Geomechanics and geodynamics of rock masses: proceedings of the 2018 European Rock Mechanics Symposium 9781138616455, 9781138617353, 9781138617360, 9780429461774, 9780429461767, 1138616451

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VOLUMES1and2

GEOMECHANICS AND GEODYNAMICS OF ROCK MASSES

PROCEEDINGS OF THE 2018 EUROPEAN ROCK MECHANICS SYMPOSIUM (EUROCK 2018, SAINT PETERSBURG, RUSSIA, 22–26 MAY 2018)

EUROCK2018: Geomechanics and Geodynamics of Rock Masses VOLUMES 1 and 2 Editor Vladimir Litvinenko Rector, Saint-Petersburg Mining University, St. Petersburg, Russia Chairperson of the EUROCK 2018 Organizing Committee

CRC Press/Balkema is an imprint of the Taylor & Francis Group, an informa business © 2018 Taylor & Francis Group, London, UK Typeset by V Publishing Solutions Pvt Ltd., Chennai, India Printed and bound in Great Britain by CPI Group (UK) Ltd, Croydon, CR0 4YY All rights reserved. No part of this publication or the information contained herein may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, by photocopying, recording or otherwise, without written prior permission from the publisher. Although all care is taken to ensure integrity and the quality of this publication and the information herein, no responsibility is assumed by the publishers nor the author for any damage to the property or persons as a result of operation or use of this publication and/or the information contained herein. Published by: CRC Press/Balkema Schipholweg 107C, 2316 XC Leiden, The Netherlands e-mail: [email protected] www.crcpress.com – www.taylorandfrancis.com ISBN: 978-1-138-61645-5 (set of 2 volumes) ISBN: 978-1-138-61735-3 (Vol 1) ISBN: 978-1-138-61736-0 (Vol 2) ISBN: 978-0-429-46177-4 (eBook, Vol 1) ISBN: 978-0-429-46176-7 (eBook, Vol 2)

Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Table of contents

Preface

xxi

Committees

xxvii

VOLUME 1 Key lectures Advancement of geomechanics and geodynamics at the mineral ore mining and underground space development V. Litvinenko Complete laboratory experimentation on hydraulic fracturing H.H. Einstein, O. Al-Dajani, B. Gonçalves da Silva, G. Bing Li & S. Morgan Strength and deformability of brittle polycrystalline materials in multiaxial stress-strain state: Rupture energy evaluation for brittle materials E.G. Gaziev

3 17

31

Anisotropic and nonlinear properties of rock including fluid under pressure I. Gray, X. Xhao & L. Liu

41

Dynamic rock support in burst-prone rock masses C.C. Li

47

Deep mining rock mechanics in China—the 3rd mining technology revolution M. He

63

Diagnostics and prediction of geomechanical objects state based on back analysis L. Nazarova

73

Rock mechanics and environmental engineering for energy and geo-resources F.L. Pellet

87

The development of geomechanical engineering in mining V.L. Trushko, I.B. Sergeev & A.N. Shabarov

95

Review papers Geodynamic safety of subsurface management A.N. Shabarov & S.V. Tsirel

105

Methods and approaches to geomechanical ensuring of mining safety at potash mines A.A. Baryakh & V.A. Asanov

121

The Ural scientific school of geomechanics: Fundamental and applied research S.V. Kornilkov, A.D. Sashourin & A.A. Panzhin

131

v

Geomechanical substantiation of mining in rockburst-hazardous deposits A.A. Kozyrev, V.I. Panin & I.E. Semenova

139

The researches of burst-hazard on mines in Russian Far East I.Ju. Rasskazov, B.G. Saksin, M.I. Potapchuk & P.A. Anikin

153

Modeling geomechanical and geodynamic behavior of mining-altered rock mass with justifying mechanisms of initiation and growth of failure zones V.N. Zakharov & O.N. Malinnikova

167

Physical and mechanical properties of fractured rock Determination of the errors arising from apparatus and operator during applying the point load index D. Akbay & R. Altindag

181

Determination of rock deformability using the coastal sections of concrete dams as a large-scale stamp E.S. Argal & V.M. Korolev

189

Characterization of hydromechanical damage of claystones using X-ray tomography C. Auvray & R. Giot

193

Creation of regional database of physical-and-mechanical characteristics of man-induced dispersed soils S.P. Bakhaeva & D.V. Guryev

199

Analysis of crack initiation and crack damage of metamorphic rocks with emphasis on acoustic emission measurements K. Bartmann & M. Alber

205

Comparison between conventional and multi-sensor geotechnical core logging methods M. Bhuiyan & K. Esmaieli

211

Graphical evaluation of 3D rock surface roughness: Its demonstration through direct shear strength tests on Bátaapáti Granites and Mont Terri Opalinus Claystones I. Buocz, N. Rozgonyi-Boissinot & Á. Török

219

Feasibility study on the influence of discontinuities on anisotropic rock masses regarding the stiffness A. Buyer, L. Gottsbacher & W. Schubert

227

The effect of mining layout, regional pillars and backfill support on delaying expected shaft deformation at Bambanani mine P.M. Couto

235

Fractured clay rocks as a surrounding medium of underground structures: The features of geotechnical and hydrogeological assessment R.E. Dashko & P.V. Kotiukov

241

New methods to fit a Hœk Brown failure criterion to data sets from multiaxial laboratory tests A. Defay & S. Maïolino

249

Application of a new clustering method for automatic identification of rock joint sets S. Fereshtenejad & J.-J. Song Experimental evidences of thermo-mechanical induced effects on jointed rock masses through infrared thermography and stress-strain monitoring M. Fiorucci, G.M. Marmoni, S. Martino & A. Paciello

vi

255

263

A correlation between thermal conductivity and P-wave velocity of damaged granite P.K. Gautam, A.K. Verma, P. Sharma & T.N. Singh

269

Characterization of shear behavior of discontinuities of Brioverian schist S. Guiheneuf, D. Rangeard, V. Merrien-Soukatchoff & M.-P. Dabard

275

Effects of stress, anisotropy and brittle-to-ductile transition on fracturing and fluid flow in shales M. Gutierrez Geomechanical characterization of the upper carboniferous under thermal stress for the evaluation of a High Temperature-Mine Thermal Energy Storage (HT-MTES) F. Hahn, T. Jabs, R. Bracke & M. Alber

281

287

Investigating the mechanism contributing to large scale structurally driven hangingwall instabilities on the UG2 reef horizon A.G. Hartzenberg & M. du Plessis

293

Strength estimation of fractured rock using compression—a specimen with spherical indenters V.A. Korshunov, D.A. Solomoychenko & A.A. Bazhukov

299

Measurements of thermal properties of rock samples under high temperature conditions W. Lin, O. Tadai, T. Sugimoto, T. Hirose, W. Tanikawa & Y. Hamada

307

Static and dynamic effective stress coefficient of St. Peter sandstone during depletion and injection X. Ma & M.D. Zoback

313

Jointed rock mass characterization using field and point-cloud data M. Marjanović, M. Pejić, J. Krušić & B. Abolmasov

319

New failure criterion for rocks by using compression tests C.G. Nicieza, M.I.Á. Fernández, C.C.G. Fernández, R.F. Rodríguez & J.R.G. Menéndez

325

Ore strength property evaluation in the design of ore preparation cycles N.V. Nikolaeva, T.N. Aleksandrova & A.M. Elbendari

333

Geomechanical behaviour of a rock barricade and cemented paste backfill: Laboratory experiments on a reduced-scale model M. Nujaim, C. Auvray & T. Belem

339

Multivariate Artificial Neural Network (ANN) models for predicting uniaxial compressive strength from index tests B.S. Othman, N.T. Özcan, A. Kalender & H. Sönmez

345

Investigation of scale effects on uniaxial compressive strength for Kars-Kagızman Rock Salt, Turkey I. Ozkan & Z. Kızıltaş

353

Practical aspects of boundary condition selection on direct shear laboratory tests T.R.M. Packulak, J.J. Day & M.S. Diederichs

361

Experimental studies of saliferous rock direct tension I. Pankov, V. Asanov, V. Kuzminykh & I. Morozov

369

Understanding tilt-test results on saw-cut planar rock surfaces from a statistical perspective I. Pérez-Rey, L.R. Alejano, J. Martínez, M. Muñiz & J. Muralha

vii

377

The use of InSAR as a tool to manage precursor ground displacement in rock masses J. Raventós, C. Sánchez & A. Conde

383

Correlations of geomechanical indices for Andean environments S.S. Rodríguez, J.D.L. Valero & C.L. Gómez

389

Thermal behavior of Indian shale rock after high temperature treatment S. Sardana, A.K. Verma, M.K. Jha & P. Sharma

395

Swelling pressures of some rocks using different test procedures L. Selen, K.K. Panthi & M.R. Vergara

401

The implementation of de-stress gold mining technique along complex geological structures and heavily fractured ground conditions F. Sengani & T. Zvarivadza

411

The use of face perpendicular preconditioning technique to destress a dyke located 60 m ahead of mining faces F. Sengani & T. Zvarivadza

417

Prospects of the physical model-based study of geomechanical processes A.N. Shabarov, B.Yu. Zuev & N.V. Krotov

423

Long term creep pressuremeter tests in soft rock (St. Petersburg, Russia) A. Shidlovskaya, J.-L. Briaud, M. Chedid & S. Tafti

431

Reviewing length, density and orientation data of fractures in a granitic rock mass G. Somodi, Á. Krupa, L. Kovács & G. Szujó

439

Change in elastic properties of hard rocks passing from thawed to frozen state S.V. Suknev

445

Tensile behavior of rock under intermediate dynamic loading for Hwangdeung granite and Linyi sandstone Y. Wicaksana, S. Jeon, G. Min & S. Cho Development of a rock blasting management system M. Yamagami & S. Katayama

451 457

Experimental study on damaged zone around an opening due to thermo-mechanical loading N. Zhang, S. Jeon & S. Wang

465

Ground closure monitoring systems on trial in deep to ultra-deep mechanized gold mining T. Zvarivadza & F. Sengani

471

Geophysics in rock mechanics Study of factors behind rock slope displacement at Higashi Shikagoe limestone quarry, Japan C.N. Bandazi, R. Uy, J.-i. Kodama, Y. Fujii, D. Fukuda, H. Iwasaki & S. Ikegami

479

Seismic measurements to recognize rock mass damaging induced by recurrent vibrations D. D’Angiò, R. Iannucci, L. Lenti, S. Martino & A. Paciello

485

Dynamic investigations of EDZs from Bátaapáti radwaste repository based on passive seismoacoustic measurements F. Deák & I. Szűcs

491

viii

Reactivation of the old landslide caused by the land development—the case study L. Florkowska, I. Bryt-Nitarska, R. Gawałkiewicz & R. Murzyn

499

Rock stress assessment based on the fracture induced electromagnetic radiation V. Frid & S.N. Mulev

505

Modern principles of nondestructive stress monitoring in mine workings—overview V. Frid & A.N. Shabarov

513

Empirical-Statical-Dynamic (ESD) methodology for extrapolation in rock mechanics M. Jovanovski, I. Peshevski & J. Papic

519

State-of-the-art damage assessment methods for brittle rock using digital image correlation and infrared thermography M. Karakus, S. Akdag, L.S. Randhawa, Y. Zhao & Z. Cao

525

The increasing of exploitation safety of potassium salt deposit based on geologicalgeomechanical simulation Yu. Kashnikov, A. Ermashov, D. Shustov & D. Khvostantcev

533

Effect of viscosity of fault filling on stick-slip dynamics of seismogenic fault motion: A numerical approach S. Kostić, N. Vasović & I. Franović

539

Integrated seismic measurement techniques to determine the velocity distribution near underground drifts at the Sanford Underground Research Facility (SURF) W.M. Roggenthen

545

Geophysical monitoring as an inherent part of the technological process in deep open pits V.V. Rybin, V.I. Panin, M.M. Kagan & K.N. Konstantinov

551

Changes in the time of the properties of rock foundations of large hydraulic structures according to geophysical monitoring data A.I. Savich, E.A. Gorokhova & M.M. Ilin

557

Recovery of in-situ orientation of drilled rock core samples for crustal stress measurements T. Sugimoto, Y. Yamamoto, W. Lin, Y. Yamamoto, T. Hirose & N. Kamiya

563

Monitoring and analysis of a large mass movement area in clay endangering a motorway in Bavaria, Germany L. Wilfing, C. Meier, C. Boley & T. Pfeifer

567

Rock mass strength and failure On a model of geomechanical effect of underground explosion in the massif of block-like structure and the mechanism of rock destruction V.V. Adushkin, I.V. Brigadin & S.A. Krasnov

575

Effect of thermal damage on strain burst mechanism of brittle rock using acoustic emission S. Akdag, M. Karakus, A. Taheri, G. Nguyen & H. Manchao

581

Gel explosives—a tool to improve the efficiency of drilling and blasting operations V.E. Annikov, N.I. Akinin, V.A. Belin, D.I. Mikheev, S.I. Doroshenko, I.V. Brigadin, V.M. Gubaidullin, A.V. Shirokov, A.N. Hasov & V.M. Mytarev

ix

587

Dynamical destruction of rock mass due to excavation of a coal seam A.S. Batugin, V.N. Odintsev, K.S. Kolikov & Eu.I. Hotchenkov

593

Quantitative assessment of variability in values of Geological Strength Index (GSI) A. Bedi, M. Invernici & J.P. Harrison

599

The effect of stress level on the compressive strength of the rock samples subjected to cyclic loading M.H. Beşer & K. Aydiner

605

Normandy cliff stability: Analysis and repair J.-L. Briaud

611

Analytical formulation of stand-up time based on 1989 Beniawski’s chart E. Estébanez & A. Lage

617

Assessing the influence of discontinuities and clayey filling materials on the rock slope instability D. Fereidooni

625

Laboratory investigation of crack initiation on hourglass-shaped granite specimens L. Jacobsson & J.E. Lindqvist

633

Comparison of different approaches to predict the shear strength of large rock discontinuities M. Jeffery, L. Lapastoure Gritchou, A. Giacomini, V. Griffiths & O. Buzzi

639

Effects of excavation damage on the electrical properties of rock mass P. Kantia, R. Kiuru & M. Rinne Study of physical-mechanical properties of hard rocks under water-saturated conditions N. Kuznetcov, I. Fedotova & A. Pak On the effectiveness of rocks and materials destruction based on shock-wave cutting technology N.P. Mikhailov, E.A. Znamenskiy, S.I. Doroshenko, Y.A. Telegin, I.V. Brigadin, V.M. Gubaidullin & G.P. Paramovov

647

653

659

Modelling of fault reactivation in applications of mining and petroleum industry R. Quevedo, C. Mejia & D. Roehl

663

Acoustic emission precursor criteria of rock damage A.O. Rozanov, D.N. Petrov, A.M. Rozenbaum, A.A. Tereshkin & M.D. Ilinov

669

Numerical simulation of stress distribution within a rock discontinuity asperity A. Sainoki, Y. Obara & H.S. Mitri

673

Thermo-temporal behaviour of uniaxial compressive strength of a fine-grained Indian sandstone N. Sirdesai, V. Srinivasan, R. Singh & T.N. Singh

681

Acoustic and failure behaviour of Gondwana shale under uniaxial compressive and indirect Brazilian tensile loading—an experimental study A. Tripathy, V. Srinivasan, K.K. Maurya, N. Sirdesai & T.N. Singh

687

Rocks drillability classification based on comparison of physico-mechanical properties with drilling rate timing A. Trofimov, A. Rumyantsev, V. Vilchinsky, K. Breus & A. Skokov

695

x

About specific energy intensity behavior under multistage triaxial compression of sandstone specimens P.A. Tsoi, O.M. Usol’tseva & V.N. Semenov The relationship between strain, microstrain, temperature fields and microseismic emission parameters in geomodels with hole under uniaxial and biaxial loading V.I. Vostrikov, O.M. Usol’tseva, P.A. Tsoi, V.N. Semenov & O.A. Persidskaya Monitoring of coal pillars yielding during room and pillar extraction at the great depth P. Waclawik, R. Kukutsch, P. Konicek & V. Kajzar

701

705

711

Nonlinear problems in rock mechanics Ultimate bearing capacity analysis of foundation on rock masses using the Hoek-Brown failure criterion A.A. Chepurnova

719

Conception of highly stressed rock and rock mass—as the step to theory of hierarchical cracking mesostructures M.A. Guzev, V.V. Makarov & V.N. Odintsev

727

Zonal type mesostructures around single openings in deep rock mass L.S. Ksendzenko & V.V. Makarov

733

Models of strength and fracture of rocks A.G. Protosenya & M.A. Karasev

739

Geophysics in rock mechanics Tunnel restoration in unstable rock masses: Numerical analysis and validation of monitoring data from innovative instrumentation A. Segalini, A. Carri, R. Savi, E. Cavalca, C. Alessio & G. Kalamaras

747

Forecast of rock mass stability under industrial open pit mine facilities during the open pit deepening. A case study of the Zhelezny open pit, JSC Kovdorsky GOK I.M. Avetisian & I.E. Semenova

755

Benefits and limitations of applying directional shear strengths in 2D and 3D limit equilibrium models to predict slope stability in highly anisotropic rock masses N. Bar, G. Weekes & S. Welideniya

761

Mathematical modelling of limit states for load bearing elements in room-and-pillar mining of saliferous rocks A. Baryakh, S. Lobanov, I. Lomakin & A. Tsayukov

767

Quantitative risk analysis of fragmental rockfalls: A case study J. Corominas, G. Matas & R. Ruiz-Carulla Experimental and numerical investigation the divergence of horizontal and vertical displacement in longwall mining E.T. Denkevich, O.L. Konovalov & M.A. Zhuravkov Numerical analysis of the rheological behaviour of the Socompa debris avalanche, Chile F. Vagnon, M. Pirulli, I. Manzella, K. Kelfoun & A.M. Ferrero Numerical study on the strategies to reduce the risk of induced seismicity in an enhanced geothermal system W. Feng, Z. Hou, J. Liao & P. Were

xi

775

781 785

791

The reasons of landslides activization at Sakhalin Island (on the example of landslide exploration at the river Lazovaya) I.K. Fomenko, D.N. Gorobtsov, V.V. Pendin & M.E. Nikulina

797

Prediction of rock movements using a finite-discrete element method B. Ilyasov, A. Makarov & I. Biryuchiov

805

Simulation of fracture propagation depth and failure in long hole open stoping P.J. le Roux & K.R. Brentley

811

Hydraulically fractured hard rock aquifer for seasonal storage of solar thermal energy M. Janiszewski, B. Shen & M. Rinne

821

Peculiarities of numerical modeling of the conditions for the formation of water inflows into open-pit workings when constructing the protective watertight structures at the Koashvinsky quarry S. Kotlov, D. Saveliev & A. Shamshev

827

Numerical study of the hydraulic fracturing and energy production of a geothermal well in Northern Germany M. Li, M.Z. Hou, L. Zhou & Y. Gou

833

A mathematical approach for prediction of inclinometer measurements in open-pit coal mine slopes M. Mesutoglu & I. Ozkan

839

Comparison of limit equilibrium and finite element methods to slope stability estimation A.B. Makarov, I.S. Livinsky, V.I. Spirin & A.A. Pavlovich

845

Analyzing slope stability in bimrocks by means of a stochastic approach M.L. Napoli, M. Barbero & C. Scavia

851

3D finite element modelling of fracturing in heterogeneous rock: From pure solid to coupled fluid/solid analysis R. Pakzad, S. Wang & S.W. Sloan

859

Global sensitivity analysis on thermo-hydro-mechanical coupled processes in a low strength sedimentary rock S. Parsons, G. Stuart, B. Murphy & D. Price

865

The effect of rock mass stiffness on crush pillar behaviour M. du Plessis & D.F. Malan

871

Discrete element modelling of a soil-mesh interaction problem A. Pol, F. Gabrieli, K. Thoeni & N. Mazzon

877

Numerical modelling of fracture processes in thermal shock weakened rock M. Pressacco & T. Saksala

883

Static and dynamic analysis of a rock slope in Sikkim: A case study N.R. Kallam & M.K. Adapa

889

Finite-element analysis as a means of solving geomechanics problems in deep mines A.E. Rumyantsev, A.V. Trofimov, V.B. Vilchinsky & V.P. Marysiuk

895

Numerical modelling of rock fracture with a Hoek-Brown viscoplastic-damage model implemented with polygonal finite elements T. Saksala

903

Numerical modeling and back analysis method for optimal design of Butterfly Valve Chamber (BVC) of Tehri HPP D.V. Singh, R.K. Vishnoi, T.S. Rautela, U.D. Dangwal & A.K. Badoni

909

xii

3D finite element modelling of chain-link drapery system S. Tahmasbi, A. Giacomini, C. Wendeler & O. Buzzi

917

Analysis of instability mechanisms of a high rock prism standing on a cliff face L. Verrucci, P. Tommasi, A.D. Giulio, P. Campedel & T. Rotonda

923

The propagation of hydraulic fractures in coal seams based on discrete element method Y. Lu, Z. Yang, V.V. Shelepov, J. Han, X. Li, Y. Zhu, J. Guo & Z. Ma

929

The influence of the interface of drilled socketed shafts and rock mass on their behavior M.G. Zertsalov, V.E. Merkin & I.N. Khokhlov

937

The determination of crack resistance of circular shaped fiber reinforced concrete tunnel lining by means of linear fracture mechanics M. Zertsalov, V. Merkin & E. Khoteev

943

Kinematics and discreet modelling for ramp intersections T. Zvarivadza & F. Sengani

949

Author index

955

VOLUME 2 Mineral resources development: Methods and rock mechanics problems Prediction of excavation damaged zone in underground blasts using artificial neural networks A. Asadi, A. Abbasi & E. Asadi

963

Using large-scale geotechnical modelling to solve mining tasks at a gold-copper mine I. Avramov, T. Velkov, I. Garkov, D. Stefanov & I. Georgakiev

967

Geotechnical data management and visualization systems: Meeting the data challenge of the 21st century and maximizing value for open pit mines N. Bar, S. Nicoll, M. Reynolds & D. Bran

973

On sinkhole formation at the site of fresh water breakthrough into salt mine A.A. Baryakh, S.Y. Devyatkov & A.K. Fedoseev Experimental and theoretical studies of undermined strata deformation during room and pillar mining A. Evseev, V. Asanov, I. Lomakin & A. Tsayukov Progressive damages in hard rock by utilising an oscillating undercut technology M. Ghamgosar, S. Duffield & N. Erarslan An integrated geostatistical-geomechanical approach for predicting potential risk of failure in pit walls N. Ghasempour, K. Esmaieli & H. Eivazy

979

985 991

999

A new method on extraction of two thick seams simultaneously on extremely difficult ground condition—a case study C.N. Ghosh, Prashant, P.K. Mandal & S.K. Behera

1005

The study and test on the development regularity of the mining speed of coal seam separated from the overburden strata G. Yu, B. Yu, S. Lu, S. Yuan, I.V. Menshova, M. Kovalenko, Y. Qing & X. Zeng

1011

xiii

Rock mechanics implications of microwave treatment of rock as part of a hybrid system for mechanical excavation of rock for civil and mining applications P. Hartlieb & J. Rostami Subsidence assessment of ghaplogh stope and pillar mine by using numerical analysis Y. Jalili Kashtiban, K. Shahriar & E. Bakhtavar

1017 1025

Geomechanical evaluation of the parameters of the open-stoping method for the Oleniy Ruchey deposit A.A. Kozyrev, I.E. Semenova & A.V. Zemtsovskii

1031

Experience of geomechanical research and calculations toward ore deposit development in complex mining conditions A. Kuranov, I. Bagautdinov, A. Popov, V. Marysiuk & V. Trusov

1037

Rock mechanics of pillars extraction A. Makarov & D. Mosyakin

1043

The need for formal rock engineering expertise in deep mining J. Maritz & H. Wagner

1047

Geomechanical substantiation of calculate indicators of the rock mass strength for slopes stability analysis of open pit A.A. Pavlovich, V.A. Korshunov, S.V. Tsirel, N.YA. Melnikov & A.A. Bazhukov

1053

Forecast of probability of shock hazard in conditions of underground development of Zarmitan gold deposit zones S. Sayyidkosimov & A. Kazakov

1059

Bioleaching and engineering properties of ore materials (overview) A.V. Shidlovskaya, A.A. Timchenko & M.E. Smith

1065

DEM modeling of the ore discharge from blocks A.V. Trofimov, I.V. Amosov, A.Ju. Feoktistov & G.A. Iusupov

1071

Formation of technogenic zones of effective degassing at development of coal-bed V.V. Zubkov & I.A. Zubkova Zones of technogenic water-conducting cracks by room-and-pillar mining V.V. Zubkov & I.A. Zubkova Evaluation of factors influencing the effectiveness of backfill support in mechanized deep to ultra-deep gold mining T. Zvarivadza & F. Sengani

1075 1081

1085

Rock mechanics and underground construction in mining, hydropower industry and civil engineering Mixed Face Conditions (MFC) in hard rock TBM drives—causes, effects and solutions M. Alber, R. Plinninger & J. Düllmann Plunge pool project and implementation at the Lom Pangar dam site (Cameroon) F. D’Alessandro, M. L’Hostis, C. Grouset & J.-C. Yogo The earth settlements prediction method due to tunnels construction through tunnel boring machines with active face support pressure based on multivariate numerical modelling N.A. Belyakov

xiv

1093 1101

1109

Stress corrosion failure of cable bolts in underground mines H. Chen, H. Miller, S. Wu, H.L. Ramandi, A. Crosky & S. Saydam

1115

Preliminary results of gypsum mechanical characterization C. Caselle, S.M.R. Bonetto, F. Vagnon & D. Costanzo

1123

Water inflow prediction in tunneling on the base of geostructural survey M. Coli, N. Coli, A. Pinzani, G. Pranzini & M. Tanzini

1129

Multivariable effect of hydrogeological conditions on the long-term stability of structures on a rock foundation R.E. Dashko & Y.A. Lebedeva

1137

Analysis and comparison of the measurements of Fréjus road tunnel and of its safety gallery M. De La Fuente, R. Taherzadeh, J. Sulem & D. Subrin

1143

Geomechanical aspects of the developing of man-made massives of tailing dams at the mining enterprises A.M. Galperin, V.V. Moseykin & S.A. Punevsky

1149

Strength behaviour of Middle Siwalik sandstone under uniaxial and triaxial conditions G. Mainak, K.S. Rao & S. Tarun

1155

Modelling the process of rock landslides cave-in through the program suite Rocscience D.N. Gorobtsov, I.K. Fomenko, V.V. Pendin & M.E. Nikulina

1165

Numerical simulation of the multistage hydraulic fracturing and production in a tight gas horizontal well—history matching and preliminary optimization Y. Gou, W. Feng, M. Li & M.Z. Hou

1173

Evaluation of effective strength parameters in mudrocks C. Günther, R. Kauther & C. Lempp

1179

Variation of laboratory test results with specimen size in carbonates of Bavarian Malm N. Hedtmann & M. Alber

1185

Integration of the analytical, empirical, and numerical methods in analyzing support requirements for tunneling in weak rock mass S.H. Prassetyo & M. Gutierrez

1191

Numerical and field investigation for the stability analysis of a powerhouse cavern in dolomitic limestone N. Houshmand, K. Shahriar, H. Zarei & A. Kamali

1197

Comparison between an energetic continuum approach and a local failure criterion for rock fracture prediction J. Justo, J. Castro, S. Cicero, M.A. Sánchez-Carro & C. Sagaseta

1203

Challenging estimation of seepage in powerhouse cavern and drainage tunnel in Iran A. Kamali, K. Shahriar, M. El Tani, A. Aalianvari & M.A. Gholami

1209

Roadway slope stability assessment in mudstone layers of Sochi (Russia) K. Kang, O.V. Zerkal, S. Huang & A.A. Ponomarev

1217

Searching for indicators of excavation damage using R statistics environment R. Kiuru, P. Kantia & M. Rinne

1223

Estimation of coal cutting force based on the impact of geomechanical factors S. Kostić, J. Trivan & N. Gojković

1229

xv

Comprehensive earth scientific documentation and data processing applying GIS technologies Á. Krupa, L. Kovács, G. Szujó, G. Somodi & R. Schön

1235

Geomechanical provision of phosphogypsum stockpiling in high stacks Yu.I. Kutepov, N.A. Kutepova, B.V. Levin & V.E. Mironov

1241

An analytical model for load-displacement performance of modified cable bolts D. Li, H. Masoumi, S. Saydam & P.C. Hagan

1249

Improving stopes stability limits using Mineroc software R. Miranda, J. Vallejos, J. Azorin, D. Chavez, M. Mondaca, C. Garrido & O. Catalan

1259

Challenges related to water inflow during construction of deep Norwegian subsea tunnels B. Nilsen

1267

Numerical model of fluid-saturated rock mass with phase transitions as a theoretical basis for artificial ground freezing control system I. Panteleev, A. Kostina, M. Zhelnin, O. Plekhov & L. Levin

1273

The results of comprehensive studies of properties of the foundation of the concrete dam in Yakutia V.I. Rechitsky, R.S. Zuzin, A.M. Zamahaev & V.K. Vavilova

1279

TBM performance assessment of an exploratory tunnel in hard rock A. Rispoli, A.M. Ferrero, M. Cardu & A. Farinetti Verification of a prediction method for ground conditions ahead of a tunnel face by means of inclination monitoring K. Sakai, T. Tani, T. Aoki & H. Ohtsu Features of mining and geomechanical justification of the parameters of the system for the development of soluble salt deposits through wells drilled from the earth surface A.Yu. Sapachev & R.Yu. Sapachev

1287

1297

1305

In-situ estimation of stress-strain behavior of reinforced-concrete landing support S. Sergeev, A. Zinchenko & G. Yurchenko

1311

Assessment of anisotropic deformation properties of tuff by a single test on a single specimen Y. Togashi, M. Kikumoto, K. Tani, K. Hosoda & K. Ogawa

1317

Determination of the ultimate bearing capacity at the Misicuni Dam, Bolivia A. Torrico Siacara, L.M. Salinas Pereira & F.M. Massao Mechanized installation of high-tensile chain-link mesh for underground support C. Wendeler, A. Barinov & R. Luis Interface behaviour along the boundary between the rock bolt and bond material Y. Yokota, Z. Zhao, W. Nie, K. Date, K. Iwano & Y. Okada

1325

1333 1341

Rock mechanics in petroleum engineering New approach for evaluation of geomechanical parameters of low-permeable anisotropic rocks E.M. Chekhonin, A.V. Gabova, E.Y. Popov, Yu.V. Ovcharenko & Yu.A. Popov

xvi

1351

Experimental investigations of thermal expansion coefficient of Bazhenov Formation rocks A.V. Gabova, E.M. Chekhonin, E.Y. Popov, E.G. Savelev, E.V. Kozlova, Y.A. Popov & I.A. Karpov

1357

Poroelastic response of an induced hydraulic fracture to water injection: A case study of the Horstberg geothermal reservoir, Germany A. Hassanzadegan & T. Tischner

1363

Implosive acoustic emissions induced by injection of supercritical carbon dioxide into a hot granitic rock mass T. Ishida, S. Desaki, Y. Kishimoto, M. Naoi & H. Fujii

1369

Physical modeling of real geomechanical processes by true triaxial apparatus V.I. Karev, D.M. Klimov, Y.F. Kovalenko & K.B. Ustinov Modeling of deformation and filtration processes near producing wells: Influence of stress state and anisotropy V.I. Karev, D.M. Klimov, Y.F. Kovalenko & K.B. Ustinov

1375

1381

Drilling deviated wells in a highly unstable gas field in southern part of Iran S. Khatibi, A. Aghajanpour, M. Ostadhassan & Y. Kovaleva

1387

Various effect of faults on mechanical earth models: A case study of integrated study S. Khatibi, M. Ostadhassan, A. Aghajanpour, Y. Kovaleva & R.A. Mohammed

1395

Porosity measurement of 3-D printed gypsum rock by means of X-ray computed tomography L. Kong, M. Ostadhassan & C. Li

1401

Geomechanical modeling in the design and construction of wells, experience and prospects A.A. Predein & P.I. Klykov

1407

Hybrid numerical modeling of Mandel’s problem and investigating its various aspects A. Ranjbar, H. Hassani, K. Shahriar & M.J.A. Shahrabi

1413

Effect of rock anistropy on hydraulic fracture propagation V. Sesetty & A. Ghassemi

1419

3D geological geomechanical reservoir modeling for the purposes of oil and gas field development optimization D.V. Shustov, Yu.A. Kashnikov, S.G. Ashikhmin & A.E. Kukhtinskiy

1425

Calculation of convergence induced rock mass and ground surface movements in salt caverns for storage of liquid and gaseous energy carriers A. Sroka, R. Misa & K. Tajduś

1431

Fracture propagation in layered carboniferous strata F. Stoeckhert, C. Solibida & M. Alber

1437

Geodynamics and monitoring of rock mass behavior Hydra-U—a revolutionised ground based radar for safety critical monitoring in underground mines N. Boldrini, D. Sizov, M. Cecchetti, M. Rossi, F. Coppi & N. Coli Strain monitoring of hard rock mine slopes I. Fedotova, E. Kasparian, I. Rozanov, M. Kuznetsov & R. Dostovalov Assessment of geodynamic and seismic conditions when mining rockburst-hazardous deposits A.A. Kozyrev, I.E. Semenova & O.G. Zhuravleva

xvii

1445 1451

1457

Geodynamics of interblock and intrablock movements in the rock mass during the extraction of the Lovozero rare-metal deposit A.V. Lovchikov

1463

Rockburst prevention in roadway with wide coal pillar of full-mechanized caving face: A case study B. Nie, Y. Ma, J. Chen, Y. Qiao & H. Yu

1469

Karier measurement system. Monitoring of geodynamic behavior of deep open pit mine rock mass V.N. Oparin, V.I. Vostrikov, N.S. Polotnyanko, A.S. Trofimov & A.A. Potaka

1477

Emission of submicron particles for rock burst prediction A.A. Osokin

1483

Deformation monitoring of a tectonically active fault A.A. Ostapchuk & V.V. Ruzhich

1489

Manifestations of nonlinearity of deformation properties of a regional fault D.V. Pavlov, V.I. Kulikov, V.K. Markov, A.A. Ostapchuk & V.V. Sedochenko

1495

Methods and technical facilities for the assessment of geodynamic risk and geomechanical monitoring of burst-hazard rock massif I.Ju. Rasskazov, B.G. Saksin, P.A. Anikin, A.V. Gladyr, M.I. Potapchuk, V.I. Usikov, A.A. Tereshkin & A.V. Sidljar

1501

Discussion on dynamical system of rockburst under tectonic stress field in coal mine T. Lan, H. Zhang, A.S. Batugin, S. Li, J. Han, B. Cao & X. Zhou

1507

Energy conversion and transfer in block-rock media on dynamics propagation K. Wang, V.N. Oparin, Y. Pan, N.I. Aleksandrova & A.I. Chanyshev

1515

Modeling of stress concentration zones in heterogeneous rock masses within slopes O.V. Zerkal, E.V. Kalinin & L.L. Panasyan

1521

Risks and hazards An approach for evaluating the effects of protection measures on rock fall hazard zoning for land use planning J.M. Abbruzzese & E.P. Howald

1529

Prediction of excavation damage zone depth variability in brittle rocks N. Dadashzadeh & M.S. Diederichs

1537

Reliability based design for rock fall barriers F. Vagnon, J.P. Harrison, A.M. Ferrero & U. Gessica

1543

Experience and results of geodynamic risks management when mining the rockburst-hazardous deposits of the Khibiny rock massif I.V. Fedotova & V.I. Panin

1549

Evaluating the importance of factors affecting short-term rock burst damage using rock engineering systems N. Li, M. Zare & R. Jimenez

1555

Debris Flow: A new design approach C. Morstabilini & M. Deana

1563

A simple methodology for hazard assessment of slopes in volcanic rocks from the Canary Islands: First steps. MACASTAB project M. Muñiz Menéndez & J. González-Gallego

xviii

1569

The qualification program for mining professions on identification of hazards and risks associated with the loss of stability of rock mass Y.I. Rubchevskii An approach for the probability of wedge failure in the excavation direction A. Turanboy, E. Ülker & C. Burak Küçüksütçü Geomechanical aspects of remediation of quarries in the flysch: Case study of abandoned quarry in Majdan, Croatia G. Vlastelica, P. Miščević, N. Štambuk Cvitanović & A. Glibota

1575 1579

1585

Young session Evaluation of a potential shear in the vicinity of structural violations by calculation results of stress-strain state of the rock mass S.V. Dmitriev

1593

Research of the factors making negative impact on the stress-strain condition of a system «support—massif» T.F. Kharisov & O.D. Kharisova

1597

Characterization of micromechanical properties of coals of different types by nanoindentation E. Kossovich

1603

Geomechanical analysis of pre-oriented hydraulic fracture propagation A.E. Kukhtinskiy

1607

The study of formation mechanism of earth surface failures due to longwall coal mining Yu.Yu. Kutepov

1615

Method to reconstruct rock mass stress state by solving inverse problems using full-scale experimental data A. Skulkin Assessment of burst-hazard rock massif by geoacoustic method A.A. Tereshkin & M.I. Rasskazov

1621 1627

Guidelines of geomechanical and engineering-geological research on subsurface microbiota impact on hard rocks in the underground space of megalopolises I.V. Alekseev

1633

Deformation monitoring of open pit mine slopes using an Unmanned Aerial Vehicle (UAV) system R. Gubaydullina & M. Mustafin

1639

Hydrogeomechanical processes in development of spoil dumps and hydraulic fills Yu.I. Kutepov, N.A. Kutepova, M.A. Karasev, A.D. Vasilieva & Yu.Yu. Kutepov

1645

Stableness improvement of the excavations during the chamber-and-pillar development of Yakovlevsky Deposit reserves K. Sozonov

1653

Model of the stress-strain state prediction of a building during the construction of a tunnel under it P.E. Verbilo

1659

Author index

1665

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Preface

Distinguished participants of the Symposium! “Geomechanics and Geodynamics of Rock Masses” contains the contributions to the International European Rock Mechanics Symposium EUROCK-2018 (Saint Petersburg, Russia, 22–26 May 2018), and covers all high-tech solutions and advanced engineering developments in the field of geomechanics, from theory to application. Taking into account the rapid growth of industry requirements, there is an obvious need to strengthen research activities maximally, to provide professional assessment and build science-based predictions in various industrial sectors to ensure the economy running and the state development. At the same time there is a growing role of quality engineering service delivery to enterprises, which would be characterized by high scientific content and would provide the commercialization of research. It is of primary importance for scientific developments in geomechanics. Today, it is impossible to imagine the design and operation of a mining enterprise without geodynamic classification of a deposit, detailed analysis of the rock mechanics, and geophysical analysis of the massifs geological aspects. In conditions of global intersectoral and interdisciplinary integration, certain economic sectors (complexes) will be increasingly influenced by scientific and technological achievements as well as by economic and scientific changes in related industries. Geoinformation technologies provide plentiful opportunities for the labour productivity improvement in prospecting, exploration and mining of mineral resources. Based on information and communication infrastructure, the advances in aerial and space means of Earth remote sensing and the Global Positioning System enable to form integrated systems for managing the processes of prospecting, exploration, extraction and transportation of mineral resources. Looking ahead, the development of biotechnologies may have revolutionary effect on the demand pattern in the mining industry: − substitution of natural petroleum for biomass-based fuel; − biological underground metal leaching instead of hazardous chemical leaching; − ecosystem recovery through bioremediation of soils and grounds contaminated by hydrocarbons. The technology of Earth sensing is being actively used in order to decrease the cost of labour force and minimize the influence on biosphere. Science-based technologies are being intensively developed for the following geophysical studies: − − − − −

nuclear-geophysical and seismoacoustics; abyssal geoelectrics; geodetic gravimetry; geothermics; electroprospecting based on the Earth’s natural electrical fields.

The major discovered deposits are located in hard-to-reach places. They are characterized by high resource and energy intensity of their exploration and the creation of necessary infrastructure. xxi

Today’s oil production is very costly. For instance, 30 years ago over a hundred barrels were produced from 1 barrel by means of energy, but nowadays, 10 barrels are averagely produced from 1 barrel and this figure is increasing sharply. The ratio may be 1:1 in the coming 30–50 years. This business is not appropriate. According to the US Geological Survey for 2014, undiscovered resources of conventional hydrocarbons in the Arctic are around 90 bln barrels (13 bln. tonnes) of oil, 44 bln. barrels (6.5 bil tonnes) of gas condensate and 1669 trn cubic feet (47 trn cubic meters) of natural gas. It equals to 13% of total undiscovered oil resources in the world, 30% of total undiscovered natural gas resources and 20% of the world gas condensate resources. Grand-scale exploitation of mineral deposits in the Arctic zone implies the application of effective environmentally sound technologies and their development requires significant investment. Serious risks are associated with climate changes capable to cause destruction of mining sites in the Arctic and ecological disasters. Modern research in the field of mineral processing is aimed at increasing ecological and economic efficiency of technological processes. Another important tendency is the transition to the maximal level of fineness (dispersiveness) of separation thus providing more enhanced extraction of useful component from the ore. In that regard, new systems for grinding to micro size will be developed. Introduction of new technologies of processing will result in reducing water loss by 15–20%, electricity and reagents—by 30–50%. Extracting of useful components from mining waste is currently becoming feasible. Every year, 17.4 bln. tonnes of solid and liquid wastes are accumulated as a result of mining and mineral processing. Most of them are solid mining wastes. In many countries technological wastes are considered to be an important segment of the economy resource base. The increased use of renewable energy sources will call for their supplement with systems of energy accumulation, and “flexible” hydro- and gas generation to provide reserve duplication  in the absence of suitable conditions of power production from renewable sources. Work is ongoing to develop solutions for enhancing economic and technological efficiency of renewable generation, in particular to reduce demand in rare earth metals when manufacturing generating equipment. For example, the project “Smart Mine” funded by the EU aims to develop a variety of technologies and know-how to create automated mines with minimal human presence and zero impact on the environment. The key characteristics of a “smart mine” are: − − − − −

the highest standards of personnel safety; absence of harmful effect on landscapes; low specific hydrocarbon emissions; high rate of useful component extraction from ore; maximum use of telemechanics (remote control of processes) which makes it possible to deploy a considerable part of personnel outside production zones, but to big cities, which are comfortable for living; − storage of waste rock within the mine (without hoisting), or production of building materials and other useful things from mine wastes; − higher energy efficiency. Major well-known technologies of enhancing oil recovery are characterized by high cost, energy and material consumption. As a rule, their implementation is effective at the oil cost of more than $70 a barrel. In recent decade tertiary methods of advanced oil recovery have been used actively in the world including thermal, gas, chemical and microbiological ones. Thermal methods include steam treatment, the initiation of interbedding combustion, the use of thermogas, displacement of oil and asphaltenes by hot water. xxii

Chemical methods are based on displacement of oil by other substances: surfactant solutions, polymers, thickening agents, froth systems, alkaline solutions, acids and compositions of chemical reagents. By enhancing oil recovery through tertiary methods, the additional 110–130 mln. tonnes of oil equivalent (2.5% of the world production) per year are produced in the world. According to expert estimates, from 3 to 7% of recovered oil is wasted in oil fields, and the most part of pollutants (up to 75%) is emitted into the atmosphere, 20% – into water sources, 5% – into soils. In the context of global warming the risk of oil pollution of the sea is growing due to a decline in ice sheet uniformity, better conditions for oil spills drift, the increased likelihood of coast line oil contamination. High rates of growth are forecast for the waste management market. The most in-demand technologies will be those of less resource intensity, the complex use of raw materials, the prevention of negative impacts of pollutants on the environment. Huge social responsibility falls on rock mechanics engineers when operating hydrotechnical structures, subways, mining deposits under cities and water bodies. The level of mining operations gets deeper with each passing year, increasing the impact on the enclosing rocks; the built-up density of mining and civil property is growing. This significantly complicates the extraction and leads to the need to develop new unconventional technical, technologyintensive solutions. The areas of development of technologies and scientific-and-technological advance in the mineral and raw materials complex for the foreseeable future will be: 1. Creation of the equipment for the development and production of non-conventional hydrocarbons will provide conditions for the commercial development of new deposits. The use of these technologies will predetermine a multiple increase in the volume of recoverable reserves, expansion of extraction geography, introduction of resources alternative to traditional oil and natural gas to the hydrocarbon raw materials market (gas hydrates, shale gas, heavy oil and bituminous sands, high-gas-bearing coal methane, etc.). 2. The role of systems and methods for enhancing the oil recovery factor will increase, including controlled changes in the reservoir characteristics on depleted hydrocarbon fields and low-pressure fields. This is a combination of technological solutions, instruments and systems for chemical and physical impact on hydrocarbon-containing reservoirs as a whole and their individual components (hydrocarbon rocks, hydrocarbons themselves, water, etc.), contributing to enhanced oil recovery. New technologies will help improve the efficiency of hydrocarbon production in existing fields, reopen those that were previously abandoned, and start developing difficult-to-recover reserves. In the long term this will significantly prolonge life of already known deposits and will delay the moment of depletion of industrial stocks of traditional hydrocarbon raw materials for decades. 3. Introduction of integrated and deep processing of mineral raw materials to increase the extraction ratio of both major and associated components in the fields will ensure a significant increase in the efficiency of minerals processing and reduction in the volume of generation of production waste. 4. The discovery of new genetic types of deposits, as well as the expansion of the geography of prospecting and exploration of mineral deposits, will lead to a change in the geography of the countries—exporters and importers, and increased market competition. 5. Development of sustainable technologies for complex ore benefication can lead to reduction of the minimum commercial content, which will make it advantageous to involve unpayable ores into processing, and will make it possible to profitably use waste from concentrating mills. In addition, the introduction of new inventions will help to reduce the level of environmental pollution, including minimizing the areas for storing and dumping waste in industrial areas, thus eliminating the risk of highly toxic compounds entering ground, sewage waters and the atmosphere. 6. Introduction of roughing equipment used on the edge of an open-pit mine or in a mine and operating on different principles – gravitational, magnetic, electrical, flotation, pulsed, xxiii

radiation and radiation-thermal—will significantly reduce the primary cost of processing by lowering the cost of ore transportation to concentrating mills. The ability to think systematically, at an interdisciplinary level is of great importance today. Geomechanics closely interacts with other branches of science in its scientific foundations, methods and means: mathematics, geophysics, thermodynamics, mine surveying, geology, geotechnology. Therefore, the challenge of our time is the need to ensure constant cooperation of experts of various areas in order to solve complex tasks. I am confident that St. Petersburg Mining University, which is in the process of establishing the International Competence Center in Mining Education under the auspices of UNESCO, will be able to start the realization of its main goal this year—the integration of leading world scientists and mining specialists under its roof for the fruitful exchange of experience and the design of trends in the development of the industry. Strengthening the international capacity to develop sound policies in the field of higher education and sectoral science will help the world community to address the challenges of equity, quality, inclusiveness and mobility. Integration of scientific branch interaction into the system of technical and vocational education and training of specialists in the mineral and raw materials sector of the economy will contribute to the formation of optimal control systems for the processes of prospecting, exploration, extraction, transportation and processing of minerals. The forecast of scientific and technological development of the world mineral and raw materials complex takes into account the need to create conditions for uniting the efforts of the world community in solving the following problems: 1. Exploration work, including new production areas, meeting economic and environmental requirements; development of geophysical methods of oil and gas exploration in non-conventional geological conditions; evaluation of oil reservoir productivity; methods of searching for zones of possible ore manifestation. 2. Methods of enhancing oil recovery, including controlled change in reservoir properties of reservoirs, which allows to increase the hydrocarbon extraction factor, including depleted fields and low-pressure gas fields. 3. Obtainment and use of non-conventional sources of raw materials, including hydrocarbon, including heavy oil, gas hydrates, shale gas, etc. 4. Physical, technical and physicochemical technologies for processing high-gas bearing coal seams with the prevention of coalmine methane emissions, including for the purposes of gaseous and liquid synthetic hydrocarbons production. 5. Technologies for efficient processing of solid minerals, including energy-saving complex processing of refractory natural and technogenic mineral ore with a high concentration of mineral complexes. 6. Use of waste from extraction and minerals processing on a commercial scale. 7. Ecologically safe marine exploration and extraction of various types of mineral resources in the extreme natural and climatic conditions of the World Ocean, the Arctic and the Antarctic. 8. Technologies of seismic exploration in ice-covered water areas. 9. Technologies for ensuring the integrated safety of operations on the continental shelf of the Russian Federation, in the Arctic and the Antarctic, including monitoring and forecasting of natural and man-made emergency situations. 10. Prevention and containment of oil spills, primarily in ice conditions, including technologies for detecting oil under the ice sheet. 11. Advanced technologies for seismic prospecting. 12. Advanced technologies of oil and gas production. 13. Advanced coal mining technologies. 14. New technologies for deep conversion of oil and gas condensate. 15. Effective technologies for the use of petroleum associated gas. 16. New technologies for deep conversion of natural gas with the production of liquid motor fuels and a wide range of chemical products. xxiv

17. Next-generation technologies for deep processing of solid fuels with integrated use of mineral parts. 18. New technologies for efficient transportation of natural gas. 19. New functional coatings for pipelines. 20. New membrane materials with a given pore size. 21. New types of catalysts. I hope that experts and scientists of the International Society for Rock Mechanics (ISRM) will be able to meet and cooperate within the framework of the International Competence Center, enriching its activities with the in-demand skills and knowledge and making use of its advantages. I would like to note that only together we can create a high-quality institutional potential in the field of natural and engineering sciences in the interests of ensuring sustainable development of society. I am confident that EUROCK-2018 will bring large benefits to the scientific and technical cooperation and the development of geomechanics as a separate field in the mining industry and will enable its participants to exchange their experience and valuable knowledge. Vladimir Litvinenko Rector of St. Petersburg Mining University Chairman of the EUROCK 2018 Organizing Committee

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Committees

ORGANIZING COMMITTEE Vladimir Litvinenko

Igor Sergeev Vladimir Trushko Arkady Shabarov

Anatoly Protosenya

Victor Rechitsky Valery Zakharov

Rector of St. Petersburg Mining University, Russia Chairperson of the EUROCK 2018 organizing committee Vice-Rector for Scientific Work, St. Petersburg Mining University, Russia Head of the Department of Mechanics, St. Petersburg Mining University, Russia Director of the Scientific Center for Geomechanics and Mining Problems, St. Petersburg Mining University, Russia Head of the Department of the Construction of Mining Enterprises and Underground Structures, St.  Petersburg Mining University, Russia Secretary of Russian Geomechanics Association of ISRM, Russia Director of Institute RAS IPKON, Russia

INTERNATIONAL ADVISORY COMMITTEE Walter Wittke Doug Stead Norikazu Shimizu Stuart Read Luís Lamas Petr Konicek William Joughin Seokwon Jeon Sergio A.B. Da Fontoura Eda Freitas De Quadros Manchao He Charlie Chunlin Li

ISRM Past President ISRM Vice President for North America ISRM Vice President at Large ISRM Vice President for Australasia ISRM Secretary General ISRM Vice President at Large ISRM Vice President for Africa ISRM Vice President for Asia ISRM Vice President for South America ISRM President ISRM Vice President at Large ISRM Vice President for Europe

INTERNATIONAL SCIENTIFIC COMMITTEE Leandro R. Alejano Alexander Barjakh Giovanni Barla Nick Barton Erast Gaziev John Hadjigeorgiou Michael Zhengmeng Hou Erik Johansson

Spain Russia Italy UK Russia Canada Germany Finland xxvii

Iurii Kashnikov Heinz Konietzky Sergey Kornilkov Anatoly Kozyrev Srđan Kostić Charlie C. Li Sergey Lukichev Larisa Nazarova Erling Nordlund Frederic Pellet Igor Rasskazov Anatoly Sashourin Dick Stacey Manoj Verman Christophe Vibert Ivan Vrkljan Mikhail Zertsalov Zhao Zhiye Yingxin Zhou

Russia Germany Russia Russia Serbia Norway Russia Russia Sweden France Russia Russia South Africa India France Croatia Russia Singapore Singapore

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Key lectures

Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Advancement of geomechanics and geodynamics at the mineral ore mining and underground space development Vladimir Litvinenko Rector, St. Petersburg Mining University, St. Petersburg, Russia

ABSTRACT: The article provides findings for topical geomechanical and geodynamic problems of mining companies, the problems arising from deposit and underground space mining. The prediction of geomechanical processes and the justification of method parameters of mining by open-pit, subsurface and combined methods in complicated mining and geological conditions of tectonically stressed mass and under confined aquifers were carried out. Geomechanics of deposits development in the Arctic area is studied. The methodology of geomechanically safe underground space mining is stated for metropolises. Keywords: geomechanics, depression, solid mass, stress pattern, mine, strength, model, numerical method, surface

1

INTRODUCTION

Geomechanical problems in deposit mining at great depth and in complicated hydrogeological and geodynamical conditions require experimental and theoretical methods development for stressed-deformed state of a rock mass, nonlinear geomechanics of saturated complex porous and fractured rock masses development, creating of the mass geomechanical model in space and methods for geodynamical zoning of rock masses. Based on the recent geomechanics and geodynamics advances, the following problems were solved: geomechanically safe ore deposit mining in complicated mining and geological conditions and creation of calculation method for stressed-deformed state of a mass around mines in tectonic stress field affected by seismic waves from rock shocks and bulk blasts; creation of prediction methods for geomechanical processes at the mining of gas-saturated blanket deposits; monitoring of geomechanical processes and geodynamical zoning of rock masses, underground space mining for metropolises in complicated engineering-geological and city-planning conditions. The Mining University possesses a complex of advanced equipment, which allows solving the entire range of aims related to the study of rock mass properties and modelling of conditions similar to real mass conditions and wide varieties of load modes. The processes of loading, gathering and processing the information are automated and enable to carry out compression, tension and bulk strength tests of hard and half rock with simultaneous recording of a number of indicators (deformation, load, acoustic emission, speed of elastic waves, pore pressure) with a process visualization of crack formation and development. Values of lateral and pore pressure may vary from 0 to 50 Mpa, axial load—up to 4600 kN, temperature—from –15 to +200°C. Scientific studies are conducted with special software complexes based on a finitedifference approach for solution of continuum mechanical problems and discrete elements method which are designed to solve fractured, or block medium. Modelling of a blade shield moving through a mass is introduced into practice.

3

The more is depth, the more intense solid masses are, and the tendency to dynamic display of rock pressure. All the ore deposits mined at great depth are classified as bump hazardous. That is why one of the main problems of rock geomechanics is a prediction of stress-strain behavior of a mass and justification of safe ways and field mining methods at great depth conditioned with active dynamic phenomena. The further progress is needed in scientific works on recording properties of real rock mass of block, layered and complicated geology, having tectonic faults, and any type of destructions being under geostatic pressure and effect of tectonic forces and movements. 2

PREDICTION OF GEOMECHANICAL PROCESSES AND JUSTIFICATION OF SAFE PARAMETERS AND COMBINED METHODS OF DEPOSIT MINING IN A TECTONICALLY STRESSED MASS

·OAO Apatit is active in the business of underground, surface and combined mining of apatite-nepheline ores from six deposits. Nearby surface and underground mines, quarries, which are close to limiting zone, and open pits, where adjacent stocks are extracted, critically complicate mining activities. The stability of mine outcroppings is negatively impacted by redistribution of gravity-tectonic stress field in adjacent mass [1,2] and the change in strength and deformation properties of a mass affected by blasting operations at a quarry [1,3]. Extraction practice of a quarry adjacent stock by underground method demonstrates that at mining activity the energy of dynamic phenomena also quantitatively increases in rock masses, and rock tectonic bumps and induced earthquakes are also possible to occur [4,5]. A number of fundamental papers [6,7,8] are devoted to the study of geomechanical process at combined ore mining, but not all problems have been solved yet. It is required to ensure stability of permanent and development mines [9] carried out in tectonically stressed adjacent mass (Table 1). The stope is studied in the impact area of the Koashvinsky quarry (Figure 1) conditioned with operations at OAO Apatit Eastern mine, at extraction of which the topslicing and ore sublevel caving is applied. Height of sublevel is 20 m, distance between drill-haulage mines is 18 m. Room works are carried out from the mass to the quarry transversely to the stretch of ore body. Table 1.

Acting values of tectonic stress in mass.

Item No.

Depth from the surface, m

Value of stress along the stretch of ore body, MPa

Value of stress transversely to the stretch of ore body, MPa

1 2 3 4 5

5 50 250 450 650

5 45 54 60 66

2,5 20 28 35 40

Figure 1. Detail of finite-element model formed with account of the topographical relief and geological features of mass.

4

Finite element model is developed for a stope located at depth of 400 m from surface, on the distance from the open pit wall horizontally is 200 m (to the centre of block). At underground works the chosen block is the most complex in relation to the acting stress in solid mass (Figure 1). All the rock formations in the model are given as heavy, homogeneous, isotropic, linearly deformed materials. Boundary conditions are given as follows (Figure 1). On the edge of the model in direction of Ox and Oz axes, stresses are given obtained as a result of modelling of adjacent rock mass to the commencement of underground works. The movements for opposite boundaries are prohibited along the corresponding directions. Boundary conditions along the top edge are given as distributed loads, values of which corresponds to the weight of the overlying rocks with the account of sub-extracted rock pressure formed by the moment of block extraction. The algorithm for the problem solution includes five modelling stages: formation of stress and strain state of virgin mass, formed due to tectonic and gravity stress fields, with the effect of sub-developed rock pressure taken into account; development mines at all sublevels which are carried out by mass extraction within the boundaries of mines; fall of the first sublevel, which is implemented by assigning of decayed rock properties to the material within the boundaries of rock fall; fall of the second sublevel; fall of the third sublevel. Thus, the model takes clearly into consideration the technology of consequential extraction of a sublevel with nominal idealization, i.e. a sequence of sublevel mining operations is not taken into account, in the same way as the stages of ore crushing, but ore fall is admitted along the area of the entire sublevel for a modelling stage. The admitted idealization of the model allows analysing of stress and strain state of mass at the final stages of mines and fall of sublevels without analysis of stress development in the course of block caving. Main maximal stresses are found in Oxy, Oxz, Oyz sectional planes cutting through the centre of the block and sublevel in order to ensure qualitative analysis of stress distribution within the considered model of the stope (Figure 2). The analysis of stress distribution shows the stressed state of a mass has a critical crossimpact formed after putting the wall to the final position of gravity and tectonic stress field and bearing pressure from fallen ores and mass material. Stresses are increasing with moving from the side wall to the foot wall and from ore mass to the caved mass. In order to estimate quantitatively the stressed state of adjacent rock mass containing underground mines, changes in tangential stresses are recorded on the boundary. The obtained data enable us to estimate quantitatively degree of impact from the open pit wall on stressed state in mass around the mines in adjacent rock mass. In roofs of the mines carried out perpendicular to the wall in the stress concentration area in the adjacent rock

Figure 2. Distribution of main maximal stresses in a mass of the first sublevel with account of the quarry effect prior to room works.

5

mass, stresses are found to be 30–40% less than beyond the zone of effect, with compressive stress forming in mine walls within the zone of quarry effect, and tensile stress beyond the zone of effect. Quite different, in terms of qualities, behaviour of stress distribution takes place for mines carried out parallel to the quarry. Increase of tangential stress concentrations is registered both on the boundaries: 1.5–1.6 more, and wall, as well as in the mine roof. At that, untypical change in stress values is registered per calculation stages, which may be explained by unsymmetrical formation of stress concentration zones on the mine boundary. Roofs and walls of mines, which are perpendicular to the open pit wall and mine beyond the zone of wall effect, are marked by 10–20% increase in stresses with the fall of overlying sublevels. Change in the stressed state in walls and roof is not regular in mines parallel to the open pit wall, which indicates the formation of stress concentration areas not in walls and roof but in points turned along the effect line of main stresses in adjacent rock mass. 3D model study of the stress and strain state of a mass around mines enables to reveal features of stress and strain state of a mass around mines in the zone of quarry effect, involving the enhanced concentration of compressive stresses in a roof of the mines perpendicular to the open pit wall and maximal component of tectonic stresses, and asymmetry of tangential stress distribution along the boundaries of mines parallel to the open pit wall and maximal component of tectonic stresses Based on the calculation of a mass stress value, it is possible to conclude that the mines stability category decreases in the zone of quarry effect [10]. If, on the average, the second category of stability prevails for the block, then it becomes the third or the forth within the zone of quarry effect. The similar picture is observed in the areas of mine junctions and in the area of effect by room works. Therefore, in order to ensure safety of operations, type and parameters of supports for the mines within the zone of quarry effect shall be changed toward strengthening under III–IV stability categories.

3

CHOICE METHOD FOR GEOMECHANICALLY SAFE AND EFFICIENT PARAMETERS OF PILLARS

Current methods of parameter calculation for pillars do not regard the variety of interdependent factors related to the mine geological and engineering conditions of a deposit as well as technological features of applied mining methods. In particular, as it applies to apatitenepheline mines on the Kola Peninsula, it is needed to consider, among other factors, a nonuniform gravity and tectonic stress field, active in a mass, and for some cases – cross-effect of open and underground mining works. To determine size of pillars, we suggest starting with the use of the existing experiential methods for finding parameters of chamber-and-pillar mining method based on the allowable chamber [4,5], and then calculating stressed state of pillars with the aid of 3D models with mining stages of ore body blocks. The method provides for defining the actual values of reserve strength ratios in pillars and, if their values are large—for finding [11] efficient parameters of pillars. An option of the chamber-and-pillar mining method for Nyurpakkhskoye apatitenepheline deposit is considered for the depth of 400  m. Stress-strain behaviour of ores are admitted as follows: for ores: modulus of elasticity: E  =  61600  MPa, Poisson ratio: ν = 0.28, uniaxial compression strength for material: Rcomp = 150 MPa; for enclosing rocks: E = 64200 MPa, Poisson ratio: ν = 0.25, Rcomp = 200 MPa. As failures in mass are typical for Nyurpakkhskoye deposit, this paperwork regards the medium fractured mass. Angle of incidence for the ore body is taken as 15°, its thickness – 40 m. The stressed state is defined in the context of pillar weight of overlying material and acting tectonic stresses and amounts to: vertical stress y = 10.59 MPa; the maximal component of tectonic stresses, oriented along the stretch of ore body: max = 30.0 MPa; the minimal component, oriented transversely to the stretch of ore body: min = 16.7 MPa. General view of the developed model is shown in Figure 3. 6

Figure 3.

General view of geometry and layout of pillars in the finite-element model.

Block mining modelling for the deposit is made in respect of main stages of its consequent extraction shown in Figure 4. The relationship of stresses acting along the centre line of level and interstall pillars is determined at the first stage of modelling (Figures 5 and 6). Analysis of dependences shows that in general only compressive stresses act in interstall and level pillars with demonstrating the asymmetric behaviour in the areas of intersection with pillars, perpendicular to them, which is determined by angle of incidence for ore body and the sequence of mining stages. A component, perpendicular to pillars, has the maximal stress values (for level pillars – σz; for interstall pillars – σx). Growth in values of vertical stresses is typical for isolated interstall pillars with the opening of block chambers, at that growth is noted to attenuate with the removal of room works. Maximal vertical stress value amounts to 105.8  MPa at the final stage of the calculation model, which does not exceed the limit of strength for medium fractured mass equal to 150 MPa, and complies with the required actual reserve strength ratio for pillars. In Table 2 actual reserve strength ratios are presented in pillars of various purposes for a base case estimated pursuant to allowable spans of mines [12, 13]. This calculation method of chamber-and-pillar mining parameters provides for the overstated parameters of chamber-and-pillar mining and high strength reserve ratios. 7

Figure 4.

Stage sequence of block mining for ore body in finite-element model.

Figure 5.

Relationship of stresses along central axes of a level pillar.

That is why let us consider 3 optimisation cases for the efficiency of pillar parameters: case 1 – decrease in width of the interstall pillar for 1 metre; case 2 – decrease in width of the level pillar; case 3 – decrease in width of interstall and level pillars for 1 metre. At that, the change of one of mining parameters results in the change of the stressed state of pillars in the whole system of pillars of various purposes. The calculation demonstrates that in view of minimal reserve strength ratio equal to 2, it is appropriate to decrease the cross-section of insulated chamber pillars for 1 m and decrease the width either of a level, or an interstall pillar for 1 m. 8

Figure 6.

Table 2.

Relationship of stresses along central axes of an interstall pillar.

Values of acting stresses and actual reserve strength ratios in pillars of various purposes. Compressive stress in pillar, MPa/Actual reserve strength ratio for a pillar

Pillar

Direction of stresses

Base case

Case 1

Case 2

Case 3

Interstall

vertical along axis of a pillar σx transverse to a pillar axis σz vertical σy along axis of a pillar σz transverse to a pillar axis σx vertical σy

23.1/6.49 22.1/6.79 28.3/5.30 25.9/5.79 42.1/3.56 16.0/9.38 37.3/4.02

45.1/3.33 42.3/3.55 49.6/3.02 36.8/4.08 61.2/2.45 28.1/5.34 96.2/2.27

37.6/3.99 27.3/5.49 31.4/4.78 56.2/2.67 71.2/2.11 36.1/4.16 92.3/2.19

83.6/1.79 71.2/2.11 83.4/1.80 94.5/1.59 137.4/1.09 72.4/2.07 112.1/1.85

Level

Chamber

4

PREDICTION OF GEOMECHANICAL PROCESSES AT OPEN-PIT MINING

Automated algorithms are developed for analytic solutions of problems to define parameters of side slopes by various methods. The method of geometrical forces summation is developed which is based on introducing corrections to the method of algebraic forces summation. The engineering method is suggested for the calculation of slope stability in the 3D scene. The calculation findings, together with correlation of locations for more stressed surface of sliding obtained by the engineering method and those obtained by 3D numerical modelling show them to have a sufficient convergence (Figure 7). The numerical modelling of an open pit walls and dumps is now becoming the norm at the analysis of their stability. The more complex geomechanical models applied for solving various problems allows for the more trusted findings. Yet, backward calculations regarding the occurred deformations demonstrate that it is more reasonable to apply the finite element modelling method and Mohr-Coulomb criterion for the prediction of the slope deformation in the context of its stability when reserve ratios exceed the reference values. If the reserve ratio decreases further, physical modelling results should be used, see Figure 8. To extend the scope of application for the finite element 9

Figure 7. Instance of calculation of rectilinear slope stability by the ultimate equilibrium method and finite-element method.

Figure 8.

Development of deformations in a slope at various reserve strength ratios.

modelling it is advisable, depending on the slope stability degree, to introduce a correction into the modulus of deformation in accordance with the below proposed formula: E p = E(4,3n–4,5), where: n –strength reserve ratio; E – initial modulus of deformation. This formula is applicable at strength reserve ratio values from 1.08 to 1.3. In order to analyse impact from earthquakes on the stability of open pit walls and dump slopes, a method has been developed to enable taking into account not only intensity of seismic vibrations, but also magnitude at the same time (Figure 9). The application of physical modelling together with conventional calculation methods allows for the more accurate calculation of open pit wall parameters for the complicated engineering and geological conditions. Particularly, when stability of slopes is estimated with falling of mass in the range 65–90 degrees, existing reference documents suggest introducing a correction of about 10–15 degrees into the resulting angle of slope. However, at open-pit mining in areas with underdeveloped infrastructure the application of such a conventional solution may quite substantially affect the project profitability. The research, we carried out, 10

Figure 9. Diagrams showing dependency of displacement for slopes with various initial reserve ratios at various intensity and magnitude of earthquakes.

Figure 10. Physical modelling of open pit wall, with layers falling towards mass within the range of 65–90 degrees.

shows such corrections should be introduced only at the very low strength along mine rock contacts and in severe hydrogeological conditions. At the same time, in permafrost rock conditions, the correction to the resulting angle amounts to around 5 degrees. The instance of physical modelling for the described instance is shown in Figure 10.

5

PREDICTION OF GEOMECHANICAL PROCESSES AT THE MINING IN THE COMPLICATED ENGINEERING, GEOLOGICAL AND HYDROGEOLOGICAL CONDITIONS UNDER CONFINED AQUIFERS

High degree of inundation is typical for Yakovlevskoye deposit. Ground water at the deposit is expanded in the sedimentary cover within which seven confined aquifers are distinguished. High-pressure Lower Carboniferous confined aquifer of 420–440  m head associated with limestone is located immediately above ore body, which deeper section displaces irregular clay layers. Yakovlevskoye deposit is outstanding regarding not only iron ore stock reaching 11

Figure  11. Diagram distribution.

of

vertical

Figure  12. Diagram of distribution.

stress

horizontal stress

65–70% iron, but also complexity of mining, geological and hydrogeological conditions. Tensile strength of high-grade iron ore in uniaxial compression does not exceed 1 MPa. A combination of high pressure of ground water and very low strength of ores greatly complicates the mining. For the deposit development, a chamber mining is suggested with goaf stowing. Ore is extracted in layers from top to bottom. At the extraction under the Lower Carboniferous aquifer, a 65 m thick ore pillar is left in order to prevent an inrush of water from undrained confined aquifers overlying sedimentary. Geomechanical bases [14, 15] are developed for friable iron ore mining in complicated conditions of mining and geology at the unique Yakovlevskoye deposit. Figures 11 and 12 show the stress distribution in ore and crystalline mass prior to mining. Components of vertical and horizontal stresses are uniformly distributed and reach the largest values in contacts with enclosing rocks. The untypical effect of ore body relaxation by harder and more solid enclosing rocks is disclosed. Building of a concrete ceiling is suggested to ensure stability of the roofs for the first layer mining chambers. Loads on a protective ceiling, ore and stowing pillars are determined, with their parameters being found. A regulation on complex hydrogeomechanical and hydrochemical monitoring is composed as a part of the system for monitoring, prediction and prevention of dangerous mining and geological processes development in underground mines. 5.1

Geomechanics of deposits development in the Arctic area

Prospects of deposits’ development in the Arctic zone at the first stage require a systematic study of the properties of ice massifs. For these purposes ice physical and structural properties forming the Antarctic ice sheet in the area of Lake Vostok, which are characterized by evolutionary changes of the process of compaction and dynamometamorphism of ice rock layers have been studied. It is determined that variations of many structural characteristics for the depth are connected to climatic fluctuations which took place on ice sheet surface in the past [21]. The vertical ice profile (Fig. 13) shows that in depth intervals 20–3450 m grain size increased approximately 100 times: from 1 to 100 mm in diameter (estimated rock age at the depth of 3450 m) during 600 thousand years. At the same time on the background of common tendency to the growth of ice crystal size with the increase of the depth fluctuations, which reveal clear correlation with the change of ice isotopic composition and concentration of aerosol impurities in it are observed. 12

Figure 13.

Changing of ice grains size with depth.

The unknown earlier phenomenon that the cyclic variations on the surface of ice sheet, which are, in particular, caused by climatic factors, form the layered subparallel accumulation surface and differentiation of ice rheological properties has been discovered. Ice sheet has the layered subhorizontal structure of the distribution of the material composition parameters, petrophysical, petrographic properties, as well as, respectively the velocity and direction of the ice masses flow [22]. Revealed dependences at the development of technology and drilling in the Antarctica ice sheet have been taken into account, this allowed to successfully penetrate in subglacial lake «Vostok» at the depth of 3769,3 m. Achieved results were acknowledged by the world community as an outstanding scientific breakthrough and they can be used during the fields’ development in the Arctic zone in future. 5.2

Methodology of geomechanically safe underground development in metropolises

The proposed methodology for geomechanically safe underground development in metropolises regards all stages of building and operation of an underground facility, including stages of the geological survey, designing of an underground facility, the construction of an underground facility, and operation of an underground facility. Prediction methodology of geomechanical processes is based [16, 17, 18] on the following principles: − representative and unbiased estimation of engineering, geological and hydrogeological conditions and features of soil mass, − equations of state and laws of soil mass deformation, including those considering nonlinear deformations of media and their creep, − 3D geomechanical models of a mass [19], provided for the interaction of above-grade buildings and underground structures, − stages of their construction, − multi-variant numerical experiments allowing structural and technological modifications in construction facilities. Mitigation of the impact caused by the underground construction on urban infrastructure, as well as building and structures located above the ground may be achieved by either the application of so-called low subsidence construction techniques for underground structures, or the application of the compensatory methods, or the reinforcement of the existing buildings and structures, or the combination of them all. The process of choosing the building protective measures may take considerable time and is of the iteration nature. Let us consider the instance of the prediction of deformations of the land surface at the construction of complex 3D underground structure—transfer hub of two metro stations located in different altitudes, which includes 22 facilities (Figure 14). 13

Figure 14. Geometrical representation of space planning solution for the metro transfer hub: 1 – metro station No.1; 2 – metro station No.2; 3 – transfer hub; 4 – access track port; 5 – running tunnels.

The metro stations are initially divided in separate underground structures so that their cross-effect is maximally limited. After that, the sequence of construction for such underground structures is defined in accordance with a flowchart on the construction of a station. The local numerical models with fine detailed simulation of their construction method are developed for each structure. For long-stretching structures negligibly changing their configuration along their length, it is possible to consider the construction of part of the structure along the length only. Then the numerical model is built for the entire metro station and ground mass (global model). The global model represents the process of construction of the station in simplified form, with the most important stages of construction being distinguished, at that the predictions of ground surface deformations is carried out for the completion of each stage. Usually, the construction of one of the main station elements—station tunnel, port, auxiliary tunnel, connection area of tunnels and alike, is admitted as a stage of construction. Such an approach allows significant reducing time of calculation as the number of calculation stages does not usually exceed 15–20. Pattern of land surface subsidence at different construction stages of the station is represented as diagrams at various enlarged stages of construction (Figure 15). Value of vertical displacements of land surface equaling to 1 mm is admitted as a border of the underground construction impact. As is obvious from the represented results, pattern of trough of land surface subsidence extends with the construction of underground structure, affecting even greater area of land surface within the construction area of impact. The largest deformation of land surface forms over the areas with maximal concentration of underground structures, where displacement values reach 55 mm. The construction of large cross-section ports is to be given the special consideration, as those particular structures critically affect the pattern of land surface subsidence trough. The obtained values of displacements for the underground structure rock boundaries and resulting displacements of land surface are calculated in the context of the accepted low subsidence construction techniques, all procedures of which are to be followed at actual works. Based on obtained results of land surface deformation, the estimation of the obtained deformations permissibility is carried out, as well as development of mitigation measures of the underground construction impact on buildings located above the ground. 14

Figure 15. Prediction of land surface subsidence (mm) after the construction completion of all underground structures.

This represented concept of the geomechanically safe underground development of metropolises has successfully approbated at 10 facilities of St. Petersburg and Moscow metro system. The obtained results demonstrate the represented method is able to provide the accident-free construction of complex underground structures having a complex space configuration, in complicated engineering and geological conditions.

REFERENCES [1] Kaplunov D.R., Kalmykov V.N., Kaplunov D.R., Rylnikova M.V. The Combined Geotechnology. Moscow: Publishing House «Ore and Metals», 2003, p. 560. [2] Enyutin A.N., Semenova I.E. On Stress-Strain State of Mass in Structural Elements in the TwoStage Block Caving System at the Development of Pit Reserves. Challenges of Mineral Mining and Underground Development in North-West Russia, p. 3. – Apatity: Krasnoyarsk Research Centre, Russian Academy of Science Publishing, 2001. – pp. 49–55. [3] Rylnikova M.V., Kalmykov V.N., Meshcheryakov E.Yu. Practice of Adjacent Reserve Underground Mining of Uchalinsk copper-sulphide deposit. Mining Information-Analytical Bulletin – M.: MSMU, 1997. No. 3, p. 56–61. [4] Litvinenko V.S. Zubov V.P., Mikhaylenko O.V. Kholodninskoe Deposit: the Concept for Environmentally Safe Working, Main Technical Solutions, Prospects for Mining. Joural of Mining institute. 2012. Volume 196, p. 80–83. [5] Kozyrev A.A. Panin V.I., Maltsev V.A. System Approach to the Prediction and Prevention of Dynamic Phenomena in Mines. Mining Information-Analytical Bulletin – Moscow: MSMU, 2003. No. 12, p. 78–81. [6] Kozyrev A.A., Demidov Yu.V., Yenyutin A.N. and others. Geomechanical Support of Mining Operations Development Design for the Earlier Exhausted Space. Geomechanics at Mining Operations in Highly Stressed Masses – Apatity: Krasnoyarsk Research Centre, Russian Academy of Science Publishing, 1998, p. 25–37. [7] Litvinenko V.S., Boguslavsky E.I., Andreev M.N. Technology and Organization of Mining Works in Pit Reserves Extraction of Kimberlite Pipes of Yakutia in Complex Hydrogeological Conditions. Journal of the Mining institute. 2011. Volume 194, p. 79–83. [8] Kazikayev D.M. Geomechanical Processes at Ore Combined Mining and Remining. Moscow: Mineral Resources, 1989, p. 192. [9] Protosenya A.G., Kuranov A.D., Protosenya A.G. Prediction Method of Stress-Strain State of a Rock Mass at Combined Mining of Koashvinsk Deposit. Mining Journal No.1. Moscow: Publishing House «Ore and Metals», 2015, p. 17–20. [10] Trushko V.L., Protosenya A.G., Matveyev P.F., Sovmen Kh.M. Geomechanics of Masses and Dynamics of Deep Ore Mines. Saint Petersburg: St. Petersburg State Mining Institute, 2000, p. 396.

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[11] Protosenya A.G., Shokov A.N. Calculation of Pillar Parameters at Chamber-and Pillar Ore Mining with the Use of 3D models. News of Higher Education Institute. Mining Journal. 2015. No.11, p. 20–23. [12] Methodology Guidelines on the Determining of Sizes of Chambers and Pillars at Chamber NonFerrous Metal Ore Mining. VNIMI, L.: 1972, p. 85. [13] Petukhov I.M. and others. Calculation Methods in Mechanics of Rock Bumps and Outburst. Moscow, Mineral Resources, 1992, p. 256. [14] Trushko V.L., Protosenya A.G., Plashchinsky V.F. Estimation of Stability of Outcrops and Calculation of Loads on Caving Supports at Yakovlevskoye Mine. Journal of the Mining institute. 2006. Volume 168, p. 115–122. [15] Protosenya A.G., Trushko V.L. Prediction of Mine Stability in Low-Strength Iron Ores of Yakovlevskoye Deposit. Journal of Mining Science. 2013. No. 4, p. 49–61. [16] Karasev M.A. Development of Nonlinear Elastic Transversely Isotropic model of Medium. Challenges of Geomechanics, Geotechnology, and Mine Survey. Journal of Mining institute. 2012. Volume 198, p. 202–206. [17] Karasev M.A. Prediction of Land Surface Subsidence at Underground Construction of Deep-Laid Structures in urban conditions of St. Petersburg. Challenges of Geomechanics, Geotechnology, and Mine Survey//Journal of Mining institute. 2014. Volume 204, p. 248–252. [18] Protosenya A.G., Karasev M.A., Verbilo P.E. The prediction of elastic-plastic state of the soil mass near the tunnel with taking into account its strength anisotropy. International Journal of Civil Engineering and Technology (IJCIET). Vol. 8, Issue 11, 2017, p. 682–694. [19] Protosenya A.G., Ogorodnikov Yu.N., Demenkov P.A., Karasev M.A., Potemkin D.A., Kozin Ye.G. Mechanics of Underground Structures. 3D Models and Monitoring. Saint Petersburg: St. Petersburg Mining University-MANEB, 2011. – p. 355. [20] Litvinenko V.S., Boguslavsky E.I., Korzhavykh P.V. Physical and Mathematical Modeling of Technological Parameters of the Horizone-Chamber Mining for Lower Horizon of the Gubkina Mine/Journal of Mining Institute. 2012. Volume 195, p. 115–119. [21] Lipenkov V.Ya. Specific features of the Antarctic ice sheet structure in the area of station “Vostok” based on the results of petrostructural studies of ice core/V.Ya. Lipenkov, E.V. Polyakova, P. Dyuval, A.V. Preobrazhenskaya//Problems of the Arctic and Antarctic. 2007. Issue 76. p. 68–77. [22] Vasilyev N.I., Dmitriev A.N., Lipenkov V.Ya. The results of drilling 5G borehole at the Russian station “Vostok” and the study of ice cores. – Journal of Mining institute. 2016. Volume 218, p. 161–171.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Complete laboratory experimentation on hydraulic fracturing Herbert H. Einstein & Omar Al-Dajani Massachusetts Institute of Technology, USA

Bruno Gonçalves da Silva John A. Reif Jr., Department of Civil and Environmental Engineering, Newark College of Engineering, New Jersey Institute of Technology, New Jersey

G. Bing Li & Stephen Morgan Massachusetts Institute of Technology, USA

ABSTRACT: Hydraulic fracturing is widely used to create new fractures or extend and open existing ones. However, what exactly happens in the field is not well understood because, in most cases, only indirect information in form of pumping records, microseisms and the in-situ stress field are known. The MIT Rock Mechanics Group has developed and used a unique test equipment, with which the hydraulic fracture propagation can be visually observed while acoustic emissions are simultaneously recorded. All this can be done under different far field (external) stresses and different hydraulic pressures and flow rates. Interestingly, it is also possible to observe how the hydraulic fluid moves in the fractures. This allows one to relate details of the fracturing process to the micro-seismic observations and the boundary conditions thus providing the complete information that the field applications cannot. The testing equipment will be described first, followed by detailed descriptions of hydraulic fracturing experiments on granite and shale. These two rock types represent the typical usage of hydraulic fracturing: Granite for EGS (Engineered Geothermal Systems) and shale for hydrocarbon extraction.

1

INTRODUCTION

Hydraulic fracturing, often referred to as “fracking”, is frequently discussed both in technical and general publications and this mostly in the context of petroleum engineering, specifically, hydrocarbon (oil and gas) extraction. It is discussed both because of its benefits by “unlocking” vast additional amounts of oil and gas, and because of its problematic environmental effects ranging from induced seismicity to groundwater contamination. Before getting into the details of why and how we want to better understand hydraulic fracturing, it is necessary to briefly review where hydraulic fracturing occurs or is used, which goes beyond hydrocarbon extraction. Hydraulic fracturing can be a natural process, in which faults are (re)activated because of increasing pore pressures (Hubbard and Rubey, 1959; Zoback, 2010) or tensile fractures (joints) are caused by pore pressure changes (Secor, 1965; Pollard and Holzhausen, 1979; Engelder and Lacasette, 1990). Pore pressure changes, in turn, can be caused by tectonic processes or by temperature increase related to plutonic activity. It appears that hydraulic fracturing in engineering has first been conceptualized and used in civil engineering in the 1920’s in conjunction with grouting, where intentionally induced fractures filled with grout can be used to inhibit or reduce subsurface groundwater flow. Cambefort (1961) refers to this process as “claquage”. Hydrofracturing in the petroleum industry seems to have started in 1947 and is described in a paper by Clark (1947). At that time, the process involved injection of a high viscosity gel, which is then broken up to eventually allow oil to flow through the newly created fractures. 17

This is different from the process used today particularly in conjunction with unconventionals. These are very low (natural) permeability shales from which oil gas can only be extracted through an intense artificially created fracture network. Specifically, multiple fractures are induced from a horizontal borehole (well) using either the “plug and perf ” or “sliding sleeve” method (see e.g. Shiozawa and McClure, 2014; Ahmed and Meehan, 2016; clearly a multitude of other detailed descriptions exist). The horizontal well is usually drilled in the direction parallel to the smallest principal natural horizontal stress; this facilitates the creation of hydraulic fractures perpendicular to the well and thus to the smallest horizontal stress. From this description, it is evident that one needs to know the in-situ stress field and much literature exists on how one can do this based on knowledge of the existing faulting regime (normal, reverse/thrust, strike-slip) (see e.g. Anderson, 1950; Zoback, 2010). Alternatively, or in addition, hydraulic fracturing often called mini-fracking is used to determine the stress field. This technique (see e.g. Fairhurst, 1964; Haimson, 1978) has been and is being also extensively used in civil and mining engineering. Hydraulic fracturing or hydraulic stimulation of existing fractures is also used in EGS (Engineered Geothermal Systems). There the intention is to create a fracture system at depths greater than 5 to 6 km, circulate water or another fluid through the fractures to heat it to 180°C or greater and then transform the heat through a heat exchanger and power plant into electric energy (possibly using some of the heat also directly). The original version of EGS, called HDR (hot dry rock) to differentiate it from the well-established hydrothermal energy extraction, relied on the same hydraulic fracturing process as discussed for hydrocarbon extraction, i.e. creating artificial fractures in a largely unfractured rock mass (see e.g. Brown et al. 1999, 2012). EGS in contrast relies mostly on hydroshearing, i.e. the stimulation of existing fractures through pore pressure changes such that fractures displace in shear and produce greater apertures. It is interesting to note that this process is analogous to what has been mentioned above under natural geologic hydrofracturing processes, namely the activation of faults. The seismicity related to fault (re-)activation is one of the problems related to hydraulic fracturing and stimulation (see e.g. Cornet et al. 2007; Cornet, 2016; Jung, 2013; Mukuhira et al. 2013). See also NRC, 2013.

