Soil-Steel Bridges: Design, Maintenance and Durability (Geotechnical, Geological and Earthquake Engineering, 49) 3030347877, 9783030347871

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Geotechnical, Geological and Earthquake Engineering

Damian Beben

Soil-Steel Bridges

Design, Maintenance and Durability

Geotechnical, Geological and Earthquake Engineering

Volume 49

Series Editor Atilla Ansal, School of Engineering, Özyegin University, Istanbul, Turkey Editorial Advisory Boards Julian Bommer, Imperial College London, U.K. Jonathan D. Bray, University of California, Berkeley, U.S.A. Kyriazis Pitilakis, Aristotle University of Thessaloniki, Greece Susumu Yasuda, Tokyo Denki University, Japan

More information about this series at http://www.springer.com/series/6011

Damian Beben

Soil-Steel Bridges Design, Maintenance and Durability

Damian Beben Faculty of Civil Engineering and Architecture Opole University of Technology Opole, Poland Reviewers Giovanni Bosco Professor, LaAqilla University Italy

Halil Sezen Professor, Ohio State University USA

ISSN 1573-6059 ISSN 1872-4671 (electronic) Geotechnical, Geological and Earthquake Engineering ISBN 978-3-030-34787-1 ISBN 978-3-030-34788-8 (eBook) https://doi.org/10.1007/978-3-030-34788-8 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

The soil-steel bridges and culverts constitute more and more often an element of transportation infrastructure in various parts of the world. For this reason, the presented book fits in the actual trends in bridge engineering and additionally fulfils the gap in the world literature concerning to such type of bridge structures. The book is intended mainly for people interested in soil-steel bridges and culverts, in particular for designers, scientists, practitioners, students, contractors and managers of transportation infrastructure. The primary objective of this book is to provide designers with a set of analysis and design specifications for soil-steel bridges and culverts so also called the flexible structures. Brief but informative, this guide to the analysis and design of soil-steel bridges is based on a quick lookup approach to code applications, design and analysis methods/calculations as well as applications and solved examples. Additionally, the corrosion problem and durability of soil-steel bridges will be also analysed. The book presents information on current methods and standards for the design of soil-steel bridges. The book starts with a clear and rigorous exposition of the various codes, which govern design, including the American Association of State Highway and Transportation Officials and Canadian Highway Bridge Design Code. The Swedish design method as the most modern calculation method will be presented in detail. Problems and design and implementation errors that may occur during the design and construction phase of these bridges were also characterized. Methods of numerical modelling of soil-steel bridges and exemplary results of calculations using the finite element method are presented. This is especially important for large-span soil-steel bridges. An important problem of corrosion in soil-steel bridges and methods of protecting these objects against corrosive and abrasion damages has been described. Then, the results of experimental tests on several soil-steel bridges under service and standard loads were presented. At the end, the problem of durability of soil-steel bridges was characterized. Soil-Steel Bridges: Design, Maintenance and Durability brings together the analytical tools and methods based on lessons learned which were accumulated v

vi

Preface

over 19 years of experience as a structural and bridge engineer, academic teacher and project and design manager for transportation and industrial clients. The information presented in the book is the result of research and analysis on soil-steel bridges and culverts. The work contains data from own experimental and numerical analyses, as well as obtained from the analysis of the world literature in this field. Issues covered in the book are interdisciplinary on the borderline of several scientific disciplines, i.e. civil engineering, in particular bridge engineering and soil mechanics, as well as material engineering, including materials corrosion. As in any scientific book, some shortcomings and remarks may appear at work; therefore, the author asks for comments ([email protected]), which in the future will allow to improve the content of the book in subsequent editions. The author would like to thank the reviewers of the book in a special way: Professor Giovanni Bosco from L’Aquila University and Professor Halil Sezen from Ohio State University and anonymous reviewers for their valuable comments that contributed to the final form of the book. At the end, the author would like to thank Professor Zbigniew Zembaty for his inspiration to write the book and for all the help in this area. Opole, Poland July 2019

Damian Beben

Contents

1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Short Historic Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Problems in Soil-Steel Bridges . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Basic Terms and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . .

1 1 4 5 11 13

2

Selected Issues of Soil-Steel Bridge Design and Analysis . . . . . . . . . . 2.1 Code Requirements and Design Methods . . . . . . . . . . . . . . . . . . . 2.1.1 General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Swedish Design Method (Pettersson and Sundquist 2014) . . . 2.1.3 The AASHTO Method (AASHTO LFRD 2017) . . . . . . . . 2.1.4 The CHBDC Method (CHBDC 2014) . . . . . . . . . . . . . . . . 2.1.5 Design of Soil-Steel Bridges with Long-Span (McGrath et al. 2002) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.7 Recapitulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Construction of Soil-Steel Bridges . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Elements of Corrugated Plate and Shell Profiles . . . . . . . . . 2.2.3 Construction-Assembly Works . . . . . . . . . . . . . . . . . . . . . 2.2.4 Reinforcing Bridges with Use of CSP Structures . . . . . . . . 2.2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Design Problems and Construction Mistakes in Soil-Steel Bridges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Design Problems and Errors . . . . . . . . . . . . . . . . . . . . . . .

17 17 17 19 41 49 61 66 73 73 73 74 76 84 89 90 90 90

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4

Contents

2.3.3 Construction Phase Mistakes . . . . . . . . . . . . . . . . . . . . . 2.3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 FEM Analysis of Soil-Steel Bridges and Culverts . . . . . . . . . . . . 2.4.1 Introduction and State of the Art . . . . . . . . . . . . . . . . . . . 2.4.2 Description of Numerical Modelling . . . . . . . . . . . . . . . . 2.4.3 Examples of Numerical Results . . . . . . . . . . . . . . . . . . . 2.4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . .

95 97 98 98 100 107 113 114

Corrosion Problem of Soil-Steel Bridges . . . . . . . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Beginnings of Corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Soil Corrosivity Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Effect of Soil Resistivity . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Effect of Soil pH and Moisture Content . . . . . . . . . . . . . . 3.4 Atmospheric Corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Changes in Air Caused by Acidification of the Environment and its Influence upon Corrosion . . . . 3.5 Corrosion in Water and Erosion-Abrasion Damages . . . . . . . . . . 3.6 Mathematical Model of Corrosion Description of a Soil-Steel Bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.2 Model Describing Propagation of Corrosion Damages . . . 3.6.3 Model of Corrosive Damage . . . . . . . . . . . . . . . . . . . . . . 3.6.4 Formation of Corrosive Cracks . . . . . . . . . . . . . . . . . . . . 3.7 Corrosion and Abrasion Protection . . . . . . . . . . . . . . . . . . . . . . 3.8 Recapitulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . .

119 119 123 126 126 128 129 132 132

. . . . . . . .

139 139 140 140 144 146 150 151

Testing and Durability of Soil-Steel Bridges . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Testing of Soil-Steel Bridges Under Service Loads . . . . . . . . . . . 4.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Impact of the Road and Railway Service Loads . . . . . . . . 4.2.3 Dynamic Amplification Factors in Soil-Steel Bridges . . . . 4.2.4 Load Rating of Soil-Steel Bridges . . . . . . . . . . . . . . . . . . 4.3 Durability Tests of the Backfill Corrosivity . . . . . . . . . . . . . . . . . 4.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Soil Resistivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Study on Acidity and Moisture Content . . . . . . . . . . . . . . 4.3.4 Discussion of Test Results . . . . . . . . . . . . . . . . . . . . . . . 4.3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . .

155 155 157 157 159 168 178 180 180 181 184 186 195

. 133 . 134

Contents

4.4

Deformation of the Backfill Caused by the Traffic Live Load . . . 4.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Characteristics of the Problem . . . . . . . . . . . . . . . . . . . . 4.4.3 Damping in Soil Medium (Backfill) . . . . . . . . . . . . . . . . 4.4.4 Mathematic Model of Soil Deformation . . . . . . . . . . . . . 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

. . . . . . .

196 196 197 200 203 207 208

Final Recapitulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

Chapter 1

Introduction

Abstract The chapter contains a general introduction to the soil-steel bridges and culverts (terminology, difference between the bridge and culvert, advantages and disadvantages, overall classification). Financial benefits resulting from the use of the soil-steel bridges versus typical steel and reinforced concrete bridges for transportation investments is also briefly presented on the basis of the literature review. A historical outline of development of such bridges is presented. Besides, the technological, design and scientific problems appearing in the soil-steel bridges are shortly described. The author defined eight different stages of structural analysis of soil-steel bridges taking into account primarily the various loads appearing during construction stage and normal operation (static, dynamic, service, seismic, anthropogenic). At the end of the chapter, the most commonly used terms related to the soil-steel bridges are also shown and defined.

1.1

General

Bridge structures are the longest operated engineering structures and they will remain as such at least in the nearest future. Even the richest countries, such as the USA, Canada, Japan, Sweden or Germany, cannot replace bridges with new ones within a period shorter than a 100 years, because that would mean building 1% of bridges per year alongside with the necessity to undertake modernisation and maintenance works. Bridges are most often made of reinforced or prestressed concrete (ca. 86%), steel (ca. 12%) and other materials (ca. 2%). The average result of evaluation of bridges technical condition does not exceed “sufficient” which proves their condition worrisome. American sources report that about 40% of general amount of bridges require urgent renovation works. In road network comprising all types of roads in Europe, there are many bridge structures requiring urgent modernisation or reconstruction or even replacement. A frequent result of deterioration of a bridge structure is a considerable decrease in load capacity, often as an effect of destructive natural forces such as flood, improper service or late reaction to appearing damages. Importance of bridge structures related, e.g., to their strategic location, causes necessity to search for modern construction solutions combining © Springer Nature Switzerland AG 2020 D. Beben, Soil-Steel Bridges, Geotechnical, Geological and Earthquake Engineering 49, https://doi.org/10.1007/978-3-030-34788-8_1

1

2

1 Introduction

fast execution, low costs and satisfactory service life. All the qualities can, no doubts, be found in soil-steel bridges. Soil-steel bridges are engineering structures made of corrugated or flat steel sheets forming a pipe or a vaulted structure. The essence of work of such structures is mutual influence and interaction with soil – a composite soil-steel structure (Vaslestad 1990; Beben 2005; Kunecki 2006; Pettersson 2007; Antoniszyn 2009; Flener 2009a; Pettersson and Sundquist 2014; Michalski 2016; Wadi 2019). This type of structures is also called a multi-layered shell structure, a soil-shell structure (Machelski 2008), a flexible bridge structure, a corrugated plate culvert or a composite soil-steel bridge (Janusz and Madaj 2009). Up to date, there is no unequivocal terminology for bridge structures made of corrugated steel plates (CSP). Each country has its own term depending on, for instance, the span, structure length, or type of foundation. For example, a Canadian Highway Bridge Design Code (CHBDC 2014) calls this type of bridge structures “soil-steel structures”. A British Standard (BD 12/01 2001) and an Australian one (AS/NZS 2041 2010) use term “buried corrugated sheet structures”. Whereas the AASHTO LRFD (2017) standard uses a couple of such terms: “a corrugated metal pipe”, “a long-span pipe structure”, “a box structure”, “a deep corrugation structure”. A similar situation is in the case of the definition of bridge and culvert. Each country has own regulations in this regard. The National Corrugated Steel Pipe Association (NCSPA 2008) defines a culvert as a channel that maintains the continuity of a stream when it encounters an artificial obstacle such as an embankment, roadway, or levee. The shapes utilized in culvert construction are a pipe, pipe-arch, elliptical pipe, and box. The AASHTO LRFD (2017) defines the bridge as any structure having an opening not less than 6.0 m (20.0 ft) that forms part of a highway or that is located over or under a highway. However, each state is allowed to add exceptions, additions and restrictions to federal (AASHTO) requirements. For example, the Ohio Department of Transportation (ODOT 2003) defines a culvert as a structure with a pipe diameter, box, elliptical or arch span, or multi-cell having a total span less than 3.0 m (10.0 ft). In this case, the ODOT is more conservative than the federal rules because inspection and design requirements for bridges are more stringent than for culverts. Europe does not have an explicit term for the culverts; usually two requirements should be fulfilled. The first concerns the cross section (it should be closed), and second is related to the span length (no more than 3.0 m). The Hong Kong regulations (Highways Department 2013) say that the bridge is any structure with span higher than 2.0 m. In the following parts of the book, a term „soil-steel bridges” will be used. An example has been shown in Fig. 1.1. It also needs to be underlined that the biggest number of bridge structures in the world are structures of theoretical span up to 30 m. Introduction of soil-steel bridge technology to the market of transportation engineering has revolutionized bridge engineering and it means considerable savings in budgets of road management units. The above can be confirmed by observations made by the author within the last 20 years (Groth and Moström 1995; Manko and Beben 2005a, b, c; Machelski 2008; Janusz and Madaj 2009; Pettersson and Sundquist 2014). In the USA, for instance, a long concrete culvert was repaired by means of adding a reinforcing structure of corrugated plate of dimensions: 4.26
2.80
80.00 m from the inside. The result

1.1 General

3

Fig. 1.1 Side view on the soil-steel bridge

was an engineering structure of good durability parameters for only 54% of a total price of the traditional solution (Duncan 1984). Similarly, in Norway, in years 1987–1988, 646 m of soil-steel bridges were built, which allowed to save about 25,000 Norwegian crowns per meter, in comparison to traditional bridge structures, and total savings amounted at 16 million NOK (Vaslestad 1989). Construction of animal passages in this technology in Poland gave savings of 50–65% in comparison with traditional solutions of precast reinforced concrete beams. Also, Kennedy and Laba 1984 and Mohammed et al. 2002 pointed to the increasingly wider use of this type of structures, as an alternative to concrete bridge structures of the medium theoretical span. Co-operation of soil and steel shell structure is mutual interaction of both the elements constituting a composite structural system. A properly formed composite system allows to transfer external loads, which are far bigger than it would result from treating just the shell as the main load bearing structure of the bridge. A flexible structural system allows for transfer of relatively heavy loads without causing increased stress or displacements in the steel shell. Leonhardt (Vaslestad 1990) introduced, in 1979, a equation in the following form: n ¼ EI/(M
S) for classification of flexible and rigid structures, depending on degree of stiffness of the material used to build them, where E is Young modulus, I – inertia moment of the structure, M – is stiffness modulus, S – span of a structure element. If n < 0.10, a structure can be considered as flexible, however when the value of n falls within the range of 0.10–1.0, a structure is classified between flexible and rigid, and if n > 1.0 a structure is considered as rigid. Allgood and Takahashi (1972) developed similar classification of shell flexibility.

4

1 Introduction

High load carrying capacity of these bridges is an effect of composite character and mutual interaction of the system, which is hard to express within traditional, analytical way of designing. Therefore methods are being searched for that would allow to define this interaction through numerical calculations with use of finite element method (FEM) and finite differences method (FDM). The main aims of this book are: 1. 2. 3. 4.

Extending readers’ knowledge about soil-steel bridges. Presenting up to date standard requirements for soil-steel bridges. Presenting examples of numerical modelling of soil-steel bridges based on FEM. Presenting selected results of experimental tests on soil-steel bridges.

Reaching the aims of the work will allow to make engineering and academic experts in the world acquainted with work and methods of analysis of these modern soil-steel bridges. An indirect effect of this work will be an increase in confidence towards soil-steel bridges and wider use of this solution in transport infrastructure engineering, for building or modernising low- or medium-span bridges (up to 40 m).

1.2

Short Historic Outline

The history of soil-steel bridges starts in late nineteenth century when first such structures were used in the form of round pipes of small diameters. As it can be concluded, it was the first generation of such bridges. Russian publications prove that in the year 1875, corrugated steel pipes were produced, and in the years 1887–1888, total length of 1300 m culverts were placed (of diameters 0.53–1.07 m) under railways. Whereas in years 1887–1914 in all tsarist Russia approximately 64,000 m of corrugated steel plates were built, which constituted about 5000 structures of various dimensions (Kolokolov 1973). In the year 1896, in the United States of America, Watson patented a corrugated steel pipe and in the same year a mass production of the structures began on the American continent. Bigger cross-sections were being separated into construction elements, put together by means of screw joints. In the following decades these elements, being economical, resistant and durable structural solutions, contributed to quick increase of various applications of structures made of corrugated steel plates in transportation infrastructure all over the world. In Europe, this technology started being widely applied only after World War II. In the former USSR in the 70s of the twentieth century, typing of this type of structures was introduced and their mass production started – about 2500 structures per year (Jankowski 1979). The main stream of development of soil-steel bridges was however observed in North America and Canada. For instance, as early as in 1970, three world biggest (at that time) structures were built of a shape of horizontal ellipsis and span of 11.28 m (Moore et al. 1995), which constitute the second generation of these bridges. Corrugation dimensions did not exceed 200
55 mm. Span of bridges built with these sheets did not generally exceed 12.00 m, which constituted some sort of limitation, for example

1.3 Problems in Soil-Steel Bridges

5

for building motorways. For this reason, it was decided to increase corrugation parameters to 380
140 mm, 400
150 mm and 500
240 mm, strength of which is more than ten times higher than in case of bridges made of sheets with corrugation 200
55 mm. First applications in Europe of soil-steel bridges of, so called, deep corrugation, took place in Poland. They were used to modernise two road bridges destroyed at the time of flood in 1997 in Lower Silesia, and some test results of the two longest structures at the time in Europe (12.315 m and 12.270 m) have been presented in papers (Manko and Beben 2005a, b, c). After this period, a considerable increase of bridges built in this technology was observed. Examples can be found in Poland, Sweden, Holland, Slovakia, Czechia, Austria, Germany, and Italy. Currently, the soil-steel bridge with the biggest span of 32.5 m is built in the United Arab Emirates. It is the third generation of soil-steel bridge structures, which can reach span length up to 40 m. Soil-steel bridges are built mainly for economic reasons and they are getting more often used as all kinds of bridge crossings, especially of medium span (10–25 m) and in locations where short construction time and road or railway traffic continuity is required (Abdel-Sayed et al. 1994; Rowinska et al. 2004; Janusz and Madaj 2009). They constitute a perfect alternative for traditional bridges of concrete or steel. The discussed structures, due to their characteristics, i.e. flexible steel structure, interaction with backfill, can transfer very heavy live loads caused by vehicles travelling along them (Beben 2005; Kunecki 2006; Sezen et al. 2008; Flener and Karoumi 2009; Antoniszyn 2009; Elshimi 2011; Mellat et al. 2014; Wadi 2019). Soil-steel bridges are mainly built as structures on local roads (Fig. 1.2), but also as railway structures (Fig. 1.3), or even motorway overbridges and, more recently, as ecological structures – animal crossings (Fig. 1.4).

1.3

Problems in Soil-Steel Bridges

Technology used for construction of soil-steel bridges made of corrugated steel plates consists in close interaction of steel shell with surrounding soil and using the effect of arching. The aim of corrugation is to increase stiffness of the system structure and to cause interaction of the shell with backfill. Structures are composed of profiled corrugated plates, also called shells, or construction elements which were put together by means of high-strength bolts in cross-section and along the structure length. Such solutions allow for easy, quick and economical mounting of the structure (Abdel-Sayed et al. 1994; Janusz and Madaj 2009; Machelski 2013). An assumption made for behaviour of this type of structures is such an execution of joints between corrugated plate sheets as to guarantee fully static and dynamic transfer of mutual impacts between the elements. As a result, a flexible steel shell is obtained. And from the second way, the joints should be as strong as to withstand the fatigue effect (Pettersson et al. 2012; Ju and Oh 2016).

6

Fig. 1.2 Soil-steel bridge on a local road

Fig. 1.3 Side view on the railway tunnel made from CSPs

1 Introduction

1.3 Problems in Soil-Steel Bridges

7

Fig. 1.4 Side view on the animal crossing over highway A4 (Poland)

There are many problems and unknown factors related to designing of soil-steel bridges because of loading, for example, with backfill, static, dynamic, fatigue caused by normal service loads as well as seismic and anthropogenic loading (Haggag 1989; Vaslestad 1990; Beben 2005; Kunecki 2006; Pettersson 2007; Flener 2009a, b; Antoniszyn 2009; Elshimi 2011; Michalski 2016; Sobotka 2016; Maleska and Beben 2018a, b). Standards used to design soil-steel bridges are based on conservative assumptions, which is the reason why the structures are often overdesigned. Kay and Abel (1976) underlined the fact that there are difficulties with rational designing of soil-steel bridges due to multithreaded character of the task, complexity of work and structure shell behaviour under different types of loads. Conservative approach of the AASHTO standard to calculation of estimated values of internal forces has also been underlined in papers (Sargand et al. 1995; Beben 2013) where analyses made on the basis of experimental tests on different structures were presented and then compared with calculations made on the basis of AASHTO standard. Structure shell response caused by side pressure of backfill at the time of compaction is especially dangerous. Due to the fact, that a thin shell of plate of thickness within the range of 1.5–12.5 mm with no backfill has not yet got a relevant (safe) and required load carrying capacity, by relevant standards and laws (AASHTO LRFD 2017; CHBDC 2014; BD 12/01 2001; AS/NZS 2041 2010). The full load carrying capacity will be achieved after a period of a couple of months of normal service. It is believed that working of shells of soil-steel bridges of corrugated plates at the phase of backfilling is one of major problems observed at the time of construction (all kinds of buckling and loss of stability), contrary to the case of

8

1 Introduction

Fig. 1.5 The view on global shell deformation caused by improper assembly works

typical arch or box structures of reinforced concrete (Jenkins 2000; McGrath and Mastroianni 2002; Masada et al. 2007; Pimentel et al. 2009; Vega et al. 2012; Hermanns et al. 2013; Orton et al. 2015; Abuhajar et al. 2016). It needs to be noted that construction works carried out by unqualified teams with no experience or supervision by suppliers of these structures can lead to considerable extension of construction time, and, in the worst case, to a construction disaster, which can, as a result, lower attractiveness of these structures. It has also been noticed that many structures show signs of hazard (Fig. 1.5), i.e. possibility of stability loss by the shell or the soil (appearance of plastic joints and mechanisms of destruction). Damages to the structure are most often caused by loss of stability and bearing capacity by the surrounding backfill, which can be a result of freezing and thawing appearing in cycles. For that reason backfill is often reinforced with geotextiles, concrete beams stiffening the shell structure and causing a better soilflexible shell interaction. Introduction of these solutions can increase applicability of this type of structures in regions with high winter-summer amplitude of temperature. Analysis of soil-steel bridges arouses quite a lot of interest in world literature (for example McGrath et al. 2002; Vaslestad et al. 2004; Machelski 2008; Mai et al. 2014; Mellat et al. 2014; Wadi et al. 2015; Beben and Stryczek 2016; Beben and Wrzeciono 2017; Maleska and Beben 2019; Maleska et al. 2019). However not many phenomena observed at all construction stages: from joining steel sheet elements together, through backfilling, to normal service have been fully,

1.3 Problems in Soil-Steel Bridges

9

theoretically and experimentally, analysed and unequivocally identified. Despite numerous attempts to formulate relevant mathematical dependencies describing phenomena observed in the soil, among others, where the soil touches the steel structure – the interface layer (Taleb and Moore 1999; McGrath et al. 2002; Beben 2009, 2012; Sutubadi and Khatibi 2013; Yeau et al. 2015; Wadi et al. 2015), and around the shell – arching effect in soil, there is still no proper algorithm to calculate this bridge structures that would fully reflect their work and load carrying capacity. They are complex problems and they require use of advanced mathematicalcalculation apparatus. Many research centres in the world undertake numerical analyses of soil-steel bridges and they require knowledge of advanced numerical methods. At present, the FEM is widely used to analyse stress conditions, strains and displacements of soil-steel bridges. The results of numerical calculations obtained recently are quite satisfactory, however transfer from advanced analyses to engineering practice is lacking. The methods and standards used at present to design soilsteel bridges still require improvement in this respect (Flener 2009a, b, 2010; Mai et al. 2012; Beben 2013; Pettersson et al. 2015; Maleska and Beben 2019). The most widely used analytical calculation methods are rather based on designers’ experience than on applicable calculation models. It is because building a rational and optimal design method, reflecting actual behaviour of soil-steel bridges with respect to interaction of the steel shell with the backfill and describing the effect of arching, is very complex and complicated. Undertaking, on a large scale, experimental research and numerical analyses of the modern soil-steel bridges, where the issues of interaction of steel shell with backfill are of high importance and difficult to define, unequivocally seems unavoidable. For some time it was believed that soil-steel bridges should not be used in locations with quite big external loads and big spans, for example motorway overbridges. However, it needs to be underlined that there has been some progress observed recently with respect to that (Janusz and Madaj 2009; Williams et al. 2012; Machelski et al. 2017). Two main research methods applied to bridge structures, including soil-steel ones, are known. One of them is based on research done on a real bridge structure and it requires that all measurements are undertaken under the known (static or dynamic) load as provided for in research program or under backfill load (at the time of construction works) and service load (real load moving along the analysed bridge). The second method applied in research centres in the world is doing research on bridge models in natural scale on special research site, so called stends (Sargand et al. 1995; Vaslestad and Wysokowski 2002; White et al. 2007; Regier et al. 2017). The obtained results from such research works need to be made up with correct theoretical and calculation considerations, which, as a result, makes it possible to reach full estimate of susceptibility to stability and bearing capacity loss of the steel shell and the whole compound structural system. It needs to be underlined that experimental tests are still some of basic ways to determine properties and capacity characteristics of soil-steel bridges. The main aim of tests is working out of such calculation methods to minimize expensive tests on real structures or in special labs of research centres. Maybe in the future, they will no more be necessary, due to considerable recurrence of traditional structural solutions.

10

1 Introduction

However, now it is advised that, especially for structures with span exceeding 15–20 m, it is necessary to control strains and displacements mainly at the phase of backfilling and compacting the backfill around the shell structure and under known static and dynamic load before it is put into operation, and, at random, under normal service. Analyses and research on soil-steel bridges need to be discussed in eight basic phases. Each of them concerns a different construction phase (and reinforcement) and service of soil-steel bridges, i.e.: PHASE I

PHASE II

PHASE III

PHASE IV

PHASE V

PHASE VI

static and dynamic tests at the time of compacting the backfill around shell structure. The backfill itself and working of compactors and vibrators constitute the load then. Evaluation of shell behaviour mainly concerns possibility of stability loss, buckling, appearance of elastic joints, mechanisms of destruction etc. concerns static and dynamic tests at the time of construction (shell is backfilled with soil and properly compacted, however without basic foundation and pavement layers, sidewalks or facilities). Static loads are heavy load vehicles. Dynamic load comes from passages of vehicles with various speed and in various mutual configurations. The aim of the test is evaluation of behaviour of the shell structure depending on soil cover depth over its crown and influence of respective road layers on internal forces in within the shell, and also evaluation of soil-shell interaction. they are tests on ready structure with respect to static loads. Similar loads are used as in phase II. The aim of these tests is evaluation of the structure with respect to soil stability and influence of soil and road (railroad) layers on strains and displacements of shell structure, and also comparing results from phases II and III. concerns dynamic test of a bridge. Load comes from heavy load vehicles driving along with agreed speed and also passages of vehicles across a threshold and braking in various configurations. Evaluation of behaviour of this type of bridges under dynamic load, identification of strains and displacements and also of vibrations frequency, doing a modal analysis. static and dynamic tests after a certain period of normal service (for instance after 6, 12, 18, 24 months). Loads similar to ones from phases II, III and IV are used. Evaluation of influence of soil layers consolidation and their interaction with the steel shell and cyclic freezing and thawing of backfill on final load capacity of the structure. tests under seismic load. Their aim is evaluation of behaviour of soilsteel bridges under influence of seismic and anthropogenic loads (for example mining quakes).

1.4 Basic Terms and Definitions

PHASE VII

PHASE VIII

11

operation phase tests under real and current road or railway traffic loads. Evaluation of load capacity, service life, durability and reliability of soil-steel structures. Another important issue is evaluation of susceptibility to corrosion of the backfill after a certain period of service and influence of damage on load capacity of the bridge. static and dynamic tests of structures reinforced with a shell made of corrugated steel plates. Applied loads are similar to ones from phase II, III and IV. Tests should be done prior to and after reinforcement of the structure. The aim of the test is evaluation of reinforcement and of interaction between different elements of the structure.

Moreover, in each phase, it is necessary to check the condition of bolt joints between the steel plates. Test results from each phase need to be verified by means of numerical calculations, with use of software like: ABAQUS, PLAXIS and DIANA based on the FEM.

1.4

Basic Terms and Definitions

Issues related to soil-steel bridges lay in between two academic disciplines: structure mechanics and soil mechanics. There are values, terms and dependences specific to them: Arching – is a phenomenon of transfer (redistribution) of loads between backfill adjacent to and above shell that move relative to one another. Positive arching causes the transfer of loads away from the shell; negative arching makes the opposite effect. Backfill – is soil used for construction (backfilling) of buried structures which is of relevant mechanical properties and strength characteristics. Proper choice and compaction of backfill around the shell structure makes it possible to achieve a composite soil-steel structure able to transfer external loads (Fig. 1.6). Backfilling – is controlled filling of space between shell structure (pipe, arch) and the native ground. At the time of the backfilling process, safety regime needs to be respected, i.e. with respect to backfill layers thickness, symmetry of backfilling on both sides of the structure, compacting, controlling deformations and relocations of the steel structure. Buckling – is bending of a shell structure under impact of compressive forces, being a sign of lack of stability in case when compressive forces exceed critical (permissible) value. Closed structure – is a structure with a closed profile in cross-section, for example circular, elliptic, etc. and is seated indirectly on ground (Fig. 1.6b). Corner or haunch – is a term similar to springlines, however it can be found in some shells only, for example in box culver type (Fig. 1.6a). Crown – is the top point of the structure in cross-section (Fig. 1.6).

12

1 Introduction

Fig. 1.6 The graphical explanation of marks used in the book for CSP structures with a crosssection: (a) open, (b) closed

Flatting – is an idealised tendency of corrugated plates to level under load. Flexibility – is a structure property consisting in, among others, regaining the original shape and dimensions, following removal of external forces causing deformation. Foundation – is a structure element by means of which load is transferred to the native soil. In soil-steel bridges there are three main types of foundation: reinforced concrete continuous foundation (Fig. 1.6a), steel foundations for open structures and bedding (Fig. 1.6b) as aggregate foundations (carefully chosen, placed and compacted aggregate) or concrete foundations (profiled to match the shape of the lower part of the shell) for closed structures. Interface – is mainly represented by normal and transverse stiffness between two planes that are supposed to be in contact, for example a steel shell and backfill. Open structure – is a structure seated in ground in its transversal section, for example on continuous foundation (Fig. 1.6a).

References

13

Soil cover depth – backfill height between the shell structure crown and the road vertical alignment or the bottom of railway tie measured together with construction layers of the road or the railroad bed (Fig. 1.6). Soil thrust or soil pressure – two basic types are distinguished: passive pressure is pressure in soil caused as a result of loading with the structure, aiming at separating some part of the soil and relocation of it, whereas active pressure is soil pressure on the structure shell. Span – is a distance between two closest supports of a shell structure – in case of structures seated on continuous foundations. However for closed profile structures a term of horizontal clearance is used, which means the biggest internal distance between side walls of the shell measured in axes of steel plates (Fig. 1.6). Springline – they are the furthest points of a soil-steel bridge in the transversal direction. Structure height – is the biggest distance from the structure crown to the place where the shell is seated on continuous foundations or, in case of closed structures, to the external corrugation edges. Reinforcement, stiffeners – are additional sheets of corrugated plate (ribs) fixed to basic shell structure in places with the biggest internal forces, e.g. in the crown, at the footing, etc. There are also continuous reinforcements in structures of big span, in spacing, filled with concrete mix, or even reinforcements of concrete only or in the form of steel profiles (Fig. 1.6a). In addition, the concrete relief slabs are used over the structures at the crown, geogrids or geotextiles. Vertical clearance – it the biggest internal distance between the structure crown and the external level of the obstacle crossed, like road vertical alignment or natural water level, etc.

