengths of the COX claystone.

thus in turn the sealing of fractures in the damaged zone. This issue was studied by measuring swelling strain and pressure during wetting samples that had been pre-heated and dried at 100◦ C and 120◦ C. The swelling deformation was measured during wetting the samples in unconstraint conditions. The swelling pressure was obtained by measuring the reaction of axial stress under axially-fixed and laterally-free conditions. Details of this test method are given in (Zhang et al., 2010; 2013). Figure 9 shows the evolution of swelling pressure obtained on two COX samples preheated at 100 and 120◦ C. It can be found out that wetting by increasing the humidity to 100% increased the swelling pressure from the pre-loads of 1–2.5 MPa up to 4–5 MPa. The free swelling tests showed the volume expansion of the preheated claystone up to 10–12%. Obviously, the heated claystone still possesses significant swelling potential, but somewhat lower than that of the unheated claystone. For instance, the unheated claystones exhibit higher swelling pressures up to 10–12 MPa at COX samples and 4.5–5.5 MPa at OPA samples (Zhang et al., 2013; Zhang, 2015). 3.6 Thermal impact on fracture sealing As shown before, the swelling capacity of the claystone becomes relatively lower after heating. Logically the self-sealing potential of the heated claystone, which is largely determined by the swelling, shall be altered. This issue was examined by measuring water permeability of fractured claystones in various thermal conditions (Zhang, 2011; 2013). Figure 10 shows the water permeability measured on three cracked and pre-heated COX samples at 50, 100 and 150◦ C respectively. They were compressed at relatively low confining stresses of 2 to 3.5 MPa and flowed with synthetic porewater through over more than 3 years. As soon as the water was supplied, the high initial permeability of 3·10−12 m2 measured with

Figure 9. Development of swelling pressure in the COX samples pre-heated and dried at 100–120◦ C.

Figure 10. Water permeability of fractured COX samples preheated at 50, 100 and 150◦ C.

gas dropped immediately by five to seven orders of magnitude down to 10−17 –10−19 m2 , depending on the fracture intensity of each sample. This drastic drop in permeability is mainly attributed to the water-induced swelling, slaking, and clogging of the fractures. At each load level, the permeability decreased gradually with time and tended to constant. The influence of the confining stress on the permeability variation was not significant in the testing range. Interesting is that the pre-heating up to 150◦ C did not hinder the sealing process of the fractures. The final permeability values determined after 3 years are very low at 3·10−20 –7·10−21 m2 , being the same as that of the intact clay rock. Figure 11 shows the similar results obtained on cracked COX and OPA samples during heating and cooling between 20◦ C and 90◦ C for more than 3 years.

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Figure 11. Water permeability of fractured COX and OPA samples during heating and cooling.

Figure 13. Principle of borehole simulation tests with large hollow cylindrical samples.

decrease more or less with increasing temperature during heating and decrease during cooling. Generally speaking, the self-sealing of fractures in the claystones is not affected by the applied thermal loads. 4

Figure 12. Water permeability of fractured claystones as a function of temperature.

The water-enhanced sealing of fractures is more significant during the first stage at 20◦ C. The permeability decreased with time from 1·10−15 to 3·10−18 m2 at OPA sample and from 1·10−17 to 5·10−19 m2 at COX sample, respectively. The permeability reduction rate was less affected by the temperature increase up to 60◦ C. Further heating up to 90◦ C and also cooling down back to 60◦ C had no or only little effect on the permeability reached before. Further cooling down to 20◦ C, however, caused a further reduction of the permeability down to 3·10−19 at OPA sample and 1·10−19 m2 at COX sample respectively. The water permeability values obtained after stabilization of each temperature stage are depicted in Fig. 12 as a function of temperature. It is obvious that the permeabilities of the fractured claystones are slightly influenced by heating and cooling. They

LARGE HOLLOW CYLINDER TESTS

In order to investigate thermal impact on the EDZ around HLW boreholes, a series of large-scale heating tests were conducted on big hollow claystone cylinders in a triaxial apparatus, which permits a maximum lateral stress of 50 MPa, axial stress up to 75 MPa, temperature up to 150◦ C, and fluid pressure up to 15 MPa. The big hollow samples were prepared to an outer diameter of 280 mm and lengths between 460 mm and 530 mm with axially-drilled central boreholes of 100 mm diameter. Figure 13 shows the test layout. The heater-packer in the borehole allows simulating the heat output from HLW up to a maximum temperature of 150◦ C and a maximum back pressure of 15 MPa. Thermal load can also be applied by means of an outer heater mounted around the cell. Axial strain is measured by a LVDT deformation transducer mounted outside the cell, while external radial strain is recorded using two circumferential extensometers installed at the middle and the lower position of ¼ sample length. Borehole convergence is measured by the oil volume in the inner packer. A hydraulic system is connected with the inlet and outlet for measurement of water or gas flow through the sample. The large hollow cylinder tests were performed by simulating the borehole conditions such as excavation, backfill support, fluid flow, heating and cooling. Fig. 14 presents results of a borehole simulation test in terms of applied stress and temperature (a), resulting convergence (b), permeability change (c), and water flow (d) during a heating/cooling cycle. The test started from an isotropic stress of 15 MPa. The borehole excavation (II) was simulated

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observation implies that in the much longer disposal boreholes of tens of meters, fractures in the EDZ may not be connected to form hydraulic pathways along the boreholes. An intensive damage was generated by increasing the external stress up to 20 to 24 MPa (III), which yielded a drastic increase in gas permeability from 10−21 to 10−15 m2 (Fig. 14c). However, the following injection of synthetic porewater (IV) led to sealing of the fractures. The measured water permeability of 1·10−18 m2 is three orders of magnitude lower than the gas permeability measured before. The subsequent heating (V) from 30◦ C to 75◦ C resulted in a significant rock deformation towards the borehole and thus a large convergence. At the increased temperature, the convergent deformation continued with time and the water permeability increased only slightly to 3·10−18 m2 (Fig. 14d). The cooling phase (VI) caused a divergence of the borehole but a small displacement of the outer surface towards the borehole due to the thermal contraction of the material. At the lowered temperature, the borehole tended to close up with time due to the rock creep and the permeability decreased slightly down to 2·10−18 m2 . The small variation of the permeability during heating and cooling is consistent with the observations made on the small samples (cf. Figs. 11–12).

5

Figure 14. Results of a borehole simulation test with initial state (I), excavation (II), EDZ generation (III), water flow (IV), heating (V) and cooling (VI).

by reducing the borehole pressure from 15 MPa down to 1 MPa. As unexpected, no increase in permeability was observed (Fig. 14c), indicating no build-up of any flow pathway through the sample of half a meter. This

SUMMARY AND CONCLUSIONS

Thermal impact on the barrier properties and the integrity of a clay host rock is the key concern for deep geological disposal of HLW. This issue was comprehensively investigated with the thermal experiments on the COX and OPA claystones under the prevailing repository conditions. Significant responses of the claystones to thermal loading were observed, including thermal expansion and contraction, thermallyinduced porewater pressure, temperature influences on deformation and strength, thermal impacts on swelling, fracture sealing and permeability. These are strongly determined by the inherent properties (minerals, porosity, water saturation, anisotropy etc.) of the material itself and the external conditions (stress, drainage and temperature). In the water-saturated claystones, the thermal expansion is predominantly controlled by the porewater because of its much higher expansion coefficient compared to that of the solid grains. Heating yields expansion and mobilization of the porewater. Under undrained conditions, the water expansion results in high porewater pressures decreasing the effective stress. Because of the thermally-induced reduction of the inherent cohesion and friction resistance between particles, the claystone becomes more ductile at elevated temperatures and the creep is accelerated. In contrast, drained heating drives the thermallymobilized porewater out of the pore space. Under external load, the release of the bound porewater leads to collapse of the pore structure and thus consolidation of the porous medium. Even under high

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deviatoric stresses, the consolidation is dominating during the pre-failure stage. With heating and drying, the contacts between particles become increasingly of the solid-to-solid type, so that the friction resistance between particles increases, enhancing the stiffness and strength. Another important finding is that the high sealing capability of the claystones is not affected by the applied thermal loads. The fractures in the claystones pre-heated up to 100–150◦ C and under low stresses of 2–3.5 MPa can be resealed to very low water permeabilities of 10−19 to 10−21 m2 within months to years. It is evident that the favorable barrier properties of the clay rocks will not be altered during the thermal loading from HLW. ACKNOWLEDGEMENTS The author gratefully acknowledges the funding by the German Federal Ministry of Economics and Technology (BMWi) and by the European Commission (EC) in the framework of several R&D projects (HE-D, THM-TON, TIMODAZ). The support from Andra for providing the core samples and for the fruitful discussions is also gratefully acknowledged. REFERENCES Andra 2005: DOSSIER 2005, Synthesis – Evaluation of the feasibility of a geological repository in an argillaceous formation. Bock, H., Dehandschutter, B., Martin, C.D., Mazurek, M., Haller, A.D., Skoczylas, F., Davy, C. 2010: Self-Sealing of Fractures in Argillaceous Formations in the Context of Geological Disposal of Radioactive Waste – Review and Synthesis. Clay Club Report, OECD, NEA No. 6184. Bossart, P. and Wermeille, S. 2003: The Stress Field in the Mont Terri Region – Data Compilation. In:

Heitzmann, P. & Tripet, J.-P. (ed.): Mont Terri Project – Geology, Paeohydrology and Stress Field of the Mont Terri Region – Reports of Federal Office for Water and Geology (FOWG), Geology Series 4, 65–92. Horseman S.T., Higgo J.J.W., Alexander J., Harrington J.F. 1996: Water, Gas and Solute Movement through Argillaceous Media. Nuclear Energy Agency Report CC-96/1, OECD, Paris. Mitchell, J.K. 1976: Fundamentals of Soil Behavior, University of California, Berkeley, USA. Nagra 2002: Project Opalinus Clay, Models, Codes and Data for Safety Assessment – Demonstration of disposal feasibility for spent fuel, vitrified high-level waste and long-lived intermediate-level waste. 2002. Noynaert, L. (Ed.) 2000: Heat and radiation effects on the near field of a HLW or spent fuel repository in a clay formation (CERBERUS Project). EUR 19125EN, Contract No F14W-CT95-0008. Zhang, C.L., Rothfuchs, T., Moog, H., Dittrich, J., Müller, J. 2004: Thermo-Hydro-Mechanical and Geochemical Behaviour of the Callovo-Oxfordian Argillite and the Opalinus Clay. Project Report, GRS-202. Zhang, C.L., Rothfuchs, T., Jockwer, N., Wieczorek, K., Dittrich, J., Müller, J., Hartwig, L., Komischke, M. 2007: Thermal Effects on the Opalinus Clay – A Joint Heating Experiment of ANDRA and GRS at the Mont Terri URL (HE-D Project), Final Report, GRS-224. Zhang, C.L., Czaikowski O., Rothfuchs, T. 2010: ThermoHydro-Mechanical Behaviour of the Callovo-Oxfordian Clay Rock – Final report of the TIMODAZ/BURE project, GRS-266. Zhang C.L. 2011: Experimental Evidence for Self-sealing of Fractures in Claystone, Physics and Chemistry of the Earth, Vol. 36, 2011, 1972–1980. Zhang C.L. 2013: Sealing of Fractures in Claystone, Journal of Rock Mechanics and Geotechnical Engineering 5, 2013, 214–220. Zhang C.L., Czaikowski O., Rothfuchs T., Wieczorek, K. 2013: Thermo-Hydro-Mechanical Processes in the Nearfield around a HLW Repository in Argillaceous Formations, Project Report THM-TON, GRS-312, 2013. Zhang, C.L. 2015: Deformation of Clay Rock under THM Conditions, Geomechanics and Tunnelling 8 (2015), No. 5, 426–435.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Temperature impact on the creep behaviour of compacted illitic clay N. Jarad, O. Cuisinier & F. Masrouri LEMTA – UMR 7563 CNRS/Université de Lorraine, Vandœuvre-lés-Nancy, France

ABSTRACT: In some engineering applications such as geothermal piles, nuclear waste storages, etc clayey soils could be exposed to thermal cycles. These temperature changes could affect dramatically the mechanical behaviour of these soils. Especially in the long term the creep deformation could be completely modified. Creep deformation which contributes to the volume changes of clay is related to the viscous property of the clay skeleton. In this context, the paper aims to investigate the temperature effect on the creep behavior of saturated compacted illitic clay. Temperature controlled oedometric cells have been developed to perform Constant Rate of Strain (CRS) consolidation tests under different strain rates (0.002%/min to 0.02%/min) within a temperature range of 20 to 70◦ C. Results indicated that the compression and swelling indices could be considered independent of temperature and strain rate. The preconsolidation pressure, and creep index, decreased, and increased with temperature increase respectively. The hydraulic conductivity increased with temperature increase, while the intrinsic permeability remained independent of temperature.