2

PROBLEM STATEMENT AND POSSIBLE SOLUTION

Several issues arise in the context of hydraulic fracturing. In the introduction above, the environmental effects (groundwater contamination, induced or triggered seismicity) have been mentioned. For this, one needs to know how hydraulic pressure produces new fractures or causes existing ones to displace in shear and/or open in tension. Hubbard and Willis (1957) produced path-breaking experimental and theoretical work to predict the creation of new fractures relative to existing stress fields. Many others have increased the understanding often using sophisticated experiments and models (Zoback et  al.,1977; Rubin, 1983; Teufel and Clark, 1984; Cleary, 1988; Stoekhert et  al., 2014; Stanchits et  al., 2015; Lecampion et  al., 2015). Similarly, fracture flow has received much attention including several studies by the National Research Council (NRC, 1996, 2015). Somewhat related to the issue of environmental effects but particularly important for optimizing the gas/oil production from hydrocarbon reservoirs or heat in EGS is the creation of a specific fracture network in the ground. As mentioned earlier and discussed in the cited literature, one can theoretically relate fracture orientation to the in-situ stress field and use the observed injected volume of the fracking fluid to predict the overall extent of fractures. However, given the fact that one cannot directly see the created fractures the “observation” of fracturing is only indirect, namely, through measurement of the pressure-time behavior during the injection and observation of microseisms. Not surprisingly, researchers have tried to improve the knowledge by conducting increasingly sophisticated laboratory experiments and relate the results to reality through scaling laws (e.g. Bunger et al., 2005). Such laboratory experiments also contribute to fundamental understanding of the detailed mechanisms and thus form the basis of models. 18

Two types of pressurization devices were used. In Device 1 (shown in Figure 5) the entire face This approach to solving the problem is also what is presented below. We try to use known natural material, apply known external (far field) stresses, apply and measure hydraulic pressure in a variety of fracture geometries and, very importantly, observe the hydraulic fracturing process both visually and through acoustic emissions. This allows us to relate the visually observed fracturing process to the “indirect” observation of acoustic emission. While others, e.g. with CT Scanning (e.g. Kawakata et  al., 1999) and transparent materials (e.g. Bunger et al., 2005) have attempted similar solutions our visual observations are unique.

3

EXPERIMENTAL SETUP

The principle of our experiments follows what was done in the past (Reyes and Einstein, 1991; Bobet and Einstein, 1998, 2002; Wong and Einstein 2009a, b) namely using prismatic blocks with pre-existing fractures, so called flaws, shown in Figure 1. The prismatic specimens are cut from cores or slabs of the particular rock, and the flaws are cut with saws (shale) or water jet (marble, granite). The specimen-preparation process is quite demanding and must be done with care (Al Dajani et  al., 2017). Figure  2  shows the possible applied boundary conditions, namely uniaxial or biaxial external stresses without or with hydraulic pressure in the flaws. The equipment we use is shown in the photo of Figure 3 and the schematic of Figure 4. As mentioned above, what we do is unique with simultaneous visual and

Figure 1. Typical prismatic specimen geometry with pre-existing flaws.—The flaw location and orientation can be varied.

Figure 2.

Possible loading conditions applied to prismatic specimen.

19

Figure 3. Hydraulic fracturing experimental setup: (a) Central data acquisition (b) Hydraulic fracture apparatus (PVA, LVDT, Pressure Transducer) (c) Lateral load (d) Axial load (e) High resolution images (f) High speed video (g) High resolution video (h) Load frame computer (i) High resolution camera computer (j) High speed video computer (k) Acoustic emissions system.

Figure 4.

Schematic of the experimental setup.

AE observations. Specifically, the just mentioned boundary conditions are applied while we visually observe with high speed—and high resolution photography how new cracks emanate from the flaw(s), then propagate, and how this can lead to coalescence if there is more than one flaw. The photographic observations allow us to distinguish shear and tensile cracks and, if there is hydraulic fracturing, how the fluid flows in the newly created crack. Two types of pressurization devices were used. In Device 1 (shown in Figure 5) the entire face is under water pressure while in Device 2 (Figure 6) only the flaws are pressurized under a local seal. In both cases the front is transparent to make visual observations possible, while the pressure is produced through a Pressure Volume Actuator. The placement of the AE sensors is somewhat different depending on the device, but a minimum of six sensors are placed as shown in Figure 7 while the schematic of the AE system is shown in Figure 8. 20

Figure 5. the back.

Flaw pressurization device 1. Full-face pressurization; pressurizing fluid entering through

Figure 6. Flaw pressurization device 2. Local seal behind a transparent window; three “needles” are used to fill the flaw with the pressurization fluid and to measure the pressure in the flaw. Note: The device is copyrighted by the authors.

Figure 7. Placement of AE sensors.

21

Figure 8.

3 3.1

Schematic of AE recording system.

EXPERIMENTAL RESULTS Experimental evaluation process

This is shown with the experiment on a single flaw inclined at 30° in granite subject of a constant vertical (uniaxial) stress of 5 MPa. Figure 9a, b show the time pressure/volume record. “Sketches” indicate when photos (either high resolution or high speed) were taken. They were then analyzed as in Figure 10, which also includes the evaluation process used in the analysis. Figure 10 shows the initial and final stages of the test the latter with a fully developed HF crack. Intermediate sketches such as Sketch 6 (Figure 11) show how the cracks develop and link up. Interesting is the fact that, as shown in Figure 11, so called “white patches” precede the development of visible cracks. White patches are the visual evidence of process zones consisting of microcracks as was described by Wong and Einstein (2009 a,b) and Morgan et al. (2013). The white patch and crack development can also be seen through acoustic emissions as shown in Figure  12, in which the events are categorized by amplitude. It is also possible to interpret the source mechanisms as will be discussed later. This example of HF propagation in an experiment shows that one can indeed relate visual and AE observations under specific external conditions. 3.2

Granite

Since hydraulic fracturing of granite (Barre Granite, see e.g. Morgan et al., 2013) was to some extent discussed above, the results presented in this section will be limited to summarizing the visually observed crack patterns and to aspects regarding acoustic emissions that have not been discussed before. Gonçalves da Silva (2016) conducted an extensive series of hydraulic fracturing tests with Device 1 on double flaw geometries, in which the flaw inclination angle β (see Figure  1) was kept constant at 30° but with variation of the bridging angle α and applying either "0" external stresses or 5 MPa uniaxial stress. The observed cracking patterns are summarized in Figure 13 while the maximum water pressures are shown in Figure 14. Both for fundamental and practical purposes, it is interesting to know if hydraulic fractures can produce coalescence or not. As shown in Figure 13, coalescence does occur under all conditions if the flaws are significantly offset (bridging angle 60° or greater). For lower bridging angles, the occur22

Figure 9. Typical pressure/volume—time behavior in hydraulic fracturing test. a. Entire experiment; b. Close-up of final stage. “Sketches” refers to images taken at that time (see Figs. 10 and 11).

Figure 10. Images and superimposed sketches “0” and “8” of experiment shown in Fig. 9. The figure also shows the nomenclature used in the sketch.

23

Figure  11. Detailed analysis of sketch “6” of experiment shown in Fig. 9. For Nomenclature, see Figure 10.

Figure 12.

Acoustic emissions of experiment shown in Fig 9.

Figure 13.

Summary of hydraulic fracturing tests on granite—Induced cracking patterns.

24

rence and type of coalescence depend both on the flaw geometry and the external stresses. Given the scatter in Figure 14 (very low coefficients of determination) one can only say that the maximum water pressure increases if an external stress is applied. The other item specifically related to granite is documented in Figure 15 with an interpretation of the acoustic events using moment tensor inversion for the same test as shown in

Figure 14.

Summary of hydraulic fracturing tests on granite—Maximum water pressure.

Figure 15. Hydraulic fracturing tests on granite—interpretation of source mechanisms. DC = Double couple; NDC = Non- double couple explosion/implosion.

25

Fig 12. Interestingly, the source mechanisms obtained from AE show both tensile and shear mechanisms although the crack was visually identified as tensile ((Fig. 11). Investigations by Gonçalves da Silva (2016) show that the process zone (white patching) involves both mechanisms and some small-scale shearing in a crack that opens in tension. 3.3

Shale

Different types of shale, namely, Opalinus Chayshale from the Mt. Terri laboratory in Switzerland and Vaca Muerta shale from Argentina have been investigated. The Opalinus Clayshale comes from different locations in the Mt. Terri Lab and the facies therefore differ. Nevertheless, there is a reasonable consistency of the results (see Morgan, 2015). Opalinus Clayshale is not a source or reservoir rock. It was chosen because very carefully extracted cores were made available (courtesy Mt. Terri Laboratory and SwissTopo). Also, Al Dajani (2017) compared the behavior of Opalinus Clayshale to Vaca Muerta shale to make certain that the behavior of the two shales is comparable The shale test series conducted so far differs from that on granite in that additional parameters were investigated, namely, the bedding plane orientations, application of biaxial external stresses and varied flow rates. All experiments were conducted with pressurization Device 2 (see Figure 6). In tests with horizontal bedding planes under uniaxial external stress (Figure 16), it appears that when hydraulic fractures intersect bedding planes, flow occurs through some bedding planes before the hydraulic fracture continues, in other words, the hydraulic fracture is offset (Figure 17). The different types of HF crossings of bedding planes are shown in Figure 18. This behavior is reasonably well known (Fisher and Warpinski, 2011; Einstein, 1993) and is naturally very important since the crossing behavior contributes to the overall complexity of the induced fractures. The effect of bedding plane orientation becomes more evident when conducting tests on specimens with differently oriented bedding planes (Figure 19) but even then, there is some stepping. Another observation is equally important: Figure 20 shows that the liquid (40 cp oil in this case) lags behind the crack tip. This behavior is also often cited in the literature (Christianovich et al., 1978; Daneshi, 1978; Feng and Gray 2017) but actually seeing it (and thus being able to measure the lag) in a natural material is unique. When one varies the flow rate as shown in Figure  21a, the resulting HF crack pattern become increasingly complex with increasing flow rate. Simple energy relations explain this but additional tests need to be run to obtain accurate details. These flow rate experiments also involved AE readings which are shown in Figure 21b, and this shows that the just mentioned increasing crack complexity goes hand in hand with increasing number of events.

Figure 16. Schematic of Hydraulic Fracturing Tests on Opalinus Clayshale with Horizontal Bedding Planes under Uniaxial Stress. Seal (blue outline) Indicates Pressurized Flaw.

26

Figure 17.

Cracking patterns induced by hydraulic fracturing in the tests of Fig. 16.

Figure 18. Schematic of hydraulic fracture crossing bedding planes. 1: direct crossing, 2: offset crossing with flow into bedding planes, 3: direct crossing with flow into bedding planes, 4: arrest with flow into bedding planes, 5: arrest.

Figure 19. Cracking Patterns Induced by Hydraulic Fracturing in Tests on Opalinus Clayshale with a Single Flaw and Differently Oriented Bedding Planes.

27

Figure 20. Observation of Fluid Lag.

Figure  21. Hydraulic Fracturing in Tests on Opalinus Clayshale with Different Flow Rates; a. Cracking patterns; b. Source mechanisms (crosses = shear event; line = tensile event).

4

SUMMARY AND CONCLUSIONS

A unique experimental setup that allows one to observe the hydraulic fracture process both visually and with AE (acoustic emission) was developed at MIT. This setup was briefly described together with the parameters that can be controlled and the typical visual and AE observations obtained. The paper then shows that experiments on granite and shale produce results that relate the visual and AE observations; in other words, the underlying mechanisms can be explained. Such results not only provide fundamental understanding but also provide the basis for models that can eventually be upscaled to represent field conditions. Given that 28

both granite and shale have been investigated, the applications will encompass both hydrocarbon extraction and Engineered Geothermal Systems.

ACKNOWLEDGEMENTS The research on granite and the initial equipment development was sponsored by the US Dept. of Energy (Project Recovery Act: Decision Analysis for Enhanced Geothermal Systems) and TOTAL (Project MSGC—Multiscale Gasshale Collaboratory), while the shale work was sponsored by TOTAL (Project MSGC) and ARAMCO (fellowship). As mentioned in the text the Opalinus Clayshale was made available by the Mt Terri Lab of SwissTopo. The authors would like to express their gratitude for all this support.

REFERENCES Ahmed, U., & Meehan, D.N. (Eds.). (2016). Unconventional Oil and Gas Resources: Exploitation and Development. CRC Press. AlDajani, O.A. (2017). Fracture and Hydraulic Fracture Initiation, Propagation and Coalescence in Shale (Master’s Dissertation, Massachusetts Institute of Technology). AlDajani, O.A; Morgan, S.P; Germaine, J.T; Einstein, H.H. (2017 b). Vaca Muerta Shale—Basic Properties, Specimen Preparation, and Fracture Processes. 51st US Rock Mechanics/Geomechanics Symposium. Anderson, E.M. (1951). The Dynamics of Faulting and Dyke Formation with Applications to Britain. Hafner Pub. Co. Bobet, A.; Einstein, H.H. (1998). Fracture Coalescence in Rock-Type Materials under Uniaxial and Biaxial Compression. International Journal of Rock Mechanics and Mining Sciences, 35(7), 863–888. Bobet, A.; Einstein, H.H. (2004). Crack Coalescence in Brittle Materials—Overview of Current Knowledge. Rock Engineering—Theory and Practice. Proceedings of the ISRM Symposium. W. Schubert (ed.): EUROCK 2004 and the 53rd Geomechanics Colloquy, Salzburg, Austria, pp. 475–478. Brown, D.; DuTeaux, R.; Kruger, P.; Swenson, D.; Yamaguchi, T. (1999). Fluid Circulation and Extraction from Engineered Geothermal Reservoirs. Geothermics, 28(4), 553–572. Brown, D.W.; Duchane, D.V.; Heiken, G.; Hriscu, V.T. (2012). Mining the Earth’s Heat: Hot Dry Rock Geothermal Energy. Springer Science & Business Media. Bunger, A.P.; Jeffrey, R.G.; Detournay, E. (2005). Application of Scaling Laws to Laboratory-Scale Hydrocarbon Fractures. Proceedings U.S. Rock Mechanics Symposium, Anchorage. Cambefort H., (1961). L’Injection et ses problèmes, Bulletin Technique de la Suisse Romande, Vol. 87. Christianovich, S.A.; Zheltov, Y.P. (1955). Formation of Vertical Fractures by Means of a Highly Viscous Fluid. In Proc. 4th World Petroleum Congress (Vol. 2, pp. 579–586). Clark J.B. (1947). A Hydraulic Process for Increasing the Productivity of Wells, AIME Petroleum Transactions. Cleary, M.P. (1988). The Engineering of Hydraulic Fractures State-of-the-Art and Technology of the Future. Jrnl. of Petroleum Tech. pp. 13–21. Cornet, F.H. (2016). Seismic and Aseismic Motions Generated by Fluid Injections. Geomechanics for Energy and the Environment, 5, 42–54. Cornet, F.H.; Bérard, T.; Bourouis, S. (2007). How Close to Failure is a Granite Rock Depth?. International Journal of Rock Mechanics and Mining Sciences, 44(1), 47–66. Daneshy, A.A. (1978, February 1). Hydraulic Fracture Propagation in Layered Formations. Society of Petroleum Engineers. Einstein, H.H. (1993). Modern Developments in Discontinuity Analysis—The Persistence-Connectivity Problem. In Comprehensive Rock Engineering. J. Hudson, ed. Pergamon Press. Fairhurst C. (1964). Measurement of In-Situ Rock Stresses with Particular Reference to Hydraulic Fracturing Rock Mechanics Vol. 2 pp. 129–147. Feng, Y.; Gray, K.E. (2017). Discussion on Field Injectivity Tests During Drilling. Rock Mechanics and Rock Engineering, 50(2), 493–498. Fisher M.K.; Warpinski N.R., (2011). Hydraulic Fracture Height Growth Real Data, SPE Annual Techhnical Conference and Exhibition. Gonçalves da Silva, B. (2016). Fracturing Processes and Induced Seismicity Due to the Hydraulic Fracturing of Rocks. MIT. Ph.D. Thesis.

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Haimson, B.C. (1974), A Simple Method for Estimating In-Situ Stresses at Great Depths. Field Testing and Instrumentation of Rock ASTM STP 554, pp. 156–182. Hubbard M.K., Willis D.G. (1957). Mechanics of Hydraulic Fracturing AIME Petroleum Transactions Hubbard M.K.; Rubey, W.W. (1959). Role of Fluid Pressure in Mechanics of Overthrust Faulting, Bulletin of the Geological Society of America Vol. 70 pp. 115–166. Jung, R. (2013). EGS—Goodbye or Back to the Future 95. In Effective and Sustainable Hydraulic Fracturing. InTech. Kawakata, H.; Cho, A.; Kiyama, T.; Yanagidani, T.; Kusunose, K.; Shimada, M. (1999). ThreeDimensional Observations of Faulting Process in Westerly Granite under Uniaxial and Triaxial Conditions by X-ray CT Scan. Tectonophysics, 313(3), 293–305. Lecampion, B.; Desroches, J.; Jeffrey, R.G.; Bunger, A.P.; Burghardt, J. (2015). Initiation versus Breakdown Pressure of Transverse Radial Hydraulic Fracturing, Theory and Experiments. Proc. Int’l. Congress of the ISRM. Morgan, S.P.; Einstein, H.H. (2014). The Effect of Bedding Plane Orientation on Crack Propagation and Coalescence in Shale. In: Proceedings of the 48th U.S. Rock Mechanics/Geomechanics Symposium, Minneapolis, Minnesota. Morgan, S.P.; Johnson, C.A.; Einstein, H.H. (2013). Cracking Processes in Barre Granite: Fracture Process Zones and Crack Coalescence. International Journal of Fracture, 180 (2), 177–204. Mukuhira, Y.; Asanuma, H.; Niitsuma, H.; Häring, M.O. (2013). Characteristics of Large-Magnitude Microseismic Events Recorded During and After Stimulation of a Geothermal Reservoir at Basel, Switzerland. Geothermics, 45, 1–17. National Research Council (2015) Fracture Characterization at Depth. National Research Council. (1996). Rock Fractures and Flow. National Academies Press. National Research Council. (2013). Induced Seismicity Potential in Energy Technologies. National Academies Press. Pollard D.D.; Aydin A. (1988). Progress in Understanding Jointing over the Past Century. Bulletin of the Geological Society of America Vol. 100 pp. 1181−1204. Pollard, D.D.; Holzhaisenn G. (1979). On the Mechanical Interaction between Fluid-Filled Fracture and the Earth’s Surface Tectonophysics Vol. 53 pp. 27–57. Reyes, O.; Einstein, H.H. (1991). Failure Mechanisms of Fractured Rock—a Fracture Coalescence Model. In: Proceedings of the 7th ISRM Congress, Aachen, Germany. Rubin, M.B. (1983). Experimental Study of Hydraulic Fracturing in an Impermeable Material. Jrnl. of Energy Resources Tech. Vol. 105. Sarmadivaleh, M.; Rasouli, V. (2015). Test Design and Sample Preparation Procedure for Experimental Investigation of Hydraulic Fracturing Interaction Modes. Rock Mech. and Rock Eng. Vol. 48. Secor, D.T. (1965). Role of Fluid in Pressure Jointing, American Journal of Science Vol. 263, pp. 633–646. Shiozawa, S.; McClure, M. (2014). EGS Designs with Horizontal Wells, Multiple Stages, and Proppant. In Proceedings of the 39th Workshop on Geothermal Reservoir Engineering, Stanford. Stanchits, S.; Burghardt, J.; Surdi, A. (2015). Hydraulic Fracturing of Heterogeneous Rock Monitored by Acoustic Emission. Rock Mech. Rock Eng. Vol. 48. Stoeckhert, F.; Brenne, S.; Molenda, M.; Alber, M. (2014). Hydraulic Fracturing of a Devonian Slate under Confining Pressure—with Emphasis on Cleavage Inclination. Rock Mech. and Rock Eng. Teufel, L.W.; Clark, J.A. (1984). Hydraulic Fracture Propagation in Layered Rock: Experimental Studies of Fracture Containment. Jrnl. of Society of Petroleum Engineers. pp. 19–32. Wong, L.N.Y.; Einstein, H.H. (2009a). Crack Coalescence in Molded Gypsum and Carrara Marble: Part  1. Macroscopic Observations and Interpretation. Rock Mechanics and Rock Engineering, 42 (3), 475–511. Wong, L.N.Y.; Einstein, H.H. (2009b). Crack Coalescence in Molded Gypsum and Carrara Marble: Part 2. Microscopic Observations and Interpretation. Rock Mechanics and Rock Engineering, 42 (3), 513–545. Zoback M. (2010), Reservoir Geomechanics, Cambridge University Press. Zoback, M.D.; Rummel, F.; Jungi, R.; Raleigh, C.B. (1977). Laboratory Hydraulic Fracturing Experiments in Intact and Pre-Fractured Rock. Intl. Jrnl. Rock Mech. and Mining Sciences Vol. 14 (2).

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Strength and deformability of brittle polycrystalline materials in multiaxial stress-strain state: Rupture energy evaluation for brittle materials Erast G. Gaziev Center of Geodynamical Researches, Hydroproject Institute, Moscow, Russia

ABSTRACT: A phenomenological strength criterion for brittle polycrystalline materials (including rock) in multi-axial stress states is proposed. This criterion allows for the strength of materials to be assessed practically with any combination of principal stresses. It is based on the maximum distortion energy theory. It does not contain parameters which could require additional evaluation (excluding uniaxial compressive and tensile strength data). The results well agree with the available experimental data. This criterion can be used for assessment of strength of brittle polycrystalline materials, such as rocks and concrete, for strength analysis of concrete structures and their foundations by numerical methods. Proposed criterion can also be used to assess the strength of the riprap. This conclusion is confirmed by numerous experiments conducted for a number of rockfill dams in Mexico, as well as to evaluate the strength of rockfill materials under uniaxial loading, which can be used as a classification parameter. The process of material destruction is always associated with the release of the energy expended for loading. The failure process of a material is always connected with the energy consumption. Work performed by external forces leads to the accumulation of energy by the constituting elements of the material structure; failure of the material suddenly releases part of the cumulative energy. The researches carried out indicate that there is a close relationship between rupture energy and intensity of the stress applied at the moment of failure. This relationship is valid for both the uniaxial and triaxial strength tests confirming that during the failure process there is a simultaneous mobilization of the tensile and shear strengths whereas the rupture energy is the result of energy distortion. Keywords: Principal stresses, strength criterion, intensity of stresses and deformations, stress-strain diagrams, rupture energy, strength of rockfill materials

1

INTRODUCTION

Determination of the strength of brittle polycrystalline materials, including rock, in a complicated stressed state is one of the fundamental problems of rock mechanics, which has not yet found a satisfactory practical solution. The destruction of such materials during combined loading, and especially brittle fracture, has been the subject of numerous theoretical and experimental studies in recent decades. It was proposed many empirical strength criteria, each of which describes the strength within a certain range of loading the materials studied that points to the necessity of further studies in order to identify the nature of the destruction of such materials, including the study of micro- and macro-fracturing and deformation processes in the entire range of loading both in the pre-failure and post-failure zones. 31

The main feature of brittle rock behavior under triaxial loading is that in natural conditions, as a rule, it is deprived of the possibility of free lateral expansion and, therefore, with increasing one of acting principal stresses two others also increase. Moreover, this increase of the “lateral” principal stresses continues after “fracturing” of the material as a result of the increase of the coefficient of lateral expansion and tight conditions existing in the rock mass. Even a slight increase in the lateral compression causes the increases of the load-bearing capacity of the rock mass creating the so-called “hardening” effect. Fig. 1 shows a typical stress-strain curve obtained by continuous recording of the stress and strain in uniaxial loading and breaking gypsum sample. It can be noted that the process of micro-destruction of the sample began almost from the very beginning of its loading, reaching the maximum value with the load reaching approximately 80% of the maximum compressive strength Rc, after which the macro-destruction has started. The combination of the principal stresses that generate a sharp increase in the deformation of the sample with insignificant increase in the stress tensor shall be considered as the strength of the polycrystalline material subject to a triaxial stress state. The state of stress at the moment of failure can be described by three principal stresses σ1, σ2, and σ3, representing a point in the coordinate system of principal stresses. If all the points, corresponding to the failure of the material are connected, we will obtain the strength surface in the coordinates of principal stresses: f (σ1, σ2, σ3) = 0

(1)

It can be assumed that the strength surface will not exist under hydrostatic compression conditions (σ1 = σ2 = σ3) when destruction is considered impossible. In addition, the condition for the hierarchy of principal stresses σ1 ≥ σ2 ≥ σ3 requires consideration of the existence of a strength surface only where this condition is satisfied. Numerous experimental studies of rock samples, cement and gypsum stones in 3-D stress state showed that the brittle materials under these conditions acquire the plastic properties and at the same time their strength increases significantly. At the same time there is an alignment of the lateral (second and third) principal stresses. To “automatically” reproduce this process of increasing “lateral” stresses with increasing the first main stress in the Laboratory of Rock Mechanics of the Institute “Hydroproject”, in 1982 a special installation was designed and manufactured (Fig. 2). The sample was placed in a cage of steel plates connected in pairs with steel rods simulating the stiffness of the surrounding rock mass. The test was conducted with increasing a vertical compressive load imparted by a press (σ1) with detent the lateral stresses (σ2 and σ3), and the acoustic emission in the sample body. At the same time the vertical and lateral deformations were measured. The main advantage of this method of research is that, after reaching the limit state by the stress tensor, it continued to “slide” across the strength surface, thus making it possible to obtain not just a single point of the strength surface in one experiment as usually obtained in conventional tests with constant lateral stresses, but a series of consecutive points, i.e. the whole fragment of it (Fig. 3) representing a stress-strain diagram of the concrete specimen obtained with this equipment (Gaziev et al. 1984). The moment when the stress tensor reaches the “strength surface” can be determined from the diagram of the sample deformation. Fig. 4 shows photographs of the side faces of the sample as a result of the first destruction, and then the test has been continued with the fractured sample. The studies have shown that after reaching the “strength surface” by the sample, followed by unloading and new loading, the sample deformation diagram returns to the same “strength surface” and continues to slide along it. This effect is explained by the fact that during the fracturing the sample lateral stresses σ2 and σ3 start increasing due to a sharp increase of the coefficient of dilatation (Poisson’s ratio), as seen in Fig. 5, which shows the growth of lateral stresses of a sample of cement stone after the beginning of its destruction at 55 MPa. 32

2

RUPTURE CRITERION EVALUATION

As early as in 1855 E. Beltrami proposed to consider the amount of energy required for deformation as a criterion of strength of the material. However, this proposal has not been confirmed, since it is a well-known fact that during triaxial hydrostatic compression of a specimen, the material is capable of accumulating a huge amount of energy without evidencing visible indications of failure. Therefore, not all energy spent for deformation becomes determinant but only the component necessary for distorting the specimen. This idea was advanced by J.C. Maxwell in his letter to W. Thomson of 1856: “I have strong reasons for believing that when [the strain energy of distortion] reaches a certain limit then the element will begin to give way”. We see that Maxwell already had the theory of yielding which we now call the maximum distortion energy theory. But he never came back again to this subject and his ideas became known only after publication of Maxwell’s letters (Timoshenko, 1953). It took many years until first M.T. Huber in 1904 and independently of him in 1913 von Mises (R. von Mises) came to the same idea and proposed a theory called the theory of maximum distortion energy of Huber-Mises (Timoshenko, 1953). This theory that was proposed to describe the beginning of a plastic-type behavior of soft steel alloys is based on the fact that the limiting state starts when the so-called specific distortion energy becomes equal to a certain value. Several trials were made subsequently to develop a theory based on the distortion energy. One of such criteria describing the strength of a polycrystalline material subjected to a multiaxial stress state based on the same theory with a satisfactory accuracy of the results obtained was proposed by the author of this paper (Gaziev et al., 1984; Gaziev, 1996; Gaziev & Levtchouk, 1999). Taking into account the considerable difficulties in obtaining a purely theoretical criterion of description of the failure process for such materials, the only reliable solution of this problem for developing the practicable criterion can be the creation of a phenomenological criterion that considers the most important factors involved in the material failure. The condition σ1 ≥ σ2 ≥ σ3 must be satisfied. For working out this phenomenological failure criterion it was assumed that the strength of brittle material is mainly conditioned by distortion energy of a sample. Then, the main parameters determining the strength of the rock under multiaxial stress state are the following: − the first invariant of stresses: J1 =

1

+ σ2 + σ3

− the second invariant of stress deviator: J2 = (

1

−

2

)2 + (

2

−

3

)2 + (

1

−

3

)2

− compressive strength (uniaxial compression) Rc; − tensile strength (uniaxial tension) Rt (Rt as the strength parameter is always positive). Further in this analysis, it will be assumed that the compression is positive and σ1>σ2>σ3. The following strength criterion for brittle materials under multiaxial complex stress state was proposed (Gaziev, 1996): n

σ* + ⎛ τ − m⎞ =⎜ * ⎟ , 1+ m ⎝ 1− m ⎠

(2)

where all participating parameters are dimensionless:

σ* =

σ1 + σ 2 + σ 3 , Rc 33

(3)

τ* =

(σ 1 σ 2 )2 + (σ 2 σ 3 )2 + (σ 1 σ 3 )2 2R Rc2 m = Rt/Rc.

(4) (5)

The expression for “n” was derived from experimental studies: 1.15 ≤ n ≤ 1.3

(6)

The proposed criterial relationship (2) describes the “strength surface” in the principal stress coordinates (Fig. 6). The results of thorough investigations of Dr. M. Takahashi and H. Koide (1989), kindly sent at our disposal by Dr. Takahashi (studies of Shirahama and Izumi sandstones, Westerly granite, Yuubari shale and Yamaguchi marble), as well as the experimental results of Z.T. Bieniawski (1971), N.S. Parate (1969), G. Vouille and D. Laurent (1969) were used for verification of the criterion for different magnitudes of all three principal stresses (with n = 1.3) To justify the proposed criterion for different combinations of principal stresses at failure, the linear dependence between the left and right parts of the equation (2) were used: X=

σ∗ + m 1+ m

n

⎛ τ − m⎞ Y =⎜ ∗ . ⎝ 1 − m ⎟⎠ These experimental results are presented in Fig. 7. Good agreement of the criterion with experimental data is observed over a fairly wide spectrum of the principal stresses. In all cases when there is no reliable tensile strength data, the suggested criterion allows for evaluating m value as a parameter of criterion equation (2), by processing the experimental data on triaxial stress state. Any simple mathematical method can be used. Fig. 8 shows a diagram of strength of the siltstone enclosing underground structures of the Rogún hydropower station (Tajikistan). The strength was calculated in the same coordinates of equation (2) with n = 1.15 based on the results of triaxial tests performed in Turin (Dr. Barla) and Tehran (Samonian) (Rogún, 2015). Despite the fact that the studies were carried out in different laboratories in different series of siltstone samples, we can say that they are very well matched to the proposed criterion. Later on with participation of the author in the Engineering Institute of the National Autonomous University of Mexico City a new installation has been created for testing the cubic samples measuring 15 × 15 × 15 cm with independent application of the three principal stresses (Gaziev & Levtchouk, 1997). Photo of the installation is shown in Fig. 9. For recording and analyzing the obtained experimental results, such as: the value of the applied load, the magnitude of deformation and acoustic emission occurring within the sample during its cracking, the program allows for simultaneous recording 32 analog signals at a rate of 10,000 samples per second (up to 100,000 samples per second when using only one channel). Measurements of the frequency and amplitude of acoustic emission was made by small-size microphone mounted directly on the load plate. The program allowed for plotting the relationship between the measured parameters on the computer screen, as well as the dependence of these parameters on time producing the accumulation of information on the computer hard disk in “real time” for reconstructing the experiment and pre-processing the information (Gaziev & Levtchouk, 1997). To obtain a “complete diagram” of deformation of the sample prior to and during the rupture a high-speed recording of the experimental results in real time was used. Such highspeed deformation recording made it possible to obtain the diagram shown in Fig. 1, as well as all diagrams ε = f (σ) below. 34

Fig.  10 is a diagram of the concrete sample deformation (c.21) (Gaziev & Levtchouk, 1997) with initial values of confining stresses σ2 = σ3 = 2.16 MPa during 3 cycles of loading and unloading obtained in Mexico triaxial loading installation (Fig. 9). The peak stress τi at the beginning of rupture can be determined from the criterion proposed, i.e.: 1

( i )cr = Rt

(

⎛ σ 1 + σ 2 + σ 3 + Rt ⎞ n t )⎜ ⎟⎠ R R ⎝

c

c

(7)

t

To determine the moment when failure starts, the acting stress τi can be divided into its predetermined limiting value. At the moment when τi/(τi)cr  =  1 the strength surface is reached and if the value of τi continues rising, the representative point “slides” for a certain time along this surface (the failure process in a three-dimensional state of stress) (Fig. 10). Table 1 and Fig. 11 depict the data of a triaxial test performed on a cement stone specimen (c3). With the criterion proposed it is possible to determine the moment of rupture that occurred when the principal stresses reached the values of (σ1)cr  =  46.08  MPa, (σ2)cr  =  (σ3)cr = 0.98 MPa. The corresponding strains became equal to (ε1)cr = 0.00871 and (ε2)cr = (ε3)cr = −0.00345. The magnitude of the critical stress was equal to (τ)cr = 45.1 MPa and that of the critical strain became (ε)cr = 0.012161. It can also be noted that the application of lateral pressure to the sample, which amounted approximately 2.5% of the uniaxial strength of the sample (0.98 MPa from 39.4 MPa) led to an increase in its strength by 17% (46.1 MPa instead of 39.4 MPa).

3

RUPTURE ENERGY EVALUATION

For analyzing the work performed by external forces it is convenient to operate with the so-called stress intensity (Bezukhov, 1961) that is determined from the following equation:

τi

3 1 τ oct = (σ 1 − σ 2 )2 + (σ 2 − σ 3 )2 + (σ 1 σ 3 )2 2 2

(8)

as well as from the deformation intensity that is in turn obtained from expression:

εi

1 ( ε1 − ε 2 ) 2 + ( ε 2 − ε 3 ) 2 + ( ε1 − ε 3 ) 2 2

(9)

These two parameters are directly proportional to the square root of the second invariant of the deviatoric stress and strain tensor. At the moment of failure the stress intensity τι  =  τcr. In the case of the uniaxial testτcr becomes equal to the unconfined compressive strength, τcr = Rc, whereas for the «conventional» triaxial test (when σ2 = σ3) it assumes the value of the peak shear strength, τcr = (σ1 – σ3), just at the time when failure starts. The work of the external distortion forces when failure starts or the rupture energy for a unit volume of the specimen can be calculated from, ε ccr

Ecr

∫τ

i

i

) dεi

(10)

0

For a triaxial test, the moment when failure starts is determined by the phenomenological criterion (2). Table 1 and Fig. 11 depict the data of the triaxial test performed on a cement specimen (c3). 35

Table 1.

Concrete specimen (c3) triaxial test data.

σ1 MPa

σ1 = σ3 MPa

ε1

ε2 = ε3

εi

τi MPa

(τi)cr MPa

τi /(τi)cr

0.98 1.96 2.94 3.92 4.90 5.88 6.86 7.84 8.82 9.80 14.71 19.61 22.55 23.53 24.51 25.49 26.47 27.45 28.43 29.41 30.39 31.37 32.35 33.33 34.31 35.29 36.27 37.25 38.24 39.22 40.20 41.18 42.16 43.14 44.12 45.10 46.08 46.64 46.62

0.006 0.012 0.018 0.024 0.030 0.036 0.043 0.049 0.055 0.061 0.092 0.123 0.144 0.147 0.157 0.167 0.186 0.196 0.206 0.225 0.235 0.255 0.275 0.294 0.314 0.343 0.373 0.392 0.431 0.461 0.500 0.559 0.608 0.686 0.775 0.882 0.980 1.049 1.765

0.00011 0.00022 0.00033 0.00044 0.00055 0.00066 0.00077 0.00088 0.00099 0.0011 0.00165 0.0022 0.00253 0.002642 0.002757 0.002876 0.002998 0.003126 0.003259 0.003399 0.003547 0.003705 0.003873 0.004053 0.004246 0.004454 0.00468 0.004923 0.005183 0.005469 0.005785 0.006133 0.006525 0.00696 0.00746 0.00804 0.00871 0.0094 0.0094

−1.5E-05 −0.00003 −4.5E-05 −0.00006 −7.5E-05 −0.00009 −0.00011 −0.00012 −0.00014 −0.00015 −0.00023 −0.0003 −0.00035 −0.00036 −0.00038 −0.00039 −0.00041 −0.00044 −0.00046 −0.0005 −0.00054 −0.00059 −0.00067 −0.00073 −0.00082 −0.00093 −0.00105 −0.00119 −0.00134 −0.00153 −0.00174 −0.00197 −0.00222 −0.0025 −0.00279 −0.00311 −0.00345 −0.00374 −0.00372

0.000125 0.00025 0.000375 0.0005 0.000625 0.00075 0.000875 0.001 0.001125 0.00125 0.001875 0.0025 0.002875 0.003002 0.003133 0.003269 0.00341 0.003561 0.003722 0.003897 0.004088 0.004299 0.004539 0.004785 0.005066 0.005379 0.005725 0.006108 0.006527 0.006999 0.007524 0.008102 0.008747 0.009457 0.010253 0.011151 0.012161 0.01314 0.01313

0.974 1.949 2.923 3.897 4.872 5.846 6.820 7.795 8.769 9.743 14.614 19.485 22.405 23.382 24.353 25.324 26.284 27.255 28.225 29.186 30.157 31.118 32.078 33.039 34.000 34.951 35.902 36.863 37.804 38.755 39.696 40.618 41.549 42.451 43.343 44.216 45.098 45.588 45.441

8.348 9.482 10.562 11.599 12.601 13.573 14.520 15.445 16.349 17.236 21.459 25.409 27.687 28.426 29.168 29.905 30.650 31.374 32.093 32.821 33.530 34.248 34.961 35.669 36.373 37.085 37.794 38.484 39.197 39.893 40.598 41.325 42.035 42.780 43.533 44.307 45.065 45.512 45.662

0.117 0.205 0.277 0.336 0.387 0.431 0.470 0.505 0.536 0.565 0.681 0.767 0.809 0.823 0.835 0.847 0.858 0.869 0.879 0.889 0.899 0.909 0.917 0.926 0.935 0.942 0.950 0.958 0.964 0.971 0.978 0.983 0.988 0.992 0.996 0.998 1.000 1.002 0.996

The magnitude of the critical stress was equal to τcr = 45.1 MPa and that of the critical strain became εcr = 0.012161. The corresponding rupture energy resulted equal to Ecr = 340 kJ/m3 (area of the hatched zone in the diagram in Fig. 11). The results of several uniaxial tests carried out by various authors are presented in Table 2, whereas Table 3 contains the results of some triaxial tests performed at the Engineering Institute of the National Autonomous University of Mexico. The diagram that relates to the rupture energy Ecr with the stress intensity τcr (or the unconfined compression strength in the case of uniaxial tests, Rc) is depicted in Fig. 12. A very reasonable relationship can be observed. 36

Table 2.

Uniaxial strength tests.

The icon on the diagram in Fig. 12

Rock type

Rc, MPa

(εi)cr

Ecr kJ/m3

1 2 3 4 5 6 7 8 9 S T DC B c21 g

Diabase breccias Diabase and quartz Diabase Metadiabases breccias Metadiabases with quartz Metadiabase Quartz schist Chlorite schist Shale breccia Sandstone Tuff Diabase (Coggins) Basalt (Lower Granite) Concrete Gypsum

130–153 87–128 60–76 90–95 53–58 30–35 40–45 17–24 18–28 143 44 341 223 51.7 12

0.0143–0.0175 0.0121–0.0141 0.0102–0.0123 0.0108–0.0121 0.0084–0.0105 0.0070–0.0094 0.0038–0.0089 0.0071–0.0089 0.0115–0.0133 0.0084 0.0074 0.00738 0.00761 0.0087 0.0029

849–1139 474–788 336–432 416–528 217–265 157–187 191–282 89–183 59–153 601 165 1531 1092 390 19

Source A

B C D

A. Pininska, J., Lukaszewski, P., 1991. The relationships between post-failure state and compression strength of Sudetic fractured rocks. Bulletin of the International Association of Engineering Geology, (43), 81–86. B. Kawamoto, T., Saito, T., 1991. The behavior of rock-like materials in some controlled strain states. 7th International Congress on Rock Mechanics, Aachen (Germany), vol. 1, 161–166. C. Miller, R.P., 1965. Engineering classification and index properties for intact rock. Thesis doctoral, University of Illinois, Urbana. D. Gaziev, E., 2001. Rupture energy evaluation for brittle materials, International Journal of Solids and Structures, v. 38, pp. 7681–7690.

Table 3.

Multiaxial strength testing.

The icon on the diagram in Fig. 12 c2

c3

c4

c5

Material Concrete Rc = 45 MPa Rt = 2.9 MPa Concrete Rc = 39.4 MPa Rt = 2.7 MPa Concrete Rc = 45 MPa Rt = 3.1 MPa Cement stone Rc = 39.4 MPa Rt = 2.7 MPa

τcr MPa

εicr

Ecr kJ/m3

σ1cr = 63.3 MPa σ2cr = σ3cr = 2.9 MPa

43.35

0.00612

180

σ1cr = 46.1 MPa σ2cr = σ3cr = 1.0 MPa

45.1

0.01212

340

σ1cr = 63.44 MPa σ2cr = σ3cr = 2.97 MPa σ1cr = 61 MPa σ2cr = 4.65 MPa σ3cr = 3.13 MPa

60.47

0.00942

415

57.14

0.01230

380

Stresses at rupture

The fact that the rupture energy for both uniaxial and triaxial tests is described in terms of the same relationship based on the distortion energy evidences that the failure process of rock materials is induced by the joint action of normal and shear stresses. The normal tensile stresses develop the conditions necessary for the failure to occur (at a macroscopic level) under the action of shear stresses. The experimental work on the failure mechanism during shear performed with specimens on the models and in-situ showed that this process starts 37

with development of tension-induced micro-cracks in the zone where the shear stresses will occur (Vouille & Laurent, 1969; Fishman & Gaziev, 1974; Pininska & Lukaszewski, 1991; Kawamoto & Saito, 1991). The same conclusion was derived by Martin and Chandler (1994) according to which tensile and shear strengths develop simultaneously.

4

ROCKFILL STRENGTH

For the case of triaxial compression tests of rockfill materials, when Rt = 0, equation (2) can be written in dimensionless form as n

σ 1 + 2σ 3 ⎛ σ 1 σ 3 ⎞ =⎜ . Rc ⎝ Rc ⎟⎠

(11)

The proposed expression for the rockfill strength evaluation well corresponds to the experimental results, and it is well supported by experimental data obtained for different types of rockfill materials. It is necessary to note, that Rc here is a virtual compressive strength of the rockfill, which cannot be determined directly from the experiment, however, can be used as a classification parameter for the rockfill material. Consequently and based on the experimental data from two triaxial compression tests executed on the same material but with different confining stresses σ3, the experimental values of Rc and of n can be calculated by means of the following expressions ( 1 + 3 )i ( 1 + 3 )i +1 n= ( − 3 )i log 1 ( 1 − 3 )i +1 log

log

c

1 [log ( 1− n

)i − n log (

(12)

−

)i ]

(13)

in which the subscripts (i) and (i+1) correspond to tests (i) and (i+1). On applying these expressions to the set of data on the triaxial compression tests carried out by R.J. Marsal (1977, 1980), A.A. Vega Pinto (1983), D. Marachi, C.K. Chan, & H.B. Seed (1972) it was found that the value of n can be estimated equal to the average value of 1.15. Taking the magnitude of n as a constant value of 1.15, then

σ 1 + 2σ 3 ⎛ σ 1 σ 3 ⎞ =⎜ Rc ⎝ Rc ⎟⎠

1.15

(14)

Presented in Fig. 13 comparison of this expression with the experimental results demonstrated its good accordance with these data. 5

CONCLUSIONS

1. The main feature of the behavior of brittle rock materials under triaxial loading is the limitation of its volume expansion. With an increase of one principal stress increases two others. Moreover, this increase of the “lateral” principal stresses continues during fracturing of the material as a result of increasing the coefficient of lateral dilatation and the current tightness in the rock mass. Even a slight increase in lateral compression increases the carrying capacity of the rock, so-called “hardening”. 38

2. The strength of the polycrystalline material submitted to a triaxial state of stress can be considered as the result of the combination of the principal stresses that generate a sharp increase in the deformation of the sample. 3. The proposed phenomenological strength criterion allows for the strength evaluation practically for any combination of principal stresses in triaxial, as well as in biaxial stress states. It does not contain parameters which could require additional evaluation (excluding uniaxial compressive and tensile strength data). 4. The distortion energy spent by the rupture mechanism represents a parameter that is in good correlation with the strength and deformability characteristics of material. There exists a close relationship between the rupture energy and the intensity of the stress applied at the moment of failure. This relationship is valid for both the uniaxial and triaxial tests, therefore, confirming that the tensile and shear strengths are simultaneously mobilized and the rupture energy is determined from the distortion energy. 5. It has been proposed to use for analyzing the rupture energy of brittle polycrystalline materials the stress and deformation intensities expressed by equations (8) and (9). 6. The analytical expression (14) describing the strength of rockfill materials in triaxial stress state is well supported by experimental data obtained for different types of rockfills. Given the multiplicity of factors influencing the strength of rockfills, it might be preferable to use parameter Rc as a global index parameter of the rockfill material. ACKNOWLEDGEMENTS The author gratefully acknowledges the support for this work received from the Institute Hydroproject (Moscow, Russia), and the practical assistance in the experimental studies received from the collaborators of the Rock Mechanics laboratory of the same Institute. The author expresses his deep gratitude to Professor Manabu Takahashi (Geological Survey of Japan) for his help in the noble providing the results of his experimental researches that played an important role in development of the presented strength criterion. This research could not have been carried out without the involvement, although posthumously, of Professor Raúl J. Marsal (CFE, Mexico) who executed with immense talent and zeal the experimental work and who has inherited his data base and his enlightening publications. Analysis of the results of these studies as well as works of other authors formed the basis set in strength evaluation of rockfill materials. In the analysis of the results of the triaxial tests of rockfill materials, an honorary researcher of the Engineering Institute of the National Autonomous University of Mexico, my friend and colleague Jesús Alberto Aramburu took part, whose bright memory I dedicate this report. REFERENCES Bezukhov, N.I., 1961. The bases of the theory of elasticity, plasticity and creep (in Russian). Editorial “Vysshaya Shkola” (“High School”), Moscow. Bieniawski, Z.T., 1971. Deformational behaviour of fractured rock under multiaxial compression. In M. Te’eni (Ed), Structure, Solid Mechanics and Engineering Design, London, Wiley-Interscience, Part 1, 589–598. Fishman, Yu.A., Gaziev, E.G., 1974. In situ and model studies of rock foundation failure in concrete block shear tests. 3rd International Congress of the ISRM, Denver (USA), vol. II-B, 879–883. Gaziev, E., Morozov, A., Chaganian, V., 1984. Comportement expérimental des roches sous contraintes et deformations triaxiales. Revue Française de Géotechnique, Paris, (29), 43–48. Gaziev, E., 1996. Criterio de resistencia para rocas y materiales frágiles policristalinos. Segunda Conferencia Magistral “Raúl J. Marsal”, Sociedad Mexicana de Mecánica de Rocas, Mexico, 47 pp. Gaziev, E., Levchouk, V. 1997. Study of the behavior of brittle polycrystalline materials in the postfailure stress-strain state (in Russian), XI Russian Conference on Rock Mechanics, St. Petersburg, p. 103–114.

39

Gaziev, E., Levtchouk, V., 1999. Strength characterization for rock under multiaxial stress states. 9th International Congress on Rock Mechanics, Paris (France), 601–604. Gaziev, E., 2001. Rupture energy evaluation for brittle materials, International Journal of Solids and Structures, v. 38, pp. 7681–7690. Gaziev, E., 2005. Rock foundations of concrete dams (in Russian). Editorial ASV, Moscow, 280 pp. Kawamoto, T., Saito, T., 1991. The behavior of rock-like materials in some controlled strain states. 7th International Congress on Rock Mechanics, Aachen (Germany), vol.1, 161–166. Marachi, D., Chan, C.K., & Seed, H.B., 1972. Evaluation of properties of rockfill materials, Journal of Soil Mechanics and Foundation Engineering, ASCE, Vol. 98, SM1, 95–114. Marsal, R.J., 1965. Discussion, Proceedings of the 6th International Conference on Soil Mechanics and Foundation Engineering, Montreal (Canada), Vol. 3, 310–316. Marsal, R.J., 1977. Research on granular materials. Rockfills and soil-gravel mixtures, Instituto de Ingeniería, Universidad Nacional Autónoma de México, Publicación E-25. Marsal, R.J., 1980. Contribuciones a la mecánica de medios granulares, Comisión Federal de Electricidad, México. Martin, C.D., Chandler, N.A., 1994. The progressive fracture of Lac du Bonnet granite. Int. Journal Rock Mech. Min. Sciences & Geomechanical Abstracts, 31(6), 643–659. Miller, R.P., 1965. Engineering classification and index properties for intact rock. Thesis doctoral, University of Illinois, Urbana. Parate, N.S., 1969. Critère de rupture des roches fragiles. Annales de l’Institut Technique du Batiment et des Travaux Publiques, Paris, (253), 149–160. Pininska, J., Lukaszewski, P., 1991. The relationships between post-failure state and compression strength of Sudeten fractured rocks. Bulletin of the International Association of Engineering Geology, (43), 81–86. Rogún HPP Construction Project. Powerhouse cavern complex., 2015. Siltstone rock characterization from laboratory tests, Appendices. Coyne et Bellier – Electroconsult Consortium. Takahashi, M., Koide, H., 1989. Effect of the intermediate principal stress on strength and deformation behavior of sedimentary rocks at the depth shallower than 2000 m. Proceedings of the ISRM-SPE International Symposium “Rock at Great Depth”, Pau (France), 19–26. Timoshenko, S.P., 1953. History of strength of materials. McGraw-Hill Book Company, New York, Toronto, London, 368–371. Vega Pinto, A.A., 1983. Previsâo do comportamento estructural de barragens de enrocamento, Laboratorio Nacional de Engenharia Civil, Lisboa. Vouille, G., Laurent, D., 1969. Etude de la courbe intrinsèque de quelques granites. Revue de l’Industrie Minérale, Paris, Numero spécial, 15 juillet 1969, 25–28.

40

Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Anisotropic and nonlinear properties of rock including fluid under pressure Ian Gray, Xiaoli Xhao & Lucy Liu Sigra Pty Ltd, Acacia Ridge, Queensland, Australia

ABSTRACT: This paper presents the mathematics and procedures to determine elastic rock properties from testing cylindrical core based upon orthotropic elastic theory. It also examines the extremely non-linear, but elastic, stress strain characteristics of some sandstones and what controls their Young’s moduli and Poisson’s ratios. The effects of fluid pressure changes within the rock are also considered. Two different modes of fluid behaviour are considered. The first is associated with poroelastic behaviour, while the second is associated with the effect of fluid within fractures. The use of these parameters leads to stress distributions and deformations that vary from those arrived at using conventional, but incorrect, assumptions of rock behaviour. Keywords:

1

rock, effective stress, Young’s moduli, fluid pressure, rock, poroelastic

INTRODUCTION

Fluids may be thought to act mechanically within rock in two different ways. The first is by a poroelastic response to fluid pressure which affects the deformation of the rock mass. The second is by the direct action of the fluid within fractures. In each case the fluid pressure changes what may be considered to be the effective stress within the rock, but in different ways. If we examine the general equation for effective stress within a rock mass it may be thought to follow the form of Equation 1 (Gray, 2017).

σ ij′ = σ ij − δ ijα i P

(1)

where: σ ij′ σij δij αi

is the effective stress on a plane perpendicular to the vector i in the direction j. is the total stress on a plane perpendicular to the vector i in the direction j. is the Kronecker delta. If i ≠ j then δij = 0, while if i = j then δij = 1. is a poroelastic coefficient affecting the plane perpendicular to the vector i. Its value lies between 0 and 1. P is the fluid pressure in pores and fractures within the rock.

The Kronecker delta term is used because a static fluid cannot transmit shear. The directional subscript indicating direction in the poroelastic coefficient is not usual practice where, for measurement reasons, only a scalar value is obtained. If the choice of coordinates aligns with that of an open joint, then the poroelastic coefficient orthogonal to the joint is unity. More generally in a porous rock mass it lies somewhere between zero and unity. In a volcanic glass the values of the poroelastic coefficients are zero.

41

2

DEFORMATION AND THE DETERMINATION OF THE STIFFNESS MATRIX FROM ROCK CORE

The deformation of a rock mass is dependent upon the stresses it is subject to and its stiffness. If a rock is subject to a complex stress with six components of direct and shear stress it will deform to produce six strains. The correlation between stress and strain is a compliance matrix of 36 components. Determining all of these is practically impossible. The common simplification where the rock is treated as being isotropic, having a single value of Young’s modulus and Poisson’s ratio, is however frequently in error. If we make a simplifying assumption that the rock mass is orthotropic then the compliance matrix has twelve components. These are shown in Equation 2 below. ⎡ 1 ⎢ E ⎢ 1 ⎢ ν12 ⎢− ⎧ ε11 ⎫ ⎢ E1 ⎪ε ⎪ ⎢ ⎪ 22 ⎪ ⎢ − ν13 ⎪ ε 33 ⎪ ⎢ E1 ⎨ ⎬=⎢ ⎪γ 23 ⎪ ⎢ 0 ⎪γ 31 ⎪ ⎢ ⎪ ⎪ ⎢ ⎩γ 12 ⎭ ⎢ 0 ⎢ ⎢ ⎢ 0 ⎢⎣

ν 21 E2 1 E2 ν − 223 E2

ν 31 E3 ν − 332 E3 1 E3

0

−

−

0

0

0

0

0

0

0

1 G223

0

0

0

0

1 G331

0

0

0

0

⎤ 0 ⎥ ⎥ ⎥ 0 ⎥ ⎥ ⎧σ 111 ⎫ ⎥ ⎪σ ⎪ 0 ⎥ ⎪ 222 ⎪ ⎥ ⎪σ 333 ⎪ ⎥ ⎨τ ⎬ 0 ⎥ ⎪ 223 ⎪ ⎥ ⎪ τ 31 ⎪ ⎥ ⎪τ ⎪ 0 ⎥ ⎩ 12 ⎭ ⎥ ⎥ 1 ⎥ G112 ⎥⎦

(2)

If we take a sample that is aligned perpendicularly to some plane of obvious symmetry then we have reduced the unknowns. An example of this is a core drilled perpendicularly to the bedding planes of a sedimentary rock. If we subject that core to testing in a triaxial loading rig which can apply a stress along the axis of symmetry of a round core sample and a confining stress perpendicular to that axis, we can measure the resulting axial and perpendicular strains with each stress increment. If there are axial strain gauges and at least three tangential strain gauges it is possible to calculate the major and minor tangential strains in addition to the axial strain. We can therefore derive three strains which can be assumed to represent the orthogonal cases. Because we are dealing with principal stresses and strains the compliance matrix to be solved for the rock behaviour has therefore been reduced to nine components. It may be reduced still further to six unknowns because the matrix is symmetrical. This means that the off diagonal components are equal as shown in Equation 3. This symmetry provides a link between the values of Young’s moduli and Poisson’s ratios. vij Ei

=

v ji

(3)

Ej

However three principal strains and two loading cases does not provide an adequate basis to determine the six unknowns. To determine the three Young’s moduli and associated Poisson’s ratios it is necessary to assume something. The assumption that we have made to determine the values of Young’s moduli and Poisson’s ratios is shown in Equation 4. Here the geometric mean Poisson’s ratio, νa, is assumed to have the same value for the three combinations of νji.

(v v ) = v ij ji

42

a

(4)

In a triaxial situation the axial load, in the 1 axis, may be changed and the associated strain changes measured. From this loading and strain measurement the axial Young’s modulus, E1, and the two Poisson’s ratios, ν12 and ν13, may be directly determined. However when the confining stress is changed, the situation is more complex to analyse because the 2 and 3 axis loadings are the same and applied simultaneously. Equation 5 describes strain in an elastic solid under three varying stresses. Δε i

v ji 1 Δσ i − Δσ j Ei Ej

vki Δσ k Ek

(5)

Using the relationship of Equation 3, Equation 5 may be re-written as Equation 6. Δε i

(

1 Δσ i − viijj Δσ j Ei

ik

Δσ k

)

(6)

Equation 6 can in turn be re-written using the relation of Equation 4 as Equation 7. Ei =

⎞ 1 ⎛ Ei Ei va Δσ j − va Δσ k ⎟ ⎜ Δσ i − Δε i ⎝ Ej Ek ⎠

(7)

Three nonlinear equations of the form of Equation 7 may be derived for each of the principal Young’s moduli. These may be solved simultaneously using some value of the geometric mean Poisson’s ratio, νa. A specific value of νa will solve Equation 7 to provide the same value of E1 as derived from a purely axial stress change at the same stress range. This value of νa provides a basis for the determination of the other values of Young’s moduli and Poisson’s ratios. A series of step changes in axial and confining loading can thus be used to determine the orthotropic moduli of a core sample.

3

POROELASTIC EFFECTS

If we now consider the case where the rock contains fluid in its internal pore space Equation  5  may be rewritten in terms of effective stress as causing deformation simply by replacing Δσi with Δσ i′. By substituting Equation (1) into Equation (5) for effective stress, we may arrive at Equation (8) which describes deformation in terms of the three principal total stresses, fluid pressure and the poroelastic coefficients applying to these directions. Δε i

v ji 1 Δσ i − Δσ j Ei Ej

⎛ 1 vki Δσ k − ΔP ⎜ α i Ek ⎝ Ei

v ji Ej

αj −

vki ⎞ αk⎟ Ek ⎠

(8)

As described previously it is possible to determine the orthotropic Young’s moduli and Poisson’s ratio for a core sample by a stepwise testing process involving changes in axial and confining stress. If we also incorporate cycles of fluid pressure variation into the test routine on the same strain gauged sample, it is possible to determine the values of the poroelastic coefficients via simultaneous solution of the three strain equations based on Equation 8 (Gray, 2017). The poroelastic coefficients so determined are in the direction of the axes of the principal orthogonal stiffness determined by the test procedure previously described. It is possible that the principal directions of the poroelastic coefficients are in fact different from the elastic ones. Unlike the work by Biot and Wills (1957) the poroelastic coefficients derived are a tensor. Their results are a function of the volumetric determination of poroelastic behaviour. 43

4

EXPERIMENTAL RESULTS

Let us examine the results of testing and analysis of Hawkesbury sandstones from the Sydney area of New South Wales, Australia. These samples have been core drilled approximately perpendicular to their bedding planes. The core diameter was 61 mm. The first sample is of a porous medium grained sandstone. Figure 1 shows its Young’s modulus perpendicular to the bedding plane plotted against axial (perpendicular to the bedding plane) and confining stress. Figure 2 shows the Young’s modulus in a direction parallel to the

Figure 1.

The Young’s modulus perpendicular to bedding of a porous sandstone (MPa).

Figure 2.

The Young’s modulus parallel to bedding of a porous sandstone (MPa).

44

bedding plane. In each case Young’s modulus increases with stress and is primarily a function of the stress in the same direction. Figure  3  shows the Poisson’s ratio associated with axial (cross bedding) stress and deformation parallel to the bedding plane. It characteristically shows an increase in Poisson’s ratio with shear stress. Figure 4 shows the poroelastic coefficient in the direction of the axis of the sample. It also increases with shear stress. Both the increase in Poisson’s ratio and poroelastic coefficient may be dependent on some level of dilation.

Figure  3. The Poisson’s ratio associated with cross bedding stress and deformation parallel to the bedding for a porous sandstone.

Figure 4.

The poroelastic coefficient referred to the cross bedding axis of a porous sandstone.

45

Testing of a fine to medium grained low porosity sample of Hawkesbury sandstone containing some silty and clay components provided some quite different characteristics. The value of the Young’s modulus across the bedding plane (E1) was dependent on both the axial and confining stresses and the poroelastic coefficients were very small. Testing on granite from the Snowy Mountains area of New South Wales has shown generally isotropic behaviour with a virtually constant Young’s modulus and Poisson’s ratio and a negligible poroelastic coefficient. The poroelastic coefficient appears sensible given the crystalline nature of the rock, but is at variance with values reported by Detournay and Cheng, 1993.

5

FRACTURED ROCK BEHAVIOUR

The previous sections deal with poroelastic behaviour. The effective stress associated with this is an apparent effective stress dependent on the action of fluid within the pores, and micro fractures of the rock causing strain within the rock matrix. If the rock contains clear fractures then the term αi describes a ratio of fracture area to total area over which fluid acts. This case has no relation to the poroelastic behaviour of the rock matrix.

6

CONCLUSIONS

This paper describes the process and mathematics involved in obtaining orthotropic elastic parameters including poroelastic behaviour from the triaxial testing of core. To do this requires the assumptions that the rock behaves in an orthotropic manner, that a likely axis of symmetry is common with the core axis and that a unique value of a geometric mean Poisson’s ratio exists for each stress state. Using the procedures and mathematics outlined the results of testing Hawkesbury sandstones show that the Young’s moduli are highly dependent on the state of stress, varying some four to five fold from zero to 20 MPa axial and confining load. In a porous sample the Young’s moduli seem to be dependent on the state of stress in the direction being measured. In the case of a low porosity sample the Young’s moduli were dependent on both the axial and confining stress. In this sample the poroelastic coefficients were close to zero. Tests on some siltstones have shown less variation of modulus with stress, however the general trend of increasing modulus with stress exists. Some coals tested show an increase in stiffness of an order of magnitude. Generally we have found that sedimentary rocks we have tested show an anisotropy of less than 1.5:1 but with some exceptions which are nearly 5:1. Most rock mechanics design is based on linear elastic models until strength based failure is reached. In addition the effects of fluid pressure are generally ignored. This paper shows that these assumptions are, in the case of the sedimentary rocks tested, quite incorrect. The elastic but very nonlinear behaviour is of particular importance. The consequences are that predicted deformations and stresses using linear elastic assumptions will be, in some cases, quite significantly in error.

REFERENCES Biot, M A, & Wills, D G, 1957. The elastic coefficients of the theory of consolidation. ASME Journal of Applied Mechanics, 24:594–601. Detournay, E & Cheng, AH-D, 1993. ‘Fundamentals of poroelasticity’, in C Fairhurst (ed), Comprehensive Rock Engineering: Principles, Practice and Projects, Volume 2: Analysis and Design Methods, Pergamon Press, pp. 113–171. Gray, I, 2017. Effective Stress In Rock. Deep Mining 2017: Eighth International Conference on Deep and High Stress Mining – J Wesseloo (ed.) © 2017 Australian Centre for Geomechanics, Perth, ISBN 978-0-9924810-6-3.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Dynamic rock support in burst-prone rock masses Charlie C. Li Norwegian University of Science and Technology (NTNU), Trondheim, Norway

ABSTRACT: Rockburst occurs in hard and strong rock after excavation when the in situ rock stresses are high. The “driving force” for rockburst is the energy released from the rock mass. The released strain and seismic energy is transformed to the kinetic energy of rock ejection during rockburst. To prevent out-of-controlled rock ejection, the released energy has to be absorbed by the rock support system when a rockburst event occurs. Therefore, it is required in dynamic rock support design that the support elements must be capable of absorbing a good amount of energy in burst-prone rock conditions. On the other hand, it is required that the displacement of the tunnel wall must be neither larger than the ultimate displacement capacity of the support elements nor the maximum allowable operational displacement. The types of rockburst, the dynamic loading conditions, the design principles of dynamic rock support, and typical yield rockbolts used for combating rockburst issues are presented in the paper. Keywords: rockburst, dynamic loading, dynamic rock support, yield rockbolt, energyabsorbing rockbolt

1

INTRODUCTION

Serious rockburst events could occur in hard rock excavations when the depth is beyond 1000 m. The rock support system must be able to adapt to the dynamic loading condition. Attentions are paid to the strength of support elements in the traditional support design. Under dynamic loading conditions, however, it is required that the support elements must not only be strong but also deformable in order to avoid premature failure of the support elements. In other words, support elements must be energy-absorbent. The concept of yield support elements, such as yield rockbolts, was first proposed by Cook and Ortlepp in 1968 in the Bulletin of the Chamber of Mines of South Africa Research Organisation. One year later, Ortlepp (1969) published his field tests on yield rockbolts in a symposium in Oslo, Norway. Ortlepp was probably the first one who carried out dynamic field tests of rock support. His tests were summarized by himself (Ortlepp 1992) and others, for instance Stacey later (2012). Ortlepp carried out the tests on two rockbolt-mesh support systems installed in a tunnel, one with fully grouted conventional rockbolts and the other one with the yield rockbolts that he developed. The rockburst load was simulated by blasting, with blastholes 430 mm apart drilled parallel to the tunnel axis about 600 mm outside the tunnel perimeter. The first test failed because of the high blast intensity. The second one with reduced blast intensity proved that the support system, consisting of the yield rockbolts and a double layer of wire mesh, could contain the energy of the blast. The sketch of the tunnel profile after the test, shown in Fig. 1, clearly illustrates the effectiveness of the yield support system on the right hand side of the tunnel, and the ineffectiveness of the conventional support system on the left hand side. The field tests of Ortlepp demonstrated that use of a support system incorporating yielding rockbolts could successfully contain rock damage. It has become a common practice to combat rockburst with yield rockbolts in deep metal mines in the recent decade.

47

Figure 1.

The tunnel profile after the blasting test (Ortlepp 1969, Stacey 2012).

In this paper, the types of rockburst and the relationships of the ejection velocity with the strain energy in the rock and the fault-slip seismic energy are talked about first. The design requirements and the factor of safety for dynamic rock support are presented afterward. Finally, some typical yield rockbolts for dynamic rock support are introduced.

2

TYPES OF ROCKBURST

Rockburst events can be classified to three types based on their triggering mechanisms and energy sources. In hard and massive rock, the tangential stress in the contour rock is so significantly eleveated that the intact rock in the tunnel wall simply explodes after excavation, Fig. 2. This is the so-called strain burst (Type 1). The burst energy of a strain burst event is simply contributed by the potential strain energy stored in the ejected rock. There is no seismic activities before the event with this type of rockburst (Fig. 2a). Seismicity with a limited intensity is generated after strain burst events (Fig. 2b). A strain burst event is often characteristized by thin slices of rock in the rock pile (Fig. 2c). Underground excavation changes the stress state in the rock mass in such a manner that the tangential stress around the opening is elevated but the radial stress is reduced. The reduction in the radial stress would lead to a decrease in the normal stress on some pre-existing faults nearby and in turn the shear resistance on the faults is reduced. Slippage, therefore, may occur along some faults. Such fault slippage will generate stress waves that propagate spherically outward from the epicenter of the slippage. This is called mine seismicity in the mining industry. In some cases, the tangential stress in the contour rock is significantly elevated after rock excavation, but they are not high enough to break the rock. The arrival of fault-slip seismic waves could trigger a rockburst event in the highly stress rock. This is the so-called fault-slip strain burst (Type 2), Fig. 3. The magnitude of this type of rockburst could be stronger than the strain burst of Type 1 because the burst energy is the sum of the strain energy in the burst rock and a portion of the fault-slip seismic energy. Seismic activities exist both before and after the event with this type of rockburst. It is only the fault-slip seismicity before the burst event (Fig. 3a), but burst seisimicity is also generated after the event (Fig. 3b). In a relatively weak or fractured rock mass, the contour rock could become fractrued immediately after excavation, resulting in a fracture zone around the the tunnel. A portion 48

Figure  2. Type 1—Strain burst. Sketches illustrating (a) the stress concentration in the rock before rock ejection and (b) the seismicity after rock ejection, and (c) a strain burst event in a metal mine.

Figure 3. Type 2: Fault-slip strain burst. Sketches illustrating (a) the stress concentration and the faultslip seismicity before rock ejection and (b) the rock ejection and the burst seismicity.

of the fractured rock may be ejected by fault-slip seismic waves when a fault-slip movement occurs in the rock mass, Fig. 4. This is the so-called fault-slip rockburst (Type 3). The ejection energy of this type of rockburst is mainly contributed by the fault-slip seismic waves. Some fault-slip events release a significant amount of energy. A fault-slip rockburst could be more violent than a strain burst and thus cause more serious damage to underground infrastructures than a strain burst does. It was once registered a fault-slip rockburst of up to 3.8 Mn in a deep metal mine in Canada (Counter 2014). Rock debris from a fault-slip burst is composed of rock pieces of different sizes, ranging from finely fragmented debris to large blocks. Fig. 4c shows the rock pile after the fault-slip rockburst event of 3.8 Mn in the deep metal mine in Canada. That event was triggered by a fault-slippage located approximately 100 m behind the rockburst position. Hoek (2006) defined rockburst as “explosive failures of rock which occur when very high stress concentrations are induced around underground openings”. Obviously Hoek referred to the rockburst of Type 1, that is, the strain burst. Kaiser et al. (1995) defined rockburst as “damage to an excavation that occurs in a sudden or violent manner and is associated with a seismic event”. They meant the rockburst of Type 3, that is, the fault-slip rockburst. The essential characteristic of a rockburst event is its dynamic feature. We call it rockburst if the 49

Figure 4. Type 3: Fault-slip rockburst. Sketches illustrating (a) the fractured rock before rock ejection and (b) the seismicity during rock ejection, and (c) the fragmented rock after a fault-slip rockburst event of 3.8 Mn in a deep metal mine (Counter 2014).

rock is ejected with a certain velocity. A proper definition for rockburst, therefore, may be simply “damage to an excavation that occurs in a sudden or violent manner”. The cause for a rockburst event can be either stress concentration or fault-slip or both.

3

DYNAMIC LOADING CONDITIONS

In a rockburst event, the failed rock is ejected in a certain ejection velocity that is associated with the strain energy in the rock as well as the fault-slip seismic energy. 3.1

Ejection velocity in a strain burst (Type 1)

Strain burst (Type 1) is caused directly by the stress concentration in the rock surrounding the underground opening. Strain burst does not involve any seismic activity prior to the 50

rockburst event. It is simply owing to the energy release after rock failure. In other words, the strain energy stored in the failed rock is transformed to kinetic energy when the rockburst event occurs. The elastic strain energy (i.e. the potential energy) stored in the ejected rock party is expressed by: Potential energy =

m ∑ σ i2 2ρE

(1)

where m is the mass of the ejected rock, ρ the density of the rock, E is the Young’s modulus of the rock and σi the average principal stresses in the rock party (i = 1, 2 and 3). The kinetic energy of the ejected rock is expressed by 1 Kinetic energy = mv12 2

(2)

where v1 is the ejection velocity of the rock. The right sides of the above two expressions should be equal according to the law of energy conservation. Thus, the ejection velocity of a strain burst event is obtained as: v1 =

1 ∑ σ i2 . ρE

(3)

Assume that the density of a massive rock mass is 2700 kg/m3, the Young’s modulus of the rock is 60 GPa, and the secondary rock stresses in the contour rock after excavation are σ1 = 60 MPa, σ2 = 20 MPa, σ3 = 0 MPa with σ1 and σ2 parallel with the tunnel wall and σ2 perpendicular to the wall. The ejection velocity of the rock when a rock burst event occurs is obtained from Eq. (3) as v1 = 5 m/s which is a quite reasonable ejection velocity for a strain burst event in hard rock. 3.2

Ejection velocity in fault-slip bursts (Type 2 and Type 3)

With rockburst of Type 2 and Type 3, fault-slip seismicity is involved in the burst event. The kinetic energy of the ejected rock is equal to the sum of the elastic strain energy in the ejected rock and a portion of the seismic wave energy. The seismic wave energy is derived below.  Assume that a fault-slip event generates a sinusoidal seismic wave (Fig.  5) that is expressed by: ux

Asin( A ωt kx )

(4)

where ux = particle displacement at position x, A = the displacement amplitude, ω = angular frequency, ω = 2πf, f = frequency, t = time, k = wave number, k = ω/C, C = wave velocity and x = position.

Figure 5.

A sinusoidal seismic wave pulse.

51

The seismic wave induces particle vibrations in the rock it passes through. The vibrations bring about a strain and stress in the rock so that a static strain energy density, ws, is thus induced in the rock by the seismic wave. On the other hand, the wave propagation means that a kinetic energy component, wk, is also induced by the seismic wave. Therefore, the total energy induced by the seismic wave, w, is the sum of the two components ws and wk, that is, w = ws + wk. In the case of a longitudinal wave (i.e. the P wave), the normal strain induced by the wave is ε x = ∂ux ∂x and the normal stress is σ x E ε x . The static wave strain energy density is expressed as ws = σ xε x 2. The average static strain energy density of the seismic wave is then obtained as ws =

1 ρ ( PPV )2 4

(5)

where ρ is the density of the rock and PPV represents the Peak Particle Velocity, PPV = Aω . The particle velocity is expressed by ux ∂ux ∂t . The kinetic energy density is calculated as wk ρux2 2. The average kinetic energy density is then obtained as wk =

1 ρ ( PPV )2 . 4

(6)

The total energy density in the rock, which is caused by the seismic wave, is thus w = ws + wk =

1 ρ ( PPV )2 . 2

(7)

Let v2 represent the wave-induced velocity of the ejected rock. The following equilibrium must exist: 1 2 mv2 = wV 2

(8)

where V is the volume of the ejected rock, V = m/ρ. The ejection velocity v2 is then obtained as: v2 = PPV .

(9)

The total ejection velocity is then obtained as v = v12 + v22 =

1 ∑ σ i2 + PPV 2 . ρE

(10)

The study by Yi and Kaiser (1993) showed that it is reasonable to assume the rock ejection velocity is equal to the peak particle velocity (PPV) under typical mining and seismicity conditions. The theoretical solution of Eq. (9) agrees with their conclusion if we only talk about the ejection velocity induced by seismicity. In the case of a fault-slip triggered rockburst event, the ejection velocity is a vector superposition of two components: the velocity due to the release of the strain energy in the rock, v1, and the velocity due to the seismic wave, v2, as expressed by Eq. (10). The near-field PPV of a fault-slip seismic event of Nuttli magnitude 3–4 is approximately 3 m/s according to Kaiser et al. (1995). The ejection velocity caused by the seismicity will be thus v2 = PPV = 3 m/s according to Eq. (9). Assume that the rock has been subjected to the stresses as given in the example above, that is, σ1 = 60 MPa, σ2 = 20 MPa, σ3 = 0 MPa, which would result an ejection velocity v1 = 5 m/s. The total ejection velocity is thus obtained, according to Eq. (10), to be 5.8 m/s. It seems that the seismicity mainly plays a role of trigger in rockburst events of such magnitudes. The ejection velocity is mainly dependent on the prevailing stress state in the rock prior to the burst event. 52

Figure 6. The equilibrium displacement ueq and the maximum allowable displacement umax related to a rockburst event.

4

DESIGN REQUIREMENTS

The basic requirement for rock support elements is their energy absorption capacity in burstprone rock. In a rockburst event, a part of the released energy is converted to kinetic energy to eject the rock. It is required that the rock support elements in a support system must be able to absorb the kinetic energy in order to prevent the rock from being ejected. Let Eab represent the total energy absorption of the support elements in a support system and Eej is the kinetic energy of the ejected rock, which is expressed by: Eej

1 2 v 2

(11)

The ratio of Eab to Eej has to be larger than 1 in order to avoid rock ejection, that is, Eab > 1. Eej

(12)

With a competent support system, the ejected rock will stop moving after a displacement ueq (Fig. 6). it is required that the displacement ueq must be smaller than the ultimate displacement uult of the support system in order to avoid failure of the system, that is, (uult/ueq) > 1. In engineering practice, there usually exists a maximum allowable displacement, denoted as umax, from the point of view of operation. For example, the radial displacement of a TBM tunnel usually is not allowed to be larger than 150 mm in order to avoid clogging of the TBM cutter head. In other words, the ratio of the umax to the displacement at equilibrium, ueq, must be larger than 1, that is, (umax/ueq) > 1. The value of the factor of safety in the burst-prone rock condition is the minimum one among the three ratios above, that is, ⎛E u u ⎞ FS = min ⎜ ab , max , ult ⎟ . E u ⎝ ej eq ueq ⎠

5

(13)

TYPICAL YIELD ROCKBOLTS

Yield (or energy-absorbing) rockbolts are the most powerful support elements for dynamic rock support so far. The first commercial yield rockbolt, the so-called cone bolt, was invented in the Southern Africa in the beginning of the 1990s (Jager 1992, Ortlepp 1992), but it was not widely accepted until the 2000s. In the past decade, a number of other yield rockbolts 53

have appeared in the market. The typical yield rockbolts used for dynamic rock support are introduced below. 5.1

The cone bolt

The cone bolt consists of a smooth steel bar and a flattened conical flaring forged at the far end of the bolt shank. It has two versions, the original one for cement grout (Fig. 7a) and a modified one for resin grout (Fig. 7b). A blade is added at the end of the modified cone bolt for the purpose of resin mixing. The cone bolt is fully grouted in a borehole. Rock dilation will induce a load on the face plate, which then transfers the load to the bolt shank and the cone at the bolt end. The grout facing the conical side of the cone is crushed when the pull load is high enough and the cone then ploughs in the grout to do work. A cone bolt can displace for a considerable distance if it ploughs as desired. A series of pull tests were once carried out on cement-grouted cone bolts in an underground mine in Sweden. The bolts displaced up to 900 mm at a pull load of approximately 170 kN. In order to achieve the desired ploughing mechanism, the shape of the cone and the crushing strength of the grout must have a satisfactory match. In reality, the strength of the grout varies because of variations in the type of grout material and the water–cement ratio or the mixing quality in the case of using resin grout. This leads to significant variations in the yield load of the cone bolts. Many static pull and dynamic drop tests have been carried out both in the field and in laboratories over the past decades. Fig. 8 shows representative results of such tests. The static yield load varies from approximately 60 kN to 150 kN (Fig. 8a). The drop test results shown in Fig. 8b are for 22 mm cone bolts tested with a kinetic energy input of 33 kJ. The dynamic yield load of those bolts is 150–175 kN for the 40 MPa resin grout, but drops to approximately 100 kN for the 20 MPa resin grout. It was observed in field tests that the cone of the bolts might plough little or not at all in some cases, so that the displacement was purely

Figure 7. The cone bolt. (a) The original version for cement grout, (b) the modified version for resin grout (Simser, 2001), (c) the work principle.

Figure 8. Static and dynamic test results of modified cone bolts with resin grouts. (a) Static pull tests, redrawn after Simser et al. (2006), (b) dynamic drop tests, redrawn after Varden et al. (2008).

54

coming from the stretching of the bolt shank (Simser et al. 2006). In those cases, the yield load of the bolts was equal to the yield limit of the bolt steels. Such a large spread in the load capacity could cause uncertainty for rock support design. The cone bolt has been used for rock support in many metal mines in Canada and Australia in the past decade. 5.2

The D-Bolt

The D-Bolt, invented in Norway, comprises a smooth steel bar and a number of integrated anchors along the bolt length (Fig. 9) (Li, 2010). The bolt is either cement or resin encapsulated in a borehole. The short anchors are firmly fixed in the grout, while the long smooth bar sections between the anchors elongate upon rock dilation. The bolt absorbs energy through full mobilization of the strength and deformation capacity of the bolt steel. Static and dynamic test results for D-Bolts are presented in Fig.  10. The bolt sections tested are 22 mm in diameter and 1.5 m in length between the anchors. The ultimate static load and displacement are 260  kN and 165  mm, respectively (Fig.  10a), and the ultimate dynamic load and displacement are 285 kN and 220 mm, respectively (Fig. 10b). The bolt section absorbs approximately 60 kJ of energy prior to failure under dynamic loading. Every section of the bolt works independently; the failure of one section does not result in the loss of the entire bolt, with the remaining sections continuing to provide rock reinforcement. In general, the ultimate load of the D-Bolt is equal to the tensile strength of the steel and the ultimate displacement is approximately 15% of the bolt length. D-Bolts have been used in metal mines for dynamic rock support in Sweden, Canada, USA, Chile and Australia.

Figure 9. The D-Bolt.

Figure 10. Test results of the D-Bolt sections of 22 mm × 1.5 m (Li, 2012; Li & Doucet, 2012). (a) Static pull test results, (b) dynamic drop test result (drop mass 2897 kg, drop height 1.97 m and input energy 56 kJ).

55

5.3

The Yield-Lok

The Yield-Lok bolt consists of a round steel bar of 17.2  mm in diameter (Fig.  11). The anchor, or Upset, of the bolt is encapsulated in an engineered polymer coating. The bolt is encapsulated in the borehole with resin grout. The Upset ploughs within the polymer coating when the pull load exceeds the predefined load limit. The mechanics of the Yield-Lok is similar to the cone bolt. Static and dynamic test results of the bolt are shown in Fig. 12. The dynamic load is in general lower than the static load. Yield-Lok bolts are used in some metal mines for dynamic rock support in Canada. 5.4

The Garford solid bolt

The Garford solid bolt, invented in Australia, consists of a smooth solid steel bar, an anchor and a coarse-threaded sleeve at the far end (Fig. 13). This bolt is characterised by its engineered anchor, the inner diameter of which is smaller than the diameter of the solid bolt bar. The bolt is spun into the borehole, which is filled with resin cartridges. The resin is mixed by the threaded sleeve at the bolt end. The anchor is resin encapsulated in the borehole after installation. When the rock dilates, the pull load in the solid bar forces the solid bar to be extruded through the hole of the anchor. The yield load is determined by the difference in the diameters of the anchor hole and the solid bar. The ultimate displacement of the bolt is determined by the length of the bar tail contained within the threaded sleeve. Fig. 14 shows the dynamic test results of two 20 mm bolts, which were loaded with a kinetic energy input

Figure 11.

The Yield-Lok (Wu and Oldsen 2010).

Figure 12. Test results of the Yield-Lok bolts. (a) Static pull test results, (b) dynamic test result (drop mass 1115 kg, drop height 1.5 m and input energy 16.4 kJ). Redrawn from Wu & Oldsen (2010).

Figure 13.

The Garford solid bolt.

56

Figure 14. Dynamic test results of 20 mm Garford bolts with impact input of 33 kJ. Redrawn after Varden et al. (2008).

Figure 15.

The Roofex rockbolt.

of 33 kJ (Varden et al., 2008). The Garford bolts are used in some Australian metal mines for dynamic rock support. 5.5

The Roofex

Roofex is not on the market anymore, but several publications on the bolt exist so that it is introduced here. Roofex is composed of an engineered anchor and a smooth bar (Fig. 15) (Charette & Plouffe, 2007; Galler et al., 2011). Its work principle is similar to the Garford solid bolt, that is, the smooth solid steel bar is extruded through the hole of the anchor at the designed load level. The bolt is spun into a borehole that is filled with resin cartridges and the resin mixer at the end of the bolt mixes the resin. It is required that the anchor must be fully encapsulated in the resin grout. The smooth steel bar slips through the anchor to dissipate the energy and accommodate the rock displacement. The mechanics of the Roofex is similar to that of the Garford bolt, as described by Eq. (14), but the factor k would have a different value for Roofex because of the different shape of its anchor. Fig. 16 shows static pull and dynamic drop test results for Roofex rockbolts. The results indicate that the dynamic load of the Roofex bolt is much smaller than its static load. 5.6

Durabar

Durabar is another yielding rockbolt invented in South Africa (Ortlepp et al., 2001). The bolt is composed of a smooth bar and a sinusoidally waved portion as well as the face plate and the nut (Fig. 17). The bolt has a smooth tail in the far end, which determines the maximum displacement capacity of the bolt. The bolt is fully grouted into a hole in the rock. It is 57

Figure 16. Laboratory test results of Roofex R × 20 rockbolts (Galler et al., 2011). (a) Static pull test results, (b) dynamic test result.

Figure 17. Durabar (Ortlepp et al., 2001).

required that the shape of the waved portion must be carefully configured and the full length of the bar is de-bonded from the grout in order that the desired performance of the bolt is achieved. The Durabar is able to yield by sliding through the hardened cement grout. As the load on the Durabar reaches the designed yield load, it starts to slip through the wave path created in the grout by the waved shape of the Durabar. The friction in the wave path is the main energy dissipation mechanism. The ultimate load of the Durabar is related to the slope angle of the wave portion and the frictional coefficient between the bolt shank and the grout. A normal load is induced on the wave portion as a pull load is applied to the bolt. The magnitude of the normal load is associated with the slope angle i that is represented by the ratio of the amplitude of the wave to the half-wave length. The performance of Durabar is mainly dependent on the properties of the steel and requires that the strength of the grout exceeds a minimum value of about 25 MPa. A 16 mm 2.2 m long Durabar can dissipate 45 kJ over a 500 mm displacement under a static pull loading according to Ortlepp et al. (2001). The static load of the 16 mm Durabar stabilizes at a level of 80 kN, while its dynamic load drops to approximately 60 kN for a drop velocity of 3 m/s (Fig. 18). 5.7

The He bolt

The He bolt, invented in China, is composed of a solid bar, a cone-shaped piston, a sleeve, a face plate and a nut (Fig. 19). The far end of the solid bar is groove threaded, which is the anchor of the bolt. The diameter of the cone-shaped piston is slightly smaller than the inner diameter of the sleeve so that it is tightly assembled in the sleeve, which is attached to the face plate and the nut. The bolt is fully grouted in a borehole with either cement mortar or resin. Both the threaded anchor of the bolt at the far end and the sleeve are encapsulated in the 58

Figure 18.

Static and dynamic performances of Durabar. Redrawn from the Durabar brochure.