References AASHTO LRFD (2017) LRFD bridge design specifications. American Association of State Highway and Transportation Officials. 8th edn, Washington, DC 1781 p Abdel-Sayed G, Bakht B, Jaeger LG (1994) Soil-steel bridges: design and construction. McGrawHill, Inc, New York Abuhajar O, El Naggar H, Newson T (2016) Numerical modeling of soil and surface foundation pressure effects on buried box culvert behavior. J Geotech Geoenviron Eng 142(12). https://doi. org/10.1061/(ASCE)GT.1943-5606.0001567 Allgood JR, Takahashi SK (1972) Balanced design and finite element analyses of culverts. Highway Research Record, no. 413, Highway Research Board, Washington, DC, pp 45–56 Antoniszyn G (2009) The strength of the steel shell situated in the ground as the main load-carrying element of the soil-shell bridge. PhD thesis, Wroclaw Univ Technol, Wroclaw AS/NZS 2041 (2010) Buried corrugated metal structures. Standards Australia. Sydney BD 12/01 (2001) Design manual for roads and bridges. Design of corrugated steel buried structures with spans greater than 0.9 metres and up to 8.0 metres. The Highways Agency Beben D (2005) Soil-structure interaction in bridges made from steel corrugated plates. PhD thesis, Opole Univ Technol, Opole, Poland Beben D (2009) Numerical analysis of soil-steel bridge structure. Baltic J Road Bridge Eng 4 (1):13–21

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1 Introduction

Beben D (2012) Numerical study of performance of soil-steel bridge during soil backfilling. Struct Eng Mech 42(4):571–587 Beben D (2013) Field performance of corrugated steel plate road culvert under normal live load conditions. J Perform Constr Facil 27(6):807–817 Beben D, Stryczek A (2016) Numerical analysis of corrugated steel plate bridge with reinforced concrete relieving slab. J Civ Eng Manag 22(5):585–596 Beben D, Wrzeciono M (2017) Numerical analysis of steel-soil composite (SSC) culvert under static loads. Steel Compos Struct Int J 23(6):715–726 CHBDC (2014) Canadian highway bridge design code. CAN/CSA-S6-14, Canadian Standards Association International, Mississauga, Ontario, 846 p Duncan CR (1984) Innovated repair of a large failing structural steel plate arch culvert. Transportation Research Record no. 1001, Transportation Research Board, Washington, DC, pp 98–101 Elshimi TM (2011) Three-dimensional nonlinear analysis of deep corrugated steel culverts. PhD thesis. Department of Civil Engineering, Queen’s Univ, Kingston, Ontario, Canada Flener BE (2009a) Static and dynamic behaviour of soil–steel composite bridges obtained by field testing. PhD thesis, Royal Inst Technol, Stockholm, Sweden Flener BE (2009b) Response of long-span box type soil-steel composite structures during ultimate loading tests. J Bridg Eng 14(6):496–506 Flener BE (2010) Testing the response of box-type soil-steel structures under static service loads. J Bridg Eng 15(1):90–97 Flener BE, Karoumi R (2009) Dynamic testing of a soil-steel composite railway bridge. Eng Struct 31(12):2803–2811 Groth HL, Moström T (1995) Road culverts in stainless steel. Nordic Steel Construction Conference, Malmö, pp 155–160 Haggag AT (1989) Structural backfill design for corrugated metal buried structures. PhD thesis. University of Massachusetts, Amherst Hermanns L, Fernández J, Alarcón E, Fraile A (2013) Effects of traffic loads on reinforced concrete railroad culverts. In: Dimitrovová Z et al (eds) 11th international conference on vibration problems, Lisbon, Portugal, 9–12 September 2013 Highways Department (2013) Structures design manual for highways and railways. The Government of the Hong Kong, Special Administrative Region, Hong Kong Jankowski OA (1979) Instructions for the design and construction of metal culverts from corrugated sheets. Ministry of Transport Construction of the USSR, ВСН, Moscow, pp 176–178 Janusz L, Madaj A (2009) Engineering structures from corrugated plates. Design and construction. Transport and Communication Publishers, Warsaw, Poland, 427 p Jenkins D (2000) Barcoo outlet culvert – the influence of soil structure interaction on the design of a buried arch culvert. Report with the Barcoo project and FEM analysis. Adelaide, Australia Ju M, Oh H (2016) Static and fatigue performance of the bolt-connected structural jointed of deep corrugated steel plate member. Adv Struct Eng 19(9):1435–1445 Kay JN, Abel JF (1976) Design approach for circular buried conduits (abridgement). Transportation Research Record, no. 616, Transportation Research Board, Washington, DC, pp 78–80 Kennedy JB, Laba JT (1984) Suggested improvements in designing soil-steel structures. Transportation Research Record, no. 1231, Transportation Research Board, Washington, DC, pp 96–104 Kolokolov NM (1973) Metallic corrugated pipes under bunds. Transport, Moscow, USSR Kunecki B (2006) The behavior of orthotropic cylindrical shells in the ground media under static and dynamic external loads. PhD thesis, Wroclaw Univ Technol, Wroclaw Machelski C (2008) Modeling of soil-shell bridge structures. The Lower Silesian Educational Publishers, Wroclaw Machelski C (2013) Construction of soil-shell structures. The Lower Silesian Educational Publishers, Wroclaw Machelski C, Tomala P, Kunecki B, Korusiewicz L, Williams K, El-Sharnouby MM (2017) Ultracor – 1st realization in Europe, design, erection, testing. Arch Inst Civ Eng 23:189–197

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Mai V, Hoult NA, Moore ID (2012) Use of CANDE and design codes to assess stability of deteriorated metal culverts. Transportation Research Board, Washington, DC Mai V, Hoult NA, Moore ID (2014) Effect of deterioration on the performance of corrugated steel culverts. J Geotech Geoenviron Eng 140(2):04013007-1–04013007-11 Maleska T, Beben D (2018a) The effect of mine induced tremors on seismic response of soil-steel bridges. In: Beben D, Rak A, Perkowski Z (eds) Proceedings of the environmental challenges in civil engineering, MATEC Web of Conferences 174, 04002 Maleska T, Beben D (2018b) The impact of backfill quality on soil-steel composite bridge response under seismic excitation. International Symposium on Steel Bridges, IOP Conf Series: Materials Science and Engineering 419, 012040 Maleska T, Beben D (2019) Numerical analysis of a soil-steel bridge during backfilling using various shell models. Eng Struct 196:109358 Maleska T, Nowacka J, Beben D (2019) Application of EPS Geofoam to a soil–steel bridge to reduce seismic excitations. Geosciences 9(10):448 Manko Z, Beben D (2005a) Static load tests of a road bridge with a flexible structure made from super Cor type steel corrugated plates. J Bridg Eng 10(5):604–621 Manko Z, Beben D (2005b) Research on steel shell of a road bridge made of corrugated plates during backfilling. J Bridg Eng 10(5):592–603 Manko Z, Beben D (2005c) Tests during three stages of construction of a road bridge with a flexible load-carrying structure made of Super Cor type steel corrugated plates interacting with soil. J Bridg Eng 10(5):570–591 Masada T, Sargand SM, Tarawneh B, Mitchell GF, Gruver D (2007) Inspection and risk assessment of concrete culverts under Ohio’s highways. J Perform Constr Facil 21(3):225–233 McGrath TJ, Mastroianni EP (2002) Finite-element modeling of reinforced concrete arch under live load. Transportation Research Record, no. 1814, Transportation Research Board, Washington, DC, pp 203–210 McGrath T J, Moore I D, Selig E T, Webb M C, Taleb B (2002) Recommended Specifications for Large-Span Culverts. Transportation Research Board Simpson Gumpertz and Heger Incorporated. NCHRP Report, no. 473, Washington D.C. Mellat P, Andersson A, Pettersson L, Karoumi R (2014) Dynamic behaviour of a short span soil– steel composite bridge for high-speed railways – field measurements and FE-analysis. Eng Struct 69:49–61 Michalski JB (2016) Geometric measures of shell compression in soil-shell structures. PhD thesis, Wroclaw Univ Technol, Poland Mohammed H, Kennedy JB, Smith P (2002) Improving the response of soil-metal structures during construction. J Bridg Eng 7(1):6–13 Moore RG, Bedell PR, Moore ID (1995) Design and implementation of repairs to corrugated steel plate culverts. J Perform Constr Facil 9(2):103–116 National Corrugated Steel Pipe Association (NCSPA) (2008) Corrugated steel pipe design manual. National Corrugated Steel Pipe Association, Dallas Ohio Department of Transportation (ODOT) (2003) Culvert management manual. Columbus, Ohio Orton SL, Loehr JE, Boeckmann A, Havens G (2015) Live-load effect in reinforced concrete box culverts under soil fill. J Bridg Eng 20(11). https://doi.org/10.1061/(ASCE)BE.1943-5592. 0000745 Pettersson L (2007) Full scale tests and structural evaluation of soil-steel flexible culverts with low height of cover. PhD thesis, Royal Institute of Technology, Stockholm, Sweden Pettersson L, Sundquist H (2014) Design of soil steel composite bridges, 5th edn. TRITA-BKN, Stockholm Pettersson L, Leander J, Hansing L (2012) Fatigue design of soil steel composite bridges. Arch Inst Civ Eng 12:237–242 Pettersson L, Flener BE, Sundquist H (2015) Design of soil–steel composite bridges. Struct Eng Int 25(2):159–172 Pimentel M, Costa P, Félix C, Figueiras J (2009) Behavior of reinforced concrete box culverts under high embankments. J Struct Eng 135(4):366–375

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1 Introduction

Regier C, Hoult NA, Moore ID (2017) Laboratory study on the behavior of a horizontal-ellipse culvert during service and ultimate load testing. J Bridg Eng 22(3). https://doi.org/10.1061/ (ASCE)BE.1943-5592.0001016 Rowinska W, Wysokowski A, Pryga A (2004) Design and technology recommendations for flexible structures with corrugated steel plates. Road Bridge Res Inst, Warsaw, 72 p Sargand SM, Hazen GA, Masada T, Hurd JO (1995) Performance of a structural plate pipe arch culvert in a cohesive backfill under large live load. Nordic Steel Construction Conference, Malmö, pp 585–591 Sezen H, Yeau KY, Fox PJ (2008) In-situ load testing of corrugated steel pipe-arch culverts. J Perform Constr Facil 22(4):245–252 Sobotka MT (2016) Multi-scale numerical modeling of the interaction of backfill with a shell in soil-shell structures. PhD thesis, Wroclaw University of Science and Technology, Poland Sutubadi MH, Khatibi BR (2013) Effect of soil properties on stability of soil–steel culverts. Turk J Eng Environ Sci 37:79–90 Taleb B, Moore I D (1999) Three dimensional bending in long span culverts. Proceedings 52nd Canadian geotechnical conference, Regina, Saskatchewan, pp 305–312 Vaslestad J (1989) Long-term behavior of flexible large-span culverts. Transportation Research Record, no. 1231, Transportation Research Board, Washington, DC, pp 14–24 Vaslestad J (1990) Soil structures interaction of buried culverts. PhD thesis, Norwegian Institute of Technology, Trondheim, Norway Vaslestad J, Wysokowski A (2002) Full scale fatigue of large – diameter multi-plate corrugated steel culverts. Arch Civ Eng, XLVIII, no. 1 Vaslestad J, Madaj A, Janusz L, Bednarek B (2004) Field measurements of an old brick culvert sliplined with a corrugated steel culvert. Transportation Research Record, Transportation Research Board, Washington, DC Vega J, Fraile A, Alarcon E, Hermanns L (2012) Dynamic response of underpasses for high-speed train lines. J Sound Vib 331:5125–5140 Wadi AHH (2019) Soil-steel composite bridges. Research advances and application. PhD thesis, Royal Institute of Technology, Stockholm, Sweden Wadi AHH, Pettersson L, Karoumi R (2015) Flexible culverts in sloping terrain: numerical simulation of soil loading effects. Eng Struct 101:111–124 White K, Sargand S, Masada T (2007) Laboratory and numerical investigations of large-diameter structural plate steel pipe culvert behaviour. Arch Inst Civ Eng 1:245–259 Williams K, MacKinnon S, Newhook J (2012) New and innovative developments for design and installation of deep corrugated buried flexible steel structures. Arch Inst Civ Eng 12:265–274 Yeau KY, Sezen H, Fox PJ (2015) Simulation of behavior of in-service metal culverts. J Pipeline Syst Eng Pract 5(2):1009–1016

Chapter 2

Selected Issues of Soil-Steel Bridge Design and Analysis

Abstract The chapter contains an introduction to the design of soil-steel bridges (applied theories and methods). Three most commonly used methods of designing soil-steel bridges are presented in detail. The first method developed by Hakan Sundquist and Lars Pettersson (known as the Swedish Design Method) is described. American Association of State Highway and Transportation Officials (AASHTO method) and Canadian Highway Bridge Design Code (CHBDC method) also proposes the calculation methods of soil-steel bridges (they constitute the second and third methods, respectively). Besides, the procedure of design of soil-steel bridges with long span (exceeding 8.0 m) is also shown. Discussion of the selected calculation results using design methods compared with test results is presented. Next, the construction methods of the soil-steel bridges is described. In addition, the method of reinforcing of old bridges using the corrugated steel plates is also shown. The most commonly construction and design errors occurring at the soil-steel bridges are presented on the real examples. The finite element analyses of the soil-steel bridges are described taking into account the crucial model-ling elements such as interface, modelling of corrugation plates, soil models. The selected results of numerical analyses are presented for the box culvert, pipe-arch, arch structure with reinforced concrete slab, and arch with flat plates versus corrugated. At the end the general conclusions of finite element analysis of the soil-steel bridges are given.

2.1 2.1.1

Code Requirements and Design Methods General Notes

All the design methods and code requirements available now for soil-steel bridges and culverts are based on three main theories and their modifications, i.e.: • The deflection theory (criterion). It is used to formulate displacement equations and is known as the Iowa deflection theory. It was developed by Spangler and Matrson (Spangler 1941; White and Layer 1960) to calculate changes in horizontal diameter of a steel structure. This formula contains controversial assumptions regarding modulus of soil effect. The assumptions of this theory are as © Springer Nature Switzerland AG 2020 D. Beben, Soil-Steel Bridges, Geotechnical, Geological and Earthquake Engineering 49, https://doi.org/10.1007/978-3-030-34788-8_2

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18

2 Selected Issues of Soil-Steel Bridge Design and Analysis

follows: (i) perpendicular pressure (load) is steadily spread over the structure width; (ii) influence on the bottom part of the structure equals vertical pressure and is steadily spread over the structure width contact with the subsoil part; (iii) horizontal pressure is spread in a parabolic way over the central part (100 degrees) of the shell and the maximum unitary pressure is a result of passive resistance modulus and can be observed in half of the horizontal displacements of a structure. • The Ring Compression Theory developed by White and Layer (White and Layer 1960). This theory uses soil pressure on the walls of a steel structure. The pressure is limited to a certain value for which a case of damage to joints of individual metal plates is not possible. The theory is based upon assumption that the non-uniform distribution of pressure observed by Marston and Spangler has only a slight effect on value and distribution of circumferential thrusts. At the same time the following condition needs to be met: the soil cover over the structure needs to exceed 1/8 of the structure diameter. This theory claims that the steel structure of a shell needs to be designed to match compression stress caused by hydrostatic pressure of soil that equals the pressure of the soil cover over the structure. • The theory (criterion) of buckling also known as the Meyerhof method (Meyerhof and Baikie 1963; Luscher 1966). The theory claims that an elastic buckling starts as a local bulge and is mainly observed at the shell structure crown or in a different place (depending on the places where the critical combination of soil pressure, bending moments, some structural imperfections occurs, together with the initial occurrence of residual stress). Meyerhof and Baikie (1963) have observed that highly flexible structures working in soils of low deformation modulus were destroyed due to shell buckling. It has been observed that with an increase of a shell structure stiffness and soil modulus, the destruction occurred as a result of exceed of the yield strength of steel. Some design methods like AASHTO and CHBDC offer a different procedure of designing box-shaped soil-steel structures than in the case of typical cross-sections, like arches, arch-circular, etc. It is connected with a slightly different character of behaviour of these structures as their shape is close to a frame. In this case distribution of bending moments at the crown and haunches is proportional to the stiffness in these sections. Increase in stiffness of any of these sections (at the crown or the haunch) causes reduction of moment value carried by the remaining sections. The procedure included in the Swedish design method (Pettersson and Sundquist 2014) comprises the most popular cross-sections used in soil-steel structures. A common practice is to design soil-steel bridges with use of numerical methods based on the finite elements method (FEM) and the finite differences method (FDM). It is mainly applicable to structures of longer span. The most popular software includes: ABAQUS, CandeCad Professional, DIANA, FLAC, PLAXIS. In this section, the most popular methods and standards of the design of soil-steel bridges and culverts are described such as Swedish design method (Pettersson and Sundquist 2014), AASHTO LFRD (2017) method, CHBDC (2014) method.

2.1 Code Requirements and Design Methods

19

Moreover, the design of large span of soil-steel bridges proposed by McGrath et al. (2002) is also shown. Besides the presented methods and standards, there are exist other design codes require by other countries, for example, Australian code (AS/NZS 2041 2010), British (BD 12/01 2001), American manual for soil-steel bridges constructed on the railway lines (AREMA 2012).

2.1.2

Swedish Design Method (Pettersson and Sundquist 2014)

Hakan Sundquist and Lars Pettersson developed the method in 2000, and in the following years several modifications were made. The basis for the development of this method was a series of experimental studies on various types of soil-steel bridges and culverts (Beben 2005; Pettersson 2007; Flener 2009; Wadi 2012). The described method is currently the most modern in Europe for the dimensioning of soil-steel bridges and culverts. The method takes into account the Eurocode provisions in dimensioning and load range. This method is comprehensive because it allows to apply the load patterns and safety factors applicable in given country. The method allows designing the soil-steel bridges with different corrugation profiles and using various materials. The calculation model that has been constructed in such a way as to cover as wide a range of performance conditions. The previous methods and theories, i.e. White-Layer (1960), Klöppel-Glock (1970), Duncan (1979), Vaslestad (1990) and CHBDC (2006) were taken into consideration during creating this method.

2.1.2.1

The Range of Method Application

The application of the Swedish design method was limited by the following conditions: – the relationship between the backfill stiffness and the shell structure stiffness fulfills the condition 100
λf
50,000 (see Eq. 2.15), – the minimum soil cover depth is hc ¼ 0.5 m (hc includes a part of the road or track over the shell structure), – the backfill must have a suitable density index and provide adequate rigidity in relation to rigidity of the shell structure, – the surrounding soil and the way the backfill laying meets the appropriate requirements, – the cross-sections shown in Fig. 2.1 can be considered. Taking into account the cross-sections presented in Fig. 2.1, the following conditions for various structure shapes should be fulfilled: round pipe (Fig. 2.1a) have a constant radius (R). For horizontal ellipses (Fig. 2.1b): the relations between

2 Selected Issues of Soil-Steel Bridge Design and Analysis

a)

hc

hc

20

b)

Rt

H

H

R

Rb

h

h

Rs

S d)

H

H

Rt

Rt

hc

c)

hc

S

h

Rs

h

Rs

Rb

Rb

Rc

S

hc

e)

hc

S f)

H

Rt

H h

h

R

Rb

Rc S

hc

S

hc

g)

H h

H h

Rt S

Rt

Rs

Rs

h)

Rc S

Fig. 2.1 The shape of considered cross-sections in the Swedish design method: (a) round pipe, (b) horizontal ellipse, (c) pipe-arch (determined by four radii), (d) vertical ellipse, (e) arch, (f) pipe-arch (determined by three radii), (g) box culvert, (h) arch structure (determined by two or three different radii)

2.1 Code Requirements and Design Methods

21

the radii should fulfil: Rt/Rs
4 and Rb/Rs
4. Three radii determine pipe-arches (Fig. 2.1f): top radius (Rt), bottom radius (Rb) and corner radius (Rc) and the requirements are as follows Rt/Rc
5.5 and Rb/Rc
10. In the case of pipe-arches with four radii (Fig. 2.1c): top radius (Rt), bottom radius (Rb), corner radius (Rc) and side radius (Rs), the following requirements should be satisfied Rt/Rc
5.5, Rb/Rc
10 and Rs/Rt
2.0. For vertical ellipses (Fig. 2.1d): a relation of the top (Rt) or bottom (Rb) radii and the side radius (Rs) is about 0.80, and additionally the condition should be fulfilled 1.0 < 2H/S
1.2. For box culverts (Fig. 2.1g), the relation of radii may be as follows Rt/Rs
12. Arch structures (Fig. 2.1e) including a uniform radius (so-called the top radius (R ¼ Rt)). For arch structures (Fig. 2.1h) determined by two (or three) various radii (top radius (Rt) side radius (Rs) and corner radius (Rc)); the appropriate radius should be selected to fulfil the conditions Rt/Rs
4 and 1
Rc/Rs
4. The transversal and longitudinal road profile situated above the soil-steel bridge should be examined. A lateral inclination suggests that the soil cover depth should be also checked because it can be varied. It should be added that the effect of the live loads can grow significantly, even with little variability of the soil cover depth, therefore the calculations should be conducted for the minimum cover depth for a given bridge. Regarding the longitudinal road inclination, the Swedish design method can be applied for inclinations not exceeding 10%. In the case of soil-steel bridges situated under railway lines, the soil cover depth should be greater than 1.0 m (0.50 m + 0.50 m (ballast thickness)) to guarantee that the needed soil cover depth is maintained in the case of the ballast modernization. The Swedish design method can be used also for the structures situated parallel (side-by-side). The method recommended that the minimum space (a) between two parallel shell structures of types a), b), c), d), f) (Fig. 2.1) should be estimated using the formula S
10 m; a  b and 10 m < S; a ¼ S/10, where: b ¼ 1.0 m is the minimum space for shell structures of types a), b), c), d) and f). In the case of soil-steel bridges with cross-sections of types e), g) or h) the minimum space between the structures can be estimated as S
6 m; a  b and 6 m < S; a ¼ S/10, where: b ¼ 0.6 m is the minimum space for structures defined in point e), g) or h), and the contiguous structures are placed on one foundation. The compactors dimension used for the backfill compaction may also restrict the minimum space between contiguous shell structures. In the case when the space between the structures is lower than the minimum values, the load-carrying capacity of the whole bridge can be decreased. The method suggests that this decrease should affect the design effective tangent modulus of the backfill by a coefficient fm (decrease coefficient for minimum space): fm ¼ 0.7 + 0.3 a/anom
1.0, where a is the space, anom is the nominal minimum space. The design of concrete foundations for soil-steel bridges should be conducted using the appropriate geotechnical and bridge standards (e.g. EN 1997-1:2004 (1997); AASHTO LRFD (2017)). It can be pointed out that the shell structures influence the foundations with a design normal force. The bending moments from the arch structure is not taken into account (structures are normally mounted in the foundation in cast-in steel channels using U-profiles).

22

2 Selected Issues of Soil-Steel Bridge Design and Analysis a3

a3

S

hc

a5

[I]

a4

[II]

[III]

h

[III]

[IV]

a2

a1

[V]

Fig. 2.2 Scheme and characteristics of backfill zones in the soil-steel bridge

2.1.2.2

Requirements for Backfill

The calculation principle of the Swedish design method is based on the effective interaction between the shell structure and the soil. Therefore the method adopts that the backfill should be characterized by the controlled and measurable features. It also adopts that the backfill areas showed in Fig. 2.2 include the designed soil (according to the requirements presented below). For the areas where the soil does not directly interact with the shell structure, other soil materials (for example native soil) can be accepted. The backfill requirements for properties and dimensions (Fig. 2.2) that are essential for application of the Swedish design method are: • Backfill [I]: A minimum thickness of base course for roads should not be less than 0.3 m. Besides, for the design aims, the soil density over the shell crown (ρcrown) should be an average of the backfill densities within areas [I], [II] and [III]. • Backfill [II]: The backfill quality is required to be at least the same quality as for backfill [III]. Special backfill requirements can be specified for the railway and road infrastructures. • Backfill [III]: a3 ¼ min (S/2; 3.0 m), a4  0 m. The backfill properties should be at least similar for [IV]. In some cases, it may be justifiable to growth the heights a1 and a2 especially if the structures are situated on the areas where the freeze depth is relatively high. These backfill densities are indicate as ρsurr. • Backfill [IV]: a2 > 0.3 m, a1  0.2 S. Regarding backfill denoted as [IV], its properties are established at a distance greater than 0.5 m from the steel structure. • Soil [V]: The soil requirements in relation to the native soil properties are not influenced by the size of the soil-steel bridge.

2.1 Code Requirements and Design Methods

2.1.2.3

23

General Rules of Design

Soil-steel bridges and culverts can be designed taking into account the rules given by the Eurocodes together with additional requirements. The foundations of arch structures should be designed using appropriate standards. During designing a soil-steel bridge, it may be assumed that the shell structure has a constant section in the longitudinal direction. Additionally, it can be assumed that the calculation model allows to considering section with a width of 1.0 m where the forces act perpendicularly to the axis of the shell structure. When the shell sections of the bridge are different, each section should be examined separately. In the case of various soil cover height over the shell structure, the most unfavourable height of cover may be adopted in the calculations. The top part of the bridge section (the area between the quarter points) should be analysed individually during live loads. The top part of the arch possesses elastic supports that can be characterised by the side supports (it can be assured by the backfill). Moreover, the structures are normally elastically supported by using the backfill located over the structure. The crucial calculations are related to the top parts of the structure because mainly this section is influenced by the live loads. In the top part of the shell section, the constant normal force can be taken into account, whereas the bending moments coming from the live loads on one half of the arch is positive and the second half is negative. It should be added that Swedish design method does not cover the soil-steel bridges and culverts in which backfill includes lightweight filling materials. In such cases, the backfill properties (mainly the tangent modulus and its density) should be determined to calculate a stiffness parameter. The backfill layer laid above the shell structure (vibration damping) usually reduces the dynamic load impact. However, in the Swedish design method this reduction is less than is usually used for calculating the structures on which the backfill is found, e.g. arch or frame reinforced concrete structures. Conducted tests (Beben 2013a, b; Yeau et al. 2015) have shown, that the higher depth of the soil cover over the structure does not significantly effect on the reduction of dynamic amplification. Therefore, in the case of the soil-steel bridges, the Swedish design method proposes a lower reduction of the dynamic amplification factor with increasing depth of soil cover thickness. For soil-steel bridges with a soil cover depth more than 2.0 m, a conservative reduction coefficient rd is used (Eq. 2.1) in order to diminish the dynamic amplification. hc red < 2 m ) r d ¼ 1:0, 2 m < hc red < 6 m ) r d ¼ 1:0  0:05hc red , 6 m < hc red ) r d ¼ 0:8, where: hc red is reduced depth of soil cover.

ð2:1Þ

24

2 Selected Issues of Soil-Steel Bridge Design and Analysis

The Swedish design method is generally based on the SCI (Soil-Culvert Interaction) method developed by Duncan (1978, 1979), which is based on FEM calculations. The method allows estimating the cross-sectional forces resulting from loads coming from the backfilling process and from live loads. In order to decrease the possibility of local failures of the shell structure under given loads, a soil cover depth over the structure should be more than 0.5 m.

2.1.2.4

Design Procedure in the Swedish Design Method

During designing of soil-steel bridges and culverts, the following checks should be made: (a) verification of the structure in the serviceability limit state (SLS): – the safety before the beginning of yielding in the shell structure wall, – the backfill movement near the steel shell structure. (b) verification on the load-carrying capacity of the shell structure in the ultimate limit state (ULS): – are the plastic hinge mechanisms (or plastic hinges) do not appear in any sections of the shell structure? – is the buckling phenomenon does not happen at the bottom parts of the shell structure? – are the strengths of the screwed connection are not exceeded? – is the strength of the corrugated plate wall at the corners is not exceeded due to radial soil pressure (mainly in the pipe-arches shapes)? – is the load-bearing capacity of concrete foundations is not exceeded due to the dead and live loads (it concerns the arched structures)? (c) During fatigue design need to be checked: – general and fatigue soil modulus, – loads applied for the fatigue design, – fatigue load-carrying capacity of the CSPs, – fatigue load-carrying capacity of the applied screws. (d) During construction stage, the following variants should be checked: – is the shell structure shows an adequate stiffness during assembly process of the CSPs (it means handling stiffness)? – is the load-carrying capacity of the shell structure at zero soil cover depth is not exceeded? – is the shell structure strength in the intermediate stages of construction process is kept?

2.1 Code Requirements and Design Methods

2.1.2.5

25

Reduction of Soil Cover Depth over the Structure

During the backfilling process in soil-steel bridge, the shell crown goes up due to the lateral soil pressure on the shell structure sides. This reduces of the soil cover height over the structure (it means the distance between the shell top and the roadway). Therefore, the reduced soil cover height can be calculated using equation: hc red ¼ hc  δcrown ,

ð2:2Þ

where hc means the soil cover height (according to Fig. 2.1), δcrown means the rise of the shell structure height during the backfilling process and can be computed using δcrown ¼ 0.015 S, or in order to a more detailed estimation the following equation can be applied:  ρ S H 2:8 ½0:560:2 ln ðHSÞ δcrown ρsurr S
f H H=S, λf ¼ 0:013 surr λ , ¼ S E soil K E soil K S

ð2:3Þ

where: S is span or diameter of the shell structure (according to Fig. 2.1), H is vertical distance between the structure crown and the point at which the bridge has its greatest span (Fig. 2.1), λf is stiffness parameter that means the dependency between the structure stiffness and backfill, ρsurr is unit weight of backfill counted up to the crown height, Esoil K is tangent modulus of the backfill, fH is the parameter (function applied for computation of crown growth during a shell backfilling) is demonstrated for selected H/S ratios in Fig. 2.3, λ is the relationship between the backfill stiffness and the shell structure stiffness.

2.1.2.6

Normal Force Caused by Backfilling Process

The normal force resulting from the soil loads appearing at the backfilling process can be estimated using the formula: N soilK ¼ 0:2

  H h h H ρsurr S2 þ Sar 0:9 c red  0:5 c red ρ S2 , S S S S crown

ð2:4Þ

where: Sar is reduction coefficient related to the arching effect for backfill load situated over the shell structure, ρcrown is average weight density of the backfill over the shell crown (generally the unsaturated soil should be used to calculation).

26

2 Selected Issues of Soil-Steel Bridge Design and Analysis 10.0 Ratio H/S: 0.4 0.5 0.6

dcrown Esoil, k / rsur S 2

1.00

0.10

0.01 100

1000

f

10 000

100 000

Fig. 2.3 Graph showing the growth of the shell crown during the backfilling process

Figures 2.4 and 2.5 present graphical interpretation of Eq. (2.4) with two various parameters, i.e. if ρ ¼ ρsurr ¼ ρcrown and the arching factor Sar ¼ 1.0. The arching factor Sar considers the arching phenomenon of the backfill over the shell structure that appears in the case of great soil cover heights. When the steel shell structures are situated in an natural excavation, this effect can be estimated using φcover,d (it means the design angle of internal friction for the soil cover): tan φcover,d ¼

tan φcover,k , γ M,soil

ð2:5Þ

where: φcover,k is characteristic value of internal friction angle for backfill over the shell structure, γ M,soil is partial safety factor depend on the backfill (usually assume as 1.3).

2.1 Code Requirements and Design Methods

27

2.00 1.75 1.50

Ratio H/S: 0.2

Ns /rS 2

1.25

0.3 0.4

1.00

0.5 0.6

0.75 0.50 0.25 0.00 0.0

0.5

1.0

1.5

2.0

hc,red / S

Fig. 2.4 The interrelation of the normal force resulting from the dead loads (backfill), the soil cover-to-span ratio (hc/S) and the height-to-span ratio (H/S). The backfill unit weight (ρ) is homogeneous in whole bridge

In this case, the arching coefficient Sar can be calculated using formula: Sar ¼

1  eκ1 , κ1

ð2:6Þ

where: hc red , S 0:8 tan φ Sv ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cover,d 2 : 2 1 þ tan φcover,d þ 0:45 tan φcover,d κ1 ¼ 2Sv

ð2:7Þ ð2:8Þ

28

2 Selected Issues of Soil-Steel Bridge Design and Analysis 2.00

1.80

Ratio H/S: 0.2

Ns l (rhc,red S)

1.60

0.3 0.4

1.40

0.5 0.6

1.20

1.00

0.80

0.60 0.10

1.00

10.00

hc,red / S

Fig. 2.5 The interrelation of the normal force resulting from the dead loads (backfill), the reduced soil cover-to-span ratio (hc red/S) and the height-to-span ratio (H/S). The backfill unit weight (ρ) is homogeneous in whole bridge

2.1.2.7

Normal Force Caused by Live Loads

The Swedish design method proposes, that the distribution of load coming from loads (point or line, i.e. wheels of trucks) can be computed taking into account the Boussinesq’s approach. The cause for using this procedure is the fact that so far known distribution methods give too conservative results (i.e. 2:1 – overestimated values and 1:1 – underestimated values). Besides, the simplified load spread technique gives discontinuity in the pressure coming from the vehicles if it is analysed in relation to the soil cover depth. Applied loads are changed to the corresponding them the line loads at the road level ( plive).

Equivalent Line Load The SCI method takes into account the idea that the real live-load is transformed using the stress distribution in a half-space elastic body in accordance with the

2.1 Code Requirements and Design Methods

29

Boussinesq approach, to the comparable line load ( p) that causes similar upright stresses at the shell crown using the equation: σv ¼

2p , πz

ð2:9aÞ

where z is height calculated from the load application area. In the same way for the point load (P), the formula (2.9a) has a form: σv ¼

3 P h3c red , 2π s5

ð2:9bÞ

in which s is the length between the given point load (tire of the vehicle) at the road surface and the structure points at a depth of hc red. Line and point loads are transformed to the comparable line load ( plive). If there is no more accurate calculation manner, the formulae (2.9a) and (2.9b) can be applied. Furthermore, the equivalent line-load at the given point that is loaded with the largest upright stresses may be determined by the formula: plive ¼

π hc red σv: 2

ð2:10Þ

On the basis of above assumptions, the characteristics normal force (Nlive, k) in the shell structure wall can be computed as follows: if hc red =S
0:25 ! N live,k ¼ plive þ ðS=2Þqk , if 0:25 < hc red =S
0:75 ! N live,k ¼ ð1:25  hc,red =SÞplive þ ðS=2Þqk , if 0:75 < hc red =S ! N live,k ¼ 0:5plive þ ðS=2Þqk ,

ð2:11aÞ ð2:11bÞ ð2:11cÞ

where qk is distributed pressure from live load.

2.1.2.8

Design Normal Force

The design normal force in the SLS may be expressed as: N SLS,d ¼ γ soil,SLS N soil,k þ γ live,SLS N live,k ,

ð2:12Þ



N ULS,d ¼ γ d γ soil,ULS N soil,k þ γ live,ULS N live,k ,

ð2:13Þ

and in the ULS by:

as well as in the fatigue limit state (FLS) by:

30

2 Selected Issues of Soil-Steel Bridge Design and Analysis

N live d,FAT ¼ γ live,FAT N live,k,FAT ,

ð2:14Þ

where: γ d is the partial factor dependent on the safety class, Nsoil, k, Nlive, k represent the characteristic normal forces caused by the soil and live loads, respectively. The values of the partial factors approved by the appropriate authorities are included in the above-mentioned formulae.

2.1.2.9

Bending Moments

The bending moments in the shell structure are dependent on the relation between the stiffnesses of the shell structure and the surrounding backfill. This dependence (λf) can be expressed as: λf ¼

E soil,k S3 , ðEI Þsteel =γ M,soil

ð2:15Þ

where: Esoil, k is the characteristic tangent modulus for the backfill, (EI)steel is the bending rigidity of the steel shell structure (E is elasticity modulus of steel, I is moment of inertia of the shell structure), γM, soil is the partial factor for the backfill stiffness. The tangent modulus of the backfill depends on the dominant stress distribution in the backfill. When designing a soil-steel bridge with various backfill at a height according to (hc + H ), a mean value of Esoil,k should be applied for the estimation of λf. For the simplified calculations, the degree of backfill compaction is only needed. It may be specified both taking into account the Standard Proctor (RPstd) or the Modified Proctor (RPmod). The relation of the Standard Proctor and the Modified Proctor for backfill can be calculated using RPstd ¼ RPmod + 5%. The backfill compaction degree should be used as a percentage value. In the formula, the stress in the area directly below the quarter points of the shell structure, at the depth of (hc + H/2) is applied.

Caused by Backfill Load The bending moments coming from the backfill load (dead load and compaction influence) for the SLS and ULS is given by the formula:

2.1 Code Requirements and Design Methods

31

M soil,k M soil,surr,k M soil,cover,k ¼ þ S3 S3 S3

 0:75 hc red Rt ¼ ρsurr f 1 f 3 f 2,surr þ Sar ρcover f 1 f 2,cover , S Rs

ð2:16Þ

where: Rt and Rs are the top and side radius, respectively, and (a) the function f1 can be computed as follows: – if 0.2 < H/S
0.35 ! f1 ¼ [0.67 + 0.87 (H/S – 0.2)], – if 0.35 < H/S
0.5 ! f1 ¼ [0.8 + 1.33 (H/S – 0.35)], – if 0.5 < H/S
0.6 ! f1 ¼ 2 (H/S). (b) the function f2,surr may be estimated using: – if λf
5000 ! f2,surr ¼ 0.0046–0.0010 10log(λf), – if λf > 5000 ! f2,surr ¼ 0.0009, (c) the function f3 can be calculated as: f 3 ¼ 6:67 HS  1:33. When the backfill is laid and compacted the over the shell crown the below formulae can be used: – if λf
5000 ! f2,cover ¼ 0.018–0.004 10log(λf), – if λf > 5000 ! f2,cover ¼ 0.0032.