1

INTRODUCTION

The issue of temperature impact on the hydraulic and mechanical behavior of clayey soils including creep deformation is a major issue in geotechnical engineering. A better understanding of this phenomenon will help to reduce the undesired effects of temperature changes and to a better selection of design methods (Sultan et al. 2002, Cekerevac & Laloui 2004, Watabe et al. 2012, Kholghifard et al. 2014). For example, compacted clayey soils are used as engineered barriers for the disposal of high and long-life radioactive wastes at great depth, and therefore they are usually subjected to cyclic changes of temperature. Among the mechanical properties of the compacted clay, creep may contribute to the settlement changes of the structure in the long term. Although temperature variations could highly affect the creep behavior, there are still very few studies on this subject. Gupta (1960) performed creep tests at different temperatures and stated that the creep index increases with temperature increase. Towhata (1993) raised the room temperature up to 90◦ C during secondary consolidation phase, and observed a volume contraction of the sample. Burghignoli et al. (1992) indicated that the thermal loading accelerates the mechanical creep phenomena. Green (1969) noted a higher value of creep index at higher temperature values, but the influence of temperature on the creep was dependent on the effective stress level. In other words, the creep was more affected by temperature at lower effective stress levels. A few researchers studied the influence of temperature on the strain rate-preconsolidation pressure

relationship (e.g. Boudali et al. 1994, and Marques et al. 2004). Boudali et al. (1994) carried out different constant rate of strain (CRS) consolidation tests at different temperatures to investigate the viscous behavior of natural clay. They found that the strain rate-preconsolidation pressure relationship is independent of temperature. A similar behavior of natural clay was also observed by Marques et al. (2004). Boudali et al. (1994) and Marques et al. (2004) found approximately parallel slopes of logarithmic strain rate-preconsolidation pressure relationship at different temperatures. These studies were however focused on the natural and structured clays only. In this context, the main objective of this study was to investigate the influence of temperature on the hydraulic and mechanical behavior of a compacted clay soil including the long term consolidation behavior (creep). To characterize the behavior in terms of strain rate effect, constant rate of strain consolidation tests with different strain rates were performed within temperature range between 20 and 70◦ C using temperature controlled oedometric cells. A saturated compacted illitc soil was used to assess the thermohydro-mechanical-behavior of compacted soils.

2

MATERIALS AND METHODS

2.1 Material Saturated compacted illitic clay was studied. It consists of 77% illite, 10% kaolinite, 12% calcite and traces of quartz and feldspar. Illite is a non-expanding clay material which is common in many argillaceous sediments (Gaudette et al. 1964, Srodon et al. 1986,

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Lynch 1997, Adamis et al. 2005). Atterberg limits (AFNOR 1993) and Proctor curve (AFNOR 1999) for studied clay was determined (Table 1). The maximum dry density of illitic clay was 1.43 Mg/m3 at the optimum water content of 31.3%. A laser diffraction particle size analyser (Malvern Mastersizer 2000®) was used to determine the particle size distributions of the soil. Studied clay contains about 85% of clay particles (smaller than 0.002 mm) and 15% of silt particles (smaller than 0.02 mm).The classification of that clay according to the French standard for soil classification (GTR 2000) is A3, and classified as a fat clay, CH, in accordance with the Unified Soil Classification System (Standard ASTM 2006). 2.2 Experimental device A schematic diagram for the modified temperature controlled oedometric cell is shown in the Figure 1. The whole system includes load frame, oedometric cell, temperature device, and water injector. The oedometric cell was designed to hold high temperatures up to 90◦ C. The sample was inserted in the pressure chamber between two ceramic porous stones with using filter papers on the top and bottom of the sample. The cell base contains drainage system for saturation, and the pore water pressure can be measured through a cell pressure transducer. The oedometric cell Table 1. Characteristics of illitic clay. Setting

Value

Liquid limit (%) Plastic limit (%) Plasticity index (%) Optimum moisture content (%) Maximum dry density (Mg/m3 ) Specific gravity

65 34 31 31.3 1.43 2.65

was installed into the load frame after assembly. An external load was applied to the specimen using the load frame to generate a load with a predefined constant rate of strain on the specimen, and the vertical deformation of the specimen was measured using a displacement sensor. The temperature device can operate in a temperature range from −40◦ to 80◦ C. It supplies a thermal liquid to the oedometric cell through insulated tubes for heating or cooling the sample. The thermal liquid circulates through these tubes from the device to the cell and vice versa. In addition, the thermal liquid circulates around the sample through a spiral tube for purpose of heating or cooling. Water injector was used as a water supply to saturate the sample by applying pore water pressure through the sample base. During testing, all sensors data were stored in the data logger, and then were displayed on the PC. 2.3

Sample preparation

The powder of illitic clay soil was mixed with distilled water at room temperature to adjust the water content corresponding to the value of the optimum water content (at maximum dry density). The prepared slurries were then kept into closed bags for 24 hours at least to obtain the homogeneity. Samples were then statically compacted in a vertical dimension into a rigid mold in one layer to form specimens with 71.4 mm diameter and 20 mm height. The weights of the compacted specimens are representative to the maximum dry density at optimum water content. The average compaction stress for the material is 467 kPa. At this condition, the initial void ratio of the compacted samples is 0.85. 2.4

Experimental procedures

Before saturation starting, the sample was loaded vertically under constant vertical stress of 10 kPa. Both

Figure 1. a. Schematic diagram of the apparatus. b. oedometric cell detail.

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Where Ht = sample height at specific time, t; Ho = Initial sample height, and ε˙ t = the strain rate at specific time, t, and can be calculated as following (ASTM 2008):

Table 2. Experimental program. Strain rate Setting Value

Temperature ◦ C

%/min

20 47.6 69.2

0.002 0.002 0.002

0.01 0.01 0.01

0.02 0.02 0.02

porous stones at the bottom and top were saturated, and the air was flushed from the base and top of the cell. One of the base drainage was closed off for pore water pressure reading, while the top drainage was permitted. A pore water pressure of 10 kPa was applied through the porous element of the base to saturate the sample. After fully saturation with deaired water, the sample was heated to the desired temperature, and when the stabilization was reached after 48 hrs, the constant rate of strain (CRS) consolidation test was carried out on the sample according to ASTM (2008) recommendations. In CRS test, the sample is loaded at a constant rate of vertical deformation. Drainage is permitted only at the top surface of the specimen. During testing, the excess pore water pressure is generated through the sample with a variation from the maximum at the base until zero at the top surface. The reaction force, axial deformation, and pore water pressure at the base have been measured during the testing at certain time interval. The sample was loaded from 10 kPa until reaching, the maximum stress of 5120 kPa. 2.5

Experimental program

Table 2 shows the experimental program to study the influence of temperature on the illitic soil. 2.6

Experimental theory

Constant rate of strain oedometric test (CRS) was used in this study. By considering a parabolic distribution of pore water pressure through the sample during CRS test, the effective stress can be evaluated as the following (Wissa et al. 1971):

Where σ = measured total stress during the test, and u = measured pore water pressure at the base of the specimen during the test. The measured parameters during isothermal CRS consolidation tests were employed to determine the hydraulic conductivity kt of the studied clay soil at specific temperature and strain rate as indirect method of measurement according to the following equation (ASTM 2008):

The effect of temperature on the hydraulic conductivity of clays can be understood better in terms of the intrinsic permeability, K, as following:

Where µ = pore water viscosity at the tested temperature, T. The value of free pure water viscosity change with temperature (T) as the following equation:

3

RESULTS

3.1 Temperature and strain rate influence on the stress strain curve Figure 2 shows the variation of strain with vertical effective stress under different temperatures (20, 47.6, 69.2◦ C) for CRS tests at .01%/min strain rate. At least, there is no large difference in stress strain behavior between temperatures 20◦ C and 50◦ C. However, at specific effective stress, higher values of strain were observed under temperature of 69◦ C compared with other temperatures. From another perspective, figures 3-5 show the variation of strain with vertical effective stress under different strain rates at a certain temperature. For example at 20◦ C, the values of strain at strain rate of 0.02%/min are lower than others at specific effective stress at this temperature due to the pore pressure increase with strain rate increase. Results showed that the strain-log σ’ curves slightly changed with temperature. A similar behavior for clay was reported by Kholghifard et al. (2014). They mentioned that for dense samples, the soil response is controlled by the compression caused by the applied load. In contrast, lower values of void ratio were obtained at higher temperatures using oedometer tests by Towhata et al. (1993), Boudali et al. (1994), & Marques et al. (2004). However, Burghignoli et al. (2000) indicated that the void ratio changes due to rearrangement of particles, partially from the temperature variation, and also influenced by other factors like stress history, thermal history, over consolidation ratio (OCR), time duration between the application of the last mechanical load and the start of heating, and the duration of the heating phases.

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Figure 2. Influence of temperature on the effective stress-strain curve and pore water pressure.

Figure 3. Influence of strain rate on the effective stress-strain curve and pore water pressure at 20◦ C.

Values of compression index which represent the slope of the compression line converge to the same value at different temperatures. The values for all tests range between 0.191 and 0.217 at temperatures of 20, 47.6, and 69.2◦ C. Also, the compression lines are almost parallel at different strain rates of 0.002, 0.01, and 0.02%/min at a given temperature. The values of swelling index which were obtained from the slopes of the first part of the consolidation curves at different temperatures varied between 0.0051 and 0.016. Figure 6 shows the variation of compression and swelling indexes with temperature and strain rate for 9 tests on the tested clay. Accordingly, compression index for studied clay could be considered independent of temperature and strain rate. Also, the extent of change in the values for all tests indicates that the swelling index remains not strongly dependent on temperature and strain rate. 3.2 Temperature and strain rate effect on the pore water pressure Figures 2-5 show the variation of excess pore pressure with different temperatures and strain rates. For example at 0.01%/min strain rate, the maximum excess pore pressure generated at 47.6◦ C is 1.53 times smaller than at room temperature, while the pore pressure generated at 69.2◦ C is 2.5 times smaller than at room temperature.

Figure 4. Influence of strain rate on the effective stress-strain curve and pore water pressure at 47.6◦ C.

At a certain temperature, results showed that the excess pore pressure decreases as strain rate decreases where it is smallest at low strain rate of 0.002%/min.

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Figure 7. Influence of temperature and strain rate on the preconsolidation pressure obtained from 9 CRS tests.

pressure which was measured at the base of the specimen showed a strong dependency on the temperature and strain rate for the tested illitic clay. The generated excess pore pressure relative to the total stress is less than 15% which is consistent with the ASTM (2008) recommendations.

Figure 5. Influence of strain rate on the effective stress-strain curve and pore water pressure at 69.2◦ C.

Figure 6. Influence of temperature and strain rate on the compression and swelling indices.

In general, at a certain strain rate, the lower the temperature, the higher the generated pore pressure at the base of the specimen and for high temperatures, the generated excess pore pressure decreased. Indeed, the occurrence of high permeability at high temperatures beside the drainage from one side limits the buildup of pore pressure in the specimen. At specific temperature, the higher the strain rate, the higher the generated pore pressure at the base of the specimen. Therefore, at low strain rates, the generated pore water pressure is negligeable, and cannot be measured at very low strain rates. Furthermore, it is noted that at combined high temperature and low strain rate, the generated excess pore pressure is smaller. The generated excess pore

3.3 Temperature and strain rate influence on the preconsolidation pressure The preconsolidation pressure relationship with temperature was experimentally identified by running different isothermal CRS tests at different tem peratures. The determined preconsolidation pressure for illitic clay for all tests at different temperatures (20, 47.6, and 69.2◦ C) was decreased with temperature increase as a linear representation. In addition, preconsolidation pressure was found higher at high strain rate (0.02%/min). Figure 7 shows the variation range of preconsolidation pressure with temperature at different strain rates which was determined from 9 CRS tests on illitic clay. The main reason for the the elastic domain decrease with temperature increase is the reduced viscosity at high temperatures. This reduction in viscosity increases the number of mineral-to-mineral contacts instead of mineral-to-water-to-mineral contacts, and this causes the plastic deformation (Shariatmadari & Saeidijam, 2012). In fact, water acts as an elastic material between two clay particles. A similar result of negative temperature dependency was found by Sultan et al. (2002), and Moritz (1995). Conversely, Mon et al. (2013) concluded that heating causes increasing in the preconsolidation pressure. 3.4 Temperature and strain rate influence on the permeability Table 3 shows the variation of hydraulic conductivity and the intrinsic permeability with temperature for tested clay at void ratio of 0.65 as an example. The hydraulic conductivity at 69.2◦ C was larger than the hydraulic conductivity at 20◦ C by a factor of 3.

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Table 3. Influence of temperature on the permeability (k) and intrinsic permeability (K) for e = 0.65. Temperature

Strain rate %/min 0,002

0,01

0,02

C

k m/s E-11

K m2 E-19

k m/s E-11

K m2 E-19

k m/s E-11

K m2 E-19

20 47.6 69.2

1,31 2,08 3,76

1,33 1,27 1,64

1,59 1,44 5,93

1,61 87,9 2,58

1,62 4,29 6,31

1,64 2,62 2,75

◦

Figure 9. Influence of temperature on the creep index of studied clay.

Figure 8. Variation of preconsolidation pressure with strain rate at different temperatures.