Figure 19. The He bolt (He et al., 2014). (a) The work principle, (b) a close-up sketch of the match between the cone and the sleeve.

grout according to the authors (He et al., 2014). The cone slips in the sleeve to accommodate the rock dilation, Fig. 19a. In accordance with the drawing illustrating the match between the cone and the sleeve during slippage (Fig. 19b), it seems that the sleeve is radially expanded when the conical piston slips. Therefore, the pull resistance load of the bolt is not simply due to the friction between the cone and the sleeve wall, but also to the plastic deformation of the sleeve. The bolt was both statically and dynamically tested in the laboratory. The diameter of the solid bars of the bolt specimens was 22 mm and the outer and inner diameters of the sleeves were 33 and 24 mm, respectively. The diameter of the conical piston was 0.7–1 mm larger than the inner diameter of the sleeve, that is, varying from 24.7 to 25 mm. Fig. 20a shows the static test result of the bolt specimen with a cone diameter of 24.9 mm. The stick–slip phenomenon occurred during slippage of the cone in the sleeve, with a load oscillation between 140 and 180 kN. The mean values of the static load were 108, 125 and 106 kN, corresponding to cone diameters of 24.7, 24.8 and 24.9 mm, respectively. It seems that the load capacity of the bolt is sensitive to the cone diameter. Three He bolts were drop tested with a drop mass of 1000 kg and a drop height of 0.5, 0.7 or 1 m (He et al., 2014). The average load of the bolts varied from 67 to 88 kN, which is smaller than the static load. Fig. 20b shows the dynamic test result of a He bolt tested with a drop mass of 1000 kg and a drop height of 0.7 m. It is seen that the amplitude of the load oscillations in the dynamic test is much larger than that in the static tests. It is noticed that all of the rockbolts were tested in open air instead of in real or simulated boreholes. It is not clear how the encapsulation affects the behaviour of the bolt when the bolt is installed in a borehole. 59

Figure 20. Laboratory test results of the He bolts (He et al., 2014). (a) The static pull test result of the bolt with a cone diameter 24.9 mm, (b) the drop test result of the bolt (drop mass 1000 kg, drop height 0.7 m).

6

CONCLUDING REMARKS

Rockburst events classified to three types on the basis of their triggering mechanisms and energy sources. Type 1 is called strain burst that is purely caused by the stress concentration. With a strain burst event, the intact rock explodes and the strain energy in the rock is transformed to fracture energy and burst energy. Type 2 is called fault-slip strain burst. With such a burst event, the feature of the burst is the same as Type 1, that is, the intact rock explodes, but the trigger is the fault-slip seismic waves. The burst energy in a fault-slip strain burst event are contributed both by the strain energy in the rock and the seismic waves. Type 3 is called fault-slip rockburst. With a burst event of Type 3, the fault-slip seismic waves both trigger the event and contribute the burst energy. In burst-prone rock masses, it is required that the rock support system must be able to absorb the kinetic energy of the ejected rock in order to prevent out-of-controlled dynamic rock falls. All support elements in a support system must be energy absorbent, that is, not only strong but also deformable. The practice has proven that use of energy-absorbing (or yield) rockbolts is the most efficent means to combat rockburst issues in underground rock excavation. There are a number of energy-absorbing rockbolts avialable on the market at present. Examples of them are the cone bolt, the D-Bolt and the Yield-Lok. An energy-absorbing bolt is characterised by its high load and displacement capacities, and it can dissipate a large amount of energy prior to failure. The existing energy-absorbing rockbolts absorb energy either through material stretching (the D-Bolt) or through friction or ploughing in the grout (all the other yield bolts). The factor of safety of a rock support element, such as a rockbolt, cannot be calculated with the strength of the element and the load on it since the load on the support element is dependent on the deformation in underground excavation. The energy absorption and the ultimate displacement of the support elements, the amount of the released energy and the tunnel wall displacement have to be taken into account for the calculation of the factor of the safety. Under dynamic loading conditions like rockburst, the factor of safety of a support element is the minimum one of the following three ratios: the ratio of the energy absorption of the support element to the kinetic energy of the ejected rock, the ratio of the ultimate displacement of the element to the equilibrium displacement and the ratio of the maximum allowable displacement of the tunnel to the equilibrium displacement.

REFERENCES Charette F, Plouffe M. Roofex—results of laboratory testing of a new concept of yieldable tendon. In: Potvin, Y. (ed.) Deep Mining 07—Proceeding of the 4th International Seminar on Deep and High Stress Mining. Australian Centre for Geomechanics. pp. 395–404.

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Cook, N.G.W. & Ortlepp, W.D. (1968) A yileding rockbolt. Chamber of Mines of South Africa Research Organisation Bulletin, No. 14., 6–8. Counter D. 2014. Kidd mine—dealing with the issues of deep and high stress mining—past, present and future. DeepMining 2014—Proc. Of the 7th Int. Conf. on Deep and High Stress Mining, 16–18 Sept. 2014, Sudbury, Canada. Australian Centre for Geomechanics. 3–22. Galler, R., Gschwandtner, G.G. & Doucet, C. (2011) Roofex bolt and its application in tunnelling by dealing with high stress ground conditions. In: ITA-AITES World Tunnel Congress, Helsinki, Finland. 11p. He, M., Gong, W., Wang, J., Qi, P., Tao, Z., Du, S. and Peng Y. 2014. Development of a novel energyabsorbing bolt with extraordinarily large elongation and constant resistance. Int J Rock Mech Min Sci, 67: 29–42. Hoek E, 2006. Practical Rock Engineering. North Vancouver, British Columbia: Evert Hoek Consulting Engineer Inc. Jager AJ, 1992. Two new support units for the control of rockburst damage. In: Kaiser, P.K. and McCreath, D.R. (eds.) Proc Int Symp on Rock Support. Rotterdam: Balkema. pp. 621–631. Kaiser PK, McCreath DR and Tannant DD, 1995. Volume 2: Rockburst Support. In: C. Graham, ed. Canadian Rockburst Research Program 1990–1995. Ontario: CAMIRO Mining Division. Li CC and Doucet C, 2012. Performance of D-bolts under dynamic loading conditions. Rock Mech & Rock Engng, 45(2), 193–204. Li CC, 2010. A new energy-absorbing bolt for rock support in high stress rock masses. Int J Rock Mech Min Sci, 47(3), 396–404. Li CC, 2012. Performance of D-bolts under static loading conditions. Rock Mech & Rock Engng; 45(2), 183–192. Ortlepp WD, 1969. An empirical determination of the effectiveness of rockbolt support under impulse loading. Proc Int Symp on Large Permanent Underground Openings, Oslo, Sept 1969. Brekke, T.L. and Jorstad, F.A. (eds.). Universitats-forlaget. 197–205. Ortlepp WD, 1992. The design of support for the containment of rockburst damage in tunnels—an engineering approach. In: Rock Support in Mining and Underground Construction. Rotterdam: Balkema, 593–609. Ortlepp WD, Bornman JJ and Erasmus N, 2001. The Durabar—a yieldable support tendon—design rationale and laboratory results. In: Rockbursts and Seismicity in Mines—RaSiM5. South African Institute of Mining and Metallurgy. pp. 263–264. Simser B, 2001. Geotechnical Review of the July 29th, 2001. West Ore Zone Mass Blast and the Performance of the Brunswick/NTC Rockburst Support System. Technical report, 46p. Simser B, Andrieux P, Langevin F, Parrott T and Turcotte P, 2006. Field Behaviour and Failure Modes of Modified Conebolts at the Craig, LaRonde and Brunswick Mines in Canada. In: Deep and High Stress Mining. Quebec. 13p. Stacey TR, 2012. A philosophical view on the testing of rock support for rockburst conditions. The Journal of The Southern African Institute of Mining and Metallurgy, 112, 703–710. Varden R, Lachenicht R, Player J, Thompson A and Villaescusa E, 2008. Development and implementation of the Garford Dynamic Bolt at the Kanowna Belle Mine. In: 10th Underground Operators’ Conference. Launceston. 19p. Wu YK and Oldsen J, 2010. Development of a New Yielding Rock Bolt – Yield-Lok Bolt. In: Proc. Of the 44th US Rock Mechanics Symposium, Salt Lake City, USA. Paper ARMA 10–197, 6p. Yi X and Kaiser PK, 1993. Impact testing of rockbolt for design in rockburst conditions. Int J Rock Mech Min Sci & Geomech Absstr, 31, 671–685.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Deep mining rock mechanics in China—the 3rd mining technology revolution Manchao He State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Beijing, China

ABSTRACT: With the increasing of mining depth, more and more mining activities are being conducted in deep strata. A series of hazards such as rockburst, large deformation, and collapse occur frequently in deep mines. Researches show that the main reason causing these deep mine hazards are related to the high stress level environment. Therefore, innovating the mining technology is one of the important ways to mitigate and to reduce mine hazards. In this paper, a study about the longwall mining method is presented in order to permit solving these high stress problems. The traditional longwall mining method was introduced at the beginning of 18th century the so-called as 121 mining method (1 working face, 2 excavation gateways and 1 remaining coal pillar). The method was widely used in China. According to the statistics in coal mines, more than 92% of the accidents occurred during the excavation of gateways. To reduce mining accidents associated with longwall mining method and to increase the productivity of the mining explorations, the author proposed a new longwall mining method in 2008, called the 110 mining method (1 working face, 1 excavation gateway and no coal pillar), including directional pre-splitting cutting and the use of large deformation bolt/anchor supporting systems. Using the new method, 50% of the gateways are no longer needed to be excavated; instead, they are formed by a controlled roof collapse. By reducing the need for gateway excavation, mining accidents and consequently costs could be significantly decreased. In this sense, the third mining technology revolution is underway in China. Keywords: Mining innovation; Deep mining; Longwall mining method; Non-pillar mining; 110 mining method

1

INTRODUCTION

The traditional longwall mining method was introduced at the beginning of 18th century the so-called as 121 mining method (1 working face, 2 excavation gateways and 1 remaining coal pillar). This method was widely used in China until recently. In 2016, 3.41 billion ton coal were outputted and 13,000 km gateways were excavated by using the 121 mining method. According to the statistics, more than 91.6% of accidents happened in the gateways. And a series of hazards such as rockburst, large deformation, collapse became more challenging with the increasing of mining depth (He, 2004; 2005; He et al., 2014). Due to the high stress conditions, it was basically considered that the traditional 121 mining method was considered not suitable for deep mining purposes for safety and economical reasons (Zhai and Zhou, 1999; Li, 2000; Liu and Shi, 2007; Fei, 2008). In 2008, the theory of “Cutting Cantilever Beam Theory” (CCBT) was first put forward. In this theory it can be noted that the ground pressure was used for the purpose of advanced roof caving by precutting to form a cantilever beam above the gob-side gateway. When the precutting was performed on the roof of gateway, the transmission of overburden pressure was cut off, which mitigated the periodic pressure when using the 121 mining method, and part of roof rock mass was driven down, forming one side of the gateway for the next stope 63

mining cycle. The CCBT provides a new basis for the non-pillar mining, under which the “Longwall Mining 110 method” was developed (He et al., 2007; Zhang et al., 2011; Liu and Zhang, 2013; Song and Xie; 2012; Wang and Wang; 2012; Sun et  al., 2014). The method 110 means that there is one working face, after the first mining cycle, and only needs one advanced gateway excavation, while the other one is automatically formed during the last mining cycle with no coal pillars left in the mining area by using this mining technology. The core idea of 110 mining method is that, firstly, the natural ground pressure is used to help human drive down part of the roof rock, instead of fully resisting it by an artificial supporting system and by a coal pillar; secondly, the gob roof rock is used to form one side wall of the gob-side gateway; and thirdly, the characteristic of broken expand for gob roof rock is used in gob to reduce the surface subsidence. This mining method will reduce 50% of gateway excavation in the stope and fulfill 100% coal pillar recovery, which achieves a significant reduction in mining costs and more important it will reduce the accidents in the stope. In this paper, China’s mining associated theories, particularly the 121 mining method and 110 mining method will be discussed. The key technologies and features will be introduced, and also the numerical simulation methods that have been used to analyze the mining-induced stress distributions in the application of 110 mining method. The CCBT and 110 mining method will be considered to be the basis for China’s next-generation mining industry development. Up to now, 110 mining method has been successfully applied in many underground coal mines in some giant coal mining groups across China, e.g. China National Coal Group Corporation, Shen Hua Group, Sichuan Coal Industry Group Limited Liability Company, etc. The total length of the gateway tunnel created by the 110 method is more than 19,000 m. In the coal mines where the 110 method are employed, engineering disasters caused by the gateway excavation and coal pillars along the goaf are almost completely eliminated, such as roof accidents, rockburst, coal and gas outburst, and the else potential dynamical-events. At the same time, great economic benefits and noticeable social benefits were achieved due to the significant reduction of the gateway tunnel excavation and elimination of the coal pillars, as well as the safety production.

2

THE CCBT AND 110 MINING METHOD

Due to the limits of the traditional 121 mining method, the CCBT and 110 mining method were proposed in order to address the problems in longwall mining. The CCBT was verified in field by using advanced roof caving, and was first applied in 2010 to No. 2442 working face in Baijiao coal mine, Sichuan. In the project, a non-pillar mining technique was used in the gateway near the goaf formed automatically by advanced pressure relief and roof caving (Zhang et al., 2011). The CCBT was established on the basis of interactions of stress fields, supports, and surrounding rocks during the process of advanced pressure release and roof caving. One of the key technologies was the orientation cutting in the goaf side roof, which alters the roof

Figure 1. 3D-view schematic diagram of the long wall mining 121 mining method (left) & 110 mining method (right).

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connection status and prevents stress propagation from the gob roof to entry roof. Other key technologies are involved to achieve CCBT. This is the case of a new supporting bolt or anchor with constant resistance and large deformation (CRLD), that is employed in the gobside gateway roof supporting to keep the gateway stable during the advanced caving. A three-dimensional schematic drawing of a coal panel mined by the 121 and 110 mining methods along the working face direction is illustrated in Fig. 1. It is seen in the figure, that the 121 mining method, requires the excavating of two gateways and retaining one coal pillar. When the coal is mined out, the two gateways will be abandoned and destroyed by the periodic pressure as a result of the mechanized for the stoping mining. In contrast, the mining of a panel using the 110 mining method requires two gateways that will be excavated during mining the first panel; in the subsequent stoping process, forming a gateway by cutting a tunnel-length slit beside the next mining panel. Therefore, the coal pillar between the two mined panels will be cancelled, i.e. only one gateway is enough.

3

KEY TECHNOLOGIES IN 110 MINING METHOD

For the fulfillment of 110 mining method, several key technologies are employed, as illustrated in Fig. 2, in a 3D view. The method includes the following steps: 1) cutting the roof with directional pre-splitting; 2) supporting the roof using CRLD bolt/cables; and 3) blocking gangue by hydraulic props. Thus, the 110 mining system with non-pillar mining and automatic formation of gob-side gateway for the next mining cycle by precutting and advanced roof caving is established. For a more detailed description of these key technologies, another 3D schematic drawing of 110 mining methods is illustrated in Fig. 3. Firstly, cutting the roof with directional presplitting is performed to cut down the transmission passage of ground pressure in part of overlying rock strata, and the gob-side pressure is used to drive part of gob roof rock down, instead of totally resisting it. And the roof rock is used to form one side of the gateway wall, and the gob-side gateway is reserved for the next mining cycle. After the working face advance, the upper strata will collapse, although the connection within upper strata is partially separated, but outside the slit depth, both part, part up the gateway and up the gob-side, are still connected and interact. When the upper strata in gobside breaks down, between the two parts will have a relatively large shear force at this moment. The traditional support material in response to this instant impact will be destroyed, and the integrity of gateway cannot be guaranteed. Thus, for this situation, it was developed a new kind NPR (Negative Poisson Ratio) cable/anchor, the designated CRLD bolt/cable, which has a constant resistance and large deformation characteristics. When the gateway-side roof is affected by the drop-down shear force, the NPR cable would provide high resistance and at same time a large deformation. As shown in Fig. 3, the cables are applied to close the slit, forming a fulcrum, thus ensuring the integrity of the gateway.

Figure  2. 3D-view schematic diagram of the 110 mining method.

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Figure  3. Another 3D-view schematic diagram of the 110 mining method.

Finally, after the working face mined back, part of gateway roof will be driven down by the ground pressure, and gangues will be blocked by using hydraulic props and barbed wire which closed to the gob-side. So not only isolate the goaf and ensure the integrity of the gateway, and this gateway will be used by the next working face. The following sub-sections mainly describe the mechanical properties of two key technologies. 3.1

Directional pre-splitting roof cutting technology

For the design of a pre-splitting roof technology the characteristics of high rock compressive strength and low tensile strength were comprehensively considered, and it was developed an appropriate blasting device to achieve the two-directional blasting in order to generate concentrated tensile stresses. The blasting device is employed with normal explosives, and the depth of boreholes is judged by the coal seam depth, gateway height and other conditions in the field. The depth of the boreholes varies from 1.5 to 5 m, or more. The explosive charge follows the general blasting design, normally from 2 to 8 packages of explosives with directional blasting device for different engineering conditions. The top plate is set in accordance with the direction of the formation of pre-splitting tensile fracture surfaces (Fig.  4). Field application results (Fig. 5) show that this technology can achieve good directional roof

Figure 4.

Mechanism of directional pre-splitting roof cutting technology.

Figure 5.

Photographs for field application of the pre-splitting cutting technology.

66

Figure 6.

The CRLD bolt/anchor.

Figure 7. Curves of different mechanical properties of CRLD bolts.

Figure  8. Impact dynamics features of the CRLD support material.

pre-splitting according to the design at exact positions, and reach the designed depth along the roof with actively advanced pre-splitting roof cutting but will not destroy the gateway roof. 3.2

CRLD supporting system

The problems of mining pressure transfer are one of the key issues during advanced presplitting cutting and roof caving. Part of the roof in the existing gateway needs to be reserved. The traditional support system, with normal mesh, bolts and anchors, can be easily broken when surrounding rocks have large deformations. In this case, the manual roof caving will produce large tensile force to the gateway roof, although the precutting has been performed to reduce the force transition. For this reason, a new supporting material, the CRLD bolt, is used to control the gateway deformation and reserve the roof, as shown in Fig. 6. A large number of experiments have been conducted on this material. Testing results show that its mechanical properties are quite unique and can keep the designed constant resistance during elongation. As shown in Fig. 8, the CRLD bolt is able to adapt to the dynamic pressures generated by the gateway roof caving and effectively control part of the reserved roof. The CRLD bolt can also withstand various dynamic impacts, and high impact energy absorbing abilities are observed in both laboratory and field tests. Therefore, CRLD bolt can achieve high impact resistance and deformation energy released during roof caving, which can effectively guarantee the overall stability of gateway safety (He, 2014; He et al., 2017).

4

SHORT-ARM BEAM STRUCTURE IN 110 MINING METHOD

The CCBT was established on the basis of interactions of stress fields, supports, and surrounding rocks during the process of advanced pressure release and roof caving. One of the key technologies is the orientation cutting in the goaf side roof, which transfers the overburden pressure on the roof to the gob area. Before roof cutting, the gateway roof is one part 67

Figure 9.

Structure model of short-arm beam.

of the long hanging roof structure, and their movements are intimately associated, just as in 121 mining method. After roof splitting, the gob roof strata fracture and cave under the action of roof weighting. The caved gangues expand to support and control the deformation of the upper main roof. Nevertheless, the entry roof remains stable under the entry-in support. By this way, roof above the gateway is completely protected. The pressure in the main roof pass itself through the lower portion strata, which is the part of the delivery pressure of rock can be considered to consist four boundaries: 1) Artificial boundary along the seam face. 2) The gateway roof free surface boundary. 3) The horizontal interface between disconnection and connection parts, since the deep end of seam face inside the rock formed a natural geometric parting, the plane parallel to the gateway roof and through the seam end can be considered as a stress boundary, which is passed down uniform loading. 4) At the coal wall side of the gateway forming a natural support surface, which can be considered to form a fixed end. As shown in the blue line circled on the roof rock strata in Fig. 3. Along the working face direction, the structure model of short-arm beam is shown in Fig. 9. In Figure 9, rock formation B is the main roof above the goaf, which is driven by overburden pressure. Rock formations A− and A+ are the main roof above the pillar and gateway. Since part of main roof was cut off, rock B is complete separated from rock A+. Regarded the rock formation above the main roof as the upper load, the area of short-arm beam is between the dotted line and rock B, and under rock A+. The load on the short-arm beam consist of three parts: P0 is the gravity of immediate roof (kN), P1 is the gravity of main roof (kN), P2 is the gravity of upper load (kN), h0 is the depth of roof precutting (m), h1 is the depth of main roof, h2 is the depth of rock formation above the main roof. The essence of 110 mining method is the active control of the entry roof and effective utilization of the bulking characteristics of the gob roof rock. As the short-arm beam is controlled, the stability of the gateway can be well guaranteed. 5

NUMERICAL ANALYSIS OF THE MINING-INDUCED STRESSES

Based on the mining design and geological conditions of No. 1105 working face in Hecaogou 2# coal mine, Shanxi, China, a numerical model was developed including two working faces: No. 1105 and No. 1103, as green area shown in Fig. 10. The rock stress distribution was analyzed by numerical simulation. The results provide a guideline for future mining design and entry supports. The rock mechanics properties used in the simulation are shown at Table 1. The roof strata are in ascending order sandy mudstone, gritstone. While the floor strata are in decline order argillaceous siltstone and fine sandstone. In the numerical simulation, there were seven types of strata considered, from the top to the bottom as follows: loess, sandstone, gritstone, sandy mudstone, coal, argillaceous siltstone and fine sandstone. 5.1

Boundary condition of the model

Considering the boundary effects of the model on the entry, the model size is selected to be 310 × 55 × 100 m3, as shown in Fig. 11. In this case, the FLAC3D code was used to simulate the stress distribution around the gateroad (Itasca). The gravity stress is imposed to the body of the model. The displacement of X and Y directions are limited to the horizontal of the 68

Figure 10. Table 1.

Panel location where the object region of numerical analysis.

Rock mechanics properties of the surrounding rocks.

Rock formation

Bulk modulus (GPa)

Shear modulus (GPa)

Tensile strength (MPa)

Cohesion (MPa)

Internal friction angle (°)

Density (kg/m3)

Loess Sandstone Gritstone Sandy Mudstone Coal Argillaceous Siltstone Fine Sandstone

1.02 3.9 4.12 2.12 0.85 2.68 4.3

0.58 2.3 2.45 1.45 0.48 1.34 2.61

0.35 1.12 1.31 0.63 0.32 0.75 1.22

0.21 0.36 0.49 0.35 0.18 0.38 0.43

21 24 26 23 21 22 25

2335 2567 2678 2587 1447 2543 2693

Figure 11.

3D numerical model.

Figure 12.

Boundary condition of the model.

model, and Z direction is fixed of the bottom boundary, as shown in Fig. 12. To highlight the effects of roof splitting, 110 mining method and 121 mining method were simulated in the same model, but different gateways. The roof of the air return way was cut, while the roof of the haulage gate was in its intact state (see Fig. 12). 5.2

Analysis of obtained results

During the simulation process, the variation of the vertical stresses in the front of working face seam were recorded. The simulation results were then imported into MATLAB to process. The 3D vertical stress distribution around the gateway is presented in Fig. 13. After mining 30 m, the vertical peak stress of the seam appears in the certain range before the working face, and the stress level is gradually reduced to the original level outside the scope. Compared with the vertical stress in the face ends, 121  method side rises a vertical stress peak zone, about 20 m wide and a maximum of about 4 MPa. With the deepening to the central region of working face, the vertical stress gradually reduced to 2.5 MPa. The other side 110 method also had a vertical stress peak zone, but only about 8 m wide and a maximum of about 3.2 MPa and trend was same with the deepening to the central region of working face. The cycle pressure of the working face and shear stress on the coal seam were also obtained, as shown in Figs. 14 and 15. It is obvious that the cycle pressure and shear stress in 69

Figure 13.

Vertical stresses in the seam after mining 30 m (Unit: Pa).

Figure 15. The shear stress distribution of ahead regional of mining face after advancing 70  m (Unit: Pa).

Figure 14. The cycle pressure in the coal seam (Unit: Pa).

Figure 16.

Entry retaining effects using 110 mining method.

110 mining method was much smaller than those in 121 mining method. The maximum cycle pressure and shear stress in 121 mining method were 4.8 MPa and 14.3 MPa, respectively, while the maximum cycle pressure and shear stress in 110 mining method were only 3.6 MPa and 5.2 MPa, appropriately 25% and 63% decrease than those in 110 mining method. All these results indicate that the retained entry was in a low stress environment after adopting 110 mining method.

6

FIELD TEST OF 110 MINING METHOD

To verify the reliability of 110 mining method, field tests have been performed at many mines in China (He et al., 2017; Gao et al., 2017; He et al., 2015). Here, No. 1105 working face in Hecaogou 2# coal mine was taken as an example. Figure 16 shows the final entry retaining 70

photos after adopting the new method. The gob roof collapsed into gangues along the splitting line. The caved gangues became another gateroad rib. During caving and compaction of the gangues, gangue prevention structures and metal nets were used to prevent the gangues from extending out into the gateway. It is clear that the cross-section of the retained entry could fully meet requirements of the next mining panel, revealing that 110 mining method is feasible and effective.

7

CONCLUSIONS

The paper presents major technological changes in China’s mining science and technology in terms of its representative theories. Longwall 121 and 110 mining methods were introduced based on the theoretical basis, numerical analysis and field test. The main conclusions are drawn as follows: 1. The traditional longwall mining 121 method made important contributions to the development of China’s mining science and technology. 2. With the increasing of mining depth, large deformation of surrounding rocks in deep tunnel becomes a challenging issue. Then the CCBT method using advanced roof caving is put forward. With the use of directional pre-splitting roof cutting, periodic pressures can be reduced or eliminated. The CCBT provides a basis for non-pillar mining and automatic tunneling technology, under which the longwall 110 mining method was established. 3. Special emphases were played on the numerical simulation of the geostress distribution found in the mining panel using the 110 method. At the same time, the stress distribution on the “short beam” left by the roof cutting when performing the 110 mining method was also investigated using numerical simulation. 4. The 110 mining methodology has been applied already with great success in many underground coal mines in China. Large benefits were introduced in terms of reducing substantially engineering disasters and in the involved costs in mining operations in tunnel excavations and by eliminating coal pillars. Therefore, a mining technology revolution in coal mines is underway in China. REFERENCES Fei X. The status-quo of support technology on gob-side entry retaining laneway and existing problem discussion. China Science and Technology Information, 2008, (3): 31–32 (in Chinese). Gao Y., Liu D., Zhang X., He M. Analysis and optimization of entry etability in underground longwall mining. Sustainability, 2017, 9(11): 2079. He M., Gao Y., Yang J., Gong W. An innovative approach for gob-side entry retaining in thick coal seam longwall mining. Energies, 2017, 10(11): 1785. He M., Gong W., Wang J., Qi P., Tao Z., Du S., Peng Y. Development of a novel energy-absorbing bolt with extraordinarily large elongation and constant resistance. International Journal of Rock Mechanics & Mining Sciences, 2014, 67: 29–42. He M., Li C., Gong W., Sousa L.R., Li S. Dynamic tests for a conrant-resistance-large-deformation bolt using a modified SHTB system. Tunnelling and Underground Space Technology, 2017, 64: 103–116. He M., Zhang G., Qi G., Li Q., Jia Q., Zhou J. Stability control of surrounding rocks in deep entry of Jiahe coal mine. Journal of Mining & Safety Engineering, 2007, 24(1): 27–31 (in Chinese). He M., Zhu G., Guo Z. Longwall mining “cutting cantilever beam theory” and 110 mining method in China-The third mining science innovation. Journal of Rock Mechanics and Geotechnical Engineering, 2015, 5: 483–492. He M. Conception system and evaluation indexes for deep engineering. Chinese Journal of Rock Mechanics and Engineering, 2005, 24(16): 2854–2859 (in Chinese). He M. Latest progress of soft rock mechanics and engineering in China. Journal of Rock Mechanics and Geotechnical Engineering, 2014, 6 (3): 165–179. He M. Present situation and prospect of rock mechanics in deep mining engineering. In: Proceedings of the 8th Conference of Chinese Rock Mechanics and Engineering. Beijing: Science Press, 2004: 88–94 (in Chinese).

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Itasca, Consulting Group Inc. Fast language analysis of continua in 3dimensions (version 5.0). User’s Guide. Li H. Roof strata control design for gob-side gateway. Chinese Journal of Rock Mechanics and Engineering, 2000, 19(5): 651–654 (in Chinese). Liu X., Zhang G. Technology of roof cutting pressure relief gob-side entry retaining in soft fractured stratum. Coal Science and Technology, 2013, (S2):133–134 (in Chinese). Liu Y., Shi P. Existing problem on long wall remaining coal pillars support mining. Journal of China Coal Society, 2007, 32(6): 565–569 (in Chinese). Song R., Xie J. The application of pre-splitting roof cutting and pressure releasing technology at working face and gob-side gateway maintaining. Coal Science & Technology magazine, 2012, (3): 52–54 (in Chinese). Sun X., Liu X., Liang G. Key parameters of gob-side entry retaining formed by roof cut and pressure releasing in thin coal seams. Chinese Journal of Rock Mechanics and Engineering, 2014, 33 (7):1449–1456 (in Chinese). Wang J., Wang G. Discussion on gateway retained along goaf technology with roof breaking and pressure releasing. Coal Engineering, 2012, (1): 24–26 (in Chinese). Zhai X., Zhou Y. Research on the filling body for gob-side gateway and its interaction with roof strata. Coal Mine Design, 1999, (8): 6–8 (in Chinese). Zhang G., He M., Yu X., Huang Z. Research on the technique of no-pillar mining with gob-side entry formed by advanced roof caving in the protective seam in Baijiao coal mine. Journal of Mining & Safety Engineering, 2011, 28 (4): 511–516 (in Chinese).

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Diagnostics and prediction of geomechanical objects state based on back analysis Larisa Nazarova Chinakal Institute of Mining of the Siberian Branch of the RAS, Novosibirsk, Russia

ABSTRACT: The formulations and general approaches to the back analysis problems in verification of geomechanical models and in estimation of the parameters that govern the state and properties of mine-technical objects of any scale are considered. For the illustrative purposes, the authors propose the methods: canister test data interpretation which allows quantitative evaluation of gas-kinetic characteristic od coal (gas content, coefficients of diffusion and mass exchange) by the value of pressure in the sealed vessel containing slurry coal; determination of rheological characteristics of petroliferous strata with high content of organic matter by the thermobaric test results; prediction of weak seismicity level in the Baikal rift zone, induced by variation of water-level in the Lake Baikal; diagnosis of state of antiseepage screen at liquid effluent pond dam by the piezometric measurements in terms of thermohydrodynamic model of thawed and frozen rock mass. Keywords:

1

non-linear geomechanical model, rock mass, coal, inverse problem, verification

INTRODUCTION

Geomechanical evaluation of hard mineral mining technologies, estimation of stability of structures in underground and surface mines, geodynamic zoning of areas, analysis of hydrocarbon exposure and recovery scenarios—this is a far from complete list of problems solution of which needs data on deformation-strength characteristics of rocks and reservoir properties, as well as on external natural and induced fields. The implementation approaches are: 1. traditional method (Jaeger et al., 2007) when properties of rocks (parameters of state equations) are determined at a laboratory scale, while boundary conditions are set based on direct (in situ stress measurements) (Zang & Stephansson, 2010) or indirect (for instance geodetic) data (Hudson, 1995; Nazarova, 1999); 2. back analysis (Sakurai, 2017) when mathematical modeling includes integrally laboratory or in situ data by minimizing objective function. The second approach is more broad-based as it allows using data of different physical nature (electromagnetic, temperature, hydrodynamic) by means of introduction of relevant objective functions: Ψ( 1,..., , ,α m )

∑γ ψ s

s

(α1,..., , ,α m ),

(1)

s

g where arguments are free parameters of a selected mathematical model, and a minimum point (α 1* , ,α m* ) ensures the best match of measurement data and simulation results. A proper set of non-negative weight numbers γs (åγs = 1) makes it possible to take into account quality of input data (relative accuracy of different measurement methods) and, sometimes, ensures unimodality of Ψ. There are two basis types of the function ψs in (1): 73

Is

I s 1 ∑ [1

ψ s (α ,...,α m )

s

( pi ,α

α m ) / Ws ( pi )]2 ;

(2)

i =1

ψ s (α ,...,α m )

Is

I s ∑ [Ws ( pi )

s

( pi α

α m )]2

i =1

Is

∑W ( p ), s

i

(3)

i 1

where Ws(pi) – input data of a s-th type recorded at an i-th point of space, and/or at an i-th moment of time; ws(pi,α1,…, αm) – the conformable values calculated using the selected model at some values of free parameters. The functions (2) are used if Ws are obtained from measurements based on different physical principles. The implementation of the back analysis in geomechanics has some peculiarities. 1. Most of geomechanical processes connected with mineral mining and stability of natural and anthropogenic objects are quasi-stationary processes; for this reason, the amount of input data (governing, in particular, the number m of arguments in Ψ), obtainable in a short time, is comparatively small. 2. The cost of “quantum” of information is, as a rule, much higher during in situ experimentation than in the seismic or electrical exploration. 3. For the analysis of stress state of large geological objects (lithospheric plates, cratons, terrains), the point measurements are useless; thus, it is advisable to use input data from satellite (SAR, InSAR, GPS) and seismology (trajectories of seismotectonic deformations) observations.

2

BACK ANALYSIS AND INVERSE PROBLEMS. SELECTION OF FREE PARAMETERS

Majority of continuum models describing deformation, heat and mass exchange processes in rocks are physically (more seldom, geometrically) nonlinear (except for linearly elastic models for infinitesimal strains, perhaps). There is no strict proof of existence and uniqueness of solution to the respective initial boundary value problems. For this reason, although often used in solving inverse problems (Tarantola, 2004), the gradient methods of minimum search of function of several variables (Avriel, 2003) do not much good. Therefore it is required to carry out brute force search of arguments of Ψ in a priori preset ranges. This approach is the ordinary practice of back analysis. Evidently, amount and quality of input data govern resolvability of the problem Ψ( 1,..., , ,α m )

min

(4)

for the selected number m of free parameters. In particular, in case that

α q Ψ,α q  TE: self-supported excavation if T 70 dB, we see that activities starts around 182 MPa for specimen R98-3, 158 MPa for R225-1 and 108 MPa for R375-3. There is a scatter between results of different specimens and notches (not shown here), but a general trend can be clearly be seen. Figure 4 shows the maximum tangential stress at AE initiation for different amplitudes. The ratio of the maximum tangential stress over the compressive strength obtained from the uniaxial compression tests versus twice the notch radius (equivalent hole diameter) are shown in Figure 4. 3.3

DIC

The out-of-plane deformations on specimen R98-4 and R225-4, measured using the Aramis 12 M system, are shown in Figure 5. Local peak values “hot spots” (red) with size of c 5–8 mm could be observed. This is probably individual grains that either split or detach at grain boundaries. By looking at the average displacement on a small region (c 4 mm) within a hot spot relative to neighboring regions (c 4–5 mm) versus stress it becomes evident when the displacements locally starts to deviate from a linear response (Figure 6). For two selected hot

Figure 4. Left: Ratio of the maximum tangential stress at AE initiation for different amplitudes over compressive strength σc versus equivalent hole diameter; Right: Observed initial tangential stress in MPa at initiation of acoustic emission (Accumulated events = 2). The values within the parentheses denote tangential stress/σc.

Figure  5. Out-of-plane displacement at notches measured by DIC. Left: R98-4 (c 55  mm picture width); Right: R225-4 (c 88 mm picture width).

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Figure 6. Out-of-plane measurements of local regions with possible spalling. The specimen R225-4 was partially unloaded twice until loading up to fracturing.

Figure 7.

Thin sections impregnated with fluorescent epoxy. Left: R98-1 (3); Right: R98-3 (3).

spots each in the notches monitored by DIC on specimens R98-3, R98-4, R225-3 and R225-4 it can be noted that the out-of-plane displacement successively starts to deviate from a linear response at 160-190 MPa on the R98 specimens and around140-190 MPa on the R225 specimens. Sudden increase of the out-of-plane displacement can be seen on the R225  specimens. Moreover, it can be seen that the noise and out-of-plane displacement is larger on the R225 specimens. The larger noise in the R225 results is due to less measurement points in the averaging in the selected areas. 3.4

Crack observations

Thin sections (R98) and polished slabs (R225 and R375) with the rock material impregnated with fluorescent epoxy showing a cross section over the notch were prepared for some specimens (Figures  7 and 8). The cracks and fractures were studied and photographed in fluorescence light. Shallow cracks, subparallel to the notch surface in the direction of the largest compressive stress, were formed at several locations. Some grains, somewhat with a deeper location, were also split at some locations in the same direction. These types of results were also seen on experiments on diorite (Jacobsson et al. 2015). It can be seen that the subparallel cracks to the notch surface are formed more shallowly in the R98 specimens and the depth increases with increasing radius. The mineral micro structure plays a crucial role for the initiation, shape and propagation of these near surface cracks. Further crack investigations using thin sections will be carried out to study the crack paths in relation to the minerals and crystallographic directions. 637

Figure 8.

4

Polished slabs impregnated with fluorescent epoxy.

CONCLUSIONS

The mechanical experiments on specimens with notches resembling the hole geometry around circular openings show a trend that cracks form at a lower stress when the notch radius increases, which is in correspondence with previous investigations (Martin 1993, 1997). A combination of AE and deformation field measurements was used to investigate the crack initiation in the notches. The out of-plane deformations reveal local dilations on up to 0.01– 0.02  mm. The measured localized AE-events and out-of-plane displacements correlate to each other for one of the spots.

ACKNOWLEDGEMENTS The work presented in this paper has been funded by Swedish Nuclear Fuel and Waste Management Co (SKB). Assistance during measurements by Torsten Sjögren, Mathias Flansbjer and staff in the laboratory at RISE is gratefully acknowledged. The experimental work was carried out during 2014–2015 at SP Technical research Institute of Sweden in Borås, which since then changed name to RISE in January 2016.

REFERENCES Jacobsson, L., Appelquist, K. & Lindqvist, J.E., 2015. Spalling experiments on large hard rock specimens. Rock Mechanics and Rock Engineering 48(4):1485–1503, doi: 10.1007/s00603-014-0655-0. Martin, C.D., 1993. The strength of massive Lac du Bonnet granite around circular openings. PhDthesis, University of Manitoba, Canada. Martin, C.D., 1997. Seventeenth Canadian Geotechnical Colloquium: The effect of cohesion loss and stress path on brittle rock strength. Canadian Geotechnical Journal, 34(5), 698–725. doi:10.1139/ t97-030.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Comparison of different approaches to predict the shear strength of large rock discontinuities M. Jeffery, L. Lapastoure Gritchou & A. Giacomini Priority Research Centre for Geotechnical Science and Engineering, University of Newcastle, Callaghan, NSW, Australia

V. Griffiths Department of Civil and Environmental Engineering, Colorado School of Mines, Golden, CO, USA

O. Buzzi Priority Research Centre for Geotechnical Science and Engineering, University of Newcastle, Callaghan, NSW, Australia

ABSTRACT: Reliable prediction of shear strength for engineering scale in-situ discontinuities is still problematic. There is currently no consensus or a satisfactory method to estimate shear strength, account for surface variability and manage the effects of the recognised ‘scale effect’ phenomenon. Shear behaviour of a discontinuity rock mass greatly depends upon the rock joint roughness, which is generally concealed within the rock mass. As such, the limited amount of accessible surface information complicates even further the exercise of shear strength prediction. Often, small size specimens (e.g. rock core) are recovered to conduct experimental tests and predictions can be made from analysing traces. In this paper, three different shear strength prediction approaches were followed and their relative performances were compared. The results reveal that the prediction of shear strength from recovered sub samples can be significantly variable. The application of Barton’s empirical model to four selected traces, produced a large scattering of results, with the prediction highly dependent on the trace used. Conversely, the application of Casagrande and co-workers’ stochastic approach on the same traces, produced the least scatter and provides statistical data to quantify variability and uncertainty.

1

INTRODUCTION

The prediction of shear strength is an important component in large scale engineering rock mass stability analysis and design applications. It is well known that roughness is a key factor influencing the mechanical response of a discontinuity and its peak shear strength. There is currently no consensus or a satisfactory method to estimate shear strength of a large discontinuity, whilst accounting for surface roughness variability and managing the effects of the recognised ‘scale effect’. As such, reliable prediction of the shear strength of large in situ discontinuity is still problematic. Extensive work has been undertaken over the last four decades to characterise joint surface information (Ge et al, 2015). However, the first difficulty with estimating shear strength of a large in-situ discontinuity, stems from the limited amount of available surface information. Due to convenience and a lack of reliable alternatives, researchers and engineers typically employ empirical approaches, or use small scale specimens and either numerical or experimental methods to predict a shear strength (Buzzi et al, 2017). Approaches for estimating shear strength of large discontinuities generally rely on the assumption that obtained roughness data, is representative and shares some characteristics 639

of the whole surface (Fardin et al, 2001, Buzzi et al, 2017). If this assumption is incorrect or disregarded, having an understanding of the potential variability is critical. Since the 1960’s numerous studies have investigated the scale effects on roughness, shear strength development and deformability. With respect to the shear strength studies, opposite conclusions have been drawn, regarding the need for positive or negative upscaling requirements. Given a laboratory size sample, it is extremely difficult to determine the degree of scaling required (Giani, 1992). One of the most used empirical model for shear strength, has been modified to try and capture the scale dependence (Barton and Bandis, 1980). More recently a new stochastic approach for predicting peak and residual shear strength was developed by Casagrande et al. (2017). This approach is applicable at field scale and has the potential to minimise or entirely circumvent the scale effect issue. This paper compares the results obtained from three shear strength prediction approaches, to gain an understanding of prediction performance with respect to prediction behaviour, magnitude and variability as well as managing scale effects.

2

OBJECTIVES

Assessing the shear strength of a large in situ discontinuity is a non-trivial task. Amongst the different options, it is possible to core the rock to obtain small size specimens (here referred to as “sub-sample”) that will be tested in the laboratory or to estimate the strength from the roughness information that can be collected from visible traces. Consequently, this paper compares the shear strength predictions obtained by following three different approaches: 1. Using sub-samples of 100 mm per 100 mm. 2. Using Barton’s model (Barton and Choubey, 1977), applied to a single trace. 3. Using a new stochastic approach proposed and validated by the authors, also applied to a single trace.

3

STUDY SURFACE

This study is based on a natural discontinuity located in a former sandstone quarry, in the Pilkington Street Reserve in Newcastle (NSW, Australia). The surface was accurately surveyed using 16 coded ground control points (GCP) that were evenly placed on the wall with their coordinates measured twice using a reflectorless total station (Leica TPS1205). More than 250 photographs were taken (Canon E0S 7D camera) at a distance of 1 m and the commercial software called “Structure for Motion Agisoft Photoscan” was used for a 3D reconstruction. The point cloud was structured into a grid with a 1 mm spatial increment. More information on the reconstruction process, is presented in Casagrande et al. (2017). The reconstructed surface is presented in Figure 1.

4 4.1

APPROACHES TO PREDICT SHEAR STRENGTH Using sub-samples

For this first approach, the surface was sub-divided into 400 sub-samples, 100 mm × 100 mm domains as shown in Figure 1a. All 400 samples were analysed using the semi analytical shear strength model developed by Casagrande et al. (2017), which can predict peak and residual shear strength of rough, perfectly matched discontinuities for given shear direction, normal stress (0.02, 0.1, 0.25 and 0.5 MPa) and material properties (unaxial compressive strength (UCS)/joint compressive strength (JCS) value of 39.67 MPa, basic/residual friction angle (φb/φr) of 35°, cohesion (c) value of 4.74 MPa). Note that the values of normal stress and material properties given above were used for all three methods. 640

Figure 1. Reconstructed Pilkington study surface (a), contour map with (b) domains of the 400 subsurface and (c) selected traces for shear strength prediction.

4.2

Barton’s empirical model

Barton’s empirical failure criterion (Barton and Choubey, 1977) is commonly employed to predict the shear strength of discontinuities. The model accounts for the effect of roughness via the Joint Roughness Coefficient (JRC): ⎛ ⎛ JCS C ⎞⎞ τ peak = σ nta t n ⎜ φr + JRClog110 ⎜ ⎝ σ n ⎟⎠ ⎟⎠ ⎝

(1)

where σn is the normal stress acting on the discontinuity, JCS is the Joint Compressive Strength and φr is the residual friction angle. The residual strength is obtained by equating the JRC to 0 in Equation 3.2, i.e.:

τ resiidual

σ ntan (φr )

(2)

The JRC value is here back calculated from the surface descriptor Z2 and Yang et al (2001) equation; JRC = 32.69 +

. 8 llog10Z2

(3)

where Z2 is defined as:

(

⎛ 1 L Z2 = ⎜ ∑z ⎝ L.Δx 2 i =1 ( y(i 1) )

)

1

⎞2 zy ( (i ) ) ⎟⎠ 2

(4)

Equations (1) to (4) were applied to the four traces highlighted in Figure 1c. 4.3

Stochastic approach

Casagrande et al. (2017) developed a new stochastic approach to predict the peak and residual shear strength of rock discontinuities. This approach is applicable at field scale and has the potential to minimise or entirely circumvent the scale effect issue. The foundation of the method is to use the statistics of a visible trace, to form a large number of statistically similar synthetic surfaces via the rigorous application of a random field model. Shear strength 641

distributions of shear strength (peak and residual) are obtained through analysing all of the synthetic surfaces using a semi analytical shear strength model. Note that this is the same semi-analytical model that is used for the approach described in section 4.1. The prediction is expressed in terms of mean shear strength with an error bar equal to the standard deviation. The reader is invited to refer to Casagrande et al. (2017) for more information on the details of the stochastic method. The statistics of the four traces highlighted in Figure 1c were used as an input of the random field model and the stochastic approach. 100 synthetic surfaces were created for each trace. 4.4

Reference shear strength

In absence of experimental data on the surface used here (it is located in a protected reserve and cannot be tested), the predictions of the three approaches described above will be compared to the peak and residual shear strength pertaining to the whole surface and obtained via the semi-analytical model described in Casagrande et al. (2017). The same material properties than those given in section 4.1 prevail.

5 5.1

RESULTS Prediction of shear strength using sub-samples

The cumulative distribution of strength (obtained on the 400 sub-samples) shows a considerable variability under all five normal stresses (see Figure 2a). For example, under 0.02 MPa, there is a factor 10 between the lowest and the highest predicted value of peak shear strength, and 50 for the residual strength. Comparing the mean shear strengths (peak and residual) obtained from the 400 subsamples to the peak and residual shear strength of the whole surface (obtained from the semi-analytical model, and referred to as “deterministic”) reveals a clear negative scale effect (Figure 2b). Indeed, the whole surface consistently displays a higher strength than the

Figure 2. Cumulative relative frequency distribution of peak (continuous line) and residual (dashed line) shear strength for the 400 sub surfaces (a) and a comparison of mean peak and residual shear strength for the 400 sub surfaces and deterministic peak and residual shear predictions on the whole surface (b).

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sub-samples tested. At this stage, this is not fully explained (it has not been fully analysed) but is believed to be a matter of the roughness features captured in the each sub-sample. 5.2

Prediction using Barton’s model

The JRC values for traces 1, 2, 4 and 7 were back-calculated as 19.12, 14.63, 7.01 and 5.52, respectively. Figure 3a compares the deterministic criterion of the whole surface (peak and residual) to the predictions obtained from Barton’s model. Based on the trace selected, it is possible to under-estimate (by as much as 40%) or over-estimate (by as much as 60%) the peak shear strength of the surface. The failure criterion obtained for trace #1 is quite questionable: the peak shear strength is negative at low normal stress before increasing significantly and over-predicting the peak shear strength (by about 50% at 0.5 MPa of normal stress). This behaviour is due to equating the tangent of a combined friction angle value that is close to π/2 (98.41° at 0.02 MPa and 85.05° at 0.1 MPa), before multiplying by the normal stress to determine the peak shear strength. In the instance of trace 1, the large JRC value contributed to the combined angle terms to be greater than π/3, for the considered normal stresses. The JRC being nil for the residual strength prediction, all traces have the same residual failure criterion (Figure 3b), which falls under the deterministic value (under estimation ranging from 40% to 70%). 5.3

Prediction using the new stochastic approach

The peak and residual failure criteria obtained by the stochastic method, presented in Figure 4, show a good agreement with the deterministic failure criteria. Note that the approach relies on creating synthetic surfaces created from the statistics of the seed trace. In that sense, the new approach does not use the shear strength of the whole surface. At low normal stresses, the difference between the predicted and deterministic criterion is only in the order to −25% to 15%. Under 0.5 MPa, the difference between the highest and lowest shear strength increases to 0.21 MPa and 0.173 MPa for peak and residual shear strength, respectively. Note that for the sake of clarity, the error bars are not shown.

Figure 3. Comparison between peak (a) and residual (b) shear failure criteria obtained from Barton’s model (using traces 1, 2, 4 and 7) and deterministic criteria pertaining to the whole surface.

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Figure 4. Comparison between peak (a) and residual (b) shear failure criteria obtained from the new stochastic approach (using traces 1, 2, 4 and 7) and deterministic criteria pertaining to the whole surface.

6

DISCUSSION

The distributions of shear strength obtained for the 400 subsamples presented in Figure 2a, highlight one of the main disadvantages of testing sub-samples, namely the possibility of large variability. The extent of variability can be correlated to the degree of morphology variability of the parent surface, which cannot be easily assessed if the surface is contained within a rock mass. The surface studied here is quite variable with some marked roughness features (such as steps), resulting in a wide distribution of predictions. Figure 2 also confirms another long-known problem: the existence of a scale effect. Published results in the literature demonstrate that there is no such thing as a systematic scale effect. Positive (REF) and negative effects (REF) have been observed as well as no scale dependence (REF). To date, there are no reliable methods that can help characterise, qualitatively or quantitatively, the scale effect. The application of the JRC approach for the four traces tested produced mixed results. The degree of variability between the four failure criteria and the unusual failure criterion associated to trace #1 is concerning. The failure criteria obtained under and overestimate the strength by about −40 to +60%. Note that the reference strength (deterministic value) is obtained from the semi-analytical model used for the other two approaches, so there is a slight bias in the results. However, the focus is here more on the scattering of results between the different approaches rather than reaching a slightly biased target value. The variability of these results can be attributed to the effect of surface morphology on the evolution of the Z2 and JRC value. Figure 5a and b, show traces 1 and 2 encounter a morphological feature characterised by a significant and abrupt increases in elevation. The evolution of Z2 and JRC along the traces, presented by Figure 5c and d respectively, illustrates that the magnitude of these values, is increased by an order of 2–3 times after the feature is encountered. These figures also show, the values of Z2 and JRC to gradually reduce in magnitude away from the crest, but appear to be still affected by the initial encounter at the end of the trace length. In contrast, despite different elevation profiles, traces 4 and 7, produced Z2 and JRC evolution profiles that show only minor localised variations values along the traces length. From this it can be concluded that morphological features such as steps can affect the evolution of Z2 and JRC values, which will in turn effect the prediction of shear strength and contribute to an increase in prediction variability. 644

Figure 5. Comparison of Z2 and JRC value realisation for the 4 traces: trace elevation profiles (a), trace profile incremental elevation difference (b), evolution of Z2 values (c) and evolution of JRC value (d).

The prediction of both peak and residual shear strength using the new stochastic approach produced results with much more reduced scattering. It has to be reminded here that the rationale of this approach is that there is enough information on a visible trace to create a range of realistic discontinuities that underpin the stochastic prediction of shear strength. As such, the full surface does not constitute an input of the new stochastic approach. The new approach does not rely on a scale dependent descriptor (such as JRC) and hence circumvents the scale effect, the approach produces mean values of shear strength with reduced scattering (despite using four different traces, and unlike the JRC approach) and a standard deviation, which can be used to compute confidence intervals.

7

CONCLUSIONS

This paper compares three approaches to predict shear strength of a large discontinuity (2m per 2m) coming from a natural reserve in the vicinity of Newcastle, NSW, Australia. The first approach consists of testing sub-samples (from cored rock). The study revealed that the results variability can be very large, with as much as a factor 50 between one prediction and another. Also, the occurrence of a scale effect was confirmed, meaning that the results obtained in the laboratory cannot easily be extrapolated to the whole surface. The second approach consists of applying Barton’s model, based on back calculated JRC, to a selection of traces. A large scattering of results was observed, with the prediction being highly dependent on the trace used. One trace produced an inconsistent failure criterion with a negative value of shear strength. It was concluded that the JRC approach generally produces conservative predictions of shear strength. The study noted that abrupt morphological features can detrimentally effect the evolution of Z2 calculated JRC values. The third approach tested is that developed by Casagrande et al. (2017) which relies on random field model and stochastic analysis via a semi-analytical model for shear strength. It was found that this approach produced the most accurate predictions of shear strength and the least scatter. The obtained peak and residual shear strength distributions can be used to attain statistically confident mean estimates and an indication of confidence interval via the standard deviation. One of the advantages of this approach is that scale free surface characteristics are obtained at the intended scale and therefore the scale effect can potentially be avoided. 645

ACKNOWLEDGEMENTS The authors would like to acknowledge the financial contribution received from Pells Sullivan Meynink, Engineering Consultants, Sydney.

REFERENCES Barton N. (1976). The Shear Strength of Rock and Rock Joints. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 13, 255–279. Barton N., Choubey V. (1977). The shear strength of rock joints in theory and practice. Rock Mechanics and Rock Engineering, 10, 1–54. Barton, N., Bandis, S. (1980). Some effects of scale on the shear strength of joints. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 17, 69–73. Buzzi O., Casagrande, D., Giacomini, A., Lambert, C. Fenton, G. (2017). A new approach to avoid the scale effect when predicting the shear strength of large in situ discontinuity. In: Proceeding of 70th Canadian Geotechnical Conference, Ottawa, Canada. Casagrande, D., Buzzi, O., Giacomini, A., Lambert, C., Fenton, G. (2017). A New Stochastic Approach to Predict Peak and Residual Shear Strength of Natural Rock Discontinuities. Rock Mechanics and Rock Engineering, 1–31. Fardin, N., Stephansson, O., Jing, L. (2001). The scale dependence of rock joint surface roughness. International Journal of Rock Mechanics and Mining Sciences, 38 (5), 659–669. Ge, Y., Tang, H., Eldin, M.A.M.E., Chen, P., Wang, L., Wang, J. (2015). A Description for Rock Joint Roughness Based on Terrestrial Laser Scanner and Image Analysis. Scientific Reports, 5, 16999. http://doi.org/10.1038/srep16999. Giani, G.P., Ferrero, A.M., Passarello, G., Reinaudo, L. (1992). Scale effect evaluation on natural discontinuity shear strength. In Proceedings of the international congress fractured jointed rock mass. Lake Tahoe, California, 456–462. Maerz, N.H., Franklin, J.A. and Bennett, C.P. (1990). Joint roughness measurement using shadow profilometry. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 27(5): 329–343. Yang, Z.Y., Lo, S.C., Di, C.C. (2001). Reassessing the joint roughness coefficient (JRC) estimation using Z2. Rock Mechanics and Rock Engineering, 34(3), 243–251.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Effects of excavation damage on the electrical properties of rock mass Pekka Kantia Geofcon, Rovaniemi, Finland

Risto Kiuru & Mikael Rinne Department of Civil Engineering, School of Engineering, Aalto University, Espoo, Finland

ABSTRACT: Electrical and Electromagnetic (EM) methods have been used for characterisation of Excavation Damage Zone (EDZ) in conjunction with long-term safety evaluation of geological disposal of spent nuclear fuel. Physical properties of the rock have been tested in laboratory to characterise the property changes related to EDZ. EM research has focused around Ground Penetrating Radar (GPR) utilizing GPR EDZ method, developed for excavation quality control in means of EDZ extend. For 20 specimens, resistivity, relative dielectric permittivity (εr) as well as high frequency scattering parameters (electrical conductivity and εr) were measured. Induced Polarization (IP) values were calculated from resistivity data. Resistivity, IP and εr, was produced to support the use of GPR image analysis and the GPR EDZ method. Results were analysed to reveal links between εr and conductivity, and to analyse possible depth dependencies. A positive association between electrical conductivity and εr was observed. Changes in the electrical properties linked to shallow depths and visual EDZ features were observed, which seems to validate the theoretical basis of the GPR EDZ method. Electrical property data allows further modelling, development and assessment of the GPR EDZ method. Keywords: Excavation damage, scattering parameters, electrical resistivity, electrical conductivity, induced polarisation, relative dielectric permittivity, network analyser

1

INTRODUCTION

Excavation damages the rock in the tunnel vicinity and this weakens the rock mass. Formed damage zone in the tunnel vicinity, microscopic as well as open fractures, are referred to as Excavation Damage Zone (EDZ). Understanding the formation and physical characteristics of excavation damage is critical for the long-term safety evaluation of deep geological disposal of spent nuclear fuel. More intense and deeper the EDZ penetrates, the higher is the risk for formation of pathways for the radio nuclides to the organic nature. As the EDZ is seen as a long-term disposal safety issue, it has to be controlled. Methods for controlling EDZ are Drill and Blast (D&B) method related (drilling, charging and workmanship, e.g.) but a measurement method for EDZ is needed as well. The Finnish company Posiva has been developing high frequency Ground Penetrating Radar (GPR) method for the task since 2008, resulting in a GPR signal frequency content analysing method called GPR EDZ method (Kantia et al., 2012; Kantia et al., 2013; Kantia et al., 2016a). It appears that the GPR EDZ method can be used in EDZ characterization (Heikkinen et  al., 2010) as well as in EDZ extent measurements (Kantia et al., 2016b). In this work, electrical properties of intact and damaged rock specimens were determined to verify the feasibility of the GPR EDZ method and allow theoretical modelling of the GPR signal in the rock mass.

647

2

EXCAVATION DAMAGE ZONE

Terminology used in EDZ investigations is based on a paper by Dinis da Gama and Torres (2002) which defines several levels of distinctly different damaged zones: (1) zone of crushing, (2) zone of radial cracking, (3) zone of extension and expansion of fractures and (4) elastic zone where no cracks are formed (Figure 1). Siren et al. (2014) separate the most important formation mechanisms of EDZ as (1) EDZCI – Construction induced excavation damage zone, which is instantly formed by the construction method and (2) EDZSI – Stress-induced excavation damage zone, which is consequence of the redistribution of the stress field in the rock (Figure 2). EDZ influences the physical and mechanical properties of the rock mass and EDZ effects are different in different rock types. For example, granitic pegmatoid (PGR) with

Figure 1. Schematic presentation of different type of damages near the blasting hole and tunnel surface as classified by Dinis da Gama and Torres, 2002: (1) zone of crushing, (2) zone of radial cracking, (3) zone of extension and expansion of fractures and (4) elastic zone, where no cracks are formed. Adapted from Kantia et al. (2016).

Figure  2. (2014).

Definitions of the different damage zones used in this work. Modified from Siren et al.

648

intense micro fracturing differs from veined gneiss (VGN) characterised by clear individual fractures that penetrate deeper.

3

MEASURED ELECTRICAL PROPERTIES AND OBSERVED CHANGES

For 20 specimens, electrical resistivity, induced polarisation (IP effect, describes chargeability of the material) and relative dielectric permittivity (describes attenuation of an electromagnetic wave in the material) values as well as high frequency scattering parameters (electrical conductivity and relative dielectric permittivity) were determined. Resistivity was first measured at 0.1 Hz, 10 Hz and 500 Hz using a proprietary measurement system developed by the Geological Survey of Finland. From the measured resistivity values, IP effects (0.1 Hz/10 Hz and 0.1 Hz/500 Hz) were calculated. Relative dielectric permittivity was measured using an Adek v.7 percometer operating in the 40–50 MHz range (for 19 of the 20 specimens). Description of the resistivity, IP effect and relative dielectric permittivity measurements can be found in Kiuru (2017). High frequency scattering parameters (electrical conductivity and relative dielectric permittivity) were measured for all specimens both saturated and dry at 2 GHz and 3 GHz using an Agilent network analyser. Results are shown in Table 1. Results were analysed to reveal associations between electrical parameters and their possible depth dependencies. A general increase in relative dielectric permittivity was observed with increasing resistivity (Figure 3), while scatter of the observed values also increases. At the low frequencies (0.1 Hz, 10 Hz and 500 Hz) resistivity is generally higher in the first 20 cm of the excavated surface, and shows higher variation than deeper (Figure 4, left). A similar effect was also observed at higher (2 GHz and 3 GHz frequencies), if not as pronounced (Figure 4, right).

Table 1. Results from the measurements. Resistivity Depth

Porosity

Sample

Rock type

m

%

ED123 ED124 ED131 ED132 ED141 ED142 ED144 ED145 ED146 ED147 ED152 ED153 ED154 ED165 ED166 ED170 ED172 ED173 ED174 ED175

VGN VGN VGN VGN VGN VGN PGR PGR PGR PGR PGR PGR PGR PGR PGR PGR VGN VGN VGN VGN

0.054 0.135 0.115 0.170 0.590 0.645 0.200 0.255 0.310 0.365 0.530 0.585 0.640 0.115 0.170 0.390 0.055 0.110 0.165 0.220

0.81 0.60 0.24 0.25 0.45 0.55 0.41 0.36 0.27 0.32 0.32 0.40 0.26 0.31 0.28 0.41 0.22 0.23 0.26 0.20

R0.1

R10

R500

Permittivity 2G

3G

Ohm.m 11900 18200 34600 21500 8540 7190 5050 6010 14600 9850 8100 5920 7370 4780 6260 9900 16400 24000 36300 38700

11200 16700 31300 20100 7810 6990 5190 6450 14300 9470 7990 5740 7240 4640 6150 9500 15300 21800 31500 34300

10200 14500 27300 18400 7080 6640 5140 6340 13700 9060 7740 5480 7000 4500 5960 8910 13800 18500 25800 28900

67.0 114.9 188.0 264.8 118.7 87.8 200.5 155.9 107.9 105.9 189.7 180.4 184.7 199.2 180.8 188.0 214.6 87.7 117.7 210.7

R0.1 is measurement at 0.1 Hz, R10 at 10 Hz and R500 at 500 Hz. 2G is the measurement at 2 GHz and at 3 GHz. εr is the measurement at 40–50 MHz, εr′1 at 2 GHz and εr′2 at 3 GHz.

649

47.4 87.3 151.8 247.5 103.1 71.6 189.6 142.1 93.9 94.5 179.8 166.3 170.4 190.9 169.8 181.3 173.9 65.8 91.5 179.1

εr

εr′1

εr′2

6.30 6.44 6.17 6.35 6.40 6.26 5.32 5.28 5.81 5.71 5.59 5.61 5.22 5.56 5.48

6.65 6.15 5.53 5.19 6.28 5.99 5.39 5.28 5.51 5.47 5.31 5.35 5.41 5.23 5.30 5.28 5.59 7.02 6.52 5.54

6.58 6.10 5.51 5.17 6.19 5.91 5.34 5.24 5.43 5.41 5.26 5.31 5.38 5.20 5.26 5.24 5.54 6.95 6.47 5.50

5.99 6.31 6.38 5.85

Figure 3. Relative dielectric permittivity appears to increase with increasing resistivity. R0.1, R10 and R500 correspond to measurements at 0.1 Hz, 10 Hz and 500 Hz, respectively.

Figure 4. Resistivity vs depth from excavated surface. At low frequencies (0.1 Hz, 10 Hz and 500 Hz, left figure), resistivity variation within the first 20 cm is much higher than deeper from the excavated surface. R0.1, R10 and R500 correspond to measurements at 0.1 Hz,  Hz and 500 Hz, respectively. Similar effect is observed with high (2 GHz and 3 GHz) frequencies as well (right figure).

Relative dielectric permittivity shows higher values and variation near the excavated surface as well (Figure 5). Changes in the electrical properties linked to shallower depths could in some cases also be linked to visually observed EDZ fractures in core samples (Kiuru et al., this publication), which seems to validate the theoretical basis of the GPR EDZ method.

4

CONCLUSIONS

Changes in the electrical properties linked to shallow depths and visually observed EDZ features were observed, which seems to validate the theoretical basis of the GPR EDZ method. Knowing the electrical properties of intact as well as damaged rock allows assessing the feasibility of the method and enables theoretical modelling of the GPR signal behaviour in the site-specific rock mass. Improved understanding of the correlation between the geophysical and mechanical parameters of the rock mass provides better capability to detect and model the development of the excavation damage zone with help of the GPR EDZ method. 650

Figure 5. Higher relative dielectric permittivity is observed in the surface layer, regardless of the measurement frequency. εr is the measurement at 40–50 MHz, εr′1 at 2 GHz and εr′2 at 3 GHz.

DISCLAIMER AND ACKNOWLEDGEMENTS The views expressed are those of the authors and do not necessarily reflect those of Posiva. We would like to thank Academy of Finland for funding (grant 297770), Posiva Oy and Geofcon for providing the possibility to publish the data, VTT Technical Research Centre of Finland and the Geological Survey of Finland for help with the measurements and Sanna Mustonen, Eetu Pussinen, Eero Heikkinen, Noora Riihiluoma, Johannes Suikkanen, Lasse Koskinen and Eeva Käpyaho for cooperation on the EDZ research.

REFERENCES Dinis da Gama, C. and V.F. Navarro Torres, 2002. Prediction of EDZ (excavation damaged zone) from explosive detonation in underground openings. In Proceedings of the ISRM International Symposium on Rock Engineering for Mountainous Regions—Eurock 2002 Funchal, Portugal, 26–28 November 2002. Eds. C. Dinis da Gama and L. Riberia E Sousa. Heikkinen E., Kantia P., Lehtimäki T., Silvast M. and Wiljanen B., 2010 EDZ Assessments in Various Geological Environments Using GPR Method. Posiva Working Report 2010–04. Kantia, P., Mustonen, S. and Mellanen, S., 2016b. EDZ Control in Nuclear Waste Disposal Facility in Finland. ISEE 42nd Annual Conference on Explosives and Blasting Technique, Las Vegas, Nevada, Jan. 31st—Feb. 3rd 2016. Kantia, P., Mustonen, S., Kouvonen, T., Lehtimäki, T. and Olsson, M., 2016a. Excavation damaged zone research in Tampere test mine Finland. ISRM International Symposium 2016. Cappadocia, Turkey. Kantia P., Heikkinen E., Mustonen S., Lehtimäki T. and Silvast M., 2012. Excavation Damage Zone Mapping Using EDZ GPR Method. EAGE Near Surface Geoscience 2012–18th European Meeting of Environmental and Engineering Geophysics. Kantia P., Heikkinen E., Mustonen S., Mellanen S., Lehtimäki T. and Silvast M., 2013. Quality control of drill and blast excavated tunnels using GPR EDZ method. In: World Tunnel Congress 2013 Geneva. Eds.: G. Anagnostou & H. Ehrbar. Kiuru, R., 2017. EDZ Study Area in ONK-TKU-3620: Association Analysis of Petrophysical and Rock Mechanics Data. Posiva Oy, Working Report 2016-42. In press. Siren, T., Kantia, P. and Rinne, M., 2014. Considerations and observations of stress-induced and construction-induced excavation damage zone in crystalline rock. International Journal of Rock Mechanics & Mining Sciences. Elsevier Ltd 2014.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Study of physical-mechanical properties of hard rocks under water-saturated conditions Nikolai Kuznetcov, Iuliia Fedotova & Alexander Pak MI KSC RAS, Apatity, Russia

ABSTRACT: The development of mineral deposits both by open and underground mining methods is always accompanied by the mining-induced stress field formation in the rock mass. The specificity of such stresses occurs in the form of their concentration or release in the geological medium structures. The rock mass in such conditions is subjected to permanent loadings and unloadings. This influence also results in the change of rock properties. The hard rock mass is characterized by high strength and deformation parameters. However, the watered areas (aquifers), the structural discontinuities of different rank and the water-soluble minerals along with permanent loadings and unloadings in the rock mass can cause dynamic fracturing of rocks. In this regard it is important to study the variation of rock properties under the change of loading character under the water-saturated conditions. The paper presents the results of laboratory studies on hard rock samples (carbonatite, fenite and gneiss) from the Kovdor deposit under uniaxial stress state with the change of their water-saturation time (from 1 to 13 days). A series of deformation tests in the form of loading and unloading up to a value of 30% of the compressive strength with subsequent fracturing of samples were performed simultaneously with the water-saturation process. The dependence between the change of physical-mechanical properties of studied rocks and the quasistatic alternating loadings was established by comparing the test results. The authors have determined a degree of influence of water-saturation time increase on the acceleration of rock samples’ fracturing and the possibility of dynamic rock pressure occurrences in the hard rock mass.

1

INTRODUCTION

The rock mass is a complex hierarchically-blocked geological environment subjected to various man-made and nature factors (Turchaninov, 1977). One of the possible sequences from such influences is the occurrence of alternating loads in the rock mass due to the stress concentration and unloading (Oparin, 2011). The long-term action of such processes can promote the rock softening which, in turn, can lead to the formation of joints and rock mass fracturing. The alternating loads can trigger the dynamic failure of a brittle hard rocks. In general, it is considered that loading and unloading of hard rocks up to 30% of their compressive strength occur in the elastic area and don’t cause the rock failure (Stavrogin, 2001; Suknev, 2012). However, additional factors can decrease the elastic strength of such rocks. One of such factors is water saturation at a part of the rock mass (Grebenkin, 2010). The water saturation mainly effects on the water-soluble minerals and fractured rocks. Nevertheless, it should also take into account its contribution to the decrease of strength properties of the hard rocks having high-order structural discontinuities. This is related to the fact that the hierarchicallyblocked rock mass characterized by different-scale fractures is exposed to the over-saturation of near-surface rocks during the intensive snow melting and heavy raining. In this case the increase of rock mass fracturing and water saturation decreases the cohesion of interblock links, which can disturbed the open-pit slope stability (Fedotova, 2013; Fedotova, 2015).

653

One of the main parameters characterizing the physical-mechanical properties of hard rocks is their deformability depending on the applied loads. In the case when the loads are alternating and act together with the water saturation, the change of deformation values of various rocks can be different. Consequently, the proneness of such rocks to dynamic failure under given conditions will also vary. In this regard, it is important to study the deformability parameters of hard rocks under water-saturated and alternating loading conditions.

2

OBJECT AND METHODS OF THE STUDY

The study object is the Kovdor rock massif, a complex multiphase intrusion of the central type made of different rocks and ores. Its annular structure is explained by gradual injection of various intrusive rocks attracted to a single center and their intensive metasomatic modification. The most ancient rocks are the olivinites composing the rock massif’s core. The marginal zone is made of alkaline rocks of ijolites and turiyaites. Their injection at the contact of olivinites with embedded gneisses was accompanied by active change in both types of rocks. As a result, gneisses have turned into alkaline rocks—fenites, and olivinites—into pyroxenites with more or less quantity of phlogopite, melilithic and monticellite metasomatites. One of the final formation stages was formation of numerous carbonatite stockworks. These rocks are very different and represent the greatest industrial interest because of the association with baddeleyite-apatite-magnetite, rare metal, carbonate and apatite-carbonate ore deposits. The outcrop of the main ore body before the exploitation was observed as a brow at the PilkomaSelgi slope. At the present time on its place there is a dip open-pit, a rounded pit bowl of about 2 × 1.5 km across. The results of a hydrogeological research carried out in the open-pit of the Zhelezny mine, JSC Kovdorsky GOK, have revealed groundwater inflows filtered by the slopes of the upper benches to the lower levels, up to the bottom open-pit. At the same time the values of water inflows in different parts of the open-pit are different throughout the year. This is connected with the physical-mechanical properties of the different rocks composing the rock massif (Reshetnyak, 2008). To determine the properties, the core samples of the hard rocks were taken from various parts of the deposit mined. Twenty-seven samples were made with the height-todiameter ratio as 1:1 (Fig. 1) and divided into 5 groups by dedicated lithotypes. The amount of samples in each group was as follow: 6 for both types of fenite and 5 for the rest of the rocks. The research was carried out in four stages. At the first stage several samples had been selected from each lithologic group to determine an average compressive strength in each group. At the second stage the samples were subjected to 5 cycles of alternating loads up to 30% of an average compressive strength value and the values of longitudinal deformations were recorded. A testing method is presented in (Kuznetcov, 2015). At the third stage the samples were kept under water-saturated conditions for 6 days and after that were loaded and unloaded according to the scheme presented in the second stage. At the fourth stage the samples were kept under water-saturated conditions for 13 days. After that they were loaded and unloaded according to the scheme of the second stage and then were destroyed.

Figure 1. Samples: a – carbonatite, b – fenite amphibole-biotite fine-grained, c – fenite amphibolefeldspar medium-coarse-grained, d – gneiss biotite, e – gneiss biotite with streaks of fine-grained micaceous carbonatite.

654

3

RESULTS AND DISCUSSION

At the first research stage the rock samples were exposed to the uniaxial compression tests and their average compressive strength values were determined (Table 1). The maximum values of compressive strength found corresponding to two types of gneiss, while the minimum ones—to carbonatite and fenite amphibole-feldspar. The character of the rock samples failure was also different. The gneiss samples were failed dynamically, with a wide dispersion of rock particles. The carbonatite and fenite amphibole-feldspar samples were subsided under the load with a slight dispersion of rock particles. Based on the further study results, the graphs of variations of average values of relative longitudinal deformations in the rock samples under dry and water-saturated conditions were plotted. According to obtained data, three deformation types of samples were identified. The first deformation type under uniaxial compression (Fig. 2) was determined for two types of gneiss and fenite amphibole-biotite, the strongest rock samples among the studied ones. The deformation is characteristic by the increase of the longitudinal deformation values both on each loading cycle and with increase of the water saturation time. In the case of absolutely elastic deformation without influence of the water saturation, the sample deformation graph wouldn’t have changed. According to the results, under the permanent cyclic alternating loads and water-saturated conditions the relative deformation of samples increases and doesn’t return to zero. This indicates the occurrence of micro-fracturing processes. If we compare the compressive strength values of gneisses and fenite amphibole-biotite under dry and water-saturated conditions on the 13th day (Table  1), we can observe the Table 1. The strength values of the rock samples under compression under dry and water-saturated conditions on the 13th day.

Rock

Average compressive strength value under dry conditions, (MPa)

Average compressive strength value under water-saturated conditions, (MPa)

Carbonatite Fenite amphibole-biotite Fenite amphibole-feldspar Gneiss biotite Gneiss biotite with carbonatite

43 106 50 143 136

39 71 24 132 95

Figure 2. Deformation of gneiss biotite samples during five cycles of alternating loads under dry and water-saturated conditions on the 6th and 13th day.

655

decrease of the values under the latter conditions. For the gneiss biotite, the average strength value decreases by 8%, for the remaining two rocks—by 30%. Therefore, we can suppose that the considered factors can lead to the failure of the studied rocks. In this case it should be noted that the long-time alternating loads and water saturation will contribute to the decrease of the rock strength. Also these factors can reduce the possibility of rocks’ dynamic fracturing but increase the probability of stability loss. In the case when the alternating loads are more intensive, the possibility of dynamic fracturing of the studied rocks may increase. The second deformation type (Fig. 3) was identified for the carbonatite samples. It is characterized by the fact that the increase of the alternating loading cycles leads to the insignificant rise of the longitudinal deformation values of the samples. Also, the deformation curve under water-saturated conditions on the 13th day almost repeats the deformation curve under dry conditions. It is also interesting that the average compressive strength values of the carbonatite samples under dry and water-saturated conditions on the 13th day don’t differ (Table 1). According to the test results, we can make the conclusion that the applied alternating loading under water-saturated conditions was insufficient to initiate significant failure. Therefore, it can be supposed that if an alternating load is small (less than 30% of the compressive strength) and the rocks have the highest-order structural discontinuities only, the rock failure under specified conditions may not occur or occur after a long period of time. The third deformation type (Fig. 4) was determined for fenite amphibole-feldspar samples. Its characteristic feature is a steep increase of longitudinal deformations in the samples under water-saturated conditions. At the same time, the change of the deformation values on the 13th day of the water saturation differs slightly from the values on the 6th day. Also, it should be noted that an average compressive strength value under water-saturated conditions on the 13th day has decreased by half in comparison to a value under dry conditions (Table 1). The change of the relative longitudinal deformation values under water-saturated conditions for fenite amphibole-feldspar samples is mainly connected to streaks and shallow fractures. At the same time, according to the graph (Fig. 4), further water saturation didn’t influence the deformation mode of the samples studied. Nevertheless, it is important that the active water inflows in autumn and spring periods can significantly decrease the strength parameters of rocks having similar structural discontinuities. The influence of alternating loads in these periods can lead to loss of stability of such rocks.

Figure 3. Deformation of carbonatite samples during five cycles of alternating loads under dry and water-saturated conditions on the 6th and 13th day.

656

Figure 4. Deformation of fenite amphibole-feldspar samples during five cycles of alternating loads under dry and water-saturated conditions on the 6th and 13th day.

4

CONCLUSION

Based on the experimental study results, three deformation types of rock samples from the Kovdor rock massif have been identified. The first deformation type is characterized by the gradual increase in the longitudinal deformation values of the rock samples with increasing the alternating loading cycles both under dry and water-saturated conditions. In this case, the long-time alternating loads under water-saturated conditions will decrease the rock strength properties which can lead to the rock instability. The increase of intensity of quasi-static alternating loads, in turn, can lead to dynamic failure of the rocks. The second deformation type is typical for rocks having the highest order of structural discontinuities (micro-cracks and grain contacts). In this case water saturated conditions don’t result in the water saturation and alternating loads don’t lead to the fissure propagation. However, as for the previous deformation type, the increase in the load intensity can result either in the rise of the probable dynamic failures in such rocks or in the loss of their stability. The third deformation type is associated with a steep increase of longitudinal deformations in the rocks having streaks and shallow fractures under water-saturated conditions. The influence of alternating loads during active water inflows can result in the significant decrease of the strength properties of the rocks and to the stability loss. From the physical point of view, the considered deformations and failure can be explained as follows. Firstly, in the hard rock mass without water-soluble inclusions the stresses are concentrated in individual blocks because of the pore pressure increase in the rocks under water-saturated conditions and alternating loads. This results in dynamic fracturing. The deformation velocity rises abruptly up to dynamic failure under the pore pressure and increasing alternating load velocity, as the rock mass doesn’t have time to unload from the excess stresses. Secondly, the mechanical properties of the hard rock mass with the water-soluble inclusions change when the inclusions dissolve under the abundant water inflows and simultaneous effect of alternating loads. This, in turn, leads to the formation of shear planes due to more intensive rock mass fracturing within the boundaries of the blocks and, eventually, to the instability of individual structural blocks. This process is characterized by permanent static loading velocity. 657

Thus, the study of the deformation mode under alternating loadings and water-saturated conditions allows establishing the proneness of hard rocks to different dynamic failures or loss of stability in the form of rock falls under the given conditions.

REFERENCES Fedotova Iu.V., Zhukova S.A. Natural and Man-made Factors Influence on Seismicity Changing of Hard Rock//Proceeding of the 23rd International Mining Congress of Turkey. April 16–19, 2013. Antalya, Turkey. Ed.Ilkay Celik & Mehtap Kilic. Publ. TMMOD Maden Muhendisleri Odasi Selanic Cad. 19/14 Kizilay-Ankara. – Pp. 2111–2120. Fedotova Iu.V., Zorin A.V. Analysis of meteorological data from the monitoring system for the inner open-pit atmosphere and estimation of microseismic activity in the open-pit slope of the Zhelezny mine, JSC Kovdorskii GOK//Deep mining: Mining informational and analytical bulletin, 11, 2015 (special issue 56). – Moscow: Mining Book, 2015. – Pp. 294–309. Grebenkin S.S., Pavlysh V.N., Samoilov V.L., Petrenko Iu.A. Rock mass state management. – Doneck: VIK, 2010. – 193 p. Kuznetcov N.N., Pak A.K., Fedotova Iu.V. Study of deformation behavior and energy intensity of hard rock samples from the Kovdor deposit//Deep mining: Mining informational and analytical bulletin, 11, 2015 (special issue 56). – Moscow: Mining Book, 2015. – Pp. 286–292. Oparin V.N., Tanaino A.S. Canonical scale of hierarchical representations in rock science. – Novosibirsk: Nauka, 2011. – 259 p. Reshetnyak S.P., Melikhova G.S., Fedotova Yu.V., Melikhov M.V. Problems of Deep Open Pits Closure in the Kola Peninsula//Proceedings of Mine Water and Environment. – Ostrava, Czech Republic, 2008. – Pp. 171–174. Stavrogin A.N., Tarasov B.G. Experimental physics and mechanics of rocks. – Saint-Petersburg: Nauka, 2001. – 343 p. Suknev S.V., Fedorov S.P. Standard methods for determining the elastic properties of rocks//Mining informational and analytical bulletin, 12, 2012. – Moscow: Mining Book, 2012. – Pp. 17–21. Turchaninov I.A., Iofis M.A., Kasparyan E.V. Fundamentals of rock mechanics. – Saint-Petersburg: Nedra, 1977. – 503 p.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

On the effectiveness of rocks and materials destruction based on shock-wave cutting technology Nikolay P. Mikhailov, Evgeniy A. Znamenskiy, Stanislav I. Doroshenko & Yurii A. Telegin Baltic State Technical University «VOENMEH» named after D.F. Ustinov, Saint-Petersburg, Russia

Ivan V. Brigadin Promstroyvzryv Ltd., Saint Petersburg, Russia

Vitaliy M. Gubaidullin Promstroyvzryv Ltd. The Russian Federation, Saint Petersburg, Russia

Gennadii P. Paramovov National mineral resources University «MINING UNIVERSITY», St. Petersburg, Russia

ABSTRACT: The paper assesses the effectiveness of shock-wave technology cutting for rocks, based on irregular modes of shockwaves interference. That modes occurs when angle in the waves collision greater then critical angle. Shock waves forms in the material upon synchronous detonation of bilinear charges, that designed in the BSTU “VOENMEH”. A theoretical and experimental comparison of materials cutting technologies using a shockwave and a shaped charge is done. The usage of cumulative cutting in emergency rescue operations is limited by the presence of a hazardous effect on objects behind a barrier. Unlike the shaped charge, the shock-wave cutting destruct materials without mass transfer, and does not damage objects behind the barrier. A reduced in 2...5 times consumption of explosives and higher efficiency of the shock-wave cutting technology is experimentally shown. As the result of significant reduction in consumption of explosives reduces lead times, transportation costs and environmental damage. It follows that the shock-wave cutting technology can be successfully used in mining and emergency rescue operations. Keywords: shock-wave charge, bilinear charge, mathematical model, Mach wave, experiment, rock, concrete block

1

INTRODUCTION

Emergency situations irrespective of their nature and causes, require complex engineering tasks associated with large amount of rescue and other emergency operations. Complexity, danger and strict deadlines of such works dictate the need for widespread usage of explosion energy. Structural divisions of various departments involved in liquidation of emergency situations should be equipped with modern innovative explosive technologies enabling them to effectively tackle these tasks. Currently, the primary means of materials (metals) cutting by explosion are shaped charges, which are based on the high-speed removal of material from the cut cavity, which volume is roughly proportional to the second degree of the barrier thickness. The same dependence is preserved between the weight of the shaped charge explosive and the thickness of the barrier. With through cutting of barriers by high-speed jet its particles affect the objects behind barrier. This fact limits the applicability of shaped charges cutting technology. 659

Unlike the shaped charge, the shock-wave cutting is based on extreme (Mach) modes of shock waves interference, which are formed in the material upon synchronous detonation of parallel to the barrier’s surface charges. The destruction happens almost without mass transfer due to the interaction of three rarefaction waves behind the front of Mach wave. As the result, the barrier is cut following the least resistance line by flat cracks. A linear dependence between shock-wave charge mass and the barrier thickness was found.

2

THEORETICAL STUDY

In order to assess the applicability of shock-wave cutting to the rocks, an analytical calculation of kinematic parameters of the shock waves collision in granite coming from parallel charges was done. As it’s known, the velocity of shock waves (Dv) in granite remains equal to the speed of sound (C ) up to the pressure p ≤ 37 GPa [1]. In the general case, the formation of conically and cylindrically shaped shock waves is provided in term DH > Dv = C, where DH – detonation speed of the charges. The main parameter that determines the mode of waves’ interference is their collision angle (α). Irregular (Mach) mode occurs when α ≥ αcr ≈ 68...74° (Orlenko, 2002). The dependence of the angle α in the conical waves’ collision (DH ≥ C ) is defined analytically as (Mikhailov, 2012): sin (α 2)

1−

cos 2 β , 1+ y L

(1)

where β = arcsin ( ), L – distance between the charges; y – distance ) = arcsin ( from the surface of the barrier to the point of the waves’ collision. For cylindrical waves, β = 0, and from (1) we obtain sin (α 2)

1 L

(

+

).

(2)

As follows from (2) for the irregular mode of cylindrical waves collision is realized in the wide range of bilinear charges’ parameters. That ensures its applicability for breaking rocks, concrete and other crystalline materials. As the result of theoretical and experimental research performed in the BSTU “VOENMEH”, a number of shock-wave charges models has been developed. In order to improve the shock-wave cutting technology the theoretical studies of barriers destruction by implosive (symmetrically converging) shock waves were carried out. Physical and mathematical models described by systems of equations (Brigadin, 2014) were developed.

3

EXPERIMENTAL STUDY

Tests of rocks and concrete blocks cutting by implosive shockwaves were performed on the “Promstroyvzryv” premises. Bilinear charges made of emulsion explosives Nitronit-P and Gelpor (Brigadin, 2014) were used for cutting. Experiments on the bilinear charges were conducted in order to remove the piece of rock hanging above “St. Petersburg-Sortavala” road. The dimensions of that piece were 3.1 × 1.3 × 1.5 m. The cut area was up to 3.5 m2. Charges were located on the block surface in two parallel rows along the cut line. Distance between the rows was 100 mm.

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As the result of the explosion, separation of the block was observed in the bilinear charge plane of symmetry. Specific consumption of explosives was 1.26 g/cm2, which is 2...5 times less comparing to a separation by concentrated charge.