Caused by Live Loads The bending moment resulting from the live loads ( plive and q) can be expressed using the formulae: M live,k ¼

f I4



f II4



f III 4



f IV 4

 0:75 R  S  plive,k þ Sar t f 1  f 2,cover  qk  S2 , Rs

where:

 f I4 ¼ 0:65 1‐0:2 10 log λf ,

 f II4 ¼ 0:12 1‐0:15 10 log λf , ðhc red =SÞ f III þ 0:4, 4 ¼ 4  0:01

ð2:17Þ

32

2 Selected Issues of Soil-Steel Bridge Design and Analysis

f IV 4 ¼

 0:25 Rt : Rs

Besides, the requirement f I4  f III 4 < 1:0 should be applied. For the bridges with shapes in which the relation of Rt/Rs is higher (or equal) than 1, the bending moment in the side sheets can be determined as 1/3 of the bending moment computed using the formula (2.16).

Distribution of Bending Moments in Soil-Steel Bridges with Different Cross Sections Soil-steel bridges and culverts are normally designed with a uniform cross section. It means that the bending moment is calculated only for the place where the biggest value is expected. For some shell profiles, especially box culverts, the additional plates (ribs) are usually used from the safety and economy point of view. Such ribs strengthen and increase the load-carrying capacity of the most strenuous shell sections, e.g. crown, corners and haunches (Fig. 2.6). The designing of the strengthening sheets are determined taking into account the rules saying that the bending moments are distributed for both backfill and live loads. The design bending moments at the haunches are the total bending moments caused by the backfill and live loads, and it can be expressed by: 2 1 M haunch ¼ M crown þ M crown : 3 soil,k 3 live,k

ð2:18Þ

Fig. 2.6 Examples of using additional reinforcement plates (ribs) to strengthening the most strenuous sections (crown and haunches)

2.1 Code Requirements and Design Methods

33

Design Bending Moments The design bending moments resulting from the backfill and live loads characterize by positive and negative signs at various cross sections. For this reason, the verifications should be conducted taking into account the below principles. The design bending moment (MSLS, d) in the SLS can be calculated using the equation: M SLS,d ¼ γ soil,surr,SLS M soil,surr,k þ γ soil,cover,SLS M soil,cover,k þ γ live,SLS M live,k : ð2:19Þ The design bending moments resulting from the live loads in the SLS may be computed by: 9 M max live,SLS ¼ γ live,SLS M live,k  = , M live,k min ; M live,SLS ¼ γ live,SLS  2

ð2:20Þ

and in the ULS, the design bending moments can be determined with the formula:  M ULS,d ¼ γ d γ soil,surr,ULS M soil,surr,k þ γ soil,cover,ULS M soil,cover,k þ γ live,ULS M live,k : ð2:21Þ The design bending moments coming from the live loads in the ULS can be calculated using the formula: 9 M max live,ULS ¼ γ live,ULS M live,k  = : M live,k ; M min live,ULS ¼ γ live,ULS  2

ð2:22Þ

In the FLS, the design bending moments can be determined by: M live,d,FAT ¼ γ live,FAT M live,k,FAT :

ð2:23Þ

It can be underlined that the partial factors during designing are commonly required by the bridge administration. These factors may change depending on the country.

2.1.2.10

The Safety Before the Beginning of Yielding in the Shell Structure Wall in the SLS

The maximum stress in the shell structure wall can be determined using the equation propose by Navier:

34

2 Selected Issues of Soil-Steel Bridge Design and Analysis

σ¼

N SLS,d M SLS,d þ < f yd , A W

ð2:24Þ

where: NSLS, d, MSLS, d are design normal force and bending moment, respectively in the SLS, A is cross-sectional area, W is section modulus, fyd is yield strength of steel. The design normal forces and bending moments can be determined as the total value of the maximum normal forces and the maximum bending moments. These maximum values should be computed separately for the backfill and the live loads. The partial factors concern the SLS. A verification should be conducted in order to confirm that the yield strength of steel ( fyd) was not exceeded at the top section of the structure shell during the service-load conditions. The backfill movements should be checked using the geotechnical codes and rules.

2.1.2.11

Verifications in the ULS

The Possibility of the Plastic Hinges Appearance in the Top Section of the Shell Structure The code EN 1993-1-1 (2005) gives a verification procedure at the ULS. It is assumed that the plates do not deflect from the z-axes (χLT ¼ 1.0 and χz ¼ 1.0). Besides, the bending moment Mz,Ed ¼ ΔMz,Ed ¼ 0 and, when the neutral axis of CSP sheets does not shift resulting from the local dislocation (ΔMy,Ed ¼ 0). Thus, the formula presented in EN 1993-1-1 (2005) can be expressed in the form: M y,Ed N Ed þ kyy
1:0, χ y N Rk M y,Rk γ M1,steel γ M1,steel

ð2:25Þ

where NEd and My,Ed are the design values for axial thrust (NULS, d) and bending moment (MULS, d), respectively. It can be observed that in some cases, the moment capacity (My,Rk) can be simplified by expression: !!   f 1=2 mt yk ð2:26Þ M ¼ 1:429  0:156 ln Mu t 227 χ y ¼ Ncr/Nu is a reduction coefficient dependent on the flexural buckling, NRk ¼ fy A and My,Rk ¼ fy W are resistances for axial thrusts and bending moments, respectively. γM1,steel is a partial factor for the steel (usually it is assumed as 1.0).

2.1 Code Requirements and Design Methods

35

kyy is an interaction coefficient given by EN 1993-1-1 (2005). The interaction coefficient kyy may be reduced to a simpler form and in the case of cross section classes 1 and 2, it can be expressed as: Cmy  k yy ¼  N Ed 1χ C , N cr,y yy

ð2:27Þ

in which Cmy ¼ Cmy,0 is the correction coefficient permitting for the moment distributions along the shell structure as stated by EN 1993-1-1 (2005). Thus, it may be considered that the correction coefficient (Cmy) is equal to 1.0 as well as Ncr, y ¼ Ncr,el and it can be calculated using: N cr,el

3ξ ¼ μ

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Esoil,d ðEI Þsteel : Rt

ð2:28Þ

Cyy is the correction coefficient for the cross-section classes 1 and 2. When λ0 ¼ 0 and λZ ¼ 0, the correction coefficient may be presented in the form:
 C yy ¼ 1 þ wy  1

   1:6 2 2 C my λy 1 þ λ 0 ηpl , wy

ð2:29Þ

and C yy 

W el,y , W pl,y

ð2:30Þ

W

where wy ¼ W pl,y
1:5 constitutes the relation of plastic (Wpl,y) and elastic (Wel,y) el,y modulus of section. The relative slenderness λy can be presented using formula: rffiffiffiffiffiffiffiffiffiffi Nu λy ¼ , N cr,el

ð2:31Þ

where Nu ¼ fyd A and Ncr,el. ¼ Ncr.

2.1.2.12

Verification of Load-Carrying Capacity of the Bottom Part of the Structure

The load-carrying capacity presented above is verified for the top part of the shell structure with radius Rt. Furthermore, the load-carrying capacity of any cross sections of the shell structure should be verified taking into account dominant normal

36

2 Selected Issues of Soil-Steel Bridge Design and Analysis

forces. The normal force around the shell profiles should be considered as a constant value and to correspond to the biggest design value. Besides, the load-carrying capacity can be verified using: N ULS,d
N cr ,

ð2:32Þ

where Ncr should be computed as shown above with the changes: ηj ¼ ξ ¼ 1.0, μ ¼ 1.22 and Rt means the radius of the section concerned.

2.1.2.13

Check the Strengths of the Screw Joints

Bending Capacity of the Screw Joints The screw joints between corrugated plate sheets in the soil-steel bridges should be planned in such a manner that the dominant normal force (perpendicular to the structure) and the bending moment may be carried. The recommended information for the load-carrying capacity is selected after the tests of joints formed using a special type of screw applied for such structures. The way between parallel lines of screws (Fig. 2.7) to achieve the necessary moment capacity (if the screws number is given) in the joint can be received using the formula: n x F t,Rd  W  f yd , 2

ð2:33Þ

where: F t,Rd ¼

0:9f u,bolt,k Anet bolt : γ M2

ð2:34Þ

If distance (x) becomes irrationally big, the number of screws (n) shall be increased. It should be noted that in Eq. (2.33) the number of screws in the screw lines is identical. Supposing a linear spread of the bending strain over the screwed joints, each screw lines can be considered during calculation of the capacity. In the case of unsymmetrical screwed joints (the number of screws is not identical in the lines), only screws composing symmetrical layout should be considered. x

Fig. 2.7 Distance between screws n/2

n/2 x

2.1 Code Requirements and Design Methods

37

Shear Force Considering the screwed joints (for contiguous crests and troughs), at least two screws are applied and their locations are selected so that the bending moments should be carried. The load-carrying capacity of the joint can be estimated taking into account the rules given by EN 1993-1-8 (2005). The load-carrying capacity of screw joints can be verified by formula (2.35). The design normal force (Nd,ULS) contains the total of the backfill loads and live loads with partial factors given by the appropriate codes or/and regulations. The number of screws (n/metre) needed for safe operation of the soil-steel bridge can be estimated using the following formulae: N ULS,d < min ðn F v,Rd ; n F b,Rd Þ N ULS,d < min ðn F v,Rd ; n F bolt,Rd Þ

 ,

ð2:35Þ

where: F v,Rd ¼

0:6f u,bolt,k Anet bolt , γ M2

ð2:36Þ

2:5f uk d bolt t , γ M2

ð2:37Þ

F b,Rd ¼ where t is thickness of steel plate.

Tension Force The tensile forces in the screwed joints may be computed using: Ft ULS,b ¼

2M ULS,d : xn

ð2:38Þ

Interaction in Screws In the ULS, the case of total tension and shear forces should be verified by the formula: F ULS,v F þ ULS,t
1:0, F v,Rd 1:4F t,Rd where the shear forces in the joint can be determined using:

ð2:39Þ

38

2 Selected Issues of Soil-Steel Bridge Design and Analysis

F ULS,v ¼

2.1.2.14

N ULS,d : n

ð2:40Þ

Verification of Corrugated Plate Wall At the Corners Due to Radial Soil Pressure

The Swedish design method does not propose a special procedure for verification the radial soil pressure on the shell structure with regard to the radii presented in Fig. 2.1. However, the simplified formula can be used to verify the soil pressure on the corner plates in the shell: pc ¼

Rt p, Rc t

ð2:41Þ

where pc and pt are the radial pressures acting on the haunch and top plates, respectively.

2.1.2.15

Fatigue Design

The fatigue strength of the steel plates and the screwed joints in the soil-steel bridges shall be also examined. In the case of the screwed joints, the CSP sheets near the joint as well as the screws in the joint shall be verified. The design backfill modulus applied for verification the fatigue strength (Esoil,FAT,d) can be computed using formula:  Esoil,k ¼ 0:42  m  100kPa  kv

 ð1  sin φk ÞρhcþH=2 Sar ðhc þ H=2Þ 1β : ð2:42Þ 100kPa

The obtained design backfill modulus is multiplied by a coefficient f6 ¼ 1.5  1.5. The first coefficient (1.5) is responsible for the change between ULS and SLS and the second one (1.5) is associated with the long-term backfill behaviour. It can be underlined that the condition λf
50,000 should be satisfied with introducing a limitation for the maximum backfill modulus for the calculation purposes. The greater backfill modulus applied for the fatigue determination should be used to the live loads only. The favourable effect of part of the compressive stress range should be considered according to the requirements given by EN 1993-1-9 (2005). For road bridges, the fatigue strength can be checked taking into account the accumulated damage method. In the case of railway bridges, the lambda method can be applied according to EN 1991-2 (2003).

2.1 Code Requirements and Design Methods

39

During estimation of fatigue strength of soil-steel bridges, the model FLM4 should be applied according to EN 1991-2 (2003). The accumulated damages may be computed for each vehicle axles (do not take into account the closely spaced axles). The Swedish design method says that the vehicle location on the bridge (considering the transverse direction), usually is not the identical for the individual ride of vehicles (EN 1991-2 (2003)), therefore the stress ranges can be decreased as follows: • no decrease of computed stress range if the 50% of the rides, • 97% of the computed stress range if 36% of the rides, • 90% of the computed stress range if 14% of the rides.

2.1.2.16

Fatigue Strength of the CSP Sheets

The range of stresses in CSPs under live loads in the crown of soil-steel bridges (taking into account the one axle acting on the shell) should be computed for the upper and bottom fibres of the corrugations. Therefore, the stress ranges can be computed using the formulae: 9 M live,d,FAT > = W , N live,d,FAT M live,d,FAT > ; ¼  A W

σ top live,FAT, max ¼ 0:2 σ top live,FAT, min

N live,d,FAT M þ 1:2 live,d,FAT , A W

ð2:44Þ

9 N live,d,FAT M =  0:2 live,d,FAT > A W , N M > ; ¼  live,d,FAT þ live,d,FAT A W

ð2:45Þ

Δσ top live,d,FAT ¼

σ bottom live,FAT, min ¼  σ bottom live,FAT, max

ð2:43Þ

Δσ bottom live,d,FAT ¼ 1:2

M live,d,FAT : W

ð2:46Þ

Nlive,d,FAT and Mlive,d,FAT are determined for each axle taking into account model FLM4 and Eqs. (2.11a, 2.11b, 2.11c) and (2.17). It should be noted that for the CSPs, the fatigue strength can be verified at the crown of the soil-steel bridge (using detail category equal to 125).

40

2 Selected Issues of Soil-Steel Bridge Design and Analysis

2.1.2.17

Fatigue Strength of the Screwed Joints

The Swedish design method recommends that the range of stresses in CSPs due to the live load effect at the screwed joints has been determined using formulae (2.43, 2.44, 2.45 and 2.46). In the case of location of joints outside the crown of the soilsteel bridges, reduction of bending moment due to the live loads can be applied. Consequently, the bending moment from live loads may be decreased using a ratio (hc/hbolt)2, where hbolt means the distance to the axle of bolts from the roadway level. For the CSPs, the detail category can be assumed as 90 and m ¼ 5 (a slope in log-log scale (Leander et al. 2017)). The range of stresses in screw joints due to the live loads (coming from the axle to the shell structure) can be determined using the below formulae considering that tensile and shear stresses appear simultaneously: Δσ ¼ 0:8

2M live:FAT : x  Anet bolt  n

ð2:47Þ

It should be noted that the detail category (tension stress) is equal to 50 and the coefficient 0.8 considers the effect of screwing of the screws. Δτ ¼

N live:FAT : Anet bolt  n

ð2:48Þ

In this case, the detail category (shear stress) amounted to 100 and m is equal to 5.

2.1.2.18

Behaviour of Shell Structure Under Construction Loads

The behaviour of soil-steel bridges under construction loads (backfill compaction, the impact of compactors, etc.) is very sensitive. Therefore, these works should be conducted properly and safely in order to the shell does not deform significantly during backfilling. For this reason, some verification procedures should be applied. The Swedish design method requires the appropriate rigidity of the CSP shell proposed as: ηm =ðm=kNÞ ¼

S2 : ðEI Þsteel

ð2:49Þ

For various shapes, the CSP shell rigidity can be fulfilled the below relations: – for circular sections, it should be less than 0.13, and – for arches and low-rise sections, it should be smaller than 0.20. Due to the fact that the stress in the soil-steel bridge at the crown at zero soil cover depth is significant, additional checks are needed. The normal forces and bending moments shall be determined using formulae (2.3) and (2.15). It should be noted that

2.1 Code Requirements and Design Methods

41

only portions of the formulae corresponding to the zero soil cover depth can be considered. Besides, the Navier’s formula can be applied for verification the design yield stress level of CSP shell. During construction of the soil-steel bridges can appear the soil cover height and external loads different from those applied for the designing of the final structure. Therefore, these construction steps can be important for the structure safety, and the temporary bridge requires to be examined in the same manner as for the permanent bridge.

2.1.3

The AASHTO Method (AASHTO LFRD 2017)

According to the assumptions of the American code AASHTO (American Association of State Highway and Transportation Officials) the following structures of CSP can be distinguished: 1. Structures with the radius of curvature not exceeding 4.0 m and the proportion of height to span (for arches) is not lower than 0.3. The minimal soil cover depth above the shell is 0.3 m or 1/8 of the span (backfill does not include pavement unless it is rigid). 2. Structures with parameters exceeding limitations mentioned in item 1, of the shape of an ellipse, low and high profile arches, of pear and of closed pear profile of long span. Long-span structures may have additional reinforcements such as: (i) longitudinal stiffening ribs of steel profiles or reinforced concrete (ii) continuous or sectional cross stiffenings of steel profiles or CSP, (iii) reinforced concrete relieving slabs. 3. Box-shaped structures of span up to 10.97 m. The AASHTO LFRD (2017) method provides for the possibility to design soilsteel bridges in accordance with the service limit state and strength limit state with the load combinations. It ignores impact of bending moments on stresses in the structure wall, but it takes into consideration the axial thrust from dead and live loads. It considers three destruction models: (i) exceeding the yield strength of steel in the structure wall, (ii) shell buckling, and (iii) destruction of screw connections. The load-carrying capacity (resistance) should be calculated for each applicable limit states: Rr ¼ ϕRn ,

ð2:50Þ

where: ϕ is the load-carrying capacity (resistance) factor ϕ ¼ 0.67 for screw joints or 1.0 for spiral pipes (AASHTO LFRD 2017), Rn is nominal load-carrying capacity (resistance) of the wall in compliance with the considered model of destruction:

42

2 Selected Issues of Soil-Steel Bridge Design and Analysis

Rn ¼ ϕF y A,

ð2:51Þ

where A is cross-section area of the wall on length unit [mm2/mm], Fy is yield stress of the shell material [MPa].

2.1.3.1

Calculation of Normal Thrust in the Shell of Soil-Steel Bridge

Calculation of thrust in steel shell (pipe, arch-pipe and arch structure) can be executed with use of the formula: T LL ¼

PDL S PLL C L F 1 þ , 2 2

ð2:52Þ

where: S is structure span [m], CL is width of the structure on which the live load is applied parallel to the span (CL ¼ lw
S), 0:75S 15  F min , where F min ¼ 12S  1, lw 0:54S for the long-span structures: F 1 ¼ wt , 12 þ LLDW ðhc Þ þ 0:03S for corrugated metal pipe: F 1 ¼

LLDW is live load distribution factor, lw is live load patch length at depth hc, wt is tire patch width, PDL and PLL are substitute load from dead and live loads, respectively, on the level of the structure crown [kN/m2]. Dead loads should be considered with VAF (vertical arching factor) specified as:

VAF ¼ 0:76  0:71

  SH  1:17 , SH þ 2:92

ð2:53Þ

where: SH is hoop stiffness factor. For the long-span soil-steel bridges (except the box culvert shape), the thrust should be calculated using Eq. (2.52) replacing S by twice the value of top radius of the arc (Rt). The dynamic factor to be applied to the static load shall be taken as: φ ¼ 1 + DLA/100, where DLA is the dynamic load allowance for soil-steel bridges and culverts and other buried structures, in percent, shall be taken as:

2.1 Code Requirements and Design Methods

43

DLA ¼ 33ð1:0  0:125hc Þ  0%,

ð2:54Þ

in which: hc – soil cover depth.

2.1.3.2

Load Distribution Through Backfill

Instead of a more accurate analysis, or the use of other acceptable approximate methods of load distribution, where the depth of backfill is 0.61 m or greater, wheel loads may be considered to be uniformly distributed over a rectangular area with sides equal to the dimension of the tire contact area, and increased by either 1.15 times the depth of the backfill. For soil-steel bridges and culverts with a single span, the effects of live loads may be neglected where the depth of backfill is larger than 2.44 m and exceeds the span length. For multiple span bridges (and culverts), the effects may be neglected where the depth of backfill exceeds the distance between faces of end walls. In the case where the backfill depth is smaller than 0.61 m, live loads shall be distributed to the top slabs of bridges (or culverts) taking into account two cases: – the vehicle travels parallel to span: the bridges (or culverts) shall be examined for a single loaded lane with the single lane multiple presence factor. The axle load shall be distributed to the top part of shell for determining moment, thrust, and shear as follows: E⊥ ¼ 96 + 1.44 S, (ii) parallel to the span: EII ¼ LT + LLDF (hc), where: LT – length of tire contact area parallel to span, LLDT – factor for distribution of live load with depth of backfill (1.15), – the vehicle travels perpendicular to span: live loads shall be distributed to the top part of the shell. Soil-steel bridges and culverts with traffic traveling perpendicular to the span can have two or more trucks on the same design strip at the same time. This must be considered, with the appropriate multiple presence factor, in analysis of the structural response of the bridge (or culvert).

2.1.3.3

Buckling

Checking the structure (pipe, arch-pipe and arch structure) safety against buckling is determined on the basis of the following formula: A

T LL , ϕ f cr

where: fcr is minimal buckling critical stresses of the shell steel wall [MPa].

ð2:55Þ

44

2 Selected Issues of Soil-Steel Bridge Design and Analysis

The AASHTO code says, that if fcr < fy, it is then necessary to correct the value A replacing fcr with Fy. The value of fcr is determined depending on the structure span using the following dependences. If: i S< k

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s  24E , fu

ð2:56Þ

then: f cr ¼ f u 


F u k S2 i

48E

,

ð2:57Þ

and if i S> k

s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  24E , fu

ð2:58Þ

then: 12E f cr ¼  2 , kS i

ð2:59Þ

where: i is radius of inertia of the corrugation cross-section [mm], k is soil stiffness factor (k ¼ 0.22), E is elasticity modulus of the steel shell structure [MPa], fu is tensile strength of the steel shell structure [MPa]. For deep corrugated structural plate structures, the thrust in the shell wall under the final installed condition shall not exceed the nominal load-carrying capacity to general buckling capacity of the bridge, computed as: Rb ¼ 1:2ϕb Cn ðEI Þ1=3 ðϕs K b M s Þ2=3 Rh , where: ϕb is resistance factor for general buckling, Cn is scalar calibration factor to account for some nonlinear effects ¼ 0.55, ϕs is resistance factor for backfill, Ms is constrained modulus of embedment, Kb ¼ (1  2ν)/(1  ν2), ν is Poisson’s ratio of backfill, Rh is correction factor for backfill geometry (11.4/(11 + S/hc)).

ð2:60Þ

2.1 Code Requirements and Design Methods

2.1.3.4

45

The Screw Joint Strength

Joint strength can be determined by means of the method of limit states or the method of allowable stresses. According to the method of allowable stresses the joint strength SS should amount at: SS  TLLsf, where sf ¼ 3.0 (global safety factor), and the characteristic value should be used as TLL. Whereas in the method of limit states the condition for joint strength SS has been formulated as ϕ SS  TLL, where ϕ ¼ 0.67 (strength factor for screw joints), the design value should be accepted as TLL, the SS value depends on the type of joint, plate thickness and size (corrugation) and the number of screws. The AASHTO LFRD (2017) code also gives the values of minimal soil covers depending on the thickness of the structure wall and the radius of curvature of the vault. For deep corrugated structural plate structures, the factored moment capacity of longitudinal connections shall be at least equal to the factored applied moment but not less than the greater of: (i) 75% of the factored moment capacity of the member or (ii) the average of the factored applied moment and the factored moment capacity of the member.

2.1.3.5

Handling Stiffness

Soil-steel bridges should be characterised by relevant bending stiffness and it mainly concerns steel structure of the shell. This stiffness is called handling stiffness in the AASHTO code and is determined by flexibility factor FF in accordance with the formula: FF ¼

S2 : EI

ð2:61Þ

AASHTO states, that flexibility factors FF should be as follows: – spiral steel pipes: 0.25
FF
0.19 mm/N for corrugation depth 6.35–25.4 mm, – spirally aluminium pipes: 0.54
FF
0.34 mm/N for corrugation depth 6.35–25.4 mm, – screwed structures of CSP (corrugations 150  50 mm): – circular profiles (pipes): FF
0.11 mm/N, – arch-circular profiles (so-called pipe-arch) and arches: FF
0.17 mm/N. The code treats separately designing of so-called long-span structures. In accordance with the AASHTO LFRD (2017) code, they do not require considering buckling and handling stiffness at the designing stage. Instead, the span is replaced by double value of the radius of the top vault curvature Rt when axial thrust in the wall is calculated, therefore S ¼ 2Rt (see eq. 2.52).

46

2.1.3.6

2 Selected Issues of Soil-Steel Bridge Design and Analysis

Requirements for Backfill

According to the AASHTO LFRD (2017) code, the backfill should meet code requirements in compliance with AASHTO M 145:1991 (2012). For structures with deep corrugations, the backfill should meet with unified American soil classification IAEG (ASTM D-2487-11 (2011)) which means groups I and II with respect to the contents (i.e. well-granulated sands and gravels, of harsh, coarse, or round grains) and compacted (density index min. 0.90). A backfill of the above parameters should reach beyond the shell structure, on each side for at least 1.8 m, and additionally min. 0.61–1.22 m over the structure. Special attention needs to be drawn to transfer of pressure by the backfill at the corner (haunch) of the arch-pipe structure, the value of which equals the quotient of wall strength and the radius of curvature in the haunch.

Minimum Soil Cover Depth The minimum soil cover, including a well-compacted granular backfill, shall not be less than: – S/8  0.30 m for corrugated metal pipe and structural plate pipe structures, – 0.61–1.22 m for long-span structural plate (this depends on the top radius and steel thickness (without ribs)), – S/4  0.30 m for spiral metal pipe, – 0.43 m for metal box structures, – 0.91 m or the limits for long-span structural plate structures based on top radius and plate thickness for structure with deep corrugations (according to AASHTO LFRD (2017) requirements). Minimum soil cover is counted from top of rigid pavement or bottom of flexible pavement.

Design of Soil-Steel Bridges with Box Cross-Section The AASHTO LFRD (2017) code states that the soil-steel bridges with box crosssection are dimensioned in limit states of load-carrying capacity. Geometry of the structure needs to fulfil the following requirements: – for spans from 2.67 m to 7.75 m: height 0.76–3.20 m, top radius Rt
7.56 m, haunch radius Rhau  0.76 m, internal angle of the haunch radius 50 –70 , length of side walls D: 0.12–1.80 m, minimal length of the stiffening rib on side walls (the lower value of 0.48 m or (D  0.076 m), limit dimensions of the soil cover depth above the shell 0.43–1.52 m. If additional reinforcement ribs are used, their spacing at the crown should not exceed 0.61 m, and 1.37 m in haunches.

2.1 Code Requirements and Design Methods

47

– for spans from 7.76 m to 10.97 m: height 1.70–4.27 m, top radius Rt
8.03 m, haunch radius Rhau  1.12 m, internal angle of the haunch radius 48 –68 , length of side walls 0.12–1.80 m, minimal length of the stiffening rib on side walls (the lower value of 0.48 m or (S  0.75 m), limit dimensions of the soil cover depth above the shell 0.43–1.52 m. If additional reinforcement ribs are used, their spacing at the crown should not exceed 0.61 m, and 1.37 m in haunches. In accordance with the AASHTO code, the stiffness is the basic parameter that influences dimensioning of box structures. Therefore dimensioning considers only the influence of bending moments. The backfill around the structure should be a well-granulated mixture of sand and gravel of density index at least 0.95 according to the standard Proctor test. Moreover, the AASHTO gives tabular values of bending moments at the crown and the haunches depending on the span and the soil cover depth calculated from the top of the structure to the vertical alignment of the road. The results are tabulated for a dead load from the backfill weight of 19 kN/m3. From the practical point of view, it is necessary to use load factors (equalling 1.5 in accordance with the method). The given values of moments from live loads relate to the standard load of triaxial vehicle of a maximum load on an individual axle of 145 kN (type HL-93). In order to adapt it to different load conditions and different backfill weight, the tabular values need to be multiplied by corrective factors. For dead loads: – for spans
7.75 m:

M dl ¼ gs S3 ½0:0053  0:00024 ðS  12Þ þ 0:053 ðhc  1:4ÞS2 :

ð2:62Þ

– for spans >7.76 m:


M dl ¼ gs S3 ð0:00194  0:0002S  26hc  1:1Þ þ hc  1:4 0:053S2 þ 0:6S  262 : ð2:63Þ For live loads: M ll ¼ C ll K 1 ðS=K 2 Þ, where: Cll is adjusted live-loads (C1 C2 AL), C1 ¼ 1.0 for singular axles and 0.5 + S/15 m  1.0 for double axles, C2 is corrective factor depending on the number of wheels per axle,

ð2:64Þ

48

2 Selected Issues of Soil-Steel Bridge Design and Analysis

! K1 ¼ K1 ¼

0:08 ðhc =SÞ0:2

for 2:43 m
S < 6:09 m,

0:08  0:02ðS  20Þ ðhc =SÞ0:2

! for 6:09 m
S < 10:97 m,

K2 ¼ 0.54 hc2–0.4 hc + 5.05, for 0.43 m
hc < 0.91 m, K2 ¼ 1.90 hc + 3.00, for 0.91 m
hc < 1.52 m. The design plastic yielding moments at the crown (Mpc) and the haunches (Mph) should not be smaller than the total amount of proportionally distributed bending moments from dead and live loads: M pc  CH Pc ðM dlu þ M llu Þ,

ð2:65Þ

M ph  C H ð1  Pc ÞðM dlu þ Rh M llu Þ,

ð2:66Þ

where: CH is soil cover factor: CH ¼ 1.0 for hc  1.07 m; if 0.43 m < hc
1.07 m, CH ¼ 1.15  [(hc  0.43)/4.3], Pc is allowable range of the ratio of total moment carried by the crown depending on the span, Rh is acceptable values of the haunch moment reduction factor depending on the span and cover depth, Mdlu is bending moment from dead loads [Nm], Mllu is bending moment from live loads [Nm]. The AASHTO code suggests that the reaction force from the soil-steel bridge on the foundation is calculated in accordance with the following formula:   hc S S 2 AL V ¼ γs þ þ : 2 40 2:44 þ 2ðhc þ H Þ

2.1.3.7

ð2:67Þ

Special Elements Supporting the Load-Carrying Capacity

The AASHTO LFRD (2017) code gives a possibility to design reinforced concrete relieving slabs above steel structures which are supposed to diminish bending moments in the structure shell. The slabs thickness should range from 0.19 m to 0.22 m. The slab should exceed in size the contour of the box structure by min. 0.30 m on each side. It is important that the slab has no contact with the crown of shell structure. The minimal distance between the relieving slab and the box

2.1 Code Requirements and Design Methods

49

Fig. 2.8 Application of RC relieving slab for box culvert

structure should fall within the range of 25–75 mm (Fig. 2.8). The minimal thickness of a relieving slab t can be calculated as follows: t ¼ t b RAL Rc Rf ,

ð2:68Þ

where: tb is basic slab thickness depending on the soil density index and type of soil under the slab, RAL is corrective factor depending on load on an axle, Rc is corrective factor depending on compressive strength of concrete, Rf is corrective factor at span below 7.92 m (Rf ¼ 1.22). The compressive strength of concrete Rc, the relieving slab is made of should amount at least at 20 MPa. For loads bigger than 145 kN/axle and compressive strength of concrete below 34 MPa, the factors that increase the basic thickness of the slab need to be applied (AASHTO LFRD 2017).

2.1.4

The CHBDC Method (CHBDC 2014)

The latest version of the CHBDC method (Canadian Highway Bridge Design Code) was established in 2014 (CHBDC 2014), modifies the formerly in force codes CHBDC (2000, 2006) and OHBDC (1992). This code is the first to mention CSP structures of corrugations deeper that traditional ones (380  140 mm for steel structures and 230  64 mm for structures made of aluminium). The CHBDC (2014) code requires that soil-steel bridges and culverts should be dimensioned in respect with the following: 1. Serviceability limit state (SLS) for all types of sections concerns the deformations at the construction phase.

50

2 Selected Issues of Soil-Steel Bridge Design and Analysis

2. Ultimate limit state (ULS): (a) typical soil-steel structures: – occurrence of a plastic hinge at mounting phase, – destruction by exceeding the yield stress of the steel wall as a result of axial compression (service phase), – destruction of a screw joint, (b) box structures: – occurrence of a plastic hinge at the vault, – destruction of screw joints. 3. Fatigue limit state (FLS) of box structures: the scope of acceptable changes in stresses from live loads. Moreover, the CHBDC code provides for using safety factors due to loadcarrying capacity (the so-called load capacity factors) in the analysed limit state in accordance with the following way: (a) for typical soil-steel structures (corrugation dimensions from 380  140 mm): – compression strength ϕt ¼ 0.80, – occurrence of a hinge joint ϕh ¼ 0.85, – occurrence of a hinge joint at construction phase ϕhc ¼ 0.90, – strength of screw joints ϕj ¼ 0.70; (b) for typical soil-steel structures (corrugation dimensions up to 200  55 mm): – compression strength ϕt ¼ 0.80, – occurrence of a hinge joint at construction phase ϕhc ¼ 0.90, – strength of screw joints ϕj ¼ 0.70; (c) for soil-steel structures with box cross-section: – compression strength ϕt ¼ 0.90, – occurrence of a plastic hinge ϕh ¼ 0.90, – strength of screw joints ϕj ¼ 0.70. The CHBDC code allows for the following maximum displacement of the structure (i) 2% of the structure height for typical soil-steel structures during construction (ii) 1% of the span for box structures (iii) 0.5% of the span for box structures at service phase. The conducted tests confirmed that the allowable displacements of soil-steel structures are conservative (Beben 2014). In order to dimension soil-steel bridges the CHBDC code recommends using the following load factors: γ s ¼ 1.25 (from dead loads) and γz ¼ 1.70 (from live loads). Whereas the dynamic factor φ ¼ l + DLA is dependent on the soil cover height above the shell structure. According to CHBDC, the value of the DLA coefficient decreases linearly from the value of 0.4 (no soil cover) to 0.1 (the thickness of soil cover at least 1.5 m) in compliance with the following formula: DLA ¼ 0:4ð1  0:5hc Þ  0:1:

ð2:69Þ

2.1 Code Requirements and Design Methods

51

For box-shaped soil-steel bridges, the above equation applies for span length up to 3.6 m. When the span is longer, the following dependence needs to be applied: DLA ¼ 1  0:5hc  0:1:

ð2:70Þ

According to the CHBDC code the standard vehicle CL-625 of 625 kN of weight and maximal axial load of 175 kN is reliable for load capacity test.