However, at a specific temperature, the hydraulic conductivity increases as strain rate increases for tested clay. According to the obtained results of the studied material, the hydraulic conductivity is temperature dependent, while the variation of the intrinsic permeability with temperature is negligible. There is no important change in the unit weight of water with temperature compared with the viscosity. 3.5 Temperature influence on the creep The cα /cc concept developed by Mesri & Godlewski (1977) was used in this study to determine the creep index value, cα . At a specific temperature, the value of cα /cc together with the compression index, cc , were used to determine the value of creep index.The value of cα /cc was obtained from the slope (α) of the preconsolidation pressure–strain rate logarithmic curve at different strain rates (0.002%/min, 0.01%/min, 0.02%/min) at a specific temperature. Figure 8 shows the variation range of preconsolidation pressure with strain rate at different temperatures for the studied clay. The preconsolidation pressure values were estimated among the variation to determine the cα /cc values. The values of cα /cc varied with temperature. These estimated values were 0.081, 0.056, and 0.106 at temperatures

20, 47.6, and 69.2◦ C, respectively. The compression index, cc , was obtained from the slope of the void ratio versus logarithm of effective stress curve (e-log) at the end of primary consolidation (EOP) at a specific temperature. According to the values of cα /cc and cc , creep index, cα , increased with temperature increase. Figure 9 shows the variation range of creep index with temperature. The estimated values of creep index were 0.0165, 0.012, and 0.0223 corresponding to temperatures of 20, 47.6, and 69.2◦ C, respectively. The amount or rate of creep increases with temperature increase because of the reduction in the apparent viscosity of the contacts between particles at higher temperatures (Gupta 2013). The results showed that the value of cα /cc of illitic clay varied with temperature between 0.039 and 0.125. According to Mesri et al. (1999), the highest value of cα /cc for geotechnical materials rarely exceeds 0.07, but it is significantly less than 0.21. However, Boudali et al. (1994) & Marques et al. (2004) found a parallel slopes at different temperatures.

4

CONCLUSIONS

The results of the experimental study performed on saturated compacted illitic clay using a temperature controlled oedometric cell to investigate the temper ature influence on the hydraulic and mechanical behavior of clay including the creep deformation can be concluded as following:

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Compression index (cc ) and swelling index (cs ) variation with temperature and strain rate can be considered to be negligeable. • The preconsolidation pressure (pc ) is temperature and strain rate dependent. It decreases with temperature increase, while it increases with strain rate increase. • The creep index (cα ) increases with temperature increase. • The hydraulic conductivity (k) increases with heating and strain rate, while the intrinsic permeability (K) can be considered independent of temperature. •

The hydraulic conductivity at 69.2◦ C was larger than the hydraulic conductivity at 20◦ C by a factor of 3. • Pore water pressure (u) decreases with temperature increase and strain rate decrease during CRS tests. • Stress strain behavior of dense samples changes slightly with temperature, while it is strain rate dependent. Strain value increases with strain rate decrease at specific effective stress. REFERENCES Adamis, Z. & Richard, W. 2005. Bentonite, kaolin, and selected clay minerals. Geneva: International programme on chemical safety. AFNOR. 1993. NF P94-051 Sols: reconnaissance et essais; Détermination des limites d’Atterberg – Limite de liquidité à la coupelle- Limite de plasticité au rouleau [Soil: Inverstigation and testing. Determination of Atterberg’s li its. Liquid limit test using cassagrande apparatus. Plastic limit test on rolled thread] (p. 15). Paris: Association Française de Normalisation. AFNOR. 1999. NF P 94-093 Sols: Reconnaissance et essais Détermination des références de compactage d ‘un matériau. Essai Proctor Normal-Essai Proctor Modifié [Soils: Investigation and testing. Determination of the compaction characteristics of a soil. Standard Proctor test. Modified Proctor test] (p. 18). Paris: Association Française de Normalisation. Boudali, M., Leroueil, S. & Srinivasa Murthy, B.R. 1994. Viscous behaviour of natural clays. In: Proceedings of the 13th International Conference on Soil Mechanics and Foundation Engineering1: 411–416. New Delhi, India. Burghignoli, A., Desideri, A. & Miliziano, S. 1992. Deformability of clays under non isothermal conditions. Rivista italiana di Geotecnica 92(4): 227–236. Burghignoli, A., Desideri, A. & Milizia no, S. 2000. A laborat ry study on the thermomechanical behaviour of clayey soils. Can. Geotech. J. 37: 764–780. Crawford, C. B. 1967. Interpretation of the consolidation test. J. Soil Mech. Found. Div., ASCE: 90: 87–102. Cekerevac, C. & Laloui, L. 2004. Experimental study of thermal effects on the mechanical behaviour of a clay. International Journal for Numerical and Analytical Methods in Geomechanics 28(3): 209–228. Gaudette, H.E., Eades, J.L. & Grim, R.E. 1966. The nature of illite. Clays and Clay Minerals 13:33–48. GTR. 2000. Réalisation des remblais et des couches de forme (p. 102). Paris: Laboratoire Central des Ponts et Chaussées. (In French). Green, W.J. 1969. The influence of several factors on the rate of secondary compression of soil. Master thesis, The Missouri University of Science and Technology, Rolla, Missouri, USA. Gupta, B. 1960. Creep of saturated soil at different temperatures. Master Thesis, The University of British Columbia, Canada. Gupta, V. K. 2013. An Experimental Study on Secondary Consolidation of Organic Clay. Master Thesis, Jadavpur University, Kolkata, India.

Kholghifard, M., Ahmad, K., Ali, N., Kassim, A., Kalatehiari, R. & Babakanpour, F. 2014. Temperature effect on compression and collapsibility of residual granitic soil. GRAÐEVINAR 66(3): 1–10. Lynch, F.L. 1997. Frio shale mineralogy and the stoichiometry of the smectite-to-illite reaction: the most important reaction in clastic sedimentary diagenesis. Clays and Clay Minerals 45(5):618-631. Mon, E.E., Hamamoto, K., Kawamoto, S., Komatsu, T. & Møldrup, P. 2013. Temperature effects on geotechnical properties of kaolin clay: simultaneous measurements of consolidation characteristics, shear stiffness, and permeability using a modified oedometer. GSTF International Journal of Geological Sciences (JGS) 1(1). Marques, M. E., Leroueil, S. & Almeida, M. S. 2004. Viscous behaviour of St Roch-de-l’Achigan clay, Quebec, Can. Geotech. J. 41: 25–38. Mesri, G. & Godlewski, P.M. 1977. Time- and stresscompressibility interrelationship. Journal of the Geotechnical Engineering, ASCE 103: 417–430. Mesri, G., Feng, T.W. & Shahien, M. 1999. coefficient of consolidation by inflection point method. Journal of the Geotechnical and geoenvironmental Engineering: 716– 718. Moritz, L. 1995. Geotechnical properties of clay at elevated temperatures. Swedish Geotechnical Institute (SGI). Linköping, Sweden. Sultan, N., Delage, P. & Cui,Y.J. 2002. Temperature effects on the volume change behaviour of Boom clay, Engineering Geology 64(2-3): 135–145. Srodon, J., Morgan, D.J., Eslinger, E.V., Eberl, D. D. & Karlinger , M.A. 1986. Chemistry of illite/smectite and end-member illite. Clays and Clay Minerals 34: 368–378. Standard ASTM. 2006. D2487 Standard practice for classification of soils for engineering purposes (Unified Soil Classification System) (p. 12). West Conshohocken, PA: ASTM International. Standard ASTM. 2008. D4186-06 Standard test method for one-dimensional consolidation properties of soils using controlled-strain loading (American Society of Testing Materials). West Conshohocken, PA: ASTM International. Shariatmadari, N. & Saeidijam, S. 2012. The effect of thermal history on thermo-mechanical behavior of bentonite-sand mixture. International Journal of Civil Engineering 10(2): 162–167. Towhata, I., Kuntiwattanakul, P. & Seko, I. 1993. Volume change of clays induced by heating as observed in consolidation tests. Soils and Foundations 33(4): 170–183. Wissa,A.E.Z., Christian, J.T., Davis, E.H. & Heiberg, S. 1971. Consolidation at constant rate of strain. Journal of Soil Mechanics and Foundations Division, ASCE 97(SM10): 1393–1413. Watabe, Y., Udaka, K., Nakatani, Y. & Leroueil, S. 2012. Long term consolidation behavior interpreted with isotache concept for worldwide clays. Soils & Foundations 52(3): 449–464.

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Impact of temperature variation on pressuremeter test parameters in compacted soils A. Boukelia & H. Eslami LEMTA (CNRS, UMR 7563), Université de Lorraine, Vandœuvre-lès-Nancy-France ESITC de Metz, Metz-France

S. Rosin-Paumier & F. Masrouri LEMTA (CNRS, UMR 7563), Université de Lorraine, Vandœuvre-lès-Nancy-France

ABSTRACT: In geotechnical engineering, the proper design of thermo-active geostructures (piles, foundations, etc.) and deep waste storage disposals requires a better understanding of the thermo-hydro-mechanical behaviour of natural and compacted soils. For design purposes, important mechanical parameters of the soils such as the pressuremeter modulus (EP ), limit pressure (Pl ) and creep pressure (Pf ) are usually obtained by pressuremeter in-situ tests. In the present study, pressuremeter tests were conducted in laboratory, using a mini-pressuremeter, to characterise compacted soils. The objective was to examine and quantify the influence of temperature changes on pressuremeter parameters of two different compacted soils: a clay and a loam. These soils were compacted at their optimal water content and 90% of their maximal dry density (standard Proctor) in a thermo-regulated metric scale container of 800 mm in height and 600 mm in diameter. The compacted soils were then subjected to a range of temperatures from 20 to 50◦ C. Only six tests were performed in each container to prevent edge effects and interaction between the tests. The thermal cycles were applied to the soil massif as following: A heating-cooling cycle (20–40–20◦ C) for the clay; three heating-cooling cycles (20–50◦ C) for the loam. Pressuremeter tests were conducted at the end of several temperature steps. The obtained results showed a decrease in Pl and Pf with increasing temperature for both tested soils, while the variation of EP was less significant. Through the temperature range tested, a quasi-reversibility of the effect of a heating cycle is obtained.

1

INTRODUCTION

In geotechnical engineering the effect of temperature has to be studied particularly for applications such as the storage of nuclear waste (Rutqvist et al. 2002), the burying of high-voltage cables (De Lieto Vollaro et al. 2011) and the thermo-active geostructures (Pahud 2002). These thermo-active geostructures are used to provide sustainable heating and cooling by thermal exchange between buildings and the ground through liquids that flow through closed-loop circulation systems integrated into the geostructures. Thermo-active geostructures may be piles, diaphragm walls, tunnel linings, basement slabs or walls (Brandl, 2006; Fromentin et al., 1999; Laloui et al., 2003). The classical way in which they are used results in temperature cyclic changes in the surrounding ground temperature. Consequently, there are important questions about the effect of temperature variations on hydro-mechanical soil properties which may affect long-term structure performance. In particular, the contraction of the elastic domain (i.e., the yield locus) with increasing temperature has been demonstrated for various clay materials on centimetric samples (Tanaka

et al., 1997; Graham et al., 2001; Cekerevac and Laloui 2004; Marques, 2004; Uchaipichat and Khalili 2009). In this study, tests on larger samples of contrasted materials are performed. The pressuremeter test is currently used to calculate the bearing capacity of deep foundations (AFNOR, 2000; Standard ASTM, 1999). This test consists in introducing in the soil a cylindrical probe with a flexible cover membrane which can expand radially in a hole. As the soil has a pseudo-elastic reaction versus the probe pressure during a part of the test, it is possible to calculate a pressuremeter modulus EP . After that, at higher pressures, large displacements take place and the soil becomes plastic. The creep pressure, Pf is defined as the yielding pressure between the pseudo-elastic and plastic behavior. This parameter is directly correlated to the yield locus. As a result it should be possible to quantify the potential contraction of the elastic domain using pressuremeter tests. Thus, we developed an experimental method to carry out mini-pressuremeter tests on homogeneous soils compacted at a controlled density and water content and subjected to monotonic and cyclic thermal variations (Eslami, 2014).

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Figure 1. Granulometric curves of the studied materials. Table 1. Basic characterization of studied materials. PL %

LL %

PI

Material

MBV g/100 g

wOPN %

ρdmax Mg/m3

Illitic soil Plaisir loam

34 21

65 27

31 6

5.41 1.85

31 16

1.43 1.81

Figure 2. Compaction curves of the studied materials. Table 2. Characteristics of the prepared samples. Material

In the following sections, the material and the developed experimental device are first described. Then, the results are detailed and the impact of thermal variations on the pressuremeter parameters is discussed. 2

MATERIAL AND METHOD

In this part, first the studied material is presented, then experimental device is described and finally the minipressuremeter tests are detailed.