4

CONCLUSIONS

Shock-wave cutting of rocks is an innovative technology, for significantly reducing the explosive consumption. The positive effect is achieved through the usage of bilinear charges, implementing cutting by Mach waves. As the result of reduction in explosives consumption reduces lead times, transportation costs and environmental damage. The shock-wave cutting technology can be successfully used in mining and emergency rescue operations.

REFERENCES [1] Brigadin I.V. [and others]. On the issue of effective elimination of natural disasters on the basis of innovative technologies of shock wave cutting: Problems of ensuring security in the aftermath of emergencies: a Collection of articles of III all-Russian NPK with international participation. Voronezh, December 19, 2014 Voronezh: Voronezh Institute of state fire service of EMERCOM of Russia; 2014. pp. 246–249. [2] Mikhailov N.P. Fundamentals of mathematical simulation of explosion and impact: Textbook/N.P. Mikhailov. Balt. state. tech. un-t. SPb., 2012. 202 p. [3] Orlenko L.P. [and others] Physics of explosion./Under edited by L.P. Orlenko. Ed. 3rd, revised, in 2 Vol. M.: FIZMATLIT, 2002.

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Modelling of fault reactivation in applications of mining and petroleum industry Roberto Quevedo & Cristian Mejia Institute Tecgraf/PUC-Rio, Rio de Janeiro, Rio de Janeiro, Brazil

Deane Roehl Institute Tecgraf/PUC-Rio, Rio de Janeiro, Rio de Janeiro, Brazil Civil and Environmental Engineering Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil

ABSTRACT: The seal of critically stressed faults can be compromised by deformation/ stress changes induced by external solicitations. The stress relief due to excavations or reservoir pressure changes, for example, can create favorable conditions for reactivation of faults by shear or tensile modes. Among several problems, fault reactivation may result in slope detachment, the generation of a fault scarp along the ground surface, oil exudation and seismicity. This study presents a methodology for the evaluation of fault reactivation using numerical modelling. With the finite element method, it is possible simulate the effect of both, excavations and reservoir pressure changes over geological faults. Those faults are introduced in the models using zero thickness interface elements. Some 2D and 3D models are analyzed with focus on mining and petroleum engineering applications. In relation to the mining industry, fault reactivation caused by open-pit and underground mines are taken into account. Regarding the oil industry, a case of fault slip due to hydrocarbon production is also presented. The results call attention to the different causes and effects of fault reactivation and provide some clarity to the understanding of this phenomenon. Keywords: Fault reactivation, numerical modelling, mining, underground excavation, petroleum

1

INTRODUCTION

In the mining industry, the stress relief owing to superficial or underground excavations usually induces relative displacements of the rock masses along pre-existent discontinuities or faults. This phenomenon is known as fault reactivation and can be responsible for several geotechnical problems such as, tunnel collapse, slope instability, mining shaft deformation, topographic scarp and surface subsidence (Jeon et al. 2004, Donnelly 2006, Donnelly 2009, Zhao et al. 2013). In a similar way, in hydrogeology and the petroleum industry, the strain owing to the pressure changes in reservoirs compartmentalized by geological faults can reactivate them, triggering potential geomechanical problems, such as seismicity, well collapse, loss of reservoir sealing and exudation (Baranova et al. 1999, Wiprut and Zoback, 2002). Focusing on those geotechnical and geomechanical applications, three different activities can induce fault reactivation: slope excavation, mineral extraction and water/hydrocarbon production. The use of numerical modelling to identify potential fault reactivation is widespread in the mining (Bruneau et al. 2003, Zhao et al. 2013) and the petroleum industry (Rutqvist et al. 2013, Quevedo et al. 2017). However, numerical simulations of fault reactivation in the three activities previously mentioned have not been performed in a single study for discussion and comparison purposes. Observe that some issues, such as geometric shapes, loadings, and stress and displacements fields can create different reactivation mechanisms over the fault 663

planes. Probably, difficulties associated with different methodologies, complex model building and large computational effort have not allowed the comparison of those mechanisms of fault reactivation. In this paper, we introduce a numerical methodology based on the Finite element Method for representation of different situations in which geological faults are reactivated. This methodology was implemented in an in-house code for modelling of 2D and 3D problems. Numerical simulations of open-pit mining process and mineral and hydrocarbon extraction were carried out. The results call attention to the different causes, mechanisms and effects of fault reactivation and provide some clarity to the understanding of this phenomenon.

2

METHODOLOGY

Using the traditional Galerkin Finite Element method, the governing equation of mechanical process can be written in an incremental way as follows:

∫

Ω

E R u = ΔFeext + ΔFeext

B T DBd

(1)

where Δu represents the variation of nodal displacements, B is the matrix that relates the strains and the displacements, D is the stiffness matrix and Ω is the spatial domain of the model. ΔF FexEt represents the nodal external forces due to the material removal in open-pit slope and underground mining, this vector is given according to the next relationship:

∫

ΔF FexEt

ΩE

B T σ d ΩE + γ ∫

ΩE

N T d ΩE

(2)

in which Ω E is the excavated domain, σ is the stress tensor of the elements in the excavated zone, N is the element shape functions and γ is the material unit weight. FexRt represents the nodal external forces due to pressure changes in water or oil In turn, ΔF reservoirs, this vector is assessed according to the following relationship: Δ

R ext

=∫

ΩR

T

α md

R

Δp

(3)

where Ω R is the reservoir domain, α is the Biot coefficient, Δp is the nodal pressure change within the reservoir and m is a vector that introduces the effects of that pressure change. The rock layers are assumed to have elastic behavior. Thus, only the Young elastic modulus (E) and the Poisson ratio (ν) define the stiffness matrix D. In turn, the geological faults are represented trough zero-thickness interface elements. In this case, the tangential (ks) and the normal (kn) elastic stiffness are considered in the assessment of D. 3 3.1

NUMERICAL SIMULATIONS Open-pit mining model

This section deals with the reactivation of faults adjacent to open-pit mines. According to several geological investigations conducted in open-pit mines (Zhao et al. 2013), when steep faults are located in the upper part of excavated slopes, fault reactivation usually results in a downward movement of the hanging wall relative to the footwall, regardless of the trend and the original properties of the fault. Figure 1 presents two idealized scenarios to analyze fault reactivation, two in open-pit mining. The initial stresses before excavation consider homogeneous rock unit weight of 27 kN/ m3. At this step, the horizontal stresses were taken equal to the vertical stresses. The elastic modulus and the Poisson ratio have the values 0.6GPa and 0.4, respectively. For the geological faults, the tangential and normal stiffness are 0.1 MPa/m and 0.1GPa/m, respectively. 664

Figure  1. Models used for simulation of fault reactivation induced by an open-pit excavation over a) the hanging wall and over b) the footwall.

Figure 2. Displacement vectors for an open-pit excavation in the hanging wall considering a) a single set of elastic parameters and b) two sets of elastic parameters.

In a first simulation, those elastic parameters were adopted in the whole model of Figure 1a. Figure  2a shows the corresponding vector of displacements found after the excavation. Different from field observations, the slope shows upward movements over the entire region of the hanging wall. Zhao et al. (2013) found similar results. Before the excavation, all elements suffer volume compression and store elastic strain energy that is released when some elements are removed. For this reason, in a second simulation, the slope configuration in Figure 1a has a stiffer layer in the bottom of the slope (region II) with 10 times the original elastic modulus. Two main arguments support this assumption. First, deeper layers are prone to be stiffer due to the higher stresses in which they are subjected. Second, deeper layers are less exposed to environmental factors that degrade and affect the properties of superficial rock layers. Figure 2b shows the results corresponding to the use of a stiffer layer in the bottom of the model. Now, the top of the slope in the hanging wall follows a downward movement, while the middle and inferior regions follow movements towards the pit. Figure 3 shows the corresponding contour map of the vertical displacements in the models of Figure 1 considering stiffer rock layers in the bottom. A normal fault-style movement is present in both cases, characterized by downward movements of the hanging wall relative to the footwall. Those results indicate the reactivation of faults induced by the tensile stresses over the fault planes due to the open-pit slope excavation. 665

Figure 3. Contour map of vertical displacements and fault reactivation due to open-pit excavation in a) the hanging wall and b) the footwall.

Figure 4.

Simulation model for fault reactivation induced by underground mining excavation.

Figure 5. Results for the underground mining excavation at the hanging wall a) Vertical displacements and subsidence bowl. (b) Contour map of vertical displacements and fault reactivation.

3.2

Underground mining

Fault reactivation induced by underground mining excavation is the focus of this section. In this case, the excavated zone is located at an average depth of 255 m. Figure 4 shows the corresponding model and its dimensions. Before the excavation, initial stresses are due to the rock unit weight of 22 kN/m3, and the horizontal stresses are equal to the vertical ones. From the surface to the depth of 250 m, the elastic modulus is 0.6GPa; from 250 m to 260 m it is 1.0GPa; and, from 260 m to 310 m it is 5.0GPa. The Poisson ratio is equal to 0.3 in all layers. For the geological faults, the tangential and normal stiffness are 3.0 MPa/m and 0.5GPa/m, 666

respectively. The excavated region is located over the footwall and defines a parallelepiped with the dimensions 250 m×10 m×15 m. Figure 5 shows the corresponding results after the excavation. Figure 5a shows the contour lines of the resulting displacements. The maximum values are concentrated around the excavation region. The vertical convergence in the gallery, i.e. the difference between the largest displacement of the floor and that of the roof of the excavated zone, was around 0.13 m. Over the surface of the model, there is a maximum subsidence of 1 cm. Figure 5b shows the contour plots of the displacements on a cutting surface. It shows a reverse fault-style movement characterized by downward movements of the footwall relative to the hanging wall. According to the results, fault planes close to the gallery reactivate due to the tensile stresses. However, in regions near the surface, reactivation is due to shear stresses. 3.3

Hydrocarbon production

This last section presents a simulation of fault reactivation induced by hydrocarbon production. Differently from the previous examples, field deformations occur because of pressure reductions inside the reservoir. The model considers plane strain conditions, a common assumption when the reservoir is laterally extended in the horizontal directions. Before reservoir depletion, the initial stresses reflect a vertical effective stress gradient of 12  kN/m3. At this step, the initialization of the horizontal stresses takes into account a lateral stress coefficient of 0.75. In the Overburden, Sideburden, Reservoir and Underburden layers, the elastic modulus are 1.0GPa, 5.0GPa, 2.0GPa and 5.0GPa, respectively. The Poisson ratio is equal to 0.25 in all layers. The tangential and normal stiffness are 0.2GPa/m and 5.0GPa/m, respectively. The reservoir was depleted in 10 MPa with a Biot coefficient equal to 1.0. Figure 6 shows the contour map of the vertical displacements, showing downward movements concentrated above the depleted reservoir. The maximum reservoir compaction is about 0.63 m while the maximum surface subsidence is 0.48 m. In the hanging wall, where the reservoir is located, relative displacements to the footwall are present, indicating the reactivation of the fault in a normal fault-style movement. The results indicate that fault planes

Figure 6.

Model for the simulation of fault reactivation induced by hydrocarbon production.

Figure  7. Contour map of vertical displacements and fault reactivation in a simulation of hydrocarbon production.

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around the reservoir reactivate by tensile stresses. On the other hand, fault planes located in the overburden reactivate by shear stresses. In such situation, the high depletion of the reservoir and the induced fault reactivation increase risks for loss of reservoir sealing integrity, seismicity and exudation.

4

CONCLUSIONS

A methodology for the assessment of fault reactivation induced by mining operations and hydrocarbon production was introduced in this study. Synthetic scenarios with different conditions of geometry, loadings and contrast of properties provide the test cases for the methodology. The analysis of the results of the test cases provided better understanding of the mechanisms of fault reactivation. In addition, the results highlight the applicability of numerical modelling in the assessment of geological fault reactivation and its usability for the forecasting of potential geotechnical and geomechanical problems.

ACKNOWLEDGEMENTS The authors gratefully acknowledge support from Shell Brasil through the “Coupled Geomechanics” project at TecGraf Institute (PUC-Rio) and the strategic importance of the support given by ANP through the R&D levy regulation.

REFERENCES Baranova V., Mustaqeem A., Bell S. 1999. “A Model for Induced Seismicity Caused by Hydrocarbon Production in the Western Canada Sedimentary Basin.” Canadian Journal of Earth Sciences 36 (1): 47–64. doi:10.1139/e98-080. Bruneau GDB, Hadjigeorgiou T., Potvin Y. 2003. “Influence of Faulting on a Mine Shaft a Case Study Part II Numerical Modelling.” International Journal of Rock Mechanics and Mining Sciences 40 (1): 95–111. doi:10.1016/S1365-1609(02)00115-6. Donnelly L.J. 2009. “A Review of International Cases of Fault Reactivation during Mining Subsidence and Fluid Abstraction.” Quarterly Journal of Engineering Geology and Hydrogeology 42 (1): 73–94. doi:10.1144/1470-9236/07-017. Donnelly L.J. 2006. “A Review of Coal Mining Induced Fault Reactivation in Great Britain.” Quarterly Journal of Engineering Geology and Hydrogeology 39 (1): 5–50. doi:10.1144/1470-9236/05-015. Jeon S., Kim Y., Seo Y., Hong Ch. 2004. “Effect of a Fault and Weak Plane on the Stability of a Tunnel in Rock - A Scaled Model Test and Numerical Analysis.” International Journal of Rock Mechanics and Mining Sciences 41 (SUPPL. 1): 1–6. doi:10.1016/j.ijrmms.2004.03.115. Quevedo R.J., Ramirez M.A., Roehl D. 2017. “2d and 3d Numerical Modeling of Fault Reactivation.” 51st U.S. Rock Mechanics/Geomechanics Symposium, 25–28 June, San Francisco, California, USA. Rutqvist J., Rinaldi A., Cappa F., Moridis G.J. 2013. “Modeling of Fault Reactivation and Induced Seismicity During Hydraulic Fracturing of Shale-Gas Reservoirs” 44: 31–44. Wiprut D., Zoback M.D. 2002. “Fault Reactivation, Leakage Potential, and Hydrocarbon Column Heights in the Northern North Sea.” Norwegian Petroleum Society Special Publications 11 (C): 203–19. doi:10.1016/S0928-8937(02)80016-9. Zhao H., Ma F., Xu J., Guo J. 2013. “Preliminary Quantitative Study of Fault Reactivation Induced by Open-Pit Mining.” International Journal of Rock Mechanics and Mining Sciences 59. Elsevier: 120–27. doi:10.1016/j.ijrmms.2012.12.012.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Acoustic emission precursor criteria of rock damage Alexander O. Rozanov, Dmitri N. Petrov & Aleksei M. Rozenbaum Saint-Petersburg Mining University, Saint-Petersburg, Russia

Andrei A. Tereshkin Khabarovsk Mining Institute, The Russian Academy of Sciences, Khabarovsk, Russia

Michael D. Ilinov Saint-Petersburg Mining University, Saint-Petersburg, Russia

ABSTRACT: Such processes as production of ore deposits and mining excavation are associated with the phenomenon of Acoustic Emission (AE). Changes of in situ stress conditions can result in sudden movements along pre-existing faults or can generate new fractures which in turn induce the emission of acoustic energy. Monitoring and analysis of AE events can detect dangerous areas in minings and predict rockbursts during actual mining procedure. A huge AE data have been acquired under different mining conditions in the PhosAgro apatite mines. The measurements have been carried out with the help of one-channel multifunctional device «Prognoz-L» developed in the Mining Institute of Khabarovsk, Russia. The spectral correlation analysis combined with conventional event statistics were used to gain reliable AE criteria of rockbursts. Verification of these criteria has been carried out in laboratory on samples of three main types of rock contained in massif.

1

INTRODUCTION

Now different geophysical safety systems are widely introduced in mining. One of them is geoacoustics. Geoacoustic systems are developed in order to provide a remote permanent control of rock massif state under mining. These systems are based on acoustic emission (AE) phenomenon and relate to non-destructive kind of material tests. A conclusion on rock state is provided by intellectual software solution developed on wide range AE data analysis. For instance, nowadays new technology of geoacoustic systems is developed in the Mining Institute of Khabarovsk, Russia. These are a system of mine section control (PrognozADS) and a system of mine local control (Prognoz-L). Both systems have been successfully deployed in PhosAgro ore mines for AE data acquisition procedure. Now an intensive AE data processing is carried out both by scientific center of Saint-Petersburg Mining University and the Mining Institute of Khabarovsk in order to advance rock burst precursor algorithms.

2

RESULTS

In this work a problem of precursor criteria is attacked from a new standpoint. A.A. Griffith showed in 1921 that inherent material inhomogeneities such as microcracks substantially reduce the strength of material (Griffith A.A., 1921). Moreover it is derived from lab triaxial tests of hard rocks that the strength strongly depends on confining pressure. That is we may encounter various manifestations of rock pressure activity depending on strain energy level in the vicinity of mine excavation. We classify AE signatures of fracture process and identify each signature to a certain stage of fracturing. A developed package of spectral-correlation algorithm is used to analyze AE signatures (Rozanov A.O., 2003, Rozanov A.O., 2012). 669

To study fracture process in rocks ten triaxial compression tests were performed on samples with different content of P2O5 – samples with P2O5 ∼ 12–14%, with P2O5 ∼ 4–6%, and with P2O5 < 4%. The experimental setup we used consists of the loading frame (servocontrolled MTS 815 frame, 4600 kN), and the AE acquisition system ErgoTech. One series of samples was tested under 20 MPa of confining pressure, and another one under 40 MPa. All experiments were fixed displacement rate tests (0.01 mm/min). To map the hypocenters of AE events a commercial code package ASC has been used. For spectral correlation analysis a self-developed code written in Pascal is used. We calculated two main AE spectral parameters in order to qualify fracturing process in rock. The first one is so called median frequency which depends on the ratio of high and low frequencies in AE signal spectrum. And another one is standard deviation which is proportional to signal duration and amplitude square. Thus AE median frequency characterizes a value proportional to crack growth rate and inverse proportional to crack growth length. Meanwhile AE standard deviation characterizes crack radiated energy. A typical stress-strain diagram from hard-rock lab triaxial test on PhosAgro ore mine samples is shown in Figure 1. Four stages of fracturing and a rupture formation are depicted there to point out different AE manifestations usually observed during fracturing. Stage A characterizes a process of linearization at the very beginning of loading. Stage B indicates the yield response of rock. Then comes stage C of quasi-plastic behavior. When the strain exceeds the strength of rock a rupture occurs and a stress drop is observed. This is a tensile Griffith’s fracture mode. During the post-strength stage D the rock deforms as two parts of it shear along the rupture surfaces. In seismology this stage is usually called a stick-slip frictional mode. The earthquake they consider to happen is the “slip” along an existing fault, and the “stick” is the interseismic period of elastic strain accumulation. Figure 2 shows the results of AE signal analysis obtained during mining excavation. AE median frequency trend (black line) and AE energy trend (grey line) evidently indicate the transition point from the stable process of strain energy accumulation to the unstable process of rupture formation as it is observed during lab experiments (Figure 1). Such kind of AE parameter behavior specifies a state of rock massif as dangerous.

Figure 1. The stress-strain diagram of lab triaxial compression test of urtite sample. The picture performs four stages of AE radiation and a rupture occurrence.

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Figure  2. The AE frequency (black line) and energy (grey line) spectral parameters perform strain energy accumulation and a rupture occurrence during mining excavation.

Figure 3.

The typical hypocenter display of 677 AE events in pegmatoid urtite (P2O5 ∼ 4–6%).

Figure 3 shows a sample of pegmatoid urtite with P2O5 ∼ 4–6% after a test under 40 MPa of confining pressure, and a typical AE hypocenter distribution. One can see that nucleation process develops along a plane making an angle of about 30° with respect to the maximum compression axis. 671

3

CONCLUSIONS

Thus we can make the following conclusions: 1. The AE median frequency and standard deviation are explicitly indicate an in situ stress change in mines. 2. AE hypocenter distribution delivers information about nucleation process of damage in rocks. 3. AE signatures provides a perfect approach to real stress state in mines and can deliver relevant criteria for rock state characterization.

REFERENCES Griffith A.A. The Phenomena of Rupture and Flow in Solids, Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character. 1921, Vol. 221. – P. 163–198. Rozanov A.O. Spectral and Correlation Analysis of Acoustic Emission Waveforms and Failure Micromechanics in Rocks, Int. Geophys. Conf. & Exhibition “Geophysics of 21 Century—The Leap into Future”, Extended Abstracts, Session OS22, 2003. Rozanov A.O. Microseismic Event Spectrum Control and Strain Energy Release in Stressed Rocks, GEO 10th Middle East Geosciences Conference & Exhibition, 2012.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Numerical simulation of stress distribution within a rock discontinuity asperity Atsushi Sainoki International Research Organization for Advanced Science and Technology, Kumamoto University, Japan

Yuzo Obara Department of Civil and Environmental Engineering, Kumamoto University, Japan

Hani S. Mitri Mining and Materials Engineering, McGill University, Canada

ABSTRACT: The present study investigates the stress distribution and the extent of failure within rock discontinuity asperities. The fractal geometry of the discontinuity surface is generated with successive random addition and mid point method, based on which numerical analyses are quasi-statically performed with the three-dimensional discrete element method (3DEC). The analysis results show that extremely high compressive stress is locally generated by the collision of asperities, while tensile stress fields are extensively produced in the surrounding region because the asperity collision draws the surrounding rock. The generation of the large compressive stress implies the occurrence of tertiary creep, resulting in asperity comminution and the increase in the contact area. On the other hand, the tensile stress field is assumed to form extension fractures with a length being the order of mm or less.

1

INTRODUCTION AND NUMERICAL MODEL DESCRIPTIONS

The deformational behaviour of a rock discontinuity and its shear strength is of paramount importance in various engineering projects. Over the past decades, significant efforts have been made to elucidate the mechanical behaviour and strength of rock discontinuities (Barton, 1977). In the developed frictional resistance models, the influence of the surface asperities is considered implicitly by proposing representative parameters, while to explicitly model the surface asperity abrasion, numerical simulation techniques have been employed (Elmo, 2006; Bahaaddini et al., 2013). These studies showed fracture formation, propagation and its coalescence within the surface asperities during the shear behaviour of a rock joint. However, the detailed analysis of the stress distribution within the asperities has not yet been extensively conducted as the previous studies mainly focused on “fracture development”. When the stress state of a rock discontinuity is below its critical stress state, asperity creep behaviour is assumed to play a critical role in its deformation behaviour, e.g. the contact area would increase with asperity deterioration due to the occurrence of tertiary creep. Such timedependent behaviour is crucial when estimating the long-term stability of faults and jointed rock masses. As the first step to achieve the goal, this study aims to better understand the stress distribution within the surface asperities of a rock joint as well as their failure modes when subjected to high confining stress.

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2

NUMERICAL MODEL DESCRIPTION

This study employs 3DEC software, which is based on the three-dimensional distinct element method, to analyze the stress distribution and resultant failure within joint surface asperities. Figure  1  shows the numerical model generated. The discontinuity geometry of the upper block is the same as that of the lower block, but the upper block is slightly displaced to replicate a non-interlocking discontinuity. It is well-known that the surface geometry of a fault or natural rock joint is fractal. To consider such fractal characteristics, the surface geometry of the numerical model was generated with the successive random addition and midpoint method proposed by Voss (1985). In this method, a key parameter is Hurst exponent, which is related to fractal dimension with the following equation in the case of two dimensions. D

2 H

where D and H denote fractal dimension and Hurst exponent. The detailed mathematical concept and implementation of the method are found in the study (Ozdemirtas et al., 2009). According to Eq. (1), a rougher discontinuity surface is formed with a lower H. We generated four numerical models while varying H from 0.6 to 0.9 as shown in Figure 2. It is found that the surface with H = 0.9 is the smoothest, while the model with H = 0.6 has the irregular surface with many asperities. The range corresponds to joint roughness coefficients from 10 to 19 (Jia, 2011).

Figure 1.

Basic geometrical configuration of a numerical model to be analyzed.

Figure  2. Asperity geometry on the cross-section at y  =  5  cm generated with different fractal dimensions.

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Table 1. Rock type

E (GPa)

σc (MPa)

Φ (˚)

ν

γ (kN/m3)

σT (MPa)

ψ (˚)

Granite

31

240

63

0.26

25.5

11

8.75

Table 2.

3

Mechanical properties of the rock for the numerical model.

Mechanical properties of a joint between the upper and lower blocks.

ks (GPa/m)

kn (GPa/m)

φ (˚)

C (MPa)

σT (MPa)

12800

31000

30

1

1

MECHANICAL PARAMETERS AND SIMULATION PROCEDURE

This study focuses on a rock joint formed in a hard rock. Accordingly, the mechanical properties of granite are extracted from previous study (Melek et al., 2015) and are applied to the numerical model. The parameters are summarized in Table  1. As the numerical simulation is performed with the purpose of investigating the stress distribution and resultant failure of the asperities when subjected to only normal stress, fracture generation due to shearing is not considered in the present study. Thus, the upper and lower blocks are considered to be a continuum material, while contacts are produced on the boundary between the blocks. The mechanical properties of the contacts are listed in Table 2. The contact stiffness was calculated according to the equation (kn = E/L and ks = G/L). L is a thickness of an interface, and G is the shear modulus. In the calculation, we assumed L = 0.001 m since the upper block has a contact with the lower block. The other parameters do not have large influences on the analysis result. Numerical simulation is carried out while applying a normal stress of 30 MPa on the top boundary of the upper block under static condition. The lateral boundaries of the upper and lower blocks as well as the bottom of the lower block are constrained in the direction perpendicular to the boundaries. The analysis is continued until unbalanced force in the numerical model reaches a sufficiently small value.

4 4.1

ANALYSIS RESULTS Stress distribution of the simulated rock joint

Figures  3  shows the maximum and minimum principle stress fields of the lower block obtained from the static analysis. Note that in the model the negative values represent compression. As the upper block is displaced by 1 mm as shown in Figure 1, the asperities of the lower block do not perfectly interlock with those of the upper block, thus generating the high compressive stress in the contact regions. It is further found from the result that as the surface becomes rougher with a high fractal dimension (low Hurst exponent), the stress distribution becomes more complex. And, interestingly, not only compressive stress but also tensile stress is produced in the extensive area of the discontinuity. The high compressive stress is obviously attributed to the small contact area between the lower and upper blocks generated by displacing the upper block by 1 mm in the x-direction. However, the generation of the tensile stress field cannot be readily explained from the contact of asperities subjected to normal stress. To elucidate the mechanism of the tensile stress field, the stress tensor orientation obtained from the model with H = 0.9 is plotted in Figure 4. In the figure, the lines represent the orientation of stresses; for each zone, three lines are drawn, and the longest line corresponds to the orientation of the maximum principle stress. It is found from the figure that the tensile stress is oriented in the direction parallel to the discontinuity surface, whereas compressive stress is oriented perpendicular to the surface. From this result, it can be conjectured that the tensile 675

stress field is generated by the asperity penetration that draws the surrounding rock into the contact region. The mechanism is further explored in the following section. In order to verify the postulation, a simple numerical simulation is carried out to replicate an asperity penetrating to the other block. Figure 5 shows the model geometry as well as the

Figure 3.

Minimum and maximum compressive stress distribution (compression as negative).

Figure 4.

Stress tensor orientation on the cross section at y = 5 cm in the model with H = 0.9.

Figure 5. Numerical simulation of a block penetrating into the lower block: (a) Model geometry and analysis result, (b) Schematic illustration showing tensile stress generation caused by the block penetration dragging the surrounding region into the inside of the lower block.

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analysis result. As can be seen, the model is composed of two blocks. The lower block has the same geometry and the same boundary conditions as that in Figure 1, while the upper block is a cuboid, which is quasi-statically moved down towards the lower block by applying a normal stress of 30 MPa on the top boundary of the cuboid. As expected, the upper block (cuboid) is compressed because of the generation of the contact with the lower block. More importantly, it can be seen that in the extensive area on the upper surface of the lower block, the tensile stress field is formed. A plausible explanation for this is that the surface region is pulled into the contact area because of the penetrating upper block; as the lateral boundaries are fixed, this leads to the generation of tensile stress. Hence, this would be the plausible mechanism of the tensile field generation observed in Figure 3. It is to be noted that even if the lateral boundaries are not fixed, the tensile stress field can be produced when there are multiple asperity contacts, i.e. each contact causes the surrounding region to be pulled into the contact areas. Thus, the region located at the midpoint of the contact would undergo tensile stress. 4.2

Failure of asperities subjected to high normal stress

The extent of failure is shown in Figures 6 and 7. In these figures, green, sky blue, red colors represent shear failure, shear and tensile failure, and tensile failure that took place during the static analyses, respectively. Figure 6 indicates the complex distribution of shear and tensile

Figure 6.

Extent of failure in the lower block.

Figure 7.

Extent of failure on the cross-section at y = 5 cm.

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failure on the rock discontinuity subjected to high normal stress. It seems that the smooth surfaces (high H ) generate a more extensive tensile failure area on their surfaces than the rough surfaces. Specifically, in the model with H = 0.6, the red-colored surface area approximately accounts for less than one-third of the entire surface, while more than half of the surface undergoes tensile failure for the model with H = 0.9. It is speculated that the uniform stress condition formed on the smooth surface results in the extensive tensile failure area. This can be justified by the result shown in Figure 5, where the entire surface area except the contact region uniformly undergoes tensile stress because of the block penetrating into the completely planar surface. The model with a high Hurst exponent is presumed to yield a similar stress condition because of the non-irregular surface geometry. On the other hand, the irregular, rough discontinuity surface would create a more complex stress field due to the irregular geometry, i.e. the presence of a number of asperities and apertures. In terms of the depth of failure from the discontinuity surface, it is found from Figure 7 that the shear failure caused by the collision of asperities reaches approximately 1 cm from the surface, although the depth varies place to place, while the damage depth related to the tensile failure ranges from 0.5 mm to about 8 mm. Compared to the shear failure-induced damage, the damage caused by tensile failure is limited to the region in the vicinity of the discontinuity surface.

5

DISCUSSION

To author’s knowledge, previous studies predominantly investigated asperity degradation while simulating the shear movement of a rock discontinuity, of which initial surface asperities are fully interlocked (e.g. Bahaaddini et  al., 2013), and do not consider the complex stress distribution of the rock discontinuity surface. The present study has characterized the stress state on the rock discontinuity while varying fractal dimension from 1.1 to 1.4. Consequently, it was found out that extremely high compressive stress conditions are generated at locations where the collision of asperities takes place, while the tensile stress field is extensively formed around the contact area. The high compressive stress state is deemed to have a strong relationship with the time-dependent increase in frictional resistance. It has been reported in a number of studies that the frictional resistance of a fault increases with time. It was then assumed that the creep behaviour of fault surface asperities is responsible for the time-dependent resistance increase, which was implemented into the well-known rate- and state-dependent law. It is to be noted, however, that the constitutive equation was empirically formulated based on experimental results. The result obtained from the present study contributes to explicitly modelling the creep behaviour of surface asperities. As shown in Figure 6, the complex stress field is formed on the discontinuity surface, which in tern results in complex time-dependent behaviour causing the degradation of the asperities with the increase in contact area. Most likely, the regions with high compressive stresses in Figure 6 would undergo creep deformation, starting from primary creep. When tertiary creep is initiated, the asperities would experience sever damage associated with comminution, eventually alleviating the stress concentration. The high compressive stress distribution simulated in the present study thus agrees well with the empirical knowledge accumulated with the experiments in previous studies. What is unclear is the implication of the tensile stress field caused by the penetration of the asperities explored in Figures 3 and 5. Presumably, the tensile stress generates a number of extension fractures in the region. Based on the extent of tensile failure in the depth direction shown in Figure 7, the extension fracture would be the order of mm or less, if fracture generation is taken into account in the simulation. It would be future study to investigate the influence of the micro- and mesoscopic extension fractures on the frictional behaviour of a rock joint surface, including its verification.

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6

CONCLUSIONS

The present study investigates the stress distribution and the extent of failure within rock joint surface asperities subjected to high confining stress with the aim of gaining fundamental knowledge of the stress state of rock discontinuities before being sheared. Fractal surfaces are generated with successive random addition and midpoint method, and numerical simulation was quasi-statically performed with 3DEC employing the three-dimensional discrete element method. The analysis revealed that a complex stress field is formed on the surface of the rock joint, producing extremely high compressive stress in the asperity contact regions as well as moderate tensile stress in the surrounding region. It was demonstrated that the tensile stress is caused by asperity collision that draws the surrounding rock into the contact area. The high compressive stress regions are assumed to be associated with the creep behaviour of asperities that results in the time-dependent increase in frictional resistance found in the empirical friction models, such as rate- and state-dependent friction laws. The tensile stress field is, on the other hand, assumed to produce extension fractures with a length being the order of mm or less on the surface, estimating from the extent of tensile failure. The influence of the extension fractures produced in the tensile stress region on the frictional resistance and/or the mechanical behaviour of a rock discontinuity needs to be studied in the future.

REFERENCES Bahaaddini, M., Hagan, P., Mitra, R. & Hebblewhite, B.H. Numerical investigation of asperity degradation in the direct shear test of rock joints. In: Kwasniewski & Lydzba, eds. Eurock, 2013 Poland. Taylor & Francis Group, 391–397. Barton, N. & Choubey, V. 1977. The shear strength of rock joints in theory and practice. Rock Mechanics and Rock Engineering, 10, 1–54. Elmo, D. 2006. Evaluation of a hybrid FEM/DEM approach for determination of rock mass strength using a combination of discontinuity mapping and fracture mechanics modelling, with paricular emphasis on modelling of jointed pillars. PhD, University of Exeter. Jia, H. Q. 2011. Experimental research on joint surface state and the characteristics of shear failure. Master of Science, Central South University. Malek, F., Suorineni, F. T. & Vasak, P. Geomechanics Strategies for Rockburst Management at Vale Inco Creighton Mine. In: Diederichs, M. & Grasselli, G., eds. Rockeng 09, 2009 Toronto. Ozdemitras, A., Babadagli, T. & Kuru, E. 2009. Effects of fractal fracture surface roughness on borehole ballooning. Vadose Zone Journal 8, 250–257. Voss, R.F. 1985. Random fractal forgeries. In: Earnshaw, R.A. (ed.) Fundamenatl algorithms for computer graphics. Berlin: Springer.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Thermo-temporal behaviour of uniaxial compressive strength of a fine-grained Indian sandstone Nikhil Sirdesai & Vinoth Srinivasan Department of Earth Sciences, Indian Institute of Technology Bombay, Mumbai, Maharashtra, India

Rajesh Singh Department of Geology, University of Lucknow, Uttar Pradesh, India

T.N. Singh Department of Earth Sciences, Indian Institute of Technology Bombay, Mumbai, Maharashtra, India

ABSTRACT: Several energy recovery processes such as Underground Coal Gasification (UCG), Enhanced Geothermal Systems (EGS) and Enhanced Oil Recovery (EOR), and processes involving the disposal of nuclear waste in Deep Geological Repositories (DGR) involve the interaction of host rocks with temperature. However, a large variance can be observed in the pattern and nature of thermal interaction within these processes. Since the success and efficiency of the process rely largely on the state of the nearby strata, it is imperative to understand the behaviour of the geotechnical properties under high temperature conditions. Although, lot of research discuss the effect of temperature on the geotechnical properties, studies on effect of duration of thermal treatment are relatively fewer in number. Therefore, in this study, the effect of duration of thermal treatment on the Uniaxial Compressive Strength (UCS) of the rock has been analysed. Samples of fine-grained Dholpur sandstone were treated and tested up to 500°C. The effect of duration of thermal treatment was studied by varying the exposure time from 5 to 30 days. Additionally, the effect of thermal condition of the sample at the time of mechanical tests, namely, hot or cool, was also analysed. The results suggest that a distinct relation exists between the UCS and duration of thermal treatment. The study can be help add upon the existing pool of knowledge on the effect of heat on geomaterials. Keywords:

1

Sandstone Thermal treatment Strength Time Microcracks

INTRODUCTION

Detailed information of rocks and their geotechnical properties is imperative for the success of any civil, mining or energy recovery process. However, studies conducted by several researchers suggest that the geotechnical properties are susceptible to large variations when exposed to high temperatures (Sharma et al. 2018; Somerton 1992; Tian et al. 2012). Rocks in processes such as underground coal gasification (UCG), enhanced geothermal systems (EGS), enhanced oil recovery (EOR) and disposal of nuclear wastes in deep geological repositories (DGR) are exposed to high temperatures during the operational stages (Siratovich et al. 2015; Sirdesai et al. 2015). Additionally, in the case of fires in buildings, tunnels and mines, the rocks and other geo-materials are subjected to varying degree of thermal treatment (Das et al. 2017; Mahanta et al. 2017). However, the nature and magnitude of thermal profile differs substantially from one process to the other. Such large variations in the thermal treatment profile (maximum temperature and the duration of exposure) makes it imperative to study the geomechanics of these processes, individually, to ensure operation success. Several morphological and mineralogical 681

changes occur in rocks when exposed to high temperatures. As observed in all physical material, rocks and rock-forming minerals expand upon heating. However, as studied by Clark (1966), the thermal expansion behaviour of various minerals is anisotropic in nature. Additionally, the thermal expansion along the various crystallographic axes of a mineral is inconsistent. This induces large amounts of thermal stress within the mineral assemblage, which subsequently alters the microcrack network. Besides morphological changes, several chemical reactions occur in a rock at elevated temperatures (Hajpál and Török 2004). The α-ß transition of quartz that occurs at temperatures around 573°C, is associated with a volumetric (2%) and linear (0.7%) expansion of the quartz grain (Schacht 2004). The expansion accelerates the process of thermal microcracking. Further, studies suggest that the effect of transition is completely reversible at slow cooling rates (Kerr et al. 2004). Higher cooling rates induces thermal shock within the microstructure, thereby accelerating the process of microcracking. Therefore, the rate of cooling also plays an important role in the morphological transformation of the rock. The closure, formation and coalescence of the microcracks subsequently alters the physico-mechanical response of the rocks (Sirdesai et al. 2017c). The creation of microcracks in any of the above-mentioned processes can lead to catastrophes such as subsidence and groundwater contamination, as seen at the Linc Energy’s UCG project at Chinchilla in the state of Queensland, Australia (The Courier Mail 2017). Since the nature of thermal treatment varies across these process, it becomes imperative to perform detailed study of the thermo-mechanical performance of the rocks to ensure safe and successful operation. Therefore, in this study, the mechanical response of an Indian sandstone has been analysed under varied durations of thermal treatment.

2 2.1

MATERIAL AND METHODS Sample characterisation and preparation

Specimen of fine-grained sandstone belonging to the Upper Bhander Group of the Vindhyan Supergroup, were collected from the Dholpur district of Rajasthan, India (Figure 1). The sandstone is rich in quartz and feldspar, and the mineral grains are held together by a siliceous cement. Dholpur sandstone is a major construction material in India, and in the past, it has been widely used to build some of the major political and cultural monuments (DMG-Rajasthan 2006). Additionally, the sandstone shares similar geological features to those present in the coal/lignite seams that have been chosen for the Indian UCG trials (Ministry of Coal 2015). Diamond core-bits were used to recover cylindrical specimen from the

Figure 1.

Geological map of Rajasthan, India.

682

Figure 2. Experimental setup.

blocks of Dholpur sandstone. The cores were recovered perpendicular to the bedding plane, and thereafter, they were cut to attain a length-to-diameter ratio of 2:1. 2.2

Thermal treatment

Parameters such as rate of heating, duration of exposure, type and rate of cooling have a large impact on the physico-mechanical response of a rock. Additionally, high rates of heating or cooling induce thermal shock subsequently leading to accelerated microcracking (Den’gina et al. 1993; Tian et al. 2015). Therefore, in this study, the samples were heated to the target temperatures (50– 500°C, every 50°C) at a rate of 5°C/min. The samples were exposed to the target temperatures for a duration ranging from 5 to 30 days. Further, in order to analyse the effect of thermal condition at the time of testing, two sets of samples, each containing three specimens, were treated simultaneously at each temperature level. While the first set was tested at heated condition, the other set of samples was allowed to cool, at room temperature conditions, for the exact duration as that of the heating. The samples that were tested at heated condition were named ‘NC ’ to represent ‘No Cooling’, while the samples that were tested after cooling were named ‘WC ’ to represent ‘With Cooling’. The scheme of thermal treatment has been enlisted in Table 1. 2.3 Methodology for strength tests The thermally-treated samples were tested for their UCS in accordance to the standards mandated by ASTM (2014). The strength tests were performed in a universal testing machine (UTM) under a constant loading rate of 0.1 mm/min. In the case of NC samples, an environmental chamber was used to provide heating during the strength test (Figure 2). The samples were allowed to soak at the target temperature in the chamber in order to compensate for the loss of heat. The surface temperature of the sample was continuously monitored with the help of thermocouples.

3

RESULTS AND DISCUSSION

The strength of non-treated (NT) and thermally treated samples have been enlisted in Tables 2a and 2b, respectively. The cumulative effect of time and temperature on the compressive strength of hot (NC) and heat-treated (WC) samples has been illustrated in Figure 3, wherein, the trends of strength of NC and WC for all every treatment duration have been plotted for better comparison. As seen in Figure 3, the strengths of all the specimens decrease at the onset of thermal treatment (50–100°C). This can be attributed to the exposure of the inherent pores and microcracks due to 683

Table 2b.

Table 2a.

Strength of non-treated samples.

Sample

UCS (MPa)

Average UCS (MPa)

NT1 NT2 NT3

54.98 56.24 56.78

56.00

Average compressive strength of treated samples.

Temp 5NC

5WC 10NC 10WC 15NC 15WC 20NC 20WC 25NC 25WC 30NC 30WC

50 100 150 200 250 300 350 400 450 500

46.95 48.64 68.01 75.53 48.56 44.27 42.39 50.59 57.19 53.27

52.91 54.87 63.86 70.60 52.03 52.50 48.93 45.06 49.08 58.72

Figure 3.

50.04 53.69 72.13 75.53 48.74 52.77 51.19 37.82 48.33 60.39

55.11 57.80 72.91 72.80 47.65 48.82 45.02 51.74 55.02 59.72

54.54 57.31 70.59 59.81 54.08 53.62 43.71 57.63 57.08 49.96

45.63 65.16 70.10 62.16 47.93 55.64 53.29 50.79 56.20 52.98

49.67 62.20 68.27 61.72 55.83 49.62 51.84 47.61 55.09 55.64

45.33 61.94 69.81 60.81 53.57 56.10 45.40 55.84 51.69 54.16

49.26 48.89 75.10 64.02 53.02 50.53 50.52 44.24 51.36 59.82

UCS of variedly treated specimens with respect to temperature.

684

42.83 45.41 73.97 65.49 50.63 55.13 44.94 51.04 52.37 55.49

55.26 61.92 55.22 67.01 63.64 47.87 53.61 44.15 46.53 55.98

52.24 60.21 60.15 65.13 62.06 45.91 51.20 45.05 48.50 52.35

Figure 4.

Variation in UCS as a function of duration and treatment temperature.

the evaporation of free-water. On further heating, the mineral grains begin to expand which subsequently leads to the closure of the pores and microcracks. This increases the compaction of the rock, thereby leading to an increase in strength. However, on further heating, the expansion of the mineral grains continues, thereby leading to the formation of new microcracks along the grain boundaries. The formation of microcracks reduces the compaction of the rock, thereby causing the sample to fail. The phenomenon is consistent for all the samples, and can be observed at temperatures over 200°C. The temperature-range between 150–200°C serves as the inflection point for strength, and is known as the critical temperature zone (CTZ). Additionally, Figure 3 suggests that the strength of WC samples is less than that of the NC sample. This can be attributed to the state of microcracks within a specimen. Since the WC sample are cooled at room temperature conditions, the resultant thermal shock results in the creation of microcracks, thereby causing an irreversible reduction in strength. Similar results have been reported by various researchers (Brotóns et al. 2013; Sirdesai et al. 2017a; Sirdesai et al. 2016; Sirdesai et al. 2017b; Sirdesai et al. 2017d). In order to analyse the strength as a function of both, duration and temperature, the results of NC and WC samples were studied using MATLAB software to obtain contour plots (Figure 4). The plots confirm the presence of CTZ between 150–200°C. Additionally, it can be observed that the NC specimens, which have been treated for a duration of 10 days, exhibit the highest strength. On the other hand, the strength of the WC samples is highest after 5 days of thermal treatment. This variation can be attributed to the phenomenon of accelerated microcracking in the WC samples due to thermal shock. The contour plot helps in visualising the thermo-temporal behaviour of strength of the fine-grained Dholpur sandstone.

4

CONCLUSIONS

In this study, cylindrical specimens of thermally-treated, fine-grained Dholpur sandstone were examined for their uniaxial compressive strength (UCS). The target temperature and the duration of exposure at the target temperature were varied in order to observe the thermo-temporal behaviour of UCS. The samples were treated at temperature between 50–500°C for 6 durations ranging between 5–30 days. Additionally, the effect of thermal condition at the time of testing was also considered. The results suggest that the mechanical response of the samples varies significantly with the change in duration, temperature and/or thermal condition. The primary cause of the variation can be attributed to the change in the nature and volume of microcracks. Additionally, the results suggest that the highest strength of all the samples can be observed between 150–200°C, thereby, suggesting the presence of a critical temperature zone (CTZ). The results of this study will help in understanding the physico-mechanical response of strata in insitu coal gasification, nuclear waste disposal and enhanced geothermal systems. 685

REFERENCES ASTM. 2014. D7012-14E: Standard Test Methods for Compressive Strength and Elastic Moduli of Intact Rock Core Specimens under Varying States of Stress and Temperatures. ASTM International. Brotóns, V., Tomás, R., Ivorra, S. & Alarcón, J.C. 2013. Temperature influence on the physical and mechanical properties of a porous rock: San Julian’s calcarenite. Engineering Geology, 167, 117–127. Clark, S.P. 1966. Handbook of physical constants. Geological Society of America. Das, R., Sirdesai, N. & Singh, T. 2017. Analysis of deformational behavior of circular underground opening in soft ground using three-dimensional physical model. 51st US Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association. Den’gina, N.I., Kazak, V.N. & Pristash, V.V. 1993. Changes in Rocks at High-Temperatures. Journal of Mining Science, 29, 472–477. DMG-Rajasthan. 2006. Sandstone - Rajasthan. World Wide Web Address: www.dmg-raj.org/sandstone. html. Hajpál, M. & Török, Á. 2004. Mineralogical and colour changes of quartz sandstones by heat. Environmental Geology, 46. Kerr, R., Needham, J. & Wood, N. 2004. Science and Civilisation in China: Volume 5, Chemistry and Chemical Technology, Part 12, Ceramic Technology. Cambridge University Press. Mahanta, B., Sirdesai, N., Singh, T. & Ranjith, P. 2017. Experimental study of strain rate sensitivity to fracture toughness of rock using flattened Brazilian disc. Procedia Engineering, 191, 256–262. Ministry of Coal, G.o.I. 2015. Steps for Development of Underground Coal Gasification Technology. World Wide Web Address: http://pib.nic.in/newsite/PrintRelease.aspx?relid=132935. Schacht, C. 2004. Refractories handbook. CRC Press. Sharma, L.K., Sirdesai, N.N., Sharma, K.M. & Singh, T.N. 2018. Experimental study to examine the independent roles of lime and cement on the stabilization of a mountain soil: A comparative study. Applied clay science, 152, 183–195. Siratovich, P.A., Villeneuve, M.C., Cole, J.W., Kennedy, B.M. & Bégué, F. 2015. Saturated heating and quenching of three crustal rocks and implications for thermal stimulation of permeability in geothermal reservoirs. International Journal of Rock Mechanics and Mining Sciences, 80, 265–280. Sirdesai, N., Mahanta, B., Ranjith, P. & Singh, T. 2017a. Effects of thermal treatment on physicomorphological properties of Indian fine-grained sandstone. Bulletin of Engineering Geology and the Environment, 1–15. Sirdesai, N., Mahanta, B., Singh, T. & Ranjith, P. 2016. Elastic modulus of thermally treated fine grained sandstone using non-contact laser extensometer. Recent Advances in Rock Engineering (RARE 2016), Bangalore. Sirdesai, N., Singh, R., Singh, T. & Ranjith, P. 2015. Numerical and experimental study of strata behavior and land subsidence in an underground coal gasification project. Proceedings of the International Association of Hydrological Sciences, 372, 455. Sirdesai, N., Singh, T., Ranjith, P. & Singh, R. 2017b. Effect of varied durations of thermal treatment on the tensile strength of Red Sandstone. Rock Mechanics and Rock Engineering, 50, 205–213. Sirdesai, N.N., Singh, A., Sharma, L.K., Singh, R. & Singh, T. 2017c. Development of novel methods to predict the strength properties of thermally treated sandstone using statistical and soft-computing approach. Neural Computing and Applications, 1–27. Sirdesai, N.N., Singh, T.N. & Gamage, R.P. 2017d. Thermal alterations in the poro-mechanical characteristic of an Indian sandstone–A comparative study. Engineering Geology, 226, 208–220. Somerton, W.H. 1992. Thermal properties and temperature-related behavior of rock/fluid systems. Elsevier. The Courier Mail. 2017. Contamination ‘much worse than thought’. World Wide Web Address: http:// www.couriermail.com.au/news/queensland/chinchilla-contamination-worse-than-thought-warning-onmount-isa-lead-levels/news-story/a19a56e1289c98023438fce45a28c681. Tian, H., Kempka, T., Xu, N.-X. & Ziegler, M. 2012. Physical Properties of Sandstones After High Temperature Treatment. Rock Mechanics and Rock Engineering, 45, 1113–1117. Tian, H., Kempka, T., Yu, S. & Ziegler, M. 2015. Mechanical Properties of Sandstones Exposed to High Temperature. Rock Mechanics and Rock Engineering, 49, 321–327.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Acoustic and failure behaviour of Gondwana shale under uniaxial compressive and indirect Brazilian tensile loading—an experimental study Ashutosh Tripathy, Vinoth Srinivasan, Krishna Kumar Maurya, Nikhil Sirdesai & T.N. Singh Department of Earth Sciences, Indian Institute of Technology Bombay, Mumbai, Maharashtra, India

ABSTRACT: Shale has become a principle source of future energy in India. Therefore, research on mechanical and fracture behavior of shale rock has proven imperative in rock engineering. The present study investigated significance of acoustic behavior in shale rock under constant uniaxial compression and tensile Brazilian loading. The XRD and SEM analysis revealed that the investigated shale samples exhibited natural flaws at micro levels with higher percent of flaky micaceous minerals. The compaction of laminations and microstructural flaws is evident during the compression than in tensile condition. This was marked by gradual acoustic rate increase during the preliminary stages in compression. However, the rate of acoustic emission in medial time sequence is feeble under both loading conditions. This indicated the damage accumulation with associated deformation. The stress increase seems to have initiated propagation of fractures leading to failure of rock witnessed by steep increase in acoustic data at final stages. Likewise, tensile failure under Brazilian loading was observed with burst of acoustic signals. The acoustic patterns revealed that layering in shale failure during compression and tensile loading. The present study tried to understand the failure behavior of shale through acoustic emission parameters to infer fracture initiation and propagation stages. The research can be extended to study the fracture stimulation in shale gas exploration and CO2 injection as an aid to understand shale behavior under compression and tensile loading. Keywords:

1

Acoustic Emission, Shale, AE Rate, AE Energy, Fracture, Damage accumulation

INTRODUCTION

Shale has become a key rock in many rock engineering investigations in India. The relative importance of shale is magnified in the recent years due to its abundance in both natural gas extraction and as an important coal measure rock in Indian subcontinent conditions. Therefore, much focus has been diverted on inferring the mechanical behavior of shale rock. However, the lower permeability and complex fracture properties of the shale deposits enriched with natural gas has been the area of greater concern. This added uncertainty and difficulty in understanding its deformation and their failure behavior great depths. Hence, a complete knowledge of rock stability and its damage conditions of shale rock proved important. This may add sufficient confidence for planning deeper exploration and to arrest any unexpected geo hazards. The exploration of shale gas principally involves injection of hydraulic fluid into the stratum and inducing artificial fractures, thereby stimulating the flow of gas through the rock. Also, shale can be utilized as ideal cap rock for CO2 sequestration into the deep unmined coal measure rocks. Controlled fracture stimulation at greater depth requires sound knowledge on rock mass behavior while fracturing. Also, these activities will be carried out at very deeper depth, where in-situ estimation of rock behavior is highly difficult. Under the circumstances, laboratory investigations on shale behavior during fracturing and failure proves vital. 687

The concept of AE monitoring has opened window for wider perspective of rock engineering studies in the recent years. The method is based on the principle that, rocks, when loaded externally will develop micro-cracks due to the stress accumulation and the subsequent re-distribution leading to failure. This will lead to the generation of acoustic signals, which can be captured through a serious of sensors attached to the rock specimen during loading. On processing and inferring those acoustic emission signals effectively, will be help to understand the deformation and the damage in rocks and to locate pre-failure zones with stress redistribution. The application of AE technique for inferring rock damage and deformation through stress release and subsequent generation of microfractures and their propagation has been plentiful. Various researchers have discussed and reported the successful application of AE technique for rock damage assessment and deformation forecasting. Notable work in the recent years include those of (Al-Bazali et al. 2008; Fortin et al. 2009; Stanchits et al. 2009, 2014; Ishida et al. 2012; Inserra et al. 2013; Khazaei et al. 2015; Stoeckhert et al. 2015; Xiao et al. 2016; Rodríguez et al. 2016; Kong et al. 2017; Zhang et al. 2018) and much more. In the present study, the mechanical and acoustic behavior of shale rock from deep underground coal mine with potential natural gas resource is studied. The specimens were loaded both under compression and Brazilian conditions, so as to study the effect of layering on the acoustic behavior of the shale samples. The change in AE features were directly correlated with the damage conditions and failure characteristics of the loaded specimens. Another significant aspect of the study is to infer the effect of layering on the acoustic behavior of rocks using parametric analysis. 2 2.1

MATERIALS AND METHODS Sample description

The shale samples tested in the present study were collected from boreholes of Jamadoba coal mine in Jharia coal fields of Damodar river valley belonging to the Gondwana formation in the North East Peninsular Indian State of Jharkhand (Fig. 1). The Jharia coal field is an oval shaped coal field with areal distribution of about 458 sq.km and is located in the eastern end of the damodar valley basin. The damodar basin forms a part of east-west trending the Saptupra—Damodar with a thick sedimentary sequence of about 2900 m of shallow water, fluviatile, lacustrine and glacial environment ranging from Carboniferous to Permian (Verma et al. 1979; Saikia and Sarkar 2013). Sand stones, shales and sandy shales are the principal

Figure 1.

Location and geological map of Jharia Coal Field.

688

rocks encountered in the region with intrusion of dolerite and mica-peridotite dykes. Structurally, the region consists of some normal-tensional fault with several strike-slip faults and is surrounded on all sides by crystalline geneiss of Archean age. Also, the region is highly fire prone, the hot fumes extending up to several kilometers with some normal. The samples were dark black in color with visible layered sedimentation. The core logs collected from the field were cut in the smaller specimens of variable length with the constant diameter of 44  mm. The samples were prepared following the ISRM specifications by ensuring the length to diameter ratio of 2.0 to 2.5. Also, the specimen sides were polished to ensure the tolerance limit is within the prescribed in the standards. Before performing experiments, the samples were analyzed for inferring their compositional and microstructural characteristics. The microstructural characteristics were inferred using scanning electron microscopic analysis and the results are furnished in Fig. 2a. The mineralogical composition of the sample was determined using XRD analysis from the powered samples sieved down to 75-micron mesh (Fig. 2b). The XRD analysis suggested that the samples consisted predominantly of non-siliceous minerals (Fig. 2a). This was strongly supported by SEM imaging results gave insights about the flaky mineral layers of micaceous in nature (Fig. 2b). These bedding layers constituted natural micro-structural weak planes of the rock. The compressional wave velocities suggested that the shale is densely compacted possessing good strength with increase in depth (Fig. 2c). Experiments were carried out in cylindrical samples with height varying from 90 to 104 mm and tensile disc specimens with dimension of 1:1.25 as per the ISRM standards (ISRM 1978; ASTM 1988). 2.1

Experimental setup

The schematic representation of AE setup used in the present study is shown in Fig. 2. The instrumentation for recording acoustic signals consisted of two piezoelectric transducers (R6D Type) with acoustic data logger from Physical Acoustics Corporation (MISTRAS) connected to a PC. The transducers were connected with a pre-amplifier of 40 dB to the 60 dB front amplifier. The signals were filtered to the frequency range of 20 kHz to 3 MHz. The signal threshold of the AE system was set to 45 dB with the sampling frequency of 1 million samples per second (MSPS). The AE experiments were performed as suggested by standards in ISRM (Ishida et al. 2017). The samples were then loaded using semi servo-controlled loading system having fixed upper platen with force applied by movement of the lower platen. In order to minimize the defects in recorded acoustic signals, a thick glue was applied between the contact of sensor and the samples. The cylindrical samples were loaded perpendicular to the sedimentation layer and the Brazilian discs were loaded parallel to the bedding planes of the shale.

Figure 2. (a) SEM image, (b) XRD Spectra and (c) Stress Strain Data Curve of the Jharia shale sample. Table 1.

Important properties of Jharia shale used in the study.

Property

VP (m/sec)

VS (m/sec)

BTS (MPa)

UCS (MPa)

E (GPa)

ν

Shale

3344

1319

4.54

9.11

21.4

0.19

689

Figure 3.

3

Schematic of AE Monitoring and Loading System used in the experiment.

EXPERIMENTAL RESULTS ANALYSIS OF ACOUSTIC CHARACTERISTICS

Acoustic Emission data will give insight information on the damage initiation and failure precursor of the samples under load (Ohnaka and Mogi 1982). As Acoustic data is rapid release of stored stress of a loaded material through fracture channels, they will help to understand the rock deformation and natural flaws present in rocks. This may be useful in infer the pre-fracture damage and failure characteristics of rock while planning deep underground structures in shales such as in natural gas extraction and in coal mines. In the present study, the acoustic characteristics such as AE Count, Cumulative AE Count (∑AE Count), AE Energy, Cumulative AE Energy (∑AE Energy) were correlated with load. 3.1

Uniaxial compressive loading

Although many research on effect of uniaxial compression with acoustic monitoring studies are reported, rarely found research studying the shale behavior with acoustic monitoring. This is due to fact that, shales are highly anisotropic and inhomogeneous in nature with natural bedding layers. Therefore, the present study aims to infer the acoustic behavior of Gondwana shale rock under compression. The results of rate and energy characteristics of acoustic monitoring for cylindrical specimen under compressive loading is given in Fig. 4 and Fig. 5 in correlation with applied load. The results suggested that Acoustic emission attained its peak, just prior to the rock failure, depicted from abnormal increase in both acoustic counts and associated energy. The initial excitation in acoustic signals suggested the closing of the micro-cracks with release of feeble energy. The acoustic signals attained peak after every fracture initiation leading to failure. Since, shale tested in this study is of relatively low strength, the fracture peaks were least prominent from the acoustic data recorded as depicted in Fig. 4. The correlative plot of studied acoustic parameters with the load is presented in Fig. 5. Both acoustic count and energy levels displayed similar trend throughout the experiment cycle. Also, the cumulative plot of acoustic event count and energy suggested that the samples exhibited three phase of acoustic behavior under compressive loading (Fig. 5). The first phase of rock deformation is represented with a gentle increment in number of acoustic counts having feeble energy. Furthermore, the slope of the cumulative acoustic data flattens signifying further consolidation of weak layers within shale with damage accumulation. The third phase perceived a drastic increase in intensity of acoustic signals in terms of both number and energy preceding the failure of the sample. This phase is associated with both accumulated stress release linked with fracture propagation. 690

Figure 4. Results of AE parameter behavior under Uniaxial Compression. Correlating Load with (a) AE Count (b) AE Energy.

Figure 5.

3.2

Correlation of Cumulative AE count and Cumulative AE Energy with load.

Tensile loading under indirect brazilian condition

The tensile strength of rock is very important in any excavation processes and failure under tensile loading is one of the predominant failure mode in deep underground excavations (Zhang et al. 2018). One of the principle aim of the present study is to understand the failure behavior of shale under tensile loading and to infer their acoustic behavior. The tensile disc samples were loaded parallel to the bedding layer orientation with simultaneous monitoring of the acoustic signals. The time sequence plot of acoustic data revealed the recording of weak energy associated with rock deformation. The acoustic data projected more count peak with lower energy peaks. The high acoustic peak revealed generation of microcracks during rock deformation. However, the recorded energy in contrast exhibited very low peaks signifying the distribution of stress along the microfractures prior to failure. The correlation between the cumulative acoustic count and cumulative energy with load is presented in Fig. 7. Unlike uniaxial compression, tensile loading in Brazilian disc exhibited relative inconsistent pattern between acoustic rate and subsequent energy. A gradual increase in acoustic rate was witnessed against low acoustic energy release. However, relative near the peak strength there has been a drastic release of acoustic signals prior to the failure. This drastic increase in acoustic behavior may be due to the sudden release of accumulated stress during the middle period of deformation. The results suggested that the stress 691

Figure 6. Results of AE parameter behavior under Brazilian Tensile Loading. Correlating Load with (a) AE Count (b) AE Energy.

Figure 7.

Correlation of Cumulative AE count and Cumulative AE Energy with load.

accumulation was feeble during loading which dissipated along micro-cracks generated and sudden increase in energy was due to the major crack resulting in the failure of the sample.

4

CONCLUSION

In the present study, the acoustic emission datasets generated during compressive and tensile loading in shale were investigated to understand their fracturing behavior during deformation and associated failure. The shale samples from deep underground coal mine belonging to Gondwana formation were studied. A parametric analysis is carried out with acoustic rate and acoustic energy correlated with load. During compressive, shale sample underwent three stages of deformation evidenced from cumulative curves of acoustic parameters. Both the acoustic rate and energy release followed a significantly similar trend under compression. The first state is marked with compaction of existing natural microcracks, followed by reduced acoustic data representing the damage accumulation leading to fracturing. At the last stage, there is gradual increase in frequency and rate of acoustic signals which signified the propagation of fractures with increased acoustic rate leading to failure. However, the tensile loading resulted in contrast acoustic emission behavior. The tensile loading is marked with gradual increase in acoustic rate with minimal energy at initial stages, and a sudden 692

burst of acoustic energy prior to the failure. This represented the generation of microcracks as evidenced from acoustic rate peak leading to the dispersion of accumulated energy and stress. However, in both the loading conditions, the acoustic emission attained its peak prior to the failure. These results suggested the potential application of acoustic monitoring for predicting rock deformation behavior at loading and failure. The results from the present study could to extended for controlled stimulation of fracture in shale reservoirs during hydraulic fracturing, inferring the potential of shale as a cap rock in CO2 sequestration site in unmineable coal resources and to determine their injection rate.

REFERENCES [1] Al-Bazali T, Zhang J, Chenevert ME, Sharma MM (2008) Factors controlling the compressive strength and acoustic properties of shales when interacting with water-based fluids. Int J Rock Mech Min Sci 45:729–738. doi: 10.1016/j.ijrmms.2007.08.012. [2] Fortin J, Stanchits S, Dresen G, Gueguen Y (2009) Acoustic emissions monitoring during inelastic deformation of porous sandstone: Comparison of three modes of deformation. Pure Appl Geophys 166:823–841. doi: 10.1007/s00024-009-0479-0 [3] Inserra C, Biwa S, Chen Y (2013) Influence of thermal damage on linear and nonlinear acoustic properties of granite. Int J Rock Mech Min Sci 62:96–104. doi: 10.1016/j.ijrmms.2013.05.001 [4] Ishida T, Aoyagi K, Niwa T, et al (2012) Acoustic emission monitoring of hydraulic fracturing laboratory experiment with supercritical and liquid CO2. Geophys Res Lett 39. doi:10.1029/2012GL052788 [5] Ishida T, Labuz JF, Manthei G, et al. (2017) ISRM Suggested Method for Laboratory Acoustic Emission Monitoring. Rock Mech Rock Eng 50:665–674. doi: 10.1007/s00603-016-1165-z [6] Khazaei C, Hazzard J, Chalaturnyk R (2015) Damage quantification of intact rocks using acoustic emission energies recorded during uniaxial compression test and discrete element modeling. Comput Geotech 67:94–102. doi: 10.1016/j.compgeo.2015.02.012 [7] Kong B, Wang E, Li Z, et al. (2017) Acoustic emission signals frequency-amplitude characteristics of sandstone after thermal treated under uniaxial compression. J Appl Geophys 136:190–197. [8] Ohnaka M, Mogi K (1982) Frequency characteristics of acoustic emission in rocks under uniaxial compression and its relation to the fracturing process to failure. J Geophys Res 87:3873–3884. [9] Rodríguez P, Arab PB, Celestino TB (2016) Characterization of rock cracking patterns in diametral compression tests by acoustic emission and petrographic analysis. Int J Rock Mech Min Sci 83:73–85. [10] Saikia K, Sarkar BC (2013) Coal exploration modelling using geostatistics in Jharia coal field, India. Int J Coal Geol 112:36–52. [11] Stanchits S, Fortin J, Gueguen Y, Dresen G (2009) Initiation and propagation of compaction bands in dry and wet bentheim sandstone. Pure Appl Geophys 166:843–868. [12] Stanchits S, Surdi A, Gathogo P, et al. (2014) Onset of hydraulic fracture initiation monitored by acoustic emission and volumetric deformation measurements. Rock Mech Rock Eng 47:1521–1532. [13] Stoeckhert F, Molenda M, Brenne S, Alber M (2015) Engineering Fracture propagation in sandstone and slate e Laboratory experiments, acoustic emissions and fracture mechanics. J Rock Mech Geotech Eng 7:237–249. doi: 10.1016/j.jrmge.2015.03.011 [14] Verma RK, Bhuin NC, Mukhopadhyay M (1979) Geology, Structure and Tectonics of the Jharia Field, India-A Three-Dimensional Model. Geoexploration 17:305–324. [15] Xiao F, Liu G, Zhang Z, et al. (2016) Acoustic emission characteristics and stress release rate of coal samples in different dynamic destruction time. Int J Min Sci Technol 26:981–988. [16] Zhang SW, Shou KJ, Xian XF, et al. (2018) Fractal characteristics and acoustic emission of anisotropic shale in Brazilian tests. Tunn Undergr Sp Technol 71:298–308.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Rocks drillability classification based on comparison of physico-mechanical properties with drilling rate timing Andrey Trofimov, Alexandr Rumyantsev, Vladislav Vilchinsky & Konstantin Breus LLC “Institute Gipronikel”, Saint-Petersburg, Russia

Andrey Skokov Department Industrial Assets, PJSC “MMC “Norilsk Nickel”, Moscow, Russia

ABSTRACT: The article considers various approaches to the assessment of rock drilling. Domestic classifications and methods for estimating the drillability according to physicomechanical properties are given. Based on the analysis of the results of international practice and various studies, the use of strength properties as a characteristic of drillability is justified. To determine the local productivity of drilling rigs, a video-timing of the pure drilling rate and a complex of mechanical tests are performed. Timing was carried out on various models of the Atlas Copco and Sandvik drilling rigs and various drilling diameters. The best correlation between the pure drilling rate is established with the strength of the rocks for uniaxial tension in accordance with the procedure of GOST 21153.3 paragraph 2. To account for the diameter of drilling and the power of the drummer, a transition to the conditional specific volume rate of drilling is performed. To account for the diameter of drilling and the power of the hummer, a transition to the conditional specific volume rate of drilling is performed. As a result of the generalization of the results, dependencies have been obtained that make it possible to determine the pure drilling speed of drilling rigs, depending on the power of the hummer, the drilling diameter and the tensile strength. Dependencies are presented separately for face and long-hole drilling rigs. For the long-hole, the coefficient of reducing the drilling speed from depth is given. Keywords:

1

drillability, drilling rate, drilling rigs, mechanical tests of rock, tensile strength

INTRODUCTION

The most widely used in the domestic mining industry has got the classification of drillability in which rocks are classified according to the duration of the regular time of drilling one meter hole of different machines and tools such as SNiP IV-2-82 classification (11 classes) and Uniform classification of rocks drillability (20 classes). Scales of classifications are not comparable, since they are constructed from the time of drilling by different machines. However, the Standard developed by Soyuzdorstroy provides a reference table of different drillability classification. A different approach to the classification of drilling rocks is proposed to be evaluated as a function of the UCS, the shear strength and the density of the rocks. A comparison of domestic scales, criteria and methods for estimating the drillability of rocks is discussed in detail by A. Tanayno. In modern conditions, up to 10 models of different generation drilling rigs and jumbos and hammer power can be applied to one type of drilling operations and also the drilling tool used from different suppliers and diameters. In this regard, the assignment of the category of rocks in the classical sense of a certain reference drilling speed is very conditional. For the most accurate description of drillability, it is necessary to characterize the rocks by the mechanical property responsible for the resistance of the material to the formation and propagation of cracks when a concentrated dynamic load is applied. 695

In international practice, rocks drillability characterize the mechanical properties defined in accordance with the standards ASTM or ISRM, or by specific tests, such as index DRI drillability—drilling rate index (Figure 1). From the mechanical properties, we can attach the USC and Brazilian UTS method, shore hardness test and Point load index (Figure 2). The obvious disadvantage of special tests to determine the drillability is the large complexity in the preparation of samples and tests, also required a unique laboratory stands with a large number of given initial parameters, which affects the accuracy of test and repeatability of results. In scientific works compared, the index of DRI and the mechanical properties of rocks and with the above properties there is a good correlation.

Figure 1.

Determination of DRI index.

Figure 2. Correlation between DRI index, UCS and BTS test (Kelessidis, 2011; Yarali and Soyer, 2011).

Figure 3.

Sandvik and Atlas Copco recommendations on the choice of the hammer type.

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Figure 4.

Drilling rate timing.

Figure 5.

Mechanical test of rocks.

In the works [Heinio 1999; Thuro 1997; Bilgin and Kahraman 2003], as well as the estimation of rock drilling by physico-mechanical characteristics. Similarly, the recommendations of the leading manufacturers of the drilling rigs and jumbos (Sandvik and Atlas Copco) on the choice of the hammer type are also based on the rock properties (Figure 3). Thus, the use of mechanical properties of rocks to assess the drillability is justified by international practice.

2

RESEARCH METHOD AND MECHANICAL TESTS OF ROCK

To determine local performance of drilling rigs from the physico-mechanical properties of rocks was made pure drilling rate timing (Figure 4). During the timing, the following s models were tested: face drilling jumbos—Boomer M2C, L2D, DD 420–60, 421–60, Axera D5–140, Minimatik D07 260 C and long-hole rigs—Simba M7C, M6C, L6C, SOLO 7–7F, DL 421–15, 321–7, 420–7, 411–15, 420–10, DS 421. The following drilling diameters were tested: 43, 48, 64, 76, 89, 102, 115 mm. Based on drill timing had gotten drilling speed for different diameters and lithological types of rocks. With the aim of obtaining correlations between pure drilling rate and strength and deformation properties of a complex mechanical test of rocks (Figure 5) that have been taken on the venue of drill timing.

3

RESULTS PROCESSING

Based on the correlation coefficients highlighted the dependence of the conditional volume of the drilling speed of the tensile strength, since this properties most accurately describes drilling of rocks. The investigated differences are represented by sulphide rich, cuprous and 697

Figure 6. The dependence of the conditional volume drilling rate of the indirect tensile strength, for face drilling rigs (left), long-hole drilling rigs (right).

disseminated ores, hornfelses and metasomatites, diabases, anhydrite, limestone, peridotite, serpentinite. In order to operate with a large amount of statistical data and establish a more accurate relationship, a change is made from the drilling speed in m/min for each drilling diameter to the volume drilling speed m3/min. In order to exclude the influence of the power of the hammer drill, in the presented dependences the volume drilling speed is presented in the dimension m3/min*kW. This approach allows us to estimate the specific energy consumption for rock destruction. Such an approach makes it possible to estimate specific energy costs for the destruction of rock and to determine a single dependence on all sampling points. According to the best correlation is shown in Figure 6. To determine the pure drilling rate of face drilling rigs, the empirical formula is used: vface _ drill =

exp( −0, 057 ⋅ σ utt ) ⋅W , π / 4 ⋅ d 2 ⋅κ r

361,

/min

(1)

were: σutt – indirect uniaxial tensile strength determined in accordance with GOST 21153.3 paragraph 2, MPa. W – drilling hummer power, kW; d – borehole diameter, mm; r – coefficient for drilling in the roof and sides, r = 1,135. For long-hole drilling rigs: vlong _ holel =

500 ⋅ exp( , 077 ⋅ σ utt )⋅ W , π / 4⋅ d 2 ⋅

/min

(2)

The effect of the depth of the long-hole llong-hole on the drilling rate is determined by the formula: vl

vlong _ hholel ⋅ klong -holel

klong-holel = 1, 082 − 0, 0161⋅ llong-hole

4

(3) (4)

CONCLUSION

Based on the results of the study, a dependence has been obtained that makes it possible to estimate the pure drilling rate in rocks of different strengths (tensile strength) for drilling rigs with a varied impact power and drilling diameters. The results obtained are valid only for drilling with top-hammers percussive drilling rigs in the range of sizes of drill bits 43–115 mm. 698

REFERENCES Bilgin. N., S. Kahraman. Drillability Prediction in Rotary Blast Hole Drilling. 1a” International Mining Congress and Exhibition ot Turkey-IMCET 2003. Kelessidis, V.C. Rock drillability prediction from in situ determined unconfined compressive strength of rock. The Journal of the Southern African Institute of Mining and Metallurgy. June 2011. Rock Excavation Course Notes—Spring 2003 University of Arizona Mining and Geological Engineering. Matti Heinio. Rock Excavation handbook. Sandvik Tamrock Corp. 1999. Olgay Yarali and Eren Soyer. The effect of mechanical rock properties and brittleness on drillability. Scientific Research and Essays Vol. 6(5), pp. 1077–1088, 4 March, 2011. SNiP IV-2-82, Rules for the development and application of elemental estimates for building structures and applications. Collections of elemental estimates for building structures and work. Volume 1. Collection 3. Blasting and exploratory work (not cited). Thuro K. Drillability prediction—geological influences in hard rock drill and blast tunnelling. Geol Rundsch (1997) 86: pp. 426–438.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

About specific energy intensity behavior under multistage triaxial compression of sandstone specimens Pavel Aleksandrovich Tsoi Chinakal Institute of Mining of the Siberian Branch of the RAS, Novosibirsk, Russia Novosibirsk State Technical University, Novosibirsk, Russia

Olga Mikhailovna Usol’tseva Chinakal Institute of Mining of the Siberian Branch of the RAS, Head of the Shared Use Center of Geomechanical, Geophysical, and Geodynamic Measurements, Novosibirsk, Russia

Vladimir Nikolaevich Semenov Chinakal Institute of Mining of the Siberian Branch of the RAS, Novosibirsk, Russia

ABSTRACT: There are cases when it is very difficult to extract enough unbroken cores for the aims of geo-engineering works and studies. Therefore (in the case of core deficiency) the required (by standards) number of laboratory conventional mechanical tests can’t be carried out. To overcome this obstacle, a compromise settlement based on the use of a multi-stage compression test was used. The data of such the experiments were used in this work. On the basis of the Instron-8802 testing machine, multistage tests were performed under triaxial compression of cylindrical sandstone specimens. The “axial stress-axial strain” diagrams were obtained for the six tested specimens. Based on the diagram data, the specific energy intensities for each of the five loading stages were determined. It is proposed to assess the predisposition to the brittle or plastic behavior of the studied rock from the change in specific energy intensity during the transition from one loading stage to another. Keywords: multistage, triaxial compression, specific energy intensity, sandstone, specimen, lab testing

1

INTRODUCTION

The construction of mining objects deals with the natural or technogeneous activities (involving regular loads-unloads) and leads to the mechanical degradation of rocks. Rock mass microfissures induced by development, weakening and corresponding changes in the initial stress state can cause changes of strength and elastic properties [Song et al., 2016]. Therefore calculating techniques based on the use of conventional mechanical properties may be the cause of inaccurate estimation of stress-strain state. There is also complication in extracting the undisturbed core from petroleum deposits. Thus, to characterize the strength parameters, a scant amount of specimens must be tested. Carrying out the multistage triaxial compression tests make it possible to get Mohr-Coulomb envelope involving single specimen data [Myers et al., 2015]. The lab tests data that composed the presented paper are based on multistage triaxial compression of the sandstone, the lateral pressure was varied depending on the stage of the loading program. A number of the international research studies are devoted to such or related topic [Gatelier et al., 2002, Youshinaka et al., 1998, Youn et al., 2010, Bro, 1997]. The aim of the present paper was to consider the assessing of specific energy intensity and its possible interdependence with plastic or brittle behavior during the multistage triaxial compression. 701

2

EXPERIMENT TECHNIQUE AND ACQUIRED DATA ANALYSIS

The sandstone cores were chosen from the rock collection of the Shared Use Center of Geomechanical, Geophysical and Geodynamic Measurements, Siberian Branch, Russian Academy of Sciences. Six cylindrical specimens of the standard diameter (30 mm) were made using the CPM 400 Coretest System. To be sure the parallelism of the end faces and required length (60 mm) were reached, drilled specimens were sawed on the DTS-430 high precise apparatus. The sandstone specimens (Figure 1) were tested under the multistage triaxial compression. During the multistage test the axial stress value reached to the compressive elastic limit at each loading stage at defined confining pressures. Their values were 0.5, 1.5, 7, 9.5, 11 MPa, respectively, for 1st, 2nd, 3rd, 4th, 5th testing stages. Each specimen was put into the stabilometer. The specimens were wrapped by special rubber shell to prevent confining liquid (machine oil) from penetration into the sample pores during tests. The oil is used to for even distribution of confining pressure. The axial load was applied to the specimen ends. The technique for testing rock samples under the multistage triaxial compression consists of several steps [Myers et al., 2015]. The first confining pressure value is applied, and then the axial load (by given loading path) increases until the plastic strain begin. After this, given unloading of the specimen up to the equality value of confining and axial pressures is carrying out. Then the confining pressure increases up to the second value of lateral pressure, the axial load reaches the second value of plastic strain. This procedure is repeated several times (it depends on given quantity of stages). The specimen is brought to disintegration at the experiment completion. The typical instance of obtained «Stress–strain» curve is shown in Figure 2. The value of specific energy intensity (kJ/m2) was estimated for each loading stage. Specific energy intensity is the energy value accumulated in the specimen at each loading stage of loading up to compressive elastic limit value. This characteristic is described by the definite integral below: uzi 2

W

∫ ( (u ) − i z

i z

uzi 1

Figure 1.

i

) ⋅ du , z

Specimens No 1–3, 2–2 before (a, b) and after (c, d) the multistage tests.

702

(1)

( )

where σ zi uzi is the polynomial dependence of the axial stress σ zi on the axial displacement uzi up to elastic limit value before unloading; σ ϕi is the value of the confining pressure; u zi1 and u zi 2 are related to the range of integration; index i means the i-th (i = 1, ..., 5) loading stage. The interesting task was to trace the changes of the value of from one stage to another in order to describe the sample energy behavior within the framework of its multistage degradation. As can be seen, there is no clear regularity in the specific energy intensity variation

Figure 2.

«Stress-strain» curve for sandstone specimen No 2-1.

Figure  3. The plots of dependence of the specific energy intensity on the stage number for tested sandstone samples.

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(Figure  3). It can be noted (from Figure  3) that for samples 1–3 and 2–3 during the last (5th) stage, the specific energy intensity increased dramatically, while for the remaining four samples, 2-1, 2-2, 1-2, 1-4 decreased. The first observation, apparently, is due to the fact that the material has not yet fully accumulated enough energy for ultimate destruction (it looks like the behavior of a brittle material), and the second observation can be explained by the fact that as plastic deformation preceded the destruction of the sample, a certain amount of the accumulated energy has already been released (for example a sample 1–4 had the highest value on the 4th stage; on the 5th stage the material behaved as plastic).

3 CONCLUSION In this study, multistage triaxial compression tests on sandstone samples were carried out with the making emphasis on the result related to a specific energy intensity behavior. Based on the processed experimental data, the following conclusions can be drawn: − In the case of each tested sample the specific energy intensities for each of the five loading stages were determined. − It was revealed that there is no common clear pattern of variation in the specific energy intensity (weak dependency on stage number). − But in the same time a tracing the changes of the value of (from one stage to another) can give some apparent explanation of material behavior. That is, depending on the sample and loading stage, geomaterial demonstrates more brittle (material has not yet fully accumulated enough energy for ultimate destruction) or more plastic (a certain amount of the accumulated energy has already been released) state.

ACKNOWLEDGMENTS We appreciate the contribution of the Shared Use Center of Geomechanical, Geophysical and Geodynamic Measurements, Siberian Branch, Russian Academy of Sciences to the present research work (State registration No AAAA-A17-117121140065-7).

REFERENCES Bro A. Analysis of multistage triaxial test results for a strain-hardening rock // International Journal of Rock Mechanics & Mining Sciences. Vol. 34, iss. 1, pp. 143–145, 1997. Gatelier N., Pellet F., Loret B. Mechanical damage of an anisotropic porous rock in cyclic triaxial tests // International Journal of Rock Mechanics & Mining Sciences. Vol. 39, iss. 3, pp. 335–354, 2002. Myers M.T. and Sharf-Aldin M.H. Comparison of Multistage to Single Stage Triaxial Tests // 2015 Proc. ARMA-2015-767, 49th U.S. Rock Mechanics, 11 p. Song H., Zhang H., Fu D., Zhang Q. Experimental analysis and characterization of damage evolution in rock under cyclic loading // International Journal of Rock Mechanics & Mining Sciences. Vol. 88, pp. 157–164, 2016. Yoshinaka R., Tran T.V., Osada M. Non-linear, stress- and strain-dependent behavior of soft rocks under cyclic triaxial conditions // International Journal of Rock Mechanics & Mining Sciences. Vol. 35, iss. 7, pp. 941–955, 1998. Youn H., Tonon F. Multi-stage triaxial test on brittle rock // International Journal of Rock Mechanics & Mining Sciences. Vol. 47, iss. 4, pp. 678–684, 2010.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

The relationship between strain, microstrain, temperature fields and microseismic emission parameters in geomodels with hole under uniaxial and biaxial loading Vladimir Ivanovich Vostrikov Chinakal Institute of Mining of the Siberian Branch of the RAS, Head of Mining Geophysics Laboratory, Novosibirsk, Russia

Olga Mikhailovna Usol’tseva Chinakal Institute of Mining of the Siberian Branch of the RAS, Head of the Shared Use Center of Geomechanical, Geophysical, and Geodynamic Measurements, Novosibirsk, Russia

Pavel Aleksandrovich Tsoi Chinakal Institute of Mining of the Siberian Branch of the RAS, Novosibirsk, Russia Novosibirsk State Technical University, Novosibirsk, Russia

Vladimir Nikolaevich Semenov Chinakal Institute of Mining of the Siberian Branch of the RAS, Chief Specialist, Novosibirsk, Russia

Olga Alekseevna Persidskaya Chinakal Institute of Mining of the Siberian Branch of the RAS, Lead Engineer, Novosibirsk, Russia

ABSTRACT: In this research the authors have carried out uniaxial and biaxial compression tests of artificial cube specimens with hole and argillite to study the process of deformation prior to failure using the multiparametric equipment designed for synchronous recording of physical fields of stresses, macrostrains, Microseismic Emission (MSE) and microstrains by speckle method. The complex data of evolution of microseismic emission signals, temperature field and microdeformation field under uniaxial and biaxial loading prior to the destruction of prismatic samples from artificial geomaterial allowed to establish the timespace relationship between the features of signal changes depending on loading level. The evolution of deformation process, development of microdamages and the formation of main rupture fracture lead to significant transformation of spectral composition of microseismic emission signals, microdeformation field, and the temperature field. In the region of future main discontinuity the temperature increases, localization of maximum microdeformations occurs and velocities of microdeformations components increase. Generation of powerful low-frequency harmonics at loads approaching the peak, can serve as a precursor of a rupture on the surface and, consequently, destruction of the geomaterial. Keywords: laboratory test, stress, strain, microseismic emission, speckle method, temperature

1

BRIEF INTRODUCTION

The processes of crack formation, discontinuity propagation and generating fields of various physical natures under the influence of critical loads in materials are related to: deformation, microseismic and electromagnetic emission, and temperature. The task of adequate description of mechanical behavior of various materials, rocks and massifs under the influence of different

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Figure 1. General view of the experiment: 1 – optical/tv measurement complex ALMEC-tv; 2 – argillite specimen; 3 – compression grips of the Instron-8802; 4 – artificial geomaterial sample.

types loading in underground construction and mining requires the investigation these field regularities, the identification of intercorrelation between them, and, ultimately, the development of new assessment parameters of geo-environment disruption, which can be used to predict the destruction of rock massifs (dumps, rock blows, technogenic earthquakes). Over the past year the review of the literature has shown that there are a number of papers devoted to the study of the features of physical fields of a different nature—the field of microdeformations by the speckle method (Wang, 2015, Kim, 2015, Shi, 2010], acoustic emission signals (Nejati, 2014, Kim, 2015, Shkuratnik, 2014, Zuev, 2014], the temperature field (Shi, 2010] at deformation of rocks. In (Nejati, 2014], the characteristics of acoustic emission signals are correlated with the deformation of various rocks with their fragility and durability. In [Hedayat, 2014] seismic wave transmission and digital image correlation were employed to study slip processes along frictional discontinuities in biaxial compression experiments were performed on gypsum specimens composed of two blocks with non-homogeneous contact surfaces. In (Kim, 2015, Shkuratnik, 2014, Zuev, 2014], the temperature field (Shi, 2010] in the deformation of rocks. In (Nejati, 2014] experimental studies and theoretical justification of the evolution of acoustic emission signals appearing in different genotypes rock samples under their mechanical loading are presented. Studies using the speckle method make it possible to study in detail at the micro level the process of formation and development of microdamages in a rock under the action of stresses (Wang, 2015, Shi, 2010]. The purpose of this study was to establish the features of the change and the relationship between stresses, deformations, microdeformations, temperature field and parameters of microseismic emission signals (MSE) under uniaxial and biaxial loading of geomaterial and rock samples. Figure 1 illustrates general view of the experiment.