2.1.4.1

Determination of the Backfill Extent

The CHBDC (2014) code gives the minimum extent of the backfill beyond the shell structure contour and generally it should not be smaller S/2 (Fig. 2.9). The extent of backfill above the structure (soil cover depth) should be compliant with the minimal requirement for a backfill discussed in the following part of the chapter. In case of many structures located next to one another, the requirement concerns extent of backfill beyond the edge structures, provided the minimal required thickness of soil cover as for an individual structure is preserved. The backfill should be placed simultaneously on both sides of the shell by layers not thicker than 0.20 m. When plates of low corrugation are used for soil-steel structures, the minimal distance between the neighbouring structures should not be smaller than 1.0 m and of no less than 1/10 of span (S). In case of plates with deep corrugations (for example 380  140 mm and 400  150 mm) the minimal distance between the structures should be at least 1.0 m. The minimal height of soil cover above the shell structure should amount at the bigger of the following values: 9 0:6 m > >   > = S S 0:5 > , ð2:71Þ 6 H  2 > > > S > ; 0:4 H where H means structure height in accordance with the CHBDC (2014) code, and S means the span. Fig. 2.9 Typical backfill range according to the CHBDC (2014) method for regular and box shape

52

2 Selected Issues of Soil-Steel Bridge Design and Analysis

For structures with deep corrugation plates (380  140 mm), if the minimum soil cover height calculated on the basis of the Eq. (2.71) exceeds 1.0 m, 1.0 m should be accepted as the value of minimum soil cover.

2.1.4.2

Calculation of Thrust in the Wall of a Shell Structure

The axial thrust Tf in the structure wall in the ULS can be determined in accordance with the following: T f ¼ ϕ Rn  γ D T DL þ γ L T LL φ,

ð2:72Þ

where: ϕ is dynamic factor (1 + DLA), Rn is compression strength of the wall of the shell structure, γ D and γ L are dead loads (1.25) and live loads (1.70) factors, respectively (according to (CHBDC 2014)), TDL and TLL are normal thrust in the wall from characteristic dead and live loads, respectively.

Thrust in the Structure Wall from Dead Loads Normal thrust TDL in the shell structure wall from dead loads can be calculated as follows: T DL ¼ 0:5ð1  0:1 C S ÞAf G,

ð2:73Þ

where: Af is arching factor (CHBDC (2014) gives a nomogram from which Af can be read), G is weight of soil masses located over the structure per unit of length, Cs is dimensionless parameter of axial stiffness of the shell wall depending on backfill parameters, that can be determined from the formula: Cs ¼

1000E s H , EA

ð2:74Þ

where Es means secant modulus of soil [MPa].

Thrust in the Wall from Live Loads Thrust in a structure wall from live loads is determined by the following formula: T LL ¼ 0:5 lt σ L mf ,

ð2:75Þ

2.1 Code Requirements and Design Methods

53

where: lt is magnified by the value of 2hc distance of external axes (including wheel mark) placed in accordance with the rule to locate standard vehicles in such a way within the limits of the structure, σ L is substitute load evenly distributed on the level of the structure crown (at symmetrical load with double axle 2  125 kN of a 5-axle vehicle of total weight 625 kN), assuming load distribution at the angle of 45 in the crosswise direction towards the structure axis and of 63 in the longitudinal direction, mf is factor considering number of loaded road lanes (for load on one traffic lane mf ¼ 1.0, and for two lanes mf ¼ 0.9).

2.1.4.3

Strength of a Structure Wall in Compression

The CHBDC (2014) code assumes that the load-carrying capacity of shell structure wall is related to resistance to elastic buckling and compression strength. Therefore, the structure is analysed in two areas: i.e. the top part and the side and bottom part. The division of parts is determined by angle θ0 expressed in radians and determined by means of the following equation: 

 EI θ ¼ 1:6 þ 0:2 log , E m R3

ð2:76Þ

where: I is inertia moment of corrugation cross-section on a unit of length [mm4/mm], Em is modified modulus of soil stiffness [MPa], R is radius of curvature of the structure wall measured from the neutral axis of corrugation in cross-section. Compressive stresses σ ¼ Tf /A should not exceed the ultimate limit of compressive strength fb, with the following values: – for R
Re:

f b ¼ ϕt F m f y 

!  ! f 2y KR2 1 , r ρ 12E

ð2:77Þ

– for R > Re: 3ρϕF E f b ¼  t m2 , R K r

ð2:78Þ

54

2 Selected Issues of Soil-Steel Bridge Design and Analysis

where: ϕt is load capacity factor, Fm is corrective factor depending on the number of structures; Fm ¼ 1.0 for one structure, Fm ¼ (0.85 + 0.3 a/S)
1.0 for many parallel structures (a – the smallest distance between the structures). The assumed value of Fm equals 1.0 for top parts of a structure with deep corrugations. Re is substitute radius of curvature:  0:5 r 6Eρ Re ¼ , K fy

ð2:79Þ

where K is factor dependent on relative stiffness of a wall in relation to the stiffness of adjacent soil: 

EI K¼λ E m R3

0:25 ð2:80Þ

,

ρ is reduction factor of buckling stresses in accordance with the following formula:  0:5 ð hc þ H 1 Þ ρ ¼ 1000
1:0, Rt

ð2:81Þ

H1 is half of the distance from the crown to the line of maximum structure span [m], Rt is radius of the upper part of the structure (the vault) [mm]. The CHBDC code assumes that the value of modified soil stiffness modulus (Em) for side and bottom zone is the same as for the secant modulus of the soil (Es), whereas for the upper part it amounts at: ( Em ¼ Es



Rt 1 Rt þ 1000ðhc þ H 1 Þ

2 ) :

ð2:82Þ

Value λ for the upper zone of the wall of all structures except arches of same radius, where proportion of height to span falls below 0.4 can be determined as follows: "



EI λ ¼ 1:22 1 þ 1:6 Em R3t

0:25 #

For remaining cases λ ¼ 1.22 should be adopted.

:

ð2:83Þ

2.1 Code Requirements and Design Methods

2.1.4.4

55

Load-Carrying Capacity at Construction Stage – Combined Effect of Bending and Compression

Site documentation of construction of soil-steel bridges should contain information on the acceptable maximum axle load of working vehicles (Ac) used for construction works. At any phase of construction works the effects of bending moments and axial thrusts from characteristic dead loads and equipment at work (live ones) should not exceed the ultimate load-carrying capacity limit as far as yield moments are concerned. The CHBDC (2014) code formulates the condition: 

P PPf

2

  M   
1:0, þ M Pf 

ð2:84Þ

where: P is compressive force from characteristic loads [kN/m]; P ¼ TD + Tc, PPf is design compressive strength [kN/m]; PPf ¼ ϕhc A fy, M is bending moment from characteristic loads [kNm/m]; M ¼ M1 + MB + Mc, MPf is design yield moment [kNm/m]; MPf ¼ ϕhc MP, ϕhc is load-carrying capacity factor, Mp is characteristic yielding moment of the section. If the soil cover height above the shell (hc) at the time of construction works is smaller than acceptable minimum, then the compressive force P ¼ 0. Therefore, the values M1, MB and Mc are calculated as follows: M 1 ¼ kM1 RB γ S3 ,

ð2:85aÞ

M B ¼ k M2 RB γ S2 H,

ð2:85bÞ

M c ¼ kM3 RL S Lc ,

ð2:85cÞ

where: kM1 ¼ 0:00046  0:0010 log 10 N f for N f
5000, kM1 ¼ 0:0009 for N f > 5000, kM2 ¼ 0:018  0:004 log 10 N f for N f
5000, kM2 ¼ 0:0032 for N f > 5000, kM3 ¼ 0:120  0:018 log 10 N f for N f
100 000, kM3 ¼ 0:030 for N f > 100 000, h  i R R  0:2 for 0:2

0:35, RB ¼ 0:67 þ 0:87 2S 2S h  i R R RB ¼ 0:80 þ 1:33  0:35 for 0:35

0:50, 2S 2S

56

2 Selected Issues of Soil-Steel Bridge Design and Analysis

RB ¼ RL ¼

H S

for

H > 0:50, 2S

0:265  0:053 log 10 N f
1:0,
hc 0:75 S

E s ð1000SÞ3 , EI A LC ¼ C , k4

Nf ¼

k4 is vehicle effects factor depending on the number of wheels per axle and the soil cover height (to be found in a table in CHBDC (2014)), γ is volume weight of soil [kN/m3], R is radius of curvature in analyses shell segment measured at the axis of corrugation.

2.1.4.5

Load-Carrying Capacity of a Structure under Service

The CHBDC (2014) code states that for a structure of deep corrugation i.e.  380  140 mm, combined effect of bending and axial thrusts in the ULS cannot exceed the calculated load-carrying capacity of the section in accordance with the formula: 

Tf T Pf

2

   Mf  
1:0, þ  M Pf 

where: Tf is thrust in a wall calculated in the ULS, PPf ¼ ϕh A fy, Mpf ¼ ϕh MP, Mf ¼ |γ DM1 + γ DMDL| + γ LMLL φ, M1 ¼ kM1 RB γ S3, MDL for hc < S/2 shall be calculated as follows: MDL ¼ kM2 RB γ S2 He, where: He is smaller of hc and S/2, M LL ¼

kM3 RU S AL , k4

ð2:86Þ

2.1 Code Requirements and Design Methods

57

where: RU ¼

0:265  0:053 log 10 N f ðhc =SÞ0:75


1:0,

AL is axle load of the second axle of the standard vehicle due to CHBDC (2014).

2.1.4.6

Strength of Screw Joints

Strength of screw joints is designed for effects of force Tf. The code determines ultimate capacity limits for screw joints per unit of length Ss. Its design value should meet the following condition: ϕj Ss  γ D T DL þ γ L T LL φ,

ð2:87Þ

where: ϕj is capacity factor compliant with CHBDC (2014) of 0.7, TDL and TLL are normal force in the wall from characteristic dead and live loads, respectively.

2.1.4.7

Seismic Loads

The CHBDC (2014) code provides for dimensioning of soil-steel bridges exposed to seismic effects. The code proposes dimensioning of soil-steel bridges in such a way as they would transfer the forces of inertia resulting from earthquakes at a probability of their occurrence within the next 50 years amounting at 2%. Studies carried by Byrne et al. (1996), Maleska et al. (2017) and Maleska and Beben (2018a) proved, that increase in axial thrusts in the structure wall is a result of vertical seismic effects whereas the increase in bending moments depends on horizontal seismic effects. The vertical component of earthquake acceleration ratio Av shall be calculated as Av ¼ 2 AH/3 (where AH means horizontal ground acceleration equalling zone value of acceleration depending on seismic zone, for instance some districts of Czech Republic have a determined acceleration of 1.0–1.2 m/s2, in Portugal up to 4.7 m/s2, in Spain up to 1.6 m/s2, in France up to 4.5 m/s2, in Slovenia up to 2.5 m/s2 (Solomos et al. 2008)). AH shall be set equal to the peak ground acceleration (PGA). Additional axial thrusts or bending moments in the shell wall caused by seismic effects respectively amount at: – for typical soil-metal structures: TE ¼ TDLAv, The total factored thrust including the earthquake effects shall be calculated as follows: Tf ¼ γ D TDL + TE,

58

2 Selected Issues of Soil-Steel Bridge Design and Analysis

– for box shaped metal structures the effects of axial thrusts are ignored. What is analysed is the influence of additional moments: ME ¼ MDL Av, where MDL is a banding moment in a wall from the dead loads. The total factored bending moments at crown and haunches, including the earthquake effects, can be determined using the following equations: – at crown: Mcrown f ¼ κ (γ D MDL + ME), – at haunches: Mhaunch f ¼ (1 – κ) (γ D MDL + ME).

2.1.4.8

Design of Soil-Steel Bridges with Box Cross-Section

The CHBDC (2014) code formulates limitations for using the method for construction of box shaped structures (span within the scope of 2.7–8.0 m, height 0.8–3.2 m). The soil cover height should fall within the range of 0.3–1.5 m. The backfill should meet the general requirements for soil-steel bridges described above. It should be placed symmetrically and in layers. Thickness of one layer should not exceed 0.20 m. The extent of backfill should cover the area shown in Fig. 2.9.

Calculating Internal Forces The CHBDC (2014) code assumes dimensioning of the bridges with consideration on bending moments only. The effect of axial thrusts can be ignored due to their negligible value. The code allows for proportional distribution of bending moments at the crown and haunches. For a span exceeding 8 m and/or structure height exceeding 3.2 m dimensioning needs to consider effects of the structure-soil interaction, while the procedure of dimensioning needs to be followed strictly.The design bending moments in the ULS at the crown level and at haunches of the shell structure amount at: the crown :

M crown ¼ γ D M crown,DL þ γ L M crown,LL ϕ,

the haunches : M haunch ¼ γ D M haunch,DL þ γ L M haunch,LL ϕ,

ð2:88aÞ ð2:88bÞ

where: Mcrown, DL and Mhaunch, DL are bending moments of dead loads at crown and haunch, respectively, Mcrown, LL and Mhaunch, LL are bending moment of live loads at the crown and haunch, respectively.

Bending Moment from Dead Loads The CHBDC (2014) code states that the combined bending moment in shell structure is calculated from the following formula:

2.1 Code Requirements and Design Methods

59

   d M DL ¼ k1 γ S3 þ k2 γ hc  0:3 þ c S2 , 2000

ð2:89Þ

where: k1 ¼ 0.0053–0.00024 (3.28 S – 12), k2 ¼ 0.053, γ is unit weight of the soil [kN/m3], dc is corrugation depth [mm]. Therefore, the bending moments in shell structure from dead loads are calculated from the following formulae: at crown : M crown, at haunch : M haunch,

DL

DL

¼ κ M DL ,

¼ ð1  κÞM DL ,

ð2:90aÞ ð2:90bÞ

where: κ is distribution factor of bending moment in accordance with the formula: κ ¼ 0:70  0:0328 S,

ð2:91Þ

Bending Moment from Live Loads The total bending moment in shell structure is calculated as follows: M LL ¼ C 1 k 3 LL S,

ð2:92Þ

where: C1 is factor depending on the number of vehicle axles, i.e. C1 ¼ 1.0 (for one axle), C1 ¼ 0.5 + (S/15.24)
1.0 (for many axles), 0:08 k3 ¼ for S
6.0 m, ðhc =SÞ0:2 0:08  0:002ð3:28S  20Þ for 6.0 m < S < 8.0 m, k3 ¼ ðhc =SÞ0:2 LL ¼ AL/k4, AL is single axle load of standard CHBDC vehicle for S < 3.6 m or load from two axles of the vehicle when S  3.6 m, k4 is coefficient depending on the effects of vehicle operation (the number of wheels on axis). Therefore, the bending moments in the shell structure from live loads are calculated as follows: at crown : at haunch :

M haunch,

where kR ¼ 0.425 hc + 0.48
1.0.

¼ κ M LL ,

ð2:93aÞ

¼ ð1  κ Þk R M LL ,

ð2:93bÞ

M crown, LL

LL

60

2 Selected Issues of Soil-Steel Bridge Design and Analysis

In the ULS, none of the above design bending moments can exceed the calculated yielding moments Mpl expressed by means of the formula: M pl ¼ ϕh M p ,

ð2:94Þ

where: ϕh is load-carrying capacity factor for occurrence of plastic hinge (0.9 is the accepted value), Mp is unfactored plastic moment of the steel wall.

Calculation of Force Acting on the Foundation The CHBDC code gives a formula to calculate the force acting on the bridge foundation. It allows to design the foundation in a correct way:  V ¼γ

 hc S S2 AL þ þ : 2 40 ð hc þ 2ð hc þ H Þ Þ

ð2:95Þ

Therefore the components of the impact on the foundations can be calculated in accordance with the following dependencies: horizontal: VH ¼ V sinθ, vertical: VV ¼ V cosθ, where θ means the angle between the structure wall and the vertical line.

Determination of Screw Connections The CHBDC code says that the strength of longitudinal joints in soil-steel bridges which underwent the effects of design bending moments only ϕi  SM, should not be smaller than the yielding moment Mpl. Whereas, at the time of dimensioning, the bending moment effects and axial thrusts are considered (for instance for side walls), the strength of such longitudinal joints ϕj  SS should not be smaller than Tf (the designed force in the wall). The values SM and SS need to be obtained from the manufacturer of the CSPs or taken from standards in force. Screw joints need to be dimensioned in the ULS considering the higher value of (i) design moment, or (ii) 75% of the design element strength (ϕ  Mp).

2.1.4.9

Fatigue Strength

The calculated range of stresses variations from live loads should not exceed standard limitations for CSPs and screw joints. For steel structures, the E category

2.1 Code Requirements and Design Methods

61

is adopted as far as the fatigue effects on screw joints are concerned. For CSP, the adopted category is A (in accordance with (CHBDC 2014). In addition, this code provides fatigue life constant y ¼ 36.11010 and the ultimate limit of amplitude Fsr ¼ 110 MPa. The difference in stress levels at the crown and in haunches cannot exceed 70%. Longitudinal screw joints should not be placed near the crown or within the area of maximum bending moments from live loads in the haunch area. For soil-steel bridges of span exceeding 8.0 m, fatigue effects for screw joints need to be analysed in addition.

2.1.5

Design of Soil-Steel Bridges with Long-Span (McGrath et al. 2002)

Soil-steel bridges with long-span comprise ones with span exceeding 8.0 m, at present reaching even 40 m. Arch-shaped, elliptic and arch-pipe profiles are usually used to build them. Designing long-span structures requires especially careful approach due to higher values of internal forces in the shell structure. Some methods (for example Swedish design method (Pettersson and Sundquist 2014) and CHBDC (2014)) allow for dimensioning such structures as well. Long-span structures are often designed with use of numerical methods based on FEM. Such an approach makes it possible to provide for phasing of construction works, temporary loading of the structure during backfilling, a slide at the place where the structure touches the backfill, material non-linearity of backfill and structure, variety of geometric shapes, specific features of the structure like reinforcement beams, CSP ribs, relieving slabs, EPS geofoam, etc. FEM is the best method that provides for complex boundary conditions. However, it requires knowledge of advance modelling in computational programs. Experimental tests held on soil-steel bridges and comprehensive parametrical analyses with use of FEM have constituted basis to develop guidelines for designing long-span structures in the USA, which are briefly presented underneath (McGrath et al. 2002).

2.1.5.1

Live Load Distribution

Tests have proven that in the case of long-span soil-steel bridges loads are distributed over a wider surface than in the case of rigid structures. Therefore, it was proposed to adopt a linear load over the width of 1.0 m in accordance with the following formula: pLL ¼

0:7P , ð1:15hc Þ2

where: pLL is load at the level of the upper part of the structure [kN/m2], P is load from a vehicle (axle) [kN].

ð2:96Þ

62

2 Selected Issues of Soil-Steel Bridge Design and Analysis

2.1.5.2

Forces During Backfill Process

Generally, the AASHTO code assumes that backfill loads cause compression forces in the structure wall, described by the equation: T DL ¼ G Rt ,

ð2:97Þ

where: G is pressure of the soil located above the structure [kPa], Rt is radius of the upper vault of the structure [m]. Taking into consideration the shape of the soil prism, the thrust (TDL) in the wall from dead load can be noted that: T DL ¼ VAF ðhc þ 0:2Ru Þγ S=2,

ð2:98Þ

where: VAF is arching factor, Ru is structure height measured from the level marking the maximum span [m]. The arching factor VAF can be calculated from the following equation: VAF ¼ F W=S þ F S=R þ F H=S ,

ð2:99Þ

where: Fw/s ¼ (1.9  1.15 W/S)  1.1, FS/R ¼ (1 – S/H)  0, FH/S ¼ 2.5(hc/Sc – hc/S)  0, hc/Sc ¼ (0.8 – 0.5 S/H )  0.3, Sc is a factor considering excavation width and native soil stiffness from a table in HSDHCP (2002) code, W is excavation width.

2.1.5.3

Bending Stiffness in ULS At the Time of Backfilling

Bending moments in structure wall during backfilling can be determined on the basis of the following formula: M DL ¼ ΔρðEI Þ, where Δρ means change in curvature of the structure [l/m].

ð2:100Þ

2.1 Code Requirements and Design Methods

63

The eq. (2.100) can be written as follows:  M DL ¼ EI

 1 1  , R RN

ð2:101Þ

where: R and RN are radius of structure curvature before and after deformation, respectively. Upon deformation of the shell structure, the shape of the element is still considered as a part of a circle, however of a different radius (RN) and of new deformed chord length (δ) and internal angle θN. Assuming that no shortening of perimeter occurs (c) as a result of compression, the following can be written: 

 θN R δ c ¼ 2RN sin : 2RN

2.1.5.4

ð2:102Þ

Bending Moments

Bending moments from backfill load and live loads are calculated with consideration to so-called relative bending stiffness of a structure and adjacent soil SB: SB ¼

M S S3 , EI

ð2:103Þ

where MS is oedometric soil modulus determined for live loads on the level of structure crown, and in the case of dead loads – on the level of the longest span of a structure [MPa]. Generally, stiffness of soil around the shell is of great importance for general load-carrying capacity of soil-steel bridges. One of the method to express it is to determine oedometric soil modulus depending on the level of stress and density index of soil. For instance AASHTO LFRD (2017) code gives values of edometric soil modulus depending on type of soil and level of density index. When the structure is embedded in an excavation, it is assumed that the values of oedometric soil modulus should become correlated with excavation width and quality of native soil. Therefore the value of MS can be determined from the following equation Ms ¼ SC MSSB, where Ms-SB is the oedometric modulus of the backfill. Whereas the bending moment MDL from backfill load amounts at: M DL ¼ γ s S2 hc K E ,  where K E ¼ 0:05 1 

ð2:104Þ

 SB  0:0025. 400 þ SB Bending moments in long-span soil-steel bridges caused by live load MLL are calculated from the following formula:

64

2 Selected Issues of Soil-Steel Bridge Design and Analysis

M LL ¼ 2W LL Rt K LL ,

ð2:105Þ

where: WLL is live load [kN/m], Rt is radius of structure vault [m],

K LL

2.1.5.5

 ¼ 0:2 1:05 

SB 800 þ SB

  0:001:

Buckling

Buckling in the case of long-span structures can be a decisive criterion in dimensioning. Critical axial thrust in structure wall causing buckling has been determined by the formula: RB ¼ 1:2Φb C n ðEI Þ1=3

 2=3 MS Rh , Kb

ð2:106Þ

where: Φb is load-carrying capacity factor due to the wall buckling, Cn is calibration factor considering nonlinear effects Cn ¼ 0.55, Kb ¼

ð1  2vÞ , ð 1  vÞ 2

v is Poisson coefficient for backfill, Rh is factor considering heterogeneity of support in accordance with the formula: Rh ¼

2.1.5.6

11:4 : 11 þ ðS=H Þ

Handling Stiffness

Determination of maximum handling stiffness for soil-steel bridges (FF
0.017 [mm/N]) has been extended by connection of the required value of flexibility factor FF with quality of backfill and structure stiffness:

2.1 Code Requirements and Design Methods

FF ¼

ð2RÞ2 ð1  sin ϕloose Þ3 , 0:07EI

65

ð2:107Þ

where: R is radius of curvature of the analysed part of structure [m], ϕloose is angle of internal friction of backfill in loose state.

2.1.5.7

Combined Effect of Bending Moment and Compression Force

Combined effect of bending moment and compression force described in the AASHTO LFRD (2017) code in compliance with separated safety factors method is used for shallow embedded structures (soil cover depth lower than 0.25 of the structure height) and exposed to live loads. In the case of structures with higher soil cover, where effects of bending moments do not exceed 15% of the cross-section strength, dimensioning of cross-section considers compression force exclusively. For structures with shallow soil cover, the following formulae can be used: 9   T f 8 Mu Tf > > þ  0:2 >
1:0 for = RT 9 M n RT   , > Tf Tf Mu > > þ < 0:2 ;
1:0 for 2RT Mn RT

ð2:108Þ

where: Tf and Mu are design axial thrust and bending moment, respectively, caused by backfill and live loads, Rt and Mn are design compression and bending load-carrying capacity, respectively.

2.1.5.8

Special Elements Supporting the Load-Carrying Capacity of Soil-Steel Bridges

Special elements recommended for designing long-span soil-steel structures are peripheral reinforcements (in the form of additional sheets of CSP screwed on to the basic shell) and longitudinal (most commonly in the form of longitudinal reinforced concrete beams attached to the steel structure of the shell). The reinforced concrete slab laid over the shell structure is also quite well solution for the decrease of live loads acting on the bridge (Beben and Manko 2010; Beben and Stryczek 2016a). For peripheral steel reinforcements it is assumed that their spacing should not exceed 0.75 m (when their main function is to increase load-carrying capacity of the structure at service state) and 1.50 m, (when they are supposed to increase loadcarrying capacity during backfilling works). If there are no experimental or calculation proofs that peripheral reinforcements cooperate at transfer of loads, the inertia

66

2 Selected Issues of Soil-Steel Bridge Design and Analysis

moment of the stiffened part of the structure per 1.0 m should be assumed as total of inertia moment of the main cross-section (Is) and the inertia moment of the stiffening profile (Ip), divided by their spacing (n) in accordance with the equation:
 I ¼ I S þ I p =n:

ð2:109Þ

Numerical analyses performed by Maleska and Beben (2018b, 2019) show that additional reinforcements of the shell (ribs and ribs filled by concrete mix) caused the reduction of displacements, stresses, bending moments and axial forces, during backfilling. However, it should be clearly pointed out that the shell deformations without any stiffenings do not exceed the acceptable values. Therefore, it can be concluded that they are not necessary.

2.1.6

Discussion

Analysis and discussion of selected calculation results with use of design methods compared with test results is presented below. Two types of soil-steel bridges of different profiles were analysed (pipe arch and box culvert).

2.1.6.1

Pipe-Arch Structure

The analyzed soil-steel bridge has a pipe-arch shell shape cross section. The effective span of the bridge is 5.0 m, and its vertical height 3.03 m (Fig. 2.10). The shell is constructed using a CSP of thickness 0.0055 m and has a corrugation depth of

Fig. 2.10 Analyzed soil-steel bridge with pipe-arch structure

2.1 Code Requirements and Design Methods

67

0.055 m with pitch 0.20 m (detail in Fig. 2.10). Additional stiffeners (ribs) were not applied for this structure. The installed shell structure was filled up with the backfill of thickness of 0.20–0.30 m. The backfill was suitably compacted to reach ID ¼ 0.97. The soil cover depth above the CSP shell was 1.45 m. Majority of standards and guidelines for design soil-steel bridges do not consider bending moments (box type is an exception). The axial forces coming from liveloads were calculated using the Swedish (Pettersson and Sundquist 2014), Canadian (CHBDC 2014) and American (AASHTO LRFD 2017) methods. The bending moments were calculated only using the Swedish method and compared with those obtained from field tests. Generally, the maximum axial thrusts and bending moments were noticed at the shell crown. A vehicle K-800 in accordance with Polish Norm PN-85/S-10030 (1985) was applied to compute the internal forces (it corresponds with the CL-800 vehicle according to Canadian code (CHBDC 2014). Table 2.1 presents the coefficients applied for the calculations of axial thrusts and bending moments. It should be emphasized that the field tests were conducted using a vehicle with the maximum allowable weight for the given route, i.e., 500 kN with the allowable speed on this road, i.e. 90 km/h. Such an approach helped to a direct comparison between the calculations and measurements results. Table 2.2 proves that calculated axial thrusts in soil-steel bridges based on the Swedish and Canadian methods are conservative. The calculated axial thrusts in comparison to the measured values are higher of 47% and 50%, respectively. The AASHTO method gives more even bigger differences. Bending moments are only considered by Swedish design method. The maximum bending moment obtained Table 2.1 Coefficients applied for the axial thrust and bending moment calculations Coefficient related to: Dead live load Live load Dynamic load (1 + DLA) Multiple presence

American (AASHTO LFRD 2017) 1.95 1.75 1.134

Canadian (CHBDC 2014) 1.25 1.70 1.100

Swedish design method (Pettersson and Sundquist 2014) 1.10 1.50 –

1.00

0.90

–

Table 2.2 The maximum axial thrusts and bending moments calculated based on design methods and measurements

Applied method: Swedish Canadian CHBDC American AASHTO Field test – maximum standard loads (vehicle 500 kN, v ¼ 90 km/h)

Axial thrusts and bending moments N [kN/m] M [kNm/m] 43.69 7.64 46.25 – 63.62 – 22.95 7.51

Note: Vehicle K-800 ( CL-625, HL-93) type was used in calculations

68

2 Selected Issues of Soil-Steel Bridge Design and Analysis

from the Swedish design method is almost the same in comparison to the measured value (see Table 2.2). In order to determine the maximum stresses in the analyzed soil-steel bridge, the total effects of the bending moments and axial thrusts (the Navier formula – see (2.24)) can be applied. Based on formula (2.24), the maximum stress was 94 MPa, which constitute nearly 40% of the yield strength of the CSP shell (235 MPa). Besides, it may be also emphasized that the bending moments constituted a predominant percentage (almost 96%) in the stresses arising in the CSP shell. Figure 2.11 shows a comparison of calculated axial thrusts coming from liveloads in the analyzed soil-steel bridge with measured values obtained under comparable service loads. This graph shows that the course of measured axial thrusts is a non-linear character, which is mostly associated with the influence of dynamic effects (truck velocity as well as their weights and springs) and the soil-CSP shell interaction phenomena. Whereas, the characters of the calculated axial thrusts based on the Swedish, Canadian and American design methods are clearly linear. The calculated axial thrusts received from the Canadian and Swedish methods are nearest to the measured values. Nevertheless, the Swedish method gives a better convergence (nearly 25%) to the field test results for greater live-loads (higher than 340 kN). While the greatest difference (nearly 60%) was reported from the light live-loads (smaller than 100 kN). In the case of the Canadian method, the greatest difference did not exceed 25%, however, it can be added that a greater convergences were received for lower live-loads (smaller than 340 kN). It can also be noted that the calculated axial thrusts from the Canadian method are convergent with the values obtained from the Swedish method as the live-loads increased. Taking into account the entire scope of live-loads, the Canadian method gives more sensible axial thrusts than those obtained from the Swedish method. The differences between the

Fig. 2.11 Axial thrusts versus live loads obtained from applied design methods and measurements

2.1 Code Requirements and Design Methods

69

Canadian and Swedish methods may be associated with the application of the Dynamic Amplification Factors (DAF), i.e., 1 + DLA, given by the Canadian standard (CHBDC 2014). These differences can also result from the method of live-load spread through the backfill and way of determining the arching factor. The American method (AASHTO LRFD 2017) gives the opposite results. It can be also noted that the calculated axial thrusts received from the Canadian and American methods are almost close, but only for lower live-loads (smaller than 150 kN). In the case of greater live-loads, the American method (AASHTO LRFD 2017) gives the axial thrusts much bigger than those received from the Canadian method (CHBDC 2014). Based on the Canadian and American methods, Elshimi (2011) received almost the same convergence of calculated axial thrusts in a steel culvert. Additionally, Fig. 2.11 showed that for live-loads larger than 225 kN, the axial thrusts received from the American method (AASHTO LRFD 2017) are greater than those noted from the Swedish method. The calculated axial thrusts from the American method (AASHTO LRFD 2017) vary significantly from the values received from measurements. Such results are likely associated with adoption of assumptions concerning the double value of the top radius of the pipe-arch shape in the axial thrust computations, and from the conservative way to the live-load distribution through the backfill. The American method (AASHTO LRFD 2017) accepts the ring compression theory to estimate the axial thrusts in the soil-steel bridges and culverts, however, this method is quite conservative and it does not take into account the arching effect in the backfill and soil-structure interaction phenomena. It should be emphasized that the American method (AASHTO LRFD 2017) takes into account the dynamic effects through using a coefficient, which differs linearly from 0% to 33% at 2.44 m and 0 m of fill, respectively. Generally, the AASHTO LRFD (2017) standards give a larger increase in the dynamic impacts in comparison to the AASHTO (2002) requirements. Such effect is definitely visible for soil cover depth equals to and larger than 0.91 m. The principal difference between two requirements is the use of the DLA for soil cover heights up to 2.44 m according to the AASHTO LRFD (2017) standard. The AASHTO (2002) requirements ignore the DLA for soil cover depths larger than 0.91 m. The Swedish design method does not take into account the dynamic amplification factor (DAF) and the live-loads are multiplied only by the load coefficient (1.5). Whereas the Canadian method (CHBDC 2014) considers dynamic effects using through the dynamic load allowance that varies linearly in relation to the soil cover depth. For the construction stage of the soil-steel bridge where the soil cover does not exist yet, the DLA is 0.4, when the soil cover depth equals 1.45 m (like in analyzed bridge) the DLA is 0.11. Figure 2.12 illustrates the course of bending moments obtained from the Swedish design method and field tests. It can be seen a quite good convergence of obtained results, particularly for smaller live-loads. In general, the calculated bending moments were undervalued compared to the measurements, but the largest difference does not exceed 27%. It can be also noted that the differences between the calculated bending moments from the Swedish method and the measured ones rise

70

2 Selected Issues of Soil-Steel Bridge Design and Analysis

Fig. 2.12 Bending moments in relation to liveloads obtained from Swedish design method and measurements

when the live-loads also increase. It can be concluded that the bending moments should be taken into account during designing these bridges, mainly with small soil cover depths. It should be also noted, that the Swedish method applies the rules of the soil culvert interaction developed by Duncan (1978). Then Pettersson and Sundquist (2014) introduced some changes regarding the calculation of the elasticity modulus of backfill and live-loads distribution using the Boussinesq technique in an elastic half-space. The Swedish design method was calibrated based on experimental tests (e.g., Beben 2005; Flaner 2009; Manko and Beben 2005a, b, c). In general, it can be concluded that the axial thrusts from the American method (AASHTO LFRD 2017) give over-conservative values at smaller live-loads. While axial thrusts received from the Canadian (CHBDC 2014) and Swedish (Pettersson and Sundquist 2014) methods are unconservative at greater live-loads. Besides, it seems that the Swedish method is unconservative for estimation of bending moment’s levels in the soil-steel bridges.

2.1.6.2

Box Structure

The analysed soil-steel bridge has a span of 12.27 m and a height of 3.36 m. In the cross-section forms a box structure (Fig. 2.13). The shell structure is composed of CSP with 0.007 m thick and the corrugation profile equals 0.14  0.38 m (see detail in Fig. 2.13). The primary CSP shell was strengthened in the crown and haunches with using ribs consisting of corrugated sheets with the identical thickness as in the primary shell. The shell structure was filled with 0.20–0.30 m thick of permeable backfill with 10–32 mm grading. The backfill was compacted to reach minimum ID ¼ 95% (on the Proctor Normal Density). The soil cover depth (including backfill and road structures) over the CSP shell is 1.05 m. The internal forces in soil-steel bridges were calculated with use of three analytical design methods, i.e. Swedish (Pettersson and Sundquist 2014), American (AASHTO LFRD 2017) and Canadian (CHBDC 2014). In order to assess the

2.1 Code Requirements and Design Methods

71

Fig. 2.13 Analysed soil-steel bridge with box structure

maximum stresses in the soil-steel bridges using the above methods, the combined effects of the bending moments and thrusts (the Navier formula (2.24)) can be used. In this case of bridge, maximum axial thrust and bending moment in the primary shell structure and in the reinforcement ribs of structure should be taken into account. Table 2.3 shows maximum stresses calculated on the basis of the three design methods and Eq. (2.24). As it can be seen, stresses at each stage of the analysis of the bridge (construction and service state) do not exceed the allowed value (314 MPa). A maximum stresses constitute of 33–85% and 48–60% of the yield strength of the steel, respectively for the construction and service state. However the stresses (from the live-loads) are considerably higher than values obtained from experiments (σtest ¼ 52 MPa). In the case of stresses obtained at the construction stage, the Swedish design method gives overestimated results, whereas the AASHTO LFRD and CHBDC methods underestimate them. This proves conservative assumptions in the analysed design methods (too high safety factors, conservative way of load distribution by backfill, insufficient consideration of interaction between the backfill and the CSP shell). Table 2.3 also shows calculated axial thrusts and bending moments. The maximum axial thrusts were obtained at the CSP shell crown (for all the methods), and in the case of bending moments at the crown (for Swedish and American methods) and at the haunch, for the Canadian method. In the case of test results, the most extreme bending moments were observed at the CSP shell crown, and the axial thrusts at the crown or around (2/3 of the shell height).