2.1 Basic characterization of materials The tested materials were an illitic soil and a loam taken in the Paris region (Plaisir). The soils were first dried, pulverized and sieved through 2 mm sieve before quartering and then used for various experimentations. The illitic material contains 77% illite, 10% kaolinite, 12% calcite and traces of quartz and feldspar. The Plaisir loam contains 81% quartz, 7% dolomite, 5% calcite, 5% clay materials and 3% felspar. The particle-size distribution of the illitic soil was determined using a laser Malvern Mastersizer 2000®device (AFNOR, 2009) whereas the particle size distribution of the Plaisir loam was determined using sieving and sedimentometric method. Almost 85% of the particles of the illitic material are smaller than 0.002 mm (clay particles). The Plaisir loam is coarser as only 20% of the particles are smaller than 0.002 mm. Other basic parameters like liquid limit (LL), plastic limit (PL), plasticity index (PI) (AFNOR, 1993) and specific surfaces (AFNOR, 1999a) were compiled in Table 1.

w (%)

Tmin Tmax Nb ρd (Mg/m3 ) (◦ C) (◦ C) cycles

Illitic soil 30.5 ± 0.5 1.31 ± 0.01 20 Plaisir loam 16.1 ± 0.2 1.72 ± 0.02 20

40 50

1 3

The optimum water contents (wOPN ) and maximum dry densities (ρdmax ) were obtained from the standard Proctor curves performed for each material (AFNOR, 1999b) (Figure 2). For the same compaction energy, the maximum dry density reached with the Plaisir loam is significantly higher than with the illitic soil in accordance with its coarser granulometry and its mineralogical content. The illitic soil is classified as A3 in the French standard for soil classification (GTR, 2000) and as a fat clay, MH, according to the Unified Soil Classification System (Standard ASTM, 2006). The Plaisir loam is classified as A1 in the French standard for soil classification and as a sandy lean clay, CL, according to the Unified Soil Classification System. 2.2

Experimental device and methods

To perform mini-pressuremeter tests at controlled temperatures, an homogeneous massif with a large volume is required as well as an experimental device to impose thermal variations to the massif. In this part, the developed methodology to obtain a meter-scale sample with homogeneous properties (temperature, water content and dry densities) is described. First, the required amount of water was added to the material in a large capacity fixed-speed (38 rpm) mixer (MIX120®) to reach the target water content (Table 2). The wet material was stored in 8 plastic drums for a minimum of 5 days to ensure good homogenization. A pneumatic compactor was used to compact the

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Figure 5. The 3 steps of a pressuremeter curve. Figure 3. Thermo-regulated metric scale container.

Finally, the entire device was placed in a box constructed of 40-mm-thick extruded polystyrene plates to reinforce the insulation. Seven thermal sensors PT100 were positioned within the massif at various depths and various distances from the wall of the container. The sensors were plugged to a data logger to monitor the temperature variation inside the compacted soil. 2.3

Figure 4. Position of the pressuremeter cell.

material in a cylindrical stainless steel container of 800 mm in height and 600 mm in diameter (Figure 3). The compactor applied dynamic forces on a metallic plate of 4 mm in thick and 600 mm in diameter put on the top of the material to facilitate a homogeneous compaction of the soil. To ensure a homogeneous density of the massif, the compaction was performed in eleven 70-mm-thick layers (Figure 4). A stainless steel tube welded to the outside of the container was connected to a Vulcatherm® thermoregulator to facilitate the circulation of an ethylene glycol-water solution at the target temperature (maximum range: −20 to 90◦ C) in the tube (Figure 3). Thus, the soil compacted in the container was heated or cooled by the container’s outer lateral surface to a maximal range of temperature from 20 to 50◦ C (Table 2). Insulating sleeves were placed around the tube to reduce the heat exchange with the surrounding atmosphere. The top of the massif was insulated with a plastic film to preserve the initial water content.

Mini-pressuremeter tests

The principle of a pressuremeter test is to introduce a cylindrical probe with a flexible cover membrane which can expand radially in a hole (AFNOR, 2000; ASTM, 1999). The pressuremeter curve consists in 3 steps: (i) the probe inflates to obtain the contact with the wall of the hole, (ii) the volume increases linearly with the increasing pressure allowing the calculation of the pressuremeter modulus EP (the soil pseudo-elastic reaction against the probe pressure), and (iii) the large displacements take place and the soil becomes plastic (Figure 5). The creep pressure, Pf is the boundary between the second and the third steps of the test. The limit pressure Pl is the measured pressure when the injected volume reaches twice the original volume of the cavity. Only six mini-pressuremeter tests were performed in each massif to prevent edge effects and crossinfluence between the tests. The test points were positioned on a concentric circle with a diameter half than that of the container. All the test points were located at the same radial position for a correct comparison of the results. The pressuremeter tests were conducted with an APAGEO®mini-pressuremeter probe of 380 mm in height and 28 mm in diameter. Before each pressuremeter test, a core with a diameter equal to that of the mini-pressuremeter probe was extracted using a core sampler. The 630-mm-length core was divided into small pieces to measure the water content and density of the material as a function of depth. The center of the probe was positioned halfway along the height of the compacted soil

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(385 mm). The probe was connected to a GDS® pressure-volume controller. The pressure controlled test consisted in applying increasing pressure with equal increments of 25 kPa for at least one minute per step. The equilibrium volume was measured for each increment and the volume was plotted as a function of pressure. The test was stopped when the injected volume (i.e., the volume variation limit of the probe) reached 140,000 mm3 . Immediately after the pressuremeter test at a given temperature, the borehole was filled with the same material, at the same water content, to avoid influencing the later tests. The effect of temperature variations on the resistance of the minipressuremeter membrane was measured by placing the probe in a climatic chamber at a given temperature during the calibration test of the membrane resistance. 3

RESULTS

The results of the pressuremeter tests performed on the illitic soil and the Plaisir loam are successively presented in this part. 3.1

Figure 6. Temperature variation in the illitic compacted soil at 150 mm from the edge of the container and the chronology of the tests: heating-cooling cycle (20–40–20◦ C), time of the pressuremeter tests (I20a, b, c, d, I40a, b). Table 3. Pressuremeter parameters for the test performed on illitic samples: heating cycle (20–40–20◦ C). Test

T w (◦ C) Cycle (%)

ρd Pf Pl Ep (Mg·m−3 ) (kPa) (kPa) (MPa)

I20b I40a I40b I20c I20d

20 40 40 20 20

1.31 1.31 1.31 1.31 1.32

Illitic soil

For the first test series, starting from 20◦ C, the soil was heated up to 40◦ C and then cooled down to 20◦ C. Figure 6 shows the temperature variation as recorded by a thermal sensor placed at 150 mm from the edge of the massif and at the middle of its height. The thermal equilibrium was reached after 65 h within the limit of ±1◦ C. The water content (w) was maintained unchanged all test long. To verify this point, the average water content of the soil close to the test area (from 200 to 580 mm in depth) was measured (Table 3). At 40◦ C, (w) was slightly lower than at 20◦ C. This might be due to the evaporation of water during the core drilling and the sample weighting as the (w) values measured at the end of the test (I20c,d) were identical to the (w) at the beginning of the test (I20b). The average dry densities were almost identical, confirming the homogeneity of the massif. Two mini-pressuremeter tests were performed at each temperature step: I20a, I20b, then I40a, I40b and finally I20c, I20d. The test I20a failed due to a membrane leakage. The results of the five other tests are presented in Figure 7. The evaluation of the pressuremeter parameters (Ep , Pl and Pf ), allowed the quantitative comparison of the tests at different temperatures (Table 3, Figure 11). The values of Pl and Pf decreased significantly when the massif was heated up to 40◦ C. Thus, the soil was yielded under lower pressures at 40◦ C than at 20◦ C. In other words, the results showed a softening of the soil with heating. The pressuremeter parameters for I20b and I20c–d tests were close that showed a good reversibility of the effect of the temperature variation in the range of 20–40◦ C. The softening due to the heating and

0 1 1 1 1

31.0 30.1 30.4 31.1 31.1

194 166 165 197 178

355 321 288 379 352

3.54 4.16 3.25 4.54 3.89

Figure 7. Pressuremeter curves for the tests on illitic material: I20b, I40a–b and I20c–d.

the reversibility of the observed effects on the creep pressure and the pressure limit were also noticed on the pressuremeter modulus (Ep) to a lower extent. 3.2

Loam tests

For the second test series, the test began 6 days after the compaction of the massif to ensure a good homogeneity of the moisture in the entire sample. The initial temperature of the loam compacted soil was 20◦ C, the

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Figure 8. Impact of temperature variation on pressuremeter test parameters in illitic compacted soil.

Figure 10. Pressuremeter curves for the tests on loam material: heating-cooling cycle (20–50◦ C). Table 4. Pressuremeter parameters for the test performed on loam samples: 3 heating cycles (20–50–20◦ C).

Figure 9. Temperature variation in the loam at 150 mm from the edge of the container and the chronology of the tests: 3 heating-cooling cycles (20–50–20◦ C) and time of the pressuremeter tests.

soil was submitted to three heating cycles up to 50◦ C and then cooling down to 20◦ C. Figure 9 shows the imposed temperature on the outer lateral surface of the container and the temperature variation as recorded by a sensor placed at 150 mm from the edge of the massif and at the middle of its height. The thermal equilibrium was reached after 30 h within the limits of ±1◦ C. Each step lasted 30 to 60 h. An electric failure caused a detectable decreasing of the temperature during the first heating step. The I20a–b tests were performed after the achievement of the previously set temperature. The average water content of the soil close to the test area (from 200 to 580 mm in depth) was measured (Table 4). At 50◦ C, as presented for the 1st test series, (w) was slightly lower than at 20◦ C. The average dry densities were identical, confirming the homogeneity of this parameter over the massif. Two mini-pressuremeter tests were performed at several temperature steps: L20a and L20b before the first cycle; L50a and L50b at the end of the first heating cycle and finally L20c and L20d at the end of the

Test

T w (◦ C) Cycle (%)

ρd Pf Pl Ep (Mg·m−3 ) (kPa) (kPa) (MPa)

L20a L20b L50a L50b L20c L20d

20 20 50 50 20 20

1.71 1.72 1.74 n.c. 1.73 1.71

0 0 1 1 3 3

16.2 16.2 15.9 16.0 16.3 16.0

278 280 220 218 270 250

657 591 517 480 648 535

5.39 5.18 4.90 5.46 5.63 5.86

test after the application of the 3rd cycle. The results of these six tests are presented in Figure 10. The evaluation of the pressuremeter parameters (Ep , Pl and Pf ), allowed the quantitative comparison of the tests at different temperatures (Table 4, Figure 11). The values of the three pressuremeter parameters decreased significantly when the massif was heated up to 50◦ C. As observed for the illitic compacted soil, the results showed a softening of the loam soil with heating. At the end of the cycles, at 20◦ C, the pressuremeter parameters returned back to their initial values: results of L20c-d tests were close to those of L20a-b. A reversibility of the effect of the temperature variation in the range of 20–50◦ C was noticed for this material as for the illitic soil. 4

DISCUSSION

In this part, the results obtained on both materials are compared. The pressuremeter parameters measured on the illitic soil are lower than for the Plaisir loam: – Pf illitic soil = 70% of Pf Plaisir loam; – Pl illitic soil = 57% of Pl Plaisir loam; – Ep illitic soil = 67% of Ep Plaisir loam. To compare the first and the second series of tests, the average values obtained at the end of the first step at 20◦ C, Pf (20), Pl (20) and Ep (20) were considered as

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Figure 11. Impact of temperature variation on pressuremeter test parameters in compacted loam. Table 5. Normalized pressuremeter parameters for both series. Material

T (◦ C)

Cycle

Pn.f

Pn.l

En.p

Illite Illite Illite Loam Loam Loam

20 40 20 20 50 20

0 1 1 0 1 3

1.00 0.85 0.97 1.00 0.78 0.93

1.00 0.86 1.03 1.00 0.80 0.95

1.00 1.05 1.19 1.00 0.98 1.09

reference values, and all other values were normalized with respect to these reference values (see equations 1, 2 and 3). Normalized parameters were presented in Table 5.

Figure 12 shows the evolution of the normalized parameters at each step of each test series. For the studied materials compacted at 90% of their maximal dry density, the creep pressure and the limit pressure decreased with increasing temperature that evidenced the thermal softening of both materials. These results are consistent with the literature results obtained with oedometric and triaxial tests (Marques et al., 2004, Cekerevac and Laloui, 2004, Graham et al., 2001, Tanaka et al., 1997, Hueckel & Baldi, 1990). In this study, after heating-cooling cycles, for both soils all pressuremeter parameters recovered approximately their initial values (reversibility of thermal softening). Heating the illitic sample from 20 to 40◦ C decreased Pn.f by 15% and Pn.l by 14%, while returning back to 20◦ C increased these parameters respectively up to 12% and 17%. As a similar way, heating

Figure 12. Evolution of the normalized parameters according to the test temperature for two materials.

the compacted loam from 20 to 50◦ C decreased Pn.f by 22% and Pn.l by 20%, while cooling down to 20◦ C increased these parameters up to 15%. The level of Pn.l and Pn.f measured in the compacted loam at the end of the three thermal cycles was a little lower than the initial values. This trend has to be followed in a future study with more cycles to test a possible cumulative effect. The comparison between these two materials shows that in spite of their difference in mineralogy, initial water content and dry densities, normalized parameters can be considered as linear. A simple linear regression (equations 4 and 5) may be used to determine Pf and Pl values according to the sample temperature (T):

5

CONCLUSIONS

The objective of this paper was to quantify the effect of both monotonic and cyclic temperature variations on different soil pressuremeter parameters. A specific device was developed to measure the minipressuremeter parameters in laboratory conditions and

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at different temperatures. The evolution of the pressuremeter modulus (Ep), the creep pressure (Pf ) and the limit pressure (Pl ) was measured under imposed thermal conditions on a clayey compacted soil and a compacted loam. The results of the mini-pressuremeter tests on both materials showed a decrease in the creep pressure and the limit pressure with temperature increase (thermal softening), while the variation of the pressuremeter modulus was less significant, this could be due to the well-known higher variability of this parameter. The results tended to show the reversibility of the temperature effects on the measured parameters for one and three heating cycle both for the illitic soil in the tested temperature range (20–40◦ C) and the compacted loam in the tested temperature range (20–50◦ C). ACKNOWLEDGEMENTS The authors acknowledge C. Fontaine from IC2MP laboratory (Poitiers, France) for the mineralogical analyses and the Region Lorraine for the financial support. REFERENCES AFNOR, 1993. NF P94-051 – Sols: reconnaissance et essais; Détermination des limites d’Atterberg – Limite de liquidité à la coupelle- Limite de plasticité au rouleau. Association Française de Normalisation, Paris, France, p. 15. AFNOR, 1999a. NF EN 933-9 – Tests for geometrical properties of aggregates – Part 9: Assessment of fines – Methylene blue test. Association Française de Normalisation, Paris, France, p. 12. AFNOR, 1999b. NF P94-093 – Sols: Reconnaissance et essais Détermination des références de compactage d ’un matériau. Essai Proctor Normal-Essai Proctor Modifié. Association Française de Normalisation, Paris, France, p. 18. AFNOR, 2000. NF P94-110-1 – Sols: reconnaissance et essais Essai pressiométrique Ménard. Association Française de Normalisation, Paris, France, p. 44. AFNOR, 2009. ISO 13320: Particle size analysis – Laser diffraction methods. Association française de normalization, 60p. Brandl, H. 2006. Energy foundations and other thermo-active ground structures. Géotechnique 56: 81–122.