2

EXPERIMENTAL PROCEDURE AND MEASUREMENT EQUIPMENT

Two series of experiments were carried out on the following samples: 1) prismatic samples of argillite by dimensions of 50 × 50 × 20 mm3 with a hole diameter of 15 mm in the center; 2) samples from an artificial geomaterial (“Neolit” glue – 1 part, calibrated sand with particle size 0.25 ÷ 0.315 mm – 3 parts, cement – 1 part, water), which were cubes by 200 mm edge with the cylindrical hole diameter 20 mm in the cube center. The average strength limit was 39.1 MPa for argillite prismatic samples under uniaxial compression, 20.1 MPa for artificial geomaterial samples under uniaxial compression and 20.3 MPa – under biaxial compression. Tests of argillite samples were carried out under uniaxial compression and tests of artificial geomaterial samples– under uniaxial and biaxial compression prior to failure on Instron 8802 servo-hydraulic press. Movement and force in the axial (vertical) direction was recorded by the measuring system of the press Instron 8802 and was saved to the computer file. 706

The moving speed of the movable gripper was varied in the range 0.1 ÷ 10 mm/min for various experiments. To implement the biaxial loading, the special device was used, which made it possible to create an additional side load, independent of the press, on the prismatic sample, which was also continuously recorded the computer file. Four microseismic KD 91 sensors were installed on 4 lateral faces of the cube to record the MSE signals. The measurement of the temperature field was carried out using by computer thermal imager TKVr-SVIT 101, the accuracy of the measurement is 0.03°. Figure  1 illustrates general view of the experiment. Microstrains were recorded using automated digital speckle photography analyzer ALMEC-tv at frequency of 27 frames per second and spatial resolution not less than 1 μm. The processing output is the coordinates and displacements of the specimen surface points and timing, which allows calculating strain tensor components (Shi et al., 2010). Figure 2a illustrates the diagram «stress σ/σlim – strain ε» obtained for artificial geomaterial sample under uniaxial and biaxial compression (σlim is the average strength limit under uniaxial compression), Figure 2b illustrates the diagram «stress σ/σlim – time t» under uniaxial compression. A large number of microseismic signals were recorded under uniaxial and biaxial compression prior to destruction of samples. As it turned out, the process of deformation can be conditionally divided into three stages, for which the same patterns of change are characteristic. Figure 3 shows the characteristic values of parameters of signals of microseismic emission

Figure 2. Diagram «stress σ/σlim – strain ε» for artificial geomaterial sample under uniaxial (black) and biaxial (red) compression (σlim is the average strength limit under uniaxial compression) – a; diagram «σ/σlim – time t».

Figure  3. Characteristics of microseismic emission signals averaged over 10  secondsinterval, under uniaxial loading of artificial geomaterialsample: a – acceleration amplitudevalues A (m/s2); b – number of signals N.

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obtained for the three isolated loading stages of the diagram «stress σ/σlim – time t». The data obtained under uniaxial compression loading is shown in Fig. 2b. Figure 3 illustrates the dependence of characteristics of microseismic emission signals on time under uniaxial loading of cubic samples from an artificial geomaterial, averaged over an interval of 10 seconds: 3a—values of the acceleration amplitude A (m/s2); 3b – number of MSE signals N; in accordance with the diagram «σ/σlim – t» – 3d. The insignificant number of small amplitude MSE signals fixed before levels σ/σlim = 0,3 is not shown in the diagrams, since these signals are most likely the cause of the alignment of the roughness on the side faces of the sample and are not related to the formation of the main discontinuity. At stress levels σ/σlim = 0,3 ÷ 0,4 (point 1), the first MSE signals are recorded, the acceleration magnitude is 0,1 ÷ 0,2 m/s2, the broadband frequency signal is 8 ÷ 24 kHz. Then, as the load increases, the number of signals increases too, distributing chaotically evenly in the volume of the sample. At stress levels σ/σlim = 0,5 ÷ 0,8 (point 2), the amplitude of the MSE signal increases, its magnitude reaches a value of 0.3 ÷ 0,35 m/s2. At the same time, the frequency spectrum is somewhat narrowed and shifted to low frequencies of f = 12 ÷ 18 kHz, the distance between the hypocenters decreases, which indicates the localization of microdefects. At values of stresses close to the ultimate strength, the certain period of MSE absence before the formation of the main discontinuity. At the last deformation stage at a stress close to σ/σlim = 0.8 ÷ 1 (point 3), the number of microdamages and MSE signals increases significantly, their energy increases, the frequency spectrum is further narrowed and shifted to low frequencies, up to f = 8 ÷ 10 kHz. A powerful low-frequency signal of 8 ÷ 12 kHz is generated at the time of the main discontinuity initiation. The analysis of microdeformation fields for specimens from argillite and artificial geomaterials under uniaxial and biaxial compression has shown that plastic deformation is inhomogeneous from the beginning of the loading, which is related to the mineralogical and structural inhomogeneities of test samples. Figure 4 (a, b, c) illustrates deformation mapping shots of scanned surface of the part of working surface of cubic sample for deformation component in the x-direction (perpendicular to the load axes) at three strain levels. Green color of deformation component corresponds to positive values (increasing in size), red color – decreasing in size, black color – zero deformations, white color – deformation exceeding the value of 0.007. Despite the fact that the given kind of loading of rock sample is with constant speed compression, nevertheless, both the shortening and elongation regions are present in the space-time field of microdeformations scanned surfaces. At the first stage of loading (point 1), microdeformations field is chaotically inhomogeneous, elongation-shortening zones are randomly distributed over sample surface, the vibrations of microdeformation components are practically absent. At the 2nd stage of deformation (point 2), microdeformations field becomes more inhomogeneous, maximum microdeformation zones occur, the values of which exceed the average values over sample surface, the amplitudes of the oscillations of microdeformations and their velocities in the region of future destruction increase. At the

Figure 4. Shots of deformation mapping of scanned surface of working surface part of cubic sample for deformation component in the x-direction at three strain levels: point 1 (a), point 2 (b), point 3 (c).

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Figure 5. Temperature field on the sample surface at loading moments t = 0,8 tm (a, b, c) and t = 0,9 tm (d, e, f), photograph of the corresponding destructed rock sample (g).

third stage of deformation (point 3), maximum microdeformations zones are localized in the certain volume of the sample, which indicates the beginning main discontinuity formation. Maps of the space-time distribution of the MSE signals are schematically shown in Figure 4 (d, e, f), in accordance with three stages of loading. Analysis of temperature data shows that at the beginning stage of loading, temperature field and have no obvious change (Figure 5). With the loading development, strains focus around the hole gradually, over and under of the hole appear tensile strain along the direction of loading and grow gradually. At the values t = 0,8 tm the temperature increases in the region with an X-shaped pattern near the hole. When the loading time is t = 0,9 tm, the red area to the left of the hole increases in size. On the diagram of y-component of the microdeformation there is a correspondence— this is the region of higher values of tensile microdeformations. With further increase in the load, a main crack appears at the top left of the hole, then from the top right, at the last moment—a vertical crack under the slope and the sample is completely destructed. The temperature rise in the zones of localization of the maximum microdeformation is 1.5°. With an increase of loading rate from 0.1 mm/min to 6 mm/min, these patterns of temperature field variation manifest more contrastively.

3

CONCLUSION

The complex analysis of evolution of microseismic emission signals, strain, stress, microdeformation field and temperature field made it possible to determine the regularities of the change of these parameters and their relationship with the loading stage of geomaterials and rocks samples, which makes it possible to predict the region of the main rupture appearance on the sample surface at loads less than the peak value, when the sample still maintains its visible intact state.

ACKNOWLEDGMENTS This study has been carried with partial financial support of the Russian Foundation for Basic Research, projects nos. 16-05-00992, using equipment of the Shared Use Center for Geomechanical, Geophysical and Geodynamic Measurements, Siberian Branch, Russian Academy of Sciences. 709

REFERENCES Hedayat A., Pyrak – Nolte L.J., Bobet A. Multi – Modal Monitoring of Slip Along Frictional Discontinuities. 2014, Rock Mechanics and Rock Engineering, vol. 47, issue 5, pp. 1575–1587. Kim J.S., Lee K.S., Cho W.J., Choi H.J., Cho G.C. A Comparative Evaluation of Stress–Strain and Acoustic Emission Methods for Quantitative Damage Assessments of Brittle Rock. 2015, Rock Mechanics and Rock Engineering, vol. 48, issue 2, pp. 495–508. Reza Nejati H., Ghazvinian A. Brittleness Effect on Rock Fatigue Damage Evolution//Rock Mechanics and Rock Engineering, 2014, Volume 47, Issue 5, pp. 1839–1848. Shi Y., He Q., Liu S., Wu L. The time – space relationship between strain, temperature and acoustic emission of loaded rock. 2010 Progress In Electromagnetics Research Symposium Proceedings, Xi’an, China, pp. 114–118. Shkuratnik V.L., Novikov E.A., Oshkin R.O. Experimental analysis of thermally stimulated acoustic emission in various—genotype rock specimens under uniaxial compression. 2014 Journal of Mining Science, vol. 50, issue 2, pp. 249–255. Wang L., Bornert M., Heripre E., Chanchole S., Pouya A., Halphen B. The Mechanisms of Deformation and Damage of Mudstones: A Micro—scale Study Combining ESEM and DIC. 2015, Rock Mechanics and Rock Engineering, vol. 48, issue 5, pp. 1913–1926. Zuev L.B., Barannikova S.A., Nadezhkin M.V., Gorbatenko V.V. Localization of deformation and prognostibility of rock failure. 2014 Journal of Mining Science, vol. 50, issue 1, pp. 43–49.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Monitoring of coal pillars yielding during room and pillar extraction at the great depth Petr Waclawik, Radovan Kukutsch, Petr Konicek & Vlastimil Kajzar The Czech Academy of Sciences, Institute of Geonics, Ostrava-Poruba, Studentska, Czech Republic

ABSTRACT: A considerable amount of coal reserves are located in protection pillars that lie under built-up region in active mining areas at the Czech part of the Upper Silesian Coal Basin. The commonly used controlled caving longwall mining method is not applicable in these areas because significant deformation of the surface is not permitted. For this reason the room and pillar method with stable coal pillars has been tested in order to minimise subsidence of surface. Stress-deformation monitoring was essential as this was the first application of the conventional room and pillar mining method within the Upper Silesian Coal Basin mines. More than six kilometres of roadways were driven within two panels during last three years. To determine pillar stability, vertical stress and horizontal displacement of coal pillars were measured in coal pillars which are located within a row of pillars forming the panels. Two monitored pillars diamond in shape and slightly irregular sides have been observed into the first mined panel “V” and three monitored pillars have been observed into the second panel “II”. To measure the increase in vertical stress due to mining, hydraulic stress cells were installed in each coal pillar. The 5-level multipoint rib extensometers measured displacements of all sides within each monitored pillar. The results of stress-deformation monitoring allowed pillar loading and yielding characteristics to be described. Keywords: stress-deformation, monitoring, room and pillar, coal pillar, yielding, displacement

1

INTRODUCTION

The pilot project of the mining modified room and pillar method with stable pillars has been running since 2014. The method was tested within the shaft protective pillar located in CSM-North Mine (Karvina coal sub-basin in the Czech part of the Upper Silesian Coal Basin—USCB) coal seam No. 30, where the risk of rockbursts was low and roof conditions were acceptable for bolting reinforcing. However, the variable geology and several faults of regional importance complicated the mining conditions. The project includes the detailed geomechanical monitoring of stress and deformation in the driven roadways and the surrounding rock mass. Monitored pillars with 3.5 m in high and different sizes were selected to determine stress-deformation characteristics under different geotechnical conditions. Two monitored pillars diamond in shape and slightly irregular sides were approximately 860 m2 and 1200 m2 in size into the first mined panel “V” (locality A) and three monitored pillars were approximately 590 m2, 590 m2 and 730 m2 in size into the second panel “II” (locality B). Mining depth of room and pillar trial ranged from 700 to 900 m, being perhaps the deepest room and pillar mining in the world coal mines. Monitored data and other analyses are essential to establishing procedures for a safe room and pillar method of mining within USCB. The results are also important for worldwide mining, for the largest coal producers will reach higher mining depth in near future.

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Figure 1.

2

Tectonic situation and position of monitored pillars in panel V and II.

GEOLOGICAL AND MINING CONDITIONS

The targeted coal seam (No. 30) is at a depth of approximately 700 m to 900 m below the surface. The thickness of coal seam is extremely variable (from 180 to 520 cm) within the proposed mining area. The thickness of coal seam ranges 300 cm to 350 cm in monitored pillars. The strata dip oriented in the north-east direction ranges from 8° to 17°. Occasionally the dip of the coal seam can reach up to 20°. There are several faults of regional importance in the area of the CSM-North shaft protective pillar (see Fig. 1). The significant regional tectonic fault zone “Eastern Thrust” (Waclawik et al. 2013, Grygar & Waclawik 2011) divides the area of the protective pillar into two separate blocks with different geotechnical conditions. The immediate roof above concerned coal seam No. 30 consists of a thin 0.1 m thick sandy claystone layer. This layer is relatively weak and disturbed with slickensides present on the surrounding bedding planes. Above this is 5 m thick siltstone overlain with 6 m thick medium-grained sandstone and 0.3  m thick coal seam. The immediate floor below mined seam No. 30 consists of 0.5 m thick siltstone underlain by 0.6 m thick coal seam No. 31. The interbedded siltstone and sandstone layers follow down to coal seam No. 32 located around 10 m below the seam No. 30. More details about natural and mining conditions can be found in previous published papers (e.g. Waclawik et al. 2016, Waclawik et al. 2017).

3

DESIGN OF GEOMECHANICAL MONITORING

Monitoring of stress and the deformation state of rock mass is an essential requirement for the design of safe and successful room and pillar method that can be applied in the Czech part of the USCB. In the context of stress and deformation, the monitoring are covering 712

deformability of rock overlaying the room and pillar roadways, measuring pre-mining stress and stress change monitoring in rock and coal during mining, deformability of coal pillars, load on the installed cable bolts, roadway convergence monitoring. On top of all that the seismology and seismo-acoustic monitoring were carried out to characterize fracturing of rock mass during mining. The instrument locations are shown in Figures  2 and 3. To monitor roof deformation, 5-level multipoint extensometers monitored roof displacements (VE1 to VE14  in locality A; IIE1 to IIE19  in locality B) and strain gauged rockbolts (VS1 to VS11  in locality A) were installed at various locations. The 5-level multipoint rib extensometers (VEH1 to VEH8  in locality A; IIEH1 to IIEH12  in locality B) measured displacements of all sides within each monitored pillar were installed. Vertical and horizontal displacements together with the convergence measurements (VP1 to VP9 in locality A; IIP1 to IIP12 in locality B), changes in vertical pillar loads and the periodic 3D laser scanning of the overall roadway displacements (roof, rib and floor heave) provided data to evaluate coal pillars deformability. To describe pre-mining stress-state condition of coal pillars area 3-dimensional CCBO stress overcoring cells (Obara & Sugawara, 2003; Stas, Knejzlik & Rambousky, 2004) were used (VCCBO1, VCCBO2 in locality A; IICCBO1, IICCBO2 in locality B) and 3-dimensional CCBM stress change monitoring cells (Stas, Knejzlik, Palla, Soucek & Waclawik, 2011; Stas, Soucek, & Knejzlik, 2007) were installed to measure stress changes during mining (VCCBM1 to VCCBM8 in locality A; IICCBM1 to IICCBM3  in locality B). The 1-dimensional hydraulic stress monitoring cells were installed at various depths in each pillar to measure vertical stress (VSC1 to VSC8 in locality A; IISC1 to IISC5 in locality B), seven hydraulic dynamometer load cells measured the cable bolt

Figure 2.

Positions of the monitoring equipment in locality A.

Figure 3.

Positions of the monitoring equipment in locality B.

713

loads installed at the roadway intersections (VD1 to VD7 in locality A). The monitoring equipment were reduced in locality B due to monitored results from locality A. Due to minimal roof displacement during the whole time of monitoring in locality A, the strain gauged rockbolts, hydraulic dynamometers have not been installed in locality B. The vertical 5-level multipoint extensometers were substitute by the cheaper 3-level multipoint extensometers. 4

RESULT AND DISCUSSION

The displacement and deformation development are determinative factor for assessment of coal pillar stability. The results of pillar displacement and loading monitoring allowed the monitored pillars deformation characteristics to be described. The data showed that the monitored coal pillar ribs displaced into the roadway mainly due to a large vertical stress and the presence of weak slickensides layers above and below the seam. This mechanism has caused large floor heave, rib convergence, therefore weakening the coal and causing the pillar to yield (Waclawik et al. 2016). In locality A, due to the incorrect stress cell installation within the larger coal pillar (V1), the loading results were limited to the smaller pillar (V2) only. The stress cells installed in coal pillar V2 gave the information about stress changes in coal pillar, depending on coal pillars forming. The maximum vertical load of 49 MPa on the stress cell VSC4 was registered. Considering the position of the load cell, and the registered values of the other stress cells, it was the extreme short-time load of the central part of the coal pillar V2. On basis of data from stress cells (vertical load) and horizontal extensometers (displacement) we can define development of yielding zones in coal pillar (Waclawik et al. 2016). In locality B, the maximum vertical load of 39 MPa was registered on the stress cell IISC2 (monitored pillar II1). The maximum vertical load of 16 MPa in monitored pillar II2 and 14 MPa in monitored pillar II3 were recorded only. These relatively small values of maximum vertical load were influenced by more rapid yielding of coal pillar to the depth in locality B (compare results from horizontal extensometers – see Figs.  5, 6). The smaller size of coal pillars, added number of pillars in row and presence of overthrust above monitored pillars significantly affected rate of coal pillars yielding. The displacements of the coal rib recorded by horizontal extensometers are comparatively different within the monitored pillars. In locality A, the larger displacements were recorded by horizontal extensometers installed in monitored pillar V2. The values of displacement ranged between 212 mm to 300 mm in monitored pillar V2 (see Fig. 5). The displacement coal ribs of monitored pillar V1 ranged between 59 mm to 223 mm. These values indicate that the displacement of the coal pillar V2 as large as monitored coal pillar V1, caused by higher area loading. From the results recorded by the horizontal extensometers in location B, it is evident that the maximum horizontal displacement is 478 mm (IIEh5) in the monitored pillar II2. Also, in the monitored pillar II1, the relatively higher values are recorded (468 mm – IIEh1, 379 mm – IIEh3). Even in the monitored pillar II3, which was last formed, the values of displacements of around 300 mm (IIEh9 – 344 mm, IIEh11 – 353 mm) are reached.

Figure 4. Pillar load results in monitored pillar V2 – locality A (on the left) and load results in monitored pillars II1, II2 and II3 – locality B (on the right).

714

In locality A, the major strata displacement zone occurred in the area 1.5–5 m from the pillar side (see Fig. 5). The displacement at the depth of 0–1.5 m was much smaller due to the efficiency of rock bolts. In two cases (extensometers VEH7, VEH8) had no influence of the rock bolts and the maximum strata displacements occurred at the depth of 0–3 m into the pillar. The reason for this was considered to be the primary pillar damage by fractures in highly stressed ground. In locality B, the major strata displacement zone occurred mainly at the depth of 5–8.5  m from the side (see Fig.  6). The significant strata separation was recorded at the deepest monitored zone 8.5–12  m, which indicated that the monitored pillars were totally fractured. In most cases there was no measured rockbolt influence on coal behaviour and the significant strata separation occurred at the depth of 0–1.5 m into the pillar (see Fig. 6). In addition to absolute values of pillars displacement, data from horizontal extensometers provided important information about the dynamics of displacement of coal pillars.

Figure 5. Example of horizontal displacement indicated by rib extensometers in monitored locality A.

Figure 6. Example of horizontal displacement indicated by rib extensometers in monitored locality B.

Figure 7.

Rate of the V2 coal pillar displacements versus time.

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Concerning the dynamics, we could see a decrease of displacements during the whole evaluation period (see Fig. 7). The monthly gain of displacements reduced up to 25 times during monitoring period of 32 months in locality A. The monthly gain of displacements stabilised at 3 mm/month during the last eighteen month of monitoring period. Continuous deformation processes indicate, that yielding of coal pillars is still in progress therefore the long-term stability of coal pillars has not been established yet. Similar dynamic of displacement changes was recorded in locality B during monitoring period of 15 months only. 5

CONCLUSION

Evaluation from presented part of monitoring contribute to better knowledge of yielding assessment of coal pillar during room and pillar mining in great depth and difficult natural and mining conditions. Based on the long-term stress-deformation monitoring (up to 32 months), it was possible to determine the operating stability and long-term stability of coal pillars. Safe operating stability has been proven for all coal pillars formed within the trial operation of room and pillar method. The long-term stability of coal pillars have not been confirmed yet because the deformation processes of coal pillars are still in progress The room and pillar method was trialled in the shaft protective pillar at the CSM Mine located in the Upper Silesian Coal Basin. Coal pillar monitoring was essential as this was the first application of the conventional room and pillar mining method in USCB mines. Based on the measurements, numerical modelling and other analyses were possible to assess stability of the coal pillars at the great depth. The results are also important for global mining, for the largest coal producers will reach higher mining depth in near future. ACKNOWLEDGMENTS This article was written in connection with the Project Institute of Clean Technologies for Mining and Utilization of Raw Materials for Energy Use—Sustainability Program (reg. no. CZ.1.05/2.1.00/03.0082 and MSMT LO1406), which is supported by the Research and Development for Innovations Operational Programme financed by the Structural Funds of the European Union and the Czech Republic project for the long-term conceptual development of research organisations (RVO: 68145535).

REFERENCES Grygar, R and Waclawik, P, 2011. Structural-tectonic conditions of Karvina Subbasin with regard to its position in the apical zone of Variscan accretion wedge, Acta Montanistica Slovaca, Vol. 16, No. 2, pp. 159–175. Obara, Y and Sugawara, K, 2003. Updating the use of the CCBO cell in Japan: overcoring case studies, International Journal of Rock Mechanics and Mining Sciences, Vol. 40, pp. 1189–1203. Stas, L, Knejzlik, J, Palla, L, Soucek, K and Waclawik, P, 2011. Measurement of stress changes using a Compact Conical-ended Borehole Monitoring. Geotechnical Testing Journal, Vol. 34, No. 6, p. 685–693. Stas, L, Soucek, K and Knejzlik, J, 2007. Conical borehole strain gauge probe applied to induced rock stress changes measurement. In Proceedings of 12th International Congress on Energy and Mineral Resources, p. 507–516. Stas, L, Knejzlik, J, and Rambouský, Z, 2004. Development of conical probe for stress measurement by borehole overcoring method. Acta Geodyn. Geomater, Vol. 1, No. 4. Waclawik, P, Snuparek, R and Kukutsch, R, 2017. Rock bolting at the room and pillar method at great depths. Symposium of the International Society for Rock mechanics, 20–22 June 2017, Procedia Engineering. Volume 191, pp. 575–582. Waclawik, P, Ptacek, J, Konicek, P, Kukutsch, R, and Nemcik, J, 2016. Stress state monitoring of coal pillars during room and pillar extraction, Journal of Sustainable Mining, Vol. 15, Issue 2, pp. 49–56. Waclawik, P, Ptacek, J and Grygar, R, 2013. Structural and stress analysis of mining practice in the Upper Silesian Coal Basin, Acta Geodyn. Geomater, Vol. 10, Issue 2, pp. 255–265.

716

Nonlinear problems in rock mechanics

Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Ultimate bearing capacity analysis of foundation on rock masses using the Hoek-Brown failure criterion A.A. Chepurnova Gersevanov’s Research Institute of Bases and Underground Structures (NIIOSP)—JSC Research Center of Construction, Moscow, Russia

ABSTRACT: Among many issues to be solved in the engineering structures design, one of the most controversial is estimation the strength and stability of rock masses. Rock mass is a discrete heterogeneous anisotropic medium, which properties are rather difficult to reflect correctly within the used models. In this paper, the possibility of determining the ultimate bearing capacity of foundation resting on naturally discontinuing rock mass with the HoekBrown failure criterion (Hoek, 2007) implemented in the geotechnical software Optum CE (Krabbenhoft, 2016) is presented. Numerical solutions of the bearing capacity are performed by the finite element method with determination of the upper and lower bounds of the ultimate load. The results show good agreement with analytical solution results. Alternatively, an approach to estimate the bearing capacity of rock masses by fitting the linear MohrCoulomb relationship to the curved Hoek-Brown solution is observed.

1

INTRODUCTION

Rock masses, in general case, are characterized by substantial heterogeneity at the microscopic and macroscopic level, anisotropy of properties, multiphase. Herein, estimation of a fractured rock mass strength is considered, with no dominant systems of cracks and inhomogeneities of a known direction, but multiple fracturing allows consider it as a homogeneous isotropic mass which properties are different from intact structure. In this case, analyzing the bearing capacity of closely fractured or very weak rock mass can be performed in accordance with the fracture mechanism, similar to soil mechanics (Wyllie, 1999, Zertsalov, 2014). The simplified analysis assumes straight lines for the failure surfaces and ignores the weight of the rock in the foundation as well as the shear stresses that develop along the vertical interface between two wedges. Shear strength parameters along vertical shear planes can be assumed the same as for a rock mass. The analysis is based on the assumption that active and passive pressure wedges (zones) are formed in the rock under the footing, defined by straight lines, and the shear strength parameters of these surfaces corresponds to those of the rock mass. Figure 1 shows a strip footing bearing on a horizontal rock surface under conditions of plane deformation; zone A experiences a triaxial contraction. The major principal stress in zone A is determined by the footing pressure, if the weight of rock beneath the footing is neglected with the following relation:

σ 1A = qu

(1)

Zone B also undergoes a triaxial compression with the major principal stress acting horizontally, and the minor principal stress acting vertical; with the foundation position at the ground surface σ3B = 0. At the moment of foundation failure both zones shear simultaneously

719

Figure 1.

Analysis of bearing capacity of rock mass (after Wyllie, 1999).

and the minor principal stress in zone A, σ3A equals the major principal stress in zone B, σ1B where passive pressures are realized. The minor principal stresses in zone A is produced by the resistance of zone B to be compressed and equal to the compressive strength of the rock mass σc. There are several approaches to determining the strength of a rock mass, in this paper the empirical failure criterion of Hoek-Brown, which takes into account fractures of rock and incorporated into the Optum CE software, is considered. 2

HOEK-BROWN FAILURE CRITERION

The Hoek-Brown Failure Criterion, HBFC, (Hoek, 2007) is an example of a nonlinear criterion for shear strength, developed specifically for fractured rock mass. The starting point for the criterion was the Griffiths theory for brittle fracture, however, the process of deriving the criterion was based on trial and error method. The empirical criterion is obtained as a result of processing triaxial tests of rock samples. As a result of the almost twenty-year history of the criterion development, a nonlinear relationship between the major and minor principal stresses was recorded, written in the following form: ⎛ ⎞ σ σ 1 = σ 3 + σ ci ⎜ mb ⋅ 3 + s⎟ σ ⎝ ⎠ ci

α

(2)

where σci is the uniaxial compressive strength of the intact rock, in MPa, mb, s, α are constants for the rock mass which depends on the rock type, its quality and in the process of developing the criterion undergone alteration. Table 1 shows the dependencies for their determination, developed for the criterion version of 1997 and 2002 years. In the above mentioned equations of Table 1: mi is the material constant (i = intact), GSI is the Geological Strength Index; D is a factor that depends on the degree of disturbance to which the rock mass has been subjected by blast damage and stress relaxation and vary from D = 0 for undisturbed in situ rock mass to D = 1 for disturbed rock mass properties. The GSI was introduced by Hoek and in many respects is similar to the Rock Mass Raiting (RMR) developed by Z. Bieniawski (Bieniawski, 1976). Parameter D is introduced into the criterion for a smoother transition from very good quality to extremely poor (GSI < 25). An intact rock mass is counted with parameters: mb = mi, s = 1, α = 0,5. In general, the criterion parameters mi, GSI, D are empirical constants assigned in accordance with experimental field and laboratory data, which purpose is to relate the physical and mechanical properties of rock mass to its structural discontinuities, degree of fracturing, etc. Its determination in accordance with authors (Sas, 2015) in accordance with the requirements of the Russian’ Code of Regulation is possible to achieve, and is not the subject of discussion in the article. 720

Table 1.

Estimation of Hoek-Brown parameters.

Parameter

Generalized HBFC, Hoek et al., 1997

mb

mb

s

α

Generalized HBFC, Hoek et al., 2002

S − 100 ⎞ ⎛ GSI mi exp x ⎜ ⎟⎠ ⎝ 28

mb

S − 100 ⎞ ⎛ GSI mi exp x ⎜ ⎝ 24 − 14D ⎟⎠

s

s

GSI < 25

S − 100 ⎞ ⎛ GSI exp ⎜ ⎟⎠ ⎝ 9 s=0

S − 100 ⎞ ⎛ GSI exp ⎜ ⎝ 9 − 3D ⎟⎠

GSI > 25

α = 0,5

α=

GSI < 25

α = 0, 65 −

1 1 −GSI + e S /15 − e −20 / 3 2 6

GSI > 25

GSI S 200

(

)

The unconfined compressive strength is obtained by setting σ3 = 0 in Eq. (2), giving

σ ci sα

σc

(3)

The tensile strength at σ1 = 0 from (2) is expressed as follows:

σt = −

sσ ci mb

(4)

It is important to note again that the HBFC assumes isotropic rock and rock mass behavior and extends to those rock masses in which there are a sufficient number of closely spaced discontinuities with similar surface characteristics. Thus, it is possible to assume isotropic behavior and failure through discontinuities. Where the block size is of the same order as the analyzed system (i.e. “footing-rock mass”), or when one of the discontinuities sets is significantly weaker than the others, the HBFC is not applicable (Hoek, 2007). In these cases, the stability of the structure should be analyzed by considering failure mechanisms associated with sliding or rotation of blocks and wedges defined by intersecting structural features. Despite the popularity of the HBFC and its obvious advantages, practical analysis of rock masses (using numerical methods) in most cases is carried out using a linear Mohr-Coulomb failure criterion. Equivalent Mohr-Coulomb strength parameters c′, ϕ ′ of rock with specified characteristics (σci, mi, GSI, D) can be obtained by fitting a linear relationship to the curved generated by Eq. 2 for a range of minor principal stress values defined by σ t < σ < σ 3′ max (Hoek, 2007). This results in the following equations: ⎡ ϕ ′ = sin−1 ⎢ ⎢⎣ 2 ( + c′ =

σ ci ⎡⎣( +

(

+

))((

+

)

⎤ 6α mb ( + bσ 3′ n )α −1 α −1 ⎥ ) ( + ) + 6α mb ( + bσ 3′ n ) ⎥⎦

)s + (

(

) mbσ ′

−

1 + 6α mb ( where σ 3′ n

b

(5)

⎤⎦ s + mbσ 3′ n )α −1

)

′ n )α −1 / (( +

σ 3′ n /σ ci

))((

+

))

(6)

(7)

′ ) for bearing Note, that precise recommendations for upper limit of confining stress (σ 3max capacity analysis are not given. In any case, stress state over which the relationship between the Hoek-Brown and the Mohr-Coulomb criteria is considered has to be determined for each individual case and particular problem. Thus, for example, an upper bound estimate of the stress state can be found from an elastic stress analysis for opening and slope (Sjöberg, 1997). 721

This approach gives slightly lower friction angle and slightly higher cohesion, depending on the curvature of the actual Hoek-Brown failure envelope. For the generalized HBFC criterion written in the Eq. 2, from experience and trial and error, Hoek and Brown suggest a value of σ 3′ max σ ci /4 that will provide consistent result (Hoek, 2007).

3

STATEMENT OF A PROBLEM

The plane strain bearing capacity problem of a strip footing of width B resting on jointed rock mass is illustrated in Fig. 2. The ultimate capacity can be expressed by analogy with formula (1) by the following relationship: qu

Nσ 0 ⋅ σ ci

(8)

where Nσ 0 is a dimensionless bearing capacity factor, depending on the values of the weightless (γ = 0) Hoek-Brown material mi, GSI, D. Accordingly, the HBFC implies an increase in the bearing capacity with increasing values of the parameters mi, GSI (for σci = const). Problem formulation in Eq. (8) is a convenient way of expressing the ultimate bearing capacity as a function of uniaxial compression strength of a sample and agrees with the work of other authors. The strength of rock mass is determined by the Hoek-Brown criterion (2), which establishes the major principal stress, indicating the intensity of the foundation pressure on the base. For the case where footing is located on the rock surface, the minor principal stress at the moment of failure is determined by Eq. (3). The failure mechanism of rock masses is determined in most cases by discontinuities and their location, which allows to be conditionally assigned into three structural groups schematically shown in Fig. 2 (Merifield, 2006). Rock masses suitable for the description of group I (intact tock) and group III (heavily jointed with ‘‘small spacing’’ between discontinuities so that, on the scale of the problem, it can be regarded as an isotropic assembly of interlocking particles) are applicable to the Hoek-Brown failure criterion and considered as a homogeneous and isotropic mass. Further, the ultimate bearing capacity of rock herein is estimated for a practical range of values mi, GSI at σci = 10 MPa, γ = 0, D = 0. It should be noted that in connection with some uncertainties in the Hoek-Brown model parameters designation including lack of certain recommendations for their determination and taking into account national peculiarities,

Figure 2.

Hoek-Brown failure criterion applicability for shallow foundations (after Merifield, 2006).

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analysis of rock masses stability and bearing capacity in the Russian Federation more often is produced by means of the Mohr-Coulomb model. In this connection, ultimate bearing capacity of rock is also determined through the equivalent strength parameters c′, ϕ ′, defined for two ranges of the minor principal stress. The upper estimate of the ultimate load capacity is given for 0 < σ 3 < σ 3emax (hereinafter referred to as MC (1)), and the lower limit for 0 σ 3 0 25σ ci (denoted as MC (2)). 4

HOEK-BROWN SOIL MODEL IN OPTUM CE

The Optum CE is a relatively new geotechnical software complex appeared on the international market. The plain strain version G2 (Krabbenhoft, 2016) is available for free download from the web-site http://optumce.com/, 3D beta version is under active testing now. Among the variety of geotechnical problems OptumG2 solves the system of equations of limiting equilibrium method. The key features of the computational core of the program are: − Strength condition is considered in the inequality mode; − Mathematics optimization problem is solved, namely, applied load is maximized if equality and inequalities are observed; − Implementation of an arbitrary set of boundary conditions; − Automatic adaptive mesh refinement to maximize accuracy while keeping the computational cost at a minimum (see Fig. 3). Concerning the limit analysis of the strip footing in general, OptumG2 implements features that are fundamentally different from other finite element programs, namely: 1. A cohesion identically equal to zero can be used (actual for cohesionless soils); 2. Definition of the upper and lower bounds, which gives a direct measure of the error in the numerical solution. In addition, it is often observed that the mean between the upper and lower bounds gives a good estimate of the exact solution—even if the gap between the boundaries is significant; 3. The singularity at the footing edge may be handled using a special tool (so-called the Mesh Fan). This feature constructs a fan of elements around the singularity which often leads to improved solutions, especially for lower bound elements, which leads to more precise solutions, especially for the elements of the lower boundary (Krabbenhoft, 2016). During verification OptumG2, the program developers simulated various situations, including the problem of determining the ultimate bearing capacity of rock using the HBFC (2). The maximum strength of rock foundation is determined by calculating the upper and lower bounds of the footing pressure for the range of rock parameters of the Hoek-Brown

Figure 3. Limited analysis solution for a strip footing resting on rock mass in OptumG2: mesh adaptation to calculate the lower bound (a) and an enlarged fragment of a Mesh Fan at footing edge (b).

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Figure 4. Bearing capacity factors for strip footing on weightless Hoek-Brown material (Krabbenhoft, 2016).

model mi, GSI at γ = 0, σci = 10 MPa (Krabbenhoft, 2016). Limited analysis solution is shown in Fig. 3. The results are presented as a relation of bearing capacity factors Nσ 0 on parameter of undisturbed material mi for geological strength index range GSI = 30,40,50 and are shown in Fig. 4. As can be seen from the graph, numerical results determined with OptumG2 are within the close proximity to the exact solutions (obtained by Merifield and Serrano). Numerical simulation of limit analysis in OptumG2 using the Hoek-Brown model resulted, as expected, in an increase in the ultimate bearing capacity for a given GSI with increasing mi. The Fig. 4 indicates that the bearing capacity factor Nσ 0 increases non-linearly with mi and GSI. The upper bounds tend to be somewhat more accurate than the lower bounds and the accuracy decreases with increasing material strength. Calculation results of rock with lower value of mi tend to be more accurate. 5

RESULTS OF NUMERICAL SIMULATION

In OptumG2, as well as in some others, for example, FLAC (Itasca, 2015), is implemented algorithm that allow to “convert” a curved Hoek-Brown failure envelop to a linear MohrCoulomb envelop by determining the tangent to the curved envelop at the calculation stress in each element and for each calculation step. The tangent at each section has its own pair of equivalent strength parameters (5) and (6), which vary throughout the model. However, for many practical applications it is necessary to approximate the curved envelop to with one set of equivalent strength parameters c′, ϕ ′ or the straight line Mohr-Coulomb envelope. Therefore, a methodology for determining one set of such parameters is needed. Further, Table 2 shows the results of rock strength (in terms of bearing capacity factor Nσ 0 from (8)) obtained in OptumG2 for various parameter group of the Hoek-Brown model (mi, GSI ) and for the Mohr-Coulomb model with equivalent strength parameters defined for 0 < σ 3 < σ 3emax where σ 3emax is a maximum value of the minor principal stress determined by an elastic analysis (MC (1)); and for 0 < σ3 < 0.25σci (MC (2)). Bearing capacity factor for three serious of calculation is carried out by determining the upper and lower boundaries and Table 2 shows the mean values of Nσ0 (note, that the error in determining the mean is within 4%). Fig. 5a shows the ultimate bearing capacity solutions of fractured rock GSI = 25 for different values of mi, obtained for both the Hoek-Brown (solid line) and Mohr-Coulomb (dashed lines) criteria. Strength envelops for the same parameters are shown in Fig. 5b. 724

Table 2.

Results for the bearing capacity factor Nσ0 of the fractured weightless rock.

Hoek-Brown

Mohr-Coulomb MC (1)

GSI

mi

Nσ 0 OptumG2 (Krabbenhoft, 2016)

10

1 7 10 15 17 25 1 7 10 15 17 25 1 7 10 15 17 25 1 7 10 15 17 25

0,022 0,283 0,392 0,556 0,623 0,857 0,117 0,616 0,794 1,060 1,174 1,504 0,380 1,265 1,625 2,144 2,358 2,990 0,669 1,948 2,469 3,320 3,666 5,007

25

50

65

0 < σ 3 < σ 3emax c′, kPa

MC (2) Nσ 0 OptumG2 0 500 m3) For the sake of brevity, here we present the frequency for 1, 10, and 100 m3 only, which are respectively 0.03, 0.004 and 0.0006 events/year. The probability of reaching the trail is calculated using the simulation program RockGIS developed by our research group, whose details and characteristics are found in Matas et al. (2017). The program includes a fragmentation module based on a rockfall fractal fragmentation model (Ruiz-Carulla et al. 2017). The parameters of the model for both fragmentation and propagation were calibrated using the rockfall event of February 2017 and the location of a few fallen blocks that were removed from the cliff during prevention works carried out in March 2015. Each source released 100 rock masses than remained intact along the path and 10 rock masses that fragmented, totaling 32,000 and 3,200  simulations respectively. The effect of fragmentation on the rockfall runout and impact probability is illustrated in Figure 2. For the sake of visualization, the figure only shows one trajectory of intact rock fall masses from a few selected detachment sources (top). For the same reason, only one fragmental rockfall event is shown as well (bottom). In the latter, the trajectories of the rock fragments are displayed. The simulations illustrate the effect of the topography in the generation of preferential trajectories, the effect of fragmentation on both runout and the kinetic energies of the blocks, and the efficiency of the barriers. The simulation of the fragmented 10 m3 rockfalls generates a completely different scenario. First, fragmentation produces a high number of divergent trajectories. The width of the cone of block fragments increases with the distance from the impact points and with the number

Figure 2. Top: trajectories of rockfall masses of 10 m3 without fragmentation on pathway A. Considering the presence (right) or absence of rockfall barriers; Bottom: trajectories of 10 m3 rockfall masses with fragmentation. Considering the presence (right) or absence of rockfall barriers; The existing rockfall barrier are represented by blue lines. The kinetic energies are displayed following a color code (from high to low: red orange, yellow and green).

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of impacts. At the trail, the affected length may increase by a factor of between 9 and 18. This has a direct effect on risk, which increases in the trail sections that are close to the cliffs while it is significantly reduced in those sections located far away (see Fig. 2 bottom, left). However, one of the most important effects of fragmentation is the substantial reduction of the rockfall runout. This is clearly illustrated in Figure 2 bottom. A high number of block fragments either stop or are retained by the rockfall barriers. The simulation also shows that some trajectories may avoid the barriers by passing between them and/or by high bounces. The risk for visitors to the lake, in this example, is evaluated exclusively for individuals (annual probability of loss of life) considering the annual frequency (Ni) of 1, 10 and 100 m3 rockfalls, and the runout probability P (S | D)i of reaching the trail. The probability of impact P (T | S) takes into account two factors: the probability that the person is in the rockfall trajectory and the width of the section of the trail affected by the cone of rock fragments (Wc). For intact rock fall masses, it is assumed a cubic shape. For fragmental rockfalls Wc is variable and depends on the distance to the source and on the characteristics of the path. It is determined by numerical modeling using the RockGIS program, considering different initial rockfall volumes and sources (some examples are shown in Figure 2 bottom) and summarized in Table 1. The exposure, P (T | S) is based on the number of visitors. The last 15 years, the site has received an average of about 700 persons per day. In this example, the continuous flow of visitors is assumed. For people in movement, the probability of intersection with any rockfall is as follows (adapted from Nicolet et al., 2016): P (T / S ) =

f p wc

lp )

(2)

24 ⋅ 1000 ⋅ v p

where: fp: flow of visitors (persons/day) Wc: width of the rockfall debris front (m) lp: width of the person (m) vp: is the mean velocity of persons (km/h) A worked example is presented in Tables 2 and 3. The effect of fragmentation is nicely illustrated by the rockfall runout. For 1 m3 and 10 m3 rockfalls, the percentage of rockfall events that reach the trail has reduced from 62 to 3% and from 76 to 20%, respectively. This effect vanishes progressively as the rockfall volume increases. The reduction of the kinetic energy allows considering the feasibility of protection measures, such as the rockfall barriers. For 1 m3 intact blocks, the rockfall barriers are highly efficient allowing the reduction of P(S:D) from 62% to 13%. On the other hand, high energies developed in large unfragmented rockfalls make rockfall barrier inefficient, as shown by the P(S:D) values of Table 2. In case of fragmental rockfalls, 1500 kJ barriers can intercept a number of rockfall events of 10 and 100 m3. The comparison for 10 m3 rockfall is particularly relevant because the occurrence of fragmentation shows that the percentage of 10 m3 rockfall events that reach the trail is reduced from 75% in case of intact rock masses to 13% when fragmentation is accounted for. These results are a first estimation only because the multiple impact of blocks is not considered. It is also worth noticing that a percentage of events reach the trail because their trajectories avoid the barriers (Figure 2 bottom right) or by the high bounces of the blocks.

Table  1. Width Wd (m) of the intact blocs and cone the rockfall fragments at the reference trail. Volume (m3) Intact block Cone of fragments

1 1 17.5

778

10 2.2 20

100 4.6 40

Table 2.

Annual probability of loss of life for intact (unfragmented) rockfall masses.

Pathway A (length 195 m) – contributing Cliff (length 320 m) Without protection barriers Class Mi (m3)

Ni

P(S:D)

P(T:S)

V

Risk R(A)

1 10 100

0.0331 0.0043 0.00057

0.6176 0,7619 0.8254

0.0219 0.0394 0,0744

1,0 1,0 1,0

4.50 × 10−4 1.30 × 10−4 3.52 × 10−5

0.1273 0,7472 0.8254

0.0219 0.0394 0.0744

1,0 1,0 1,0

9.19 × 10−5 1.28 × 10−4 3.53 × 10−5

With protection barriers (1500 KJ) 1 10 100

Table 3.

0.0331 0,0043 0,0006

Annual probability of loss of life considering fragmentation of rockfalls.

Pathway A (length 195 m) – contributing Cliff (length 320 m) Without protection barriers Class Mi (m3)

Ni

P(S:D)

P(T:S)

V

Risk R(A)

1 10 100

0.0331 0.0043 0.00057

0.0322 0.2035 0.6240

0.0779 0.1343 0.2981

0,5 1,0 1,0

4.35 × 10−5 1.19 × 10−4 1.07 × 10−4

0.0205 0.1318 0.5150

0.0973 0.1461 0.2973

0,5 1,0 1,0

3.29 × 10−5 8.36 × 10−5 8.80 × 10−5

With protection barriers (1500 KJ) 1 10 100

0.0331 0.0043 0.00057

Fragmentation increases the impact probability due to the presence of a cone of fragments as shown by the comparison of values of P(T:S) in Tables 2 and 3. The risk values, in the worked example are of the same order of magnitude. However, in the case of Lago del Espejo, when considering fragmentation the feasibility of protection measures for mid-size events improves because risk may be reduced up to one order or magnitude when compared to unfragmented rockfalls.

REFERENCES Agliardi F, Crosta GB, Frattini P. 2009. Integrating rockfall risk assessment and countermeasure design by 3D modelling techniques. Nat Hazards Earth Syst Sci 9:1059–1073. Corominas, J; van Westen, C.; Frattini, P.; Cascini, L.; Malet, J.P.; Fotopoulou, S.; Catani, F.; Van Den Eeckhaut, M.; Mavrouli, O; Agliardi, F.; Pitilakis, K.; Winter, M.G.; Pastor, M.; Ferlisi, S.; Tofani, V.; Hervás, J. & Smith, J.T. 2014. Recommendations for the quantitative analysis of landslide risk. Bulletin of Engineering Geology and the Environment, 73: 209–263. Matas, G., Lantada, N., Corominas, J., Gili, J.A., Ruiz-Carulla, R., Prades, A. 2017. RockGIS: a GISbased model for the analysis of fragmentation in rockfalls. Landslides, 14: 1565–1578. Nicolet, P., Jaboyedoff, M., Cloutier, C., Crosta, G., Lévy, S. 2016. Brief Communication: On direct impact probability of landslides on vehicles. Natural Hazards and Earth System Sciences 16, 995–1004. Ruiz-Carulla, R., Corominas, J., Mavrouli, O. 2017. A fractal fragmentation model for rockfalls. Landslides, 14: 875–889.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Experimental and numerical investigation the divergence of horizontal and vertical displacement in longwall mining E.T. Denkevich “TOMS-Project”, Head of Mine Survey Team, Vasilevsky Island, St. Petersburg, Russia

O.L. Konovalov & M.A. Zhuravkov Belarusian State University, Nezavisimosty av., Minsk, Belarus

Keywords: Viscoplasticity; InSAR; Displacement; Subsidence; Numerical simulation; Mixed meshing; Longwall-mining; Creep flow Mining companies are looking for higher productivity solutions for low and medium-thickness potash seams. The suitable approach here is high-speed cutting longwall-mining. The extreme excavation process require the more frequency control over stress–strain state of rock’s massif to reach safety of above process. Many specialists propose to use InSAR-technology to control the deformations of rock’s massif surface (Figure 1). Unfortunately, it is not possible to retrieve the full displacement vector from a single InSAR measurement. To overcome this there are proposed some heuristic methods based on the hypothesis of a physical relation between horizontal and vertical displacements. In above methods use the hypothesis that the horizontal displacements are proportional to the tilts (i.e. first spatial derivative of vertical deformation) [1]. During experimental study of subsidence process caused by longwall potash mining in Starobin Deposit of potassium salts, it was detected that Kratzsch’s hypothesis [1] do not take place. The high accuracy GPS monitoring of subsidence process shows that point with maximum of absolute vertical displacement (MVD) are always falls behind from the point with zero horizontal displacement (ZHD). For 400-meter excavation depth, the divergence between above extremums had place in interval from 10 to 30 meters. However, according

Figure 1.

View of subsidence process on InSAR interferometry.

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Kratzsch’s hypothesis positions of MVD and ZHD should be equal. The experimental study shows also the dependence of divergence from speed of excavation. To investigate the reason of above phenomena, the special numerical model was developed that provide to simulate high-speed longwall-mining. The goal of such developments was find the way for estimation MVD/ZHD divergence to improve InSAR deformation measurements. Take into account that we had not known the reason of the above phenomena, we had try to elaborate maximum universal and flexible numerical model. To describe hardening and softening as well as dilatancy and creep behavior of salt rocks, the numerical model with modified continuum damage model based on Mohr-Coulomb criteria was utilized. We propose the following equation for the damage calculation: ⎧⎪1 − B A D=⎨ ⎩⎪ 0

if

A>B

else

where A = 1 / 2(σ 1 − σ 3 ) + 1 / 2( 1 + 3 ) sin(ϕ ) and B C ⋅ cos(ϕ )). Here C is cohesion and ϕ friction angle. Unfortunately numerical elastic model with described above continuum damage model do not able to reproduce the real form and dynamic of subsidence surface for Starobin Deposit. The reason of this is complexity of subsidence process. The form of subsidence surface are extremely dependent from size and dynamic of failure zone “1” (Figure 3). For more accurate modeling of failure zone (zone “1”) we will take into account the laminar structure of potash deposit. We propose to add in FEM grid special contact elements

Figure 2. MVD/ZHD divergence.

Figure 3. Deformation and failure zones (1 – near zone; 2 – continous deformation zone; 3 – fracture zone; 4 – failure zone).

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(truss element) with asymmetric behavior (Figure 4) to describe the layers behavior. During compressive loading, the Young coefficient of truss element is equal to appropriate coefficient of material. In case of tension, the Young coefficient are degraded to zero. The damage model based on Mohr-Coulomb criteria and special contact elements for lamination give as possibility to reproduce form and dynamic of subsidence surface on active stage (Figure 5). However, the long-term modeling need to include in numerical model some rheology “submodel”. We follow to approach, that for thin-layering salt massif, viscoelastic deformation can be modeling as planar viscous-flow [2]. The visco-creep flow of salt rocks is controlled by the Maxwell viscosity ηM

ε(σ efff ) =

σ efff 3ηM

,

where ε is creep rate of deformation. We also consider visco-creep flow as planar process * and restrict by criterion σ efff > σ eff . To avoid numerical instability caused by extraction of some finite element from mesh, we use special technique of mixed meshing. Extracted potash seams are presented as grid of contact elements (truss element). Mixed meshing give us possibility to simulate excavation process as decreasing of length for some vertical truss elements. The example of mixed meshing is presented on Figure 6. To investigate the reason of MVD/ZHD divergence, the series of numerical experiments based on described above model was implement. Three basic sets of rock’s beds was included in FE network: sedimentary bed, argillo-marlaceous strata (AMS) and salt bed. The physicsmechanical properties of the selected sets of rock’s beds are presented in Table 1.

Figure 4.

Layers of contact elements.

Figure 5.

Observed (left) and modeling (right) subsidence.

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Figure 6.

Table 1.

The potash seams are presented as grid of contact elements.

Values of the physics-mechanical parameters. Physics-mechanical parameters

Bed

E(GPa)

v

C(MPa)

ϕ(rad)

μ(ΜPa ⋅ day)

ρ(kg/m3)

Sedimentary AMS Salt

0.7 15 20

0.3 0.3 0.3

1 2 2

0.6 0.6 0.77

1014 1014 1012

2200 2400 2400

Figure 7.

MVD/ZHD divergence for Maxwell viscosity value 1011 (left) and 1012 (right).

Extracted potash seams are presented as sub-grid of contact elements (truss element) inside FE network. Mentioned experiments showed that visco-creep flow is key process of VHE divergence. There are demonstration of MVD/ZHD divergence for different values of Maxwell viscosity of salt bed in Figure 7. The increase of viscosity lead to degradation of divergence. In case of 108 viscosity, numeric model present 20  meter MVD/ZHD divergence. The results of modeling correlates with observed values. The future improvement of presented numerical model can lead to accurate estimation of MVD/ZHD divergence and as result to increase accuracy of InSAR measurement for potash mining.

REFERENCES [1] Kratzsch H., 1983, “Mining Subsidence Engineering”, 543 pp. [2] Kononova, N.S., “Geomechanical substantiation of stability of mine workings and bore holes in viscoplastic massifs”, International Journal of Mining Institute, 152, 2002, pp. 129–132.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Numerical analysis of the rheological behaviour of the Socompa debris avalanche, Chile Federico Vagnon Department of Earth Science, University of Turin, Turin, Italy

Marina Pirulli Department of Structural, Geotechnical and Building Engineering, Politecnico of Turin, Turin, Italy

Irene Manzella School of Geography, Earth and Environmental Sciences, Plymouth University, Plymouth, UK

Karim Kelfoun Laboratoire Magmas et Volcans, OPGC, UMR Clermontn Université-CNRS-IRD, Clermont-Ferrand, France

Anna Maria Ferrero Department of Earth Science, University of Turin, Turin, Italy

ABSTRACT: Socompa Volcano provides one of the world’s best-exposed example of a sector collapse that generated debris avalanche deposit. The debris avalanche, occurred about 7000 years ago, involved 25 km3 of fragmented rock that formed a thin but widespread (500 km2) deposit. Numerical model of this event was already performed using a shock-capturing method based on double upwind Eulerian scheme in order to provide information for investigating, within realistic geological context, its dynamic and run-out (Kelfoun and Druitt 2005). This paper analyses an important aspect of the continuum numerical modeling of rapid landslides as debris avalanche: the interchangeability of rheological parameter values. The main question is: by using the same rheological parameter values, are the results, obtained with codes that implement the same constitutive equations but different numerical solvers, equal? Answering this question has required to compare the previous back analysis results with new numerical analyses performed using RASH3D code. Different rheological laws were selected and calibrated in order to identify the law that better fits the characteristics of the final debris deposit of the Socompa landslide. Keywords: Volcanic debris avalanche, Numerical modelling, Runout simulation, Depthaveraged equations, rheological laws 1

INTRODUCTION

The collapse of a giant sector of the Socompa Volcano caused a long runout debris avalanche, which represents one of the most critical and hazardous types of geological instability phenomena (Melosh, 1990). The potential for destruction of this type of flow-like landslides, due to the extremely rapid propagation velocity, requires reliable forecasting methods to predict their motion characteristics. Continuum mechanics based numerical models (e.g. Savage and Hutter, 1989, O’Brien et al., 1993, Hungr, 1995, Iverson and Delinger, 2001, Mc-Dougall and Hungr, 2004, Pirulli, 2005, Pastor et al., 2009, Manzella et al., 2016) are useful tools for investigating, within realistic geological contexts, the dynamics of these phenomena. 785

The back analysis of real events is indispensable for the correct selection of the rheological laws and the calibration of the rheological parameters. Moreover, in order to perform robust numerical analyses, two aspects shall be considered: firstly, the use of more than one code and the comparison of results are recommended (Pirulli and Sorbino, 2010). Secondly, the interchangeability of rheological parameters should be evaluated. This aspect is particularly important because it helps users in the decisional process for assessing potential risks and evaluating/designing possible countermeasures (Vagnon, 2017). The aim of this paper is to evaluate the interchangeability between calibrated values of rheological parameters comparing the simulation results of two different continuum-based numerical codes: VolcFlow (Kelfoun and Druitt, 2005) and RASH3D (Pirulli, 2005). In the next Sections, the codes are briefly described and used to back-analyse the Socompa debris avalanche. The obtained results are compared and discussed. Moreover, new simulations are carried out using Bingham rheology.

2

DESCRIPTION OF THE SOCOMPA AVALANCHE

Socompa Volcano is a stratovolcano located at the border between Chile and Argentina, in the Andes Mountains (Figure 1a). About 7000 years ago, the Chilean sector collapsed, generating a 40 km long debris avalanche that flowed into the flat and arid plan below before being deflected to northeast by a range of hills, forming a frontal lobe (Francis et al., 1985, Wadge et al., 1995, Van Wyk de Vries et al., 2001, Kelfoun and Druitt, 2005). The debris deposit covered an area of 500 km2, forming a sheet of 50 m average thickness. The deposit has an estimated volume of about 36 km3 and it results from the sum of two subsequent events. The first of 25 km3 is analysed in the paper, while the second of 11 km3 that gave origin to the Toreva blocks deposit (Figure 1b) is not analysed due to its negligible runout distance. The avalanche deposit is characterized by a mixture of brecciated lavas and volcanoclastic deposit (Socompa Breccia Facies; SB) directly originated by the Socompa edifice itself and ignimbrites, gravels, sands and minor lacustrine evaporates from the Saline Formation (Reconstruited Ignimbrite Facies; RIF) of the volcano basement). Mostly of the deposit volume is constituted of RIF and only the 20% of SB. The first avalanche was generated by a series of retrogressive failures that merged to form a single flowing mass (Wadge et al., 1995) that spread on a basal layer of RIF, characterized by very weak mechanical resistance (Van Wike de Vries et al., 2001). The deposit can be morphologically divided into two main zones by a median escarpment (ME), oriented NE-SW (Figure 1b), generated by secondary flow off the western and north-western basin margins.

Figure 1. Location of Socompa Volcano (a) and aerial image of the avalanche deposit showing the avalanche scar (AS), the Toreva blocks (TB), the median escarpment (ME), the frontal lobe (FL) and northern and western levees (NL and WL) (b). In detail: the red dotted line surrounds the deposit limits; the blue continuous line draws the margins of Toreva deposit; the black dotted line highlights the medial escarpment.

786

3

NUMERICAL MODELING

Kelfoun and Druitt (2005), starting from geological investigations and morphological observations, reconstructed the original topography of the area before the collapse. Then, they performed several numerical simulations using VolcFlow code, testing different rheological laws in order to find the best model for obtaining the actual avalanche deposit configuration. In this work, the Authors want to compare VolcFlow numerical results with those obtained with RASH3D code (Pirulli, 2005) for evaluating the interchangeability between codes of calibrated rheological values and providing new run-out simulations with a Bingham rheology. 3.1

Basic equations

The numerical simulation of rapid landslides is a common practice since in 1989, when Savage and Hutter firstly introduced the depth-averaged equations for the dynamic analysis of flowing mass. The hypotheses for applying depth-averaged equations to rapid landslides are: − both thickness and length of flowing mass are assumed to exceed the size of single moving particles of several times; − the flow thickness is considerably smaller than its length; − the real moving mixture is replaced by an “equivalent fluid” whose properties approximate the bulk behaviour of the real mixture; − the flowing mass is described as a single-phase, incompressible and homogeneous material; − a kinematic boundary condition is imposed on free and bed surfaces; − the rheological characteristics are all included in a single term acting at the interface between flow and terrain surface. Under the above listed conditions, the motion is described by the equations of mass and momentum conservation: ⎧ ⎪ ∂h ∂(vx h ) ∂(vy h ) + + =0 ⎪ ∂t ∂x ∂y ⎪ ⎪ ⎛ ⎪ ∂(vx h ) ∂(vx2 h ) ∂(vxvy h ) ⎞ ∂( xx ) ⎨ρ ⎜ + + + τ Zx( = ) + ρ gx h ⎟ =− ∂x ∂y ⎠ ∂x ⎪ ⎝ ∂t ⎪ ⎪ ⎛ ∂( ) ∂( ∂( y2 ) ⎞ ∂( yy ) y x ) ⎪ρ⎜ y + + + τ Zy( = ) + ρ g y h ⎟ =− ∂x ∂y ⎟⎠ ∂y ⎪⎩ ⎜⎝ ∂t

(

)

(1)

vx ,vy denotes the depth-averaged flow velocity in a reference frame (x, y, z) where v linked to the topography, ρ is the bulk material density, h is the flow depth, τ is the shear σ xx ,σ yy is the depth-averaged stress and gx, gy are the stress in the x and y direction, σ projections of the gravity vector along the x and y direction. The here applied VolcFlow and RASH3D codes differ in the numerical scheme adopted for solving the above equations. VolcFlow code uses a Eulerian explicit upwind scheme for solving the system of equations (1) where scalar quantities (thickness and terrain elevation) are evaluated at the centres of cells and vectors (velocity and fluxes) at the edges (Figure 2a). For a complete description of this method, see Kelfoun and Druitt 2005. The RASH3D Eulerian code, developed by Pirulli (2005) uses a finite volume scheme for modelling rapid landslide run out problems. The system of equations (1) is discretized on an unstructured triangular mesh with a finite element data structure using a particular control volume, which is the median dual cell (Pirulli, 2005). Dual cells Ci are obtained by joining the centres of mass of the triangles surrounding each vertex Pi of the mesh (Figure 2b).

(

)

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Figure 2. Definition of scalars and vector (a) in the numerical scheme of VolcFlow code (modified after Kelfoun and Druitt 2005) and triangular finite-element mesh and dual cells (C1, C2, C3, C4) in RASH3D code (b) (modified after Pirulli 2005).

3.2

Rheological laws

As stated above, the complex rheology of the flowing mass is incorporated in a single term (τ) that describes the frictional stress generated between terrain surface and flowing body. In this paper, three rheologies were selected for the numerical back-analysis of Socompa avalanche: 1. Frictional rheology in which the resisting shear stress depends only on normal stress and it is independent of velocity.

τ zi

( ρ ⋅ gz

h ⋅ tanϕ bed )

vi v

i

( x y)

(2)

where ϕbed is the bulk friction angle. 2. Constant retarding stress in which the basal shear stress is constant and consequently independent by velocity, normal stress and frictional parameters.

τ zi = − const

vi v

i

( x y)

(3)

These two rheological laws are implemented in both the presented codes and they were used to compare the RASH3D analyses with the already published VolcFlow simulations (Kelfoun and Druitt, 2005). 3. Bingham rheology combines plastic ad viscous behaviour, so that the flowing mass moves as a rigid body below a given threshold yield strength and then have a viscous behaviour above this threshold. The basal stress is determined solving the following equation:

τ zi3 +

⎛τy ⎝ 2

+

3 μB vi ⎞ 2 τ y τ − =0 zi h ⎟⎠ 2

(4)

where τy is the Bingham yield stress and μB is the Bingham viscosity. In RASH3D equation (4) is solved using polynomial economization technique proposed by Pastor et al. (2004). Bingham rheological law was selected to back-analyse Socompa avalanche since the type of material that characterized the deposit had a ductile behaviour (RIF) and behaved as a lubricant for the SB facies. 4

RESULTS

Numerical analyses were carried out following two different steps. Firstly, the VolcFlow numerical simulations (Kelfoun and Druitt, 2005) were replicated using RASH3D code for evaluating the interchangeability of rheological values. Then, once that RASH3D results were commented, a back-analysis using Bingham rheology was performed. The goodness of numerical simulations is evaluated if the following conditions are satisfied: 788

1. best fit to the north-western margin 2. best fit to overall outline of the deposit 3. reproduction of the main structures, especially the median escarpment (cfr. Figure 1). 4.1

Evaluation of the two codes interchangeability of rheological values

Figure 3 compares VolcFlow (a and c) and RASH3D (b and d) simulations of the final avalanche deposit considering a frictional behaviour (model 1, Figures 3a and 3b) and a constant retarding stress rheological law (model 2, Figures 3c and 3d). The rheological values used for model 1 are ϕbed = 2.5°, in an isotropy condition of stresses, and a constant retarding stress equal to 52 kPa for model 2. For each time step of the simulations, the thickness and the areal distribution of the deposit simulated by the two codes are satisfyingly comparable. In general, RASH3D simulations show a marked lateral spreading: however, the calculated thickness values at the margin of the simulated deposit are less than 10 cm. For what it concerns model 2, the conditions previously imposed for evaluating the goodness of the model (point 1 to 3, Section 4) were satisfied: the overall outline of the deposit was respected and the median escarpment, characteristic of this deposit, was well reproduced. 4.2

Bingham rheology

The Bingham rheology was never used before for simulating Socompa avalanche but, on the basis of previously discussed geological and geomorphological evidences, this rheology was adopted to evaluate thickness and velocity of the Socompa emplacement with the RASH3D code. A large number of analyses was performed to obtain the combination of rheological values that best simulate the deposit in terms of extension, thickness and escarpments. These conditions were satisfied considering the Bingham yield stress and the viscous coefficient respectively equal to 52 kPa and 10 kPa*s. Figure 4 shows the depositional height (a) and

Figure 3. Final deposit thickness of the Socompa avalanche considering frictional rheological law with ϕbed = 2.5° and in an isotropy condition of stresses in VolcFlow code (a) and RASH3D code (b). Figures c and d show the obtained final deposit considering a constant retarding stress rheological law with τ = 52 kPa in VolcFlow code (c) and RASH3D code (d).

Figure 4. Deposit thickness (a), flow velocity (b) and shaded relief map of the Socompa avalanche, simulated considering Bingham rheological law with τ = 52 kPa and μ = 10 kPa*s using RASH3D code and satellite image of the actual Socompa emplacement (d).

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the flow velocity (b) of the simulated emplacement. The simulated final deposit (Figure 4a) remarkably well reproduces the real event. In particular, analysing Figures 4c and 4d that represent the shaded relief map of the simulated deposit and the satellite image, a topographic discontinuity is evident (red dotted line in Figure 4c) and it represents the median escarpment. Moreover, the presence of a frontal lobe can be clearly identified. 5

CONCLUSIONS

In this paper, the two codes VolcFlow and RASH3D, based on a continuum mechanics approach, were compared. The results obtained from the carried out analyses have highlighted the good interchangeability of the rheological values between the presented codes. Moreover, the Bingham rheological law was applied to further simulate the avalanche emplacement: the results were satisfying both in terms of areal extension, depositional heights and topographical evidences (frontal lobe, median escarpment and well-defined lateral margins) compared to the actual morphological situation. Further developments of this research will include the use of others numerical codes with different numerical scheme for solving mass and momentum conservation equations (e.g. Lagrangian code) for again evaluating and comparing these approach. REFERENCES Francis, P.W., Gardeweg, M., Ramirez, C.F., and Rothery, D.A. 1985. Catastrophic debris avalanche deposit of Socompa volcano, northern Chile, Geology, 13, 600–603. Hungr, O. 1995. A model for the runout analysis of rapid flow slides, debris flows, and avalanches. Canadian Geotechnical Journal, 32(4), 610–623. Iverson, R.M., and Denlinger, R.P. 2001. “Flow of variably fluidized granular masses across threedimensional terrain: 1. Coulomb mixture theory.” Journal of Geophysical Research: Solid Earth, 106(B1), 537–552. Kelfoun, K., and Druitt, T.H. 2005. Numerical modeling of the emplacement of Socompa rock avalanche, Chile, J. of Geophysi. Res., 110, B12202, doi:10.1029/2005JB003758. Manzella, I., Penna, I., Kelfoun, K., and Jaboyedoff, M. 2016. High-mobility of unconstrained rock avalanches: Numerical simulations of a laboratory experiment and an Argentinian event, in Landslides and Engineered Slopes. Experience, Theory and Practice, 1345–1352. Mcdougall, S., and Hungr, O. 2005. Dynamic modelling of entrainment in rapid landslides. Canadian Geotechnical Journal, 42(5), 1437–1448. Melosh, H.J. 1990. Giant rock avalanches, Nature, 348, 483–484. O’brien, J.S., Julien, P.Y., and Fullerton, W.T. 1993. Two Dimensional Water Flood and Mudflow Simulation. Journal of Hydraulic Engineering, 119(2), 244–261. Pastor, M., M. Quecedo, E. Gonzalez, M.I. Herreros, J.A. Fernandez Merodo, and P. Mira. 2004. Simple approximation to bottom friction for Bingham fluid depth integrated models. Journal of Hydraulic Engineering 130(2): 149–155. Pastor, M., Haddad, B., Sorbino, G., Cuomo, S., and Drempetic, V. 2009. A depth-integrated, coupled SPH model for flow-like landslides and related phenomena. International Journal for Numerical and Analytical Methods in Geomechanics, 33(2), 143–172. Pirulli, M. 2005. Numerical modelling of landslide runout, a continuum mechanics approach. Ph.D dissertation, Politecnico of Turin, Turin, Italy. Pirulli, M., and Sorbino, G. 2008. Assessing potential debris flow runout: a comparison of two simulation models. Natural Hazards and Earth System Science, 8(4), 961–971. Savage, S.B., and Hutter, K. 1989. The motion of a finite mass of granular material down a rough incline. Journal of Fluid Mechanics, 199(1), 177. Vagnon, F. 2017. Theoretical and experimental study on the barrier optimization against debris flow risk. Ph.D dissertation, University of Turin, Turin, Italy. Van Wyk de Vries, B., Self S., Francis, P.W., and Keszthelyi, L. 2001. A gravitational spreading origin for the Socompa debris avalanche, J. Volcanol. Geotherm. Res., 105, 225–247. Wadge, G., P.W. Francis, and C.F. Ramirez (1995), The Socompa collapse and avalanche event, J. Volcanol. Geotherm. Res., 66, 309–336.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Numerical study on the strategies to reduce the risk of induced seismicity in an enhanced geothermal system Wentao Feng Energy Research Center of Lower Saxony (EFZN), Goslar, Germany

Zhengmeng Hou Energy Research Center of Lower Saxony (EFZN), Goslar, Germany Institute of Petroleum Engineering, TU Clausthal, Clausthal-Zellerfeld, Germany

Jianxing Liao & Patrick Were Energy Research Center of Lower Saxony (EFZN), Goslar, Germany

ABSTRACT: Hydraulic fracturing technology is essential for the development of Enhanced Geothermal Systems (EGS) to increase the permeability of tight rock formations and hence the energy recovery from a petro geothermal reservoir. However, fracturing and the subsequent increase in energy production may pose the risk of induced seismicity. Previous studies established the mechanisms of microseismic events during hydraulic fracturing in the Deep Heat Mining project Basel using the numerical simulator FLAC3Dplus. In this paper, an innovative injection strategy using a linear increasing injection rate to reduce the maximum magnitude of microseismic events Mmax has been proposed. In addition, the new EGS-strategy allows a combination of both the linear increased injection rate and the multiple fracture system to be studied numerically. Results show that the risk of induced seismicity can be considerably minimized by the proposed strategy. The simulation shows that increasing the number of fractures in the tight reservoir decreases Mmax significantly. It is recommendable that multiple hydraulic fracturing technology be applied in the development of enhanced geothermal systems not only to minimize the risk of induced seismicity but also to increase the surface area for heat exchange and recovery efficiency.

1

INTRODUCTION

The exploitation of renewable energy has become a crucial method for mitigating global energy and climate crises (Gou et al., 2015). Compared with other types of renewable energy, e.g. PV or wind energy, deep geothermal energy offers more advantages including being both sustainable and economical (IEA, 2017). In an enhanced geothermal system, hydraulic fracturing is a key technology to increase formation permeability (Lu et al., 2015) and improve the energy recovery from reservoir. However, this technology has its own shortcomings. Hydraulic fracturing can trigger seismicity (Hou et al., 2012), which is one of the main obstacles hindering its industrial application in production from enhanced geothermal system. In the previous study by Hou et al., 2013, the coupled Thermo-Hydro-Mechanica (THM) numerical simulator FLAC3Dplus was developed to investigate hydraulic fracturing in the Deep Heat Mining (DHM) project Basel. Meanwhile, the fundamental mechanisms of microseismic events during hydraulic fracturing have been studied in detail. In this paper, innovative injection strategies in combination with multiple hydraulic fracturing technologies have been proposed to reduce the risks of induced seismicity and to increase the heat exchange area in the reservoir and hence the efficiency of heat recovery. These parameters have been studied and tested based on the history-matched Basel model. 791

2

ASSESSMENT OF INDUCED SEISMICITY BASED ON NUMERICAL SIMULATION

In the developed numerical simulator FLAC3Dplus, the coupled HM responses were obtained by solving the basic equations of static mechanical equilibrium and geometry, (poroelastoplastic) constitutive equations as well as the fluid motion equations. These equations have been solved using the explicit finite difference method (Itasca 2009). This paper also considers the enhancement permeability by hydraulic fracturing of a petrogeothermal reservoir. The seismic events can be evaluated based on the simulated results, including node displacements and velocities. In seismology, the magnitude of a seismic event is commonly expressed as moment magnitude Mw, which can be calculated from the seismic moment M0 using Eq. 1 (Hanks & Kanamori, 1979). Seismic moment M0 is a measure of the total deformation energy released during an event. It is calculated using Eq. 2 (Kanamori & Anderson, 1975). Mw M0

2 l M 0 − 6.07 logM 3

∑ i=1Gi ⋅ ΔDi n

(1)

Ai

(2)

where Gi is shear modulus [Pa], Di is dislocation vector for the fractured element [m] and Ai the fracture area in the element [m2]. Another important assessment parameter is the local magnitude ML, which can be calculated using the empirical equation of Ahorner & Sobisch (1988) (Eq. 3). In FLAC3Dplus the released energy E would be computed as the kinetic energy from each grid point (Eq. 4) at a certain point in time. logE = 3.81 + 1.64M L E

(

1 n ∑ mi vix2 + viy2 + viz2 2 i =1

(3)

)

(4)

where E is the released kinetic energy [J], ML is the local magnitude of the seismic event [−], vij is the velocity of grid point [m/s] and mi the mass [kg].

3

NUMERICAL INVESTIGATION OF THE PROPOSED STRATEGIES TO REDUCE THE RISKS OF INDUCED SEISMICITY IN EGS

In this paper, numerical simulations were carried out using the history-matched model of the DHM project Basel from previous studies (Hou et al., 2013). The model was a ¼ symmetric model (Fig. 1a) and has been calibrated and verified relying on history matching (Fig. 2). This model has a height of 1,179 m (in the z-direction, from −4,030 m to −5,209 m) and a breadth of 500 m (in the y-direction). Its length is 700 m (in the x-direction). The grid elements are divided into three zones according to their properties: “granite” (intact granite), “granite_frac” (naturally fractured granite) and “water” (naturally fractured granite), as well as the zone of injection. The “granite_frac” zone extends over a range from z = −4,030 m to −5,109 m with a width of 100 m (in the y-direction). Its strike direction has an orientation angle of ± 15° from the direction of the maximum horizontal stress σHmax (in the x-direction). Compared to the zone “granite_frac” the zone “granite” possesses no pre-existing joints and hence characterized by a higher strength as well as a lower permeability. The zone “water” corresponds to the injection section from −4,630 m to −5,009 m (in the z-direction), i.e. a total height of ca. 380 m). Fig. 1b shows the initial stress state and Table 1 lists the mechanical and hydraulic parameters that are used in the simulation. The fluid applied in the stimulation possesses a bulk modulus of 2 GPa and a viscosity of 1cP. The measured and simulated bottomhole pressure (BHP) with the corresponding injection rates are illustrated in Fig. 2. The 792

Figure 1. (a) Quarter of geometrical model and (b) initial primary stress and pore pressure distribution vs. depth. Table 1.

Parameters for simulation of hydraulic fracturing in the DHM project, Basel.

Parameters

Units

Joint surface

Granite_Frac

Granite

Density (ρ) Young’s modulus (E) Poisson’s ratio (υ) Cohesion (c) Friction angle (ϕ) Tension strength (σt) Porosity (n) Permeability (k)

kg/m3 GPa – MPa ° MPa – m2

– – – 4 30 1 – –

2500 60 0.2 10 30 2.5 1% 4 × 10–17

2500 60 0.2 20 45 2.5 1% 4 × 10–18

Figure 2. Treatment schedule and comparison of the bottomhole pressure (BHP) calculated from the measured pressure and simulated pressure vs. time.

simulated pressure is comparable to the measured pressure. This simulation was considered as a basis for the study of the proposed injection strategies and multiple hydraulic fracturing in this paper. 3.1

Injection strategies with linear increasing injection rate

A linear increasing injection method was proposed and simulated in the new strategy. To ensure the injected volume was the same as that in the basis situation, the maximum injection rate was raised to 48.58 l/s (see Fig.  3b). The results of the basis simulation are shown in Fig. 3a for comparison. 793

The new injection strategy yielded a final stimulated reservoir volume (SRV) of 7.011 × 107 m (900 m × 100 m × 779 m). The maximum profile of the fractured zone is about 0.65 km2. The bottomhole pressure attained a maximum level of 74.5 MPa (see Fig. 3b) comparable to that in the basis simulation (78.3 MPa, Fig. 2). However, a few fluctuations in the pressure curve are noticeable at the beginning of the injection (Fig. 3c). These oscillations can be attributed to the effect of “break down pressures”. This means that a pressure drop occurs during the initiation of larger cracks, since the injected fluid has an increased accessible volume during this process. This effect is compensated for by continuous injection at an increasing rate. The seismic magnitude forms a corridor during the stimulation, i.e. the average level is relatively constant. The Mmax, which also occurs after shut-in (see Figs. 3a & 3b), is clearly reduced from ML = 2.80 and Mw = 2.30 to ML = 2.47 and Mw = 2.09 (Figs. 3a & 3b), respectively. Since the linear increasing injection method showed an immediate improvement in terms of reducing the seismic risk, further variants were also tested. In all the variants, the maximum injection rate was maintained at 46.58 l/s. However, the turning point at which the injection rate changed varied with variant. Variant 1 provided the same duration of increase and decrease (Fig. 3d), while Variant 2 consisted of a rapid rise and a slow decay (Fig. 3e). The resulting induced seismicity showed slight reductions in Mmax (ML,max) to 2.41 and 2.39, respectively. Table 2 summarizes the results for different simulations. Variant 2 of the linear increasing injection method (with a rapid increase and slow decrease) appears to be the most advantageous. The generated fracture zone profile in this variant takes first place and simultaneously releases the largest total seismic energy during the simulation period. In spite of this, the maximum seismic magnitude is the lowest in comparison with the other cases. The seismic events appear to be well distributed during the simulation period, i.e. more small events appear. 3

Figure 3. Treatment schedule for different injection strategies including (a, b, d and e) comparison of their calculated local and moment magnitude vs. time, (c) compares the calculated BHP and the linear injection rate vs. time. Table 2.

Results of the simulation cases with varying injection strategy.

Cases History matched DHM project Basis linear injection method Variant 1 Variant 2

Max. profile of the fracture zone [km2]

Total seismic energy [J]

Calculated MWmax [−]

0.66

10.8 × 103

2.3

0.65

9.49 × 103

2.09

0.69 0.71

9.83 × 103 10.2 × 103

2.03 2.03

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3.2

Injection strategies for linear increasing injection rates combined with a multiple fracture system

In a further step, a combination of the modified injection strategy (Variant 2 of the linear increasing injection method, see Fig.  3e) and different variants with multiple fractures systems were numerically tested. For these tests, a fictitious horizontal bore at the depth of −4,825 m has been assumed, from which the transverse multiple fractures were generated (Fig. 4). It was presumed that the stimulations were carried out at the same time with the same injection strategy. A model generation was performed in a similar pattern to that used in the DHM project, i.e. the models still possessed three zones (“granite”, “granite_frac” and “water”). Only its construction was adapted. For reasons of symmetry, a ½ model was used, with dimensions of 350 m (y) × 679 m (z) (from −4,530 m to −5,209 m) × 1,200 m (y) for the 2-Frac model (Fig. 4, blue line), 1,600 m (y) for the 4-Frac model (Fig. 4, red line) and 2,000 m (y) for the 6-Frac model (Fig. 4, geometric model). The zone “granite_frac” was centrally positioned in a y-direction extending over the entire model width (in an x-direction). This zone lies between −4,530 m and −5,000 m. Two, four and six injection points at a horizontal distance of 200 m were defined at a depth of −4.825 m. This distance was chosen based on the results of the history matching, which ensures that no short circuit is generated between the multiple fractures, since the simulated seismic events are distributed at a width of about 80 m (y-direction in Fig. 1) in the basis simulation (DHM project).

Figure 4. Half of geometric model for testing a new EGS-strategy with 6 fractures (the red line demonstrates the dimension of a 4-Frac model and the blue line represents that of a 2-Frac model).

Figure 5. Treatment schedule in different models and comparison of the calculated moment magnitude of each single fracture vs. time.

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In the simulated results (Fig. 5), the strategy of the multiple fractures system combined with linear increasing injection method shows a more obvious improvement. The more fractures generated, the more seismic events happened. However, the calculated MWmax was reduced (from 1.90 to 1.79 and 1.74).

4

CONCLUSION AND OUTLOOK

Based on previous work innovative linear increasing injection strategies in combination with a multiple fracture system have been proposed and studied in order to optimize the hydraulic fracturing and reduce the risks of induced seismicity. The simulated results show that the risks of induced seismicity can be reduced with the help of the new injection strategy (linear increasing injection). Variant 2 (a rapid rise and a slow decay) appeared to be more advantageous. Through this variant the seismic events gained a better distribution during the operation period, i.e. more small events in a long time interval, instead of large values at a certain point in time. In a further step, their combination with the multiple fractures system achieved a more significant improvement. The more fractures that were considered, the more seismic events happened, but the maximum magnitudes decreased. Hence, from analysis of the simulation results it can be stated that 1. By releasing the energy at a more leisurely pace for a longer period of time, the Mmax can clearly be reduced; 2. The same operation could be carried out from the perspective of space, i.e. with the help of a multiple fractures system the stimulation works will run as multiple fractures. Thus, the stimulation of each fracture can be more leisurely. At the same time, the fractured zone will become larger. The remained question is the influences between individual fractures. Finally, this work confirms that injection strategy using a linear increasing injection rate could reduce the risk of induced seismicity in hydraulic stimulation. In addition, heat recovery efficiency would be further increased, when this injection strategy is applied in combination with the multiple fracturing technology.

REFERENCES Ahorner L, Sobisch H-G (1988) Ein untertägiges Überwachungssystem im Kalibergwerk Hattorf zur Langzeiterfassung von seismischen Ereignissen im Werra-Kaligebiet. Kali und Steinsalz 10 (2): 38–49. EIA (2017) Levelized Cost and Levelized Avoided Cost of New Generation Resources in the Annual Energy Outlook 2017. U.S. Energy Information Administration. Gou Y, Zhou L, Zhao X, Hou MZ, Were P (2015) Numerical study on hydraulic fracturing in different types of georeservoirs with consideration of H2M-coupled leak-off effects. Environ. Earth Sci., 73(10):6019–6034. doi: 10.1007/s12665-015-4112-5. Hanks TC, Kanamori H (1979) A moment magnitude scale. J. Geophys. Res. 84(B5): 2348–2350. doi: 10.1029/JB084iB05p02348. Hou MZ, Kracke T, Zhou L, Wang X (2012) Rock Mechanical Influences of Hydraulic Fracturing Deep Underground the North German Basin: Geological Integrity of the Cap Rock Salt and Maximum Magnitude of Induced Microseismicity Based on the GeneSys Stimulation in May 2011. Erdöl Ergas Kohle 128(11): 454–460. Hou MZ, Zhou L, Kracke T (2013) Modelling of seismic events induced by reservoir stimulation in an enhanced geothermal system and a suggestion to reduce the deformation energy release. Rock Dynamics and Applications: 161–175. doi: 10.1201/b14916-15. Itasca (2009) FLAC3D Manual, Version 4.0. ITASCA Consulting Group, Inc. Kanamori H, Anderson DL (1975) Theoretical basis of some empirical relations in seismology. B. Seismol. Soc. of Am. 65(5): 1073–1095. Lu C, Guo J, Liu YX, Yin J, Deng Y, Lu QL, Zhao X (2015) Perforation spacing optimization for multistage hydraulic fracturing in Xujiahe formation: a tight sandstone formation in Sichuan Basin of China. Environ. Earth Sci., 73(10):5843–5854. doi: 10.1007/s12665-015-4366-y.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

The reasons of landslides activization at Sakhalin Island (on the example of landslide exploration at the river Lazovaya) I.K. Fomenko, D.N. Gorobtsov, V.V. Pendin & M.E. Nikulina Department of Geology, Russian State Geological Prospecting University n. a. Sergo Ordzhonikidze (MGRI-RSGPU), Moscow, Russia

Keywords: factors of the landslide process activation, stability calculations, probabilistic analysis, sensitivity analysis, inverse analysis, assessment of landslide hazard

1

ANNOTATION

Sakhalin area is characterized as one of the most problem in Russia. It connects with the amount of sliding phenomena expression. Understanding the reasons and mechanisms of landslides formation gives advantages in their increased activity forecast. It also helps in possible prevention of tragically accidents. Last year’s landslides activation was registered in 36 localities, i.e. 10 were urban and 26 were rural. Landslides in bykovsky mudstones formation are of particular interest as properties of such rock are not fully explored. At present sliding phenomena studying at Sakhalin area connects with the need of safety exploration the oil and gas pipelines. The section of the pipeline system, located in the Dolinsky and Makarov districts, passes through landslide areas. There take places mud and liquefaction slides with a capacity of 7,5 m and block slides characterized by 10,0 m capacity. That is likely to be hazardous to pipelines. The considered object is situated on the west slope of dividing crest which is undermined by right river Lazovaya inflow. According to the map of seismic zonation GSZ-97, the area seismic hazard is 8 points for the periodicities 500 years – map A. For the times of occurrences 1000 and 5000 years – maps B and C the area seismic hazard is about 9 points. Seismic impulses which are caused by earthquakes are the reasons of sliding processes. The assessment of sliding riskiness was made by impact analysis the sliding processes factors on the stability coefficient’s value of investigated slide. Among factors were considered seismic activity, the value of groundwater level as consequence the value of interstitial pressure and strength soil’s properties. Calculations of the stability were made using the Rocscience software. The faculty of engineering geology named in honour of F.P. Savarenski in MGRI-RSGPU is a part of Rocscience Education Program.