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2 Selected Issues of Soil-Steel Bridge Design and Analysis

Table 2.3 Axial forces, bending moments and stresses calculated based on Swedish, AASHTO LFRD and CHBDC methods

Methods Swedish (Sundquist and Pettersson 2014)

American (AASHTO LFRD 2017) Canadian (CHDBC 2014)

Test (Manko and Beben 2005b)

Phase (load) Construction (backfill) Serviceability (live load) Construction (backfill) Serviceability (live load) Construction (backfill) Serviceability (live load) Construction (backfill) Serviceability (live load)

Axial thrust kN/m 266.33

Bending moment kNm/m 90.55

Maximum stresses MPa 266.8

% of yield strength of bridge 85

45.13

46.11

154.3

49

426.21

66.97

174.0

55

545.60

63.47

150.5

48

65.90

30.27

105.0

33

107.08

54.93

189.3

60

522.87

87.88

232.0

74

5.32

52.0

17

365.0

As it results from Table 2.3, the present analytical methods to determine internal forces in soil-steel bridges are generally quite conservative when compared to values obtained from experiments. In the case of axial thrusts at the construction stage, the considered methods give underestimated values (the AASHTO method is the most accurate – the axial thrusts lower by 22.6%). At the service stage under live loads the axial thrusts calculated on the basis of the Swedish and CHBDC methods are highly underestimated, and in the case of the AASHTO method – considerably overestimated (49.5%). Whereas bending moments calculated on the basis of the Swedish design method (construction stage) are nearly identical with the ones obtained from experiments. The remaining methods give underestimated values of bending moments (31.2% for AASHTO and 190% for CHBDC methods). Bending moments during live loads are considerably overestimated for all the methods. The differences between the Canadian and Swedish methods may be associated with the application of the DAFs. As mentioned before, the Swedish method does not take into account the DAF, but it uses only the load coefficient (1.5). While, the Canadian method considers dynamic effects thank the dynamic load allowance, i.e., 1 + DLA that varies linearly in relation to the soil cover depth. Generally, differences between analytical methods and measurements may be induced by their way to the live-load distribution by backfill layers. Besides, the manner of determining the arching factor and the soil-steel structure interaction phenomena are not properly taken into account.

2.2 Construction of Soil-Steel Bridges

2.1.7

73

Recapitulation

Designing soil-steel bridges can be carried out with use of available analytical methods described in this chapter. However, it needs to be considered that the obtained results do not allow for obtaining actual internal forces acting inside these bridges. It is mainly the result of conservative approach to: (i) loads distribution by layers of soil, (ii) considering structure-soil interaction, as well as using overrated safety factors (even 1.7 and 1.95). The obtained results are safe, but they usually give overestimated results in comparison to experimental tests. Some methods do not either consider bending moments effects. A way to solve the problem would be using numerical methods like, for example FEM, however it requires knowledge of advanced computational techniques and simulations considering substantial elements in the construction of the computational model (shell corrugation, soil model, structure-soil interaction, load modelling). They are very important issues for proper numerical modelling of soil-steel bridges. Section 2.4 provides adequate information.

2.2 2.2.1

Construction of Soil-Steel Bridges Introduction

Small and medium-sized bridges and culverts (of span up to 25–30 m) can be build and modernised in many different ways. Corrugated steel plates (CSP) are often used to modernise or reinforce them due to relatively low construction cost. Selection of structure profile depends on type and size of the obstacle and existing ground and water conditions. The main factors to convince designers to use structures of this type are: short shell assembly time (usually a couple of days, 2–4 months for the whole bridge), relatively low dead weight (possibility to build the structure on weak ground), structure durability exceeding 100 years, lower construction cost and aesthetic values (Abdel-Sayed et al. 1994; Janusz and Madaj 2009). Construction and modernisation of bridge structures using CSPs have been known and widely used on almost all continents, but mainly in Canada and the USA, for many years. Many successful cases of use have contributed to the fact that the solutions are quite often used by designers in European countries (Austria, Belarus, Bulgaria, Czech Republic, Denmark, Estonia, Finland, France, Germany, Great Britain, Hungary, Italy, Latvia, Lithuania, Norway, Poland, Romania, Russia, Slovakia, Sweden, Ukraine) for modernisation and strengthening of small and medium-sized bridges and culverts. Good technical condition and existing load-carrying capacity reserves have allowed for safe operation of the bridges for many years. However, with constant increase of traffic and loads on vehicle axles, and also increasing use of salt for winter maintenance of roads, condition of many bridge structures is rapidly and

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2 Selected Issues of Soil-Steel Bridge Design and Analysis

considerably deteriorating. Use of CSP elements to reinforce old bridges is gaining importance because of the fact that it enables to carry construction works under normal (or timely limited only) traffic and to achieve effects in a short time. The main reasons for damages observed in massive bridges are among others: frequent overloading (causing cracks and breaks of the vault, loosening of front wall), damaged or faulty drainage, damaged insulation, inappropriate backfill, accumulation of salty water in a wall (resulting in stone or brick damages), leaching and damaging of mortar in joints by freezing water on plant roots. On many occasions, the damages impose demolition of old bridges and replacement with reinforced concrete (RC) or pre-stressed structures. However, such reconstruction is usually very expensive due to limitations in traffic or necessity to provide inconvenient temporary traffic diversions (Vaslestad et al. 2004).

2.2.2

Elements of Corrugated Plate and Shell Profiles

Soil-steel bridges are characterized by flexible behaviour which allows transfer of heavy loads from road or railway vehicles. The structures are usually made of metal (steel and aluminium). In Europe, steel S235JRG2 is mainly used to manufacture CSPs. In case of aluminium structures, alloys of aluminium with additions of copper, silicone, zinc and magnesium are used. Steel structures usually have corrosion protection for example: zinc, Al-Zn, polymer or paint coatings of different thickness, which increase the service life of a given structure. Soil-steel bridges are made of CSP or flat plates with spiral corrugations or sheets joined together by high strength screws. Plate thickness falls within the range of 1.50–12.50 mm. The most common corrugation depth is as follows: • for spiral corrugated pipes: 68  12 mm, 100  20 mm, 125  26 mm; • for structures assembled of plate sheets: 500  240 mm, 400  150 mm, 380  140 mm, 200  55 mm, 152  51 mm, 150  50 mm, 100  22 mm, 70 13 mm (Fig. 2.14). A CSP structure allows construction of long-span engineering structures (even up to 40 m). There are virtually no limits as far as the structure length is concerned – there are tunnels made of CSPs which exceed the length of 100 m. In order to increase load capacity and to diminish deformation of CSP structures, in addition to basic shell elements, some extra elements are used, such as additional steel stiffening ribs, concrete or steel beams, RC relieving slabs, EPS geofoam, geotextiles and geosynthetic materials strengthening the backfill, RC collars (Bacher and Kirkland 1986; Bakht 1985; Vaslestad 1990, 1994; Bathurst and Knight 1998; McGrath et al. 2002; Vaslestad et al. 2002; Essery and Williams 2007; Beben and Manko 2010; Beben and Stryczek 2016a; Maleska and Beben 2018b, 2019). Many different types of such structures can be distinguished with respect to their profile and virtually every, even the least usual profile can be designed. However, designers tend to use standard CSP profiles (Fig. 2.15) such as box, arch, circular,

2.2 Construction of Soil-Steel Bridges

a) 240

Fig. 2.14 Examples of most often CSP profiles: (a) 500  240, (b) 380  140, (c) 200  55 and (d) 150  50 mm

75

500

140

b)

380

55

c)

d)

50

200

150

Fig. 2.15 The most often happened the shapes of CSP structure: (a) circular, (b, c) elliptic vertical and horizontal, (d) pear, (e, f, g, h) arc-circular, and (i, j, k) arched, (l) box

elliptic, arch-circular or pear-shaped set on RC (or steel) foundations or directly on the ground (on a special sand or concrete layer) (Abdel-Sayed et al. 1994; Janusz and Madaj 2009; Machelski 2013). Especially structures with joints by means of highstrength bolts can be given various shapes because individual sheets of CSP can be shaped into a desired profile at the metal plate factory (in accordance with designer’s guidelines and, of course, in compliance with the main static and load-carrying capacity rules).

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2 Selected Issues of Soil-Steel Bridge Design and Analysis

2.2.3

Construction-Assembly Works

2.2.3.1

Assembly of Corrugated Plate Elements

Assembly of CSP elements can be done in many different ways. The most important issue here seems workers’ safety as the elements are quite heavy. The steel shell structure is assembled on previously made RC or steel foundations (Fig. 2.16), with a shaping profile set on the top of foundation (for open profiles) or directly on the profiled ground or concrete (for closed profiles). For assembly of CSP elements high-strength bolts are used (M20 class 8.8 or 8.10 of length ranging from 32 to 75 mm – depending on the plate thickness). The most popular assembly methods are presented below. Method I of assembly is „element by element”. It is used for construction of CSP structures of closed profile, for instance circular and elliptic, although it is also used for small arch bridges (Fig. 2.17a). For arch-circular or arch structures, initial assembly is usually used just like in the case of big closed structures. At the time of assembly of closed profile structures in accordance with method I it is necessary to start with many elements of bottom vault before side elements are joined together. These elements are installed on both sides of the bottom vault so that balance of the structure is maintained. After that, top elements of the structure vault are installed. It is important that the initial assembly of the whole structure is done with the least possible number of high-strength bolts (up to the phase when a couple of shell rings are fully mounted). In horizontal joints only a couple of screws should be initially placed, for example, two screws on each side and two near the middle of a plate sheet (they should be tightened manually). When a couple of rings are put together, the remaining screws can be tightened with torque wrench up to full value of torque moment. Screw caps can be placed both inside and outside the structure. However, to help the use of pneumatic or electric screwdrivers, it is advisable to place caps inside at the bottom part of the structure and outside in the upper shell elements. Tightening of the screws should be done from one to the opposite side of the structure, successively, ring after ring. Alternative solution in many structures is placing Fig. 2.16 View on the RC foundations with steel channel

2.2 Construction of Soil-Steel Bridges

77

Fig. 2.17 Installation of steel arch structure using method: (a) I on RC foundation, (b) II (initial prefabrication)

caps always on the crest, especially in the case of pedestrian crossings, where screw heads are directed inwards for aesthetics reasons and to protect the shell against untwisting. To make sure the side walls do not gape, too many side elements should not be assembled before the upper vault is mounted. When assembly works begin on prepared ground and during the works it is of importance that: (a) the ground itself has the same slope, (b) bottom vault elements are individually checked for their position towards the central axis of the vault, (c) the structure is placed vertically in line in such a way as the wings, chamfers and slants are correctly located, (d) shell shape is continuously monitored (in accordance with the design). Method II of assembly is called “initial prefabrication”. It is mainly used in construction of CSP shells of arch-circular and arch profiles and other long-span structures (among others box and elliptical profiles). It is the fastest assembly method consisting in the initial assembly of each full semi-ring on site. Next, the assembled element is placed, by means of cranes, in the desired place on RC footing (Fig. 2.17b) or it is fixed to CSP elements installed before. All screw caps placed outside the structure should be slightly loosened. Each initially prefabricated ring is installed in such a way as it overlaps the preceding one. Of course, it is very important that both the channels embedded in the foundation are set exactly in line and that they are parallel, and that the slope matches downwards grade of the structure and is laid out by a competent land surveyor.

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2 Selected Issues of Soil-Steel Bridge Design and Analysis

Fig. 2.18 Initial prefabrication of CSP elements

Fig. 2.19 Placement of the pre-assembled shell structure at the construction site

Method III of assembly is so-called „complete initial assembly”. For some structural solutions of CSP shells complete initial assembly may be the best option. It consists in putting the shell structure together as a whole or as a couple of segments off the site (Fig. 2.18), and then installing it in destined location (Fig. 2.19). A typical example of such procedure is the structure requiring underwater assembly for example in the case when it is supposed to reinforce an old structure above it (Fig. 2.19a, b), or when a bridge structure is to be replaced with a new one and traffic on the road can be shut down for a limited time only. Initial assembly, as well as initial prefabrication, can be done both on site and off site, in the factory of metal plates, for instance (depending on structure dimensions and contractor’s transportation capabilities). Upon consultation with the manufacturer, the contractor can choose various ways to assemble CSP elements. They can choose either to put them together as a whole next to the destined location and then to install the achieved structure on foundations, or to assemble the elements on foundations or ground in destined location, or to use a mixed technology. The choice depends on such parameters as construction site size, contractor’s equipment capability, type of obstacle, possible traffic shut-down period, etc.

2.2 Construction of Soil-Steel Bridges

79

All high-strength bolts joining the CSP shell elements should ultimately be tightened with the torque moment of at least 240 Nm. However, the recommended range is 360–400 Nm. For shells with the span of 8.0 m and arches based on foundations, the recommended torque moment is 400–450 Nm. The approximate installation time T (operation hours/m) of CSP shell in normal weather conditions by unexperienced staff of lower qualifications can be estimated in accordance with the formula: T ¼ N b =18,

ð2:110Þ

where Nb is number of screws per shell length unit (e.g. 1/m). In case of assembly of structures of plate thickness t > 6.0 mm, estimated installation time increases by about 10%. Whereas, when the CSP structure is put together in a closed hall and by experienced staff – assembly time can be considerably shortened.

2.2.3.2

Earthworks

Ensuring proper CSP structure interaction with backfill is a basic factor enabling correct transfer of static and dynamic loads by soil-steel bridges. Reaching the desired interaction requires the proper design of the steel structure itself and the use of appropriate and well-compacted backfill. In case of closed profile structures preparation of appropriate foundation of aggregate is crucial (Fig. 2.20). The subsoil under the CSP shell structure should be made of mixes of sand and gravel, of uneven granulation, compacted to reach the density index of minimum 0.97 (in Normal Proctor). The top part of subsoil (of thickness approx. 0.10–0.15 m – depending on CSP profile used) should be mounded in loose state, so that the CSP structure could easily settle within. Total thickness of the aggregate foundation should usually be designed individually, but it cannot be thinner 0.20–025 m.

Fig. 2.20 View on the pipearch structure embedded in backfill

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2 Selected Issues of Soil-Steel Bridge Design and Analysis

hc min IS=0.97

0.5 m

IS=0.94

S/2

S

S/2

Fig. 2.21 Determination of the minimum soil cover and density index of backfill

Requirements regarding choice of method and performing backfilling works around the shell structure are in many aspects similar to requirements for road embankments (e.g. EN 1997–1:2004 (1997), Geotechnical Engineering Manual (2015)). The only difference consists in the fact that a CSP shell structure can generate higher horizontal pressure than the soil inside the embankment (without a structure). The best situation is when the backfill around a CSP shell goes beyond the contour of the structure to a distance equalling 1/2 of span on each side (Fig. 2.21). In case of dimensional limitations of excavation – the minimum width of backfill measured from structure wall should equal 1.00 m. The minimum required soil cover depth (hcmin) above the shell (Fig. 2.21) varies depending on used codes and guidelines, e.g.: • AASHTO LRFD (2017) code recommends a minimum soil cover above shell: S/ 8  0.30 m (for corrugated metal pipe and structural plate pipe structures), 0.61–1.22 m for long-span structural plate, S/4  0.30 m (for spiral metal pipe), 0.43 m (for metal box structures), 0.91 m or the limits (for long-span structures based on top radius and plate thickness for structure with deep corrugations). Pavement is not included into backfill, unless it is rigid. • Polish guidelines (Rowinska et al. 2004) say that the minimum required soil cover height (backfill together with construction layers of pavement) for any structures, except box culverts, can be calculated using the following dependences (adopting the higher value) hc ¼ (S/8) + 0.2 or hc ¼ (S/6), • the CHBDC (2014) code says, that the minimum required soil cover height over the shell should equal the higher of the following values: 9 0:6 m > >   > = S S 0:5 > : 6 H  2 > > S > > ; 0:4 H

ð2:111Þ

where H means structure height in accordance with CHBDC (2014) code, S means the shell span.

2.2 Construction of Soil-Steel Bridges

81

In case of a smaller soil cover, a RC relieving slab, geotextiles (geogrid) and EPS geofoam can be used to minimize influence of static and dynamic loads on steel shell structure (Vaslestad 1990; Bathurst and Knight 1998; McGrath et al. 2002; Vaslestad et al. 2002; Essery and Williams 2007; Beben and Manko 2010; Beben and Stryczek 2016a). Backfill material should be granulate. It can be sand, river and excavated gravel, sand and gravel mixtures, because they are easy to be compacted in any weather conditions. Cohesive soils should be avoided as desired density index for them are difficult to achieve. If the water level is high, soils of very fine granulation should be avoided because they can infiltrate inside the shell structure. Permeable aggregates should be used as backfills and they should be free of agglomeration, permafrost and organic particles. Their oedometric modulus should amount at approx. 20.000 kPa. Aggregates should be of uneven granulation (D5), easy to compact, relatively unaggressive (pH 6–8), and resistivity exceeding 1.000 Ω m. In a distance of about 0.50 m from the CSP shell structure, size of aggregate fraction cannot exceed 45 mm, in a more distant location it can be bigger than 45 mm but should not exceed 2/3 of the compacted layer thickness. Backfill in direct vicinity of the steel structure should be compacted up to density index 0.94, and in other zones 0.97 in accordance with Normal Proctor test. Aggregate directly adjoining the CSP shell needs to be compacted manually (e.g. with vibratory soil plates). Heavy earth moving equipment (e.g. a roller) should be used at the distance of at least 1.0 m from the shell structure. In order to prevent infiltration of precipitation water to the inside of the structure, means of protection called “an umbrella” of HDPE foil is often used (Fig. 2.22). It is placed above the structure. This solution is obligatory for tunnels and underpasses. Geotextiles with filtering function and a system of drainage of HDPE pipes are used to lower the level of ground water. However it is important not to place the HDPE foil directly on CSP shell (which could damage the foil). It also needs to be considered that the HDPE foil should not (if possible) be placed in a distance smaller than 0.6 m from the shell (to avoid separation of backfill layers directly above the shell) and that it should not get within construction layers of the road. Fig. 2.22 Execution of the so-called “umbrella” made of HDPE foil over the shell structure

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2 Selected Issues of Soil-Steel Bridge Design and Analysis

The backfill around CSP shell structure should be placed in layers of thickness ranging 0.15–0.30 m on both sides of it at the same time, and then it should be wellcompacted. Backfilling process should be carried out symmetrically to make sure the backfill height is the same on both sides of the structure (a difference in height of one layer is acceptable). Backfill is formed on both sides of the shell structure with special attention to haunch areas where access of the compacting equipment is not easy. Therefore, in these places backfill is compacted manually with use of square timbers 50  100 mm. Mechanical compactors can be used as well the vibratory hammers with appropriate endings. Manual compactors used for compaction of horizontal backfill layers should not be lighter than 9 kg and the compaction area should not exceed 150  150 mm. Before the next layer is placed, it is important to check if the previous one has been compacted to the desired density index. To make sure no places at vicinity of the structure remain uncompacted, compaction equipment should be moved in a parallel way to the structure walls (Fig. 2.23). To compact the backfill at structure shell ends (cut towards the slope), it is recommended to use light equipment due to lack of appropriate ring stiffness there. These ends work like cantilever retaining walls and may not transfer too high pressure of soil which occurs when heavy equipment is used. Moreover, in order to avoid deformation of shell structure at these places, vertical stiffening of the structure or protection in the form of paving, gabion baskets, reinforcement by geotextile materials or RC collars are used. Shells made of CSPs can change shape at the time of installation, backfilling and compaction of backfill. In case of short-span structures, it does not constitute a major problem, however, for longer spans, special attention needs to paid to the structure stability. Three types of displacements and deformations can occur at backfilling phase: • shell uplift caused by side pressure of backfill under compaction, • shell buckling caused by non-symmetrical backfill load or by diversified compaction of backfill on one side of the structure only, • surface dislocations – horizontal within the plan of the whole structure caused by non-symmetrical backfilling. Fig. 2.23 View on the backfill compaction method around the CSP shell structure

2.2 Construction of Soil-Steel Bridges

83

Dislocations and local deflections of 2% of a circular structure diameter are acceptable or 2% of span length in open profiles. Measurement of displacements and strains should be done with specialist measurement equipment to ensure the results are as accurate and reliable as possible. However due to quite high cost of such tests, such control measurements are usually made with use of plummets attached in several places in the structure crown. The number of plummets in a given profile depends on structure diameter or span. When they do not exceed 4.0 m, only one plummet is required in the middle of span. When the profile is bigger, it is advisable to use 3 to 5 plummets. Plummets should always be fixed in the half of span length, along the structure length, symmetrically towards the longitudinal axis, in places determined by means of the following dependences and in accordance with Fig. 2.24: for L
10.0 m  1/3 L < b
1/2 L, for 10.0 < L
20.0 m  1/3 L < b
1/2 L, for L > 20.0 m  b ¼ 10.0 m, where: L is upper length of shell structure, b is distance between plummets. To prevent buckling of shell structure to one side, backfill should be placed and compacted on one side, i.e. on the side of buckling or dislocation. If the structure uplifts, it is advisable to move heavy compacting equipment away from the shell or to put additional load on the shell (or use both the solutions). If the two procedures do not work or shell deformations exceed acceptable levels, all of or a part of backfill needs to be replaced. However, it should be noted that structure deformations, unless not exceed the acceptable level or they have not the permanent character, are a common, even desired phenomenon, which proves that the flexible structure is working as expected. All flexible CSP structures have tendency to uplift during backfilling and compacting works. However, when the intended backfill thickness (soil cover depth over the shell) is achieved and upon loading from the top, the structure pressures on backfill on its sides causing passive soil pressure. It is thanks to this tendency for relatively big deformations that flexible steel structures can, with the interaction of surrounding soil, get considerable service load-carrying capacity.

Fig. 2.24 Distribution of plummets in the longitudinal section of the CSP shell structure

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2 Selected Issues of Soil-Steel Bridge Design and Analysis

2.2.4

Reinforcing Bridges with Use of CSP Structures

2.2.4.1

Relining Method

Relining is a reinforcement technology consisting of the insertion of new pipe or shell structure of CSP to the interior of an existing bridge structure. Then the space between the modernised old bridge and the steel walls of a new structure is filled with appropriate material. Such a procedure fully and effectively bonds both structures. This method allows to strengthen structures without necessity to shut down traffic over the modernised bridge and it is a way to avoid demolition of an old bridge. Really bad technical condition of the old bridge is an exception, if it could pose a risk of construction failure during modernization works. In such a case, the old structure needs to be demolished, with just foundations left, as they have no meaning in transfer of loads to the subsoil, but they can help construction works by limiting dislocations of shell structure to the sides. As a result of reinforcement, a quasicomposite structure emerges composed of the reinforced (usually old) structure, filling material and the reinforcing structure of CSPs. Due to the variety of profiles of the reinforced bridges, materials used as fillers and ways to put them in place vary as well. The most common material is liquidplastic concrete and mixes of sand and gravel. The task of the filler is to ensure required cooperation between the reinforced structure and the CSP structure, therefore it is very important to fill the empty space thoroughly and correctly (without any voids left). During assembly, it is necessary to make special limiters that would prevent dislocation of the strengthening structure at the time of pouring concrete into the empty space. When the correct profile of CSP structure to serve as reinforcement is being chosen, the following four criteria should be followed: • shape and dimensions of the modernised structure, • required vertical and horizontal clearance of the structure after renovation, determined by hydrological calculations, • target load-carrying capacity, • existing geotechnical conditions. It is, therefore, necessary to hold precise inventory works of the modernised structure and adopting such dimensions of the structure to be inbuilt, as to avoid problems at installation time. Also, the expected results of renovation should be made clear. A common desire is that the profile of CSP structure matches to an utmost extent the shape of the existing (reinforced) structure. Therefore, the profile of reinforced structure is very often individually designed to match the existing conditions on site (Fig. 2.25). Sometimes, if is it is necessary to assemble shell elements inside the reinforced structure, individual CSPs are put together by means of high-strength bolts through collars heading inwards the structure.

2.2 Construction of Soil-Steel Bridges

85

Fig. 2.25 View on the strengthening of railway tunnel using CSPs

Fig. 2.26 Extending of viaduct by putting from bottom side the CSP shell

A very common case is extending length of old bridge structures, e.g. to make the bridge match new parameters of the road (when road category changes). It causes necessity to build an additional embankment to cover ends of the reinforcing CSP shell (Fig. 2.26). This additional embankment can help prevent loosening of front walls of the existing structures. This solution is very practical as it makes it possible to increase length of a given structure (in the future) upon removal of embankment soil masses from above the inlet and outlet of the reinforced structure. The process of extension continues by attaching next CSPs to existing structure and forming the embankment again. An important problem appearing in planning strengthening using CSP structure is a decrease in both horizontal and vertical clearance of the modernised structures. This issue should be considered at design and agreement reaching (mainly hydrological) stages of works. However, it needs to be mentioned that decrease in structure clearance caused by the installation of a new steel shell does not necessarily have to limit the hydrological capability of the structure. This is because the roughness factor n determined in accordance with Manning is relatively low. For instance, for pipe and arch CSP structures, the factor value ranges from 0.013 to 0.033. Therefore reinforcement of an old structure of brick or concrete by means of a CSP structure of a lower roughness factor may, as a result, increase its hydrological capabilities.

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2 Selected Issues of Soil-Steel Bridge Design and Analysis

Fig. 2.27 View on the initial assembly phase of CSPs inside the railway viaduct

2.2.4.2

Ways of Installation of Reinforcement Structures

The assembly of structures made of CSP to reinforce an existing old bridge can be realized, as in the construction of a new bridge, as follows: • the CSPs are assembled directly inside the reinforced structure (Fig. 2.27), • partial assembly happens outside the reinforced structure and then ready elements are placed inside and installed – a so-called initial prefabrication, • complete prefabrication off-site and inserting the ready shell into the reinforced structure interior. If the old structure is reinforced by means of an arch structure of CSP set on RC footings, the first thing to do is to join the new and old foundations (existing bridge footings) together in a permanent way with the use of e.g. anchors, clamps, etc. Such a procedure is supposed to prevent possible dislocation of the shell structure when concrete is poured in and as a result of normal service. An interesting example of reinforcement has been used in Sweden (Flener and Karoumi 2009), where a CSP shell was installed from the top side of an old bridge, i.e. opposite to what is normally done. Choice of installation method depends on many factors such as availability of site near the modernised structure, available assembly space under the structure, expected assembly costs, technological capabilities of the construction works contractor, etc.

2.2.4.3

Methods to Fill the Empty Space Between the Old and the New Structure

Preparation of Subsoil General rules for the preparation of subsoil for reinforcing structure (in the case of closed profiles) are nearly identical with self-bearing structures assembled of CSPs.

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If a structure is built, for instance, along a watercourse, subsoil should be protected against inflow of water by using, for example, temporary pumping stations, culverts, sheet pilings (e.g. the Larssen type). Like in self-bearing CSP structures, subsoil under the shell structure should be composed of sand and gravel mixes of uneven granulation and compacted to reach the density index of minimum 0.97 (in Normal Proctor scale). The upper part of subsoil (of thickness 0.10–0.15 m – depending on corrugation profile used) should be loose enough to ensure that the CSP structure can settle down in it at ease. Total thickness of aggregate foundation should usually be designed individually, but it must not be smaller than 0.20–0.25 m. In the case of weak ground, the subsoil needs to be additionally strengthened with, for instance, geotextile that improves stabilization of soil. Haunch areas of the reinforcing shell structure should be filled in with aggregate in such a way as to prevent the inflow of concrete (poured at pressure) under the structure of CSPs (to avoid dislocation). If the reinforcing structure is to be installed on concrete subsoil, the assembled shell should be put directly on fresh concrete, before it finally hardens.

Filling the Empty Space Between the Structures The most commonly used concrete mixes to fill the space between structures are of low classes, such as LC12/13 and LC16/18 (in accordance with EN 206-1:2000 (2000)) existing in liquid-plastic state and poured at the pressure of approx. 0.60 MPa by means of pneumatic feeders. Also expansive concrete or selfcompacting concrete can be used, especially when, for instance, internal concrete vibrators cannot be used to compact the mix. First of all it is important that the aggregate grains diameter is not smaller than 20 mm because smaller granulation can cause inflow of the concrete mix inside the structure through clearances at joints of individual sheets of plate. Concrete mix should be poured and placed symmetrically on both sides of the reinforced structure to avoid possible dangerous dislocations of the supporting structure to one side. Internal concrete vibrators can be used to compact concrete mix. However, maximum care is required at the time of compaction not to cause excessive dislocations or permanent deformations of the CSP shell structure. Prior to commencement of concrete pouring, wooden formwork should be installed on both ends of the modernised structure. An alternative method is building walls of brick or stone that would prevent outflow of concrete. Concrete works should not commence before the protective walls reach their full strength, so that the concrete under pressure does not push them. Diameter of concrete infeed holes should make it possible for the hose end to be inserted at ease. Figure 2.28 shows example locations of infeed and inspection holes. Inspection holes located in the upper part of the shell enable correct venting of the space being filled and are used to control the level of filling.

88

2 Selected Issues of Soil-Steel Bridge Design and Analysis Holes for supplying concrete (revisory)

Contour of existing structure

B10 concrete filling The CSP structure

Fig. 2.28 Example of strengthening of old bridge using CSP shell

Concrete mix can be poured in different ways, i.e.: • from the head of the wall or protection formwork, • through boreholes in the crown of the road passing through the structure of the modernized bridge, • through boreholes in the body of embankment passing through the structure of the modernized bridge, • through technological holes in structure of corrugated plate. In the case of starting concrete works at the head of the structure, gradation of filling height should be a rule. It mainly concerns structures of relatively high vertical clearance – above 3.5 m and big bottom part necessary to be filled in (distance between old and new structure exceeds 1.0 m). The reinforcing structure of CSP should be additionally protected against unsymmetrical dislocation by using spacing wedges that ensure even spacing of both structures walls along the whole of its parameter. Filling with aggregate is relatively rare in the case of structures reinforced by means of CSP shell, due to difficult access at backfilling works. Aggregates used to fill the empty space are mainly mixes of sand and gravel of uneven granulation and grain size not exceeding 45 mm. Aggregate should be well-compacted up to minimum 0.95 of density index in Proctor scale. Aggregate is most often put in place manually with the use of mechanical compactors. Compaction should be done symmetrically by backfill layers of about 0.15–0.30 m. There is also a possibility to fill the space with sand poured in with water under pressure. In this situation, it is necessary to make sure that the empty space is fully filled and to hold control test of filling efficacy. No additional mechanical compacting is required in this case, as sand thickens by itself under pressure.

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2.2.5

89

Summary

With respect to architecture, soil-steel bridges are not less attractive or eye-catching than traditional prefabricates of concrete, steel plate girders or composite bridge structures. They also allow additional finishing works which let improve aesthetics and incorporate them in surrounding environment with low cost and workload. Strengthening of bridge structures by means of CSP structures brings the most effects in the case of arched stone or brick bridges. That is because CSP profiles perfectly fit in shape with the existing old bridges (Fig. 2.29a). In other cases, very good strengthening results were also achieved, e.g. modernisation of a railway viaduct (Fig. 2.29b). Using CSP shell structures for construction of new bridges and strengthening old ones considerably shortens time of works, minimizes investment cost and limits additional cost related to traffic relocation or shut-down, etc. They are the main advantages of using structures of this type for modernisation works. If the difference between execution cost and cost of other solutions is small (e.g. RC box culverts), these advantages may become decisive when reconstruction or strengthening technology is chosen for small beam or arch bridges made of brick, concrete or stone. This method also provides possibility of quick extension of a road crown width. In most cases, there is no need to build new foundations, unless an open profile structure is used, e.g. arch. What also matters a lot is short construction time and good soil-structure interaction which increases general load-carrying capacity of the bridge structure. Control tests should be held in order to check if the reinforcement method used has increased general load-carrying capacity of the composite hybrid bridge structure. They should be carried out before and after strengthening works with the same loads (to be in a position to compare the results directly).

Fig. 2.29 View on examples of strengthening using CSP structure: (a) road bridge, (b) railway viaduct

90

2.3 2.3.1

2 Selected Issues of Soil-Steel Bridge Design and Analysis

Design Problems and Construction Mistakes in Soil-Steel Bridges Introduction

A trend to build soil-steel bridges has been present in transport infrastructure for over 30 years. These structures are mainly built as bridges and culverts on local roads but also as railway viaducts or even motorway bridges, recently more and more often as ecological structures to allow migration of wild animals. Very often designers have limited influence on choice of structure type and on many occasions they do not fully realize all the hazards that can occur at the construction phase of such structures. In this part of the chapter selected design problems and possible mistakes at construction phase that can be observed in engineering practice have been presented. They influence durability of the structures in a negative way.