Cekerevac, C. & Laloui, L. 2004. Experimental study of thermal effects on the mechanical behaviour of a clay. Int. J. Numer. Anal. Methods Geomech. 28: 209–228. De Lieto Vollaro, R., Fontana, L. & Vallati, A., 2011. Thermal analysis of underground electrical power cables buried in non-homogeneous soils. Applied Thermal Engineering, 31(5), pp. 772–778. Eslami, H. 2014. Comportement Thermo-hydromécanique des sols au voisinage des géo-structures énergétiques. PhD Thesis, Université de lorraine, France, 214p. Eslami, H, Rosin-Paumier, S, Abdallah, A, Masrouri, F, 2014. Impact of temperature variation on penetration test parameters in compacted soils. European Journal of Environmental and Civil Engineering DOI: 10.1080/19648189.2014.960952. Fromentin, A., Pahud, D., Laloui, L., Moreni, M., 1999. Pieux échangeurs: conception et règles de prédimensionnement. Rev. Fra. GC. 3, 387–421. Graham, J.,Tanaka, N., Crilly,T. &Alfaro, M. 2001. Modified Cam-Clay modelling of temperature effects in clays. Can. Geotech. J. 38: 608–621. GTR, 2000. Réalisation des remblais et des couches de forme. Laboratoire Central des Ponts et Chaussées, Paris, p. 102. Hueckel, T., Baldi, G., 1990. Thermoplasticity of saturated clays: experimental constitutive study. J. Geotech. Eng. 116, 1778–1796. Laloui, L., Moreni, M. & Vulliet, L. 2003. Comportement d’un pieu bi-fonction, fondation et échangeur de chaleur. Can. Geotech. J. 40: 388–402. Marques, M. 2004. Viscous behaviour of St-Roch-del’Achigan clay, Quebec. Can. Geotech. J. 38: 25–38. Pahud, D., 2002. Geothermal energy and heat storage. SUPSI – DCT – LEEE Laboratorio di Energia, Ecologia ed Economia, pp. 1–133. Rutqvist, J. et al., 2002. A modeling approach for analysis of coupled multiphase fluid flow heat transfer, and deformation in fractured porous rock. International Journal of Rock Mechanics and Mining Sciences, 39(4), pp. 429–442. Standard ASTM, 1999. D4719-00 Standard test method for Prebored Pressuremeter Testing in Soils. ASTM International, West Conshohocken, PA. ASTM. p. 9. Standard ASTM, 2006. D2487 Standard practice for classification of soils for engineering purposes (Unified Soil Classification System). ASTM International, West Conshohocken, PA www.ASTM.org. Tanaka, N., Graham, J. & Crilly, T. 1997. Stress-strain behaviour of reconstituted illitic clay at different temperatures. Eng. Geol. 47: 339–350. Uchaipichat, A. & Khalili, N. 2009. Experimental investigation of thermo-hydro-mechanical behaviour of an unsaturated silt. Géotechnique 59: 339–353.

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Clay-water interactions in swelling claystones: The case of the Callovo-Oxfordian claystone H. Menaceur, P. Delage & A.M. Tang Ecole des Ponts ParisTech, Navier/CERMES, Marne la Vallée, France

J. Talandier Andra, Châtenay-Malabry, France

ABSTRACT: An investigation of the microstructure changes of the Callovo-Oxfordian (COx) claystone (a possible host rock for geological radioactive waste disposal in France) due to suction changes was conducted by means of mercury intrusion porosimetry tests. A unimodal pore population around a mean diameter of 32 nm was observed at initial state, with pore size distribution (PSD) curves slightly moved towards smaller mean diameters (27–28 nm) under suctions of 150 and 331 MPa, respectively, with diameter reducing to 20 nm after oven-drying. Wetting from the initial state (suction 34 MPa, degree of saturation of 77.6%) to 9 MPa suction led to water saturation with no significant change of the PSD curve, whereas wetting at zero suction gave rise to the appearance of cracks of several micrometers width, together with an enlargement of the initial pore population. The step hydration mechanisms of smectites by successive placement of distinct layers of water molecules within the clay platelets along the smectite faces with respect to the suction applied helped understanding these microstructure changes. An average number of 22 layers in a platelet was estimated from the dry PSD curve, based on a brick model, and it was shown that hydration at suction of various hundreds of MPa was due to the adsorption of one water layer whereas that under suction larger than 9 MPa (various tens of MPa) were characterised by the adsorption of 2 water layers. Significant microstructure changes below 9 MPa corresponded to the third adsorbed layer. This data evidence the significant difference in status of the strongly adsorbed intra-platelet water (estimated to 25–30% of the total water) compared to the inter-platelets water (70–75%) that behaves like free water and that is involved in water transfer and hydro-mechanical couplings.

1

INTRODUCTION

2

The Callovo-Oxfordian claystone (COx), an indurated clay rock 155 million years old (limit upper-middle Jurassic), is considered as a potential host rock for radioactive waste disposal at great depth in France. Due to the excavation and ventilation of the galleries, the rock mass around galleries and disposal cells is prone to desaturation, that will be followed by progressive resaturation at the end of the operating stage once the galleries are closed. In this regard, the water retention properties of the COx claystone have been investigated in details by Wan et al. (2014), following previous investigations by Pham et al. (2007) and Boulin et al. (2008) who related it to its pore size distribution (PSD) investigated by mercury intrusion porosimetry (MIP). In this paper, the changes in microstructure with respect to changes in suction are investigating based on MIP experiments that were carried out on freezedried specimens put at various suctions along both the drying and wetting paths starting from the initial state of the specimen in the laboratory.

MATERIALS AND METHODS

2.1 The Callovo-Oxfordian claystone The COx claystone specimens investigated here come from the Underground Research Laboratory excavated at a depth of 490 m close to the village of Bure (eastern France) by Andra, the French Agency for the management of radioactive wastes. The COx claystone is 155 millions years old (limit upper-middle Jurassic) and the thickness of layer is about 150 m. At this depth, the COx claystone is made up (Gaucher et al., 2004) of a clay matrix (45–50%) containing detritic grains of carbonate (20%), quartz (22%) and other minerals (feldspars, pyrite, dolomite and siderite, 9%). The clay matrix is mainly made up of interstratified minerals of illite–smectites (Yven et al. 2007). The specimens were drilled from a 80 mm diameter and 300 mm long core (EST44584) parallel to bedding. The water content was determined after drying in the oven at 105◦ C for 48 hours. The porosity and degree of saturation were calculated from carefully measuring

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Table 1. Saline solutions used. Solution

Relative humidity (%)

Suction (MPa)

KOH MgCl2 KNO3 Pure water

9 33 93.7 100

331 150 9 0

the sample volume by using hydrostatic weighing. The initial total suction was determined by using a dew point tensiometer (WP4, Decagon). The degree of saturation was around 77.6% corresponding to a suction of 34 MPa for a porosity of 17.0%. The dry density and grain density values are 2.16 and 2.7 Mg/m3 , respectively. Partial saturation resulted from the combined actions of coring, stress release, transport, storage and specimen preparation. 2.2 Experimental techniques All tests were run on specimens of 38 mm in diameter and between 8–10 mm in height. To do so, the core was firstly sliced by using a diamond wire saw at low speed in dry condition to obtain a cylinder sample of 80 mm in thickness that was then placed in a special metal confining mould and cored to the desired diameter (38 mm) by using a diamond barrel in dry condition. Finally, small specimens of 8–10 mm in thickness were cut by using a diamond saw. Suctions were imposed by the vapour control technique using saturated saline solutions as shown in Table 1. Specimens were left in the desiccators until reaching mass stabilization (checked by periodic precision weighing). Once equilibrated, a suction measurement was made by using the WP4 dew point potentiometer. Afterwards, the specimens were immediately waxed using slush wax (at lowest possible temperature before solidification, see Wan et al. (2013) for more detail). Careful weighing was carried out prior and after waxing, giving a good determination of the wax weight and volume. The specimen volume was obtained by subtracting the wax volume from that of the waxed specimen. The wax technique was also used to obtain the specimen volume at initial state (34 MPa of suction, degree of saturation of 77.6%). Finally, the specimens were cut into small pieces to measure their water content by oven drying. The void ratio and degree of saturation were determined by measuring the volume by means of hydrostatic weighing. Mercury intrusion porosimetry (MIP) tests were conducted on various specimens at different suctions along both drying or wetting paths. Dehydration was made by freeze-drying small pieces of claystone (1–3 g in weight) that were previously quickly frozen by immersion in slush nitrogen obtained by previously applying vacuum (reducing nitrogen temperature from boiling temperature at −196◦ C to freezing temperature at −210◦ C (Delage et al. 2006). MIP tests were

carried out in a Micromeritics-AutoPore IV 9500 porosimeter from a low initial pressure of 3.4 kPa up to 227.5 MPa, corresponding to entrance pore diameters of 363.6 µm and 5.5 nm respectively. The intruded mercury porosity (nHg ) was defined as the ratio VHg /V of mercury intrusion volume VHg to specimen total volume V . The pore entrance diameter (D) was determined from the intrusion pressure PHg by assuming a cylindrical pore shape according to the Laplace-Young equation (D = 4 σ cos θ/PHg ) where σ is the mercury-solid interfacial tension and θ is the mercury-solid contact angle (σ = 0.484 N/m and θ = 141.3◦ according to Diamond 1970). 2.3 Test program A first series of samples were submitted to dryingwetting path from the initial water content (equal to 6.12% with a 34 MPa suction and a degree of saturation of 77.6%). Specimens A1 and B1 were used to investigate their microstructure at 150 and 331 MPa respectively. Once dried at 331 MPa, specimens A2 and B2 were afterwards wetted at 9 MPa and zero suctions, so as to determine the main wetting path. Along the wetting path, both specimens were periodically taken out from the desiccator for weighing so as to determine their water content. Their suction was also measured by means of the WP4 dew-point tensiometer. A second series of tests corresponded to wettingdrying paths. Starting from the initial water content (6.12%), three specimens (C, D1 and D2) were firstly wetted under decreasing suctions (9 MPa for specimen C and zero suction for specimens D1, D2). Specimen D2 was then used to determine the main drying path up to suctions of 150 MPa and 331 MPa. 3 WATER RETENTION CURVE The water retention curve expressed in terms of changes in water content versus suction is presented in Figure 1. The points at zero suction are arbitrarily plotted at a suction of 0.01 MPa. Starting from the initial state (w = 6.12%, suction 34 MPa), two points were obtained from two distinct specimens (A1 and B1) with a direct single step drying at controlled suctions of 150 and 331 MPa, respectively. Similarly, two other points were obtained from specimens C and D1 with a direct single step wetting at suctions of 9 and 0 MPa. Data along the main wetting and drying paths were also obtained by suction measurements and water content determination along the wetting path from 331 to 0 MPa for specimen B2 and along the drying path from zero suction to 331 MPa for specimen D2. Good correspondence is observed along the main wetting path between the data of specimens B2 and A2 that was wetted between 331 and 9 MPa, providing some confidence in the quality of the data. Examination of the main drying and wetting paths gives evidence of a hysteresis. The data also show that

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Figure 1. Water retention curve of the COx claystone.