2

THE STUDY AREA DESCRIPTION

Landslide at the river Lazovaya is situated near 384  km of “Sakhalin-2” piping system at Makarovsky district, Sakhalin region (Figure 1). The contemporary relief of studied territory is relatively young. Its formation has started at the end of Lower Cretaceous period after the mountain building process completion and the main watershed forming. Intensive erosion and denudation processes during Paleogene and Neogene periods contributed to purchasing by the relief the low and middle mountain

797

identities. Gently undulating swelling surfaces of denudation levelling which bordered the lowlands were formed. Accumulating plain relief was formed at Quaternary period. Geomorphologically the study area is situated near the east flank of West-Sakhalin anticlinorium. The area is represented by erosion and denudative landforms. These include low hills, V-shaped river valleys which are intensively divided. The slope steepness is 20–40°. The considered object is situated on the west slope of dividing crest which is undermined by right river Lazovaya inflow. The highest degree of slope is 30°. This value is observed on sliding slope’s cliff. Cliffs alternate with aligned grade levels. Slope consists of eluvial and deluvial deposits with capacity from 1,5 to 3 m. These deposits overlap by transported claystones and clays which belong to upper subsuite of bykovsky suite (K2bk) (Sergeev, 1984). Claystones are weathered in the form of a grass and rock debris material with clayey aggregate. Such claystones are deposited at rock outcrops and sliding brow’s disruptions. Claystones transform into bluish-grey clays of soft plastic consistency. It happens at the interaction zone

Figure 1. Dividing crown and drawing to the river Lazovaya, 384 km of “Sakhalin-2” piping system.

Figure 2. Brow failure between sliding steppes. Lack of wood vegetation is one of the landslides’ activity indications.

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Figure 3. Brook’s bed. Abrupt banks are the evidence of active lateral erosion. Tree remnants in brook indicate on flow capacity at flood period.

with stratum and pore water which matches the weakness zones. These clays form the main deformed horizon of landslide’s main bodies which are represented at the territory. Landslides phenomenon on the studied area is represented by blocked landslides. There thickness is up to 15 m. Such landslides cover the whole slope from crown to thalweg’s water cource. Morphologically sliding body is in blocks. It looks like circus or frontal landslides which located along the slope. Such landslides have clearly expressed brow failures and sliding steppes (Figure 2). Lateral erosion of watercourses bed significantly increase the affect degree and sliding processes intensity. Landslides growth has a regressive character which caused by undercutting the lower slope’s parts. Starting near slope’s foots such landslides eventually may reach the divide’s crown (Figure 3). The main reasons of nature landslides development at the studied area are: clay rocks at slope’s structure which may transform into soft plastic consistency due to ground water, high slope’s steepness, stream’s erosion activity, high seismicity. The assessment of sliding riskiness was made by impact analysis the sliding processes factors on the stability factor’s value of investigated slide. Among factors were considered seismic activity, the value of groundwater level (as consequence the value of interstitial pressure) and strength soil’s properties. (Zerkal, 2016; Pendin, 2015; Recommendations, 1984; Fomenko, 2012).

3

THE RESULTS OF STABILITY DESIGN

The considered landslide belongs to sliding landslip according to mechanism of sliding process. However such landslide has features of squeezing landslides. As this landslide is multicycle this takes the form of some sliding steppes so it should be allocated to complex landslides type (Bondarik, 2007). The stability estimation of such landslides should be made per blocks (Pendin, 2015; Fomenko, 2011). Meanwhile it should be understood that sliding blocks are energetically connected. For this reason sliding slope based on morphological authorities was divided on two blocks—upper and lower. The stability estimation was made for each block. Stability estimation was made by limit equilibrium methods (Morgenstern-Price, Bishop and Janbu simple). The feature of theme and maybe the main deficiency is the miss of 799

correlation between stress and deformations (Krahn, 2004). For this reason soil’s strength properties wasn’t considered in the modelling. Soil’s strength properties (friction angle and cohesion) which are a part of Mohr-Coulomb strength criteria were estimated through triaxial test. It was accompanied by estimation the peak and residual strength in incorporated society “MOSTDORGEOTREST” laboratory. The colour legend is shown on the Table 1. It was used in preparing geomechanical schemes. Final geomechanical schemes with the results of slope’s stability estimation according to Morgenstern-Price method are shown on Figure 4 and Figure 5. The comparison between the results obtained due to various estimation versions and methods is shown at the Table 2. The results of probabilistic analysis (Krahn, 2004; Zerkal, 2015; Zerkal, 2016; Pendin, 2015; Sisoev, 2011; Fomenko, 2012) according to Morgenstern-Price method are shown at the Table 3. Integral function’s distributions of the estimated modeling slopes’ blocks stability factor are shown on Figure 6. Predication slope’s stability estimation on special combination of loads considering the seismic effect and ground water level lifting was made due to analysis of slope’s stability factor sensitivity (Sf) and factors of sliding process activation (Krahn, 2004; Pendin, 2015; Fomenko, 2012). The results of analysis are shown on Figure 7 and Figure 8. The seismic impact accounting was made on the base of pseudo static analysis (Krahn, 2004). Measurement ground water piezometric level limits were estimated according to monitoring. Table 1. Material name

The legend to geomechanical schemes. Color

Unit weight (kN/m3)

Angle internal friction (deg)

Cohesion (kPa)

2a

18.7

8.9

34.2

2b

18.7

23.0

40.5

3

19.3

38.8

23.9

4

18.3

7.4

18.0

5

19.6

7.6

37.4

6

19.6

40.4

17.7

7

22.1

63.0

30.5

Figure  4. Geomechanical scheme with results of slope’s stability estimation (M-P method), upper block.

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Figure 5. Geomechanical scheme with results of slope’s stability estimation (M-P method), lower block. Table 2.

Slope’s stability estimation.

Way of estimation Method 1. Natural condition, upper block 2. Natural condition, lower block Slope is stable

Table 3.

Morgenstern-Price (M-P)

Bishop

Janbu (simple)

1,45

1,41

1,36

1,02

1,02

0,99

The colour legend to Table 2 Slope is in limit equilibrium state

Slope is unstable

The results of slope’s stability probabilistic estimations (Morgenstern-Price method). Probabilistic parameters for the analysis of landslide formation risk

Way of estimation

Middle coefficient of slope’s stability (K)

Standard deviation

Kmin

Kmax

β

fk = 1, %

Upper block Lower block

1,51 1,06

0,19 0,13

1,04 0,68

2,09 1,46

2,7 0,47

0 32,5

Figure  6. Integral function’s distributions of the estimated modeling slopes’ blocks stability factor. 1 – Upper block; 2 – Lower block; axis X – Sc (M-P method); axis Y – the sliding process development variety.

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Figure 7. Sensitivity of Sf to the horizontal seismic acceleration’s value. 1 – Upper block; 2 – Lower block; axis X – horizontal seismic coefficient; axis Y – Sc (M-P method).

Figure  8. Sensitivity of Sf to the piezometric level change. 1 – Upper block; 2 – Lower block; axis X – predictive change in ground water piezometric level (m) (0 – level on the moment of engineering and geological researches carrying out); axis Y – Sc (M-P method).

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4

THE ANALYSIS OF QUANTITY SLOPE’S STABILITY ESTIMATION RESULTS

Estimations made by Morgenstern-Price (Morgenstern, 1965), Bishop (Bishop, 1955) and Janbu (Janbu, 1954) methods allow making a conclusion. In natural the upper block of the considered sliding area with given estimated indicators is stable. The lower block is in limit equilibrium state according to Morgenstern-Price and Bishop methods. The lower block is unstable according to Janbu method. It happens because simple Janbu method is more conservative. Thus estimated stability coefficients as a rule have minimum values in comparison with other limit equilibrium methods. Estimated results allow making a conclusion the sliding phenomena progress on the slope has regressive character. So landslide develops from the bottom up. The lower block stability decline is determined by lateral erosion of the river Lazovaya right inflow. The activation of sliding processes on the slope may happen by adverse engineering and geological situation. For example by increase the ground water piezometric level. The critical raising of ground water level is 0,5 m for lower block. The forecasting increase of the level for upper block higher than 3 m doesn’t lead to the loss of stability. Seismic effect of any intensity fewer than 6 strength may activate sliding processes at the lower block. Earthquake higher than 7 strength using Richter scale 64 is critical for upper block. Probabilistic analysis shows that the variety of sliding process activation is 0% for upper block and 32,5% for lower block. However it should be taken into account that sliding process development has a regressive character. Also the activation of landslide at the lower block will influence on the upper block. So localization activities including engineering survey should be organized for this slope. Calculations of the stability were made using the Rocscience software. The faculty of engineering geology named in honour of F.P. Savarenski in MGRI-RSGPU is a part of Rocscience Education Program. REFERENCES Bishop A.W. The use of the slip circle in the stability analysis of slopes. Géotechnique, 1955. Y. 5. P. 7–17. Bondarik G.K., Pendin V.V., Yarg L.A. Engineering geodynamic: textbook. M, 2007. pp. 439. Fomenko I.K. “Modern trends in slope’s stability assessment”//Engineering geology. 2012. 6. pp. 44–53. Fomenko I.K., Sirotkina O.N. Complex estimating methodology of slope’s stability//Digest of scientific works on the international research conference materials “Modern trends of theoretical and applied researches”. Odessa: Black Sea Region, 2011. pp. 88–96. Krahn J. Stability modeling with SLOPE/W. An Engineering Methodology: First Edition, Revision 1. Calgary, Alberta: GEO-SLOPE International Ltd., 2004. 396 p. Morgenstern N.R. and Price V.E. The analysis of the stability. of general slip surface//Géotechnique. 1965. V. 15. P. 70–93. Pendin V.V., Fomenko I.K. The assessment and prediction methodology of sliding hazard. M.: Publishing house RF Lenand, 2015. p. 320. Recommendations about quantity stability assessment of sliding slopes. PNIIS. M.: Stroiizdat, 1984. p. 80. Sergeev K.F., “New data about the relationship between late Mesozoic and Cainozoe deposits of Western Sakhalin east slopes (Makarovsky district, i. Sakhalin) // Pacific geology, 1984, 1., pp. 99–103. Sisoev J.A., Fomenko I.K. The sliding hazard variety analysis //Digest of scientific works on the international research conference materials “Scientific researches and its practical use. Current state and development trends”. Odessa: Black Sea Region, 2011. pp. 125–129. Zerkal O.V., Fomenko I.K. The variety slope’s stability assessment and it’s appliance in sliding hazard analysis // Analysis, prediction and management of natural risks in modern world: The materials of 9-th international research conferences “Georisk-2015” (October 13–14, 2015, Moscow) – Moscow, 2015.-V.1-pp. 225–231. Zerkal O.V., Fomenko I.K. The influence of various factors on the results of sliding processes variety analysis//Engineering geology.−2016.- 1.-pp. 16–22.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Prediction of rock movements using a finite-discrete element method Bulat Ilyasov TERETAU LLC, Bashkortostan Republic, Russia

Alexander Makarov SRK Consulting (Russia), Principal Geotechnical Consultant, ISRM, Moscow, Russia

Ivan Biryuchiov SRK Consulting (Russia), Geotechnical Consultant, Moscow, Russia

ABSTRACT: The aim of the study described in this article is to evaluate the suitability of a finite-discrete element method for predicting rock movement during underground mining of mineral deposits by caving systems. A comparison is made of the measured and modelled characteristics of deformation processes, which took place during mining at various deposits. The developed algorithms for simulating sub-level and block caving are described. Keywords: method

1

fractured rock failure, disintegration and displacement, finite-discrete element

INTRODUCTION

Predicting rock and ground surface movements during mining by caving methods is usually based on empirical methods, which cannot take into account all geological conditions. For this, it is necessary to simulate the processes of breaking fractured rock mass and the subsequent behaviour of disintegrated material: movement of rock blocks in the mined-out space and the caving zone. Discrete elements methods have considerable potential for solving problems with disintegration. For their practical application, it is necessary to understand their specific features and the limits of applicability. The finite-discrete element method is one of the most advanced numerical methods in mechanics of a discrete medium (Munjiza, 2004). To perform geomechanical calculations by this method, Teretau develops Prorock software package. Software processor implements the algorithm of forced stabilization with Coulomb strength criterion. In the calculations, an extreme deformation by dilatancy is simulated, along with variability of strength characteristics, tectonic discontinuities and anisotropy of strength properties, plastic deformation of finite elements. To ensure the high speed, computations are performed on general-purpose processors (Ilyasov, 2016). Prorock software was used to simulate movement of rock mass, ground surface and host rocks at mines using caving systems: Degtyarsky (Russia), Ridder-Sokolny (Kazakhstan) and Palabora (South Africa).

805

2

SUB-LEVEL AND BLOCK CAVING SIMULATION SCHEME

Caving simulation begins only after the model achieves a state of quiescence with the help of the forced stabilization algorithm (Ilyasov, 2016). This ensures a significant reduction of the impact of inertial oscillations in the system that occur after the simulation is started. After simulation is initiated, elastic modulus, Poisson’s ratio and cohesion parameters of rocks in the mining area are gradually reduced to the values corresponding to the disintegrated rock mass (rubble). This is necessary to reduce the number of elements caused by the exclusion from calculations of unrealistic dynamic effects, consisting of high-amplitude oscillations of the system, which cause extensive disintegration around the area with excluded elements. Another consequence of excluding elements from the calculations is significant acceleration of nearby non-excluded finite elements and, consequently, an unnatural increase in the level of disintegration in the mining area. To reduce such effects, the algorithm of plastic deformation of finite elements has been developed and introduced into the program code (Ilyasov, 2016), and a dissipative impact model has been added (Mahabadi, 2012). The values of the elastic modulus, Poisson’s ratio and cohesion are reduced until either one of the two conditions is met: Sc/S0 < 0.18nts > 7000 where Sc is the current area of the element, S0 is the initial area of the element, nts is the number of time steps since the beginning of simulation of the current area. After the condition is met by at least one element, all elements are excluded from calculations. For block caving, the undercut level is modelled first in the same way as for sub-level caving method. Next, to simulate the ore draw as it caves, elastic properties of the elements are changed, and the rate of change depends on the reduced distance li /L0, where li is the distance from the centre of the element to the base of the undercut level. L0 value is calculated depending on the average size of the element in the model. When the elastic modulus reaches 18% of the initial value, the element is excluded from calculations. This limit has been found empirically. Figure  1 presents a diagram explaining the ore draw modelling. The above modelling scheme provides realistic simulation of ore mining by block caving method and stable operation of the processor. It should be added, however, that even with such analytical model, it is necessary to overstate strength properties of production level

Figure 1.

Ore draw modelling diagram.

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elements by several times in order to minimize their unnatural disintegration resulting from exclusion of elements from calculations.

3

CASE STUDY: DEGTYARSKY MINE

Degtyarsky copper deposit (Urals, Russia) is a steeply-dipping tabular lode with a thickness of 6 ÷ 25 meters, which was mined by sub-level caving method. During the development of the deposit, mine survey department monitored deformations of the ground surface (Kuznetsov, 1971). According to monitoring results, first caving of the ground surface occurred during extraction of the upper level (highlighted with violet shading in Figure 2a). This fact is used to back-calculate strength properties of the rock mass. Used rock mass properties are presented in Table 1. Figures 2a and 2b show the results of modelling by mining stages. Ground surface movement based on modelling results was close to the measured one. Estimated values of vertical displacements in the hanging wall are sometimes up to 100% higher than the measured ones. Based on survey data, horizontal displacements of the surface were 1.5–1.8 higher than vertical displacements, whereas in the model, this proportion ranges between 1.3 and 1.9. Significant differences in estimated and actual surface displacements in the footwall of the deposit are explained by presence of fragmented rock mass close to surface (Kuznetsov, 1971), which could not have been accounted for in simulation, as their parameters were unknown. Based on modelling data, hazardous impact angles β were plotted, that characterize the boundary of the ground surface zone with deformations exceeding 2 mm/m; the error of the estimate versus actual values amounted to 1.7° and 2.8°.

Figure 2.

Table 1.

Rock movement at Degtyarsky mine: a) cross-section 7, b) cross-section 9.

Degtyarsky deposit rock mass properties.

Rock type

Density (t/m3)

Elastic modulus (GPa)

Poisson’s ratio

Cohesion (MPa)

Internal friction angle (deg)

Tensile strength (KPa)

Shales Ore

2.8 3.6

12 12

0.29 0.29

0.2 0.2

38 38

5 5

807

According to I.A. Kuznetsov (Kuznetsov, 1971), displacements in the hanging wall in areas with significant thickness of mineralization happened in the form of slabbing and sagging of shale formation with subsequent caving of blocks sized 40 to 60 meters. Similar movement parameters were obtained through modelling by finite-discrete elements method in Prorock.

4

CASE STUDY: RIDDER-SOKOLNY MINE

Ridder-Sokolny polymetallic deposit (Kazakhstan) comprises about 10,000 discrete lenticular ore bodies. The deposit is mined using caving method with backfill (under protected areas). Table 2 presents rock mass properties by geotechnical domains identified through statistical analysis. Cohesion values were obtained by means of back-calculation of the subsidence event shown in cross-section 5 (Figure 3a). SRK Consulting reviewed cases of ground subsidence caused by extraction of individual ore bodies using caving methods (Makarov, 2017). In all cases, ore bodies had isometric shape in plan view. Figures  3 a–c show the results of ground subsidence simulation. Simulation accounted for jointing and tectonic discontinuities and used the algorithm to incorporate horizontal tectonic stresses. Simulation of a caving zone above one of the mined-out ore bodies was also performed. The actual contours of the caving zone were established through drilling observation holes. Figure 4 shows the mining outlines and the zone of disintegration based on measurements in observation holes and modelling. In addition to jointing, the influence of excavations located above was also taken into account. Based on results of simulation it was concluded that 2D modelling of isometric ore bodies, dimensions of subsidence zones are determined with significant error. However, the very fact

Table 2.

Ridder-Sokolny deposit rock mass properties.

Rock type

Density (t/m3)

Elastic modulus (GPa)

Poisson’s ratio

Cohesion (MPa)

Internal friction angle (deg)

Tensile strength (KPa)

Aleuropelite, tuff Microquartzite Shale Quartz formations Quaternary soils

2.71 2.72 2.72 2.68 2.00

28.2 39.6 19.0 27.6 0.05

0.19 0.2 0.19 0.15 0.3

0.69 1.14 0.75 0.60 0.20

34 34 36 31 20

5 5 5 5 1

Figure  3, Modelled and actual outlines of ground subsidence at Ridder-Sokolny mine: a) crosssection 5, b) cross-section 3, c) cross-section 5a.

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Figure 4. Table 3.

Outline of the subsidence above a stope (Ridder-Sokolny mine). Palabora deposit rock properties.

Rock type

Density (t/m3)

Elastic modulus (GPa)

Poisson’s ratio

Cohesion (MPa)

Internal friction angle (deg)

Tensile strength (KPa)

Carbonatite Foskorite Micaceous pyroxenite Feldspathic pyroxenite Fenite

2.88 3.53 3.04 3.10 3.10

39.7 38.4 39.5 11.0 44.7

0.21 0.21 0.20 0.24 0.23

2.18 2.00 1.81 1.30 2.69

45 43 39 37 48

58 43 41 40 50

of subsidence was predicted correctly for all 6 models. Dimensions of the disintegration zone above a large stope were determined with an error of less than 40%.

5

CASE STUDY: PALABORA MINE

Palabora copper deposit (South Africa) was mined as an open pit to a depth of 800 meters, with subsequent underground block cave mining. The undercut level is located 400 meters below the bottom of the pit. A pit wall failure happened in late 2004 in the course of underground mining. The dynamics of development of the disintegration zone above the draw level was studied (Severin, 2017). The development of the pit wall failure was also restored by years from public domain information. Indirect data on mine productivity was used to estimate approximate ore extraction volumes by years, which made it possible to compare production volumes and disintegration process under the pit floor and in the wall. Deposit rock properties (Table 3) were adopted from Sainsbury (2016). Cohesion values were estimated by back-calculation, so that the modelled outline of the disintegration zone as of April 2003 coincided with the actual one. Calculations incorporate rock mass jointing and tectonic faulting as presented by Sainsbury (2016). Figure 5 compares the results of disintegration simulation with the actual data. As can be seen, the simulated disintegration in the course of mining generally agrees with observation data. 809

Figure 5.

6

Disintegration zones: modelled and actual.

CONCLUSIONS

It is possible to solve geomechanical practical problems related to rock movement in the course of mining by caving methods with the use of the finite-discrete element method implemented in Prorock software: predict zones of disintegration in the rock mass and on surface as mining operations progress, including in the walls of the pit in case of development of an underground mine underneath it. When extracting extended lodes, prediction of displacements in 2D can achieve an accuracy of a few meters. For isometric ore bodies, calculation errors can be much higher. Prediction is possible if there is data for back-calculation for a particular deposit on a similar scale, e.g. development of a disintegration zone at early stages of mining. Back calculations are used to determine cohesion with the account for the scale effect.

REFERENCES [1] B.T. Ilyasov (2016). Study of the kinetics of deformation of rock mass using finite-discrete element method. PhD Thesis. Ekaterinburg. P. 138. [2] S.N. Ivanov, M.I. Merkulov (1937). Degtyarskoe pyrite deposit. Moscow. P. 124. [3] M.A. Kuznetsov, A.G. Akimov, V.I. Kuzmin et  al. (1971). Movement of rocks on ore deposits. Nedra, Moscow. P. 224. [4] O.K. Mahabadi, A. Lisjak, A. Munjiza, and G. Grasselli (2012). Y-Geo: a new combined finitediscrete element numerical code for geomechanical applications. International Journal of Geomechanics, 12, pp. 676–688. [5] A.B. Makarov, A.I. Ananin, D.V. Mosyakin (2017). Weakening of failed rocks and sinking conditions. Mining Journal, 3, pp. 32–36. [6] A. Munjiza (2004). The combined finite-discrete element method. John Wiley & Sons Ltd. Chichester, UK. P. 350. [7] D.P. Sainsbury, B.L. Sainsbury, H-D. Paetzold, P. Lourens, A. Vakili (2016). Caving-induced subsidence behaviour of lift 1 at the Palabora block cave mine. Proceedings Seventh International Conference & Exhibition on Mass Mining. Sydney, 9–11 may 2016. pp. 415–426. [8] J.M. Severin (2017). Impact of faults and fault damage zones on large open pit slopes. PhD Thesis. Vancouver. P. 168.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Simulation of fracture propagation depth and failure in long hole open stoping P.J. le Roux & K.R. Brentley Brentley, Lucas and Associates, University of the Witwatersrand, Johannesburg, South Africa

ABSTRACT: There are numerous factors which affect open stope stability and often result in falls of ground. These falls of ground can be attributed to a number of factors such as beam failure due to a larger than normal roof area (hydraulic radius too large), adverse ground conditions, seismicity, the stress-strain environment, absence of support and poor drill and blast practices. The effect of fracture depth in open stope failure is sometimes underestimated and relatively unknown. Actual data collected from open stopes and the analysis thereof is used for back analysis on the failure depth. The benefits of this analysis will result in improved understanding of fracture propagation in Long Hole Open Stoping at depths.

1

INTRODUCTION

The aim and objectives of this research was to develop a method to determine the expected failure depth into the hangingwall and sidewalls of large excavations with a good degree of certainty. With the current failure criteria currently available, this cannot be done with certainty. Making use of back analyses is one of the most important aspects in any engineering field. Compared with other engineering fields such as Aeronautical, Civil and Mechanical engineering, back analysis in Rock engineering is not always being utilized efficiently. Back analyses of open stope hangingwall and sidewall failure can yield an insight into the true behaviour of these excavations in the mining environment. Knowing that these stopes failed, the magnitude and mode of failure can prove extremely useful. Ultimately, the failure of these stopes should be “designed”, and not be seen as “unexpected failure”.

2

FAILURE CRITERIA USED IN EXCAVATION DESIGN

A failure criterion can be defined as the instance where the stress condition at which the ultimate strength of the rock is reached. Failure criteria can be expressed in terms of the major principal stress σ1 that rock can tolerate for a given value of intermediate principal stresses σ2 and minor principal stresses σ3 (Ulusay and Hudson, 2007). To understand the behaviour of the rockmass around open stopes, failure criteria are used. If expected failure can be calculated the amount of expected dilution or overbreak can be determined using numerical analyses. Some of the failure criteria being used in rock engineering will include the Mohr-Coulomb criterion, Hoek-Brown criterion, Zhang-Zhu Criterion, Pan-Hudson Criterion, Priest Criterion, Simplified Priest Criterion and Drucker-Prager Criterion. The Mohr-Coulomb criterion and Hoek-Brown criterion are two-dimensional criteria in which the intermediate principal stress value is ignored. Three-dimensional criteria such as 3D Hoek-Brown criterion, Zhang-Zhu Criterion, Pan-Hudson Criterion, Priest Criterion, Simplified Priest Criterion and Drucker-Prager Criterion, include the intermediate stress value. Using these three-dimensional criteria, the influence of the intermediate stress value can be taken into account.

811

2.1

Mohr-Coulomb failure criterion

The Mohr-Coulomb failure criterion is a set of linear equations in principal stress space describing the conditions for which an isotropic material will fail, irrespective of any effect from the intermediate principal stress σ2 being neglected (Ulusay and Hudson, 2007). MohrCoulomb failure can be written as a function of major σ1 and minor σ3 principal stresses, or normal stress σn and shear stress τ on the failure plane (Jaeger and Cook, 1979). In the investigations of retaining walls by Coulomb (Heyman, 1972), the following relationship was proposed:

τ

SO + σ tan ∅

(1)

where So is the inherent shear strength, also known as cohesion, ∅ is the angle of internal friction, and the coefficient of internal friction μ = tan∅. The criterion contains two material constants, ∅ and So. The representation of Equation (1) in the Mohr diagram is a straight line inclined to the σ-axis by the angle ∅ as shown in Figure 1. Designing underground excavations utilizing numerical models can be difficult as they do not necessarily reflect the actual behaviour of the rock mass. In the case of brittle failure this is particularly true, the fundamental assumption of the Mohr-Coulomb criterion τ SO + μσ , relating the cohesion SO to a shear strength τ and a simultaneously acting frictional resistance μσ not being valid according to Kaiser and Kim (2008). As intact rock is being strained, cohesive bonds start to fail, and only after this does frictional resistance develop. Damage initiation and propagation occur at different stress thresholds according to Diederichs (2003) and the propagation of tensile fractures depends on the level of confinement as established by Hoek (1968) and used to explain brittle failure. Wiles (2006) explains that the Mohr-Coulomb failure criterion can also be mathematically expressed as shown in Equation (2):

τ

SO + σ tan ∅

(2)

where σ1 and σ3 represent, respectively, the major and minor principal stresses, Co and q represent, respectively, the rock mass unconfined compressive strength and slope of the best + ; ∅ is the friction angle fit-line as shown in Figure 2, where q tan2

(

2.2

)

Hoek-Brown failure criterion

The Hoek-Brown failure criterion follows a non-linear, parabolic form that separates it from the linear Mohr-Coulomb failure criterion. This criterion is an empirically derived relationship used to describe a non-linear increase in peak strength for isotropic rock with increasing confining stress. The criterion includes procedures developed to provide a practical means to estimate the rock mass strength from actual laboratory test values and underground observations (Ulusay and Hudson, 2007).

Figure 1.

The Mohr-Coulomb failure criterion for shear failure (Brady and Brown, 1985).

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Figure 2.

Alternative representation of the Mohr-Coulomb failure criterion (Wiles, 2006).

This criterion was developed as a means of estimating the rock mass strength by scaling the geological conditions present underground. Based on Hoek’s (1968) experiences with brittle rock failure and his use of a parabolic Mohr envelope derived from Griffith’s crack theory (Griffith, 1920, 1924) to define the relationship between shear and normal stress at fracture initiation, the criterion was conceived. Hoek and Brown (1980) proceeded through trial and error to fit a variety of parabolic curves to triaxial test data and associating rock failure and fracture initiation with fracture propagation, to derive their criterion (Ulusay and Hudson, 2007). The non-linear Hoek-Brown failure criterion for intact rock (Hoek and Brown, 1980) was introduced as shown in Equation (3):

σ 1 = σ 3 + m Cucs σ 3+ 3 + s Cucs 2

(3)

where m and s are dimensionless empirical constants and Cucs is the uniaxial compressive strength (UCS) of rock in MPa. The parameter m is comparable to the frictional strength of the rock and s indicates how fractured the rock is, and is related to the rock mass cohesion (Ulusay and Hudson, 2007). The Hoek–Brown criterion has been updated several times to address certain practical limitations, and with experience gained with its use to improve the estimate of rock mass strength (Hoek and Brown, 1988; Hoek et al, 1992, 1995, 2002). It was assumed that the criterion was valid for effective stress conditions thus the principal stress terms in the original equation had been replaced earlier with effective principal stress, σ 1′ and σ 3′ terms (Hoek, 1983). One of the major updates was the reporting of the ‘generalised’ form of the criterion (Hoek et al, 1995): ⎛ ⎞ σ′ σ 1′ = σ 3′ + Cucs ⎜ mb 3 + s ⎟ Cucs ⎝ ⎠

a

(4)

For broken rock the term mb was introduced. Hoek et al, (1992) reassessed the original mi value and found it to be depending upon the grain size of the intact rock, mineralogy and composition. To address the system’s bias towards hard rock and to better account for poorer quality rock masses by enabling the curvature of the failure envelope to be adjusted, particularly under very low normal stresses, the exponential term a was added (Hoek et al, 1992). As shown in Figure 3 the Geological Strength Index (GSI) was subsequently introduced together with several relationships relating mb, a and s, with the overall structure of the rock mass and surface conditions of the discontinuities (Hoek et al, 1995). A new factor D, also known as the blast damage factor, was introduced by Hoek et al. (2002), to account for near surface blast damage and stress relaxation in the rock mass. The factor D can range between 0 and 1 where D = 0 for undisturbed rock and D = 1 for highly disturbed rock mass. The mb, a and s were reported as: 813

Figure  3. Scaling of Hoek-Brown failure envelope for intact rock to that for rock mass strength (Ulusay and Hudson, 2007).

mb

S − 100 ⎞ ⎛ GSI mi exp ⎜ ⎝ 28 − 14 D ⎟⎠ S − 100 ⎞ ⎛ GSI s = exp ⎜ ⎝ 9 − 3D ⎟⎠

a

GSI S 20 − ⎞ 1 1 ⎛ − 15 + ⎜e + e 3 ⎟. 2 6⎝ ⎠

(5) (6)

(7)

where mi is a curve fitting parameter derived from triaxial testing of intact rock. The parameter mb is a reduced value of mi, which accounts for the strength reducing effects of the rock mass conditions defined by GSI as shown in Figure 3 (Ulusay and Hudson, 2007). 2.3

Strain-based failure criteria

There are numerous strain based criteria such as the extension strain criterion after Stacey (1981), the direct strain evaluation technique after Sakurai (1981), Fujii et al. (1998) proposed the critical tensile strain criterion for brittle failure of rock and Kwaśniewski and Takahashi, (2010) considered the relationship between the octahedral shear strain and it was found that the mean normal strain yielded much better results than the mean normal strain at strength failure.

3

NUMERICAL MODELLING

Map3D is based on Banerjee and Butterfield (1981), a very efficient Indirect Boundary Element Method, and incorporates simultaneous use of both fictitious force and displacement discontinuity elements. Special boundary elements are incorporated for the thermal and nonlinear analysis versions. This Boundary Element formulation offers many advantages over other stress analysis techniques. Direct Boundary Element formulations require approximately twice the computing effort to assemble and solve the boundary element matrix, compared to the indirect method used in Map3D (Wiles, 2006). 3.1

Input parameters for MAP3D

The rock mass in the numerical model is assumed to be homogeneous and isotropic to simplify numerical modelling (Wiles, 2006). MAP3D-SV was used to model the mining of the 814

open stopes and to determine the strain and stress values. These stress values for σ1, σ2 and σ3 are used as inputs into the Mohr-Coulomb, Hoek-Brown, Zhang-Zhu, Pan-Hudson, Priest, Simplified Priest and Drucker-Prager Criteria to determine whether any of these criteria can be used for assessing failure around open stopes. The following input parameters were used for MAP3D-SV: Young’s modulus Poisson’s ratio Density k-ratio

: 70000 MPa : 0.2 : 2700 kg/m3 : 0.5

These input parameters for Young’s modulus, Poisson’s ratio and density were obtained from laboratory testing that was conducted at the University of the Witwatersrand by Le Roux (2004) for the Eldorado Reefs. The k-ratio is an estimate based on actual underground observations and back analyses.

4 4.1

OUTCOME OF THE APPLIED FAILURE CRITERIA Failure criteria applied to Map3D results

Using the results obtained from Map3D on the hangingwall and sidewalls for the twenty-two case studies simulated, the failure criteria as discussed in section 2 will be applied. Figure 4 and Figure 5 show the results of application of the Mohr-Coulomb, Hoek-Brown, ZhangZhu, Pan-Hudson, Priest, Simplified Priest and Drucker-Prager Criteria to the median σ1, σ2 and σ3 results obtained from the Map3D analyses of the open stopes. Each of the criteria mentioned above either over or under estimate the failure around these case studies. The Drucker-Prager criterion does not fit the Map3D results and substantially overestimates the failure around open stopes. Thus it is not suitable for application to open stopes. Using the stresses and strains determined with Map3D, the various stress-based failure criteria and strain-based failure criteria mentioned above were applied to predict failure depths into the hangingwall and sidewalls of the case study open stope as shown in Figures 6 to 8. These results show that the stress-based failure criteria and strain-based failure criteria either completely overestimate or under estimate the failure for most of the case studies. It can be concluded that these methods are not appropriate for accurate design of open stopes in the hard rock gold mining environment. In Table 1 the Predicted rock mass unconfined compressive strength CUCS using different failure criteria is shown. Details of the method can be obtained from the original reference Le Roux (2015).

Figure  4. Graph showing the relation between various criteria used and obtained results for open stopes with hangingwall failure after Le Roux (2015).

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Figure  5. Graph showing the relation between various criteria used and obtained results for open stopes with sidewall failure after Le Roux (2015).

Figure 6.

Application of the Mohr-Coulomb criterion after Le Roux (2015).

Figure 7. Application of the Hoek-Brown criterion after Le Roux (2015).

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Figure 8. Application of the extension strain criterion after Stacey, (1981) with a modulus of elasticity E = 70000 MPa after Le Roux (2015).

Table  1. Predicted rock mass unconfined compressive strength CUCS using different failure criteria. Predicted Rock Mass UCS

Mohr-Coulomb criterion Hoek-Brown criterion Zhang-Zhu Criterion Pan-Hudson Criterion Priest Criterion Simplified Priest Criterion Drucker-Prager Criterion

5

Sidewall

Hangingwall

68 MPa 66 MPa 54 MPa 73 MPa 65 MPa 50 MPa –

44 MPa 44 MPa 58 MPa 68 MPa 44 MPa 18 MPa _

MEAN STRESS-VOLUMETRIC STRAIN CRITERION

Open stopes have a three-dimensional geometry and are created in a three-dimensional stress field. It is therefore to be expected that the stability of these stopes, and of course the potential dilution, will be dependent on the three-dimensional stress and strain conditions around these stopes. To take these three-dimensional conditions into account, the mean stress, σm, also known as the octahedral normal stress, was plotted against volumetric strain, εvol, in Figures 9 and 10 for open stopes with major failure, and minor failure, in the hangingwall and sidewalls respectively. These results indicate, as expected, a linear relation between the mean stress and volumetric strain-stress and strain are linked in the linear numerical model by constitutive behaviour known as Hooke’s Law (Brady and Brown, 1985). This explains the linear relation between mean stress and volumetric strain. Evaluating the stress-strain environment around these open stopes the following were observed from the numerical analyses. It would appear that there is a good relation between mean stress in MPa and volumetric strain in millistrains. A design criterion was proposed for open stopes allowing the prediction of the failure extent in the hangingwall and sidewalls of open stopes with accuracy. From the back analyses, it was found that for hard quartzite rock the tolerance for stress-strain changes in the immediate vicinity of the open stopes were very small. Mean stress σm and volumetric strain εvol can be mathematically expressed as follows:

σ1 + σ 2 + σ 3 3 = ε1 + ε 2 + ε 3

σm =

(8)

εvol

(9)

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Figure 9. Graph showing the relation between mean stress and volumetric strain for open stopes with major and minor hangingwall failure after Le Roux (2015).

Figure 10. Graph showing the relation between mean stress and volumetric strain for open stopes with major and minor sidewall failure after Le Roux (2015).

As failure of these simulated open stopes is bounded by Hooke’s Law, the Stress-Strain criterion (Ssc) also known as the Dilution Stress Strain Index (DSSI) as per Le Roux (2015), is the relation between mean stress and volumetric strain and can be mathematically expressed as follows: Ssc =

σm qεvvol

(10)

where q in GPa, which is the slope of the linear trend line of Figures 9 and 10. The q-value can be different for each operation depending on the Young’s Modulus (E) and Poisson’s Ratio (v). With this criterion the expected failure depth in the hangingwall or sidewalls of excavations can be determined. In this method the assumption is made that if the volumetric strain exceeds the critical value for mean stress, failure will occur as shown in Figure 11 in light grey. This method considers all three Principal stresses and strains components, which agrees with the actual environment these open stopes are being excavated in. The contour range for plotting the Ssc design criterion was set to minimum 0 (zero) and the maximum to 1, with intervals of 1 in Map3D. This means that if the Ssc obtained value is > 1, it will be 818

Figure 11.

Application of the stress-strain criterion after Le Roux (2015).

indicated as light grey on the grid plane. The predicted failure corresponded very well with the actual observed failure in the hangingwall as shown by the CMS (Cavity Monitoring System) of the open stope plotted in red on Figure 11.

6

DISCUSSION OF RESULTS

It was illustrated that, even with very limited information available, relatively accurate results could be obtained for the open stope design. This is significant, since when a new mine is designed there is very limited information available, and the expected fracture depth is normally assumed to be within a certain value, which could completely underestimate or overestimate your support design. The design approach that has resulted from the research allows failure depth into the hangingwall and sidewalls of open stopes to be predicted accurately, and the fracture depth can be calculated for use in large excavation design with a high degree of certainty.

7

CONCLUSION

The objective of this research was to develop a method to determine the expected failure depth into the hangingwall and sidewalls of large excavations with a good degree of certainty. With the existing methods available, this could not be done with certainty, and a very large database is required (Capes, 2009). Rockmass properties, rockmass classifications, blast design, blast techniques, the stress strain environment and hydraulic radius all have some effect on, or play a part in the evaluation of dilution. It was found however, that the stress strain environment actually plays a significant role in the behaviour of open stopes at depth. Twenty-two case studies were selected with sufficient information for the research. The results of predictions of the extents of failure into the open stope hangingwall or sidewalls, based on application of the Ssc criterion, allow open stopes to be redesigned to “fail” up to the required stope shape and thus to reduce dilution.

ACKNOWLEDGEMENTS The authors would like to thank Brentley, Lucas & Associates, Mining Consultants, for there assistance and it is greatly appreciated. 819

REFERENCES Banerjee, P.K. and Butterfield, R. (1981) Boundary Element Methods in Engineering Science. McGrawHill Book Company (UK) Limited, London. Brady, B.H.G., and Brown, E.T. (1985) Rock mechanics for underground mining. London: Allen and Unwin. Capes, G.W. (2009) Open stope hangingwall design based on general and detailed data collection in rock masses with unfavorable hangingwall conditions, PhD. Thesis, University of Saskatchewan. Diederichs, M.S. (2003) Rock fracture and collapse under low confinement conditions. Rock Mechanics and Rock Engineering 36 (5), pp. 339–381. Fujii, Y., Kiyama, T., Ishijima, Y. and Kodama, J. (1998) Examination of a rock failure criterion based on circumferential tensile strain, Pure and applied Geophysica, Vol. 152, pp. 551–577. Griffith, A.A. (1920) The phenomena of rupture and flow in solids. Philos Trans R Soc Lond Ser A Math Phys Sci 221(587), pp. 163–198. Griffith, A.A. (1924) The theory of rupture. In: Biezeno CB, Burgers JM (eds) Proceedings of the First International Congress for Applied Mechanics. Delft. J. Waltman Jr, Delft, pp. 55–63. Heyman, J. (1972) Coulomb’s Memoir on Statics. Cambridge University Press, London. Hoek, E. (1968) Brittle failure of rock. In: Stagg K.G., Zienkiewicz O.C. (eds) Rock mechanics in engineering practice. Wiley, New York, pp. 99–124. Hoek, E. and Brown, E.T. (1980) Underground excavations in rock. The Institution of Mining and Metallurgy, London. Hoek, E. (1983) Strength of jointed rock masses, 23rd Rankine Lecture. Geotechnique 33(3), pp. 187–223. Hoek, E. and Brown, E.T. (1988) The Hoek–Brown failure criterion—a 1988 update. In: Curran J (ed) Proceedings of the 15th Canadian Rock Mechanics Symposium. University of Toronto, Toronto, pp.31–38. Hoek, E., Wood, D., Shah, S. (1992) A modified Hoek–Brown criterion for jointed rock masses. In: Hudson JA (ed) Rock characterization: ISRM Symposium, Eurock ‘92, Chester, UK. Thomas Telford, London, pp. 209–213. Hoek, E., Kaiser, P.K. and Bawden, W.F. (1995) Support of Underground Excavations in Hard Rock, A.A.Balkema, Rotterdam, Brookfield. Hoek, E. and Brown, E.T. (1997) Practical estimates of rock mass strength. Int J Rock Mech Min Sci Geomech Abstr 34, pp. 1165–1186. Hoek, E., Carranza-Torres, C.T. and Corkum, B. (2002) Hoek–Brown failure criterion—2002 edition. In: Hammah R., Bawden W., Curran J., Telesnicki M. (eds). Proceedings of the Fifth North American Rock Mechanics Symposium (NARMS-TAC), University of Toronto Press, Toronto, pp. 267–273. Hoek, E. and Marinos, P. (2007) A brief history of the development of the Hoek-Brown failure criterion. Soils and Rocks, No. 2., November 2007. Jaeger, J.C. and Cook, N.G.W. (1979) Fundamentals of rock mechanics. Chapman and Hall Ltd., London Kaiser, P.K. and Kim, B-H. (2008) Rock Mechanics Advances for Underground Construction in Civil Engineering and Mining, Keynote lecture, Korea Rock Mechanics Symposium, Seoul, pp. 1–16. Kwaśniewski, M. and Takahashi, M. (2010) Strain-based failure for rocks: State of the art and recent advances, Rock Mechanics in Civil and Environmental Engineering – Zhao, Labiouse, Dudt & Mathier (eds), pp. 45–56. Le Roux, P.J. (2004) Project on Rock Mass Properties for the Free State, Mechanical Properties of Rocks and Rock Masses, University of the Witwatersrand, South Africa. Le Roux, P.J. (2015). Measurement and prediction of dilution in a gold mine operating with open stoping mining methods. PhD thesis, University of the Witwatersrand, Johannesburg. Le Roux, P.J. and Brentley, K.R. (2017). Time-dependent failure of open stopes at Target Mine. AfriRock Rock Mechanics for Africa, Cape Town, 2–7 October 2017, The Southern African Institude of Mining and Metallurgy, pp. 535–548. Ulusay, R. and Hudson, J.A. (2007) The complete ISRM suggested methods for rock characterization, testing and monitoring: 1974–2006, pp. 971–1010. Sakurai, S. (1981) Direct strain evaluation technique in construction of underground openings. Proceedings of the 22nd U.S. Symposium on Rock Mechanics, June 29 – July 2, 1981, Cambridge, MA, pp. 278–282. Stacey, T.R. (1981) A simple extension strain criterion for fracture of brittle rock. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. Vol. 18, pp. 469–474. Wiles, T.D. (2006) Course Notes, Mine Modelling Report.

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Hydraulically fractured hard rock aquifer for seasonal storage of solar thermal energy Mateusz Janiszewski Department of Civil Engineering, School of Engineering, Aalto University, Finland

Baotang Shen CSIRO Energy, Commonwealth Scientific and Industrial Research Organisation (CSIRO), Kenmore, QLD, Australia

Mikael Rinne Department of Civil Engineering, School of Engineering, Aalto University, Finland

ABSTRACT: The intermittent nature of solar thermal energy derives from its oversupply during the low season and undersupply during the peak season. The solution is to accumulate and store the surplus energy that can be used in times of high demand and low supply. The HYDROCK concept is a method developed for seasonal heat storage in artificially fractured bedrock. This study aims to investigate the rock fracturing process in the construction of hydraulically fractured hard rock aquifer for seasonal storage of thermal energy. The primary objective of this study is to perform a sensitivity analysis of numerical simulations of rock fracturing processes that are taking place during the development of artificially fractured heat storage in hard rocks. Coupled hydro-mechanical numerical models are generated using rock fracture mechanics code FRACOD2D. The sensitivity of critical parameters is presented, and all relevant influencing factors are investigated. Suggestions for practical applications of HYDROCK are given. Keywords: hydraulic fracturing, underground thermal energy storage, HYDROCK, numerical modelling, fracture mechanics

1

INTRODUCTION

The key of seasonal storage of solar thermal energy is to accumulate the surplus energy available in the low season to be used when the demand is high, and supply is low. The HYDROCK concept is a method for seasonal storage of thermal energy in artificially fractured hard rock aquifer, where the heat transfer takes place between the fluid and sub-horizontal fracture planes as depicted in Figure  1 (Larson, 1984; Hellström and Larson, 2001). The fracture planes are created by the use of hydraulic fracturing technique in boreholes, which is used commonly to increase the production rates in unconventional oil and gas reservoirs in tight shales and coal seams (Liu et al., 2015). It has also been used successfully to increase the yield of water from boreholes in hard rock aquifer (Joshi, 1996) Additionally, the method is used commonly to measure the in situ stresses in rocks (Amadei and Stephansson, 1997). In hydraulic fracturing, a liquid (most often water) is pumped into a sealed section of a borehole until the pressure reaches a level needed to initiate a hydraulic fracture. The orientation of hydraulic fracture is perpendicular to the least principal stress and parallel to maximum and medium principal stress. Hence, in reverse faulting stress regime which is typical for the Fennoscandian shield area, the hydraulic fracturing in vertical boreholes will result in sub-horizontal fracture planes. The first field experiment using HYDROCK method was conducted during 1982 in Bohus granite quarry in Rixö, Sweden (Larson et al. 1983, 821

Figure 1. Schematic diagram of the HYDROCK method. During the energy storage phase (left), the heat carrier liquid is pumped into the central hole, flows through sub-horizontal fracture planes towards the peripheral wells and heats up the surrounding rock. During the energy recovery phase (right), the cycle is reversed and the cold fluid is pumped into the peripheral wells, flows through fractures and removes the heat from rock, and is extracted from the central well.

Eriksson et al. 1983, Larson 1984, Sundquist and Wallroth 1990). The test confirmed that hydraulic fracturing could produce sub-horizontal fractures in shield areas. The HYDROCK is advantageous compared to other heat storage methods, e.g. borehole storage, as it requires fewer boreholes to be drilled and the investment cost is reduced. Latest HYDROCK field experiments have shown that reduction of 50% in the construction cost could be achieved if the energy extraction is larger than 105 MWh (Ramstad, 2004; Ramstad et al., 2007). The HYDROCK method requires a sufficient fracture hydraulic conductivity and works best in homogenous rocks, but anisotropic and layered rock can also be utilised. Grouting may be needed if natural, vertical or steeply inclined fractures are present in the rock mass. Sufficient hydraulic conductivity in the fracture plane is required for fluid flow to connect the boreholes hydraulically. Hence, one of the most critical parameters for a successful operation of a fractured hard rock aquifer for seasonal thermal energy storage is the resulting aperture of the created fracture planes. Nordell et al. (1986) proposed that a fracture aperture of 1 mm is required for a proper water circulation. Results of HYDROCK in situ experiments indicated that proppants, such as quartz sand might be required to increase the hydraulic conductivity of fractures and to get a more controlled flow (Larson, 1984; Nordell et al., 1986; Ramstad, 2004). Reaming of the borehole wall was also confirmed to reduce the impedance of the fracture (Larson, 1984). The combined effects of explicit rock fracturing (mechanical), fluid flow (hydraulic), and temperature change (thermal) are essential to understand and forecast the rock behaviour in underground thermal energy storage in hard rocks. When constructing HYDROCK thermal storage, the hydro-mechanical coupling is most important. This study focuses on fluid flow in rock fractures because in low permeability rocks the fluid flows through fractures predominantly. The pressure of the fluid in fractures may cause movement and an increase of aperture and propagation of the fracture. The changes in fracture geometry will change the hydraulic conductivity of the fracture and create new flow paths, which will enhance the flow of fluid (Shen et al. 2014). This study aims to investigate the rock fracturing process that is used in the construction of hydraulically fractured hard rock aquifer for seasonal storage of thermal energy. Coupled hydro-mechanical (HM) numerical model is prepared using the commercial FRACOD2D rock fracture mechanics code. The primary objective of this study is to perform a sensitivity analysis of the output values on varying input parameters and to give practical suggestions regarding the implementation of HYDROCK method.

2

METHODOLOGY

In this study, coupled hydro-mechanical numerical models were generated using rock fracture mechanics code FRACOD2D. FRACOD is a Boundary Element Method (BEM) and uses 822

an indirect boundary element technique—Displacement Discontinuity Method (DDM) with fracture mechanics theory integrated into it. The model consisted of one injection borehole, where the fluid was injected under high pressure to produce a single horizontal hydraulic fracture propagating from the borehole (see Figure 2). The rock was assumed to be perfectly isotropic and homogeneous with no internal fractures present. The reverse faulting stress regime was assumed, with horizontal rock stresses being five times higher than vertical. In the numerical model, a flow rate boundary condition was used to supply pressure into the injection borehole. The total flow rate in borehole was specified, and it remained constant throughout the whole process. The operational parameters of the hydraulic equipment applied in field experiments by Ramstad (2004) were employed. First, a base case scenario of hydraulic stimulation was simulated using the base value input properties presented in Table 1. The properties were selected to represent a generic case of a hard crystalline rock, which is used in the HYDROCK method. Next, a sensitivity analysis of the output values on varying input parameters in hydraulic fracturing model in FRACOD2D was performed. The input parameters were varied by ±50% (see the list in Table 1). The maximum fracture aperture was measured as the primary output result. Additionally, the maximum flow rate and maximum vertical and horizontal induced stress were measured at a monitoring point positioned 0.1 m to the right of the injection borehole.

Figure  2. Vertical displacement of the rock mass during hydraulic fracturing in a borehole after 50 cycles of fracture propagation. Table 1.

Sensitivity analysis of the input parameters for hydraulic fracturing models in FRACOD2D.

Parameter

Symbol

Low value

Base value

High value

Unit

Poisson’s ratio Young’s modulus Internal friction angle Cohesion Tensile strength Fracture normal stiffness Mode II/Mode I toughness ratio Flowrate at the boundary Initial borehole (pump) pressure Borehole volume Initial fracture aperture Residual fracture aperture Rock porosity Horizontal rock stress Vertical rock stress

ν E φ c σt Kn KIIc/KIc value_h value_pi vol_hole eini eres φ Sxx Syy

0.125 18.75 16.5 16.5 6.25 500 1 0.004 12.5 0.015 0.05 0.05 0.05 2.5 0.5

0.25 37.5 33 33 12.5 1000 2 0.008 25 0.03 0.1 0.1 0.1 5 1

0.375 56.25 49.5 49.5 18. 1500 3 0.012 37.5 0.045 0.15 0.15 0.15 7.5 1.5

– GPa ° MPa MPa GPa/m – m3/s MPa m3 mm mm % MPa MPa

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3

RESULTS AND DISCUSSION

The result of the base case simulation is presented in Figure 2. The maximum fracture aperture of 2.5 mm was reached after 50 cycles and then decreased to 1.2 mm with decreasing fluid pressure as the fracture propagated further. The resulting fracture aperture is higher than the minimum width of 1  mm required for proper circulation of water that was suggested by Nordell et al. 1986. Nevertheless, using propping agents such as quartz sand may be required to increase the flow capacity of created fractures as suggested by Larson (1984), Nordel et al. (1986) and Ramstad (2004). The fracturing process stopped after the fracture plane reached 15.6 m radius. As expected, the orientation of hydraulic fracture was perpendicular to the least principal stress and parallel to maximum and medium principal rock stress and is perfectly horizontal due to the homogenous rock without any internal discontinuities. This outcome corresponds well to the results of the first HYDROCK field experiment, where the resulting hydraulic fractures had at least a 10 m radius and were parallel to each other (Larson, 1983). However, in some in situ conditions, the hydraulic fracture may alter its orientation away from the drill hole if the local stress orientation is disturbed by discontinuities or flaws. The results of the sensitivity analysis are plotted on tornado plots in Figure 3. The maximum aperture of the resulting hydraulic fracture (Figure 3a) was most sensitive to changes in the Young’s modulus (+33.9% and −11.8% change in the aperture for −50% and +50% change in Young’s Modulus, respectively). The bigger the Elastic modulus of the rock, the lower the resulting fracture aperture. Second input parameter with high influence on the fracture aperture was the borehole volume ( 11% and 29.9% change in the aperture for -50% and +50% change in borehole volume, respectively). This is dictated by the length of the borehole

Figure 3. The sensitivity of fracture aperture (a), maximum flow rate (b), maximum induced horizontal stress (c), and vertical stress (d) to ±50% change of the input parameters in the hydraulic fracturing numerical model in FRACOD2D.

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sections at which it is pressurized. The longer the segment, the higher the borehole volume and the larger the resulting aperture of the hydraulic fracture. The maximum aperture of the fracture was also influenced by the maximum pressure of the pump used for hydraulic fracturing (−11.8% and 23.6% change in the aperture for −50% and +50% change in pump pressure, respectively). This is undoubtedly logical, as more pressure delivered by the pump results in higher pressures at the fracture tip available for fracture propagation. Other input parameters had a very low influence on the aperture (+1.6% change for −50% change in the vertical rock stress, and +1.6% change for −50% change in Poisson’s ratio) or no influence at all. Surprisingly, the increase of flow rate had a relatively low influence on resulting fracture aperture (2.4% increase). Sundquist and Wallroth (1990) suggested that high flow rate (>10 l/s) should be used to increase the hydraulic conductivity of hydraulic fractures based on the field test results in granite. However, it should be noted that the hydrological behaviour of rock fracture is not only influenced by the mechanical aperture, but also other properties such as contact area, roughness, matedness, or presence of channels (Hakami, 1995). The maximum flow rate at the monitoring point (Figure  3b) was most sensitive to the two operational parameters of the hydraulic fracturing used as a boundary condition in the model. By increasing the borehole volume and initial pump pressure by 50%, the flow rate was increased by 49.3% and by 24.8%, respectively. Interestingly, the decrease of Young’s modulus resulted in higher flow rate in the fracture. However, the change was small (+12% change). Other parameters had low or no influence on the maximum flow rate at the monitoring point. The max initial pump pressure and borehole volume were also influencing heavily the resulting induced rock stress at the monitoring point (Figure 3c,d) so that the 50% increase in their value resulted in 20% increase in both horizontal and vertical stress. The resulting rock stresses were also influenced by the elastic properties of the rock. However the increase was low (around 7% and 1% increase in stress with increased Young’s modulus and Poisson’s ratio, respectively). The main limitation of the numerical modelling results presented in this study is that no natural fractures were included in the rock mass, which could influence the outcome and alter the path of the propagating fracture as observed by Ramstad (2004). In some cases, it can even lead to a situation where the hydraulic fracture is arrested on a natural fracture and stops propagating. However, the focus of this study was to investigate how the generic rock properties and the operational parameters of the hydraulic fracturing equipment affect the resulting fracture, without the influence of existing discontinuities that are very site dependent. This phenomenon will be investigated more closely in future studies, where a back-calculation of an HYDROCK field test will be performed taking into account the distribution of natural discontinuities in the rock mass.

4

CONCLUSIONS

The hydraulic fracturing procedure for constructing an artificially fractured hard rock aquifer was successfully simulated numerically using FRACOD2D. It was found out that the most influencing input parameters in hydraulic fracturing numerical model are the operational parameters of the hydraulic fracturing equipment used (i.e. the maximum pump pressure and the borehole volume). Therefore, the proper setting of the operational parameter of the fracturing equipment is crucial. Such finding is essential for the selection of appropriate hydraulic fracturing equipment for a construction of HYDROCK storage. Larger pump capacity can increase the resulting rock fracture aperture. Hence, the hydraulic conductivity of fracture planes will be higher, and the thermal performance of the system will improve. The second group of input parameters that have a significant influence on the output are the elastic parameters (i.e. Young’s modulus and Poisson’s ratio). The higher the elastic properties, the more difficult is to create an open fracture with sufficient aperture and more pressure is required. This implies that selection of the site for HYDROCK construction and accurate site investigation will directly influence its performance. It is also crucial for numeri825

cal simulations of the hydraulic fracturing process as good quality laboratory data for the model input is needed. In the future, a variety of scenarios will be tested to investigate the influence of different geological and geomechanical conditions, such as rock types, anisotropy, in situ rock stress, and presence of discontinuities. Additionally, a back-analysis of HYDROCK field test from the literature will be performed with an upgraded numerical model.

REFERENCES Amadei, B. and Stephansson, O. (1997), Rock Stress and Its Measurement, Springer Netherlands, Dordrecht, the Netherlands. Eriksson, K.G., Larson, S.Å. and Haag, O. (1983), HYDROCK—en ny metod att lagra värme i berg (HYDROCK—a new method of storing heat in the bedrock), Technical Report R105:1983, Statens råd för byggnadsforskning, Stockholm, 117–123. Hakami E (1995) Aperture distribution of rock fractures. PhD thesis, Royal Institute of Technology, Stockholm, Sweden Hellström, G. and Larson, S.Å. (2001), Seasonal thermal energy storage—the HYDROCK concept. Bulletin of Engineering Geology and the Environment 60(2):145–156. doi:10.1007/s100640100101 Joshi, V. (1996), Borehole rejuvenation for sustainability, Proceedings of the 22nd WEDC Conference, 193–194. Larson, S.Å. (1984), Hydraulic fracturing in the Bohus granite, SW-Sweden. Test for heat storage and heat extraction. Geothermal Resources Council TRANSACTIONS 8:447–449. http://pubs.geothermal-library.org/lib/grc/1001215.pdf Accessed 7 October 2016. Larson, S.Å., Fridh, B. and Haag, Ö. (1983), Hydrock—värmelager i berg. Anläggning av värmeväxlarytor med hjälp av hydraulisk uppspräckning; HYDROCK—metoden (Hydrock method—Heat Storage in Rock: The construction of heat exchanger surfaces by hydraulic fracturing), Technical Report Publ. B 222, Chalmers University of Technology/University of Götenburg. Liu, H., Yang, T., Xu, T. and Yu, Q. (2015), A comparative study of hydraulic fracturing with various boreholes in coal seam, Geosciences Journal, 19(3), 489–502. Nordell, B., Bjarnholt, G., Stephansson, O. and Torikka, A. (1986), Fracturing of a pilot plant for borehole heat storage in rock, Tunnelling and Underground Space Technology, 1(2), 195–208. Ramstad, R.K. (2004), Ground source energy in crystalline bedrock—increased energy extraction by using hydraulic fracturing in boreholes. PhD thesis, Norwegian University of Science and Technology, Norway, http://hdl.handle.net/11250/235848. Accessed 7 October 2016. Ramstad, R.K., Hilmo, B.O., Brattli, B. and Skarphagen, H. (2007), Ground source energy in crystalline bedrock-increased energy extraction using hydraulic fracturing in boreholes. Bull Eng Geol Environ 66: 493–503. doi:10.1007/s10064-007-0100-7. Shen, B., Stephansson, O. and Rinne, M. (2014), Modelling Rock Fracture Processes: a fracture mechanics approach using FRACOD. Dordrecht, The Netherlands: Springer. doi:10.1007/978-94-007-6904-5. Sundquist, U. and Wallroth, T. (1990), Hydrock—energilager i berg—slutrapport för etapp 1 & 2 (Hydrock—energy storage in rock: final report for phase 1 & 2), Technical Report Publ. B 349, Chalmers University of Technology/University of Götenburg.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Peculiarities of numerical modeling of the conditions for the formation of water inflows into open-pit workings when constructing the protective watertight structures at the Koashvinsky quarry Sergey Kotlov, Denis Saveliev & Artemiy Shamshev Saint Petersburg Mining University, Saint-Petersburg, Vasilievsky Island, Russia

ABSTRACT: The article contains a detailed description of the peculiarities of the formation of the geofiltration regime on the northeastern side of the Koashvinsky quarry. In this area, the possibility of constructing a grout curtain is considered as one of the methods of controlling high inflows of water into the quarry. At the expectable construction site, the Quaternary age rocks, which are associated with the valley of the Vuonnemyok River, are developed and lying on the bedding crystalline rocks of ijolite-urtites; hydrogeological conditions are characterized as complex. Quaternary rocks, the influx from which is up to 2000 m3/h in normal time and up to 3000 m3/h in high-water periods, play the main role in the quarry watering. The water inflow into the quarry from crystalline rocks is approximately 500 m3/h. Formed at the time being in the open field, the filtration flow has a complex three-dimensional structure due to the presence of three aquifers in the section and a fairly close location of several boundaries feeding groundwater. The filtration calculations of the projected grout curtain with the use of analytical methods will not make it possible to take into account fully the complex hydrogeological structure of the northeastern side of the Koashvinsky quarry. The efficiency of the planned grout curtain can only be substantiated using geofiltration modeling. To create a numerical geofiltration model of the Koashvinsky quarry area, the Visual MODFLOW software complex was used. The model takes into account the filtration flows formed both in Quaternary and in crystalline rocks, the feeding of aquifers by means of rivers and lakes and through the infiltration of atmospheric precipitation, as well as by virtue of discharge into the quarry and existing drainage wells. In the course of numerical experiments, various alternate layouts for the grout curtain have been considered both in plain view and in section. It has been established that when the grout curtain is erected in the moraine aquifer that is the first from the surface, a decrease in the water inflow into the quarry will be insignificant in comparison with the total quarry drainage. In the case of the construction of the grout curtain in the artesian aquifer that is second from the surface, there will be an increase in the filtration rates in the upper part of strongly fractured and weathered crystalline rocks, the filtration properties of which have not been studied properly. As a result of the study of geofiltration processes, the optimum position of the grout curtain has been determined with the use of numerical modeling, the structure efficiency has been assessed, and recommendations have been developed for the further study of the hydrogeological structure of the site in question. Keywords: numerical geofiltration modeling, water inflows into the quarry, anti-filtration structures, hydrogeology

827

1

INTRODUCTION

The Koashvinskoye deposit of apatite-nepheline ores is confined to the southern part of the Khibin Massif and is located 14 km from the city Kirovsk. Absolute marks of the surface are in the range from +200 to +900 m. The deposit is confined to the intermountain valley of Elarge catchment area and favorable conditions for feeding aquifers due to a significant amount of precipitation. According to hydrogeological stratification, two interconnected aquifers are distinguished: a complex of Quaternary deposits represented by sandy-argillaceous sediments, and a complex of crystalline intrusive rocks of Paleozoic age represented mainly by yolite-urtites. In the complex of Quaternary rocks, two aquifers are distinguished, the first from the surface is Ostashkovsky and the hydraulic head of Podporozhsky (Figure 3). Quaternary rocks, the influx from which is up to 2000 m3/h in normal time and up to 3000 m3/h in high-water periods, play the main role in the quarry watering. The water inflow into the quarry from crystalline rocks is approximately 500 m3/h. In the immediate vicinity of the Koashvinsky Quarry, there is a large surface watercourse— Lake Porokyavr. Thus, the main inflow is formed from the northeastern side of the quarry edge, where Quaternary sediments are opened, as well as the Porokyavr Lake and Vuonnemyok River are located. On this area of the edge, filtration loss of a fine fraction of sandy rocks is registered, as a result of which sloughing tongues are formed. In order to reduce the negative impact due to high groundwater inflows, the design institutes proposed various solutions to reduce water inflows into the quarry, among which the construction of the grout curtain (GC) in the Ostashkov Aquifer was chosen as one of the methods for combating high water inflow into the quarry.

2

PROBLEM STATEMENT AND METHODS

In order to assess the efficiency of GC construction in this area, the experts of the Research Center GiPGP of the Saint Petersburg State Mining University performed work using numerical geofiltration modeling in the software application Visual MODFLOW. With the use of this software package, a model of the area of the northeastern side was created, which reveals water quarries of the Quaternary age that play the main role in the quarry watering (Figure 1). The use of the created model makes it possible to identify the main features of the formation of the geofiltration regime on the northeastern edge of the Koashvinsky Quarry, perform the forecast with regard to the change of water inflows into the quarry, and to assess the efficiency of various types of watertight structures and drainage measures. Formed at the time being in the open field, the filtration flow has a complex three-dimensional structure due to the presence of three aquifers in the section and a fairly close location of several boundaries feeding groundwater. The filtration calculations of the projected grout curtain with the use of analytical methods will not make it possible to take into account fully the complex hydrogeological structure of the northeastern side of the Koashvinsky quarry. The efficiency of the planned grout curtain can only be substantiated using geofiltration modeling. The general structure of the numerical model is shown in Figure 2. The created numeric geofiltration model takes into account the filtration flows formed both in Quaternary and in crystalline rocks, the feeding of aquifers by means of rivers and lakes and through the infiltration of atmospheric precipitation, as well as discharge into the quarry and existing drainage wells. An extensive regime network was created at the Koashvinskoye deposit, which consists of observation wells equipped for various aquifers. When creating the model, the results of plane surface surveys were used, while data from experimental filtration observations were used for model calibration. The calibration process involved comparing the real values of groundwater heads with the calculated levels obtained on the model; at the same time, the check was performed with respect to the consistency between the model costs and the actual productivity of the drainage system. In total, data from more than fifty wells was used; the values of level convergence for most of the wells are in the range of ± 2 m, for 828

Figure 1. Layout of the modeled area. 1 – Contour of the Quarry at 2027 year; 2 – GC; 3 – drainage and observations wells; 4 – observed sectors.

Figure 2. General structure of the numerical geofiltration model. A – profile breakdown into layers; B – distribution of the filtration coefficients over the model layers.

almost all the others—in the range of ± 5 m, a number of wells, approximately 8 pieces, stand out of the general range; however, despite this, we can talk about a fairly accurate mapping of the real geological and hydrogeological situation on the created numerical model, since this area is confined to the intermountain valley region. Due to a rather sharp change in the hypsometric marks of the surface, the actual values of the hydraulic heads for the given area reach 50 m–70 m, and sometimes even more. For such conditions, the results obtained with respect to level convergence are more than satisfactory. In the course of numerical experiments, various alternate layouts for the grout curtain have been considered both in plain view and in section. Thus, the main options for comparison were the following situations: Option I – GC location in the Ostashkov Aquifer, which is the first aquifer from the surface (this was considered the main option among the possible design solutions aimed at reducing water inflows into the quarry); Option II – GC construction in the Pressure Podporozhsky Aquifer (Figure 3). 829

Figure 3. Schematic geological section of the valley of the river. Vuonnemyok with options for modeling the location of the anti-filtration structures.

3

RESULTS

When considering Option I, one of the design institutes proposed the total GC length of 900 m; its erection will require to drill approximately 300 wells, and the base will rest upon a layer of relatively water-resistant banded clays. On a numerical model, a similar situation was shown, on which, according to the design decision, the GC was placed in the first calculated model layer (Figure 4). Table 1 shows the distribution of water inflows into the quarry, on the northeastern edge of the quarry, before GC construction. When modeling Option I of the GC location, the results of water inflows into the quarry were obtained taking into account the change in the filtration regime of the area (Table 1). When analyzing these results, it was determined that the total reduction of water inflow into the quarry would be approximately 200 m3/h, which is less than 10% of the total value in the side-land period. Water inflow reduction occurs due to the redistribution of underground flows and changes in the hydrodynamic regime in the Ostashkov Aquifer. The manifestation of negative phenomena and processes on quarry edges, such as sinking of the sides and filtration removal of the fine fraction, is mainly characteristic of the Ostashkov Aquifer, so GC erection in this element will undoubtedly reduce the activity of these processes; however, this design solution will not be able to affect in full a significant reduction of water inflows into the quarry and stop the edge slipping, as the value of the specific water inflow to the north-eastern edge will remain fairly high. Since the rocks of the Podporozhsky Pressure Aquifer still play the main role in the quarry watering, a decision was made to consider the possibility of placing GC on the model in the rocks of this aquifer. Edge slipping is not typical for these sediments, despite the higher value of the specific water inflow, which is associated with the spread of a larger sandy, sometimes even gravel fraction. When modeling this situation, it was found that the overall reduction in the inflow into the quarry will not exceed 180  m3/h, which is even lower than during GC erection in the Ostashkov Aquifer. This is due to the fact that during GC erection in the Podporozhsky Aquifer, more active filtration of groundwater will begin through the upper, more cracked and weatherworn part of crystalline rocks. As a result, the inflow from the Podporozhsky Aquifer will be almost halved, but at the same time, an inflow from the upper part of the crystalline rocks will increase by 30% of the initial value thereby reducing the overall efficiency of GC construction. 830

Figure 4.

Table 1.

The first design layer of the model, indicating the zone construction of GC.

The values of water inflows in the quarry, depending on the version of the simulation.

The values of water inflows from simulation results Total inflows in the Koashvinsky quarry, m3/hour Total productions of drainage system, m3/hour Inflow from Ostashkov aquifer, m3/hour Summary inflow from Podporozskiy aquifer and upper, more permeable part of crystalline rocks, m3/hour Inflow from crystalline rocks, m3/hour

4

Without GC

With GC in QIIIos (Option I)

With GC in QIIIpd (Option II)

2465

2270

2290

720

720

72

725

540

720

1100 (700 + 400)

510

1100 (700 + 400)

510

920 (390 + 530)

530

DISCUSSION AND CONCLUSIONS

As a result of the modeling work, it was found that GC erection in the first aquifer from the surface or in the pressure aquifer will have little effect on the reduction of water inflows and only to a small extent will help reduce the occurrence of such negative processes as the slipping of the quarry edges in the north-eastern section of the edge. Using numerical geofiltration modeling, the following solution was proposed to reduce water inflows into the quarry: extension and increase in the capacity of the encroachment line of dewatering wells (DWW). New DWWs were additionally set on the model (the specific yield of each of which is approximately 50 m3/h), and when analyzing the modeling results, it was concluded that the efficiency of the construction of five DWWs would outweigh the effect of GC construction (Figure 5). In case ten DWWs are constructed, the overall reduction of water inflow into the quarry from the north-eastern side will reach a value of 460 m3/h, which is much more efficient than the construction of a grout curtain, and, most importantly, requires much less capital construction costs. 831

Figure 5. Project of extra drainage wells.

Thus, as a result of studying the geofiltration processes using numerical modeling, the efficiency of the erection of the grout curtain was determined, which turned out to be quite low; the overall decrease in water inflow into the quarry will only be equal to 10% of the initial value in the side-land period. Moreover, an option was considered on the model that involved the extension and capacity expansion of the DWW encroachment line, the efficiency of which exceeds the effect of GC construction by a huge ratio. To make DWW operation more efficient, it is also possible to consider on the model options with the different location of DWWs within the area under investigation with a view to determine their rational location in order not to reduce the water-absorbing capacity of each individual well. Such numerical experiments make it possible to visually assess the efficiency of various methods of combating high values of water inflows into the quarry, consider the change in the existing hydrodynamic regime during the construction of protective structures, and help calculate in advance the efficiency and appropriateness of a certain method. Proceeding from these facts, contractors should remember that any design solution should be accepted and approved, based, among other things, on the results of numerical geofiltration modeling. Under the conditions of the development of rocks that are anisotropic and heterogeneous in terms of filtration parameters, any forecast estimates, as well as any recommendations regarding various methods aimed at combating high water inflow values should only be performed on the basis of numerical modeling results. Any numerical geofiltration model requires a large number of initial data to correctly display the real situation, but the opportunities that open up to the contractors, taking into account numerical modeling, make it possible to recoup unnecessary or inefficient design solutions performed without reliance on the modern methods of geofiltration modeling.

REFERENCES [1] Gavich I. Theory and practice of using numerical modelling in hydrogeology. 1980, Moscow. [2] Konosavskiy P., Soloveichik K. Matematical modelling of geofiltrational processes. Saintuniversity, 1988. Petersburg [3] Lomakin E., Mironenko V., Shestakov V. Numerical modelling of geofiltration, Moscow, 1988. [4] Norvatov U. Studying and predictions of technogenic regime of groundwaters. Leningrad, 1988. [5] Hill M.C. MODFLOW/P—A computer program for estimating parameters of a transient, threedimensional, groundwater flow model using nonlinear regression, U.S. Geological Survey, Open-file report, 1992.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Numerical study of the hydraulic fracturing and energy production of a geothermal well in Northern Germany Mengting Li Energy Research Center of TU Clausthal (EFZ), Goslar, Germany

Michael Z. Hou Energy Research Center of Lower Saxony (EFZN), Goslar, Germany Institute of Petroleum Engineering, TU Clausthal, Clausthal-Zellerfeld, Germany

Lei Zhou State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, China

Yang Gou Energy Research Center of Lower Saxony (EFZN), Goslar, Germany

ABSTRACT: The hydraulic fracturing is an essential tool to increase the permeability of tight formations and to increase the petrogeothermal energy recovery. In this paper, a hydraulic fracturing model was developed based on the previous work and implemented in the coupled numerical simulator TOUGH2MP-FLAC3Dplus. It considers the stress redistribution due to fracture opening and hydromechanical effects in full three dimensions. The cubic law was implemented, so that the fluid flow in both porous media and fractures can be simulated at the same time. With the advantages of TOUGH2MP, it is also capable to track the migration and distribution of injected fracturing fluid in the reservoir formation. The model has been used to study the hydraulic fracturing in the geothermal well Gross Buchholz Gt1 in Hanover, Germany. The measured data during the hydraulic fracturing treatment has been matched. The simulated fracture geometry was comparable with that analyzed from the well test. The verified model has been used to study the geothermal utilization in the Detfurth sandstone formation.

1

INTRODUCTION

The development of renewable energy is of high priority due to the world’s increasing energy consumption and climate change. As one of the most important members, the geothermal energy attracts a lot of attention because it is of huge amount, regenerable, and not dependent on weather. Especially in recent years, the development of deep geothermal energy is a hot topic (Kolditz et  al. 2015). Currently, the development of deep geothermal energy is restricted by the current drilling technology, energy transition efficiency, environmental impacts etc. The deep geothermal energy is normally stored in tight sandstone or granite formations which has normally low or ultra-low permeability. This characteristic makes it difficult to produce the original fluid in place (for hydrothermal system) or injected fluid (for petrothermal system) in an economic rate. In order to increase the deep geothermal energy recovery, the hydraulic fracturing should be carried out to increase the permeability of tight formations. The hydraulic fracturing must be well designed and optimized, on one side, to maximize the productivity, and on the other side, to remove or minimize the related risks such as environment contaminations and induced micro earthquakes. In this paper, a hydraulic fracturing model was developed based on the previous work (Zhou 2014, Gou et al. 2015) and implemented in the coupled numerical simulator TOUGH2MPFLAC3D. It considers the stress redistribution due to fracture opening and hydromechanical 833

effect in full three dimensions. The cubic law has been implemented, so that the fluid flow in both porous media and fractures can be simulated at the same time. With the advantage of TOUGH2MP, it is also capable to track the migration and distribution of injected fracturing fluid in the reservoir formation.

2

NUMERICAL MODELS

The hydraulic fracturing is a coupled hydomechanical geo-process combined with multiphasemulticomponent flow. Such processes have been considered in the developed model by Zhou (2014). However, it treated the flow in the fracture as incompressible and does not distinguish between the reservoir fluids and injected fluids. In order to overcome these shortcomings as well as consider more complicated fluid properties (e.g. the temperature—and pressuredependent density, viscosity as well as enthalpy), TOUGH2MP was adopted to simulate the fluid flow in both fractures and reservoir formations. In this study, the EOS7 (Zhang et  al. 2008) was adopted to describe the fluid properties. Following the approach in Gou et al. (2015), the second component of EOS7 (originally brine) was switched to fracturing fluid with its own properties. It was assumed that the fracturing fluid is water-based fluid (miscible with water), so that it will not form the third phase and can be described by the mass fraction in the aqueous phase (as the second primary variable). At current stage, it is simplified that the fracturing fluid has constant density and viscosity. The fluid flow in both fractures and reservoirs can be described with the following flow equation and mass conservation equation  Fβ

k

kr β ρβ   ∇pβ − ρ β g μβ

(

)

⎛ ⎞ ∂ ⎜ φ ∑ Sβ ρβ xκβ ⎟ ⎞  ⎛  ⎝ β ⎠ = −∇ ⋅ ⎜ ∑ Fβ xκβ ⎟ + qκ ∂t ⎝ β ⎠

(1)

(2)

where Fβ is the mass flow rate of phase β (β = l for liquid, g for gas) in (kg/m2/s), k is rock intrinsic permeability in (m2), krβ is phase relative permeability in (−), ρβ is phase density in (kg/m3), μβ is phase viscosity in (Pa⋅s), pβ is phase pressure in (Pa), Sß is phase saturation in (−), xκβ is mass fraction of component j in phase β in (−), and qκ is the sink/source in (kg/s). The fluid flow in the fracture is treated as flow between two parallel planes, which is normally described with the cubic law. So the fracture permeability is calculated as k=

( fw)2 12

(3)

where the w is the fracture width in [m] and f is a parameter that reflects the influence of the roughness on the transmissivity ([−]). The setup of the coupled non-linear equation systems is different for flow in the fracture and reservoir formations. For the reservoir formation, the element volume is constant. The original way in TOUGH2MP was adopted and the resulted set of coupled non-linear equations is Rnκ

k +1

M nκ ,k +1 − M nκ ,kk −

Δt ∑ Anm Fnmκ ,k +1 + Δtqκn ,k +1 = 0 Vn m

(4)

where Rκ,k+1n and Mκ,k+1n are the residuum and mass of component κ per unit volume in the n-th element at the time step k+1 in [kg/m3], respectively. Δt is the time step in [s], Vn is the volume of the n-th element, Anm is the cross section area between the n-th and m-th element 834

in [m2], Fκ,k+1nm is the flow term between the n-th and m-th element at the time step k + 1 in [kg/m2/s], and qκ,kΖ+1n is the sink/source term in the n-th element at the time step k + 1 in [kg/ m3/s]. Eq. 4 is not applicable for the modelling of fracturing, because the fracture width (or volume) is dependent on the fracture pressure, which is the first primary variable, and will change with the time. In such a case, combining the mass per unit volume with the fracture width, the set of coupled non-linear equations for fracture element is modified as Rnκ

k +1

κ ,k M )n − (wM )κn k +1 (wM

Δt κ , k +1 ∑ Anm Fnmκ ,k +1 + Δtt (wq)n = 0 An m

(5)

where Rκ,k+1n is the residuum of the width-mass per unit volume product in [kg/m2]. If two adjacent elements are both fracture element, Anm is also dependent on the fracture pressure and is evaluated at k+1 time step for numerical stability. The Eq. 4 and Eq. 5 are solved by the AZTEC parallel linear solver using the Newton method, leading to ⎛ ∂Rκ ,k +1 ⎞ −∑ ⎜ n ∂xi ⎟⎠ p i ⎝

(

−

) = Rκ ( ) n

k +1

(6)

where xi,p is the value of the i-th primary variable at the p-th Newton-Raphson iteration step.

3

CASE STUDIES

The developed model was applied in the study of the hydraulic fracturing in the GeneSys (Generated Geothermal Energy Systems) project. In this project, single well concept was developed to directly use the geothermal energy (Tischner et  al. 2010). Two wells were involved in the GeneSys project, including the well Horstberg Z1 for the testing and concept development, and another well Gross Buchholz Gt1 in Hanover for the demonstration. More details can be found in Tischner et al. (2010). In this study, the hydraulic fracturing of the well Gross Buchholz Gt1 was investigated. The well Gross Buchholz Gt1 was drilled in 2009. The well reached the depth of ca. 3900 m TVD and the target formation is Middle Buntsandstein. Hydraulic fracturing treatment was applied to create artificial fracture for heat exchange. According to Tischner et al. (2013), the hydraulic fracturing was carried out in 2011. A typical injection rate for the fracturing of tight sandstone formation, namely 90 l/s (5.4 m3/min), was adopted and no proppant was used. The whole operation lasted for 106 hours (23–28 May 2011) with 5 injection-pause-cycles, so that a final volume of 20,000 m3 fresh water was injected. After the fracturing treatment two low-rate injection tests were carried out in July and October 2011 (Pechan et al. 2014). The results of the pressure transient analysis show that the final fracture area was more than 0.5 km2. 3.1

Numerical simulation of the hydraulic fracturing in the well Groß Buchholz Gt1

According to the geological and stratigraphic conditions, a 3D ¼ model was generated with FLAC3Dplus and used for the simulation of the hydraulic fracturing (Fig.  1a). The model has a dimension of 1,700 m × 350 m × 563 m and lies at the depth between −3,287 m and −3,850 m. It was discretized into 38,016 elements. The model considers the main sandstone layers, including Solling, Detfurth and Volpriehausen formations, several interlayers as well as rock salt as caprock. The rock mechanical parameters and in-situ stresses were adjusted based on the previous study in Hou et  al. 2012 as well as Zhou 2014. The primary stress distribution was shown in Fig. 1b. The maximum principal stress was in vertical direction and calculated from the weight of the overburden. The minimum principal stress was estimated from the mini-frac tests. The ratio between the stress components shows an extensional stress regime. According to the in-situ measurement, the pressure decline at the post-injection phase 835

showed that the reservoir is highly pressurized (Tischner et al. 2013). An initial pore pressure of 65 MPa was used in this study. For the initial temperature, a natural geothermal gradient of 0.03°C/m was used. The temperature at the surface was adjusted, so that the temperature at the depth of 3700 m was 165°C (Schäfer et al. 2012). The simulation results are shown in the following figures. Fig. 2 shows the temporal evolution of the simulated bottom hole pressure (BHP). Fig.  2a shows the results during the stimulation phase. It can be seen that the simulated bottom hole pressure was slightly below 80 MPa. The simulated bottom hole pressure was comparable with the fracture pressure from Tischner et al. (2013), which was calculated from the measured well head pressure with consideration of well height and the flow friction. The pressure decline after shut-in was shown in Fig. 2b. The whole post-frac process from May until November 2011 was considered. The pressure decreased slowly after shut-in and reached 71 MPa at the end. The pressure decline after shut-in was also comparable with the measured value. Fig. 3 shows the simulated fracture geometry at shut-in (t = 185 h). It can be seen that the final fracture had a half-length of 1,390 m and height of 358 m (Fig. 3a). This corresponds to a total area of 1.1 km2 for the bi-wing fracture, which is enough for the geothermal utilization of this project. The upward fracture growth was restricted by the rock salt layers. The maximum fracture width was 2.5 cm at shut-in, while the leak-off ratio is 21% due to the low permeability

Figure 1.

(a) 3D ¼ model geometry with stratigraphy; (b) initial conditions.

Figure  2. (a) Matching of the bottom hole pressure during the hydraulic fracturing operation; (b) Matching of the bottom hole pressure during the post-frac phase.

Figure  3. (a) The fracture geometry at shut-in (t = 106 h) from the full 3D simulation with TOUGH2MPFLAC3D; (b) The simulation results from FIELDPRO (Tischner et al. 2013).

836

of the rock formations. For comparison, the simulation results with FIELDPRO based on semi-analytical solution (Tischner et al. 2013) were shown in Fig. 3b. The fracture geometry was more ideal with lower length and larger height, in comparison with the simulation with TOUGH2MP-FLAC3Dplus, which considers the full 3D stress redistribution. But the fracture opening was comparable. 3.2 Numerical simulation of the geothermal utilization Based on the simulated fracture geometry, a 3D ½ model was generated for the simulation of the geothermal utilization. The model has a dimension of 3,500 m × 7,000 m × 563 m and lies at the depth between −3000 m and −4200 m (Fig. 4a). It contains all the relevant rock formations and considers the simulated hydraulic fracture in the previous section. TOUGH2MP is used for the coupled hydro-thermal simulation. Because of the low permeability of the formation, the hydro-mechanical effects should be taken into account, especially the fracture opening, the induced storage effect and permeability enhancement. In this study, a simplified approach was adopted, on one side to consider these effects and on the other side to avoid the time-consuming hydro-mechanical coupling. In this approach, the minimum horizontal stress was taken as input parameters and the fracture width was correlated to the effective stress. Two different annual cyclic schemes were considered. For both cases, the annual injection/production volume is 50,000 m3 and the temperature of the injected water is 50°C. In case 1 the water injection took place from April to June (3 months), after which there is a 3-month pause. The water is then produced from October to March (6 months). In case 2 the cold water was injected from April to September (6 months) and hot water produced from October to March (6 months). The results are shown as follows. Fig.  4b shows the pressure distribution after 5 years’ operation. It can be seen that the pore pressure in the fractured zone reduced from 65 MPa to 50 MPa, although the annual injection volume was equal to the production volume. This is because some of the injected

Figure 4. (a) 3D ½ model geometry for the simulation of geothermal utilization; (b) Simulated pore pressure distribution after 5 years’ operation (case 1).