2.3.2

Design Problems and Errors

In the case of soil-steel bridges made of CSPs, an interaction of the shell with surrounding soil is used. The effect is called arching. The main function of CSP is to increase the stiffness of the shell structure and increase the degree of mutual interaction of the structure with the backfill in comparison with, for example, flat plates or reinforced concrete (RC) shells where such interaction is limited. Shell structures are assembled from profiled CSP joined together by means of highstrength bolts. Such a solution allows for a relatively easy, quick and economical installation of these structures. The main assumption in working of such structures is such execution of joints between corrugated sheets to make sure fully static and dynamic transfer of interactions between components of a soil-steel bridge (AbdelSayed et al. 1994; Rowinska et al. 2004; Williams et al. 2012; Machelski 2008). The biggest number of problems related to soil-steel bridges are caused by design calculations. At present, to ensure proper designing of a CSP structure, it is necessary to use highly specialist, quite expensive software like, for example, FLAC, Abaqus, DIANA, ANSYS, COSMOS, Plaxis and to have extensive knowledge concerning modelling the shell structures and soil, as well as, most of all, mapping of shell and soil interaction (Elshimi 2011; Beben 2005; Wadi 2012, 2019; Mellat 2012; Aagah and Aryannejad 2014; Maleska and Beben 2018b, 2019). Most often the programs are based on the finite elements method (FEM) and the finite differences method (FDM). Using traditional analytical methods of selecting the CSP structure from manufacturers’ catalogues, a designer takes a relatively safe path, especially when it concerns smaller structures. However, when the structures are bigger and more complex, the designer can use technical service provided by the manufacturer of CSPs. The service helps to choose correct shell parameters for the

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designed structure. However, the designer themselves has relatively small possibility to estimate the load-carrying capacity, stress-strain state and all of those issues important for a bridge structure safety. Manufacturers of CSPs recommend use of such designing methods as: the Swedish method (Pettersson and Sundquist 2014), American (AASHTO LFRD 2017), Canadian (CHBDC 2014), Australian (AS/NZS 2041 2010), or British (BD 12/01 2001). However, using these methods often leads to excessive dimensions of these structures (especially the steel plate thickness), which is mainly the result of conservative approach to distribution of loads by soil layers, lack or unsatisfactory consideration of interaction between the backfill and steel shell, and using additional safety factors, which has been more extensively discussed in the following parts of the book. In many cases conflict of interest can occur. On one hand, the designer is interested in construction of a safe and, at the same time, economical structure – on the other hand there is the supplier – the manufacturer, whose aim is to sell as many of their products as possible, also as far as weight is concerned. Therefore the structural solutions offered by the producers are not always appropriate, i.e. the best from engineering point of view, and, most of all, economical. At this moment the issue of design responsibility appears, which is obviously related to the designer’s knowledge exclusively. Below the most common design mistakes for soil-steel bridges have been discussed: • Lack of protection of the structure bottom against washout of soil, as in Fig. 2.30. It is a mistake caused by improper location of precipitation water drainage, especially at times of violent rainfalls. The problem increases in mountainous areas with considerable slopes of terrain and structures such as culverts very often get clogged by tree branches and other debris. • Bed river narrowing in front of and behind the structure, as in Fig. 2.31a. It leads directly to water damming in front of the structure and decreases its hydraulic efficiency. It also causes washing out of soil surrounding the foundations (the process of cavitation may occur).

Fig. 2.30 Examples of soil washout in roadway

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2 Selected Issues of Soil-Steel Bridge Design and Analysis

Fig. 2.31 Example of design mistakes: (a) narrowing of bed river, (b) incorrect drainage of water from the roadway

Fig. 2.32 Examples of damage caused by corrosion of soil-steel bridges with cross-sections: (a) open, (b) closed

• Lack of proper drainage of the structure as in Fig. 2.31b. It contributes to a situation when dirty water gets near the steel shell and to the backfill layers. It can result in significant changes to physical properties of the backfill, for instance, cause increase in backfill corrosion. A common situation is also lack of drainage channels that would safely drain water away from the structure. • Lack of proper corrosion or abrasion protection, as in Fig. 2.32. It causes favorable conditions for appearance of corrosion spots, especially on the side of the backfill. Another effect of lack of this type of protection is appearance of abrasion damages of the structure bottoms caused by flow of water containing grains of sand and stones. • Unfounded use of shell reinforcement (additional reinforcement ribs, filling ribs with concrete, as in Fig. 2.33). It is connected with the problem of using structural solutions that had already been patented and therefore structure manufacturers tend to lobby for them to be used on site. Reinforcement of the shell structure may be justified in the case of long-span bridges and culverts. However, if additional reinforcement ribs (which were not planned by the designers) are used (Fig. 2.33b) in a structure of, for example, 5.00 m of span and backfill height of 1.00 m – this is an unnecessary increase of steel use and investment cost.

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Fig. 2.33 Examples of shell reinforcements: (a) filling of ribs with concrete, (b) additional ribs Fig. 2.34 Example of the use of large diameter piles in the foundation of a soil-steel bridge

Filling reinforcement ribs with concrete is another issue with regard to strengthening steel shells (Maleska and Beben 2019). It is a temporary solution with no significant meaning for the further behavior of the structure, as it is difficult to find a popper way to fill the voids in ribs, and, all the more, to compact the concrete, even when self-compacting concrete is used. Moreover, it stands against the rule of flexibility of these structures. It also needs to be noticed that in such cases no reinforcement of concrete is used which results in concrete crushing after a couple of years of intensive service. When the concrete does not reinforce the shell structure any longer, it becomes unnecessary burden. • Incorrect founding of structures. In many cases, especially when open shell profiles are used, RC foundations are too big. Construction of a soil-steel bridge on the A4 Motorway (Poland) is an example (Fig. 2.34). Foundation of the shell was planned on bored piles of diameter of 1.0 m and length of 11.0 m each. Sixteen piles of this kind for each foundation were made (Gwizdala et al. 2010).

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2 Selected Issues of Soil-Steel Bridge Design and Analysis

A similar foundation solution was proposed for a structure located on the Express Road S-19. In this case, prefabricated 0.40  0.40 m piles were used, each of 10.0 m of length. The internal row of piles of both footings had inclination of 10:1. While recommending such structural solutions of founding for flexible structures interacting with soil, the designers probably do not bear in mind the behavior of these structures under loads, especially when there is a backfill of certain thickness above the structure. In both cases of bridges the soil cover depth above the shell exceeded 1.50 m. Even more alarming is the fact of using similar founding solutions in bridges which serve as animal passages. An example could be construction of animal passage over the National Road in Trzebaw village. In this case, continuous spread footings were used (of 4.00 m of width, 3.10 of height and almost 60 m of length) as if for a massive RC bridge. AASHTO LFRD (2017) recommends that the metal pipe-arch structures, long-span arch structures, and box culvert structures should not be supported on foundation materials that are relatively unyielding compared with the adjacent sidefill. In addition, the use of massive footings or piles to prevent settlement of such structures is not recommended. • Unjustified use of additional stiffenings at support area of the steel shell with the foundation, as in Fig. 2.35. It causes change to the static scheme of shell structure from hinged joint to fixed one and inspires additional internal forces in the shell. Such a solution limits possibility of deformation for a shell exposed to external loads and backfill settlement. • No safety barriers, for instance inside the structures, as in Fig. 2.36. It often leads to direct mechanical damages of CSP elements by crashing vehicles. Another important issue is developing correct structural solutions in the case of objects located at a considerable slant towards the longitudinal axis of an obstacle. In such a case the inlet and outlet part of the shell do not reach the supports, which is the reason why the distribution of loads is not symmetrical and behavior of the CSP shell gets spatial in its character. In such cases, special additional reinforcements of shell edges need to be used, like properly shaped RC collars, which increases cost and hinders construction works. Moreover, it also needs to be stated that flexible structures are made of very thin steel plates of thickness from 2.0 to 12.5 mm, which are exposed to damage at construction phase of such structures.

Fig. 2.35 View of the connection of metal sheets with the foundation stiffened with concrete

2.3 Design Problems and Construction Mistakes in Soil-Steel Bridges

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Fig. 2.36 Examples of the lack of protective barriers in the interior of objects Fig. 2.37 View of deformation of shell caused by incorrect twisting of CSPs

2.3.3

Construction Phase Mistakes

Below the most common construction phase mistakes for soil-steel bridges have been discussed: • Installation mistakes – incorrect execution of joints between CSPs, as in Fig. 2.37. It especially concerns screwing together individual sheets of plates with a too big torque moment, which is often put in practice from the beginning of assembling works to accelerate them. In the first phase, the screw joints should remain loose, in the next phase the screws should be more tightened to get the correct values of torque moments. • Damages to corrosion protection at assembly phase, as in Fig. 2.38. It is a quite common mistake made by assembly workers resulting in damages to protective layer of zinc. This leads to appearance and development of corrosion spots at service phase.

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2 Selected Issues of Soil-Steel Bridge Design and Analysis

Fig. 2.38 View of damaged corrosion protection of corrugated sheets

Fig. 2.39 Incorrect location of the base rail (non-linearity) on the foundation

• Non-linear placement of a base rail on RC continuous footings, as in Fig. 2.39. It manifests itself in mutual relocation of elements of CSPs. • Using heavy construction vehicles, like excavators, rollers etc. which often cause damages to steel structure, such as puncture or denting of some plates (Fig. 2.40), especially when drivers are not careful enough. • Improper forming of backfill. This can cause loss in shear strength of soil and lack of possibility to form the composite soil-steel system. It is also very important that the soil intended for backfilling is loose with fine or mediumsized grains enabling proper degree of compaction to be achieved. Another very common mistake is backfilling shell structures with too thick layers of soil that locally hinders proper compaction of soil and can cause dangerous deformations of the shell leading to loss of stability. • Incorrect choice of assembly method of the steel structure. The choice of assembly technology generally depends on the contractor and their equipment capabilities. A common mistake made by contractors is assembling of a big part

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Fig. 2.40 View of damage to corrugated sheet (puncture)

of the structure away from the site and then placing it on foundations by means of cranes. In such cases, uncontrolled flattening of the structure can occur and it becomes impossible to place a structure of correct geometric properties in originally designed position, on the foundation. In such cases, special ties need to be used or joints between individual steel plates should be loosened.

2.3.4

Summary

There are a couple of methods and codes of designing soil-steel bridges in the world. They are more extensively presented in Sect. 2.2. The most widely known are the Canadian code (CHBDC 2014) and the American code (AASHTO LFRD 2017). There are also design methods without code status for example the Swedish method (Pettersson and Sundquist 2014). Verification and calibration done on the basis of field tests held on soil-steel structures in natural scale (Flener 2005; Manko and Beben 2005a, b, c) constituted important contribution to elaboration of this method. In many cases in Europe, a designer needs to respect codes and instructions for traditional steel bridges, which are in force in a given country that do not consider specific behavior of soil-steel structures. Designers can only use technical service offered by the suppliers of these structures. Neither in Eurocode this type of bridge structures is considered. Soil-steel bridges have already become a natural sight – they are quite common structural solutions in bridgeworks both in Europe and in the world. The structures are attractive in respect of construction, economy, ecology and aesthetics. However, it is important to bear in mind certain hazards at construction works phase that can result from errors in designing this type of bridge structures.

98

2.4 2.4.1

2 Selected Issues of Soil-Steel Bridge Design and Analysis

FEM Analysis of Soil-Steel Bridges and Culverts Introduction and State of the Art

Numerical analysis of soil-steel bridges and culverts makes several difficulties, mainly regarding modelling of corrugated profiles, choice of an appropriate soil model and soil-structure interaction properties (Elshimi 2011; Machelski 2008; Beben and Stryczek 2016a; Maleska and Beben 2018b, 2019; Wadi 2019). From this reason, a sensible method of numerical analysis of soil-steel bridges and culverts that could be used for practical purposes has not yet been developed. McGrath et al. (2002) presented field tests and finite numerical analysis of the soil-steel bridge (with (Test 1) and without (Test 2) backfill compaction). During the Test 1, the upper part of the bridge moved more upward than from the Test 2. The bending moments at the bridge crown from Test #1 constituted about 2/3 of the moments from Test #2, while the moments at haunches were almost identical. Similar numerical analysis concerning the depth of soil cover were presented by Esmaeili et al. (2013). Abdel-Sayed and Salib (2002) examined the minimum soil cover depth in soil-steel bridges. They are concluded that the corrugation depths have an influence on the height of soil cover in the soil–steel bridges and culverts. Additionally, they stated that the formulas currently recommended by the AASHTO and CHBDC significantly overestimate the needed height of soil cover for the bridges with larger spans. El-Sawy (2003) presented the numerical analysis and field tests of soil-steel culverts under static loads. The obtained results showed quite significant differences created by the unsuitable choice of the soil model. Machelski et al. (2006) applied isotropic elements to soil modelling, however, the obtained results were also too high compared to the field measurements. Sargand et al. (2008) showed the soil-steel bridge analysis that involved comparing the measured results with numerical ones obtained from the CANDE computer program. Beben (2009, 2012) presented the 2D finite difference method for soil-steel bridge analysis. Obtained results were quite reasonable, however the process of numerical modelling was very difficult and complicated. El-Taher (2009) analysed effect of backfill erosion on stability of the deteriorated soil-steel structures with using the elastic soil modulus variabilities. The elastic buckling analyses demonstrated that the development of backfill erosion causes substantial reductions in factor of bridge safety. Katona (2010) presented a method of analysing and evaluating of soil-steel bridges and tunnels under the seismic excitation. Brachman et al. (2012) analysed a soil-steel bridge with deep corrugation steel plates without backfill. Steel shell was modelled using of the corrugated structure (first model) and the orthotropic shell theory (second model). The corrugated analysis provided calculation values closer to those that were measured. Yeau et al. (2015) performed a 2D and 3D analyses of the impact of various parameters on the behaviour of 14 soil-steel culverts under static load. Three different types of soil in 2D analysis and two boundary backfill elastic modulus in 3D analysis were considered, respectively. The hyperbolic soil model proposed by Duncan et al. (1980) and the Mohr-Coulomb linear elastic perfectly

2.4 FEM Analysis of Soil-Steel Bridges and Culverts

99

plastic model were applied for 2D and 3D, respectively. The obtained calculated displacements from the 2D analysis were larger than measured ones. Moreover, it was noted that thrust forces did not undergo significant changes depending on the applied backfills. However, the experimental and calculated axial thrusts were similar. Mai et al. (2014) presented the 2D finite element analysis for the deteriorated soil-steel culverts with a span of 1.8 m. The authors concluded that the applied FE models did not allow to consider the non-linear character of the damaged culvert with weak backfill as well as the culverts behaviour at large live-loads with the application of the linear elastic models. Mellat et al. (2014) determined the 2D and 3D FE models for the dynamic analysis of the railway soil-steel bridge. The impact of the Young’s modulus of backfill was also examined. The recommended 3D bridge model allows an estimate of the load distribution that grows at greater train velocities. Kunecki (2014) showed experimental measurements and 3D numerical analysis of soil-steel composite road tunnel. Wadi et al. (2015) presented the FEM analysis of soil-steel bridge located in sloping terrain. Simulation of the backfill loading effects were considered. The obtained results were greater than the measured ones. FEM modelling of a soil-steel bridge with reinforced concrete (RC) slab was presented by Beben and Stryczek (2016a). The received results compared to measured ones. Generally, the FEM results compared to the experiments are overestimated, which is why new FE modelling techniques of the soil-steel bridges and culverts should be still developed. In addition, the role of backfill quality and interaction properties seems to be an important element for the soil-steel bridge safety therefore the analyses in that regard should be also conducted. Moreover until now, an efficient method for dimensioning of these structures has not been developed, despite the existence of many analytical methods, e.g. Swedish (Petersson and Sundquist 2014), Canadian (CHBDC 2014), American (AASHTO LRFD 2017). However, they do not allow for exact estimation of internal forces in those bridge structures, and besides, have some limitations in the application, for example the structure span and depth of soil covers. The calculations of the soil-steel bridges executed with such methods are unsatisfactory in comparison with the results received from the experiments. This probably results from versatility of such methods as well as simplifications being too large. The present design methods of the soil-steel bridges are based on practical experiences than on reasonable analytical models that are quite complex. These difficulties concern the interaction phenomena and non-linear behaviour of backfill. In such composite systems, both the soil and steel structures are required to be taken into consideration as the load-carrying elements, it is not possible to simply accept only as the loads acting on the steel structure. Flener (2010) showed that the Swedish and Canadian methods give conservative results during bending moments and axial thrusts determination. Elaboration of a reasonable method of dimensioning of soil-steel bridges will definitely contribute to increase in safety and to even greater savings in comparison to traditional bridge structures of medium spans. That is why experimental and theoretical research are still needed for soil-steel bridges. The main purpose of this chapter is to present stages of numerical analysis of soilsteel bridges within the range of live loads. A way of numerical modelling of a CSP

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2 Selected Issues of Soil-Steel Bridge Design and Analysis

shell with the orthotropic features has been shown and the determination of backfillCSP shell interaction phenomena. The FEM analyses of the soil-steel bridges were performed using the Abaqus computer program (Abaqus Theory Manual 2014) and Plaxis program (Plaxis 2016). Some interesting calculations results were presented and compared to the experiments as well as taking into account the previous numerical calculations from other numerical programs.

2.4.2

Description of Numerical Modelling

2.4.2.1

General Remarks

The detailed calculations of soil-steel bridges are usually performed using the finite element method (FEM). There are also exists some analyses using finite differences method (FDM), for example FLAC software. The most popular programs using FEM for calculating bridges are Abaqus/CEA, ANSYS, DIANA, Plaxis, LUSAS Bridge, Z-Soil. For many years there are also computational programs specifically dedicated to soil-steel bridges, i.e. CandeCAD (Culvert ANalysis and DEsign inside autoCAD) developed by Katona et al. (1976) and NLSSIP (Non-Linear Soil-Structure Interaction Program) elaborated by Byrne and Duncan (1979). These programs are periodically updated. In the numerical models should be taken efforts to show the exact shape of the examined soil-steel bridge and the loads acting on the bridge. In many cases in order to the simplification of the numerical model, the unimportant details that may influence the complication of the modelling and time of calculations are not considered. In connection with the above, the numerical models of shell structures can be usually simplified, however, the primary bridge parameters, like the rise and span of the shell as well as various radiuses of the shell should be kept. Other elements like scarps, RC collars strengthening inlet and outlet of the shell, handrails, barriers, foundations and drainage system can be ignored during the numerical modelling. Current experience confirms that such elements should not considerably influence the numerical results because they constitute supplementary equipment of the soilsteel bridges. This is because they have limited effect on the soil-structure interaction due to the location outside the range of active loading. The best way to conduct the calculations under static and dynamic loads of soilsteel bridges is use three-dimensional space. In the case of analysis of shell structures during backfilling process, two-dimensional analysis is usually sufficient. Non-linearity behaviour in computational models can be expressed using incremental analysis, for example, by application of the Full Newton approach (Beben and Stryczek 2016a). The dimensions of soil-steel bridge model in the 3D space should be bigger than the size of a given shell of about 3 m (Fig. 2.41). Modelling the backfill located at a distance larger than 3 m from the shell structure does not considerably influence the received calculation results. This is because the boundary conditions are more important than the model size that shows the existing structure in an approximate

2.4 FEM Analysis of Soil-Steel Bridges and Culverts

101

Fig. 2.41 Finite element model of soil-steel bridges with profile: (a) open, (b) close

way. Therefore, the foundations in most cases can be neglected during the modelling of soil-steel bridges. In some cases, the shell structures intersect with an obstacle (river, road) at an angle (acute or obtuse). This should be taken into account in the numerical models due to the lower area taking over the loads coming from the roadway or railway track. It is very important because some of the shell elements do not reach the foundation and the behaviour of the shell takes a 3D nature. Depending on the environment of bridge work and established conditions, the nodes may have six degrees of freedom, i.e. displacements (U1, U2, U3) on the axes (OX, OY, OZ), and rotations (UR1, UR2, UR3) to the axis (OX, OY, OZ). Taking the above into account, the nodes of elements with their edges situated on external surfaces of the model can be blocked what constitutes the total restraint.

2.4.2.2

Material Characteristics

It is the best to use real parameters of soil-steel bridges for their numerical modelling (Fig. 2.42a). This mainly concerns the steel shell structure, backfill and roadway. 3D shell tetrahedral and hexahedral elements are usually used to model the CSP shell. The remaining elements such as backfill and roadway structures can be represented by elements with the solid properties. The characteristics of materials should be determined in the base of actual technical data received from their producers or by in-situ testing. Such data should be used during numerical modelling. (a) shell structure: it is acceptable to use simplifications in the modeling of CSP shells as flat shells (Fig. 2.42b) while preserving their main material parameters. An orthotropic shell (Fig. 2.43) can be used to calculate the substitute parameters of corrugated plate such as: • equivalent thickness of plates:

t equ:

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi I ¼ 12ð1  v2 Þ , A

ð2:112Þ

in which I is moment of inertia, A is area of cross-section, and v is Poisson ratio (v ¼ vx ¼ 0.3),

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2 Selected Issues of Soil-Steel Bridge Design and Analysis

Fig. 2.42 Shell structure modelled as: (a) corrugation profile for box shape, (b) flat profile (orthotropic shell) for arch-pipe shape Fig. 2.43 Orthotropic characteristics of flat plates used in numerical model of shell

(a)

Corrugated steel plate profil

a

t (b)

h

F (E, G, t, v)

Equivalent flat plate

Fequ. (Ex equ., Ey equ., Gequ., tequ., v equ.) t equ.

• equivalent Young modulus (elastic modulus) in circumferential direction of shell: E x equ: ¼ E

A , a t equ:

ð2:113Þ

where a is a depth of corrugation, • equivalent Young modulus in longitudinal direction of the shell:  Ey equ: ¼ E

t t equ:

3 ,

ð2:114Þ

• an average value for the equivalent shear modulus:

Gequ:

• equivalent Poisson ratio:

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ex equ: E y equ: ¼ , 2 ð 1 þ vÞ

ð2:115Þ

2.4 FEM Analysis of Soil-Steel Bridges and Culverts

vy equ: ¼ v

E y equ: : E x equ:

103

ð2:116Þ

In some cases the orthotropic steel shell is described using scale factors (Maleska and Beben 2018a) in accordance with: • the axial stiffness: Sa ¼ A  E x ,

ð2:117Þ

in which A is area of cross-section, and Ex is modulus of elasticity, • the shear stiffness: SSy ¼ Asy  Gxy ,

ð2:118Þ

SSz ¼ Asz  Gxy ,

ð2:119Þ

where Asy, Asz are shear area in X and Y directions, Gxy is shear modulus, • the torsional stiffness: ST ¼ j  Gxy ,

ð2:120Þ

SBz ¼ I zz  E x ,

ð2:121Þ

SBy ¼ I yy  Ex ,

ð2:122Þ

where j is torsional constant, • the bending stiffness:

where Izz, Iyy are moment of interia in Z and Y directions, • the section mass: M S ¼ A  m þ mpl,

ð2:123Þ

where m is mass and mpl is mass per unit length, • the section weight: W S ¼ A  w þ wpl, where w is weight and wpl is weight per unit length.

ð2:124Þ

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2 Selected Issues of Soil-Steel Bridge Design and Analysis

Machelski (2008) proposes modelling the CSP using the grid of beams consisting of the circumferential and transverse lines. A model of the geometrical characteristics of beams are determined in the following manner: • equivalent area of cross-section and moment of inertia for circumferential direction: cy , a cy Ix ¼ I , a

Ax ¼ A

ð2:125Þ ð2:126Þ

where: cy is a distance between circumferential beams, • equivalent area of cross-section and moment of inertia for transverse direction: cx cy  t 3 , π r3 r cx cy 3 Iy ¼ t , 12π r

Ay ¼

ð2:127Þ ð2:128Þ

where: cx is a distance between transverse beams, r is a radius of corrugated plate. CSP elements are usually represented by shell elements as a material with elasticplastic characteristics with a density of 78.5 kN/m3 and yield strength 235 MPa. Due to the shell complexity and their curvilinear form, the curvature control accuracy should be used at 0.01 m. In the case of shell where additional stiffening ribs were applied, such reinforcements should be taken also into consideration during modelling shell structure (Beben and Wrzeciono 2017). The screw joints between the CSP sheets are normally neglected during numerical modelling. (b) backfill can be assumed as elastic-plastic material (using the solid elements) applying many constitutive models, for example: Coulomb-Mohr model, hyperbolic Drucker-Prager yield criterion, Duncan-Chang model. Characteristic of backfill should be taken from the laboratory tests and/or project of given soilsteel bridge. Usually, the backfill has the parameters: density of 18.0–20.5 kN/ m3, Young’s modulus in the range of 80–100 MPa, angle of internal friction of 35–45 , dilation angle of 0–5 , and initial tension equal to 0 MPa. Moreover, the use of some constitutive soil models requires establishing the extent of soil strengthening. This is because the cohesion of backfill is not taken into consideration. Therefore, the soil strengthening in compression state (in the range of 5–7 MPa) is applied. (c) road foundation (usually the crushed stone) is assumed as elastic-plastic material (using the solid elements) applying the similar constitutive models as in the case of the backfill. Usually, the road structure has the following parameters: density 18–19 kN/m3, Young’s modulus in the range of 50–60 MPa, angle of internal friction 30–40 , dilation angle 5–10 , and initial tension equal to 0 MPa. (d) asphalt can be defined as an elastic material (using the solid elements) with density of 20–21 kN/m3, Young’s modulus of 6.9 GPa and Poisson’s ratio 0.41.

2.4 FEM Analysis of Soil-Steel Bridges and Culverts

105

(e) boundary conditions are depended on the specific type of analysed bridge. For example, a total restraint may be used, this means that the rotations and movements along each side and base of the shell are blocked. The soil-steel bridge should be modelled as a structure settled in the medium because in such bridges there is the lateral earth pressure phenomenon and the rigid foundations of the CSP shell. (f) calculation-steps can be considered as T ¼ t + Δt (t is the initial time (t ¼ 0 s) and Δt is time increment when the given loads are used). Thus, Δt is the time in which loads are used (commonly Δt ¼ 1 s is assumed). In the calculation-step (T ¼ 1 s), successive iterations for time-increments are calculated. Therefore it is very important to determine the calculation step and the assumptions of geometric non-linearity of the structure (determined for different elements of the bridge, i.e. backfill and CSP shell). This has a significant impact on bridge deformation effected by the loads. Next, defining the methodology to solve the equations system, a direct method of analysis can be used, for example, using the FullNewton approach. Accepted change of the load in the time during subsequent iterations is linear during the whole calculation step. This reflects a static load. Moreover, in order to define the non-linear analysis of the bridge model for the following iterations, a parabolic extrapolation from the past stages of loads acting on the soil-steel bridge should be adopted.

2.4.2.3

Interaction Between Various Materials

Generally, the model of a soil-steel bridge is created using various elements (road structure, backfill and CSP shell). These elements have various physical characteristics and it is necessary to determine the interactions between them. Usually, the interactions between various materials are modelled using the interface elements or springs. It depends on the complexity of the structure. Interactions between various elements which act to each other, for example, CSP shell–soil, soil–road structure) may be formed as rigid elements of the beam (Fig. 2.44a) carrying their particular interactions from master to slave planes (for example in the Abaqus software). Normal forces (rigidity) and friction forces (friction coefficient) are considered. Furthermore, some software enables defining the character of interactions using the slides between interacting elements. In some cases, especially when the materials have a quite similar character, for example, asphalt–crushed stone, crushed stone– backfill, the interaction between them may be assumed as “finite sliding” (it means that there is no slide). The experimental experiences prove that small sliding may happen between CSP shell and backfill. Usually, the interactions are assumed with small sliding, otherwise, such bridges would be threatened disaster. The dependence of master and slave elements (in Abaqus software) are defined using the modulus of elasticity of interacting materials and the characteristics of the soil-steel bridge behaviour. The materials with a smaller and higher Young’s modulus respectively define the slave and master surfaces. During numerical modelling of the soil-steel bridge, at least three kinds of interaction zones (CSP shell– backfill, backfill–crushed stone and crushed stone–asphalt) should be recognised. For example, the following master–slave relationships can be assumed: (a) CSP

106

2 Selected Issues of Soil-Steel Bridge Design and Analysis

Fig. 2.44 Concept of interface elements in: (a) Abaqus software (rigid contact element), (b) Plaxis software

shell–backfill (master–slave), (b) backfill–crushed stone (slave–master), and (c) crushed stone–asphalt (slave–master). The interface in Plaxis software (Plaxis Manual 2016) have properties of cohesion, friction angle, Young’s modulus, dilation angle, Poisson’s ratio and tensile strength. Usually, a model with elastic-plastic properties is used to reflect the soilstructure interaction. There is a Coulomb criterion, which can use to model various behaviour of structure, i.e. elastic (with little movements within the interface) and plastic behaviour (with constant slip). The Plaxis allows connecting the strength properties of an interface with the backfill properties using a strength reduction factor (Rinter). The interface features in Plaxis can be established by applying two approaches. The first option applies a reduction factor (Rinter
1.0) during defining the backfill properties (usually Rinter ¼ 1.0, it means that the interface is a fully bonded (rigid connection)). Figure 2.44b shows the concept of node behaviour at the interface. It can be noted, that the right-hand model has more nodes on the contact surface that work independently of each other. The second option uses the interface as an individual soil layer (with zero size). The interface properties can be also determined applying appropriate formulae (Yu et al. 2015), however it should be pointed that the backfill properties are connected with the interface properties. The second case is a more flexible approach with regard to equivalence between applied parameters. The surface types contacting with each other are the basis for determining main interaction parameters (friction coefficients and surface rigidity). Such selection of interaction properties results from the specific character of CSP structure–soil interaction, in comparison to other contact properties with quite comparable nature i.e. asphalt–road structure, road structure–soil. The important element, distinguishing such interaction type from others, is the smooth surface of the CSP structure (it means a smaller friction coefficient). Therefore, the following friction coefficients can be accepted: 0.2–0.3 for CSP structure–soil and 0.4–0.6 for other contact surfaces. In the case of the rigidity of connection is normally fixed at 2  109 kN/m – for CSP structure–soil and 2  106 kN/m – for other contact surfaces.

2.4 FEM Analysis of Soil-Steel Bridges and Culverts

2.4.3

107

Examples of Numerical Results

In this section, the selected results of numerical calculations are presented. The box culvert, pipe-arch, influence of RC slab, and flat plates are analysed.

2.4.3.1

Box Culvert

Selected calculation results of the soil-steel bridge (span: 12.27 m, high: 3.36 m, corrugation: 0.14  0.38 m, plate thickness: 7 mm, soil cover depth: 0.87 m) are presented in Fig. 2.45. It can be seen the load distributions in the backfill and CSP shell. In this case, three static load schemes were taken into consideration (symmetrical and asymmetrical). Displacements maps show that they are not regularly distributed (they are mainly concentrated in the CSP structure crown near the applied live-loads (Fig. 2.45a)). The highest deflection equals to 3.01 mm and they appeared at the shell crown from the asymmetric scheme of loads (Manko and Beben 2005b). A thorough analysis of the obtained results shows that the influence of live-loads is displayed as substantial local deformations in chosen elements of the CSP shell (irregular load distribution over the shell crown is observed). Apparently, this is due to the low depth of soil cover at the crown (0.87 m) and a curvilinear form of the structure. Distributions of stresses presented in Fig. 2.45b explicitly show that the live-loads are carried on the CSP shell in an indirect manner and the maximum value (65 MPa) occurred at the haunch and at 2/3 of the structure height (Fig. 2.45b). While at the shell crown, the obtained stresses are smaller (max. 36 MPa). It implies that applied live-loads (induced by vehicles rear tires) cause shift the stresses towards the haunch sections and the 2/3 of the shell height (in these sections the received stresses are highest). Obtained stresses in these parts of the bridge shell prove the need application of extra ribs. Generally, the highest deflections were received at the shell crown and the greatest stresses at the haunches.

Fig. 2.45 Numerical results of soil-steel bridge from I load static scheme (asymmetrical). (a) displacements (bottom view). (b) stresses (section along the longitudinal axis)

108

2 Selected Issues of Soil-Steel Bridge Design and Analysis

Computation results were correlated with the field tests (Manko and Beben 2005b). The forms of computed deflections and stresses are quite comparable to those received with the tests, however, the absolute values were always greater than obtained from the experiments. The relative differences between computed and experimental values were in the scope of 5–24% for deflections, and 14–41% for stresses. Detailed analysis of results are presented in Beben and Wrzeciono (2017).

2.4.3.2

Pipe-Arch

Maximum vertical displacements of soil-steel bridge (span: 5.0 m, high: 3.03 m, corrugation: 0.055  0.200 m, plate thickness: 5.5 mm, soil cover depth: 1.45 m) amounted to 5.3 mm (Fig. 2.46a) and they are located at the shell crown. It can be also seen that bottom part of shell deflects to a small extent (0.2 mm). The largest stresses in circumferential direction are situated at the springlines (Fig. 2.46b) and they amounted to 16.27 MPa (tension). Compressive stresses were appeared at the crown and bottom part of shell (they does not exceed 11.0 MPa). Stresses in longitudinal direction are significantly lower and they does not exceed in any place of 0.2 MPa. Maximum bending moments are appeared on the vertical direction (Y) at the springlines of shell and do not exceed 2.0 kNm (Fig. 2.47). The largest axial forces acting in the longitudinal axis of shell (Z) are not bigger than 28 kN and they are also located at the springline regions. Next in the circumferential direction (X) of shell, the axial forces do not exceed 20 kN and they are appeared at quarter points of the shell. Analytical calculations were also made for this bridge using the Swedish design method (Pettersson and Sundquist 2014). It can be stated that the results obtained are higher of those obtained from numerical analysis. The maximum stresses in the shell from the analytical calculations are significantly higher (1642%) than those obtained in the numerical analysis. The axial forces of numerical analysis are almost twice lower than in the analytical method. The smallest differences occur in the case of bending moments from the live loads. The value obtained in the numerical analysis is 24% less than the bending moment obtained from the analytical calculations.

Fig. 2.46 Maximal numerical results of soil-steel bridge with close pipe-arch profile. (a) displacements (b) stresses

2.4 FEM Analysis of Soil-Steel Bridges and Culverts

109

Fig. 2.47 Maximal bending moments in shell structure due to static load

Fig. 2.48 Maximal of (a) displacements, and (b) stresses of soil-steel bridge with RC slab

2.4.3.3

Soil-Steel Bridge with RC Relieving Slab

The analysed bridge has a span of 10.0 m, high of 4.02 m, corrugation size of 0.05  0.15 m, the plate thickness of 3.0 mm, soil cover depth of 0.65 m, and RC relieving slab thickness of 0.20 m. Selected displacements and stresses received from the numerical computation of the soil-steel bridge are shown in Fig. 2.48. The range of load distributions in applied numerical models can be seen. It can also be observed that the deflections are distributed almost evenly over the whole width of the CSP shell. Maximum deflections are situated at the shell crown and equal to 0.78 mm. In the case of maximum stresses (10.2 MPa), they are located at the quarter points of the soil-steel bridge. The deflections and stresses gained from numerical calculations vary from the experimental results (Beben and Manko 2008). Maximum relative deviations of computed and tested deflections are in the range of 59–70% and for stresses 24–62%. The influence of RC relieving plate to deflections and stresses in shell structure was also established based on the comparison of computed results from various numerical models (with and without of RC slab). Application of the RC slab in the soil-steel bridge causes significant decreases of deflections, stresses, bending

110

2 Selected Issues of Soil-Steel Bridge Design and Analysis

moments and axial forces. The relative decreases were in the range of 52–65% and 72–81% for deflections and stresses, respectively. It can also be underlined that maximum deflections and bending moments were received at the shell crown and maximum stresses and axial forces at the quarter points. Detailed analysis of results are presented in Beben and Stryczek (2016a).