the initial state resulting from desaturation from the in-situ saturated state is located, as expected, on the main drying path. The wetting path starting from the initial state shows that the point at 9 MPa of suction (specimen C) is located below the main drying path, which is typical of scanning curves (there is unfortunately no other point between 9 MPa and zero suction along this path). The point at zero suction obtained along the main wetting path starting from the dry state at 331 MPa provides a water content (11.2%) higher than that obtained after wetting the specimen from the initial water content (10.4%). The changes in degree of saturation and volume with respect to suction are presented in Figure 2. The Figure shows that the specimen becomes quasisaturated at 9 MPa (Sr = 96%, w = 7.65%) along the wetting path with however little volume changes, whereas most swelling is observed for suctions between 9 and 0 MPa with 6.1% swelling at zero suction. Along the drying path from initial state, a linear relationship is observed between the degree of saturation and the water content with an average decrease of 13% in degree of saturation for a decrease of 1% in water content. The main wetting curve obtained once the specimen has been dried to the highest suction (331 MPa) is located below the curves of dryingwetting from initial state, confirming the hysteresis observed by Wan et al. (2013). 4

MERCURY INTRUSION POROSIMETRY

The pore size distribution curve of the specimen at initial state (Sr = 77.6%, porosity n = 17.0%) is plotted in cumulative and density function curves in Figure 3. The total porosity n of the specimen is also plotted in the cumulative curve, showing that the mercury intruded porosity nHg is smaller than the total one, with an infra-porosity (n − nHg ) of 4%. Pores smaller than the lower limit of 5.5 nm (corresponding to the maximum mercury pressure of 227.5 MPa) cannot be intruded. The non negligible

Figure 2. Changes in degree of saturation and volume with respect to suction.

infra-porosity found here confirms previous findings on the COx claystone by Yven et al. (2007), Boulin et al. (2008) and Delage et al. (2014) who estimated the porosity not intruded by mercury at 25% of the total porosity, in accordance with the 23.5% value with diameter smaller than 5.5 nm found in the present research. The density function curve exhibits at initial state a typical monomodal curve with quite a well defined pore population identified by an inflection point at 32 nm. As shown by Sammartino et al. (2003),Yven et al. (2007) and Boulin et al. (2008), this pore population is related to the average entrance pore diameter within the clay matrix. Figure 4 presents an enlargement between 0.001 and 0.1 µm of the pore size distribution curves of specimens A1 and B2 submitted to a suction increase along the drying path up to 150 and 331 MPa respectively from the initial state, together with the PSD data of the specimen at initial state and that of a specimen oven-dried at 105◦ C for 48 h. The total porosities obtained from volume measurements are also given. The intruded mercury porosities nHg of the specimens dried up to 150 (A1) and 331 MPa (B1) are equal to 12.8 and 12.2%, respectively, compared to total porosities of 15.9 and 15.2%, respectively, showing that the infra-porosities not intruded by mercury (D < 5.5 nm) are again lower than the total ones. The infra-porosities are smaller than that at initial state (n − nHg = 3.0% for both specimens dried up to 150 and 331 MPa, compared to 4% at initial state). Conversely, the mercury intruded porosity of the oven-dried specimen (12%) appears to be quite close to the total one

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Figure 3. Pore size distribution curves of specimen EST44584 at initial state.

Figure 5. Pore size distribution curves along the drying path.

at initial state with a only slight increase in total porosity at 9 MPa (0.2%), showing that the infraporosity is also similar in both cases.This is compatible with the negligible volume change observed in the volume change/suction curve of Figure 2 when passing from initial state (s = 34 MPa) to a suction of 9 MPa. The specimen saturation from Sr = 78% to 96% hence occurs by complete filling of the mean pore population with very little microstructure changes both in the porosity intruded and not intruded by mercury. The reduction in suction from 9 MPa to 0 MPa occurs at quasi-saturated state with a significant 6.1% swelling giving a final water content of 10.5% and degree of saturation of 99% (Figure 2). Indeed, significant changes are also observed at the microstructure level, as shown by the change in shape of the PSD curve of specimen D1 at zero suction that becomes bimodal. Changes affect three levels of porosity: Figure 4. Pore size distribution curves along the drying path.

(13%) giving an infra-porosity n − nHg = 1% significantly smaller than at suctions of 150 and 331 MPa (3%). In Figure 5, the pore size distribution curves of the two specimens wetted from initial state at low suctions (9 MPa and zero) and higher degree of saturation (Sr = 96% and 99% for s = 9 and 0 MPa, respectively) are presented together with the data at initial state (Sr = 77,6%, s = 34 MPa). Also plotted in the Figure are the total porosities of the specimens. The PSD cumulative and density function curves at 9 MPa suction (Sr = 96%) are quite similar to that

i) The infra porosity n − nHg that increases from 4% at 9 MPa to 6.1% at zero suction with an intruded porosity of 15.6% and a total one of 21.7%; ii) The large porosity with appearance of a new pore population corresponding to a proportion of 10.5% of the total porosity in the range of diameters between 7 and 100 µm with a mean diameter around 12 µm; iii) An enlargement of the previous pore population that moves from a narrow range between 12 and 50 nm (see density function curve in Figure 5) to a wider range between 12 and 500 nm with a new plateau between 60 and 200 nm. Note however that no change is observed in the density function curves between 5 and 20 nm.

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Figure 6. Schematic model of COx microstructure (after Yven et al. 2007).

5

DISCUSSION

The interpretation of the microstructure changes with respect to suction changes is interpreted based on the conceptual model of the COx claystone microstructure of Yven et al. (2007) presented in Figure 6. The model schematically shows how individual calcite or quartz detritic grains are embedded into a clay matrix that represents 45–50% of total constituents at the depth of 490 m considered here. The well defined single pore population defined by an average value of 32 nm observed in the PSD curve at initial state can be interpreted by assimilating the clay matrix to an assembly of bricks made up of platelets of comparable thickness, as can be seen in Figure 6. As seen on the scheme, the diameter of the circular pore located within the bricks provides an estimate of the brick thickness. The mean diameter detected in the PSD curve hence provides an estimation of the average platelet thickness (32 nm). Further understanding on the changes in microstructure observed can be gained by considering the mechanisms of hydration of smectites. Many studies have been devoted to the interactions between smectite minerals and water and to the hydration mechanisms of smectites. Based on X-ray diffractometry techniques and through the observation of the changes during hydration of the d001 interbasal spacing, it has been shown that hydration from a dry state occurred through the ordered placement, step by step, of one, then two, then three and finally four layers of water molecules along the smectite surface (e.g. Mooney et al. 1952, Norris 1954). Interestingly, this mechanism is depending of the suction of the pore water. Convergent data independently obtained by various authors on various smectites (including Saiyouri et al. 2000, 2004, Ferrage et al. 2007) indicated that at high suctions of various hundreds of MPa (imposed by controlled

relative humidities), one water layer is adsorbed along the smectite surface. Two layers are adsorbed at various tens of MPa whereas a third layer is adsorbed below around 10 MPa. The limits in suction change with the origin of the smectites and nature of the cations, but these average values provide a reasonable order of magnitude of the correspondence between the number of water layers and the suction values. Observation of the PSD curves of Figure 4 along the drying path (initial state, 150, 330 MPa suctions and oven-dried specimen) indicates that drying is characterized by a reduction of the mean diameter of the single well defined pore population from 32 nm (intact) to 28 (150 MPa), 27 (331 MPa) and 21 nm (oven-dried). Based on the brick model, this corresponds to a reduction in thickness of the platelets. This reduction is only due to changes in the interlayer spacing of smectite, given that illite minerals are not sensitive to changes in water content with a constant thickness of 9.6 Å. Based on the suction values given above, it can be reasonably considered that all specimens at suction higher than 150 MPa have only one layer of adsorbed water molecules along the smectite minerals within the clay platelets. At initial state and a suction of 34 MPa, the data of Sayiouri et al. (2004) would indicate the possibility of having two layers adsorbed, in reasonable compatibility with the data of Ferrage et al. (2005). The reduction of the average diameter from 32 to 28 nm can then be linked to the transition from two to one adsorbed layer of water molecules. Oven drying resulted in having no more water layer adsorbed (Ferrage et al. 2005). An estimation of the average number of clay layers in one platelet of mixedlayer illite-smectite can then be obtained by using the mean diameter of 21 nm measured on the oven-dried specimen, that corresponds to the average platelet thickness. With an interlayer spacing of 9.6 Å, this provides a number of 21–22 layers per platelet. Considering the proportion of 50–70% smectite minerals provided by Yven et al. (2007) at the level considered in the COx layer, one can conclude that the introduction of one water layer along the smectite layers would result in the placement of between 11 and 15 layers of 3 Å thick layers of water molecules, resulting in an increase in the platelet thickness between 3.3 and of 4.6 nm, from 21 to 24.3–25.6 nm. This is not far from the 28 nm value measured by MIP under suctions of 150 and 331 MPa. Adding another water layer would then provide a thickness between 27.6 and 30.2 nm, reasonably comparable to the 32 nm measured by MIP under 34 and 9 MPa suctions. This indicates that the analysis based on the step hydration process evidenced in pure and compacted smectites is reasonably compatible with the analysis of the MIP data with respect to the changes in platelets thickness in the COx clay matrix with suction. Better fitting is actually obtained with the highest proportion of smectite of 70% in the clay fraction. The mechanism of hydration of smectites hence appears to be

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of significant interest to interpret the water retention properties and related microstructure changes of the COx claystone. As observed in Figure 5, little change was observed between the sample at initial state (34 MPa) and that at 9 MPa both in average mean pore diameter and infraporosity, indicating that the two water layers are stable under this suction range, with the third water layer only adsorbed at suction smaller than 9 MPa. The significant swelling due to wetting at zero suction was analysed through three mechanisms in section 4. The mechanism i) that concerns the infra porosity can be related to the adsorption of a third or even a fourth layer of water molecules within the infra-porosity that increased from 4% (initial state at 34 MPa) to 6.1% at zero suction. Based on the hydration model used above, adding a new water layer would result in an increase of 7 nm in the platelet thickness, giving an average value of 39 nm. Adding a fourth water layer would lead to an average thickness of 46 nm. These increases in thickness are compatible with mechanism ii) with an enlargement of the diameter of the mean pore population towards larger value. It does not however explain the appearance of pores as large as 200 or 300 nm that can be linked to a higher degree of disorder, as observed in compacted bentonites (Sayiouri et al. 2004) in which the suction reduction below 0.1 MPa (appearance of the fourth layer) also involved a reduction in thickness of the platelets due to exfoliation of clay layers together with an increase in the number of platelets. Further investigation is necessary here in the case of the COx claystone to better understand this phenomenon. The appearance of the large pore population with diameters between 7 and 100 µm is related to the appearance of cracks that can be observed visually and have also been observed by Wang et al. (2014) by using Digital Image Correlation at microscopic level. These cracks, that are saturated as observed in Figure 2, were suspected in the analysis of the water retention properties of the COx claystone provided by Wan et al. (2013). The investigation carried out here also evidenced the roles of two distinct natures of water. Given that they correspond to suctions larger than 7–9 MPa, the layers of water molecules adsorbed within the mixedlayers illite-smectite platelets at initial state, along the drying path and even at 9 MPa suction are heavily bonded to the smectite surfaces. Contrarily, the water molecules contained in the inter-platelets porosity with mean diameter of 32 nm can be considered as free water. An estimation of the relative proportion of adsorbed and free water can be obtained from the pore size distribution curve of Figure 3. According to the shape of the density function curve, the lower limit of the main pore population can be estimated at a diameter of 0.01 µm. With a total porosity of 0.170, the corresponding proportion of free water of the order of 68%. In other words, MIP provides a porosity that is not far from that occupied by free water. It is likely that

the hydro-mechanical couplings characterised by the water pore pressure as well as water transfers within the claystone are governed by this free inter-platelet water and do not concern the remaining two water molecules that are adsorbed along the smectite faces at initial state. This provides an insight into the status of water in the claystone. 6

CONCLUSION

The use of mercury intrusion porosimetry on freezedried specimens provided better understanding of the changes in microstructure that occur along the wetting and drying paths of the water retention curve of the COx claystone. The concepts developed to describe the hydration mechanisms of smectites and their dependency with respect to suction changes appeared to be applicable to the hydration of the mixed-layer illitesmectite minerals that is responsible of the change in water content and the swelling-shrinkage behaviour of the COx claystone. The initial state of the COx specimen considered in this work is located on the main drying path of the water retention curve and characterized by a suction of 34 MPa that corresponds to the adsorption of two layers of water molecules along the smectite faces. Releasing the suction to 9 MPa results in the quasi-saturation of the claystone but it does not significantly affects the COx microstructure with quite little swelling and no change in the pore size distribution curve, in accordance with the stability of the two layers of water molecules in this suction range. Conversely, passing from 9 MPa to zero suction allows the placement of a third, or even a fourth layer of water molecules that results in significant changes in the inter-platelets porosity. Simultaneously, a network of saturated cracks appears and the global swelling observed at zero suction comes from the combined action of the changes in the inter-platelet porosity and the generation of cracks. Imposing suctions of 150 and 331 MPa results in a reduction from 32 to 28–27 nm of the mean diameter of the pore size distribution curve that keeps the same shape, in agreement with the placement of one layer of water molecules in this suction range, which explain the small differences in microstructure observed at these two suctions. Conversely, oven-drying at 105◦ C results in a further decrease to 20 nm in the mean diameter of the inter-platelet porosity. These features are compatible with the state of smectite minerals at dry state, with no water layer adsorbed and an interlayer space of 9.6 Å. The validity of the concepts of hydration of smectites indeed provides deeper insight in the understanding of changes in water contents and swellingshrinkage behaviour of the COx claystone. They confirm, as also observed when comparing the water retention behaviour of powder and compacted smectites (Delage et al. 2006), that microstructure effects are mainly governed by physico-chemical interactions,

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with little effects of the initial fabric and structure of the claystone. In other words, the intensity of these interactions is strong enough to surpass and break the inter-particle bonding at initial state, even in the case of the strong inter-particle bonds within the clay matrix of the claystone. These findings should help with any problem linked to swelling in shales, like in petroleum industry (stability of boreholes in shales) or tunnelling (interaction between shales and the support). Finally, the mechanisms of water adsorption along smectites allows to better define the status of water in claystones and shales containing some smectites, with a distinction between the adsorbed water (located within the platelets and made up of two layers strongly bonded along the smectite faces with suctions larger than 9 MPa) and the free water (located in the interplatelets porosity, defining the pore pressure and submitted to water transfers). The MIP curve at initial state provides an idea of the proportions of the two types of water, with around 68% of free inter-platelets water and 32% of adsorbed intra-platelets water. ACKNOWLEDGEMENTS The authors are indebted to Andra for supporting the work and for providing the samples. REFERENCES Boulin PF, Angulo-Jaramillo R, Daian JF, Talandier J, Berne P (2008). Pore gas connectivity analysis in Callovo– Oxfordian argillite. Applied Clay Science 42(1–2): 276–283. Delage P, Marcial D, Cui YJ, Ruiz X (2006). Ageing effects in a compacted bentonite: a microstructure approach. Géotechnique 56(5):291–304. Delage P, Menaceur H, Tang AM, Talandier J (2014). Suction effects in deep Callovo-Oxfordian claystone specimen. Géotechnique Letters 3(2), 84–88.