Figure 5. (a) Simulated temperature change in the injection/production zone during the operation; (b) Simulated geothermal capacity and total extracted geothermal energy in 10 years.

837

water leaked off into the tight formation and cannot be produced easily. Fig. 5a shows the temperature evolution of the injection/production zone. The simulation results indicate that the produced water has higher temperature in the cyclic scheme 1 due to the 3 months’ pause period. This effect is obvious in the first 5–6 years. After that, the difference between the two cyclic schemes decreased. The geothermal capacity and total produced energy are shown in Fig. 5b. With the cyclic scheme, 32% more energy can be produced in 10 years’ operation.

4

CONCLUSION AND OUTLOOK

In this paper, a hydraulic fracturing model was developed and implemented in the coupled numerical simulator TOUGH2MP-FLAC3Dplus. The cubic law has been implemented, so that the fluid flow in both porous media and fractures can be simulated at the same time, with consideration of full 3D stress redistribution due to fracture opening and hydromechanical effect. The migration and distribution of injected fracturing fluid in the reservoir formation can be tracked. As the case study, the hydraulic fracturing and geothermal production of the well Gross Buchholz Gt1 in Hanover in Northern Germany was investigated. The measured well pressure during stimulation as well as post-frac phase was matched. The fracture geometry was comparable with those simulated from commercial simulator. The simulated fracture geometry was then used in the subsequent simulation of geothermal utilization. Two different annual cyclic schemes were studied with coupled hydro-thermal simulation. Based on the model, innovative cyclic schemes will be proposed and studied in the future. In addition, since the geothermal capacity of single well and single fracture was limited, the feasibility of multiple fractures with horizontal well will be studied.

REFERENCES Gou Y, Zhou L, Zhao X, Hou ZM, Were P (2015) Numerical study on hydraulic fracturing in different types of georeservoirs with consideration of H2M coupled leak-off effects. Environ Earth Sci. 73(10): 6019–6034. doi: 10.1007/s12665-015-4112-5. Hou MZ, Kracke T, Zhou L, Wang X (2012) Rock Mechanical Influences of Hydraulic Fracturing Deep Underground the North German Basin: Geological Integrity of the Cap Rock Salt and Maximum Magnitude of Induced Microseismicity Based on the GeneSys Stimulation in May 2011. Erdöl Erdga Kohle, 128(11): 454–460. Kolditz O, Xie H, Hou Z, Were P, Zhou H (Eds.) (2015) The Thematic Issue: Subsurface Energy Systems in China: production, storage and conversion. June 2015, Springer Publisher, Berlin Heidelberg, Germany. ISSN: 1866–6299. Pechan E, Tischner T, Renner J (2014) Fracture properties after hydraulic stimulation in low-permeability sediments (GeneSys-project). ISRM Regional Symposium—EUROCK 2014, Vigo, Spain, 27–29 May. Rioseco EM, Löhken J, Schellschmidt R, Tischner T (2013) 3-D Geomechanical modeling of the stress field in the North German Basin: case study GeneSys-borehole GT1 in Hannover Groß-Buchholz. Proceedings of the 38th Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, February 11–13. Schäfer F, Hesshaus A, Hunze S, Jatho R, Luppold FW, Orilski J, et al. (2012) Kurzprofil der Geothermiebohrung Groß Buchholz Gt1. Erdöl Erdgas Kohle, 128(1): 20–26. Tischner T, Evers H, Hauswirth H, Jatho R, Kosinowski M, Sulzbacher H (2010) New Concepts for Extracting Geothermal Energy from One Well: The GeneSys-Project. Proceedings World Geothermal Congress 2010, Bali, Indonesia, 25–29 April. Tischner T, Krug S, Pechan E, Hesshaus A, Jatho R, Bischoff M, Wonik T (2013) Massive hydraulic fracturing in low permeable sedimentary rock in the GeneSys project. Proceedings of the 38th Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, February 11–13. Zhang K, Wu YS, Pruess K (2008) User’s guide for TOUGH2-MP—amassively parallel version of the TOUGH2 code. Earth Sciences Division, Lawrence Berkeley National Laboratory, LBNL-315E. Zhou L (2014) New numerical approaches to model hydraulic fracturing in tight reservoirs with consideration of hydro-mechanical coupling effects. Cuvillier Verlag Göttingen. ISBN: 9783954046560.

838

Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

A mathematical approach for prediction of inclinometer measurements in open-pit coal mine slopes Mehmet Mesutoglu & Ihsan Ozkan Mining Engineering Department, Selçuk University, Konya, Turkey

ABSTRACT: The inclinometer measurement method is used widely to monitor unstable slopes encountered in open-pit mines. Although an indispensable method for determining the horizontal displacement, implementation of the method is quite expensive and difficult. In order to determine the deformation behavior, in situ measurements should be followed with frequent intervals. However, because of adverse weather conditions, inclinometer measurements sometimes cannot be performed. To predict the inclinometer measurement values that were not performed, a mathematical model was developed based on the time and rainfall. To test performance of the mathematical model, inclinometer measurement results obtained from 9 boreholes in Orhaneli-Turkey coal mine region were used. According to the data obtained from the in situ measurements monitored for approximately one year, in the mouth of the boreholes and also in the depth of the shear plane, horizontal displacement values in the north-west direction were determined as 19 mm and 20 mm, respectively. It was determined that the mathematical model results predicting the horizontal displacement values were strongly related to the in situ inclinometer measurement results. Thus, when in situ measurements cannot be performed, the engineers can interpret the graphical outputs that are prepared using the predicted displacement values.

1

INTRODUCTION

The slope design of an open pit is extremely important in terms of the safety of the enterprise. However, tension cracks in mine sites are an indicator of unstable slopes and must be monitored (Ozgenoglu, 1986). The stability of the slopes in open pit mines depend on geotechnical properties including rainfall, groundwater conditions, drilling-blasting, excavation, mine geometry and seismic activity. Depending on the open pit mine operations and effect of these parameters, slope movements increase with time and eventually reach a dangerous level (Ulusay et al., 2014). This unfavorable situation can endanger life and property. There are two different methods to track time-dependent displacement behaviors of unstable slope. One of them uses the topographic surface, and the latter use a borehole. In the measurements taken from the topographic surface, the slope movements can be determined but the depth of the shear zone formed in the rock mass cannot be determined. The inclinometer measurements carried out in the borehole determines the depth of the shear zone in important projects (Dunnicliff, 1993). The horizontal displacement at every 0.5 m depth in the borehole is measured by an inclinometer probe that has 0.01 mm sensitivity (ISRM, 2007). The inclinometer measurement is expensive and laborious because it requires: perforation of boreholes; establishment of measurement systems; protection of boreholes; and time-consuming in situ measurements. Therefore, the in situ measurements must be carried out with small time intervals. However, this situation is not always possible in the winter climatic conditions (Ozkan et al., 2010). In this study, a series of statistical analyses were performed to predict displacements when in situ measurements were not possible. As a result, a mathematical model was prepared based on time and rainfall. Thus the displacements not measurable by an inclinometer system can predict based on the developed equation. The equation was tested on the Orhaneli project results obtained from 9 boreholes (Mesutoglu, 2013 and Gokay et  al., 2013). The 839

graphical outputs based on performance results predicted displacement results for randomly selected time values and was compatible with real in situ measurements.

2 2.1

IN-SITU MEASUREMENTS Inclinometer measurement method

The inclinometer system included an inclinometer casing, an inclinometer probe and cable, and an inclinometer readout unit. Inclinometer casing is typically installed in a vertical borehole drilled up to stable rock unit. The bottom of the casing is anchored on the stable ground. The initial borehole profile was recorded as a reference by the inclinometer probe. Slope movements cause movement away from the initial position of the casing. The rate, depth, direction, and magnitude of the slope movements are calculated by comparing the initial reference and the subsequent measurements. 2.2

Orhaneli-Gümüşpınar open pit coal mine and measurement studies

Orhaneli–Gümüşpınar coal basin is 55 km south of Bursa. It has been operated by Turkish Coal Enterprises (TKI) since 1979. From 1998 and 2012, there were many unstable slope problems. Serious slope failure problems occurred due to mining operations in 2012. In situ measurements for the unstable slope formed in the mine region were begun. To measure the horizontal displacements, 9  inclinometer measurement boreholes were drilled at locations determined by preliminary studies like site investigation, geophysical, and geology. Boreholes were drilled between 17.5 m and 63 m to reach stable ground in region. Four boreholes located in bottom of open pit were cut coal seam which has approximate thickness of 7 m. The in situ measurement studies were performed one by one in the 9 boreholes. The measurements were carried out in sub-stations which were installed with 0.5 m intervals in each borehole. There were 733 sub-stations established in all boreholes. The inclinometer measurements were performed for 105 days and averaged one every 8–10 days in the boreholes. Measurements were performed 101 times for all boreholes. The data received from 9 inclinometer measurement boreholes were transferred from the data logger to the computer via Smart software. The data were then processed by a second software program named INCLI-2 to prepare graphical outputs. A typical horizontal displacement and incremental displacements were given in Fig. 1 for OINK-1.

Figure 1. 2013).

Horizontal displacement values from in situ measurement (Mesutoglu, 2013, Gokay et al.,

840

According to in situ measurements, in the mouth of the boreholes, the maximum horizontal displacement value was 19 mm in the north-west direction. In addition, the depth of the shear zone in the nine boreholes was determined as horizontal displacement graphs. At the critical depths, the maximum horizontal displacement value was approximately 20 mm in the north-west direction. The width of the slope excavation in the original mine project is 800  meters. However, according to in situ measurement results, mine management changed the excavation method. In revised excavation, unstable slopes were separated from the narrow corridors with 60–80 meter intervals. After the coal production in the corridor, the next corridor excavation was carried out. Excavated mining pit was stopped by stripping material of next corridor. Slope movements were under control highly by new excavation method. However, it was observed that the displacements based on the new mine geometry still continued with low displacement rates. 3

MATHEMATICAL MODELLING

Inclinometer measurement systems were one of the in situ measurement methods. It is time consuming and expensive. However, shear zone depth and its thickness can only be used with borehole extensometers. Therefore, inclinometer measurement systems are used widely in important projects (Dunnicliff, 1993). Slope movements are based on rock and rock mass properties, mining activities, rainfalls, mine geometry, etc. (Ulusay et al., 2014). Thus, time intervals in inclinometer measurements are very important. Site engineers in project studies generally take measurements once or twice a month. Sometimes, measurement time intervals can be expanded due to the severe weather conditions. To predict measurement values for unmeasurable days, a series statistical analysis were carried out. In analysis, Orhaneli project measurement results were used. The statistical analysis and its interpretations can be considered in four stages. They are: 3.1

Stage-1 (calculation of ΣU from U)

The direct modelling of the behavior seen between the borehole depth and inclinometer measurements (Fig.1) are very difficult. That’s why, an indirect way has been considered in this study. In analysis, first of all, time-dependent displacement (U) behavior for each substation in the boreholes were determined by inclinometer measurements (Fig. 2a). However, the displacement graph does not contain a systematic structure. Because deformations presented here are vector magnitudes. In addition, in each measurement time, the determined measuring value is equal to distance from reference point to the last position. In next measuring time, the last determined measuring value is this time equal to distance from reference point to the latest position. Therefore, to overcome this problem, the total displacement values (ΣU) were calculated (Fig. 2b). That is, the vectorial magnitudes were considered as the scalar values and then the vectorial magnitudes were collected one after the other. Finally, graphs as Fig. 3 for all inclinometer boreholes were prepared. 3.2

Stage-2 (determination of ΣUp by statistical analysis)

The statistical analysis were carried out on data of these type of graphs (Fig. 3). In addition, in statistical analysis, total of the seasonal rainfall for a year in mine region was considered. The average rainfall values observed for the last two decade are recorded. The average rainfall per months is approximately 56.1 mm in the region. The following mathematical equation was developed by the statistical analyses conducted by SPSS V16.0.

∑ Up =

C1[1− e(

t/C )

] [1+C3 (RF/(673 RF))C4 ]

(1)

Here, C1, C2, C3 and C4 are the statistical constants depending on sliding rock material, ΣUp is the total predicted horizontal displacement (mm), t is time (day) and RF is total rain 841

Figure  3. The original total displacement behaviors for all of sub-stations in OINK-1 (Mesutoğlu, 2013).

Figure 2. The original and total displacement behavior in OINK-1/0.5 (Mesutoglu, 2013).

Figure  4. A typical time-dependent displacement behavior predicted and in situ measurements for ONK-1/0.5 sub-station.

Figure 5. The predicted displacement behavior in OINK-1 (Mesutoğlu, 2013).

amount (mm) which is at the moment of measurement. Also, 673 is the total rainfall in per year for Orhaneli region. It can change for different regions. The mathematical approach recommended in this study consists of basically two parts (Eq. 1). They are:

∑ Up

(t )

∑ Up

( RF )

= C1[1 e(

= C1 [1− e(

t/C )

t/C 2 )

]

] [C3 (RF/(673 RF))C4 ]

(2) (3)

Eq. 2 depends on the time and Eq. 3 depends on the total amount of rainfall in mine region. As a result, the final equation can be rewritten as follows. The sum of the values found from the two equations gives the value of the total displacement.

∑Up ∑Up

(t )

+ ∑Up( RF )

(4)

A typical example related to the statistical results is presented in Fig. 4. The time-dependent (Eq. 2), rainfall-dependent (Eq. 3) and sum of the two data (Eq. 4 that is Eq. 1) were plotted on this graph. The graph shows that time-dependent behavior is low level and is an asymptote to the X-axis. But it is seen that the rain dependent curve is nonlinear. The sum of the time and rain dependent curves gives the total predicted displacement (ΣUp, mm). Fig. 5 shows results predicted by the model. To determine the model performance, the mathematical model results (Fig. 5) can compare with the original measurement results (Fig. 3). This success of the model is valid for the other station points (from OINK-1 to OINK-9). The statistical regression coefficients (R2) are generally 0.95 (Table 1). 842

Table  1. The statistical constants and R2 values determined for OINK-1 (reduced data). Regression Coefficient Depth (m)

C1

C2

C3

C4

R2

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

10.068 9.900 9.770 10.175 9.923 9.866 9.798 9.675 9.612 9.517

2.224 2.201 2.211 2.617 2.647 2.812 3.023 3.173 3.395 3.677

13.013 14.600 16.568 18.001 18.371 18.352 18.017 18.347 18.749 18.960

3.814 4.037 4.265 4.638 4.720 4.824 4.900 4.955 5.066 5.149

0.95 0.95 0.95 0.95 0.95 0.95 0.94 0.94 0.94 0.94

Figure  6. Success of Eq. 1 on the OINK-1 borehole with reduced data (Mesutoğlu, 2013).

3.3

Figure 7. Performance of Eq. 1 on the OINK-1 borehole data (Mesutoğlu, 2013).

Stage-3 (a new graphical presentation for evaluations about inclinometer results)

We used Eq. 1 to predicted total displacement (ΣUp) values of boreholes for all of measurement date. The database used in statistical analysis consist of time and total displacement (ΣU) values recorded for each sub-station. In other words, the time vs displacement (ΣUp) behavior for each sub-station of borehole were determined by Eq. 1. As a typical graph, Fig. 5 was given. The total displacement (ΣU, ΣUp) values defined in Fig. 3 and Fig. 5 were graphed for each sub-station which are located in each 0.5 m along borehole axis. The displacements (ΣU, ΣUp) measured and predicted for each sub-station in each measurement time can be prepared as a separate database. The new database would be based on borehole depth and displacement. In conclusion, borehole depth vs displacement behaviors can be graphed using this database. For example, in 28 sub-stations of OINK-1, the original total values (ΣU) and the predicted values (ΣUp) by Eq. 1 were presented in Fig. 6. Of note, in Eq. 1, the total displacement values were considered (Fig. 2, 3 and 5). In this stage, it would be appropriate that Fig. 1 and Fig. 6 are compared. In evaluations of inclinometer out graphs, the deviations formed in borehole axis and those depths are very important. Because shear plane will be formed at this depth. In Fig 1, it is seen that the critical depths were occurred in 21th, 14th and 9th meters. When the new graphical output (Fig. 6) declared in this paper are evaluated, it is seen that the same the critical depths (21th, 14th and 9th m) will be determined even easier. 843

3.4

Stage-4 (evaluations by the suggested approach for date that not carried out measurement)

The final result will actually bring the main a benefits. For dates that inclinometer measurements cannot be performed, the predicted displacement values can be determined. A typical example for this condition is prepared. It can be seen easily from Fig. 1 that in situ measurements for 25.05.2013 in timetable valid for OINK-1 could not be carried out. Note that this date is between two dates in which in situ measurement are carried out (22.05.2013 and 28.05.2013, in Fig. 1). By using the above mathematical approach and Table 1, the predicted displacements (ΣUp) for the randomly selected date were calculated by Eq. 1. Then, Fig. 7 was prepared. Fig. 7 consists of inclinometer results for in situ measurements (ΣU) carried out in different dates and the displacement values (ΣUp) predicted for 25.05.2013. As a result, it was seen that the predicted values were located between the original measurement values.

4

CONCLUSIONS

The approach developed here can estimate the horizontal displacements. The constants of the mathematical models can be determined for different fields. Thus, the borehole profiles along vertical axis of borehole will be determined. If used by engineers, then the unmeasurable dates in the works conducted on unstable slopes will no longer be a problem. As a result, the interpretations and evaluations about unstable slopes will be carried out in a database.

ACKNOWLEDGMENTS This study was supported by Selçuk University and TKI. The author is also indebted to the reviewers for their valuable comments.

REFERENCES Dunnicliff, J. 1993. Geotechnical instrumentation for monitoring field performance. New York NY: John Wiley & Sons, 608p. Gokay, M.K., Ozkan, I., Ozsen, H., Dogan, K., Mesutoglu, M. 2013. In-situ measurements and evaluations intended for slope stability analysis in TKI-GLI-BLI Gumuspinar open pit mining, TKI Final Report, Selcuk University, Department of Mining Engineering, Konya, 326p. (in Turkish). ISRM (International Society for Rock Mechanics), 2007. The complete ISRM suggested methods for rock characterization, testing and monitoring: 1974–2006. In: Ulusay, R., Hudson, J.A. (eds). Suggested Methods Prepared by the Commission on Testing Methods. International Society for Rock Mechanics, Compilation Arranged by the ISRM Turkish National Group. Ankara, Turkey. Mesutoglu, M. 2103. Mathematical analysis for in-situ deformations obtained from inclinometer measurement boreholes established inside rock and soil structures, MSc Thesis, Selçuk University, Department of Mining Engineering, Konya, 213p. (in Turkish). Ozgenoglu, A. 1986. Slope stability analysis approaches in mining, Scientific Mining Journal, 25, 1.17–27. Ozkan, I., Ozsen, H., Oltulu, F., Boztas, S. 2010. Mathematical model based on long term inclinometer measurements at an open pit limestone mine. 2nd Conference on Slope Tectonics, Vienna, Austria, 1–5. Ulusay, R., Ekmekci, M., Tuncay, E., Hasancebi, N. 2014. Improvement of slope stability based on integrated geotechnical evaluations and hydrogeological conceptualization at a lignite open pit. Eng. Geol. 181: 261–280.

844

Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Comparison of limit equilibrium and finite element methods to slope stability estimation A.B. Makarov, I.S. Livinsky & V.I. Spirin SRK Consulting (Russia), ISRM, Moscow, Russia

A.A. Pavlovich Center of Geomechanics and Issues of Mining Industry, Saint-Petersburg Mining University, St. Petersburg, Russia

ABSTRACT: The key aim of this study was to compare the slope stability estimation results by the limit equilibrium and numerical modelling methods on the examples of large open pit mines. This study compares factors of safety resulting from standard estimation methods for dry slopes and with account of water table, including impacts of large scale blasting and earthquakes, based on Mohr-Coulomb and Hoek-Brown criteria. Keywords: slope stability, limit equilibrium method, finite element method, factor of safety, strength reduction factor

1

INTRODUCTION

With the increase of the open pit mining depths, the slope stability issues in complex mining and geological conditions are becoming more important. In the clear majority of cases, open pit slope stability is estimated by limit equilibrium methods and, mainly, in two dimensions. These estimation methods have proven to be sufficiently reliable, however they have certain assumptions that can become very significant in deep pits, where even small changes in the slope angles can have a significant economic impact. Numerical modelling, and primarily the finite element modelling method, is an increasingly common approach to slope stability estimation. Its main advantage is not only in estimating the slope stability, but also in estimating stress and strain distributions at each point of the rock mass. The methods of limit equilibrium have been widely tested throughout the world, and specialists have learned to use them for various geomechanical conditions. The finite element method, despite the active development and implementation of newer software, requires sufficiently high qualification to obtain reliable results. However, as our experience shows, the methods of limit equilibrium and numerical modelling can complement each other. To enable practical application of the finite elements method, it is necessary to test it and its algorithm of safety factor search, named SRF (Strength Reduction Factor), in comparison with the traditional Factor of Safety (FoS). For this purpose, the comparison analysis has been carried out. The results of two-dimensional analysis of different open pits by both methods have been considered, which allowed to estimate the differences and similarities of the finite element method compared to the classical limit equilibrium method (Figure 1). The analysis was carried out in Rocscience software: the method of limit equilibrium was tested in Slide v 6.0, and the finite element method was tested in Phase v 8.0. A comparative analysis of the slope stability estimation by limit equilibrium and finite element methods in two dimensions will subsequently allow to summarize the experience and develop a methodology for slope stability estimation in three dimensions. 845

Figure 1.

2

View of Slide estimation model.

THE KEY PRINCIPLES OF GEOMECHANICAL SLOPE STABILITY MODELLING

For reliable slope stability estimation, a geomechanical model is required that will adequately reflect the actual conditions of slope failure and allow for possible unfavourable external impacts (John Read, 2009). Depending on the complexity of the geomechanical conditions, a geomechanical model can include not only pit slope boundary, geological composition and geomechanical properties of the rock mass, but also, if necessary, groundwater level (or pore pressures in the joints) and the possible earthquake impact. However, in a number of cases, it is necessary to additionally simulate the zone disturbed by blasting operations, rupture cracks, structural features (jointing, cleavage, stratification, etc.) and other factors. Figure 1 presents a geomechanical model developed in Slide for limit equilibrium slope stability estimation. Rock mass structure (jointing) must be taken into account in estimating the slope stability in hard rock material, as it predefines the failure mechanism. To account for the jointing, Slide software has the Anisotropic Function, which reduces strength properties of the rock mass in the dip directions of the joint sets to reach the adhesion and friction angle along the joints (Figure 1). The anisotropic function is used to take into account the weakening impact of the joint sets with the same strike direction as the pit slopes (± 20°), including the joint sets dipping both into the pit and into the slope. Between the joint set directions, the estimations use the jointed rock mass properties. If data on the lengths of weakening surfaces is available, equivalent properties should be defined to consider the persistence of joints and the rock mass properties between the joints. The finite element method (Phase2) allows to define the location of faults and discontinuities in the model itself. For a long time, modelling the rock mass structure was quite a difficult task using the finite element method, until the Joint Network tool for defining the rock mass composition was implemented in Phase2. This allows modelling of both continuous and intermittent joints by defining the persistence. Another jointing parameter to be defined in the software is joint spacing. Figure 2 shows an example of joint set modelling using the Joint Network module, which takes into account their statistical variability. 846

Figure 2.

Definition jointing network in Phase2.

Figure  3. Comparing the safety factor by limit equilibrium method (LEM) and finite element method (FEM).

3

RESULTS OF SLOPE STABILITY ESTIMATION FOR ACTIVE OPEN PITS

Figure 3 is a comparative diagram of Factor of Safety (FoS) estimation by the limit equilibrium method and the finite elements method using the SRF procedure. The estimations were conducted for various geomechanical conditions and for a wide range of slope parameters (slope height was from few hundreds of meters to more than 500  m). Anisotropy of the 847

jointed rock mass properties was defined. Some models also included the groundwater level, pore pressure and the seismic impact from earthquakes. The comparison of the two fundamentally different slope stability estimation methods for 5 actual open pits showed their fairly good linear correlation with correlation factor of 0.97. The deviation of the trend line from the 45° line is 3° towards higher FoS estimated by the finite element method in comparison with the limit equilibrium method. In the range of FoS values between 1.0 and 2.0, which are important from practical standpoint, the estimated SRF values in most cases differ from the FoS by ±0.1–0.2. 4

COMPARISON OF ESTIMATION RESULTS FOR STANDARD ESTIMATION SCENARIOS

A comparative analysis was conducted to assess the similarity and difference of the limit equilibrium and finite element methods applied to various estimation scenarios (Table  1, Figure 4). The following main scenarios were assessed: homogeneous slope using the Mohr-Coulomb (MC) and Hoek-Brown (HB) strength criteria, considering water table (w) and seismic impacts from earthquakes (s); inhomogeneous slope of three lithological rock types (L), using the Mohr-Coulomb and Hoek-Brown strength criteria, and with zone disturbed by blasting operations; fault/weak contact (F) – a steeply dipping and a gently dipping contact / layer were considered, with broken sliding surface (the sliding surface partially or completely coincided with the weakening surface); anisotropic rock mass (A) – with different dip angles of joints, also several joint sets were defined; toppling (T) of a set of blocks formed by the planes of layers, cleavage or fracturing, with steep dipping of layers different from the slope angle, and with an underlying contact; the diagram in Figure 4 also includes data from the “Verification Manual...” (Rocscience, 2011), marked with an asterisk, to add to the statistics. The comparative analysis allowed to estimate the variance between the two methods, which was determined as the percent difference in the factors of safety. The following conclusions can be made following the comparison of the two methods for different estimation scenarios: In most cases, there is a slight difference, which confirms the applicability of both methods for assessing the slope stability. The differences in the two methods are observed primarily in inhomogeneous and anisotropic slopes. The greatest differences are observed with a gently dipping contact / layer or a flat joint set. The similarity of the results depends on the correct selection of the structural disturbance rank in the finite element method. Setting too small joint spacing can lead to local failures, and great spacing can lead to an overestimated Factor of Safety. In our opinion, setting the joint spacing should correspond to the hierarchical level of the scale of the estimated area. Traditional methods cannot estimate the slope stability with steeply dipping joints with bedding in the inverse direction to the slope. For such scenario, the Goodman-Bray method (Goodman, RE, 1976) produced a good correlation with numerical estimation methods. Numerical analysis should also be carried out to assess the stress-strain conditions of the rock mass, because these aspects are not considered in the limit equilibrium method. Slope stability analysis by limit equilibrium method should be carried out at all stages of pit design and mining operations. It is recommended to use numerical modelling to verify the limit equilibrium estimation results.

848

849 200 200

Toppling (dip −70°)

Toppling with basic joint (dips 20° & −70°)

T_(−70°)

T_2 sets

200 200

Multijoint_Anizotropic with two sets (dips 20° & 70°)

200

200

A_2 sets_NC Multijoint_Anizotropic with two sets (dips 20° & 70°), non-circular failure surface

Sloping_Anizotropic (dip 70°), non-circular failure surface

A_(70°)_NC

A_2 sets

Sloping_Anizotropic (dip 70°)

A_(70°)

200 200

200

Inclined_Anizotropic (dip 30°)

200

200

200

200

140

140

140

200

200

200

200

Height, m

A_(−40°)_NC Steep back_Anizotropic (dip -40°), non-circular failure surface

Steep_Anizotropic (dip 14°), non-circular failure surface

Steep_Fault (dip 70°)

F_(70°)

A_(30°)

Lithologies slope (three lithologies), Hoek-Brown criterion, damage zone (D)

L_HB-D

A_(14°)_NC

Lithologies slope (three lithologies), Hoek-Brown criterion

L_HB

Steep_Anizotropic (dip 14°)

Lithologies slope (three lithologies), Mohr-Coulomb criterion

L_CM

Sloping_Fault (dip 14°), non-circular failure surface

Simple slope, Mohr-Coulomb criterion, earthquake loading

CM_s

A_(14°)

Simple slope, Mohr-Coulomb criterion, watered slope

CM_w

F_(14°)_NC

Simple slope, Hoek-Brown criterion

HB

Sloping_Fault (dip 14°)

Simple slope, Mohr-Coulomb criterion

CM

F_(14°)

Description

48

48

48

48

48

48

48

48

48

48

48

48

48

48

48

48

48

48

48

48

Angle, °

Slope parameters

0.983

1.135

1.013

1.236

1.405

1.296

1.384

0.98

1.153

1.32

1.117

1.162

1.23

2.206

2.714

1.18

1.319

1.23

1.345

1.45

Slide (FS)

0.98

1.15

1.08

1.08

1.39

1.33

1.33

1.01

1.24

1.24

1.03

1.03

1.27

2.31

2.80

1.20

1.29

1.20

1.36

1.44

Phase 2 (SRF)

Factor of Safety (FOS)

0.3%

1.3%

6.2%

14.4%

1.1%

2.6%

4.1%

3.0%

7.0%

6.5%

8.4%

12.8%

3.1%

4.5%

3.1%

1.7%

2.2%

2.5%

1.1%

0.7%

Variance

The differences between the limit equilibrium and finite elements methods under different estimation scenarios.

Name of analysis

Table 1.

Calculated by Goodman & Bray (RocTopple) due to LEM (Slide) does not suit for Back Anisotropy

LEM (Slide) exaggerates FOS

LEM (Slide) exaggerates FOS

LEM (Slide) exaggerates FOS

LEM (Slide) exaggerates FOS

Note

Figure 4. Variance of estimation results by the limit equilibrium and finite elements methods under various estimation scenarios. * – according to Rocscience, 2011.

A comparative analysis of the slope stability estimation by limit equilibrium and finite element methods in two dimensions will subsequently allow to summarize the experience and develop a methodology for slope stability estimation in three dimensions.

5

CONCLUSIONS

The comparison shows that the finite element method is acceptable for estimating the pit slope stability. The finite element method covers a wider range of slope stability estimation problems, and also provides the solution to the stress-strain modelling. Despite the universality of numerical methods in assessing the pit slope stability, these methods are very time-consuming and require high qualification of specialists. Therefore, numerical methods are recommended for verification of the classical estimation methods, as well as for specific tasks associated with analysing the stress-strain state generated by open pit mining.

REFERENCES [1] Goodman R.E. Toppling of rock slopes./R.E. Goodman, J.W. Bray // ASCE Specialty conference on rock engineering for foundations and slopes. Vol. 2. – 1976. pp. 201–234. [2] Guidelines for open pit slope design/Editors John Read, Peter Stacey. – CRC Press/Balkema, 2009. – 509 p. [3] Phase 2. Slope Stability Verification Manual. Part I. 1989–2011, Rocscience Inc.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Analyzing slope stability in bimrocks by means of a stochastic approach Maria Lia Napoli, Monica Barbero & Claudio Scavia Department of Structural, Geotechnical and Building Engineering, Politecnico di Torino, Torino, Italy

ABSTRACT: Bimrocks (block-in-matrix rocks) are chaotic geological formations defined as heterogeneous mixtures of hard rock blocks encased in a fine-graded matrix. The inherent geometric, lithological and mechanical variability of bimrocks imply a great challenge in their characterization and modeling. A common practice when planning engineering works in these complex formations is to neglect the contribution of blocks and assign the strength and deformation properties of the weaker matrix to the whole rock mass. However, this assumption can lead to erroneous results and, consequently, to technical problems during construction works. The aim of this study was to investigate stability of theoretical slopes in bimrocks using a stochastic approach, in order to consider the spatial and dimensional variability of rock inclusions. Many 2D stability analyses were performed on slope models with simple geometries, elliptical block shapes and variable block contents. The results were compared to those obtained in a previous work, where slope stability analyses were carried out on bimrocks with blocks of circular shape. The findings of this research confirm that rock inclusions play an important role and strongly influence the slope stability of bimrocks. Furthermore, the advantages of using a stochastic approach when working with these heterogeneous materials are highlighted.

1

INTRODUCTION

The term bimrock (block-in-matrix rock) was defined by Medley (1997) to be a mixture of rocks “composed of geotechnically significant blocks within a bonded matrix of finer texture”. Several geological formations, including melanges, breccias, weathered rocks, conglomerates and agglomerates, can be considered to be bimrocks (Medley, 1994; Haneberg, 2004; Wakabayashi and Medley, 2004). A reliable characterization and modeling of bimrocks is extremely complex due to the inherent spatial, lithologic and dimensional variability of rock inclusions. Hence, geotechnical engineers often plan engineering works in these challenging materials taking into account only the strength and deformation properties of the weaker matrix. However, based on many case histories reported in the literature, such a simplified approach can lead to wrong forecasts, instability problems, unexpected difficulties and delays during construction works (Medley and Zekkos, 2011; Afifipour and Moarefvand, 2014). Recently, a lot of research (laboratory tests, numerical analyses and in situ tests) has been conducted to investigate the mechanical properties of bimrocks, in order to correctly design civil engineering works in these complex formations. The main results of these studies are summarized below: − bimrocks have scale independent (or fractal) block size distributions (Medley, 1994; Medley and Lindquist, 1995; Medley and Sanz, 2004; Sonmez et al., 2016); − the block/matrix threshold, i.e. the smallest geotechnically significant block and the largest block size within a volume of bimrock, should be defined according to the scale of engineering interest, termed “characteristic engineering dimension”, Lc. It could be the slope 851

− −

−

−

−

height, the specimen diameter, the tunnel diameter, etc. (Medley, 1994; Wakabayashi and Medley, 2004); at the selected scale of interest, blocks can be considered all the inclusions with dimensions between 0,5⋅Lc (below which rock fragments are considered to belong to the matrix) and 0,75⋅Lc (Medley, 1994; Barbero et al., 2006; Medley and Zekkos, 2011); the overall strength of bimrocks is affected by many factors. The most important is the Volumetric Block Proportion (VBP), but orientation and spatial location of blocks, matrix strength, block size distributions, block count, block shapes, etc., play an important role, as well (Lindquist, 1994; Irfan and Tang, 1993); to be classified as bimrock, a sufficient mechanical contrast between blocks and surrounding matrix must be afforded by the material, so as to force failure surfaces to negotiate tortuously around the blocks. In particular, a minimum friction angle ratio (tanϕblock/ tanϕmatrix) of between 1.5 and 2 and a minimum stiffness contrast (Eblock/Ematrix) of about 2 have been suggested in the literature (Medley, 1994; Lindquist and Goodman, 1994; Barbero et al., 2007; Medley and Zekkos, 2011); an increase in the strength of bimrocks was registered for VBP between about 25% and 75% (Lindquist, 1994; Medley and Lindquist, 1995). In this range, researchers have observed an increase of both Young’s modulus and friction angle, related to the increase in tortuosity of the failure surfaces, and a decrease in the cohesion, due to the poor mechanical properties of the matrix, where deformations develop; the presence of blocks (their position, shape and number) within slopes yields to irregular and tortuous sliding surfaces, far different from those obtained in homogeneous materials (Irfan and Tang, 1993; Medley and Sanz, 2004; Barbero et al., 2006). Greater safety factors have been found for higher VBP.

Some authors developed preliminary (simplified) strength criteria, which assume bimrocks to be homogeneous and isotropic masses (Lindquist, 1994; Sonmez et  al., 2009; Kalender et  al., 2014). Block proportions and matrix strength parameters are necessary in order to define the equivalent mechanical properties of the rock mass. Lindquist (1994) proposed the empirical strength criterion reported in Eq. (1):

τp

Cmatrixi

(

V ) + σ ⋅ tan (ϕ matrixi + Δ matrixi (VBP )) VBP

(1)

where tp is the equivalent mass shear strength, cmatrix is the matrix cohesion (assumed to decrease with increasing VBP), ϕmatrix is the internal friction angle of the matrix and Δϕmatrix(VBP) is its increase, assumed by Lindquist to be, above 25% VBP, equal to 3° for every VBP increase of 10%. The approach proposed by Kalender et al. (2014), which takes also into account contact strength between blocks and matrix, is reported in Eqs. (2)–(4).

ϕ bimrock

UCS CSbimrock cbimrock

⎡ ⎤ ⎡ tan (α ) ⎤ − 1⎥ ⎢ 1000 ⎢ ⎥ ⎢ ⎣ tan (ϕ matrix ) ⎦ ⎛ VBP ⎞ ⎥ = ϕ matrixi ⎢1 + V P ⎞ ⎝ VBP + 1⎠ ⎥ ⎛ 100 − VB ⎢ 1000 + 5 ⎥ ⎝ ⎠ 15 ⎢⎣ ⎥⎦ VBP ⎡⎛ ⎤ ⎞ CSmatr matrix ix ⎢⎝ A − A ⎠ / ( A − ) ⎥UCS ⎣ ⎦

UCSbimrockk ⎡⎣ 1− si

(

bimrock

) ⎤⎦

0,1 A ≤ 500

/ ⎡⎣ 2 cos (

bbimrock

) ⎤⎦

(2)

(3) (4)

where α is the angle of repose of blocks, UCS is the uniaxial compressive strength and A is a parameter that can be defined according to both the compressive strength of the matrix and α. 852

Both the empirical approaches, as stated by the authors themselves, have some limitations and should be applied carefully and only in predesign stages of engineering applications.

2

2D STABILITY ANALYSIS OF SLOPES IN BIMROCKS

The aim of this study was to evaluate the effects of rock blocks on the stability of theoretical slopes in bimrocks, whose characteristic dimension, Lc, was their height. The slopes had an inclination of 30°, elliptical block shapes (with major axes inclined 90° to the vertical axis) and different block contents. In particular, 25%, 40%, 55% and 70% volumetric block proportions were examined. To take the spatial and dimensional variability of the inclusions into account, the stochastic approach proposed by Napoli et al. (2017) was applied. In particular, a specific Matlab routine, performing numerical Monte Carlo simulations, was implemented to randomly generate elliptical blocks within the slope models according to specific statistical rules (Barbero et al., 2012). 15 extractions and, hence, 15 stability analyses were performed for each VBP considered, so as to achieve a statistical validity of the results. 0% VBP configurations (matrix only models) were also analyzed in order to evaluate potential inaccuracies that can be made designing without taking the presence of blocks into account. Altogether, more than 120 slope stability analyses were carried out using both FEM and LEM methods, with Phase2 and Slide computer codes (from Rocscience), respectively. Safety factors were evaluated and compared. Table 1 shows the input parameters that were used in the stability analyses. Both matrix and blocks were assumed to have an elastic-perfectly plastic behavior and to follow the MohrCoulomb failure criterion. The empirical approach proposed by Lindquist was also applied, by way of comparison. Table 2 shows the input parameters that were used for analyzing these equivalent homogeneous slope models. 2.1 FEM analyses Finite element (FE) slope stability analyses were conducted using the software Phase2 (vers. 8.0). Six-node triangular elements were used and, in order to avoid stress modelling disturbance, an excavation process was simulated to reproduce the face geometry of the slopes. Table 1.

Matrix Blocks

Input parameters for matrix and blocks of heterogeneous slope models. E [GPa]

ν [–]

γ [kN/m3]

c [kPa]

ϕ [°]

0.04 5.1

0.25 0.22

22 27

30 600

24 40

Table  2. Input parameters for equivalent homogeneous materials, according to the Lindquist criterion. LINDQUIST’S APPROACH VBP [%]

(1–VBH)

cbimrock [kPa]

Δϕmatrix [°]

ϕbimrock [°]

0 25 40 55 70

1 0.75 0.6 0.45 0.3

30 22.5 18 13.5 9

0 0 4.5 9 13.5

24 24 28.5 33 37.5

853

Table 3. Average safety factors and standard deviations obtained performing FEM analyses. VBP [%]

Average SF

Standard deviation

0 (matrix-only) 25 40 55 70

0.80 0.79 0.91 1.10 1.41

– 0.036 0.094 0.144 0.189

Figure 1. FEM analyses results for one of the bimrock configurations generated for each VBP considered: failure surfaces (in the magnified views), critical safety factors (SRF) and maximum shear strains.

The results, shown in Table 3, indicate that factors of safety increase significantly for higher VBP. This result can be ascribed to the increase of failure surface tortuosity with increasing VBP (Figure 1). Furthermore, the standard deviations reported in Table 3 indicate that a high variability in the results exists, and that it increases with increasing VBP. These results are in good agreement with previous findings reported in Medley and Sanz (2004), Irfan and Tang (1993), Barbero et al. (2006) and Napoli et al. (2017). 2.2 LEM analyses Limit equilibrium analyses were carried out on the same extended slope models of the FEM analyses using the code Slide (vers. 5.0). The Simplified Bishop method was applied. As shown in Table 4, a significant increase of the safety factors and standard deviations is achieved for higher VBP values, particularly for both 70% VBP configurations, according to FEM analyses results. As shown in Figure 2, the tortuosity of failure surfaces is not taken into account, since they have circular shapes. The positions of critical surfaces are affected by the presence of blocks, having greater strength than the matrix. They tend to be, among those analyzed, the ones that encounter the lowest number of inclusions and are all quite superficial. Furthermore, the results are not representative of the real problem and significantly overestimate safety factors (SFs), with respect to FEM results. 2.3 Application of the Lindquist empirical strength criterion The empirical strength criterion proposed by Lindquist was applied, by way of comparison, on the same slope models previously analyzed. The one proposed by Kalender et al. (2014) was not applicable, since the UCSmatrix was less than 0,1 MPa. For 25%VBP, Eq. (1) provided equivalent bimrock cohesion and internal friction angle basically coincident with those of the matrix (as reported in Table 2). Hence, only 40%, 55% and 70% VBP configurations were analyzed. Table 5 compares the SFs obtained performing LEM and FEM analyses. It shows that SFs grow as the VBP increases. This trend is consistent with the one obtained assuming bimrocks 854

Table 4. Average safety factors and standard deviations obtained performing LEM analyses. VBP [%]

Average SF

Standard deviation

0 (matrix-only) 25 40 55 70

0.83 0.90 1.16 1.57 2.24

– 0.065 0.205 0.279 0.391

Figure  2. LEM analyses results for one of the fifteen bimrock configurations generated for each VBP considered: critical surfaces and minimum safety factors (SFs) provided by simplified Bishop’s method.

Table 5. Safety factors obtained by FEM and LEM analyses applying the Lindquist criterion. Safety factors—Lindquist criterion VBP [%]

LEM Analyses

FEM Analyses

25 40 55 70

– 0.84 0.92 1.0

– 0.94 0.95 1.0

to be heterogeneous materials and with previous findings from Napoli et  al. (2017), who analyzed slope stability in bimrocks using the same stochastic approach but rock inclusions of circular shape. However, it is worth pointing out that assuming bimrocks to be homogeneous and isotropic materials does not allow the tortuosity of the slip surfaces to be taken into account and the critical slip surfaces to be correctly identified. This produces an underestimation of the rock volume involved in the instability.

3

COMPARISON OF RESULTS AND CONCLUSIONS

The average SFs, provided by the different approaches applied, are compared and reported in Figure 3. The results show that: − there is a clear trend toward increasing SF with increasing VBP, whatever the analysis performed. This trend, which is more evident for VBP greater than 25%, is in line with the findings of previous studies on slope stability (Irfan and Tang, 1993; Medley and Sanz, 2004; Barbero et al., 2006; Napoli et al., 2017); 855

Figure 3. Average SFs obtained for heterogeneous and homogeneous (Lindquist criterion) bimrock models.

− FEM analyses appear to be representative of the real behavior of these materials. As shown in Figure 1, this method allows potential slip surfaces to be correctly identified (Lindquist and Goodman, 1994; Medley and Sanz, 2004; Barbero et al., 2006; Napoli et al., 2017); − when analyzing heterogeneous geomaterials such as bimrocks, LEM analyses should not be applied using the classic grid search method with circular failure surfaces. Such an approach does not allow the tortuosity of slip surfaces to develop within the matrix. Critical failure surfaces, indeed, are those encountering the lowest number of (stronger) inclusions and are usually located near the slope surfaces. This leads to overestimations of the SFs and to underestimations of unstable volumes involved, that increase with increasing VBP; − the use of a matrix-only model (0% VBP), which does not take the presence of blocks into account, leads to a significant underestimation of the SFs, especially for high VBP. Furthermore, shapes and positions of failure surfaces are not correctly identified, since their tortuosity is not taken into account. These results are in good agreement with previous studies conducted on bimrocks (Lindquist 1994; Barbero et al. 2006); − when applying the strength criterion proposed by Lindquist (1994), LEM and FEM analyses provide SFs close to each other (as shown in Table 5 and Figure 3) and quite similar to those yielded by FEM analyses in heterogeneous materials. Anyway, given the limited geometric configurations analyzed, further studies are still required to verify it. Furthermore, since the application of this approach does not allow tortuosity of sliding surfaces to be taken into account (because it assumes bimrocks as homogeneous continuous and isotropic rock masses), it seems to be acceptable if used in predesign stages only (Kalender et al., 2014); − although further analyses will be performed to validate and generalize the findings of this paper (analyzing different block orientations and shapes, i.e. eccentricity, strength parameters and slope geometries), it appears that both elliptical and circular block shapes, that were analyzed in a previous work by Napoli et al. (2017), influence slope stability of bimrocks in a comparable way. However, failure surfaces obtained in this study show less tortuous paths with respect to those found by Napoli et al. (2017) for bimrocks with circular block shapes. As illustrated in Table 3 and Table 4, both FEM and LEM results for heterogeneous materials are extremely variable, especially for higher VBP. The difference between the maximum and the minimum SF of slope models with a given VBP ranges from 0,13 (ΔSF25%VBP) up to around 0,60 (ΔSF70%VBP). This high variability can be ascribed to the different dimensions and locations of the rock inclusions within the slope models, which strongly affect the positions and shapes of sliding surfaces and the stability of the slopes. These findings, in accordance with previous results found by Napoli et al. (2017), demonstrate that blocks play 856

an important role in slope stability and that their presence should not be neglected. Furthermore, when dealing with such heterogeneous materials, the use of a stochastic approach is highly recommended in order to achieve reliable results.

REFERENCES Afifipour M, Moarefvand P (2014). Mechanical behavior of bimrocks having high rock block proportion. Int J Rock Mech Min Sci, 65, pp. 40–48. Barbero M, Bonini M, Borri Brunetto M (2006). Analisi numeriche della stabilità di un versante in bimrock. In: Incontro Annuale Dei Ricercatori Di Geotecnica 2006—IARG 2006, Pisa. Barbero M, Bonini M, Borri-Brunetto M (2007). Numerical Modelling of the Mechanical Behaviour of Bimrock. In: 11th Congress of the International Society for Rock Mechanics (ISRM 2007). Lisbon, Portugal: International Society for Rock Mechanics. Barbero M, Bonini M, Borri-Brunetto M (2012). Numerical Simulations of Compressive Tests on Bimrock. EJGE, Vol. 15, pp. 3397–3399. Haneberg WC (2004). Simulation of 3D block populations to charaterize outcrop sampling bias in bimrocks. Felsbau Rock Soil Eng J Eng Geol Geomech Tunneling, Vol. 22(5), pp. 19–26. Irfan TY, Tang KY (1993). Effect of the coarse fractions on the shear strength of colluvium. Hong Kong Geotech. Eng. Off. Civ. Eng. TN 4/92. Kalender A, Sonmez H, Medley E, Tunusluoglu C, Kasapoglu KE (2014). An approach to predicting the overall strengths of unwelded bimrocks and bimsoils. Eng Geol., 183, pp. 65–79. Lindquist ES (1994). Strength and Deformation Properties of Melange. PhD dissertation. University of California at Berkeley. Lindquist ES, Goodman RE (1994). Strength and deformation properties of a physical model melange. In: Nelson PP, Laubach SE, eds. Proc. 1st North America Rock Mech. Symposium. Austin, Texas, pp. 843–850. Medley EW (1994). The engineering characterization of melanges and similar block-in-matrix rocks (bimrocks). PhD dissertation. University of California at Berkeley. Medley EW, Lindquist ES (1995). The engineering significance of the scale-independence of some Franciscan melanges in California, USA. In: Daemen JJK, Schultz RA, eds. Rock Mechanics Proceedings of the 35th U.S. Symposium. Rotterdam: A.A. Balkema, pp. 907–914. Medley EW, Sanz Rehermann PF (2004). Characterization of Bimrocks (Rock/Soil Mixtures) with Application to Slope Stability Problems. In: Eurock 2004 & 53rd Geomech. Colloquium, pp. 425–430. Medley EW, Zekkos D (2011). Geopractitioner Approaches to Working with Antisocial Mélanges. Invited paper. In: Wakabayashi J, Dilek Y, eds. Mélanges: Processes of Formation and Societal Significance, 480. Geological Society of America Special, pp. 261–277. Napoli, M.L., Barbero, M., Ravera, E., Scavia, C., 2017. A stochastic approach to slope stability analysis in bimrocks. Int. Journal of Roch Mech. And Min. Science. In printing. Sonmez H, Ercanoglu M, Kalender A, Dagdelenler G, Tunusluoglu C (2016). Predicting uniaxial compressive strength and deformation modulus of volcanic bimrock considering engineering dimension. Int. J. Rock Mech Min Sci, 86, pp. 91–103. Sonmez H, Kasapoglu KE, Coskun A, Tunusluoglu C, Medley E, Zimmerman RA (2009). Conceptual empirical approach for the overall strength of unwelded bimrocks. In: ISRM Regional Symposium, Rock Engineering in Difficult Ground Condition, Soft Rock and Karst. Dubrovnik, Croatia. Wakabayashi J, Medley EW (2004). Geological Characterization of Melanges for Practitioners. Felsbau Rock Soil Eng J Eng Geol Geomech Tunneling, 22(5), pp. 10–18.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

3D finite element modelling of fracturing in heterogeneous rock: From pure solid to coupled fluid/solid analysis Ramin Pakzad, Shanyong Wang & Scott Williams Sloan The University of Newcastle, Callaghan, NSW, Australia

ABSTRACT: The elastic-brittle-damage constitutive model for three-dimensional stress state is incorporated into the commercial finite element code ABAQUS. To take into account the heterogeneity effect, mesoscale elements in finite element analysis are assigned by different strength and stiffness properties according to the Weibull distribution function. A FORTRAN code is developed and employed within the static equilibrium equation to analyse three-dimensional progressive failure of rock masses. The numerical model is extended to the coupled hydro-mechanical problem by adding the fluid mass conservation equation to the governing equation system and relating hydraulic conductivity of the elements to their damage and hydrostatic stress states. The results for two typical problems with the pure dry and coupled solid/fluid conditions, respectively, are presented. Good agreement between the numerical results and previously findings in the literature verify such implementation and demonstrates its significance.

1

INTRODUCTION

Three-dimensional (3D) fracture patterns in quasi-brittle geo-materials such as rocks have exhibited to be tortuous even under simple loading. This tortuosity is associated to the heterogeneity of material properties. The numerical simulation of fracture propagation in heterogeneous brittle materials has been paid much attention in recent years. With this regard, the smeared-cracking-like model has emerged as a powerful numerical procedure which is capable of capturing the macro-scale quasi-brittle fracturing response of rock formations from their micro-scale structure and meso-scale behaviour (Li and Tang, 2015). While most of the works done in this area are mainly related to two-dimensional (2D) analysis under dry conditions, just a few works are published concerning 3D analysis particularly for coupled fluid/solid analysis (Wang et al., 2014, Wang et al., 2013). In this paper, first, the 2D smeared-crackinglike model will be extended to 3D; and then the 3D smeared-like-cracking model along with a damage/stress-induced field variable will be incorporated into the coupled fluid/solid analysis of ABAQUS to simulate hydraulic fracturing. Such implementation is important because ABAQUS provides many built-in features making it possible for the users to apply their own code to more complex situation. For example, the probable partially-saturated condition in the hydraulic fracturing of low-permeability media can be simulated just by adding the partiallysaturated option of ABAQUS to the model presented in this paper (Pakzad et al., 2017). The focus of this paper is mainly on the implementation aspects of the 3D modelling of fracturing in heterogeneous rock under either dry or fully-saturated conditions. 2 2.1

MATHEMATICAL FORMULATION Solid phase contribution

In the framework of the finite element method, the equilibrium equation shown in Eq. (1) is implicitly solved by the ABAQUS/Standard solver to obtain the displacement degrees of 859

freedom for every node in the model under static conditions. The strain components are then calculated from the displacement field (Eq. (2)) and sent to the UMAT subroutine, accompanied by other state variables, at the beginning of every increment. ∂σ ij

+ Fj = 0

∂x j

(1)

1 ⎛ ∂u ∂u j ⎞ ε ij = ⎜ i + 2 ⎝ ∂x j ∂xi ⎟⎠

(2)

The user must use a constitutive model relating stresses to strains at the integration point(s) of each element. In this study, the elastic-brittle-damage constitutive model is employed as follows: 2.1.1 Elastic regime Following Hookes’ law, the principal stresses and strains are correlated through Eq. (3), in which λ = ( − νν E)( +ν ) , G = ( +Eν ) , v is Poisson’s ratio and E is the current Young’s modulus.

σ ij

2Gε ij

λε jj λε

(i, j = 1, 2, 3) (i

(3)

The stiffness begins to degrade gradually as soon as the stress state meets the damage surface. This occurs incrementally by the evolution of the damage parameter (D) in Eq. (4), where  E and E0 represent the updated and initial stiffness of the mesoscopic element, respectively. E

(

D )E 0

(4)

2.1.2 Damage initiation and evolution The damage surface is defined by two individual criteria: the tensile failure criterion and the shear failure criterion, with priority given to the former. First, the maximum principal stress (σ1) is compared with the uniaxial tensile strength of element (ft0) according to Eq. (5), under the condition that the shear criterion is less critical than the tensile criterion.

σ1 ≥ f 0

(5)

If the tensile failure criterion is met, the damage parameter is calculated by Eq. (6), depending on the value of equivalent strain (ε ) at the end of the current increment. ⎧ 0 ⎪ f ⎪ D = ⎨1 − tr0 ⎪ σ1 ⎪ 1 ⎩

ε < εt 0 εt ≤ ε < εttu

(6)

ε ≥ εttu

In this equation, the equivalent strain at which the tensile damage surface is met for the first time is symbolized by εt0, and σ 10 denotes the maximum principal stress calculated by the initial elastic modulus. The residual tensile strength and ultimate tensile strain are defined as ftr γ ft 0 and εtu ηεεt 0 , respectively. The equivalent strain corresponding to the tensile damage evolution is assumed to be a combination of the principal strains as follows:

ε = The Macaulay brackets

ε1

2

+ ε2

2

+ ε3

are defined by Eq. (8): 860

2

(7)

x≥0 x ε c 0 ε ≤ ε c 0

andd

2

≤ 0.5[(σ 1 + σ 3 ) − i φ (

1

3 )]

(10)

ε ≤ ε c 0

d σ 2 ≥ 0.5[(

1

3)

sin i φ(

1

3 )]

where fcr γ fc 0 ε = ε 3 , εc0 is the equivalent strain at the moment that the shear failure criterion meets the current strength of the element for the first time, and σ 10 , σ 20 and σ 30 are the maximum, intermediate and minimum principal stresses of the intact element calculated by the initial Young’s modulus. The convention of ABAQUS is followed in the abovementioned relationships such that the stress and strain components are negative in compression and positive in tension (Hibbitt et al., 2014).

2.2 Fluid phase contribution To capture the interaction between the fluid and solid phases in a coupled problem, the transient mass conservation equation (Eq. (11)) needs to be simultaneously solved with the equilibrium equation (Eq. (1)). ∂ ∂ ( ρn) + ( ρqi ) = 0 ∂t ∂xi

(11)

In Eq. (11), qi is the vector value of the pore fluid flux and ρ and n are the fluid density and porosity, respectively. According to this equation, the mass change of the stored fluid inside a RVE during a period (t) is equal to the net fluid flux crossing the RVE. The fluid constitutive model has already been defined by ABAQUS/Standard and it should be appropriately selected by assigning values to the related material parameters. For instance, the flux parameter (qi) in Eq. (11) is replaced by Eq. (12), which is known as Darcy’s law: qi

∂ ⎛ p⎞ kˆij z+ ∂x j ⎜⎝ ρ g ⎟⎠ 861

(12)

where z and g represent an elevation above an arbitrary vector and gravitational acceleration, respectively. The second-order hydraulic conductivity tensor has units of velocity (length/ time) and is the product of the hydraulic conductivity of a fully saturated porous medium (k) and a saturation-dependent factor (ks), which has a value of one for fully saturated conditions. In case of coupled analysis, the constitutive model presented above defines the effective stress ( ′ij ) instead of the total stress (σij) which requires to be in equilibrium with the external load vector Fj. Following the Biot’s theory of consolidation (Biot, 1941) the total stress is in relationship with the effective stress and pore pressure (p) through Eq. (13):

σ ij

σ ′ij − spδ ij

(13)

where s represents the degree of saturation and δij is the Kronecker delta, which has a value of one for similar indexes and zero for dissimilar ones. 2.2.1 Evolution of permeability The influence of damage and stress state on the hydraulic conductivity and thereby permeability of elements is included through Eq. (14): ⎧ ⎡ ⎛ σ ii + sp pδ ij ⎞ ⎤ ⎪k0 exp ⎢ β ⎜⎝ ⎟⎠ ⎥ D = 0 3 ⎪ ⎣ ⎦ k=⎨ ⎡ σ + sp p δ ⎛ ⎞ ⎪ ii ij ⎤ ⎟⎠ ⎥ D > 0 ⎪ξ k0 exp ⎣ β ⎜⎝ 3 ⎦ ⎩

(14)

where k0 and k are the initial and modified hydraulic conductivity under fully saturated conditions, respectively. Permeability is assumed to be isotropic and homogeneous for every element. The effect of damage is shown by the mutation coefficient of permeability ξ (ξ > 1). The coupling coefficient β determines the intensity of the hydrostatic effective stress (σ ′ii / ). 2.3

Material heterogeneity

The heterogeneity of rock is modelled statistically via the Weibull distribution function. To produce the random variable from the random number generated by the Monte Carlo method, the inverse of the Weibull cumulative probability function was used as follows: ⎡ ⎛ u ⎞m⎤ f ( u ) = 1 − exp ⎢ − ⎜ ⎟ ⎥ ⎢ ⎝ u0 ⎠ ⎥ ⎣ ⎦

(15)

where u corresponds to the random material property of the element and m is the shape factor of the Weibull distribution function determining the dispersal of u around u0. The parameter u approaches the value of u0 as the value of m increases. In this study, the elastic modulus and strength are considered to vary among elements with the same homogeneity indexes (m) but different initial seeds. 3

INCREMENTAL PROCEDURE AND PARALLEL EXECUTION

Fig. 1 demonstrates the solution procedure of ABAQUS/Standard for numerical simulations. ABAQUS/Standard incrementally solves a system of equations to find the changes in the degrees of freedom (ΔU) which satisfy the governing equation(s) for the current increment of loading (ΔF ). The residual vector (R) is calculated using the stresses (σ) calculated in UMAT which themselves as well as other solution dependent state variables (SDV′s) are calculated based on the strain components (ε) and other input data from the former increment. The material tangent matrix (∂Δσ/∂Δε) and stresses from UMAT are used for new approximation 862

Figure 1.

Incremental solution procedure of ABAQUS/Standard.

in the next iterations unless the residual is within a small tolerance (TOL). Once the solution is accepted, field variables are updated in USDFLD using the updated values of stress components and SDV′s. This procedure is repeated until the end of analysis. 3D problems usually entail a huge number of elements, rendering the run time impractical particularly when nonlinear effects may result in so many iterations. Parallel execution is a technique based on which the model is decomposed into different domains an each domain is handled by a specific number of processors. In this work, MPI-based parallelization (Hibbitt et al., 2014) with 40 domains each with one processor is used to increase efficiency. 4

NUMERICAL EXAMPLES

Two numerical examples are presented in this section, one of which is related to the simulation of fracture propagation in a heterogeneous dry block with a pre-existing fissure under uni-axially displacement-control compression (Fig. 2). The results obtained from this simulation are consistent with the experimental observation of other scholars (Yang and Jing, 2011), verifying the numerical modelling. Two 3D wing cracks initiate at the two end corners of the pre-existing fissure, where the maximum tensile stress is critical. Secondary tensile cracks are generated near one of the corners of the fissure, followed by the appearance of a shear-damaged region linking the corner to the secondary tensile cracks. A new shear crack emerges at the other corner of the fissure concurrent with slow extension of the previous tensile cracks until the specimen splits at its top half section. The second example represents hydraulically-induced fractures around a cavity inside a block pressurized by water and confined at its external boundaries (Fig.  3). According to Fig. 3, the fracture surfaces are generally perpendicular to the minimum far-field principal stress. Such influence of far-field principal stress on the direction of propagating hydraulic fractures has been observed and reported for physical modelling of hydraulic fracturing (Zhou et al., 2008). The asymmetric distribution of pore pressure illustrated in the right hand side of Fig. 3 is due to the asymmetric generation of damaged elements forming fractured area around the pressurized region of the cavity, indicating the proper function of our developed code for incorporating Eq. 14 in the solution procedure. 863

Figure  2. Fracture propagation in a heterogeneous dry block with a pre-existing fissure under uniaxially displacement-control compression.

Figure  3. Distribution of pore pressure throughout a hydraulically-fractured block pressurized by water at the central region of its cylindrical cavity (cross-sectioned views).

5

CONCLUSIONS

In this paper, the smeared-like-cracking model for 3D modelling of brittle failure of heterogeneous material is implemented into the commercial finite element code ABAQUS through its UMAT user-subroutine interface. The incremental change of permeability due to damage and hydrostatic effective stress is incorporated into the USDFLD user-subroutine interface of ABAQUS to be used with the developed UMAT in coupled fluid/solid analysis. The MPIbased parallel execution technique is used for both dry and wet conditions to reduce run time which plays an important role in 3D problems. For the verification purpose, 3D fracture propagation in a dry block with an inclined fissure under uni-axial compression and hydraulic fracturing in a fully-saturated block pressurized by water at its internal boundary with a cylindrical cavity are simulated with promising results. REFERENCES Biot, M.A. 1941. General theory of three-dimensional consolidation. J. appl. Mech., 12, 155–164. Hibbitt, D., Karlsson, B. & Sorensen, P. 2014. ABAQUS, ABAQUS/Standard User’s Manual, Inc. Li, G. & Tang, C.A. 2015. A statistical meso-damage mechanical method for modeling trans-scale progressive failure process of rock. Int. J. Rock Mech. Min. Sci., 74, 133–150. Pakzad, R., Wang, S.Y. & Scott, W.S. 2017. Numerical simulation of hydraulic fracturing in low/high permeability, quasi brittle, heterogeneous rocks. Rock Mech. Rock Eng., submitted. Wang, S.Y., Sloan, S.W., Fityus, S.G., Griffiths, D.V. & Tang, C.A. 2013. Numerical modeling of pore pressure influence on fracture evolution in brittle heterogeneous rocks. Rock Mech. Rock Eng., 46, 1165–1182. Wang, S.Y., Sloan, S.W., Sheng, D.C., Yang, S.Q. & Tang, C.A. 2014. Numerical study of failure behaviour of pre-cracked rock specimens under conventional triaxial compression. Int. J. Solids Struct., 51, 1132–1148. Yang, S.Q. & Jing, H.W. 2011. Strength failure and crack coalescence behavior of brittle sandstone samples containing a single fissure under uniaxial compression. International Journal of Fracture, 168, 227–250. Yu, M.H. 2006. Generalized plasticity, Springer Science & Business Media. Zhou, J., Chen, M., Jin, Y. & Zhang, G.-Q. 2008. Analysis of fracture propagation behavior and fracture geometry using a tri-axial fracturing system in naturally fractured reservoirs. Int. J. Rock Mech. Min. Sci., 45, 1143–1152.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Global sensitivity analysis on thermo-hydro-mechanical coupled processes in a low strength sedimentary rock Samuel Parsons, Graham Stuart, Bill Murphy & David Price School of Earth and Environment, University of Leeds, UK

ABSTRACT: Radioactive waste may be stored in deep geological disposal facilities. Heat-producing radioactive waste would drive coupled thermo-hydro-mechanical (THM) processes in the host rock mass. Rock mass uncertainty could affect predictions of observable properties that are perturbed by these THM processes. However, the contribution of the individual rock properties to the uncertainty is unknown and is critical for informing modelling and monitoring for reducing uncertainty. Here we rank the rock properties (model input factors) according to their contribution to uncertainty in the observable properties: temperature, pore pressure and displacement (model outputs). We identify non-influential rock properties which have a negligible effect on the uncertainty and should no longer be considered uncertain. We identify the thermal conductivity and permeability as the most influential rock properties which was expected because these are anisotropic. Interestingly we found that closer to the heat source these become more influential relative to the other rock properties. The ranking may be used to inform prioritizing further rock mass characterization efforts for uncertainty reduction. The spatial effect on thermal conductivity and permeability may be used to improve model calibration and back-calculations by counterintuitively using data proximal to the heat source. We demonstrate that global sensitivity analysis methods can be applied to geomechanical models to improve our understanding of the rock mass uncertainty. We present validated values for the number of models required for results to converge which should be used to estimate appropriate values for future sensitivity analyses on geomechanical models.

1

INTRODUCTION

Modelling and monitoring for reducing uncertainty in aspects of geological disposal of radioactive waste is a paramount aim for the community (IAEA, 2011). Often the problem for geologists is that rock masses are heterogeneous and characterized with a large degree of uncertainty. Underground research laboratories provide access to the in-situ rock mass and resultantly tend to be situated in the most characterized rock masses in the world (Jalali et al., 2017). The complex thermo-hydro-mechanical processes occurring in the geosphere around heatproducing radioactive waste are simulated by in-situ heating experiments (e.g. Conil et al., 2012; Zhang et al., 2007). The observable physical properties are temperature, pore pressure and displacement. These data may be used in benchmark tests to validate coupled THM models (e.g. Wang and Kolditz, 2013; Gens et al., 2007; Zhang et al., 2007). Despite being well characterized at test sites there is still significant uncertainty reported in rock mass properties. Gens et al. (2007) addresses this by running additional model evaluations with one-at-a-time changes to end-member values within the uncertainty for selected `important’ parameters. However, there has been a lack of investigation into the rock mass uncertainty beyond this. This is diagnostic of a broader lack of investigation into rock mass uncertainty in geomechanical models. Notable cutting-edge work on rock mass uncertainty has been presented in 865

Jobmann et al. (2016). The authors use the software tool optiSLang for CAE-based sensitivity analysis and optimization that automatically fit parameters and analyse the importance of individual parameters for the general system development. However, no results are presented towards the robustness or validity of the sensitivity analysis and the sample size of 80 for 29 input factors is an order of magnitude less than the recommended values for similar aims (Sarrazin et al., 2016). The high number of input factors for a geomechanical model is due to the THM coupling. The low number of model evaluations is because THM coupled finite element models are computationally expensive. Petropoulos and Srivastava (2016) present a credible, computationally efficient multi-method global sensitivity analysis approach for input factor ranking. Three approaches measure the sensitivity indices differently and presented together provide a more credible input factor ranking result. The approach is computationally efficient because the three approaches use the same generic input-output dataset and so no additional model evaluations are required. We apply the multi-method global sensitivity analysis approach (Petropoulos and Srivastava, 2016) to a THM model to rank input factors according to estimated sensitivity indices. We identify the most important input factors contributing to uncertainty and the input factors which do not contribute to uncertainty in temperature, pore pressure and displacement. We benchmark our THM model against an in-situ heating test to ensure that it is a good representation of reality.

2

MULTI-METHOD GLOBAL SENSITIVITY ANALYSIS

Input factor ranking is achieved using global sensitivity analysis techniques in which the whole input factor uncertainty space is investigated using Monte Carlo style simulation. Sensitivity indices are estimated for each input factor and these indices are used to rank them. The input factor uncertainty space (Table 1) is sampled using a Maximin Latin Hypercube. This sampling strategy provides enhanced coverage of the input factor space. The samples Table 1. A table of the input factors investigated in the sensitivity analysis. The maximum and minimum values describe the uncertainty range in those input factors. The Opalinus clay rock mass parametrs are established by laboratory tests performed on normally-sized samples and confirmed by back-calculations of mock-up heating tests on large-scale samples taken from the test sites (Zhang et al., 2007). Property Poisson’s ratio Reference bulk modulus Cam Clay constant Porosity Kozeny-Carmen constant Fluid density Grain density Fluid stiffness Grain stiffness Biot constant Viscosity Thermal conductivity Fluid heat capacity Solid heat capacity Rock mass linear coefficient of expansion Fluid volumetric thermal expansion coefficient Solid volumetric thermal expansion coefficient

v Bref κ φinit K0 ρf ρg Kf Kg Biot μ λ cf cs αref αf αs

866

Minimim

Maximum Recommended Unit

0.24 871.18 0.0030 0.135 1.02E-19 971 2680 2000 20000 0.48 3.53 × 10−10 1.0 3992 720 1.5 × 10−5 2.07 × 10−4 4.5 × 10−6

0.33 4564.20 0.0040 0.179 1.02E-21 1030 2740 2500 50000 1.0 1.12 × 10−9 2.1 4182 880 1.9 × 10−5 4.5 × 10−4 4.8 × 10−5

0.27 3300 0.0035 0.16 2.00E-20 1000 2710 2222 40000 0.6 1.00 × 10−9 1.7 4182 800 1.7 × 10−5 3.4 × 10−4 4.5 × 10−6

MPa

m2 kg/m3 kg/m3 MPa MPa MPa.s W/m.K J/kg.K J/kg.K K−1 K−1 K−1

form a k-by-n matrix (X) where k is the number of uncertain input factors and n is the number of samples. 500  models are built using the input factor samples. The models are evaluated and an output function is selected for each sample, forming a vector of length n (Y). The output functions investigated in this study are the temperature, pore pressure and displacement. The global sensitivity analysis method used to evaluate X and Y for input factor ranking is the multi-method approach designed in Petropoulos and Srivastava (2016). The approach enhances the credibility of the study by using three sensitivity analyses to estimate three indices for each input factor instead of one. This is achieved without increasing the computational expense of the study because the methods use the same generic input-output dataset, therefore, no additional model evaluations are required. The three sensitivity analyses are the Regional Sensitivity Analysis, PAWN (Pianosi et al., 2015), and an estimate of the main effects indices from the Variance-based Sensitivity Analysis (Petropoulos and Srivastava, 2016). SAFE Toolbox (Pianosi et al., 2015) contains Matlab functions for calculating the sensitivity indices of these approaches using X and Y. 3

THE MODEL

We use the finite element software ELFEN (Rockfield Software) for the THM modelling. We use fully-coupled thermal and porous flow fields within an implicit solution method, which are semi-coupled at regular intervals to the geomechanical field within an explicit solution method. The thermal field calculates bulk properties based on the grain and fluid properties to simulate conduction and advection (Equation 1). The porous flow field simulates Darcy fluid flow, consolidation and aqua-thermal pressure (Equation 2). ( ρ )b

∂T ∂t

di (

b∇

) ρ f c f q f ∇T

⎛ k (φ ) ⎞ ⎛ φ (α φ ) ⎞ ∂pppff α ∂φ ∂T div ⎜ − + βs f (∇pf − ρ ffg )⎟ = ⎜ + ⎟ μ ( T ) K K ∂ t 1 − φ ∂ t ∂t ⎝ f ⎠ ⎝ f s ⎠

(1) (2)

where the subscripts b, f and s denote bulk, fluid and solid grain values, ρ is density, c is specific heat capacity, T is temperature, t is time, κ is thermal conductivity and q is the Darcy fluid flux, k is intrinsic permeability, μ is viscosity, p is pore pressure, g is acceleration due to gravity, K is stiffness, α is Biot’s constant and β is thermal expansion coefficient. We use a poro-elastic material model for the Opalinus clay with the Soft Rock (SR3) state boundary surface (Crook et al., 2003) for weakly cemented rock. A smooth hardening law approximates to the Cam Clay hardening model. We define non-linear permeability using the Kozeny-Carmen model and temperature-dependent viscosity for the fluid. The THM coupled calculations include the following major assumptions. Heat transport is by conduction (Fourier’s law) through porous medium and advection of liquid water. Fluid transport is controlled by liquid water advection (Darcy’s law). A thermo-mechanical model is used for the description of the mechanical behaviour of the clay rock with the main features of thermal expansion. The clay rock is assumed to be isotropic and homogeneous. The modelled clay rock is isotropic because of the axisymmetric set-up. Since the aim of our work is not to fit parameters we are able to simplify the model to an axisymmetric representation, vastly reducing the computation time of one model evaluation to increase the total number of model evaluations. The model (Figure 1) is allowed to reach equilibrium and then a heat flux is applied to simulate the heating. As in the original test the thermal load is 650 W for 92 days and then increased to 1950 W for 252 days. The temperature increases up to around 100°C. The model was initially run using the recommended parameters for the test field. The temperature and pore pressure results were accurately predicted up to the time at which the output was taken for the sensitivity analysis. 867

Figure 1. Left: Illustration of the experiment layout and instrumentation (adapted from Zhang et al., 2007). Sensor numbers are consistent with the original experiment. (A) Plan view. (B) Profile view. Right: An illustrative description of the axisymmetric model we used to simulate the in-situ heater experiment. The heater is centred on the symmetry axis. The gallery is represented by a zero-stress boundary condition whilst the mean in situ stress is applied to the other boundaries. The in-situ pore pressure is reduced from 2.2 MPa to 0.9 MPa because of the proximity to open tunnels (Gens et al., 2007).

4

RESULTS

The multi-method approach is applied to the generic input-output dataset for temperature, pore pressure and displacement. A sensitivity indices is estimated for each input factor and for each of the three sensitivity analyses. The analyses are repeated using the different locations of sensors from the original laboratory experiment to investigate the spatial effects on input factor sensitivity. Furthermore, the analyses are repeated throughout model time to investigate the temporal effects. The spatial location affects the sensitivity of the thermal conductivity for temperature and the permeability and viscosity for pore pressure. These three input factors are the transport properties. The spatial analysis shows that the transport properties of the rock mass become more sensitive towards the heater. This is because changing the property next to the heater affects the amount of heat or fluid that is transported away from the heater, whereas away from the heater, changing the property affects the amount of heat or fluid that is transported away and towards the location which has a negative interference for the sensitivity index. This spatial effect is strong enough that within 1 m of the heater the transport properties dominate the resultant temperature and pore pressure. This enhanced understanding can improve back analyses by focusing only on the transport properties when back analysing for temperature or pore pressure proximal to a heat source. The temporal analysis identified viscosity becoming more sensitive as the model advanced because the fluid becomes less viscous as its temperature increases. We also found the sensitivity analysis required a greater number of model evaluations to achieve convergence at the beginning of the model because the output perturbations were small. We observed no other temporal effects. Figure 2 shows the results for a radial distance of 1.2 m from the heater at a time equal to the mean occurrence of peak pore pressure. The correlation between the indices predicted by the different sensitivity analysis methods demonstrates the importance in robust sensitivity analyses. We observe that the methods generally agree but with local conflicting ranking. For example, the relative ranking of Biot’s constant and viscosity depends on the sensitivity analysis method. Therefore, we rank the input factors in groups. 868

Figure 2. Multi-method sensitivity analysis results. Each subplot title indicates the model output for which the results were calculated. The y-axis values are the sensitivity indices for each input factor identified by the x-axis nomenclature. The nomenclature is defined in Table 1. Squares represent the indices calculated by the Regional sensitivity analysis, crosses represent the indices calculated by the PAWN sensitivity analysis and circles represent the indices calculated by the Variance-based sensitivity analysis.

For temperature, thermal conductivity is ranked first; grain heat capacity second; porosity third; and all other input factors are determined to have negligible uncertainty. For pore pressure, permeability is ranked first; grain and fluid thermal expansion coefficients second; viscosity and conductivity second; bulk modulus, Cam Clay constant, porosity, Biot’s constant and solid heat capacity third; and all other input factors are determined to have negligible uncertainty. For displacement, permeability is ranked first; Biot’s constant and fluid thermal expansion coefficient second; bulk modulus, viscosity, thermal conductivity and grain thermal expansion coefficient third; Cam Clay constant and porosity fourth; and all other input factors are determined to have negligible uncertainty. Input factor ranking for temperature achieved convergence in as few as 40  model evaluations. Contrastingly, pore pressure and displacement required up to 420 model evaluations to achieve convergence of the input factor ranking. We interpret this to be because pore pressure and displacement are dependent on more input factors than temperature. Finally, we found that convergence required fewer model evaluations closer to the heat source for all outputs. Therefore, spatial analysis is critical for assessing the robustness of geomechanical sensitivity analyses. When implementing the results it should be considered that we used a specific case study and experimental set-up. The case study and experimental set-up were selected to increase the applicability of the work. The case study was an in-situ heating experiment which provides a good representation of heat-producing waste packages in rock. The host rock was Opalinus clay which is a low permeability, lower strength sedimentary rock. The parameter ranges are based on uncertainty ranges in the characterisation of the experiment site, which are relatively well constrained for rock masses, as would be expected at a site for radioactive waste disposal. 5

CONCLUSIONS

We demonstrate that increasing computing power can be used for global sensitivity analyses on coupled geomechanical models to enhance our understanding of the modelled systems and their uncertainties. 869

Rock mass uncertainty at an underground laboratory in low strength sedimentary rock is investigated in the context of its effect on the range of temperature, pore pressure and displacement in forward modelling. Independent input factors that characterise the rock mass in the model are ranked according to their contribution to the range in the outputs using sensitivity indices. Uncertainty is case specific so the conceptualisation of the model is important for the applicability of the results. The results from this study can be applied to THM modelling of heating in low strength sedimentary rocks characterized at underground laboratories. The result can be used to prioritize efforts for uncertainty reduction. Efforts should focus on the thermal conductivity to reduce temperature uncertainty. And on permeability, Biot’s constant and thermal expansion coefficients of the grain and fluid to reduce pore pressure and displacement uncertainty. Furthermore, the input factor ranking enhances our understanding of the dominant controls in the THM coupled processes. It indicates that uncertainty of how the pore pressure affects the pore space contributes more significantly to the displacement uncertainty than uncertainty in the thermal expansion coefficients. This should be considered if attempting to back analyse thermal expansion coefficients during heater tests. We find that a temperature dependent viscosity is required to capture realistic pore pressure evolution. Finally, we find that the spatial analysis of input factor ranking shows the best place to back analyse the thermal conductivity from temperature data is proximal to the heat source.

REFERENCES Crook, T., Willson, S., Yu, J. and Owen, R. (2003). Computational modelling of the localized deformation associated with borehole breakout in quasi-brittle materials. Journal of Petroleum Science and Engineering 38(3), 177–186. Conil, N., Armand, G., Garitte, B., Jobmann, M., Jellouli, M., Filippi, M., De La Vaissière, R. and Morel, J. (2012). In situ heating test in Callovo-Oxfordian claystone: measurement and interpretation. In Proceeding of the 5th International meeting of Clays in Natural and Engineered Barriers for Radioactive Waste Confinement, Montpellier, October 22–25. Gens, A., Vaunat, J., Garitte, B. and Wileveau, Y. (2007). In situ behaviour of a stiff layered clay subject to thermal loading: observations and interpretation. Geotechnique 57(2), 207–228. International Atomic Energy Agency (2011). Geological disposal facilities for radioactive waste: specific safety guide. IAEA Safety Standards Series No. SSG-14, IAEA. Jalali MR, Gischig V, Doetsch J, Krietsch H, Amann F and Klepikova M. (2017). Mechanical, hydraulic and seismological behavior of crystalline rock as a response to hydraulic fracturing at the Grimsel Test Site. American Rock Mechanics Association; 51st U.S. Rock Mechanics/Geomechanics Symposium, 25–28 June, San Francisco, California, USA. Jobmann, M., Li, S., Polster, M., Breustedt, M., Schlegel, R., Vymlatil, P. and Will, J. (2016). Using Statistical Methods for Rock Parameter Identification to Analyse the THM Behaviour of Callovooxfordian Claystone. Journal of Geological Resource and Engineering 3, 125–136. Petropoulos, G. and Srivastava, P.K. (2016). Sensitivity Analysis in Earth Observation Modelling. Elsevier Science and Technology Books. Pianosi, F., Sarrazin, F. and Wagener, T. (2015). A Matlab toolbox for Global Sensitivity Analysis. Environmental Modelling and Software 70, 80–85. Sarrazin, F., Pianosi, F. and Wagener, T. (2016). Global Sensitivity Analysis of environmental models: Convergence and validation. Environmental Modelling & Software 79, 135–152. Wang, W. and Kolditz, O. (2013). High performance computing in simulation of coupled thermal, hydraulic and mechanical processes in transverse isotropic rock. Rock Characterisation, Modelling and Engineering Design Methods, 485–490. Zhang, C., Rothfuchs, T., Jockwer, N., Wieczorek, K., Dittrich, J., Müller, J., Hartwig, L. and Komischke, M. (2007). Thermal effects on the Opalinus clay. A joint heating experiment of ANDRA and GRS at the Mont Terri URL (HE-D Project). Final report. Gesellschaft fuer Anlagen-und Reaktorsicherheit mbH (GRS).

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

The effect of rock mass stiffness on crush pillar behaviour M. du Plessis Lonmin Marikana, Marikana, North West, South Africa

D.F. Malan Department of Mining Engineering, University of Pretoria, South Africa

ABSTRACT: Various parameters affect the behaviour of crush pillars in intermediate depth platinum mines. The final crush pillar dimension and overall mining layout is influenced by the original design methodology, mining discipline and the effect of unexpected geological losses. The combination of these factors can prevent the pillars from crushing and achieving the desired post-peak residual state. This may result in unpredictable pillar behaviour and damaging seismicity. Effective crush pillar design will require the pillars being crushed while being formed at the mining face. A stability analysis has been recommended in the past as a method to design yield pillars at moderate mining depths. The methodology assumes that stable pillar crushing will occur if the local rock mass stiffness is greater than the post-failure stiffness of the crush pillar at the specific pillar location. This paper explores this design methodology and some preliminary numerical results are discussed. Keywords:

1

crush pillar behaviour, stiffness, numerical modeling

INTRODUCTION

Research conducted on the behaviour of crush pillars on the Merensky Reef highlighted the detrimental effect of oversized pillars (Du Plessis and Malan 2014). These intact pillars can result in violent failure with the associated seismic energy release in the back area of stopes. Du Plessis and Malan (2016) determined that the amount of convergence experienced in a crush pillar stope can be directly related to the pillar deformation processes. In a subsequent case study, Du Plessis and Malan (2017) described the effect of an intact oversized crush pillar has on the amount of convergence experienced in the stope. The pillar triggered a magnitude 1.9 seismic event which was followed by a substantial increase in convergence. The objective of this paper is to explore a “stiffness model” to gain a better understanding of the interaction between the crush pillars and the surrounding rock mass. In future, this may provide an improved design methodology to reduce the number of cases of unstable pillar failure.

2

STIFFNESS MODELS

Cook (1965) proposed that rock bursts is a problem related to regional stability in mines and subsequently he discussed the significance of the post-peak behaviour of rock in compression (Cook, 1967). Salamon (1970) noted that the stability of a laboratory rock specimen under compression depends on the stiffness of the testing machine and the slope of the post failure behaviour of the specimen. If the stiffness of the testing machine (slope indicating soft loading system in Figure  1) is less than the slope of the post-peak load-deformation 871

Figure 1. The effect of stable (stiff) and unstable (soft) system loading on pillar behaviour. Regions AB and BC represents the pre- and post-peak pillar strength respectively. If the angle θ increases, the magnitude of the eventual unstable pillar failure also increases.

relation of the specimen (pillar), the test will result in violent failure. Stable deformation in the post-failure region will, however, occur if the stiffness of the machine (slope indicating stiff loading system in Figure 1) is greater than the slope of the post-peak load-deformation relationship of the specimen. Stiffness is defined as the ability of an object to resist deformation in response to an applied force (N/m). In an underground mining scenario, stoping operations will induce elastic deformation of the hangingwall strata. Pillars should ideally be designed to resist this deformation (loading) in a controlled and predictable manner. In the South African intermediate depth platinum mines significant convergence in the order of centimeters has been recorded in some areas (Malan et al., 2007). The stiffness of the loading system (the surrounding rock mass) and the slope of the failed crush pillars are therefore of particular interest especially as the crush pillars, in some instances, contribute to unstable lading. By applying the relationship between uniaxial rock testing and loading of an isolated pillar, Salamon (1970) showed that the equilibrium between a pillar being loaded and the postpeak behaviour is stable irrespective of the convergence experienced by the pillar if: (

λ) > 0

(1)

The parameter k represents the stiffness of the loading strata and is understood as the force required to cause a unit increment in closure between the hangingwall and footwall at the pillar position. λ defines the post-peak pillar stiffness. The parameter k is positive by definition and λ is positive in the portion of the load-deformation curve where the pillar is intact. A negative λ in the post-failure portion may result in unstable failure, but only if the relationship in equation (1) is violated. Ozbay and Roberts (1988) stated that if pillars were designed to be fractured during cutting by the face abutment stress, the pillars would already have yielded and reached a residual strength. Further deformation of the pillars would be associated with an increase in load (λ becomes positive), and according to equation (1), stability will be assured. This is, however, dependent on the assumption that the failed pillar material can be compacted so that the pillar would regenerate load. In contrast, if the pillars are intact when cut at the mining face and only fail later, λ will become negative once the pillar reaches peak strength and instability may occur (k + λ 5 would be zero or positive and therefore such pillars would become “unconditionally” stable. Pillar stiffness (λ) can be expressed by (Ryder and Ozbay, 1990):

λ=

lwE Ep Force = Displacemen s t Sm

(2)

where l is the pillar length, w is the pillar width, Ep is the post-failure modulus and Sm is the stoping width or pillar height. The stiffness of the strata is proportional to Young’s modulus. It is also strongly influenced by the mining geometry and the number of neighbouring pillars which may also be in a state of post-failure. The stiffness of the strata at an individual pillar location is termed the local stiffness (Ryder and Ozbay, 1990). The local strata stiffness can be determined through the application of a numerical model. In the model, the pillar is replaced with a variable probing force F. The change in closure ΔS resulting from a change in force ΔF gives the required local strata stiffness (kL). When all the pillars in a layout are assumed to be in a failed state, the local stiffness will also define the critical stiffness λc (minimum value of kL) kL

F /ΔS

(3)

The post-peak stiffness of pillars has predominantly been investigated through pillarmodel tests conducted in laboratories or in-situ tests carried out on coal pillars. Based on estimates from this data, Ozbay (1989) assumed the relationship between normalized postpeak stiffness (λ/E) and width to height ratios of pillars which are in the range of 0.7 < w:h 2.4 MPa in Fig. 3b). Its outer portion (the edge of the basal pedestal) locally experiences small plastic strains (not exceeding 1%, Fig. 3a). In model LI the presence of the small D1-S2 joint does not influence stress and displacement distribution. Movements in the North-South plane, parallel to the cliff face, induce a slight rotation towards North (right) with a relative horizontal displacement of about 3–4 mm. In the EI model, the displacement of the prism increases up to 4–5 mm. The pedestal is encompassed in the displacement field of the prism (Fig. 4a) and plastic strains reach 5%. Significant reaction stresses are spread also over the upper part of the joint D2-S1 on the right side of the pedestal and over the small surface of D1-S2 joint (normal and shear stresses reach 1 MPa and 0.7 MPa, respectively) which is activated by the larger movements of the prism (Fig. 4b). Nonetheless the strength assumed for the rock mass is sufficient to prevent plastic strains in the prism. Once ascertained that friction along lateral joints and the support of the basal pedestal are the main contributions to the static equilibrium of the prism, safety margins were evaluated through a strength reduction method applied to two scenarios: a) both joints D1-S1 and D2-S1 extend into the lower rock mass, as in the EI model described above; b) only

Figure 3. LI model. Octahedral shear plastic strains (a) and normal contact stress on the joints of the lower part of the prism (b). Views without the prism.