2.4.3.4

Soil-Steel Bridge with Flat Plates vs. Corrugated Plates

The analysed bridge has an arch structure with the main span of 5.25 m, height of 1.85 m, plate thickness of 23 mm, arc radius of 2.75 m and soil cover depth of 0.80 m. Two FEM models were taken into consideration. In the first model named as m1, the flat steel plates were used, and in the second one named as m2, CSP (150  50  3 mm) were applied. The effect of corrugation plate application was determined and discussed. For model m1, the maximum displacements, stresses and axial forces appeared at the shell crown, and maximum bending moments are located at the lower part of shell (near foundations). The courses of computed displacements, stresses, bending moments and axial forces (from m1 model) are similar to those obtained from experimental tests (Beben and Manko 2006). Maximum deflections are situated at the shell crown and amount of 0.96 mm and 1.72 mm for the model with flat (m1) and CSP (m2), respectively. In the calculation model with CSPs (m2), maximum stresses occurred at the quarter points (24.8 MPa), and for the model with flat plates (m1), the highest stresses (8.3 MPa) appeared at the shell crown. In both cases, maximum stress values are compressive. Numerical results from the model m2 were strongly higher than the measured results and those obtained from the model m1. Selected results for both numerical models are presented in Fig. 2.49. Figure 2.50 shows comparison of distribution of CSP shell displacements obtained from the two analysed computational models (m1 and m2) as well as with field test results. As shown in this graph, the displacements obtained from numerical analyses (models m1 and m2) differ from the values obtained from

Fig. 2.49 Map of maximum displacements for model m1 with flat plates (a) and stresses for model m2 with CSP (b) for load scheme no. 2

2.4 FEM Analysis of Soil-Steel Bridges and Culverts

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112

2 Selected Issues of Soil-Steel Bridge Design and Analysis

experimental tests. In case of the first model (m1), the maximum displacements are slightly lower (7–15%) than the experimental values (Beben and Manko 2006), but for the model m2 obtained results are strongly greater (maximum 66%) than in the experiments. Maximum deflections, stresses and bending moments in the shell (for numerical model m2) are greater than in the case of model m1. Relative increase of displacements, stresses and bending moments are in the range of 79–86%, 159–198% and 40–60%, respectively. In case of the axial forces, the trend is opposite, i.e. calculation results from the numerical model m2 are smaller than those received from the model m1. Relative decrease of axial forces ranged between 28–29%. Such obtained results are due to more stiffness of the flat plates than the corrugated. The shell stiffness to the action of internal forces (bending, compression, shear and torsion) is defined as the quotient of the geometric characteristics of the cross-section and corresponding to them elastic modulus. In case of the circumferential direction of the shell existed the stiffness resulting from compression, bending, torsion and shear. In the analysed cases, the most important are the flexural and compressive stiffness. Many factors affect the stiffness of soil-steel bridge, represented by the equation: k¼

Q , f

ð2:129Þ

where: Q – pressure of rear axles of vehicles (376 kN); f – maximum displacement (mm). The most important factor concerns the steel plate flexibility. Others are related to the physical characteristics of backfill. The geometric stiffness index used in the design of bridges is given by the ratio: f δ¼ , S

ð2:130Þ

where: S – span length. The resulting value must be less than the limit value (received from appropriate bridge standard). Substituting data to the Eq. (2.128), stiffness index km1 ¼ 392 kN/mm and km2 ¼ 219 kN/mm for model m1 and m2, respectively, were calculated. Whereas, based on the formula (2.129), geometric stiffness index δm1 ¼ 1.83  104 and δm2 ¼ 3.28  104 were obtained. The obtained results clearly indicate that the shell made from flat steel plates (model m1) has a greater stiffness than in the case of the CSPs (model m2). Stiffness index k allows to objective assessment of the stiffness of a given structures because take into consideration both the structure shape, stiffness plate, as well as geometry and load parameters. In addition, the increase of soil compaction due to live loads affects the stiffness index k, i.e. when the object is more serviced, the displacements of the soil-steel bridge are smaller, and the stiffness index k is increased. Geometric stiffness index δ allows a comparison of soil-steel bridge with other types of bridge structures, e.g. reinforced concrete or steel. Detailed analysis of results are presented in Beben and Stryczek (2016b).

2.4 FEM Analysis of Soil-Steel Bridges and Culverts

2.4.4

113

Summary

FEM analysis of the soil-steel bridges with various cross-sections can deliver the following general conclusions: 1. Numerical results usually exceed values obtained from field experimental testing. The obtained differences between experiments and FEM computations may result from: • inaccurate representation of the backfill during modelling. Moreover, it seems that the numerical analysis should take into account the impact of backfill consolidation, • omits to take the CSP structure slope into consideration in the computational model and at the same time it decreases the structure area which can take loads, • the complicated shape of the soil-steel bridges – then the computational model does not reflect exactly analysed structures, many elements usually are ignored or simplified like corrugation plates, RC collars at the end of the shell, and bolt connections between the plates, • the manner of creation the numerical model of the bridge, this means that when construction of the real structure, the backfill is placed layer-by-layer around the shell and the CSP structure is deformed during backfilling (and after this process, it has residual stresses). In the case of numerical modelling, commonly the whole bridge model is created at once and next it is loaded. 2. Numeric results, although larger than measured values, provide better possibilities for design and estimation of load capacity than currently available standards and design methods. However, it requires knowledge of advanced numerical modelling of complex structures including soil mechanics and structure mechanics. 3. The most extreme displacements and stresses of soil-steel bridges are located: • for box culvert profile: displacements at the crown, stresses at the haunches, • for pipe-arch profile: displacements at the crown, stresses at the springlines, • for arch profile: – model with the RC relieving slab: displacements at crown, stresses at the quarter points, – model without the slab: displacements at the crown, stresses insignificantly moved towards the CSP structure crown, • for arch profile: – model with CSP: displacements at the crown, stresses at the quarter points, – model with flat plate: displacements and stresses at the crown. 4. It can be certainly pointed out that there are no advantageous effects of the CSP application on the reduction of deflections, stresses, bending moments and axial forces in the soil-steel bridge. It can be stated that in the case of soil-steel bridges and culverts with small span there are no necessity of use the corrugated profile

114

2 Selected Issues of Soil-Steel Bridge Design and Analysis

(up to 5 m). This significantly reduces the construction cost of small bridges (easier production of flat sheets and their installation versus to CSPs). In order to provide the detailed regulations, further parametric studies should be conducted, especially for various shell span, plate thickness and height of backfill cover over the shell. 5. A separate topic not covered in this chapter is the modelling of CSPs used to reinforce the old bridges. As a result of the reinforcement, a complex structure with a difficult to unambiguous description of the computational model is created, inter alia, due to the interaction of materials with significantly different stiffness (e.g. brick, steel, concrete, and fill). To get the correct solution to such a difficult problem, the advanced mathematical and numerical apparatus should be used, which should take into account all the strength parameters of the materials applied to describe the computational model i.e. the existing old object, the new reinforcing structure and the fill. In order to assess whether the accepted computational model corresponds to the actual behaviour of the analysed bridge, the results obtained from the numerical calculations should be verified by conducting comprehensive experimental research on the existing bridges (prior to reinforcement and after).

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Elshimi TM (2011) Three-dimensional nonlinear analysis of deep corrugated steel culverts. PhD thesis, Queen’s University, Kingston El-Taher M (2009) The effect of wall and backfill soil deterioration on corrugated metal culvert stability. Ph.D. thesis [online]. Queen’s University, Kingston EN 1991-2 (2003) Eurocode 1: actions on structures – Part 2: traffic loads on bridges. European Committee for Standardization, Brussels EN 1993-1-1 (2005) Eurocode 3: design of steel structures – Part 1-1: general rules and rules for buildings. European Committee for Standardization, Brussels EN 1993-1-8 (2005) Eurocode 3: design of steel structures – Part 1-8: design of joints. European Committee for Standardization, Brussels EN 1993-1-9 (2005) Eurocode 3: design of steel structures – Part 1–9: fatigue. European Committee for Standardization, Brussels EN 1997–1:2004 (1997) Eurocode 7: geotechnical design – Part 1: general rules EN 206-1:2000 (2000) Concrete – Part 1: specification, performance, production and conformity Esmaeili M, Zakeri JA, Abdulrazagh PH (2013) Minimum depth of soil cover above long-span soilsteel railway bridges. Int J Adv Struct Eng 5(7):1–17. https://doi.org/10.1186/2008-6695-5-7 Essery DP, Williams K (2007) Buried flexible steel structures with wire mesh reinforcements for cut plates. Arch Inst Civ Eng 1:65–79 Flener BE (2005) Field testing of a long-span arch steel culvert railway bridge over Skivarpsån. Sweden—Part III. TRITA-BKN Rep. No. 91, Royal Institute of Technology, Stockholm Flener BE (2009) Static and dynamic behaviour of soil-steel composite bridges obtained by field testing. Ph.D. thesis, Royal Institute of Technology, Stockholm Flener BE (2010) Testing the response of box-type soil-steel structures under static service loads. J Bridg Eng 15(1):90–97 Flener BE, Karoumi R (2009) Dynamic testing of a soil-steel composite railway bridge. Eng Struct 31(12):2803–2811 Geotechnical Engineering Manual GEM-12 (2015) Guidelines for Embankment construction. Department of Transportation, New York Gwizdala K, Slabek A, Wieclawski P (2010) Structural solutions for foundation road culverts. In: 56th scientific conference of the committee of civil and water engineering of the Polish Academy of Sciences and the PZITB Scientific Committee, Kielce-Krynica, September 19–24, pp 135–144 HSDHCP (2002) Handbook of steel drainage and highway construction products. Corrugated Steel Pipe Institute, Canada Janusz L, Madaj A (2009) Engineering objects with corrugated steel plates. Design and construction. Transport and Communication Publishers, Warsaw, 427 p Katona MG (2010) Seismic design and analysis of buried culverts and structures. J Pipeline Syst Eng Pract 1(3):111–119 Katona MG, Smith JM, Odello RS, Allgood JR (1976) CANDE – a modern approach for the structural design and analysis of buried culverts. Report No. FHWA-RD-77-5, U.S. Naval Civil Engineering Lab, Port Hueneme Klöppel K, Glock D (1970) Theoretische und experimentelle Untersuchungen zu den Traglastproblemen biegeweicher, in die Erde eingebfetter Rohre, Heft 10, Veröffentlichung des Institutes für Statik und Stahlbau der Technischen Hochschule Darmstadt, Darmstadt (in Germany) Kunecki B (2014) Field test and three-dimensional numerical analysis of soil-steel tunnel during backfilling. Transp Res Rec J Transport Res Board 2462:55–60 Leander J, Wadi A, Pettersson L (2017) Fatigue testing of a bolted connection for buried flexible steel culverts. Arch Inst Civ Eng 23:153–162 Luscher U (1966) Buckling of soil-surrounded tubes. J Soil Mech Found Div 92(6):211–228 Machelski C (2008) Modeling of soil-Shell bridge structures, the lower Silesian educational publishers. Wroclaw, Poland

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Machelski C (2013) Construction of soil-shell structures. The Lower Silesian Educational Publishers, Wroclaw Machelski C, Antoniszyn G, Michalski B (2006) Live load effects on a soil-steel bridge founded on elastic supports. Stud Geotech Mech 28(2–4):65–82 Mai VT, Moore ID, Hoult NA (2014) Performance of two-dimensional analysis: deteriorated metal culverts under surface live load. Tunn Undergr Sp Tech 42:152–160 Maleska T, Beben D (2018a) Behaviour of corrugated steel plate bridge with high soil cover under seismic excitation. In: Beben D, Rak A, Perkowski Z (eds) Proceedings of 3rd scientific conference on environmental challenges in civil engineering, MATEC Web of Conferences, Opole, Poland Maleska T, Beben D (2018b) Study on soil-steel bridge response during backfilling. In: Powers N, Frangopol DM, Al-Mahaidi R, Caprani C (eds) Maintenance, monitoring, safety, risk, management and life-cycle performance of bridges. Balkema, Rotterdam, pp 547–554 Maleska T, Beben D (2019) Numerical analysis of a soil-steel bridge during backfilling using various shell models. Eng Struct 196:109358. https://doi.org/10.1016/j.engstruct.2019.109358 Maleska T, Bonkowski P, Beben D, Zembaty Z (2017) Transverse and longitudinal seismic effects on soil-steel bridges. In: Conference: 8th European workshop on the seismic behaviour of irregular and complex structures, October, Bucharest, Romania Manko Z, Beben D (2005a) Tests during three stages of construction of a road bridge with a flexible load-carrying structure made of Super Cor type steel corrugated plates interacting with soil. J Bridg Eng 10(5):570–591 Manko Z, Beben D (2005b) Research on steel shell of a road bridge made of corrugated plates during backfilling. J Bridg Eng 10(5):592–603 Manko Z, Beben D (2005c) Static load tests of a road bridge with a flexible structure made from super Cor type steel corrugated plates. J Bridg Eng 10(5):604–621 McGrath TJ, Moore ID, Selig ET, Webb MC, Taleb B (2002) Recommended specifications for large-span culverts. Transportation Research Board Simpson Gumpertz and Heger Incorporated. NCHRP Report, no. 473, Washington, DC Mellat P (2012) Dynamic analysis of soil-steel composite bridges for high speed railway traffic. Master of Thesis, Royal Institute of Technology, Stockholm Mellat P, Andersson A, Pettersson L, Karoumi R (2014) Dynamic behaviour of a short span soil– steel composite bridge for high-speed railways – field measurements and FE-analysis. Eng Struct 69:49–61 Meyerhof G G, Baikie L P (1963) Strength of steel culvert sheets against compacted sand backfill. Highway Research Record, no. 30, Transportation Research Board, Washington, DC OHBDC (1992) Ontario Ministry of Transportation and Communications. Ontario Highway Bridge Design Code, Toronto Pettersson L (2007) Full scale tests and structural evaluation of soil-steel flexible culverts with low height of cover. Ph.D. thesis, Royal Institute of Technology, Stockholm Pettersson L, Sundquist H (2014) Design of soil-steel composite bridges. TRITA-BKN Rep. No. 112, Royal Institute of Technology, Stockholm Plaxis (2016) Plaxis 3D reference manual. Delft, PN-85/S-10030 (1985) Polish bridge standards: bridge structures. Loads Rowinska W, Wysokowski A, Pryga A (2004) Design and engineering recommendations for flexible structures made from corrugated steel plates. Bridge Road Res Inst, Żmigród. 72 p Sargand S, Masada T, Moreland A (2008) Measured field performance and computer analysis of large-diameter multiplate steel pipe culvert installed in Ohio. J Perform Constr Facil 22 (6):391–397 Solomos G, Pinto A, Dimova S (2008) A review of the seismic hazard zonation in national building codes in the context of Eurocode 8. JRC Scientific and Technical Reports, Luxemburg Spangler M G (1941) The structural design of flexible pipe culverts. Iowa Engineering Experimental Station Bulletin no. 153. The Iowa State College, Ames

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Vaslestad J (1990) Soil structures interaction of buried culverts. Ph.D. thesis, Norwegian Institute of Technology, Trondheim Vaslestad J (1994) Load reduction on buried rigid pipes. Norwegian Road Research Laboratory, Norwegian Public Roads Administration, no. 74. Oslo, pp 7–20 Vaslestad J, Janusz L, Bednarek B (2002) Instrumental full-scale test with geogrid above crown of corrugated steel box culvert. In: Proceedings of the seventh international conference on geosynthetics, geosynthetics state of the art recent developments, 7ICG-Nice 2002, France, September 22–27 Vaslestad J, Madaj A, Janusz L, Bednarek B (2004) Field measurement of an old brick culvert sliplined with a corrugated steel culvert. Transportation Research Board of the National Academies, Washington, DC Wadi AHH (2012) Soil steel composite bridges. Master of Thesis, Royal Institute of Technology, Stockholm Wadi AHH (2019) Soil-steel composite bridges. Research advances and application. Ph.D. thesis, Royal Institute of Technology, Stockholm Wadi AHH, Pettersson L, Karoumi R (2015) Flexible culverts in sloping terrain: numerical simulation of soil loading effects. Eng Struct 101:111–124. https://doi.org/10.1016/j. engstruct.2015.07.004 White HL, Layer JP (1960) Corrugated metal conduit as a compressible ring. Transportation Research Record, no 39. Transportation Research Board, Washington, DC, pp 389–397 Williams K, MacKinnon S, Newhook J (2012) New and innovative developments for design and installation of deep corrugated buried flexible steel structures. In: 2nd European conference on buried flexible steel structures, Rydzyna, April 23–24 Yeau KY, Sezen H, Fox PJ (2015) Simulation of behavior of in-service metal culverts. J Pipeline Syst Eng Pract 5(2):1009–1016 Yu Y, Damians IP, Bathurst RJ (2015) Influence of choice of FLAC and PLAXIS interface models on reinforced soil–structure interactions. Comput Geotech 65:164–174

Chapter 3

Corrosion Problem of Soil-Steel Bridges

Abstract The chapter includes an introduction to corrosion problem of soil-steel bridges (classification, reason of corrosion occurs). Chemical and electrochemical corrosion of corrugated steel plates are shortly described. The beginning of the corrosion process in soil-steel bridges is also presented. The flow of stray currents around soil-steel bridges is also shown as the causing corrosion in the railway and tram bridges. Soil corrosivity problem is undertaken taking into account the soil resistivity, pH, moisture content. Atmospheric corrosion including the changes in air caused by acidification of the environment and its influence upon corrosion is described. Corrosion in water and erosion-abrasion damages of the corrugated steel plates are also shown. Mathematical model of corrosion description of a soilsteel bridge including the model of corrosive damage and formation of corrosive cracks, is proposed. At the end of chapter, the protections against corrosion and abrasion in soil-steel bridges and culverts are presented. A practical example of designing durability of soil-steel bridge is also given.

3.1

Introduction

Devastation of material by natural factors such as abrasion, chemical and electrochemical corrosion, in line with service strength, have major influence over durability of soil-steel bridges. Figure 3.1 shows classification of corrosion types including soil-steel bridges corrosion. Lack of supervision of a structure condition from the soil side is a relatively big problem in proper maintenance of soil-steel bridges. As a result, first signs of corrosion may not be noticed in time to save the structure. If a corrosion develops from the soil side, the results can only be seen when the steel structure is affected (Fig. 3.2). In soil-steel bridges, the erosion voids can appear around corrosion spots caused by infiltration of water and improper compaction of backfill around the steel shell structure. As a result, voids may spread and have a major influence over general and local stability of soil-steel bridges. Apart from that, it can also affect hydraulic capacity of a given structure. If erosion voids reach the top soil layer, road or railway can be damaged, causing a structure disaster (Fig. 3.3). © Springer Nature Switzerland AG 2020 D. Beben, Soil-Steel Bridges, Geotechnical, Geological and Earthquake Engineering 49, https://doi.org/10.1007/978-3-030-34788-8_3

119

120

3 Corrosion Problem of Soil-Steel Bridges

DIVISION OF CORROSION ON:

Environment of orgin

Form of occurrence

Processes occurring

Nature of interaction

atmospheric

general

chemical

soil

local

electrochemical

fatigue

water

galvanic

microbiological

erosion

gas

crevice

stress

friction

pitting intercrystalline selective

Fig. 3.1 Classification of the most often occurred types of corrosion. The corrosion concerning to soil-steel bridges is marked in bold boxes Fig. 3.2 View of the water action causing the corrosion of soil-steel bridge (El-Taher 2009)

Fig. 3.3 Loss stability of backfill situated over the shell structure due to infiltration action

Live load

Erosion air voids

Water infiltration Shell deformation

3.1 Introduction

121

Other reasons for corrosion in soil-steel bridges are: – damages to corrosion protection at the time of joining separate structural elements together. It is a common reason, because the majority of mounting works is done with torque wrenches with high torque (up to 400 Nm), – infiltration of water through soil layers, especially after winter, when water contains winter road maintenance agents. Another disadvantage is operation of the structure in an aggressive environment. This is related to the fact that rainwater may contain lots of pollution (sulphates, chlorides, etc.) which intensify corrosion processes. Moreover, polluted water infiltrates backfill layers and changes its basic physical and capacity parameters (e.g. change in pH and soil resistance), – frequent temperature changes, especially in autumn-winter period (reaching 0
C and below/above) which may cause shearing or bulking of soil. As a result, cavities may appear near steel structure, – lack of proper abrasion protection causing damages to the bottom and side walls of the structure by material carried by water, – lack of proper corrosion protection in case of, so called, high water levels. Soil-steel bridges are mainly exposed to two corrosion types, i.e. chemical and electrochemical. In the case of chemical corrosion, it may appear both from the side of soil and of water (Bohn et al. 2001; Tan 2010). It occurs especially when water and/or soil contain acids, alkali, dissolved salts and organic industrial waste. Such pollution can be found in ground water, sanitary wastewater, acid rains, and sea environment. Existing pollution and sulphates, carbonates and chlorides cause damages to steel (and concrete) elements. This process may be intensified in areas with freezing-thawing cycles (high and frequent temperature changes). Corrosion damages leave the material open to deep penetration by dangerous pollution. Caustic chemicals carried by water cause corrosion-abrasion damages on structures located on such watercourses. Environmental conditions containing both electrolyte and changeable concentrations of oxide may also cause electrolytic corrosion. Whereas electrochemical corrosion in soil-steel bridges may happen when galvanic cells of different potentials (anode and cathode) appear on their surfaces. Potential difference inspires electric current through electric circuit composed of electrolyte (moist soil or water), of anode (places in structure free of electrons), of cathode (places on structure containing electrons) and, obviously, of the structure as the conductor (Fig. 3.4). Losing of material happens only on the side of anode, whereas on the side of cathode material surplus appears. Another source of potential difference can be stray currents near a railway or a tramway. Another important element is corrosion aggressiveness of soil, mainly determined based on its resistivity, pH, corrosion activity and chemical composition. It can be done with help of geophysical tests by means of electrical resistivity tomography of electromagnetic method.

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3 Corrosion Problem of Soil-Steel Bridges

Fig. 3.4 The process of formation of electrochemical corrosion at the interface between water (or backfill) and a steel structure

Fig. 3.5 The examples of typical corrosion of soil-steel bridges caused by: (a) aggressive acting of water (El-Taher 2009), (b) change the water level

Acidification of the environment (atmospheric air, ground and water) is also one of the most important problems. Effects of steel structures corrosion related to acidification of the environment, mainly of polluted air containing sulphur compounds, is a well-known problem (Kucera 1988; Wysokowski 2001; Abdul-Wahab 2004). Influence of sulphur compounds, e.g. SO2 upon different materials has been analysed on many occasions both during laboratory and site tests. Current knowledge on influence of acid pollution on atmospheric corrosion has been summarized in the following works (Shreir et al. 2000; Kusmierek and Chrzescijanska 2015; Ngene et al. 2015; Kruger and Begum 2016). World experience shows that corrosion damages are a problem of major importance and require proper reaction at a very early stage (Czerepak et al. 2003; Akhoondan 2012; Jones and Ricker 2017). Figure 3.5 shows examples of corroded soil-steel bridges. The following chapter characterises different corrosion types of soil-steel bridges, with special attention to corrosion caused by the soil.

3.2 Beginnings of Corrosion

3.2

123

Beginnings of Corrosion

Effective use of metals for construction of different engineering structures must be based mainly upon understanding of their basic properties (physical, chemical and mechanical). This is mainly related to understanding the influence of different factors, most often external ones (environmental) on possibility of development of corrosion processes. A correct analysis of the structure consists in a dual approach to this matter, i.e.: (i) designing of the structure or its elements in such a way as to meet basic strength conditions, (ii) envisaging proper protection of the structure against aggressive environmental conditions. The most important factors causing possibility of corrosion in metal engineering structures are: 1. Structure of a given metal, i.e. atom structure, micro-and macroscopic heterogeneity, compressive and tension strength, cyclic (fatigue) loads. 2. Environment, meaning chemical properties, concentration of reactive substances, content of noxious pollution, bacteria, pressure, temperature, etc. 3. Metal-environment interaction, especially kinetics of oxidation and decomposition (dissolution) of metals, kinetics of reduction in a solution, nature and distribution of corrosion products, possibility of appearance of protective cover layer and its decomposition (dissolution). Bering in mind the above factors, establishing a real mechanism of corrosion is a very complex task and it consists in understanding many different phenomena from the overlap area of many scientific fields, i.e. physics of metals, chemistry, bacteriology. Visible corrosion cracks on structure of metal may result from its internal structure and from corrosive factors, they can also be caused by mechanical (service) factors. Whereas corrosion on the side of soil can be a mechanism of working of bacteriological factors and pollution in relation to kinetics of general corrosion. The first approach describing behaviour of metals in defined environments is a rule consisting in skipping a detailed structure of a metal and considering corrosion as a heterogeneous chemical reaction. It appears on contact area of a metal and a non-metallic material, and it includes metal as one of the reagents. Therefore corrosion can be expressed in the form of a simple chemical reaction: aA þ bB ¼ cC þ dD,

ð3:1Þ

where: A is a metal, B is a non-metallic material (a substrate), C and D – reaction products.

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3 Corrosion Problem of Soil-Steel Bridges

Non-metallic substrates are very often related to the environment, although in a complex environment they can play a secondary role. Therefore in an atmospheric corrosion of steel structures, nitrogen can be skipped, although it constitutes about 15% of the atmosphere. However its reaction is relatively weak in comparison with moisture, oxygen, sulphur dioxide and particulate pollutants. One of the products of reaction C can be an oxidized form of metal, then D is a reduced form of a non-metal. In most cases component C is referred to as corrosion product, although in some cases it can equal D. In its simplest form, reaction (3.1) can be presented as follows: aA þ bB ¼ Cc,

ð3:2Þ

for instance: 4Fe + 3O2 ¼ 2Fe2O3, where product of reaction can consider an oxidized form of metal or a reduced form of a non-metal. Reactions of this type, which require presence of water or water solutions are referred to as, so called, “dry” corrosion reactions. A relevant reaction in water solutions is referred to as „wet” corrosion reaction and can be expressed, e.g. in the following form: 4Fe þ 2H2 O þ 3O2 ¼ 2Fe2 O3  H2 O:

ð3:3Þ

Another reason for corrosion in soil-steel bridges is electric current in soil. According to Kirhoff’s second rule, it is a return current following the route of the lowest resistance. If a steel structure is located near an electrified railway of a tramway rail, it constitutes closure of the circuit. Electric currents flowing through ground base concentrate on steel structure, which is a better electric conductor than the ground. A part of electricity returns to the substation through the ground and is called stray currents. The term „stray” is related to random character of currents coming from return circuits of electric tractions of direct current. Their sense, direction and intensity in a given place depend on many factors and, in practice, they manifest themselves as stochastic processes, with all the consequences coming form that – above all in measurement. Figure 3.6 shows schematic representation of the phenomenon and the way of flow of stray currents around a soil-steel bridge. Traction return current branches, in a place it finds convenient, and a part of it (as a stray current) leaves the return traction – it flows to the negative rail of traction substation through ground and underground steel structures. When stray currents enter a steel structure, they do not cause any damages (the place is a cathode). It is far different in the place where a stray current leaves the structure and enters the ground again (anode). In such a situation, it sweeps along particles of metal causing electrolytic corrosion. In numerous cases, this corrosion is so big that it leads to quick destruction of the affected structure. Stray currents can be caused by local systems feeding means of transportation with electricity. Typical examples are railways, tramways, trolleybuses, systems of cathode protection, local feeding systems.

3.2 Beginnings of Corrosion

125

Traction network Feeder The main part of the return current Stray currents Return cable Steel structure

Steel structure

- places exposed to electrochemical corrosion caused by stray currents

Fig. 3.6 The scheme of stray current flow in soil-steel bridge

Standard EN 50162 (2004) devotes lots of attention to harmfulness criteria of stray currents acting on steel structures buried in ground. In a case, when there is no fluctuation of stray currents, evaluation of their harmfulness can be done based on comparison of potentials of a steel structure at their source being turned on and off. The value of potential of the underground steel structure registered at the time of absence of stray currents is considered as normal and undisturbed, whereas potential change towards positive means anode activity. At evaluation of this activity in EN 50162 (2004), structures with and without cathode protection have been distinguished. Potential shifts can be calculated from the following formula: ΔU ¼ cρ,

ð3:4Þ

where: ΔU is an acceptable potential shift [mV] depending on resistivity of soil, ρ is soil resistivity [Ωm], c ¼ 1.5 mV/Ωm (for steel). In the past, the problem of estimation of corrosion risk of steel structures working in ground, in the case of polarization change and potential shift ΔU as a result of stray currents activity, was expressed, e.g. by introduction of a term of frequency f instead of ΔU and the term of anode part of current exchange, determined on the basis of registration of potential expressed as follows: P

ψ ¼P

AðþÞ P , AðþÞ þ AðÞ

ð3:5Þ

where: ψ – anode potential of current exchange, ΣA (+) and ΣA () – respectively sums of positive and negative surfaces between flow of registered potential and the level of resting potential (TGL 18790 1979).

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3 Corrosion Problem of Soil-Steel Bridges

In the 90s of the twentieth century, a criterion of asymmetry factor of potential changes of a structure was also used (Sokolski 1996), and it was calculated with help of correlation method of testing stray currents expressed as: γ¼

Ta , T

ð3:6Þ

where: Ta – summary time of anode polarisation, T – total test time. Using the above criterion, for γ < 30% there is, practically, no corrosion risk, for 30% < γ < 50% – the risk is medium or high, and in case of γ > 50% – the risk is very high. Due to the fact that quite often correlation e ¼ f(u) differs considerably from typical ones, and different values γ are obtained for the same structure in different times of a day, the discussed criterion has not been introduced into practice.