Diamond, S (1970). Pore size distribution in clays. Clays Clay Minerals 18:7–23. Ferrage E, Lanson B, Sakharov BA, Drits VA (2005). Investigation of smectite hydration properties by modeling experimental X-ray diffraction patterns: Part I. Montmorillonite hydration properties. American Mineralogis. 90:1358–1374. Gaucher G, Robelin C, Matray JM, Négrel G, Gros Y, Heitz JF, VinsotA, Rebours H, Cassagnabère, BouchetA (2004). ANDRA underground research laboratory: interpretation of the mineralogical and geochemical data acquired in the Callovian-Oxfordian formation by investigative drilling. Physics and Chemistry of the Earth 29:55–77. Mooney RW, Keenan AC, Wood LA (1952). Adsorption of water vapor by montmorillonite. II. Effect of exchangeable ions and lattice swelling as measured from X-ray diffraction. Journal of the American Chemical Society 74:1371–1374. Norrish K (1954). The swelling of montmorillonite. Discussions of the Faraday Society, 18, 120–133. Pham QT, Vales F, Malinsky L, Nguyen Minh D, Gharbi H (2007). Effects of desaturation-resaturation on mudstone. Physics and Chemistry of the Earth 32:646–655 Saiyouri N, Tessier D, Hicher PY (2004). Experimental study of swelling in unsaturated compacted clays. Clay Minerals 39:469–479. Sammartino S, Bouchet A, Prêt D, Parneix JC, Tevissen E (2003). Spatial distribution of porosity and minerals in clay rocks from the Callovo–Oxfordian formation (Meuse/Haute-Marne, Eastern France)—implications on ionics species diffusion and rock sorption capability. Applied Clay Science 23(1–4):157–166. Wan M, Delage P, Tang AM, Talandier J (2013). Water retention properties of the Callovo-Oxfordian claystone. International Journal of Rock Mechanics and Mining Sciences 64: 96–104. Wang LL, Bornert M, Héripré E, Yang DS, Chanchole S (2014). Irreversible deformation and damage in argillaceous rocks induced by wetting/drying. Journal of Applied Geophysics 107:108–118. Yven, B., Sammartino, S., Géroud,Y., Homand, F. & Villiéras, F. (2007). Mineralogy, texture and porosity of CallovoOxfordian claystones of the Meuse/Haute-Marne region (eastern Paris Basin). Mém. Soc. Géol. France 178, 73–90.

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Energy Geotechnics – Wuttke, Bauer & Sánchez (Eds) © 2016 Taylor & Francis Group, London, ISBN 978-1-138-03299-6

Air injection tests in two argillaceous rock formations: Experimental results and modelling L. Gonzalez-Blanco & E. Romero Department of Civil and Environmental Engineering, Universitat Politècnica de Catalunya, Barcelona, Spain

X.L. Li EIG EURIDICE, Mol, Belgium

X. Sillen ONDRAF/NIRAS, Brussels, Belgium

P. Marschall NAGRA, National Cooperative for Disposal of Radioactive Waste, Wettingen, Switzerland

C. Jommi Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, The Netherlands

ABSTRACT: Air flow through two argillaceous rock formations is investigated on the basis of laboratory work and its modelling to help in the interpretation of the results. Priority in the experimental program has been given to study the volume change response of these initially water saturated materials along relatively fast and controlled volume rate air injections. These high rates intend to give preference to single-phase air flow mechanisms associated with the opening of stress-dependent pathways. Particular attention has been focused on the changes in the pore network to detect opening of fissures after air injection tests using mercury intrusion porosimetry. Selected experimental results have been simulated using a fully coupled hydro-mechanical finite element code, which incorporates an embedded fracture permeability model to account for the simulation of the gas flow along preferential pathways.

1

INTRODUCTION

Argillaceous sedimentary formations have been studied during the last decades as potential host formations for the geological disposal of long-living and heat-emitting radioactive waste in Belgium and Switzerland. A significant issue in the long-term performance of these potential host rocks concerns the generation and migration of gases. Actually, in the post-closure phase of a disposal system, gases can be produced as a result of the anaerobic corrosion of metal canisters, radiolysis, and microbial degradation of organic waste (ONDRAF/NIRAS 2013). The pressure resulting from the gas generation in an almost impermeable geological medium in the nearfield of a repository will increase. Under high gas pressures, the mechanical and hydraulic properties of the host rock are expected to change significantly. Preferential gas pathways may develop taking advantage of the material heterogeneity, anisotropy, rock discontinuities or interfaces between the different components of the repository, which eventually may lead to the release of the produced gases.

To improve the knowledge on the response to gas migration on argillaceous host formations, in particular the transport of free gas phase through preferential pathways, a comprehensive series of fast air injection tests under oedometer and isotropic conditions has been performed. Two potential host rocks have been studied to provide the basis for a comparative study: a plastic clay formation from Belgium (Boom Clay); and an indurated and deeper shale formation from Switzerland (Brown Dogger). Air injection and dissipation tests have been performed at two orientations (orthogonal and parallel to bedding planes) and at two air injection rates. Sample volume changes have been measured during air injection and dissipation. Particular attention has been given to the changes in the pore network to detect the opening of fissures or discontinuities. Simulation aided techniques have been used to better exploit the information provided by measurements and to get a better comprehension of local and coupled processes affecting the response of the material. To this aim, a coupled hydro-mechanical analysis with an embedded fracture permeability model, which is implemented in the finite element code Code_Bright (Olivella et al. 1996), has been used.

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2 2.1

MATERIALS AND EQUIPMENT

Table 1. Geotechnical properties of the samples.

Boom Clay (BC) (Northwest European Tertiary Basin, Rupelian stage) was retrieved at a depth of 223 m in the URL (Underground Research Laboratory) facility of EURIDICE at Mol, Belgium. Table 1 summarises the main geotechnical properties of this clay (20– 30% kaolinite, 20–30% illite, 10–20% smectite, 25% quartz and feldspar), including the initial suction. BC specimens displayed a relatively high initial suction, despite being saturated, due to stress relief upon sampling. The value measured with dew point mirror psychrometer was around 2.5 MPa, in good agreement with data reported by Lima et al. (2012) and Dao et al. (2014). Data obtained from Mercury Intrusion Porosimetry (MIP) allowed detecting an initial monomodal pore size distribution, as well as estimating an air-entry value of about 4.8 MPa that corresponded to the dominant entrance pore size of 70 nm (Fig. 1). Water retention data of the intact material on drying are plotted in Figure 2. The data were obtained by stepwise drying of the specimens using a dew point psychrometer, starting from the initial suction. The data were fitted to the van Genuchten’s equation indicated in the figure. 2.2

BC Symbol (223 m)

Plastic limit (%) Liquid limit (%) Dominant entrance pore size from MIP (nm) Air-entry value from dominant entrance pore size (MPa) Density of solids (Mg/m3 ) Dry density (Mg/m3 ) Water content (%) Degree of saturation Void ratio Total suction (MPa)

wP wL

ρs ρd w Sr e0 s

BD (782 m)

29 67 70

24 17 22

4.8

13

2.67 1.66–1.69 22.6–24.0 close to 1 0.57–0.61 2.5

2.69 2.48 4.78 0.95–1 0.09–0.11 37

Brown dogger

Core samples of Brown Dogger (BD) were recovered from the geothermal well Schlattingen-1 (SLA-1) at a depth of around 782 m. SLA-1 is located in the Canton Thurgau (Switzerland) in the North-eastern part of the Swiss Molasse Basin. BD corresponds to a shaly sequence and consists of silty to clay-rich marls with clay content of 25–45%, 30–50% carbonate and 20–25% quartz (Ferrari et al. 2014). The main geotechnical properties of the samples are summarised in Table 1. The information is complemented with the initial suction and the dominant entrance pore size determined by MIP. Figure 3 shows the pore size distribution of BD, which presents a mono-modal distribution with a small dominant entrance pore size of 22 nm. Water retention curves on drying are presented in Figure 4. 2.3

Main properties/ Initial conditions

Boom clay

Figure 1. Pore size density function of BC.

Experimental equipment

An instrumented high-pressure and high-stiffness oedometer cell was used to determine the compressibility parameters of the two materials and to perform the air injection tests on BC. The oedometer samples, 20 mm thick and 50 mm in diameter, were placed between top and bottom caps made of concentric stainless steel rings that work as coarse porous stones allowing the injection and recovery of water and air. Vertical displacements were measured with an external Linear Variable Differential Transformer (LVDT). The experimental set-up included four automatic Pressure/Volume Controllers (PVC): one for hydraulically applying the vertical

Figure 2. Drying branch of the water retention curve of BC.

stress, one for air injection (upstream boundarybottom of the sample-) and two for water (injection at upstream and recovery at downstream boundaries). The cell and auxiliary devices are presented in Figure 5. An equivalent experimental setup was used for the air injection tests on BD using an isotropic cell and

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Figure 3. Pore size density function of BD.

Figure 5. Scheme of the experimental oedometer set-up. 1) Sample; 2) coarse porous concentric rings; 3) axial loading piston; 4) PVC for vertical stress; 5) PVC for air injection; 6) and 7) PVC for water; 8) LVDT.

Figure 4. Drying branch of the water retention curve of BD.

low-height specimens (25 mm height, 50 mm in diameter) confined by several neoprene membranes and aluminium foils. Axial displacements were registered with an external LVDT. Each cap of the isotropic cell had inlet and outlet lines prepared for gas and liquid connections and connected to PVCs, as shown in Figure 5 for the oedometer cell. 2.4 Test protocols Protocols for air injection test on both materials are analogous. A pre-conditioning path – water undrained loading path – was followed to approximately restore the in situ effective stress of the samples. BC samples were vertically loaded to 3 MPa in the oedometer cell, while BD samples were isotropically loaded to 10 MPa. Afterwards, samples were put in contact with their synthetic water – prepared according to De Craen et al. (2004) and Mäder (2011), respectively – at atmospheric pressure. Then, the water permeability of the samples was determined under different pressure gradients and at constant total vertical/isotropic stress. Afterwards, a drained loading stage was followed to a total vertical stress of 6 MPa in BC and to a total isotropic stress of 15 MPa for BD. Just before the air

injection phase, a fast drainage of the bottom line was performed to replace water by air. An initial air pressure of 0.5 MPa for BC and 3 MPa for BD was applied at the upstream boundary. Air injection tests at two different injection rates (2 mL/min and 100 mL/min) were performed to analyse their influence on the coupled hydro-mechanical response. The selected rates were relatively fast (air pulse tests) to minimise air diffusion mechanisms through the matrix and to enhance single-phase air flow mechanisms through discontinuities (Marschall et al. 2005). The air injection piston was stopped (shutoff) when air pressure reached a maximum of 4 MPa in BC tests and 14 MPa in BD tests. These maximum values are close to the air-entry values reported in Table 1. At these stress states, the air pressure was let decaying at constant air volume of the inlet line. The recovery lines were initially full of water and the controller was kept at a constant pressure of 0.5 MPa in both set-ups. However, the PVC of the recovery system was not able to keep this constant pressure condition when the air flow was very high, and an increase in the downstream pressure occurred (up to a maximum pressure of 1.8 MPa controlled by a pressure release valve). Finally, samples were unloaded under undrained conditions. After each injection test, MIP tests were performed to study the changes in the pore size distribution of the tested samples. Details of the test protocols can be found in Romero et al. (2012), Romero & Gomez (2013), Romero & Gonzalez-Blanco (2015) and Gonzalez-Blanco et al. (2016).

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Figure 6. Time evolution of pressures at the boundaries (injection pressure in continuous line; outflow pressure in dashed line), axial strain and outflow volume for two injection tests on BC samples at a rate of 2 mL/min and two different orientations of bedding planes (normal and parallel to air flow).

3

EXPERIMENTAL RESULTS

Selected results of air injection and dissipation stages at constant vertical / isotropic stress are presented in Figure 6 for BC and Figure 7 for BD. The figures show the time evolution of the air injection pressure at the upstream boundary, the outflow pressure and volume at the downstream boundary, jointly with the axial strain, calculated based on the recorded axial displacement. Figure 6 corresponds to two tests performed on BC with bedding planes orientated parallel (BC// ) and orthogonal (BC⊥ ) to air flow, at the same injection rate, 2 mL/min. The air pressure at the upstream boundary increased from 0.5 to 4 MPa (A to B in the figure), followed by shutoff (point B) and dissipation at closed air injection line (B to C). The increase in injection pressure was accompanied by expansion (negative axial strains), followed by compression strains along the dissipation stage. The sample BC⊥ underwent larger axial strains consistent with the anisotropic behaviour observed on loading experiments. Sample BC// underwent breakthrough (the outflow volume rapidly increased) just after attaining the maximum injection pressure. On the contrary, sample BC⊥ was able to sustain the maximum pressure for a longer period after shut-off (point B). After breakthrough, the injection pressure started to decrease along the dissipation stage towards the value indicated by point C. During this dissipation stage, the constitutive stress (total vertical stress minus air pressure) increased, leading to progressive compression of the material.

Figure 7. Time evolution of pressures at the boundaries (injection pressure in continuous line, outflow pressure in dashed line), axial strain and outflow volume for two injection tests on BD samples at two different injection rates: 2 and 100 mL/min. Test at the fastest rate from Romero & Gomez (2013).

Figure 7 presents the comparison of the behaviour along air injection and dissipation stages for BD samples tested at two different controlled-volume rates (2 mL/min and 100 mL/min) and at constant isotropic stress (15 MPa). Both samples were tested with the bedding planes orthogonal to air flow. Regarding their volume change response, they displayed some small expansion during the early air injection stage (A to B in Fig. 7). Expansion continued in both samples after shut-off (point B in the figure), as the air pressure front propagated into the sample, causing an increase in the fluid pressure and a decrease of the constitutive stress. The time at which first air outflow occurred depended on the injection rate. In sample tested at 100 mL/min, the first outflow was detected during the dissipation stage, whereas in sample tested at 2 mL/min, it already occurred during the last phase of the injection stage. Air injection experiments on these two formations displayed common behavioural features. The air pressurisation process acted as an unloading stage at constant vertical or isotropic stress, inducing some expansion of the samples. For BD samples, the expansion of the samples presented some delay while the air pressure front propagated inside the samples at the two selected rates. Results on BC showed that all the expansion occurred during the injection, since the pore pressures inside the samples were nearly equilibrated. The difference in the time at which expansion occurred could be explained by the difference in porosity / permeability of both samples (refer to Table 1). To better understand the consequences of air injection, MIP tests were performed on freeze-dried samples to compare the pore size distributions before

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Figure 8. Pore size distribution changes before and after air injection tests in BC.

(intact state) and after the air tests. Figure 8 presents the pore size density functions obtained for the intact Boom Clay and after the air injection tests. Special care was taken during the unloading stage (after the air tests) that was carried out under undrained conditions to prevent further expansion of the material. A new family of large pores, which was not detected on intact samples, was systematically observed after the air injection tests. These new pores at entrance sizes larger than 2 µm (dominant pore modes around 10 µm and representing around 10% of the total pore volume) were associated with fissure opening that acted as preferential air pathways. The figure also includes the pore size distribution of a sample, which followed the same loading path but without the air injection/dissipation stages, therefore subjected just to loading and fast undrained unloading. The large pores were not detected on this sample, which suggested that they were actually related to the air injection/migration process. Similar patterns were also found in BD samples after the tests (Romero & Gonzalez-Blanco 2015).

4

NUMERICAL MODELLING

To help with the interpretation of the results in terms of injection and outflow pressures, as well as outflow volumes and axial strain, numerical simulations were performed by implementing the geometry of BC in the oedometer cell and their corresponding boundary conditions on the injection and outflow sides. The coupled mechanical and two-phase flow equations were discretised and solved using the finite element program Code_Bright (Olivella et al. 1996). An embedded fracture permeability model (Olivella & Alonso 2008) in a fully coupled hydro-mechanical approach was adopted to simulate the gas injection tests. This model takes into account the variation of the intrinsic permeability and the air entry pressure with fracture aperture, which depends on strain. A 2D axisymmetric representation of the sample geometry was selected presenting two zones having very different hydraulic properties: the matrix

Figure 9. Computed versus measured in the ZFD: a) injection and recovery pressures (gauge pressures); b) average axial strains; c) outflow volumes. BC with bedding planes parallel to air flow (2 mL/min).

(undisturbed clay) and a vertical central Zone of Fracture Development (ZFD) with a thickness of 2 mm. To properly simulate the test, it was necessary to include both the injection and recovery systems into the model, which corresponded to the drainage lines of the experimental set-up. The mechanical model adopted for both zones is the elastoplastic model BBM (Alonso et al. 1990). For the retention properties of the matrix material the van Genuchten’s model was adopted. The diffusion coefficient was selected according to Jacops et al. (2015) for samples with bedding planes parallel to the flow direction. Kozeny’s model was used for the intrinsic permeability changes of the matrix as a function of void ratio. The required parameters for the embedded fracture permeability and water retention model were fitted by using experimental data. An initial aperture of 100 nm – slightly higher than the dominant pore mode of the matrix – was selected. The set of mechanical and hydraulic parameters adopted is detailed in Gonzalez-Blanco et al. (2016). The results of the computed injection and outflow pressure response in the ZFD as a function of time together with the outflow volume and the average axial strain along the sample height are shown in Figure 9 and compared with experimental results for BC tested with bedding planes parallel to air flow at an injection rate of 2 mL/min. The figure shows that the air pressure decay at the bottom of the sample during the dissipation stage is acceptably well fitted. Good agreement is also found on the fluid pressure at the top, computed

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Figure 10. Simulated distribution of absolute gas pressure (left, in MPa), porosity (middle) and liquid degree of saturation (right) during the air injection (t = 150 min), at shut-off (t = 245 min) and during the dissipation (t = 600 min).

as the maximum between air and water pressures. The computed sample volume change represented by the average axial strain is also reasonably well reproduced. The sample undergoes expansion during the injection stage followed by compression during air dissipation. The computed results show the same expansion, while a slightly larger compression than the measured one is predicted. Moreover, the time in which the outflow takes place compares well with the measured one. The outflow volume, computed as the sum of water and air volumes, fits well with the experimental measurements. The local sample response is depicted in Figure 10, with contour plots to better understand the influence of the embedded fracture response. Absolute gas pressure, porosity and liquid degree of saturation are shown at three different time steps: 150 minutes after the start of gas injection; at the end of the gas injection (shutoff); and during the dissipation stage. On the one hand, only when the air pressure increased enough, the fracture opened and desaturated allowing the air to flow. On the other hand, as the air pressure decreased due to the outflow, the fracture gradually closed over time. The matrix of the clay remained fully saturated after the air passage. Indeed, within the matrix, the dominant transport mechanism was the diffusion of dissolved air. Figure 11 shows the contribution of the diffusive and advective flows in the matrix and in the ZFD at the same elapsed times previously indicated. The dominant advective flow in the ZFD is clearly observed in the figure.

5

CONCLUSIONS

Experimental work is important for understanding the process of gas flow through saturated argillaceous

Figure 11. Diffusive and advective fluxes along the core height in the ZFD and in the matrix at air injection (t = 150 min), shut-off (t = 245 min) and dissipation (t = 600 min) stages.

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rock formations (Boom Clay and Brown Dogger). The tests presented corresponded to a series of gas pulse tests (relatively fast air injection tests) designed to investigate the mechanisms of gas flow at different orientations of the bedding planes and at different volumetric air injection rates (2 and 100 mL/min). The main focus was given to the coupled hydro-mechanical response by measuring displacements during the air injection and dissipation stages. The air injection tests were performed in oedometer/isotropic cells at constant vertical/isotropic stress, on samples with pre-defined orientation of bedding planes. The deformation response during the process was fully coupled with the hydraulic process. The samples underwent expansion during the air injection, and compression when the air pressure decayed. Large amounts of fluid volume were measured at the downstream reservoir which indicated the break-through point was exceeded. Mercury Intrusion Porosimetry (MIP) tests allowed detecting a new family of large pores with entrance sizes larger than 2 µm after the air injection tests, which suggested the development of preferential paths during the air injection experiments. Selected experimental results were simulated using a coupled hydro-mechanical finite element code (Code_Bright), which incorporated elements with an embedded fracture permeability model to account for the simulation of the dominant single-phase (air) flow along preferential pathways. Rock intrinsic permeability and its retention curve were made dependent on fracture aperture changes based on experimental data (an initial aperture of 100 nm was selected based on MIP). A central zone of fracture development was considered to allow for the initiation of air flow pathways. Results of the simulation showed encouraging agreement not only with recorded upstream/downstream pressures and outflow volumes, but also in the volume change response of the material.The experimental results, combined with the numerical simulations, provided good insight into the role of the volumetric response and the hydraulic changes on the air transport properties of the samples. ACKNOWLEDGEMENTS The authors are grateful to the Belgian and Swiss agencies for radioactive waste management – ONDRAF/NIRAS and NAGRA, respectively – for their financial support. Thanks are also expressed to Prof. Sebastià Olivella for his valuable comments regarding the numerical modelling.

Dao, L.Q., Cui, Y. J., Tang, A. M., Pereira, J.M., Li, X.L. & Sillen, X. 2014. Investigating the anisotropy of the shear modulus of natural Boom Clay. Géotechnique Letters 4: 98–101 (doi: 10.1680/geolett.14.00015). De Craen, M., Wang, L.,Van Geet, M. & Moors, H. 2004. Geochemistry of Boom Clay pore water at the Mol site. Scientifict. Report. SCK·CEN-BLG-990. Ferrari, A., Favero, V., Marschall, P. & Laloui, L. 2014. Experimental analysis of the water retention behaviour of shales. International Journal of Rock Mechanics & Mining Science 72: 61–70. Gonzalez-Blanco, L., Romero, E., Jommi, C., Li, X. & Sillen, X. 2016. Gas migration in a Cenozoic clay: experimental results and modelling. Geomechanics for Energy and the Environment. In press (doi: 10.1016/j.gete.2016.04.002). Jacops, E., Wouters,K., Volckaert, G., Moors, H., Maes, N., Bruggeman, C., Swennen, R. & Littke, R. 2015. Measuring the effective diffusion coefficient of dissolved hydrogen in saturated Boom Clay Applied Geochemistry 61: 175–184 (doi: 10.1016/j.apgeochem.2015.05.022). Lima, A., Romero, E., Piña, Y., Gens, A. & Li X. 2012. Water retention properties of two deep Belgian clay formations. In Unsaturated Soils: Research and Applications: 179–184 (doi: 10.1007/978-3-642-31116-1_24). Mäder, U. 2011. Recipe and preparation of a simplified artificial pore water for Opalinus Clay and Brown Dogger. AN 11-159 Nagra, Wettingen, Switzerland. Marschall, P., Horseman, S., & Gimmi,T. 2005. Characterisation of Gas Transport Properties of the Opalinus Clay, a Potential Host Rock Formation for Radioactive Waste Disposal. Oil & Gas Science and Technology 60(1): 121–139 (doi:10.2516/ogst:2005008). Olivella, S. & Alonso, E.E. 2008. Gas flow through clay barriers. Géotechnique 58(3): 157–176 (doi: 10.1680/geot.2008.58.3.157). Olivella, S., Gens, A., Carrera, J. and Alonso, E.E. 1996. Numerical formulation for a simulator (CODE_BRIGHT) for the coupled analysis of saline media. Enginnering. Computations 13(7): 87–112 (doi: 10.1108/02644409610 151575). ONDRAF/NIRAS 2013. Research, Development and Demonstration (RD&D) Plan for the geological disposal of high-level and/or long-lived radioactive waste including irradiated fuel of considered as waste, State-of-the-art report as of December 2012. ONDRAF/NIRAS, report NIROND-TR 2013-12 E. Romero, E., Senger, R., Marschall, P. & Gómez, R. 2012. Air tests on low-permeability claystone formations. Experimental techniques, results and simulations. In InternationalWorkshopAdvances in MultiphysicalTesting of Soils and Shales: 69–83 (doi: 10.1007/978-3-642-32492-5_6). Romero E. & Gómez R. 2013. Water and air permeability tests on deep core samples from Schlattingen SLA-1 borehole. NAB 13–51, Nagra, Wettingen, Switzerland. Romero, E. & Gonzalez-Blanco, L. 2015. Complementary water and air permeability tests on core samples from Schlattingen SLA-1 borehole. NAB 15–06 Nagra, Wettingen, Switzerland.

REFERENCES Alonso, E.E., Gens, A. & Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique. 40(3): 405–430.

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