3.3 3.3.1

Soil Corrosivity Problem Introduction

Soil makes the corrosive medium where the bridge is located (Fig. 3.7). Corrosion assumes an electrochemical process in which dissolution of metal constitutes an anodic reaction. Usually, the cathodic reaction involves reducing oxygen. The corrosion rate is dependent mainly on moisture and salt content as well as by soil resistivity. Moreover, the soil resistivity is associated with its porosity, the concentration of dissolved salts, mineral content, temperature, as well as with the dimension and form of grains and their mutual position (Abu-Hassanein et al. 1996; Samouelian et al. 2005; Beben 2014). It should also add, that the soil pH, chloride strength, the appearance of sulfur and nitrogen and microbiological activity influence on the soil corrosion. Additionally, if the soil resistivity decreases (caused by moisture and salinity increase) it can be expected that the soil aggressiveness will be increased. Table 3.1 presents the categories of soil and water corrosivity for which the structures working in the soil should be classified as Im3 (EN ISO 12944-2 2017). Therefore, the corrosion resistance of soil-steel bridges is associated mainly with the backfill quality and soil electrochemistry phenomena, including the development of electro-cells that can be caused by potential differences and alternating currents (Beben 2014). Steel structures used for build the transportation objects working in the soil (bridges, culverts, pipe, pipelines etc.) can be destroyed due to appear the following corrosivity factors (Cunat 2001; Hepfner 2001; Gassman 2005; CSPI 2007; Beben 2014): (i) high moisture content, (ii) pH < 4.5 or > 8.0, (iii) resistivity 6) (Wranglen 1985) Soil resistivity [Ω m] 100

Salt content [mg/dcm3] > 7500 7500–750 750–75 100 100–30 30–4 3.5 1.5–3.5 1.3–1.5 0.9–1.5 6.5 >20.0 2.6–5.2 6.7–13.3 2.2–4.3 5.5–11.0 3.3–6.5 6.1–12.1 >8.6 >17.2

Table 3.5 Loss of steel thickness depending on soil pH, chloride content and soil moisture (AS/NZS 2041 2010) Soil pH >5 4–5 3–4 5.0 >20,000

Average loss of steel thickness [μm/year] Permeable soil Saturated soil 2.5 m). Nevertheless, for the LR1 bridge, it should be definitely recognised that the soil resistivity is greater than 180 Ωm and consequently there is a low-risk of corrosion. Figure 4.27a presents that received minimum backfill resistivity of the study zone (at spring period) does not exceed 30 Ωm. The resistivity was recorded a depth of about 1.2 m (measurement points #3 and #9 on the profile #1 – see Fig. 4.23) and almost 1.5 m from the roadway edge. Figure 4.27b shows that the backfill resistivity

4.3 Durability Tests of the Backfill Corrosivity

Backfill resistivity [Ω m]

(a)

Penetration depth [m] 2.25 1.2 2.25 1.2

1.2

2.25

189

2.25

120 summer 2011 spring 2011

100 80 60 40 20 0 1

2

4

3

7 6 5 Survey points

8

9

11

Penetration depth [m]

(b) 1.8

1.8

0.825

400 Backfill resistivity [Ω m]

10

summer 2011 spring 2011

350 300 250 200 150 100 50 0 1

2

3

4

5

6

7

8

9

Survey points Fig. 4.27 The distribution of the backfill resistivity at the various depths of bridge NR1 in the spring and summer seasons for chosen test profiles: (a) #1, (b) #2

in the profile #2 situated farther from the roadway border (ca. 3.5 m) exceeds 100 Ωm. A quite similar backfill resistivity level was recorded in profile #1 situated on the NR2 bridge (Fig. 4.28). For this bridge, the received resistivity did not exceed 80 Ωm; but it should be underlined that the higher backfill resistivity was reached for profile #2. It can be concluded that the resistivity is lower for the backfill situated closely to the ground level while for the deeper zones, the resistivity is greater. It should be also emphasized that during the resistivity tests, two comparative profiles (Fig. 4.23) were executed for each analysed bridge. These profiles were situated outside the range of backfill of the bridge in order to compare with the resistivity obtained from the main tests. The soil resistivity received from these

190

4 Testing and Durability of Soil-Steel Bridges

(a) 120 summer 2011

Backfill resistivity [Ω m]

100

spring 2011

80 60 40 20 0 1

2

3

4

5 Survey points

6

7

8

9

(b) 120 summer 2011 100

spring 2011

Backfill resistivity [Ω m]

80 60 40 20 0 1

2

3

4

5 Survey points

6

7

8

9

Fig. 4.28 The distribution of the backfill resistivity at the depth of 2.25 for the bridge NR2 in the spring and summer seasons for chosen test profiles: (a) #1, (b) #2

profiles was not greater than 100 Ωm (Table 4.9). Nevertheless, these resistivities are greater than the minimum values received from the testing of the soil-steel bridges situated on the NR and PR routes and they were in the range from 75 to 97 Ωm. Considering the comparative profiles (Table 4.9), maximum soil resistivity is usually smaller by 4.71–34.72% and 12.32–61.82% during summer and spring tests, respectively. Such resistivity values are due to the absence of rainfall and salt compound contents in the soil after the winter season. The bridges NR1 and PR1 are exceptions due to increasing resistivity (19.09–73.82%). Taking into consideration the minimum backfill resistivity and results obtained from the comparative profiles it can be proved that the resistivity reduced by 16.18–150.0% and 41.51–173.33% for the summer and spring investigations. In should be added that

4.3 Durability Tests of the Backfill Corrosivity

191

the bridges LR1 and LR2 (located on the local roads) constitute exceptions. This means that the backfill resistivity is raised (15.46–37.30%) in comparison to the comparative profiles. This is due to the large backfill permeability and low salt content. Besides, these roads are maintained irregularly, thus the means that can affect the backfill resistivity are not usually used. Usually, backfill resistivity drops during the spring tests (Table 4.9, Figs. 4.27 and 4.28) that unquestionably results from the raised salinity (mostly sodium chloride content, which is applied for roadways maintenance) and greater moisture content of the backfill in comparison to the summer (Table 4.8). It should be pointed out that the maximum backfill resistivity was received at the edges of the soil-steel bridges and the smallest values were collected close to the roadways. It can be also noted that the backfill resistivity near bridges situated on the main roads (NR and PR) reaches smaller values and thereby bigger risk corrosion in comparison to the structures located on the local routes. This may prove the impact of the means utilised to the road maintenance on the backfill resistivity. Generally, the alkaline soils are characterized by the biggest electric conductivities. These soils include many various chemical solutions like calcium hydroxides, ammonia solution, sodium, alkali metals as well as potassium and ammonium carbonates. Furthermore, during the spring-summer surveys, it was noted that backfill resistivity near the soil-steel bridges rises while the backfill temperature falls. It can be proved for the backfill situated at a depth of 1.5 m where the temperature reaches 2  C. In this case, the backfill resistivity was nearly 100 Ωm. Next, when the backfill temperature rises to 7  C at a depth of 0.9 m, the resistivity was about 40 Ωm. The backfill resistance survey in the winter period was executed on the NR1 and NR3 bridges. In these cases, it was also noted that the backfill resistivity rises while backfill temperature drops. For example, when the temperature is ranging from
7  C to
10  C (for the backfill situated 0.3–0.5 m from the ground level) the backfill resistivity was within 115–120 Ωm. Whereas, when the backfill temperature rises to +5
+7  C (for deeper soil location: 1.2–1.5 m), the resistivity reaches 45–50 Ωm. It can be concluded that during long-term service (13 years) of soil-steel bridges, the backfill demonstrates the smaller resistivity in the spring season than in summer. Taking into account the fact that the backfill utilised for the bridges backfilling was non-corrosive (it had a high resistivity), the received data clearly show that there is a high likelihood of backfill aggressiveness towards the steel structure. It involves mainly the soil-steel bridges that are located on the NR and PR routes, where the backfill resistivity was the smallest (ca. 30–35 Ωm). This proves that the backfill aggressiveness according to relevant criteria given by EN 12501-1 (2003) and EN 12501-2 (2003). The acidity (pH) of the analysed soils applied for construction of the bridges was within the range of 8.1 (summer) to 9.3 (spring). This proves that the backfills have an alkaline reaction. It should be noted that in the summer season acidity was forever smaller, whereas during the spring season it was greater (almost 11%). It is surely associated with large contamination concentrations accumulated in the backfill after the winter season that raises the reaction of alkaline of the backfill. It is apparently

192

4 Testing and Durability of Soil-Steel Bridges

Corrosion rate

Fig. 4.29 Corrosion rate versus the backfill moisture content

W opt. W sat. Backfill moisture content [%]

associated with the means application for maintaining the roads in the winter season (a mix of sodium chloride and calcium chloride with a pH ranging from 8.0 to 9.0). Table 4.8 shows that for the soil-steel bridges situated on the local routes (LR), the backfill acidity (pH) rises with a smaller intensity (0.90 m), the backfill moisture contents vary rather lightly. Figure 4.29 shows that the corrosion rate is related to the backfill moisture content (it means a grade of water saturation the soil pores). Taking into account a great water saturation of the backfill (more than Wsat.), the oxygen can distribute only by water. This process runs rather moderate, and consequently, the rate of corrosion is also slow (for example, it can be observed below the groundwater level). In the case when some part of the soil pores is saturated by water (for example, over the groundwater level), the oxygen diffusion may occur in the gas phase. This process is comparatively fast and thus the rate of corrosion is also faster (see Fig. 4.29). In order to check statistical interrelation between soil resistivity and moisture contents and acidity (pH), a correlation analysis was performed. To study

4.3 Durability Tests of the Backfill Corrosivity Table 4.10 The Pearson’s correlation factors for the analysed soil-steel bridges

193

Correlation factor r Summer pHsum/ρsum Wsum/ρsum Spring pHspr/ρspr Wspr/ρspr

Values
0.6812 0.3312
0.9455 0.8411

Note: Markings – please see Table 4.8

relationships of the aforementioned parameters, the Pearson’s correlation factor (rxy) was applied as follows (Bernstein and Bernstein 1999): n P

ð xi
xÞ ð yi
yÞ i¼1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi, s r xy ¼ n n P 2P 2 ðxi
xÞ ð yi
yÞ i¼1

ð4:10Þ

i¼1

in which: n is number of observations; xi, yi are values i for characteristic x and y, respectively. Generally, Pearson’s correlation factor gets results within [
1; 1]. It means that the greater the absolute value of the correlation factor, the stronger the linear interrelation between the analysed parameters. When the correlation is equal to zero, it means that there are no interrelations between the variables. The extreme values give an information that the interrelations of applied variables are perfectly negative or positive. Table 4.10 presents the Pearson’s correlation factors for the analysed soil-steel bridges in two survey seasons. Table 4.10 also shows a great correlation between the soil resistivity and acidity (pH) both spring and summer as well as resistivity and backfill moisture contents during the spring survey. Nevertheless, the pH reaches the negative correlation that means that if the backfill pH increases, the resistivity drops (this is better noticeable during the spring because the backfill includes more contaminants after the winter). For the backfill moisture contents, the positive correlation during spring tests means that if the backfill moisture content grows, the resistivity also grows. Correlation between moisture content and backfill resistivity during the summer season indicates is also positive character, however, the power of the relationships of the considered parameters are essentially lower. The obtained correlation factors clearly demonstrate that there are interrelations between the resistivity and acidity (pH) as well as backfill moisture content. Taking into consideration the notations coming from American (AASHTO 2013), Australian (AS/NZS 2041 2010) and Canadian (CHBDC 2014) standards it was checked if the analysed soil-steel bridges satisfy the conditions of the minimum durability as for culverts (40 years) and the service life expected as for typical bridges (100 years. AASHTO (2013) provides that the decline of zinc layer

194

4 Testing and Durability of Soil-Steel Bridges

Table 4.11 Durability of tested bridges based on the standards (in years) AASHTO (2013) General 58

CHBDC (2014) From backfill side 60

From water side 31

AS/NZS 2041 (2010) Soil pH, W, ρ Soil pH, W 104–127 43–55

thickness from the backfill side (taking into account that the backfill moisture content is below 17%) is 15 μm/year (during the first 2 years), and then is 4 μm/ year. Whereas, the decline of steel thickness (after the decline of the zinc layer) is 12 μm/year. CHBDC (2014) asserts that the decline of zinc thickness from the backfill side is 6 μm/year during the first 2 years (assuming the backfill moisture content is below 17%), and next it is constant and amounts to 3 μm/year. For the steel structure, it was asserted that the decline of thickness is 15 μm/year (after the decline of the zinc layer). However, the decline of the thickness of steel and zinc situated in the saturated backfill or on the water-side equals to (i) 15 μm/year (for the zinc layer) and (ii) 20 μm/year (for steel structure after the decline of the zinc layer). A somewhat different approach to determining the lifetime of soil-steel bridges (decline of zinc and steel) proposes an Australian code (AS/NZS 2041 2010). The code states the service life is dependent on the backfill pH, resistivity and moisture content. Considering the minimum backfill resistivity, which was received during the survey (Table 4.9) and the rate of steel corrosion amounting to 15 μm/year, the service life of the analysed soil-steel bridges was within of 104–127 years. Considering the results presented in Table 4.8 (backfill pH and moisture content) the service life of the tested bridges was within of 43–55 years. Consequently, taking into account the statements given by the Australian code, the backfill pH seems to be more crucial than its resistivity. Table 4.11 presents the durability of analysed soilsteel bridges (Beben 2014b). The above-mentioned implies that the considered soil-steel bridges satisfy the condition of the minimum period (40 years) of service life for culverts. However, the analysed bridges do not fulfil the condition of the minimum lifetime (100 years) foreseen for bridges. In can be noted that the second requirement of structure service life is usually needed by the European administrations responsible for the management of the bridges. In order to reach the expected service life (as foreseen for bridges), the analysed soil-steel bridges need extra anti-corrosion protection, such as painting or bitumen coatings. It should be also clearly stated that the foreseen service life of bridges applies particularly to corrosion failures. Nevertheless, in the reality, many various elements may also influence the reduction (and/or extending) of the durability for soil-steel bridges, such as damages to the joints of individual plates, the large deformation of the shell (loss of stability), the loss of carrying capacity of the backfill, improper construction process, etc. (Beben 2014b).

4.3 Durability Tests of the Backfill Corrosivity

4.3.5

195

Summary

Taking into account the electrical resistivity tests, moisture contents and pH of the backfill near the soil-steel bridges, the general conclusions can be formed: 1. Received results of the pH and soil resistivity confirm the modification of these parameters compared to the initial ones coming from the building period (pH of 5.8–7.7 and resistivity of 400–500 Ωm). Minimum soil resistivity was 30 Ωm that, it means that exist a high risk of corrosion versus the steel structure. It should be noted that the minimum backfill resistivity dropped at the spring surveys (5.8822.06%) compared to the summer tests. The backfill pH has an alkaline reaction that can influence the increase of corrosion aggressiveness. During the summer season, the pH was regularly smaller (8.1–8.6), whereas at the spring it was greater by nearly 11% (8.4–9.3). Besides, it was noted that with diminishing the backfill temperature, the resistivity rises. 2. The largest backfill moisture content was received during tests conducted after the winter (nearly 10%) and it occurred at the upper soil layers (at a depth no more than 0.90 m). Therefore, high backfill moisture contents decrease resistivity, consequently, it raises the corrosion threat in relation to the steel structures. Thus, environmental circumstances occurring in the soil near the examined bridges favour the growth of microbial corrosion. 3. Great correlations between the pH and soil resistivity during the summer and spring test periods as well as the moisture content and resistivity at the spring were observed. Nevertheless, the negative correlation obtained for pH means that if the backfill pH increases, its resistivity drops (this is more apparent during the spring). In the case of backfill moisture content, it was found the great positive correlation at spring. 4. The results obtained taking into account the statements given by AS/NZS 2041 (2010), CHBDC (2014) and AASHTO (2013) clearly proved that the examined soil-steel bridges satisfy the minimum service life condition for the culverts (40 years). While, the analysed bridges do not fulfil the lifetime condition foreseen for the typical bridges, i.e. 100 years. Thus, an additional anti-corrosion protection should be provided. 5. A high risk of corrosion due to backfill aggressiveness can be assumed for the examined soil-steel bridges. This involves essentially the bridges situated on the high-class roads (motorways, expressways). This is clearly associated with the application of agents required for the road maintenance during the winter season. Nevertheless, due to the relatively short lifetime period of these bridges, no signs of the structural perforation were noticed. In order to form further particular remarks, it is very important to continue the soil corrosivity surveys on the soilsteel bridges. The corrosion study should be still developed taking into account the corrosion aggressiveness caused by the content of chlorides, sulphates and sulphides as well as the backfill aeration.

196

4.4 4.4.1

4 Testing and Durability of Soil-Steel Bridges

Deformation of the Backfill Caused by the Traffic Live Load Introduction

As service time passes by, soil-steel bridges are susceptible to deformation of ground layers (backfill stability loss) located above steel shells. Soil stability is a condition when a given soil medium of any composition and shape of individual particles undergoes controlled deformations under loads, with constant speed and at constant porosity index, however without changes to shear stress, effective normal stress and volume. Therefore, if deformation speed changes, it causes changes to soil stability (balance). Figure 4.30 shows schematic development of deformation in soil medium on the example of a stress-strain curve. According to Fig. 4.30, three zones of deformation development in backfill can be distinguished. Zone A presents the shape which is strongly affected by backfill type, initial structure, initial state and method of loading. Initial structure and state have more influence than in any other zones. Zone B shows the initial structure and state increasingly altered by strains until steady of deformation is reached. Initial structure and method of loading also influenced the magnitude of τI and τII. At strains beyond the point II crushing has stopped and the grains have reached a steady state “structure”. The initial structure and state have been completely altered by the loading process and have no influence on τII. Nevertheless, the initial conditions do influence εI. Deformations of ground layers happen both in “micro” and “macro” scale and can cause change of ground strength parameters (McDowell and Bolton 2001; Okur and

SHEAR STRESS (τ)

I

II

Zone A

Zone C Zone B

0 AXIAL OR SHEAR STRAIN (ε or γ) Notes: - At the point 0 occurs the end of consolidation and start of loading. - At the point I occurs the maximum shear stress (shear strength). Strain at peak varies from less than 1% to more than 40%. - At the point II, the steady state of deformation is reached. Strain at point II may vary from a few (%) to extremely large values associated with displacements of 0.03 to 0.50 m.

Fig. 4.30 Deformation development of a stress-strain curve in the soil media (backfill)

Fig. 4.31 Classification of dynamic loads acting on the soil medium

NUMBER OF LOAD CYCLES

4.4 Deformation of the Backfill Caused by the Traffic Live Load

1

197

Bomb explosion

10 Earthquake

10 10 10 10

2

Drilling piles Soil compaction

3

4

Vibration from transport

5

Vibration from machine foundations -3

-2

-1

10 10 10 TIME OF LOAD ACTION [s]

1

Ansal 2007). This is caused by continuous increase in average daily traffic on roads and increasing load on vehicle axles (Kettil et al. 2007). Deformation of ground can also be caused by influence of seismic and anthropogenic phenomena (earthquakes, mining tremors). As a result of their influence, increased deformation of steel shells can occur (Sezen et al. 2008; Yeau et al. 2009; Beben 2014a; Maleska et al. 2017; Maleska and Beben 2018, 2019). The period of time when level of strains and strains in soil medium changes under the influence of external load can be called time of load impact. Changeability of load influence in time usually differs, therefore speed and level of amplitudes causing deformations in soil medium differ as well (Wrana 2008). Figure 4.31 shows characteristics of chosen dynamic loads affecting soil medium, as a resultant of influence time and number of load cycles. Influence of static and dynamic loads on soil-steel bridges has already been discussed on many occasions, however with respect to a steel shell exclusively. It has been described with details in the previous parts of this book. This chapter presents the problem of deformations of ground layers located above steel shells of these bridges and culverts, caused by traffic live load. It also proposes a mathematical model describing deformations of ground layers in micro and macro scales.

4.4.2

Characteristics of the Problem

Service loads caused by live traffic cause different types of deformations in soil medium. In case of small values, linear constitutive relations are used, but if the deformation levels are bigger: 10
2  10
1, non-linear models of soil should be used in analysis of the issue. As the number and frequency of load cycles increases, permanent loss of soil strength and stiffness occurs (Okur and Ansal 2007). It is

198

4 Testing and Durability of Soil-Steel Bridges

Fig. 4.32 Uniform loads on an elastic half-space (Boussinesq theory)

2a p0

1

x

2

0

d dh

dv

z

caused by accumulation of water pressure in soil pores and splitting of individual soil particles (Chai and Miura 2002; Nguyen and Mohajerani 2015; Gu et al. 2018). Vibrations of the soil medium caused by cyclic load (the source of vibrations) propagate in elastic medium in the form of spatial waves, i.e.: longitudinal waves P and transversal waves S (Ishimaru 1999; Degrande 2002). Additionally, passage of the waves may lead to spatial and rotational surface ground motions (Zembaty 1997, 2009). The speed of propagation of these waves in ground medium mainly depends on its physical properties. The type P waves most often propagate with speeds higher than the S type waves. In a soil medium where vibrations propagate, also surface waves can be found (Rayleigh and Love waves), which propagate in the subsurface layer (Ishimaru 1999; Degrande 2002). As the distance between vibration source and the object (receiver) increases, amplitudes of ground vibrations decrease and energy density gets dispersed on ground layer borders. To identify dynamic load caused by live road and railway traffic, one can use the Boussinesq elastic half-space. Figure 4.32 shows Boussinesq task for moving loads. In accordance with Boussinesq theory, individual components of strains can be presented in the following form (4.11, 4.12, and 4.13): p0 ½σ þ sin θ0 cos ðθ1 þ θ2 Þ, π 0 p ¼ 0 ½σ 0
sin θ0 cos ðθ1 þ θ2 Þ, π p τd ¼ 0 sin θ0 cos ðθ1 þ θ2 Þ, π

σ dv ¼

ð4:11Þ

σ dh

ð4:12Þ

where θ0 ¼ θ1 + θ2.

ð4:13Þ

4.4 Deformation of the Backfill Caused by the Traffic Live Load Fig. 4.33 Stress path in soil medium under moving loads

199

dh

Radius vector

2

dv

dh

2

0

Whereas the angle between strains σ dv and σ dh and the principal strains σ 1 and σ 3 can be calculated from the following dependence (4.14): tan 2β ¼

2τd ¼ tan ðθ1 þ θ2 Þ: σ dv
σ dh

ð4:14Þ

Figure 4.33 shows strain path in a soil medium coming from moving load caused by passing vehicles. According to Figs. 4.32 and 4.33, radius vector can be calculated from this dependence (4.15): σ d1
σ d3 p0 ¼ sin θ0 : 2 π

ð4:15Þ

Determination of dynamic properties of a soil medium is necessary to assess the reaction and stability of backfill. Primary dynamic properties of backfill include: (i) modulus of small strain shear, (ii) reduction of the shear modulus and (iii) damping ratio enlarged by an amplitude of shear strain. However small strain shear modulus Gmax (deformations ε < 1  5  10
4) is one of the most significant backfill parameters influencing deformability. Whereas, dynamic shear modulus depends on the cyclic amplitude of shear strains. At a low level of these strains, the reduction of dynamic shear modulus occurs. In addition, the reduction of dynamic shear modulus accelerates with an increase in strains amplitude. At the time of soil deformation caused by cyclic load, the energy is dispersed by hysteretic damping. At low values of shear strains, the dynamic shear modulus remains practically constant and equals the initial value. It is worth adding that an increase in pressure in soil pores causes reduction of effective stresses. In addition, the reduction of effective stresses generates growth in

4 Testing and Durability of Soil-Steel Bridges

Strains

Effective stresses at the beginning of the cyclic load

Fig. 4.34 Scheme of backfill deformation at cyclic loads

Pore pressures generated by cyclic loads

Backfill deformation resulting from the dissipation of pore pressures

200

Effective stresses

shear strains and settlement after cyclic loads recede. The pressure in soil pores disperses following cyclic stresses, and effective stresses grow to reach primary value (i.e. a value from before cyclic load). As a result of dissipation of pressure surplus in soil pores, the volume of soil medium diminishes and it undergoes additional deformations (Yıldırım and Ersan 2007). Figure 4.34 shows a scheme illustrating backfill deformation caused by cyclic load.

4.4.3

Damping in Soil Medium (Backfill)

From theoretical point of view, no dissipation of energy can occur in soil medium below the elastic borderline of strains amplitude. On the other hand, however, if a part of energy is dispersed, even at a very low level of strains (Lanzo and Vucetic 1999), it causes the fact that the damping ratio will never equal zero. Increase in hysteresis loop shows that damping ratio rises with an increase of the amplitude of cyclic strains. The dissipated energy during every cycle is usually described using the hysteresis loop surface for the considered cycles. The mathematical laws determining the form of the stress-strain loop can be treated as hyperbolic, bilinear, or Ramberg-Osgood relationship (1943), or Hardin andDrnevich one (1972). Dynamic shear modulus depends on soil plasticity and is therefore related to the damping ratio. Ishibashi and Zhang (1993) stated that the damping also affects effective pressure, especially in soils of low plasticity. The stress-strain path in linear scope can be expressed in the form of a hysteresis loop, as shown in Fig. 4.35. To generalize, some of the most important properties of hysteresis loop shape are area and inclination. The inclination is depended on soil stiffness that may be determined at each point through the modulus of tangent shear Mtan.. Due to the fact that Mtan. changes in the loading cycle, the mean value of the

4.4 Deformation of the Backfill Caused by the Traffic Live Load

Stress

Fig. 4.35 Idealized cyclic stress-strain hysteresis loop for backfill

201

C'

B'

O

M A

1

M 1 C

B

Strain

A

A'

whole hysteresis loop may approximate through the modulus of secant shear Msec. according to the formula (4.16): M sec : ¼

τc , γc

ð4:16Þ

where: γ c and τc are amplitudes of shear strain and shear stress, respectively. The surface of the hysteresis loop is related to the area, which measures energy distribution and may be expressed in the following form (4.17): ξ¼

Ap:his: WD ¼ , 4πW s 2πM sec : γ 2c

ð4:17Þ

in which: WD means dissipated energy, Ws means the highest energy of strain, and Ap.his. Means the surface of hysteresis loop. The viscotic damping can be calculated in relation to the scope of the hysteresis loop, and the strain level can be considered as an individual amplitude of cyclic strain. Therefore, in accordance with Fig. 4.35, the viscotic damping can be presented by means of the following dependency (4.18):

202

4 Testing and Durability of Soil-Steel Bridges

a)

+ 2

a

=f(

-

a'

+ 2

-

g'

a)

Mo

a

a g

a

a

-

0 g

a'

0

a

a

= f( )

g' a'

-

2

a

=f(

b)

1

1

g

M

2

a)

a'

g'

-

a'

Note: - W -W

a'

Fig. 4.36 Damping in nonlinear model: (a) hysteresis loops, (b) dissipated energy

1 β¼ 2π

! Surface of the loop CA0 C0 : Surface of triangles ðOAB þ OA0 B0 Þ

ð4:18Þ

Whereas an individual amplitude of strain can be expressed in the following form (4.19): Aε ¼

BB0 : 2

ð4:19Þ

They assume that the soil medium behaves like a damped material of viscouselastic character, which is linear only within the scope of a defined amplitude of strain. This assumption is usually used in majority of cases of dynamic analyses of soil media with low level of vibrations amplitudes (Ashmawy et al. 1995; Brinkgreve et al. 2007). In the case of viscotic damping, the hysteresis loop surface depends on frequency of variable loads, whereas in the case of linear damping it is independent of frequency. Due to the fact that some of the most often applied techniques of analysis of soil reaction use the application of comparable linear features, significant attention needs to be paid to relevant characteristics Msec. and ξ for different soil media. It is also worth underlining that, due to the fact that it is only an approximation of non-linear behaviour of soil, an equivalent linear model should not be used to anticipate permanent deformations or slide. It is related to the fact that, as it is assumed, strains are elastic and following cyclic load they regain zero. Nevertheless the assumption of linearity with iterative considering procedures (soil stiffness and damping parameters), enables solving the task as first iteration. In the case of soil medium behaviour under dynamic service load expressed as a nonlinear problem, where the loading and unloading paths do not coincide, dissipation of energy occurs in the form of the hysteresis loop (Fig. 4.36). The shape of hysteresis loop can be described by means of the following expressions (4.20), (4.21), and (4.22):

4.4 Deformation of the Backfill Caused by the Traffic Live Load

τ ¼ f ðyÞ, γ
γ  τ
τa a ¼f , 2 2 γ þ γ  τ þ τa a ¼f : 2 2

203

ð4:20Þ ð4:21Þ ð4:22Þ

Therefore, the secant shear modulus may be given the following form (4.23): M ðγ Þ ¼ M ðγ a Þ ¼

dM ðγ a Þ γ: dγ

ð4:23Þ

Whereas the hysteresis damping ratio in the form of elastic energy (4.24): 1 W ¼ γ a f ðγ a Þ, 2

ð4:24Þ

and dissipation of energy can be presented in accordance with the following formula (4.25): 2 ΔW ¼ 84

Zγa

3 f ðγ Þdγ
W 5:

ð4:25Þ

0

4.4.4

Mathematic Model of Soil Deformation

This part of chapter shows a proposition of mathematic model to describe deformations of soil layers caused by road or railway live loads. As it has been mentioned above, deformations of soil layers may occur both in micro and macro scale. Friction coefficient and soil compaction ratio are the most important factors to foresee macro deformations in soil layers located above the steel shell of a structure. Different soil models can be used for such analyses (e.g. Duncan-Chang, DruckerPrager, Coulomb-Mohr). However, it is necessary to search for such solutions that would be most accurate in mapping deformations in soil cover. To model the problem one can use, for example, an elasto-plastic model proposed by Kettil et al. (2007), using a combination of Drucker-Prager model and strength surface (Fig. 4.37). Therefore, global deformation of soil layers may be presented in the form of Eq. (4.26): eðt Þ ¼ εe ðt Þ þ εp ðt Þ þ εθ ðt Þ,

ð4:26Þ

204

4 Testing and Durability of Soil-Steel Bridges

t

Transition surface Ft

Shear failure Fs

CAP Fe

c

p

p2

c+p1 tan

(c+p 1 tan )

p

R(d+p1 tan )

Fig. 4.37 Drucker-Prager modified model (Abaqus Theory Guide 2014)

where: εe(t) – is elastic strain in time, εp(t) – is elastic strain in time caused by friction and soil compaction, εθ(t) – is a stain caused by influence of temperature in time. In comparison with complete deformation of ground layers caused by service load, influence of temperature is of minor importance and can be neglected. However, it has been retained for the sake of presentation of all external sources of influence. Non-linear elasticity law of porous materials describes elastic strain. The volume part of elastic strain εeobj: has been considered as dependant on existing pressure, in accordance with the following dependence (4.27):  εeobj: ¼ κe ln

 pet , p þ pet

ð4:27Þ

where: κe and pet are material constants. Relation between divergence of stress σ dev ¼ σ – pm and elastic divergence of strain εedev ¼ εe
εeobj: m may be given the following form (4.28): cσ dev ¼ 2G c εedev ,

ð4:28Þ

where: G¼

  3ð1
2νÞ p þ pet e exp ε obj: , 2ð 1 þ ν Þ κ e

ð4:29Þ

4.4 Deformation of the Backfill Caused by the Traffic Live Load

205

and ν is the Poisson coefficient. Thermal strains are assumed to be proportional to temperature. Therefore: εθ ¼ α m θ:

ð4:30Þ

Plastic strains of soil medium can be given the following form, using the DruckerPrager criterion (4.31): F D
P ¼ q
p tan φ
c  0,

ð4:31Þ

and CAP model (Sandler et al. 1974), expressed in the form of (4.32):

F CAP

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 12 u u u Rq B C 2 ¼u tð p
pa Þ þ @ α A
Rðc þ pa tan φÞ  0, 1þα
cos φ

ð4:32Þ

where: pa ¼

pb
Rc , 1 þ R tan φ

ð4:33Þ

φ – angle of internal friction, c – cohesion, pb – hydrostatic compressive stresses, α and R are constants, which describe the form of the borderline curve, p is an average stress determined on the basis of the following dependence (4.34): 1 p ¼ ðσ 1 þ σ 2 þ σ 3 Þ, 3

ð4:34Þ

and q is the principal stresses referred to as the deviator of stresses in accordance with the (4.35): rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 q¼ ðσ
σ 2 Þ2 þ ðσ 2
σ 3 Þ2 þ ðσ 3
σ 1 Þ2 : 2 1

ð4:35Þ

Whereas the plasticity surface of Drucker-Prager can be given the following form (4.36): f ¼ q
ptanβ
c,

ð4:36Þ

where c and β depend on cohesion c and internal friction angle φ, respectively. Non-associated flow rule is used by the application of the dilation angle (ψ) varied from the internal friction angle (φ). In-plane state of strains, the parameters c and β from Eq. (4.36) are related to durability in-plane state of strains and dilation parameters (ψ, c, φ) by the below dependencies (4.37) and (4.38):

206

4 Testing and Durability of Soil-Steel Bridges

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi tan β 3 ð9
tan 2 ψ Þ , sin φ ¼ 9
tan β tan ψ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 ð9
tan 2 ψ Þ c cos φ ¼ d: 9
tan β tan ψ

ð4:37Þ ð4:38Þ

Velocity of plastic strains can be defined by means of potential flow function G and multiplier λ._ Therefore, for Drucker-Prager surface the following dependency is obtained (4.39): ∂GD
P ε_p ¼ λ_ , ∂σ

ð4:39Þ

where:

GD
P

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 12 u u u q B C 2 ¼u tððpa
pÞ tan φÞ
@ α A, 1þα
cos φ

ð4:40Þ

whereas, for the border surface „CAP” the following dependence is obtained (4.41): ε_p ¼ λ_

∂GCAP , ∂σ

ð4:41Þ

where:

GCAP

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 12 u u u Rq B C 2 ¼u tðpa
pÞ
@ α A: 1þα
cos φ

ð4:42Þ

The low of hardening is used to describe development of equivalent plastic strains in accordance with the formula (4.43):  εeðpb Þpobj:

p

¼ κðN Þ ln

 ppt , pb þ ppt

ð4:43Þ

where:   κðN Þp ¼ κp0 1 þ k1 ðN
1Þk2 ,

ð4:44Þ

where: κ p0 , k1, k2 and ppt are material constants, and N means the number of load cycles. Whereas development of damages to soil medium (backfill) in micro scale can be described by means of constitutive models determining behaviour of loose materials

4.5 Summary

207

at the interface of individual grains (micromechanics). Numerical and lab experiments show unequivocally that stresses in loose materials are transferred by means of heterogeneous network (Cates et al. 1998). Deformations in soil medium comprise making and loosing contact among individual grains. These changes mean continuous changeability of stress-strain relation and, at the same time, change to porosity ratio under external live loads. Therefore, tensor of stress can be expressed as follows (4.45): σ ij ¼

1X b b f x, A b i j

ð4:45Þ

where: xb is the point of force application fb, A is a surface enclosed by membrane. Principal values of the tensor help define mean normal stresses, in accordance with the formula (4.46): p¼

ðσ 1 þ σ 2 Þ , 2

ð4:46Þ

ðσ 1
σ 2 Þ : 2

ð4:47Þ

and deviator of stress with Eq. (4.47): q¼

Axial strain can be calculated by means of the dependence (4.48): ε1 ¼

ΔH , H0

ð4:48Þ

where: H is the height of soil sample. Whereas volumetric strains can be expressed as follows (4.49): εV ¼

4.5

ΔA : A0

ð4:49Þ

Summary

Durability of soil-steel bridges is a very complex problem determined by influence of service loads and environmental factors. The factors may cause a number of negative effects, and in terms of bearing capacity they are: (i) fatigue cracks, (ii) deformations of soil layers (backfill) surrounding the shell (iii) loss of (or decrease in) interactions between the shell and the soil. Whereas in terms of

208

4 Testing and Durability of Soil-Steel Bridges

the environment they are all sorts of corrosion types, abrasion of corrosion protection coatings, loss of wall thickness of steel. Apart from the above factors, durability of soil-steel bridges also depends on the following elements: – thickness of corrugated plate, – quality of mounting works (possible damages to steel sheets and/or corrosion protection at the time of execution of works), – quality and thickness of corrosion and abrasion protection, – quality and type of backfill and cover height at the crown of the structure, – environment of service (environmental factors), – road category (traffic volume), – big differences in temperatures between winter and summer, – quality of maintenance and regularity of repair works of a structure. Designers and people responsible for maintenance of bridge structures need to realize that soil-steel bridges and culverts are specific structures and know possible related hazards. All of these will allow for safe and long lifetime of these structures.

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Final Recapitulation

Soil-steel bridges and culverts are getting widely used in the transport engineering as an alternative to traditional steel or concrete bridge structures. These structures consist of the corrugated steel plates and properly compacted backfill. The wellknown advantages that justify the choice of such solution are mainly short period and relatively low cost of construction. The load-carrying capacity element of these structures is the soil-steel composite system that uses arching of the load in soil and interaction between flexible steel shell and backfill. Backfill is the key element in these structural solutions. Selection of soil (backfill), which have proper characteristics and its appropriate arrangement and compaction play a key role in achievement of required load carrying capacity of soil-steel bridges. The construction of soil-steel bridges does not cause too much problems during construction, assuming that the appropriate technological regime is maintained. However, the current design process of soil-steel bridges is far from the real possibilities of these structures. Currently, designed soil-steel bridges and culverts are in most cases overdesigned. This has been proved experimentally many times. This is related to imperfect design methods, which are mostly based on unrealistic premises about the behavior of soil-steel bridges and the use of too large safety factors. However, it should be added here that building an appropriate analytical design method is not an easy task, because it should first and foremost be taken into account in the correct way: • • • • •

the interaction between the steel shell and the soil, the shell flexibility, the arching effect in soil, load distribution through soil layers, long-term non-linear behavior of soil.

Good design effects can be obtained using numerical methods with the use of specialized computer software based on the finite element method, but this requires knowledge of advanced computer modeling procedures. For the design of soil-steel bridges with large spans over 15.0 m, the finite element method is the most suitable. © Springer Nature Switzerland AG 2020 D. Beben, Soil-Steel Bridges, Geotechnical, Geological and Earthquake Engineering 49, https://doi.org/10.1007/978-3-030-34788-8

213

214

Final Recapitulation

The experimental tests carried out show that the dynamic load more influences on the degree of effort of soil-steel bridges than the same load but statically placed on the bridge. This is reflected in the level of dynamic factors (dynamic amplification factors). Even soil-steel bridges with a high soil cover are achieving high dynamic amplification factors. It is related to the type of load and the quality of the backfill used for the construction of a given bridge. An important aspect is also the analysis of the frequency of vibrations and bridge accelerations caused by passing vehicles. In this case, the most important role is played by the backfill, which is a natural vibration damper. Therefore, it is extremely important that the backfill has the appropriate quality and strength parameters. While the durability of soil-steel bridge is determined primarily by the relevant anti-abrasion and corrosion protection of steel elements, as well as the correct execution of other works, mostly laying and compaction of backfill. The corrosivity tests of the backfill in selected soil-steel bridges show that with the passage of years it tends to increase the degree of aggressiveness. This aspect should be taken into account when designing the corrosion protection of the steel shell, especially from the backfill side. The presented book does not answer all questions and concerns regarding the design, maintenance and durability of soil-steel bridges. Currently, various research works on these facilities are under way at various research centers in the world aimed at: • improvement of design methods (obtaining larger spans, reducing steel consumption), • assessments of seismic impacts (impact of earthquakes) and anthropogenic (for example rockbursts in mines), • evaluation of fatigue effects (for screw connections and soil-steel composite system), • full dynamic identification with theoretical verification with the use of numerical tools, • application other metals to construct the shell structure, • application of absorb materials (expanded polystyrene (EPS), metal geofoams and worn tires), to minimize live loads and earthquake effects, • optimization of shell foundations.