Figure 4. EI model: displacements (a); shear stresses along interfaces viewed from South (b) and SE (c).

927

D1-S1 extends downwards whilst D2-S1 terminates into the rock mass above the pedestal or is markedly discontinuous. The b) hypothesis is supported by the fading of the trace of joint D2-S1 on the cliff below the ST joint. The prism maintains the equilibrium even when the shear strength angle is reduced to low values (10% of the initial value in the a-scenario) or nil (b-scenario). Conversely, collapse is attained if the original σci value of the rock of the basal pedestal is reduced to the 95% or 75% in a- and b-scenario, respectively.

7

CONCLUSION

Evaluation of safety margins against failure of the limestone prism described in this study indicates that frequently, to account realistic collapse mechanisms, problems usually treated through limit equilibrium of rigid blocks requires modelling of deformability and irreversible deformations in the rock mass and along discontinuities. In the investigated case, kinematical analysis of the rigid prism based on the sole slip would not envisage vertical movements. Conversely if continuum deformability and plastic threshold of joints and rock mass are introduced, the prism detaches at the top (joint D3) and along the upper portions of lateral joints D1-S1 and D2-S1 due to the partial yielding of the rock extending below the prism base (pedestal). In this phase the vertical displacements are associated also to a slight lateral rotation and to an increase of normal stress on both the bottom joint ST and the inner portions of lateral joints. The prism is mainly sustained by the basal pedestal under the joint ST, with a low safety margin against its internal failure. Friction on lateral discontinuities provides however an important contribution, although their sub-vertical orientation. The numerical model accounts for deformation and damage features observed on the cliff, though calculated displacements appear to be an order of magnitude lower than those observed. The study also leads to an increased preparedness in managing possible emergency conditions and is part of a transparent policy towards local institutions and citizens.

REFERENCES Andreis F. (2016). Rilevamento geomeccanico e geostrutturale in sito di alcuni blocchi posti lungo la parete rocciosa a monte del campo sportivo della frazione Sarche nel comune di Calavino. Technical Report, Provincia Autonoma di Trento – Servizio Geologico. Adachi T., Ohnishi Y., Arai K. (1991). Investigation of toppling slope failure at Route 305 in Japan. International Congress of Rock Mechanics Aachen, 2:843–846. Barbero M., Barla G. (2010). Stability analysis of a rock column in seismic conditions. Rock Mech. Rock Eng,, 43:845–855. Barton N. (1973). Review of a new shear strength criterion for rock joints. Eng. Geol., 7, 287–332. Bandis S. (1990). Scale effects in the strength and deformability of rocks and rock joints. 1st Int. Workshop on Scale effects in rock masses, Loen, Norway, N. Barton & O. Stephansson (ed.), Balkema, Rotterdam, 59–76. Bieniawski Z.T. (1989). Engineering Rock Mass Classifications. Wiley, Chichester. Bonilla-Sierra V., Donzé F.V., Scholtès L., Elmouttie M. (2014). Coupling photogrammetric data with a discrete element model for rock slope stability assessment, Eurock 2014: Rock Engineering and Rock Mechanics: Structures in and on Rock Masses, Alejano, Perucho, Olalla, Jiménez Eds. 433–438. Hoek E., Carranza-Torres C., Corkum B. (2002). Hoek-Brown failure criterion - 2002 Edition. Proc. NARMS-TAC Conference, Toronto, 1, 267–273. Hoek E., Diederichs M. (2006). Empirical estimates of rock mass modulus. Int. J Rock Mech. Min. Sci., 43, 203–215. Itasca (2013). FLAC3D Fast Lagrangian Analysis of Continua in 3 Dimensions. Minneapolis. Tommasi P., Verrucci L., Campedel P., Veronese L., Pettinelli E., Ribacchi R. (2009). Buckling of high natural slopes: The case of Lavini di Marco (Trento-Italy), Eng. Geol., 109, 93–108.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

The propagation of hydraulic fractures in coal seams based on discrete element method Yanjun Lu Department of Geology, Moscow Lomonosov State University, Moscow, Russian Federation

Zhaozhong Yang State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, China

V.V. Shelepov & Jinxuan Han Department of Geology, Moscow Lomonosov State University, Moscow, Russian Federation

Xiaogang Li State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, China

Yongsheng Zhu Itasca Consulting China Ltd., Wuhan, China

Junfeng Guo Shanxi CBM Exploration and Development Subsidiary Company of SINOPEC, Jincheng, China

Zhongliang Ma Hua Tugou Town, Haixi, Qinghai Province, Qinghai, China

ABSTRACT: The simulation of hydraulic fractures is an important research content that can guide the engineering practice to achieve the purpose of increasing production. Coal has approximately orthogonal face cleats and butt cleats resulting in the discontinuous performance. Discrete Element Method (DEM) has obvious advantages in studying mechanical properties of discontinuous materials, so based on the distribution characteristic of cleats in coal, the research on the propagation of hydraulic fractures is carried out via DEM. The simulated results show that: hydraulic fractures mainly propagate along the cleats towards the maximum principal stress. The fracture network can be formed due to the intersection of face cleats and butt cleats that can propagate at certain pressure. The general variation trends of 3DEC numerical simulated results are consistent with physical experimental results at the same condition. With the increase of injection rate and fracturing fluid viscosity, the maximum aperture of hydraulic fracture increases, while the length of principal hydraulic fracture shortens. Therefore, to achieve the purpose of forming hydraulic fracture network in coal seams with cleats, low viscosity fracturing fluid and low injection rate need be applied to the fracturing technology. As the cleat density increases, the number of branched fractures increases, but the length of principal hydraulic fracture becomes short. Keywords: Coal, hydraulic fracturing, discrete element method, numerical simulation, cleat, hydraulic fracture 1

INTRODUCTION

Hydraulic fracturing is the key technology for realizing the industrial exploitation of CBM. It is estimated that hydraulic fracturing is applied in most of CBM wells in the United State, 929

and the CBM wells with more than 1000 m3/d almost have been stimulated by hydraulic fracturing in China (Zhang et al., 2006). Artificial fractures induced by fracturing can effectively connect the wellbore with the reservoir, which can promote desorption and diffusion of CBM and increase the CBM production. Geological parameters, fracturing fluid properties and construction parameters can have impact on the morphology of artificial fractures. Laboratory study on true triaxial fracturing of coal and fracture monitoring at the site show that hydraulic fractures in coal seams mainly initiate and propagate along the cleats, and complex and irregular multi-fractures are asymmetric distribution (Abass et al., 1990; Zhang et al., 2013; Yang et al., 2012). Conventional two-dimensional and three-dimensional fracture models can be applied in the specified coal seams to study the formation of symmetric fractures, but their applications are restricted in most of coal seams. To solve the problem of fracture propagation in the fractured reservoirs such as coal seams, a lot of work have been carried out in the numerical simulation. At present, discrete model of fracture network (Meyer et al., 2010), wire-mesh model (Xu et al., 2010) and unconventional fracture model (Weng et al., 2011) are mainly applied in the fractured reservoirs. In recent years, discrete element method (DEM) has been applied to the simulation of hydraulic fractures Zangeneh et al. (2012) used two-dimensional DEM (UDEC software) to simulate the hydraulic fracture propagation. Nagel et al. (2011) researched the law of fracture initiation and propagation and their influence factors in the fractured reservoirs with three-dimensional DEM. Hamidi and Mortazavi (2014) developed and simulated fracture initiation and propagation in the fracturing process based on three-dimensional DEM. Savitski et al. (2013) studied the interaction between hydraulic fracture propagation and generated discrete fracture network via DEM. The previous results show that complex fractures can be formed mainly due to the interference of natural fractures in the process of hydraulic fracturing, so the key of different simulated methods reveals the interaction of different fractures. The existing numerical simulations of fractures are mainly aimed at shale and tight sandstone, while the relevant simulated research on fracture propagation is less in the field of coal. Coal has approximately orthogonal distribution of face cleats and butt cleats that are not possessed in the other fractured reservoirs. DEM has a great advantage in dealing with the problems on discontinuous structural mechanics of natural fractured reservoirs. In this paper, the propagation laws of hydraulic fractures in coal seams are studied based on DEM, which can guide the engineering practice of fracturing in coal seams. 2

SIMULATED DETAILS

DEM firstly proposed by Cundall (1971) is a numerical simulated method to specially solve the problem of discontinuous medium. This method considers the rock composed of discrete blocks and cleats. Blocks can shift, rotate and deform, while cleats can be compressed,

Figure 1. Physical model of coal.

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Table 1.

Simulated parameters of coal.

Type

Parameter

Value

Petrologic parameters

Density (g/cm3) Cohesion (MPa) Internal friction angle (°) Tensile strength (MPa) Young’s modulus (GPa) Poisson’s ratio Residual hydraulic aperture (μm) Aperture at zero stress (μm) Maximum hydraulic aperture (μm) Vertical stress (MPa) Maximum horizontal principal stress (MPa) Minimum horizontal principal stress (MPa)

1.4–1.6/1.5 6.02–8.06/7.04 20.38–24.48/22.43 0.53–3.18/1.855 4 0.2–0.4/0.3 1 10 1000 10 5

Boundary conditions & Initial conditions

2

separated and slid. Therefore, the rock can be considered as the discontinuous and discrete medium that more actually reflect the nonlinear deformation characteristics of the rock with cleats. In addition, this method can express any complicated constitutive relation as tiny increments in the calculation, and no solution equations do not exist. The program of 3DEC was developed by Cundall and ITASCA consulting group. The FISH language embedded in the 3DEC program can make users define new variables and functions, which can extend the computing program and add user-defined characteristics. True triaxial fracturing experiment is a method of fracturing research that can be used to understand the mechanism of fracture initiation and propagation, and then experimental results can guide engineering practice of fracturing. However, true triaxial fracturing experiment has the problem of high cost and difficult sampling, so its widespread application is restricted. To solve the problem, numerical simulation and physical experiment are combined, which can not only improve the accuracy of numerical simulation but also widely research fracturing mechanism of rocks and its relevant influence due to the low cost. Numerical simulation model is established based on physical model. In this paper, the established numerical model is shown in Fig. 1, the parameters of model is listed in Table 1.

3 3.1

SIMULATED RESULTS The comparison of physical experiment and numerical simulation

The physical experiment (Fan and Zhang, 2014) is simulated with 3DEC at the same condition. In the simulation, the injection rate is 10 ml/min, and viscosity and density of fracturing fluid are, respective, 65 mPa.s and 1000 kg/m3. Model establishment, parameter assignment and iterative simulation are carried out via FISH program language. The simulated results are shown in Fig. 2 and Fig. 3. 3DEC simulated results indicate that hydraulic fractures propagate along the maximum horizontal principal stress. Hydraulic fractures propagate along the cleat, and the asymmetrical branched fracture network is shown. When initial pressure is 4.1 MPa, with the continuous injection of fracturing fluid, the pressure spreads rapidly with the elliptic to the boundary in the fracture, and the pressure curve fluctuates during the stage of fracture propagation. When fluid pressure spreads to the cleat, fracture propagation is suppressed easily resulting in the pressure fluctuation. Finally, the fracture propagates along the cleat at high pressure, and the branched fracture is formed. With the continuous injection of fracturing fluid, the maximum aperture increases near the injection point, while the aperture gradually decreases along the flow surface. When hydraulic fractures encounter the cleats, the cleat at the maximum principal stress preferentially propagates. 931

Figure 2.

Pressure distribution in the hydraulic fracture.

Figure 3.

The distribution of hydraulic fracture aperture.

Table 2.

Simulated parameters at different influence factors. Fracturing fluid viscosity (mPa⋅s)

Cleat density (cleats per meter)

Number

Injection rate (ml/min)

Butt cleat

Face cleat

01 02 03 11 12 13 21 22 23

10 20 30 20 20 20 20 20 20

65 65 65 10 30 65 65 65 65

50 50 50 50 50 50 12.5 25 50

100 100 100 100 100 100 25 50 100

Compared numerical simulation with physical experiment, the results show that the hydraulic fractures are the approximately vertical fractures propagating along the maximum principal stress. The injection pressure fluctuates during the propagation of fractures. When hydraulic fractures encounter the cleats, the fracture preferentially propagates along the cleat at the maximum principal stress. The final morphology of fractures is the multi-fractures, and the principal fracture locates at the center of model. In the physical experiment, hydraulic fractures in coal are mainly composed of propagated cleats, and the new fracture easily shifts due to its intersection at the cleat, which is consistent with the numerical simulated result. Therefore, the general trends of simulated results are in accordance with the experimental results, indicating that 3DEC simulated method has validity and feasibility. 3.2 The analysis of influence factors To further study the influence factors of hydraulic fracture propagation, the simulations on fracture propagation are carried out at different parameters that are listed in Table 2. The 932

same injection time or the same injection rate as the precondition is used to analyze the influence of different factors in the simulation. 3.2.1 Injection rate Injection rate as an important parameter for fracturing operation can have impact on proppant carrying capacity of fracturing fluid, fracture height control, leak-off loss and so on. Therefore, simulated results on fracture parameters (Fig. 4) are analyzed at different injection rates. As is shown in Fig. 4, with the increase of injection rate, the initial pressure of hydraulic fracture increases, and injection rates 10  ml/min, 20  ml/min and 30  ml/min correspond to initial pressures 4.1 MPa, 7.9 MPa and 11.8 MPa, respectively. The pressure fluctuates during the facture propagating, and when the propagation pressure tends to be stable, the greater the injection rate is, the higher the propagation pressure is. As the injection rate increases, the maximum hydraulic fracture aperture increases at the same injected fluid volume, while the length of principal hydraulic fracture becomes short, and branched fracture numbers are less. 3.2.2 Fracturing fluid viscosity Fracturing fluid viscosity can affect the morphology of hydraulic fractures. The higher viscosity of fracturing fluid is not only beneficial to proppant carrying but also has the advantage in controlling fracture height. Simulated results at different viscosity of fracturing fluid are shown in Fig. 5. With the increase of fracturing fluid viscosity, the initial pressure of hydraulic fracture increases, and when the propagation pressure tends to be stable, the higher the viscosity is, the

Figure 4.

Simulated results at different injection rates.

Figure 5.

Simulated results at different viscosity of fracturing fluid.

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Figure 6.

Simulated results at different cleat densities.

greater the propagation pressure is. As the viscosity of fracturing fluid increases, the maximum hydraulic fracture aperture increases at the same injection time, while the number of branched fractures lessens, and the principal hydraulic fracture with shorter length is formed. 3.2.3 Cleat density Cleats are natural fractures formed in the process of coalification, and the number of cleats is the key geological factor for the fracture network formed. The principal hydraulic fracture usually propagates along the maximum horizontal principal stress. However, it will propagate along the cleats after encountering the cleats resulting in the formation of branched fractures and complicated fracture network. The influence of cleat density on fracture network is analyzed, and the simulated results at different cleat densities are shown in Fig. 6. With the cleat density increasing, initial pressure and stable propagation pressure increase, and at the same injection time, the maximum hydraulic fracture aperture increases, but the propagated length of principal hydraulic fracture in the coal with high cleat density becomes short.

4

CONCLUSIONS

Relative to other fractured reservoirs, the cleats in coal seams have higher density and better regularity. However, the cleat existence makes coal have the discontinuous feature, so 3DEC has obvious advantages in mechanical study on discontinuous materials. In this paper, based on the simulated results from the 3DEC program, the following conclusions are obtained: 1. The numerical simulated results on initiation, propagation and morphology of hydraulic fractures are consistent with physical experimental results, indicating that 3DEC simulated method has validity and feasibility. 2. Hydraulic fractures propagate with the elliptic from the injection point to the boundary, and the spread of injection pressure has the priority, which means that fracturing fluid preferentially reaches the boundary with the leak-off, and yet the variation of fracture aperture is relative hysteresis. The pressure fluctuates when the fracture encounters the cleat during the propagation, and the higher fracture fluid pressure can break through the intersection of fractures. When the fracture reorients, the cleats have the advantage in propagating along the maximum principal stress. 3. Maximum fracture aperture near the injection point, initial pressure and propagation pressure are positively associated with injection rater, fracturing fluid viscosity and cleat density, but the length of principal hydraulic fracture is negatively correlated with these parameters. Therefore, to achieve the purpose of forming hydraulic fracture network 934

in coal seams with cleats, low viscosity fracturing fluid and low injection rate need be applied to the fracturing technology. At the same construction condition, long and narrow hydraulic fractures are easily formed in coal seams with lower cleat density.

REFERENCES Abass H H, Van Domelen M L, El Rabaa W M. Experimental Observations of Hydraulic Fracture Propagation Through Coal Blocks [C]. SPE Eastern Regional Meeting, 31 October-2  November, Columbus. Ohio, USA, 1990. Fan Tiegang, Zhang Guangqing. Influence of injection rate and fracturing fluid viscosity on hydraulic fracture geometry in coal [J]. Journal of China University of Petroleum (Edition of Natural Science), 2014, 38(4): 117–123. Gundall P A. A computer model for simulating progressive large scale movement in block rock system [J].Symposium ISRM, 1971, Proc 2:129–136. Hamidi F, Mortazavi A. A New Three Dimensional Approach to Numerically Model Hydraulic Fracturing Process [J]. Journal of Petroleum Science and Engineering, 2014, 124: 451–467. Meyer B R, Bazan L W, R H Jacot, et al. Optimization of Multiple Transverse Hydraulic Fractures in Horizontal Wellbores [C]. SPE Unconventional Gas Conference, 23–25 February, Pittsburgh, Pennsylvania, USA, 2010. Nagel N, Gil I, Sanchez-Nagel M. Simulating Hydraulic Fracturing in Real Fractured Rocks— Overcoming the Limits of Pseudo3D Models [C]. Paper SPE 140480 presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, 24–26 January 2011. Savitski AA, Lin M, Riahi A, Damjanac B, Nagel NB. Explicit modeling of hydraulic fracture propagation in fractured shales. IPTC-17073-MS, 2013. Weng X, Kresse O, Cohen C, et al. Modeling of Hydraulic-Fracture-Network Propagation in a Naturally Fractured Formation [J]. SPE Production and Operations, 2011, 26(4): 362–368. Wenyue Xu, Marc Thiercelin, Utpal Ganguly, et  al. Wiremesh: A Novel Shale Fracturing Simulator [C]. Paper SPE 132218 presented at CPS/SPE Intemational Oil & Gas Conference and Exhibition. Beijing China, 2010. Yang Jiaosheng, Wang Yibing, Li Anqi, et al. Experimental study on propagation mechanism of complex hydraulic fracture in coal-bed [J]. Journal of China Coal Society, 2012, 37(01): 73–77. Zangeneh N, Eberhardt E, Bustin R M. Application of the distinct-element method to investigate the influence of natural fractures and in situ stresses on hydrofrac propagation [C]. 46th US Rock Mechanics/Geomechanics Symposium, Chicago. 2012. Zhang Ping, Wu Jianguang, Sun Hansen, et al. Analysis the results of the downhole microseismic monitoring technique in coalbed methane well fracturing [J]. Science Technology and Engineering, 2013, 23: 6681–6685. Zhang Yapu, Yang Zhengming, Xian Baoan. Coal-bed gas stimulation technology [J]. Special Oil & Gas Reservoirs, 2006, 13(1): 95–98.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

The influence of the interface of drilled socketed shafts and rock mass on their behavior Mikhail G. Zertsalov & Valeriy E. Merkin Department of Soil Mechanics and Geotechnics, Moscow State University of Civil Engineering (National Research University), Moscow, Russia

Ivan N. Khokhlov LLC Scientific Engineering Center of Tunneling Association, USA

ABSTRACT: Socketed shafts are usually designed and constructed as foundations of high-rise buildings and bridge structures when layers of loose soil overlie bedrock. The behavior of socketed shafts in rock has a lot in common with the large diameter piles in soil. However, the structure of a rock mass and their highly variable mechanical characteristics considerably complicate the calculation of the socketed shaft bearing capacity and settlement in rocks. The factor, significantly affecting the interaction of socketed shafts with rock mass—the mechanical properties of the sidewall interface, is analyzed in this article as well as some peculiarities of calculations of settlements of socketed shafts in rock under the action of vertical loading. The major factors, affecting the bearing capacity of socketed shafts under loads, are associated with composition, structure and mechanical properties of rock mass. The results of the study of the effect of sidewall interface of socketed shafts in conditions of elasto-plastic problem are presented to assess the tangential stiffness influence on the behavior of the socketed shaft, in particular, on its settlements.

1

INTRODUCTION

The socketed drilled shafts of large diameter are typically used to transfer loads from the structures through layers of soils to stronger underlying rock. The shafts can either be based on the rock, or socketed into it. As world practice shows, the diameter of sockets can usually be changed from 0.5 to 2.0 m, and the length of the socket to reach 10.0 m or more. The arrangement of drilled shafts, as indicated in (Zhang, 2004, NCHRP, 2006) has a number of advantages: the ability to transfer heavy loads and relatively low cost; relatively simple applied construction technology, including a fairly simple process of drilling of shafts; small noise and vibration arising during the process of drilling and construction. Taking this into account, during the construction of bridges and high-rise buildings on soil, underlying bedrock, socketed drilled shafts are considered as the most efficient and economical deep foundations. Despite the fact that the behavior of the socketed shaft both in soil and in rock is similar, i.e., its bearing capacity is defined by the resistance at the side surface and the strength of the ground under the tip of the shaft, the nature of interaction between the shaft and surrounding rock mass is quite different and it is determined mainly by factors caused by the structural features and mechanical properties of rocks. The results of various studies (Osterberg, Gill, 1973; Pells, Turner, 1979; Donald et al. 1980; O’Neill, Reese, 1999; Zhang, 2004; NCHRP, 2006) show that these factors primarily include: the deformability and strength of rock mass, the ratio between the modulus of elasticity of the shaft material and the modulus

937

of deformation of rock, mechanical characteristics of the interface between the shaft and the rock mass, the ratio between the length of the shaft socket in rock and its diameter. In (Zertsalov, Nikishkin, 2015; Zertsalov et al., 2017) a method of calculation of bearing capacity and settlements of vertically loaded socketed shafts in rock is proposed. The method is based on the joint use of numerical modeling and the method of experimental design techniques. The experimental design techniques significantly expands the research opportunities, allowing to solve problems of interaction of engineering structures with rock mass, which cannot be solved analytically or by physical modeling. The results of carried out investigations allowed to obtain the regression equations – dependencies, linking the response functions (in this case, load applied to the top of the socketed shaft and, corresponding to these load, settlements in the key points A, B and C of the settlement curve) with the independent factors. As the key points the following ones had been chosen: the start and the end of the failure of the sidewall interface (points A and B), and the beginning of the failure of the shaft material or rock mass (point C). As the independent factors, which mostly affect the shafts behavior, three following factors were used: RQD, Ec/Er, L/D, where RQD is the rock quality designation, Ec/Er is the ratio of the modulus of elasticity of shaft material to the modulus of elasticity of the intact rock and L/D is the ratio of the length of the shaft to its diameter. All numerical calculations were performed in conditions of elasto-plastic problem, the Mohr-Coulomb model was used to analyze both the rock mass and interface behavior. The assignment of the limits of variation of the independent factors and values of mechanical characteristics of socketed shaft, rock mass and interface between shaft and rock mass was explicitly described in (Zertsalov, Nikishkin, 2015; Zertsalov et al., 2017). Curves of the shaft settlements based on the results of numerical calculations of the five-meter socketted shafts are presented in Fig. 1 as an example. The bearing capacity of the shaft was determined by summation of the resistance around its side surface and the strength of the rock under the tip of the shaft. The modulus of deformation of the rock mass Em was determined using the empirical dependencies of ratio of rock mass deformation modulus to the modulus of elasticity of intact rock from RQD - rock quality designation factor (Zhang, 2004). It is also worth saying, that in the above mentioned papers the factor, significantly affecting the performance of socketed shafts in rock mass—the mechanical properties of the sidewall interface, was not considered in the factor analysis. The influence of this factor was investigated separately. The results of these studies are presented in this paper.

Figure 1. Settlement curves of socketed shafts (A—the beginning of the failure of sidewall interface, B— the end of the failure of sidewall interface, C—the beginning of the failure of the rock mass or the shaft).

938

2

NUMERICAL SIMULATION AND ANALYSIS

Numerical simulations with FEM were performed using a special contact element, which allows simulation of behavior of the sidewall interface of the socketed shaft in rock—the process of elastic deformation of the interface and its failure. In Fig. 2a three-dimensional computational model, used in the research, generated using Z-Soil software package, is shown. The rock mass and the shaft body is modeled by 8-node continuum 3D elements. The bottom and outer boundaries of the model are fixed. The distance between side planes and shaft body B has been chosen after studying the influence of mesh boundaries on shaftrock interaction. The initial stresses have to be unchanging at model boundaries. The depth beneath socketed shaft tip is equal to the embedment length of the shaft. The analysis of the currently available studies, for example (Ooi, Carter, 1987; Hatami, Bathurst, 2006), shows that mechanical characteristics of the “concrete-rock” interface may vary in a wide range. This was confirmed by full-scale field shaft tests, which show that the value of sidewall interface stiffness can vary significantly depending on the properties of drilled shaft and rock mass. At the same time, the results of the in situ tests of socketed shafts (Williams, Pells, 1981; Horvath et al., 1983; Hoonil Seol et al, 2009) also showed that the state and, as a consequence, the mechanical characteristics of interface (the absence or presence of roughness of the borehole walls, the degree of roughness, the use of bentonite, etc.) have a significant impact on settlements of shaft (Fig. 2b). Taking this into account, a series of calculations to study the influence of the tangential stiffness of the interface on the shaft settlements under the action of axial compressive loads were carried out. Two socketed shafts with length of 5 m and 20 m in rock mass were studied. At first in each numerical experiment, the load on the shaft had been increasing to the value at which the failure of the interface between shaft and rock occurred (elastic portion of the settlements curve). The settlements of the shafts were determined for different values of tangential stiffness of the interface: Ks = 50 × 103, 100 × 103, 200 × 103, 300 × 103, 500 × 103 and 1 × 106 kN/m3. Series of calculations, using the following relationship of the modulus of elasticity of the shaft to modulus of deformation of the rock mass: Ec/Em = 125, 50, 25, 5, 2.5, 1.7, were conducted. Value of the normal stiffness Kn in the calculations was determined using the formula (Boresi, 1965):

Figure 2. Finite element model of interaction of drilled shaft with rock mass (a), the socketed shaft settlement curves with smooth and rough borehole walls (Horvath et al, 1983) (b).

939

Kn =

Em R( +

m

)

(1)

where R is the drilled shaft radius, νm is the Poisson ratio of the rock mass and Em is the rock mass deformation modulus. In Fig. 3 shown the results of the studies, presented in the form of curves based on the relationships between shafts settlements and the change of the tangential stiffness of the interface (Ks) for different ratios of modulus of deformation of the shaft and rock mass (Ec/Em), which correspond to rock mass of medium strength. Curves are drawn for values of the settlements at the point A (see Fig. 1) - the end of the elastic portion of the shaft settlement curve. By analyzing the curves one can see, that with increasing of stiffness (Ks) in the range from 50 × 103 kN/m3 up to 500 × 103 kN/m3 the value of the shaft settlements are reduced in the range of from 2.8 to 3.1 times, depending on the changes of the tangential stiffness and the modulus of deformation of rock mass. At the same time, with increasing of the interface tangential stiffness in the range from 500 × 103 kN/m3 up to 1 × 106 KN/m3, the value of the shaft settlements changes very little. In this range of the values of the interface stiffness (Ks) it becomes comparable with the stiffness of the rock mass, which primarily determines the magnitudes of the shaft settlements. Since the limit of variation of tangential stiffness had some uncertainty before preceding studies (Zertsalov et al., 2017, Zertsalov, Nikishkin, 2015), shear stiffness values of “concreterock” interface Ks, basing on the analysis of available publications and studies, were taken averaged and equal to Ks = 100 000 kN/m3. Therefore, the magnitude of the settlement, calculated using the obtained regression equations, is suitable only for the basic value of Ks. The curves presented on Fig. 3, allow, within the first linear part of shaft deformation curve, to determine shaft settlements in any combination of the values of the tangential stiffness of the interface and deformation modulus of rock mass in the range within the variation of values of these parameters (Ks = 50 × 103 kN/m3–1 × 106 kN/m3; Em = 0,2 × 106 kN/m2 –15 × 106 kN/ m2). Using curves (Fig.  3) it is possible to determine the settlement conversion factor Cs, which is presented in Fig. 4. With this chart, when the modulus of deformation of rock mass and the corresponding magnitude of the shaft settlement with Ks  =  100  ×  103 kN/m3 are known, it is possible to determine the settlement for any value of the interface stiffness - Ks. This requires the settlement value of the socketed shaft with Ks = 100 × 103 kN/m3 to be multiplied by the factor Cs. Similar studies of the influence of the tangential stiffness of the “shaft-rock” interface and deformation modulus of the rock mass on the shafts settlements were made for the point B (Fig. 1) – the end of the interface failure. Analysis of the results showed that in this case the nature and intensity of change of the settlement curves are quite similar to the curves shown

Figure 3. Curves of the dependence of the shaft settlements from the change of tangential stiffness of the interface under different ratios of modulus of deformation of the shaft and rock mass (Ec/Em).

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Figure 4. Conversion factor Cs depending from value Ks.

Figure 5.

Calculated curves of the shaft settlements compared with field test data.

in Fig. 3, which can be explained by mentioned above, mild nonlinearity of the settlements curves within this part of deformation diagram. The calculation results obtained using the proposed method were compared with the results of field test of the shaft. As example, the shaft behavior under compression with a diameter of 1.22 m and a length of socket into rock – 4.88 m (Zhang, 2010) is considered. Rock mass is formed by the weathered fractured limestone with the following characteristics: RQD = 55%, the modulus of elasticity of the intact rock Er = 32 × 103 MPa, the modulus of deformation of rock mass Em = 4,8 × 103 MPa. In this case, bearing capacity of the shaft is provided by the resistance along the sidewall and the strength of the rock mass under the shaft. In Fig. 5 there are four curves of the shaft settlements: field test curve and three polylines, constructed using above mentioned regression equation (Zertsalov et al., 2017) and conversion factor Cs. For these three polylines different values of tangential stiffness of the “shaft-rock” interface were accepted: Ks = 100 × 103 kN/m3 (curve 1), 200 × 103 kN/m3 (curve 2) and 300 × 103 kN/ m3 (curve 3). Comparison of the curves shows that the curves constructed on the basis of 941

numerical simulations, correspond well with the experimental curve, however, the range of deviation (Fig. 5) is completely determined by the value of Ks. For example, values of shaft settlements of the curves 1 and 3 differ from the corresponding curve values of field tests of the shaft not more than 25%, and the difference of the curve 2 does not exceed 7%. The obtained results confirm the conclusion, made after analysis of results of experimental researches, by the necessity of considering the influence of the stiffness of “shaft-rock” interface and obligatory determination of its value by conducting a field full scale shaft test. 3

CONCLUSIONS

1. In the study of the interaction of the socketed shafts with rock mass it is necessary to determine the mechanical characteristics of “shaft-rock” interface, which has a significant influence on the behavior of the shaft not only on the portion of the settlement curve, where interface failures, but also on the portion of elastic deformation of interface. 2. Taking into account, the importance of the parameter of shear stiffness of interface Ks, when considering the behavior of drilled socketed shafts, it is necessary to conduct more detailed and precise analysis of the effect of the stiffness of the “shaft-rock” interface on shaft settlements and obligatory determination of value Ks, when conducting a field full scale shaft test. 3. Taking into account, that the source of information for assigning the values of mechanical properties of sidewall interface of the socketed shafts, used in the above researches, was taken from various sources or obtained empirically, the proposed method of calculation Ks can be used for the evaluation of the interaction between socketed shafts and rock mass only at the stage of preliminary design. REFERENCES Boresi, A.P. 1965. Elasticity in engineering mechanics. Prentice-Hall, Englewood Cliffs, N.J. Donald, I.B., Sloan, S.W., Chiu, H.K. “Theoretical Analysis of Rock Socketed Piles”, Proceedings, International Conference on Structural Foundations on Rock, Vol. 1, Sydney, Australia, 1980, pp. 303–316. Hatami, K. and Bathurst, R.J. “Numerical Model for Reinforced Soil Segmental Walls under Surcharge Loading” Journal of Geotechnical and Geoenvironmental Engineering, 2006, pp. 673–684. Horvath, R.G., Kenney, T.C., and Kozicki, P. “Methods of Improving the Performance of Drilled Piers in Weak Rock”, Canadian Geotechnical Journal, Vol. 20, 1983, pp. 758–772. NCHRP Synthesis 360, “Rock-Socketed Shafts for Highway Structure Foundations,” Transportation Research Board, Washington D.C., 2006, pp. 136. O’Neil, M.W. and Reese, L.C. “Drilled Shafts: Construction Procedures and Design Methods,” Report FHWA-IF-99–025, Federal Highway Administration, Washington D.C., 1999, 758 pp. Ooi, I.H. and J.P. Carter, “Direct Shear Behavior of Concrete-Sandstone Interface”, Proceedings, 6th International Conference on Rock Mechanics, ON, Canada, 1987, pp. 467–470. Osterberg, J.O. and. Gill, S.A. “Load Transfer Mechanism for Piers Socketed in Hard Soil or Rock,” Proceedings, 9th Canadian Symposium on Rock Mechanics, Montreal, ON, Canada, 1973, pp. 235–262. Pells, P.J.N. and. Turner, R.M. “Elastic Solution for the Design and Analysis of Rock-Socketed Piles,” Canadian Geotechnical Journal, Vol. 16, 1979, pp. 481–487. Seol. H., Jeong, S. and Cho, S., 2009. Analytical Method for Characteristics of Rock-Socketed Shafts. Journal of Geotechnical and Geoenvironmental Engineering, ASCE. June 2009: 778–790. Vybornov K.A., Sainov M.P. “Influence of Seams Work on Spatial Deflected Mode of Concrete-Face Rock Fill Dam” Vestnik MGSU, Vol. 5, 2011, pp. 12–17. Williams, A.F. and P.J.N. Pells, “Side Resistance Rock Sockets in Sandstone, Mudstone, and Shale,” Canadian Geotechnical Journal, Vol. 18, 1981, pp. 502–513. Zertsalov M.G., Nikishkin M.V., and Khokhlov, I.N. “On the calculation of bored piles under axial compressive loads in rocky soils” Soil Mechanics and Foundation Engineering, Vol.3, 2017, pp. 2–8. Zertsalov M.G. and Nikishkin M.V. “Interaction of drilled shafts with rock masses” Procedia Engineering, Vol.111, 2015, pp. 877–881. Zhang, L. “Drilled Shafts in Rock (Analysis and Design),” A.A. Balkema Publishers, 2004, 383 pp. Zhang, L. Prediction of end-bearing capacity of rock-socketed shafts considering rock quality designation (RQD)” Can. Geotech. J. 47, 2010, pp. 1071–1084.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

The determination of crack resistance of circular shaped fiber reinforced concrete tunnel lining by means of linear fracture mechanics Mikhail Zertsalov NRU MGSU, Moscow, Russia

Valery Merkin Scientific Consultant LLC, “NIC TA”, Moscow, Russia

Egor Khoteev Head of Structural Analysis Department LLC, “Sigma Tau”, Moscow, Russia

ABSTRACT: In the paper the results of research of fracture toughness of fiber reinforced concrete tunnel linings of circular shape are presented. Such lining is effectively used in rock in zones of considerable fracturing, occurrence of weak weathered rocks. On the basis of laboratory testing of linings and numerical simulation of their behavior (FEM) in the same conditions it is shown that the deformation of fiber concrete under load is linear and therefor this material can be modeled as solid, elastic, homogeneous medium. In addition, the analysis of stress–strain state of these linings shows that their failure is caused by stable propagation of the single crack. At the same time, in accordance with the stress distribution along the contour of the lining, this single crack occurs, usually in its ceiling section, less in the floor section. The described mechanism of failure of the circular shape lining allows for the calculations of fracture toughness (crack resistance) to use the linear fracture mechanics. Taking into consideration the symmetry of the stress distribution, the crack appears on the inner contour of the lining and spread with the growth of load under conditions of pure tension in its own plane. In this case, the criterion for the crack propagation is the critical stress intensity factor—KIC, which is constant mechanical characteristics of the material. The article presents the results of experimental determination on the samples values of KIC and of the formula, allowing to calculate KIC for fiber-reinforced concrete of various compositions. On the basis of the conducted experimental studies, numerical simulations of the experiments and laws of fracture mechanics developed a method of calculating the fracture toughness of fiber reinforced concrete lining of circular shape. Keywords: fiber reinforced concrete tunnel lining, fracture mechanics, FEM

1

INTRODUCTION

Fiber-concrete is a modern and promising building material. It is a composition of concrete and fiber (steel or synthetic). Concrete has a high compressive strength. However, its tensile strength is negligible. Due to the use of fiber, an increase in the tensile strength of the material, an increase in its fracture toughness, and also its strength after cracking is achieved. This makes it possible to ensure the operational reliability and durability of tunnel lining made of fiber-reinforced concrete, using a minimum percentage of additional core reinforcement or completely abandoning it. Taking this into account, fiber-reinforced concrete can be

943

Figure 1.

An example of a tunnel lining made of fiber-reinforced concrete.

Figure 2. Testing of samples of fiber-reinforced concrete for bending.

Figure 3. Numerical simulation of tests of fiberreinforced concrete samples for bending.

an effective substitute for reinforced concrete in the construction of tunnel lining in rocky grounds, including in highly fractured rocks or in fracture and weak ground areas. Many works have been devoted to the research of fiber-reinforced concrete, as a result of which reliable methods of calculating its strength have been developed [5–8]. At the same time, methods for calculating the fracture toughness of structures made of fiber concrete, taking into account the features of its work, are currently lacking. In laboratory tests of samples of fiber-reinforced concrete for bending (Figure 2) and their numerical modeling (Fig. 3) it was established that fibrous concrete has the properties of an elastic homogeneous isotropic material. The tests also showed that the fracture in fibrous concrete can propagate steadily (Figure 4). The resulting crack propagates in the structure to a certain thickness and stops. Its further growth is associated only with an increase in the load. Numerical simulation of the interaction of fiber-reinforced concrete tunnel lining with a surrounding solid, homogeneous, isotropic massif (Figure 5), performed in the ZSoil program [11], made it possible to reveal certain patterns of cracking in such structures. Particular attention should be paid to the fact that cracking in tunnel lining of circular contours operating under such conditions is characterized by crack formation, which is usually formed in a lining that spreads stably or unstable in its own plane. Initially, numerical studies were carried out for monolithic lining and for lining to be built by the method of spattering of concrete. Later, additional calculations were carried out, demonstrating that the obtained regularities are also valid for prefabricated tunnel lining of a circular outline. 944

Figure 4.

An example of a sustainable crack spread in fiber-reinforced concrete.

Figure 5. Numerical simulation of stress state of tunnel lining. On the left is an example of the bending moment diagrams, on the right is an example of the longitudinal force diagram.

Figure  6. Testing of blocks of tunnel lining made of fiber-reinforced concrete.

Figure 7. Numerical simulation of tests of tunnel lining blocks made of fiber-reinforced concrete.

The performed laboratory studies of large-scale tunnel lining (Figures 6, 7) confirmed the conclusions drawn from the results of numerical simulation and testing of fiber-reinforced concrete samples. When testing large-scale fiber-reinforced concrete blocks of tunnel lining, deformations of the blocks were measured, the character of the cracking process was recorded, in particular, the width of the crack opening and the depth of its spread. Proceeding from the above, to calculate the crack formation in tunnel lining circular outline of fiber concrete can be applied to linear fracture mechanics. The foundations of the mechanics of destruction were laid in the works of G. Kirsch, G.V. Kolosova [2, 3], K. Inglis [9]. Studies show that at the tip of a thin crack, for which the ratio of the lengths of the larger semiaxis to the smaller one tends to infinity, a singular region is formed in which the stresses increase infinitely. This means that the tensile stresses can not be used as a criterion for the propagation of a crack. J.R. Irvine proposed [10] to characterize the distribution of stresses in the region around the crack tip by the stress intensity factor ( I, II, III – respectively, for cases of normal separation, longitudinal and transverse shear), the critical values of which ( IC, IIC, IIIC) allow to determine the moment of friction of the crack. Given that the tunnel 945

lining is eccentrically-compressed, and the shear stresses in it are minimal, we can speak of the formation in it of only cracks of normal separation. Therefore, the condition of crack resistance of the tunnel lining will be: KI

K IC

(1)

Once again, it must be emphasized that KI is a function of the stress state of the lining, while KIC is a constant characteristic of a particular material, in our case, a fiber concrete of a certain composition. The value of the critical stress intensity factor KIC, which depends on the composition of fiber-reinforced concrete, is determined experimentally. The results of laboratory studies on the determination of KIC fiber-reinforced concrete, given in [1], give the following mathematical dependences of KIC on the concentration of fiber and the class of concrete matrix for steel (2) and for polypropylene (3) fibers. K IC _ S K IC _ P

0, 04 F FS S 0, 08 B − 0, 00072 ⋅ FS ⋅ B − 2,84

(2)

0, 02 F FP P 0, 007 B − 0, 00033 ⋅ FS ⋅ B + 0,83

(3)

where FS, FP – is the content of steel and polypropylene fibers, respectively, kg/m3; B – is the strength of concrete of the matrix for compression, MPa. Calculation of the value of the stress intensity factor KI in the lining of a circular outline was carried out according to the procedure described in [4] for an eccentrically-compressed element, in accordance with the scheme shown in Fig. 8, according to the formula: KI

σ 0 l0 f1 (

)

σ l0 f 2 (

)

(4)

where λ0 – is the ratio of the length of the initial crack to the thickness of the structure; σ 0 – stresses from compressive forces at the mouth of the crack; Δσ – is the difference in stresses at the mouth and at the apex of the initial crack; l0 – length of the initial crack, which is a set of microdefects in the lining; f1(λ0), f2(λ0) – are tabular functions given in [4]. For tunnel lining circular outlines of fiber-reinforced concrete, there are three design cases: Condition (1) is fulfilled and a crack is not formed (Fig. 9); Condition (1) does not hold. The resulting crack propagates steadily to a certain depth (Figure 10). Here, as the results of calculations show, two variants can be distinguished. In the first variant, the crack extends to 30% of the thickness of the lining. Such a crack is acceptable, since a sufficient thickness of undisturbed fiber-reinforced concrete remains. In

Figure  8. Scheme for calculating the stress intensity factor at the tip of a normal tear crack in an eccentrically-compressed element.

946

Figure 9.

The first calculation case. A crack is not formed.

Figure 10.

The second calculation case. The crack forms and spreads steadily.

Figure 11.

The third calculation case. The crack is formed and spreads unsteadily.

the second variant, the crack passes through 90% of the thickness of the structure. Such a crack is inadmissible; Condition (1) does not hold. The resulting crack propagates unstably throughout the entire thickness of the lining and leads to its destruction (Figure 11). Such a crack is also inadmissible. A joint analysis of the results of a laboratory experiment and numerical modeling allows us to develop a method for calculating the fracture toughness of tunnel linings made of fiberreinforced concrete using the dependences of linear fracture mechanics given in [4]. The presented technique can be used also in the consideration of prefabricated tunnel lining of a circular outline. In this case, it is necessary to consider two cases: 947

The joint of blocks in the ring is located in the arch of the lining. In this case, the KIC is assumed to be zero, since the joint is regarded as a crack in the lining and the amount of its opening determines the allowable stress-strain state of the lining; The joints are offset with respect to the arch of the lining. In this case, the calculation of crack resistance is carried out, both for monolithic lining. Thus, a joint analysis of the results of a laboratory experiment and numerical simulation allows us to develop a method for calculating the fracture toughness of tunnel linings made of fiber-reinforced concrete using the dependences of linear fracture mechanics given in [4].

2

CONCLUSION

1. The theoretical and experimental justification of the possibility of applying linear fracture mechanics to the calculation of the fracture toughness of prefabricated and monolithic tunnel lining of circular outline from fiber-reinforced concrete;; 2. The possibility of developing a method for calculating the fracture toughness of tunnel lining made of fiber-reinforced concrete, which takes into account the characteristics of their interaction with the enclosing ground mass, is substantiated. As the basis of the method, an approach that was previously not used to solve this problem, combining the finite element method and linear fracture mechanics, is proposed. The method makes it possible to estimate the fracture toughness of the lining and to determine the depth spread of crack; 3. The main design cases of crack formation in tunnel lining of circular contours have been determined, which make it possible to draw a conclusion about the fracture toughness of the tunnel lining of circular outline from fiber-reinforced concrete. A method for estimating the admissibility of a crack in a fiber-reinforced concrete lining is shown.

REFERENCES [1] Zertsalov MG, Khoteev EA Experimental determination of fracture toughness characteristics of fiber-reinforced concrete. // Bulletin of MGSU (VAK). 2014. 5. Pp. 91–99. [2] Kolosov G.V. On an application of the theory of a function of a complex variable to a plane problem. Yuryev, 1909, 197 with. [3] Kolosov G.V. Application of a complex variable to the theory of elasticity. ML, Gostekhizdat, 1935, 224 p. [4] Orekhov V.G., Zertsalov M.G. Mechanics of destruction of engineering structures and mountain ranges. DIA Publishing House, 1999, 330 p. [5] Rusanov V.E. Features of the calculation of prefabricated steel-fiber-concrete lining tunnels subway. // Problems of reliability and efficiency of tunnel structures. Collection of scientific papers, Issue No. 254 ed. V.E. Merkina - M.: OAO ZNIIS, 2009. - P. 44–82. [6] Rusanov V.E. Designing tunnel structures from fiber-reinforced concrete (modern approaches). // Proceedings of the international scientific and technical conference “The main directions of the development of innovative technologies in the construction of tunnels and the development of the underground space of large megacities.” - Moscow: “Timur”, 2010. - P. 89–92. [7] SP 52-104-2006. Stalefibrobetonnye constructions. [8] ACI 544.4R-88 Design Consideration for Steel Fiber Reinforced Concrete. [9] Inglis C. E. Stresses in a plate due to the presence of cracks and sharp corners, Trans. Institute of Naval Architects. 1913. V. 55. P. 219–241. [10] Irwin, G. R., Analysis of Stress and Strains, Near the End of a Crack Traversing a Plate, Trans. ASME. J. Appl. Mech. 1957. V. 24. P. 361–364. [11] Z_Soil User Manual by: Thomas Zimmermann, Andrzej Truty, Aleksander Urbanski, Stephane Commend, Krzysztof Podles.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Kinematics and discreet modelling for ramp intersections T. Zvarivadza & F. Sengani School of Mining Engineering, University of the Witwatersrand, Johannesburg, South Africa

ABSTRACT: Geotechnical work was conducted in order to identify the required support length and other important parameters in ramp intersections at a deep level gold mine. The investigation included detailed scanline and joint mapping. Discreet models were constructed and eight different excavation orientations were analyzed in order to obtain a worst case scenario of mining direction. A sensitivity analysis was conducted and the effect of clamping stresses on the hanging wall was quantified. The probabilistic modeling program, JBlock, was utilized to quantify the probable maximum apex height of blocks forming in the ramp intersections. A geo-domain was constructed making use of all the data acquired and was analyzed. Eight excavations were constructed ranging in mining directions from 0 to 315 degrees. The excavations were assumed to have a dip of 8 degrees to ensure the largest blocks are created, subsequently catering for the worst case scenario. The output data created by the software was scrutinized for failed blocks, and cumulative distribution graphs created. In order to understand the effect of clamping stresses in the hanging wall, the worst case mining direction (180 degrees) was utilized and clamping stresses in the hanging wall were varied from 0 kPa to 30 kPa. A 32% reduction in the 50 percentile apex height was attained when the clamping stress increased to 5 kPa, a 43% reduction was attained when a clamping stress of 10 kPa was applied, and a 48% reduction in apex height was attained when the clamping stress was set to 30 kPa. Keywords: Modelling, kinematics, geo-domain, ramps, probabilistic analysis, clamping stresses, JBlock, gold mining

1

INTRODUCTION

Block Theory, introduced by Goodman and Shi, 1985, presents a geometric approach to rock mechanics based on a “key block” concept. The overall stability of an excavation was assumed to depend, in the first analysis, on the orientations of the joint sets which cut the rock mass, with respect to the free surface(s). Blocks which are kinematically “free” to translate into space were termed removable. Removable blocks were then examined for stability under the applied forces. Blocks which were both removable and unstable were the “key blocks” of the excavation, and if these blocks were stabilized (e.g. with rock bolts) the entire excavation was assumed to be safe (Goodman, 1976 and 1979). The failure modes discussed in Block Theory (sliding and lifting) involve translation only. Further studies consider another possible failure mode: rotation. It is shown that a removable block, safe against sliding, might fail in rotation. Such a block would be deemed safe in the conventional block theory analysis. This paper is intended to supplement block theory and examines: (1) the geometric conditions necessary for rotation to be possible (kinematics); and (2) the rotational stability of blocks which satisfy the kinematic conditions for rotation (equilibrium). Rotations of rock wedges have been discussed by others, including [3–6] but not previously in the context of block theory.

949

2

DATA COLLECTION

The underground Scanline mapping was conducted along the sidewall of the ramp to quantify input parameters for use in the J-Block software package. Scanline mapping involves a process of measuring joint orientations, frequency, persistence, water and joint contact surface conditions present in the host rock. An accepted scanline has to at least have three joints traversing the line so as to be able to calculate joint spacing. Nine scanlines amounting to approximately 180 m in total length were mapped. The following parameters were logged during the underground mapping process to be used as input parameters for the discreet modelling: Joint dip and direction, Joint persistence, the visibility of ends, Joint roughness coefficients, degree of moisture on joints, hardness of joint walls, degree of alteration of joints, separation of joints, joint infilling thickness and healing of joints and infilling material. The DIPS (Stereonet analysis software) was used to analyses the joint data gathered. Schmidt rebound numbers were also obtained for the rock comprising the excavation sidewalls. These numbers were used to approximate the Joint wall Compressive Strength (JCS) for the different joint wall conditions observed. The JCS values obtained were used in the Barton-Bandis (1990) model in order to calculate the respective friction angles required by JBLOCK. 3

JOINT ORIENTATIONS

Based on the underground mapping, four joint sets were identified along the mining ramp. One joint set dipping approximately south represents the various layering of the strata. Two additional joint sets dip approximately east of south-east, one almost vertical, and the fourth set of joints were vertical, striking in a northerly direction. These joint sets were then represented using Dips software package (see Figure 1). Furthermore, analysis using in-house software to determine mean, min and max dip and dip direction has shown that relatively small standard deviations exist for the various joint sets, indicating a very good correlation between the joint sets at the various scanline locations. The large dip direction’s standard deviation associated with joint set 1 (see Table 1) may be attributed to the very flat nature of its dip direction and was to be expected. 4

JOINT PERSISTENCE

The joint persistence is highly dependent on the number of ends that could be observed during the logging. For this reason, a set of general rules was constructed out of the experi-

Figure 1.

Stereonet showing joint sets orientation.

950

Table 1. Joint orientations. Dip

Joint Set 1 Joint Set 2 Joint Set 3 Joint Set 4

Dip direction

Mean

Min

Max

Std.Dev

Mean

Min

Max

Std.Dev

20.96 86.4 81.9 52.9

9 83 76 48

34 89 89 56

6.2 2.3 4.8 2.6

187 75.12 104 100.3

131 71 97 93

278 82 113 111

40 4.45 5.7 5.7

ence. The rules include: When no ends are visible for a specific joint, the persistence of the joint for modeling purposes is obtained by multiplying the excavation width by a factor of two. When only one end is visible, the persistence for modeling purposes is obtained by multiplying the excavation width by a factor of 1.5. Based on that, joint persistence results have shown that majority of the joint sets have persistence which are relatively short, ranging from 0 m to 5 m.

5

JOINT ROUGHNESS COEFFICIENT

The JRC value was estimated from visual inspection of the various joints during the underground mapping phase and correlated to a chart proposed by Barton et al. (1977). The visual correlation between the chart and actual joints results in JRC values ranging from 0 to smooth, flat joints to 20 for stepped, rough joints.

6

JOINT SPACING

The spacing of joints has a profound impact on the size of the various key blocks formed in the ramp excavation’s hanging wall. As a result of scanline bias, the joint spacing recorded during the in-situ mapping process required some correction to derive the actual/corrected joint spacing. This scanline bias was as a result of the orientation of the scanline relative to the various joint orientations. Therefore, the joint spacing representing the various joint sets in Table 2 were deemed to be very conservative (closer than the actual spacing), but adequate for this study.

7

JOINT WALL COMPRESSIVE STRENGTH

The joint wall compressive strength is required in order to moderate the base friction angle (assumed to be 32º) to a residual friction angle for use in the Barton and Bandis (1990) shear strength model. This model is then manipulated to obtain accurate friction angles per joint set. Figure 2 Depicts how the Schmidt Rebound number is converted to UCS. From Figure 2, it is evident that a JCS value of 175 MPa was attained. The average dispersion of strength can be assumed to be in the region of about 75 MPa. This dispersion value was taken as the standard deviation of JCS and incorporated in the friction angle calculations.

8

JOINT FRICTION ANGLE

Considering that the joint friction angle plays a major role in the stability of various blocks formed, accurate friction angles need to be used in the probabilistic analyses (Hencher and Richards, 1982). In order to obtain the various joint sets’ friction angles, the Barton and Bandis (1990) shear strength formula was utilized, making use of the point estimate method. 951

Table 2.

Joint sets spacing. Joint spacing

Joint Set 1 Joint Set 2 Joint Set 3 Joint Set 4 Random

Figure 2.

Mean

Min

Max

0.45 0.58 1.28 0.61 1.1

0.02 0.46 0.01 0.11 0.02

1.83 0.72 6.46 1.93 7.12

Determination of JCS using the Schmidt rebound number chart.

The results of the study have shown mean values of joint friction angle to range from 32.8° to 34.8°.

9

CLAMPING STRESS SENSITIVITY ANALYSIS

From the various collected data, it was evident that the 180º mining direction requires the greatest tendon length as well as tendon load bearing capability requirements. For this reason, and to limit modeling runtime, this mining direction was utilized in order to assess the effect of clamping stresses that might be present in the hanging wall. It was evident that the introduction of clamping stresses in the hanging wall had a significant impact on the height distribution of the formed blocks. A 95 percentile height where no clamping stresses were present equates to 1.03 m. With the introduction of a 30 kPa clamping stress, this height reduces to 0.83 m. This then shows that, with the introduction of clamping stresses, the larger blocks were reduced and subsequently the apex height. The assumption that no clamping stress was present in the hanging wall may thus be deemed to be the worst case scenario (see Figure 3).

10

DISCUSSION AND CONCLUSIONS

Based on the data collected, it was noted that the maximum 95% fall out height was attained when mining in a southerly or south-westerly direction. The 95% fall out height was approxi952

Figure 3.

Table 3.

Clamping sensitivity on the 180-degree mining direction.

Summary of the results.

Confidence level

Fall out height (m)

Block Fall out volume (m3) volume (m3)

Density (kg/m3)

Block mass (kg)

Support Support resistance resistance (kN/1.8 m2) (kN/m2)

95% 99% 99.9% 100%

1.05 1.8 3.5 14.5

0.22 2.5 14.69 91.71

2750.00 2750.00 2750.00 2750.00

396.77 1358.44 4148.05 13005.58

3.89 13.33 40.69 127.58

0.14 0.49 1.51 4.73

2.16 7.40 22.61 70.88

mately 1.05 m (see Table 3). Furthermore, analysis has indicated that the 99% fall out height for the same mining directions was approximately 1.8 m and the 99.9% fall out height for the data set was 3.5 m. The maximum fall out height recorded, taking cognizance of the fact that some 180,000 blocks were simulated was 14.5 m. However, it should be noted that the fall out the height of 14.5 m may be deemed as an outlier, based on the frequency plot. A more realistic value to consider was that of the 99 percentile (1.8 m). This parameter is needed to be considered in support design when analyzing the support load-bearing requirements. The maximum 95% volume for the various mining directions was found to be 0.22 m3. The maximum 99% volume for the various directions was 2.5 m3. The absolute maximum volume of the largest fall recorded was 91.71 m3. However, it should be noted that the fall out volume of 91.71 m3 may be deemed as an outlier. Based on the frequency plot, a more realistic value to consider was that of the 95 percentile, 0.22 m3. Another important parameter which was found to assist in the determination of the spacing of support units was the block face area. For this parameter, a smaller area resulted in a denser support pattern requirement. However, smaller face areas were generally associated with smaller volume blocks. For this purpose, and as a starting point, the mine’s standard 1.5 m × 1.2 m spacing representing an area of 1.8 m2 was considered. A cumulative distribution of block volume for face areas between 0 m2 and 1.8 m2 was created in order to understand the size of probable blocks which might form between the support units. 953

REFERENCES Goodman R.E. and Shi G.-H. (1985). Block Theory and Its Application to Rock Engineering. PrenticeHall, Englewood Cliffs, New Jersey. Goodman R.E. (1989). Introduction to Rock Mechanics, Second Ed. Wiley, New York. Goodman R.E. (1976). Alethods of Geological Engineering in Discontinuous Rocks. West, St Paul, Minn. Barton, N.R. and Bandis, S.C. 1990. Review of predictive capabilities of JRC-JCS model in engineering practice. In Rock joints, proc. int. symp. on rock joints, Loen, Norway, (eds N. Barton and O. Stephansson), 603–610. Rotterdam: Balkema. Barton, N.R. and Choubey, V. 1977. The shear strength of rock joints in theory and practice. Rock Mech. 10(1–2), 1–54. Hencher, S.R. & Richards, L.R. 1982. The basic frictional resistance of sheeting joints in Hong Kong granite Hong Kong Engineer, Feb., 21–25.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Author index

Aalianvari, A. 1209 Abbasi, A. 963 Abbruzzese, J.M. 1529 Abolmasov, B. 319 Adapa, M.K. 889 Adushkin, V.V. 575 Aghajanpour, A. 1387, 1395 Akbay, D. 181 Akdag, S. 525, 581 Akinin, N.I. 587 Alber, M. 205, 287, 1093, 1185, 1437 Al-Dajani, O. 17 Alejano, L.R. 377 Aleksandrova, N.I. 1515 Aleksandrova, T.N. 333 Alekseev, I.V. 1633 Alessio, C. 747 Altindag, R. 181 Amosov, I.V. 1071 Anikin, P.A. 153, 1501 Annikov, V.E. 587 Aoki, T. 1297 Argal, E.S. 189 Asadi, A. 963 Asadi, E. 963 Asanov, V. 369, 985 Asanov, V.A. 121 Ashikhmin, S.G. 1425 Auvray, C. 193, 339 Avetisian, I.M. 755 Avramov, I. 967 Aydiner, K. 605 Azorin, J. 1259 Badoni, A.K. 909 Bagautdinov, I. 1037 Bakhaeva, S.P. 199 Bakhtavar, E. 1025 Bandazi, C.N. 479 Bar, N. 761, 973 Barbero, M. 851 Barinov, A. 1333 Bartmann, K. 205

Baryakh, A. 767 Baryakh, A.A. 121, 979 Batugin, A.S. 593, 1507 Bazhukov, A.A. 299, 1053 Bedi, A. 599 Behera, S.K. 1005 Belem, T. 339 Belin, V.A. 587 Belyakov, N.A. 1109 Beşer, M.H. 605 Bhuiyan, M. 211 Bing Li, G. 17 Biryuchiov, I. 805 Boldrini, N. 1445 Boley, C. 567 Bonetto, S.M.R. 1123 Bracke, R. 287 Bran, D. 973 Brentley, K.R. 811 Breus, K. 695 Briaud, J.-L. 431, 611 Brigadin, I.V. 575, 587, 659 Bryt-Nitarska, I. 499 Buocz, I. 219 Burak Küçüksütçü, C. 1579 Buyer, A. 227 Buzzi, O. 639 Buzzi, O. 917 Campedel, P. 923 Cao, B. 1507 Cao, Z. 525 Cardu, M. 1287 Carri, A. 747 Caselle, C. 1123 Castro, J. 1203 Catalan, O. 1259 Cavalca, E. 747 Cecchetti, M. 1445 Chanyshev, A.I. 1515 Chavez, D. 1259 Chedid, M. 431 Chekhonin, E.M. 1351, 1357 Chen, H. 1115

955

Chen, J. 1469 Chepurnova, A.A. 719 Cho, S. 451 Cicero, S. 1203 Coli, M. 1129 Coli, N. 1129 Coli, N. 1445 Conde, A. 383 Coppi, F. 1445 Corominas, J. 775 Costanzo, D. 1123 Couto, P.M. 235 Crosky, A. 1115 Dabard, M.-P. 275 Dadashzadeh, N. 1537 D’Alessandro, F. 1101 D’Angiò, D. 485 Dangwal, U.D. 909 Dashko, R.E. 241, 1137 Date, K. 1341 Day, J.J. 361 De La Fuente, M. 1143 Deák, F. 491 Deana, M. 1563 Defay, A. 249 Denkevich, E.T. 781 Desaki, S. 1369 Devyatkov, S.Y. 979 Diederichs, M.S. 361, 1537 Dmitriev, S.V. 1593 Doroshenko, S.I. 587, 659 Dostovalov, R. 1451 du Plessis, M. 293, 871 Duffield, S. 991 Düllmann, J. 1093 Einstein, H.H. 17 Eivazy, H. 999 El Tani, M. 1209 Elbendari, A.M. 333 Erarslan, N. 991 Ermashov, A. 533 Esmaieli, K. 211, 999

Estébanez, E. 617 Evseev, A. 985 Farinetti, A. 1287 Fedoseev, A.K. 979 Fedotova, I. 653, 1451 Fedotova, I.V. 1549 Feng, W. 791, 1173 Feoktistov, A.Ju. 1071 Fereidooni, D. 625 Fereshtenejad, S. 255 Fernández, C.C.G. 325 Fernández, M.I.Á. 325 Ferrero, A.M. 785, 1543 Ferrero, A.M. 1287 Fiorucci, M. 263 Florkowska, L. 499 Fomenko, I.K. 797, 1165 Franović, I. 539 Frid, V. 505, 513 Fujii, H. 1369 Fujii, Y. 479 Fukuda, D. 479 Gabova, A.V. 1351, 1357 Gabrieli, F. 877 Galperin, A.M. 1149 Garkov, I. 967 Garrido, C. 1259 Gautam, P.K. 269 Gawałkiewicz, R. 499 Gaziev, E.G. 31 Georgakiev, I. 967 Gessica, U. 1543 Ghamgosar, M. 991 Ghasempour, N. 999 Ghassemi, A. 1419 Gholami, M.A. 1209 Ghosh, C.N. 1005 Giacomini, A. 639 Giacomini, A. 917 Giot, R. 193 Giulio, A.D. 923 Gladyr, A.V. 1501 Glibota, A. 1585 Gojković, N. 1229 Gómez, C.L. 389 Gonçalves da Silva, B. 17 González-Gallego, J. 1569 Gorobtsov, D.N. 797, 1165 Gorokhova, E.A. 557 Gottsbacher, L. 227 Gou, Y. 833, 1173 Gray, I. 41

Griffiths, V. 639 Grouset, C. 1101 Gubaidullin, V.M. 587, 659 Gubaydullina, R. 1639 Guiheneuf, S. 275 Günther, C. 1179 Guo, J. 929 Guryev, D.V. 199 Gutierrez, M. 281, 1191 Guzev, M.A. 727 Hagan, P.C. 1249 Hahn, F. 287 Hamada, Y. 307 Han, J. 929 Han, J. 1507 Harrison, J.P. 599, 1543 Hartlieb, P. 1017 Hartzenberg, A.G. 293 Hasov, A.N. 587 Hassani, H. 1413 Hassanzadegan, A. 1363 He, M. 63 Hedtmann, N. 1185 Hirose, T. 307, 563 Hosoda, K. 1317 Hotchenkov, Eu.I. 593 Hou, M.Z. 833, 1173 Hou, Z. 791 Houshmand, N. 1197 Howald, E.P. 1529 Huang, S. 1217 Iannucci, R. 485 Ikegami, S. 479 Ilin, M.M. 557 Ilinov, M.D. 669 Ilyasov, B. 805 Invernici, M. 599 Ishida, T. 1369 Iusupov, G.A. 1071 Iwano, K. 1341 Iwasaki, H. 479 Jabs, T. 287 Jacobsson, L. 633 Jalili Kashtiban, Y. 1025 Janiszewski, M. 821 Jeffery, M. 639 Jeon, S. 451, 465 Jha, M.K. 395 Jimenez, R. 1555 Jovanovski, M. 519 Justo, J. 1203 956

Kagan, M.M. 551 Kajzar, V. 711 Kalamaras, G. 747 Kalender, A. 345 Kalinin, E.V. 1521 Kallam, N.R. 889 Kamali, A. 1197, 1209 Kamiya, N. 563 Kang, K. 1217 Kantia, P. 647, 1223 Karakus, M. 525, 581 Karasev, M.A. 739, 1645 Karev, V.I. 1375, 1381 Karpov, I.A. 1357 Kashnikov, Yu. 533 Kashnikov, Yu.A. 1425 Kasparian, E. 1451 Katayama, S. 457 Kauther, R. 1179 Kazakov, A. 1059 Kelfoun, K. 785 Kharisov, T.F. 1597 Kharisova, O.D. 1597 Khatibi, S. 1387, 1395 Khokhlov, I.N. 937 Khoteev, E. 943 Khvostantcev, D. 533 Kikumoto, M. 1317 Kishimoto, Y. 1369 Kiuru, R. 647, 1223 Kızıltaş, Z. 353 Klimov, D.M. 1375, 1381 Klykov, P.I. 1407 Kodama, J.-i. 479 Kolikov, K.S. 593 Kong, L. 1401 Konicek, P. 711 Konovalov, O.L. 781 Konstantinov, K.N. 551 Kornilkov, S.V. 131 Korolev, V.M. 189 Korshunov, V.A. 299, 1053 Kossovich, E. 1603 Kostić, S. 539, 1229 Kostina, A. 1273 Kotiukov, P.V. 241 Kotlov, S. 827 Kovács, L. 439, 1235 Kovalenko, M. 1011 Kovalenko, Y.F. 1375, 1381 Kovaleva, Y. 1387, 1395 Kozlova, E.V. 1357 Kozyrev, A.A. 139, 1031, 1457 Krasnov, S.A. 575

Krotov, N.V. 423 Krupa, Á. 439, 1235 Krušić, J. 319 Ksendzenko, L.S. 733 Kukhtinskiy, A.E. 1425, 1607 Kukutsch, R. 711 Kulikov, V.I. 1495 Kuranov, A. 1037 Kutepov, Yu.I. 1241, 1645 Kutepov, Yu.Yu. 1615, 1645 Kutepova, N.A. 1241, 1645 Kuzminykh, V. 369 Kuznetcov, N. 653 Kuznetsov, M. 1451 Lage, A. 617 Lan, T. 1507 Lapastoure Gritchou, L. 639 le Roux, P.J. 811 Lebedeva, Y.A. 1137 Lempp, C. 1179 Lenti, L. 485 Levin, B.V. 1241 Levin, L. 1273 L’Hostis, M. 1101 Li, C. 1401 Li, C.C. 47 Li, D. 1249 Li, M. 833, 1173 Li, N. 1555 Li, S. 1507 Li, X. 929 Liao, J. 791 Lin, W. 307, 563 Lindqvist, J.E. 633 Litvinenko, V. 3 Liu, L. 41 Livinsky, I.S. 845 Lobanov, S. 767 Lomakin, I. 767, 985 Lovchikov, A.V. 1463 Lu, S. 1011 Lu, Y. 929 Luis, R. 1333 Ma, X. 313 Ma, Y. 1469 Ma, Z. 929 Mainak, G. 1155 Maïolino, S. 249 Makarov, A. 805, 1043 Makarov, A.B. 845 Makarov, V.V. 727, 733 Malan, D.F. 871

Malinnikova, O.N. 167 Manchao, H. 581 Mandal, P.K. 1005 Manzella, I. 785 Maritz, J. 1047 Marjanović, M. 319 Markov, V.K. 1495 Marmoni, G.M. 263 Martínez, J. 377 Martino, S. 263, 485 Marysiuk, V. 1037 Marysiuk, V.P. 895 Masoumi, H. 1249 Massao, F.M. 1325 Matas, G. 775 Maurya, K.K. 687 Mazzon, N. 877 Meier, C. 567 Mejia, C. 663 Melnikov, N.YA. 1053 Menéndez, J.R.G. 325 Menshova, I.V. 1011 Merkin, V. 943 Merkin, V.E. 937 Merrien-Soukatchoff, V. 275 Mesutoglu, M. 839 Mikhailov, N.P. 659 Mikheev, D.I. 587 Miller, H. 1115 Min, G. 451 Miranda, R. 1259 Mironov, V.E. 1241 Misa, R. 1431 Miščević, P. 1585 Mitri, H.S. 673 Mohammed, R.A. 1395 Mondaca, M. 1259 Morgan, S. 17 Morozov, I. 369 Morstabilini, C. 1563 Moseykin, V.V. 1149 Mosyakin, D. 1043 Mulev, S.N. 505 Muñiz Menéndez, M. 1569 Muñiz, M. 377 Muralha, J. 377 Murphy, B. 865 Murzyn, R. 499 Mustafin, M. 1639 Mytarev, V.M. 587 Naoi, M. 1369 Napoli, M.L. 851 Nazarova, L. 73 Nguyen, G. 581 957

Nicieza, C.G. 325 Nicoll, S. 973 Nie, B. 1469 Nie, W. 1341 Nikolaeva, N.V. 333 Nikulina, M.E. 797, 1165 Nilsen, B. 1267 Nujaim, M. 339 Obara, Y. 673 Odintsev, V.N. 593, 727 Ogawa, K. 1317 Ohtsu, H. 1297 Okada, Y. 1341 Oparin, V.N. 1477, 1515 Osokin, A.A. 1483 Ostadhassan, M. 1387, 1395, 1401 Ostapchuk, A.A. 1489, 1495 Othman, B.S. 345 Ovcharenko, Yu.V. 1351 Özcan, N.T. 345 Ozkan, I. 353, 839 Paciello, A. 263, 485 Packulak, T.R.M. 361 Pak, A. 653 Pakzad, R. 859 Pan, Y. 1515 Panasyan, L.L. 1521 Panin, V.I. 139, 551, 1549 Pankov, I. 369 Panteleev, I. 1273 Panthi, K.K. 401 Panzhin, A.A. 131 Papic, J. 519 Paramovov, G.P. 659 Parsons, S. 865 Pavlov, D.V. 1495 Pavlovich, A.A. 845, 1053 Pejić, M. 319 Pellet, F.L. 87 Pendin, V.V. 797, 1165 Pérez-Rey, I. 377 Persidskaya, O.A. 705 Peshevski, I. 519 Petrov, D.N. 669 Pfeifer, T. 567 Pinzani, A. 1129 Pirulli, M. 785 Plekhov, O. 1273 Plinninger, R. 1093 Pol, A. 877 Polotnyanko, N.S. 1477 Ponomarev, A.A. 1217

Popov, A. 1037 Popov, E.Y. 1351, 1357 Popov, Y.A. 1357 Popov, Yu.A. 1351 Potaka, A.A. 1477 Potapchuk, M.I. 153, 1501 Pranzini, G. 1129 Prashant 1005 Prassetyo, S.H. 1191 Predein, A.A. 1407 Pressacco, M. 883 Price, D. 865 Protosenya, A.G. 739 Punevsky, S.A. 1149 Qiao, Y. 1469 Qing, Y. 1011 Quevedo, R. 663 Ramandi, H.L. 1115 Randhawa, L.S. 525 Rangeard, D. 275 Ranjbar, A. 1413 Rao, K.S. 1155 Rasskazov, I.Ju. 153, 1501 Rasskazov, M.I. 1627 Rautela, T.S. 909 Raventós, J. 383 Rechitsky, V.I. 1279 Reynolds, M. 973 Rinne, M. 647, 821, 1223 Rispoli, A. 1287 Rodríguez, R.F. 325 Rodríguez, S.S. 389 Roehl, D. 663 Roggenthen, W.M. 545 Rossi, M. 1445 Rostami, J. 1017 Rotonda, T. 923 Rozanov, A.O. 669 Rozanov, I. 1451 Rozenbaum, A.M. 669 Rozgonyi-Boissinot, N. 219 Rubchevskii, Y.I. 1575 Ruiz-Carulla, R. 775 Rumyantsev, A. 695 Rumyantsev, A.E. 895 Ruzhich, V.V. 1489 Rybin, V.V. 551 Sagaseta, C. 1203 Sainoki, A. 673 Sakai, K. 1297 Saksala, T. 883, 903

Saksin, B.G. 153, 1501 Salinas Pereira, L.M. 1325 Sánchez, C. 383 Sánchez-Carro, M.A. 1203 Sapachev, A.Yu. 1305 Sapachev, R.Yu. 1305 Sardana, S. 395 Sashourin, A.D. 131 Savelev, E.G. 1357 Saveliev, D. 827 Savi, R. 747 Savich, A.I. 557 Saydam, S. 1115, 1249 Sayyidkosimov, S. 1059 Scavia, C. 851 Schön, R. 1235 Schubert, W. 227 Sedochenko, V.V. 1495 Segalini, A. 747 Selen, L. 401 Semenov, V.N. 701, 705 Semenova, I.E. 139, 755, 1031, 1457 Sengani, F. 411, 417, 471, 949, 1085 Sergeev, I.B. 95 Sergeev, S. 1311 Sesetty, V. 1419 Shabarov, A.N. 95, 105, 423, 513 Shahrabi, M.J.A. 1413 Shahriar, K. 1025, 1197, 1209, 1413 Shamshev, A. 827 Sharma, P. 269, 395 Shelepov, V.V. 929 Shen, B. 821 Shidlovskaya, A. 431 Shidlovskaya, A.V. 1065 Shirokov, A.V. 587 Shustov, D. 533 Shustov, D.V. 1425 Sidljar, A.V. 1501 Singh, D.V. 909 Singh, R. 681 Singh, T.N. 269, 681, 687 Sirdesai, N. 681, 687 Sizov, D. 1445 Skokov, A. 695 Skulkin, A. 1621 Sloan, S.W. 859 Smith, M.E. 1065 Solibida, C. 1437 Solomoychenko, D.A. 299 Somodi, G. 439, 1235 958

Song, J.-J. 255 Sönmez, H. 345 Sozonov, K. 1653 Spirin, V.I. 845 Srinivasan, V. 681, 687 Sroka, A. 1431 Štambuk Cvitanović, N. 1585 Stefanov, D. 967 Stoeckhert, F. 1437 Stuart, G. 865 Subrin, D. 1143 Sugimoto, T. 307, 563 Suknev, S.V. 445 Sulem, J. 1143 Szűcs, I. 491 Szujó, G. 439, 1235 Tadai, O. 307 Tafti, S. 431 Taheri, A. 581 Taherzadeh, R. 1143 Tahmasbi, S. 917 Tajduś, K. 1431 Tani, K. 1317 Tani, T. 1297 Tanikawa, W. 307 Tanzini, M. 1129 Tarun, S. 1155 Telegin, Y.A. 659 Tereshkin, A.A. 669, 1501, 1627 Thoeni, K. 877 Timchenko, A.A. 1065 Tischner, T. 1363 Togashi, Y. 1317 Tommasi, P. 923 Török, Á. 219 Torrico Siacara, A. 1325 Tripathy, A. 687 Trivan, J. 1229 Trofimov, A. 695 Trofimov, A.S. 1477 Trofimov, A.V. 895, 1071 Trushko, V.L. 95 Trusov, V. 1037 Tsayukov, A. 767, 985 Tsirel, S.V. 105, 1053 Tsoi, P.A. 701, 705 Turanboy, A. 1579 Ülker, E. 1579 Usikov, V.I. 1501 Usol’tseva, O.M. 701, 705 Ustinov, K.B. 1375, 1381 Uy, R. 479

Vagnon, F. 785, 1123, 1543 Valero, J.D.L. 389 Vallejos, J. 1259 Vasilieva, A.D. 1645 Vasović, N. 539 Vavilova, V.K. 1279 Velkov, T. 967 Verbilo, P.E. 1659 Vergara, M.R. 401 Verma, A.K. 269, 395 Verrucci, L. 923 Vilchinsky, V. 695 Vilchinsky, V.B. 895 Vishnoi, R.K. 909 Vlastelica, G. 1585 Vostrikov, V.I. 705, 1477 Waclawik, P. 711 Wagner, H. 1047 Wang, K. 1515 Wang, S. 465 Wang, S. 859 Weekes, G. 761 Welideniya, S. 761

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959

Zemtsovskii, A.V. 1031 Zeng, X. 1011 Zerkal, O.V. 1217, 1521 Zertsalov, M. 943 Zertsalov, M.G. 937 Zhang, H. 1507 Zhang, N. 465 Zhao, Y. 525 Zhao, Z. 1341 Zhelnin, M. 1273 Zhou, L. 833 Zhou, X. 1507 Zhu, Y. 929 Zhuravkov, M.A. 781 Zhuravleva, O.G. 1457 Zinchenko, A. 1311 Znamenskiy, E.A. 659 Zoback, M.D. 313 Zubkov, V.V. 1075, 1081 Zubkova, I.A. 1075, 1081 Zuev, B.Yu. 423 Zuzin, R.S. 1279 Zvarivadza, T. 411, 417, 471, 949, 1085

Mineral resources development: Methods and rock mechanics problems

Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Prediction of excavation damaged zone in underground blasts using artificial neural networks Adel Asadi Department of Petroleum Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

Amin Abbasi Faculty of Engineering, Shiraz Branch, Islamic Azad University, Shiraz, Fars Province, Iran

Erfan Asadi Faculty of Engineering, Marvdasht Branch, Islamic Azad University, Marvdasht, Fars Province, Iran

ABSTRACT: Development of an Excavation Damaged Zone around an underground excavation can change the physical, mechanical and hydraulic behaviours of the rock mass near the underground space. This paper presents an approach to build a prediction model for the assessment of EDZ based on an artificial intelligence method called artificial neural networks which are applied to build a prediction model for the assessment of EDZ using data of geological and blasting parameters which are chosen as a result of a literature review. Upon developing the model to evaluate rock damage from underground blasts, practical applications were accomplished for confirmation. Results showed that, because of their high accuracy in establishment of a correlation between EDZ and input parameters’ data, ANNs are appropriate tools to predict excavation damaged zone using data of parameters including perimeter powder factor, rock mass quality, tensile strength, density, wave velocity, vibration propagation coefficients and explosive detonated per delay. Keywords:

1

Excavation Damaged Zone; Underground Blasts; Artificial Neural Networks

INTRODUCTION

The extent of excavation damaged zone depends on geological structure, excavation method, overburden, and numerous other parameters. Prediction of this damage is an important factor to evaluate the quality of excavation process in tunnelling and underground mining. It would allow the optimization of explosive charges utilized in successive blasting rounds, as well as lowering risks of instability from rock loosening, less support costs and water inflows. The detonation of explosives confined in boreholes generates a large volume of gases at high pressures and temperatures. The sudden application of these effects to the cylindrical surface of the hole generates a compressive stress pulse in the rock, which may be a source of damage in the surrounding zone. The dimensions of that zone depend on the size of explosive charge detonated, rock’s dynamic strength and density, wave velocity propagation, and vibration velocities transmitted to the rock mass. The detonation of explosives confined in boreholes generates a large volume of gases at high temperatures (2000–5000ºC) and high pressures (10–40 GPa). The sudden application of these effects to the cylindrical surface of the hole generates a compressive stress pulse in the rock, which may be a source of damage in the surrounding zone. These deviations are normally undesirable because they generate higher costs in the constructive process of the underground opening [Dinis Da Gama, et al., 2002]. 963

The dimensions of that zone depend on various parameters. In this study a literature review has been conducted, and the most effective parameters on the occurrence of excavation damaged zone are determined. Then, an artificial neural network model has been suggested to estimate excavation damaged zone using data of selected input parameters. Fattahi, et al. (2013) and Asadi (2015) have studied the application of artificial intelligence techniques to assess excavation damaged zone, and acceptable results are published in their papers. Thus, the same concept is pursued in this paper to predict excavation damaged zone in underground blasts using data of some parameters which are chosen for this purpose. 2

EXCAVATION DAMAGED ZONE

When an explosive charge detonate inside a borehole several zones can be distinguished in the surrounding rocks: • • • •

Zone of crushing Zone of radial cracking Zone of extension and expansion of fractures Elastic Zone, where no cracks are formed.

The damage that may occur in nearby rock happens behind the elastic zone [Dinis Da Gama, et al., 2002]. Excavation of underground openings by rock blasting methods results in fragmentation within a certain volume that should not exceed the perimeter established in the corresponding design. Deviations of that perimeter from their outside and inside limits are called overbreak and underbreak respectively, with the word backbreak used when overbreak is excessive. The more general concept of EDZ (Excavation Damaged Zone) applies to the fractured and fragmented rock volumes that surround a cavity upon blasting [Dinis Da Gama, et al., 2002]. 3

LITERATURE REVIEW

There are currently three methods of actually measuring excavation profiles: surveying techniques, both manual or laser based, and photographic light sectioning method (LSM). The last one offers several advantages. The principle of the method is to project a radial light to the perimeter of the underground opening so that light rays intersect the perimeter contour of the cavity. The image of this perimeter is then saved in digitized form to allow further computerized analysis [Dinis Da Gama, et al., 2002]. Both graphical and numerical analyses allow the calculation of EDZ values (Overbreak and Underbreak) in a quantitative form, normally expressed as O (%) and U (%), which may be correlated with explosive powder factor and rock mass quality [Dinis Da Gama, et al., 2002]. In the study conducted by Dinis Da Gama and Navarro Torres (2002) it is concluded that in addition to Perimeter Powder Factor and Rock Mass Quality, some other parameters could be investigated to predict Excavation Damaged Zone. The predictive equation used rock dynamic proprieties (Tensile Strength “s”, Density “ρ” and Wave Velocity “u”) and Vibration Propagation Coefficients (a, b, c), as well as Explosive Detonated per Delay (Q) [Dinis Da Gama, et al., 2002]. 4

ARTIFICIAL NEURAL NETWORKS

ANNs are a form of artificial intelligence, which by means of their architecture, try to simulate the behaviour of the human brain and nervous system. A comprehensive description of ANNs is beyond the scope of this paper and can be found in many publications [Shahin, et al., 2002]. As might be expected from the wide variety of network types, there are many different areas in which ANNs have been successfully used in geomechanical systems. 964

ANNs learn from data examples presented to them and use these data to adjust their weights in an attempt to capture the relationship between the model input variables and the corresponding outputs. Consequently, ANNs do not need any prior knowledge about the nature of the relationship between the input-output variables, which is one of the benefits that ANNs have compared with most empirical and statistical methods. If the relationship between x and y is non-linear, regression analysis can only be successfully applied if prior knowledge of the nature of the non-linearity exists. On the contrary, this prior knowledge of the nature of the non-linearity is not required for ANN models [Shahin, et al., 2001]. ANNs are composed of three different layers of neurons. The input neurons consists of neurons which receive information from external sources. The hidden layer processes the information received from the input neurons, and passes it on to the output layer. The output layer receives signals from the hidden layer and transforms them into a predicted value of the output. Additionally, a bias neuron lies in hidden layer. It is connected to all the neurons in the next layer but none in the previous layer. Weights are also assigned to the connections between these neurons [Rashidian and Hassanlourad, 2013]. Feed-forward networks generally have one or more hidden that followed by one output layer of neurons. As the data presented to a feed-forward network, the information begin to propagate from the input layer. The network modify its connection weights on the presentation of a training data set and employs a learning rule to come upon a set of optimum weights that will produce the best input-output simulation that has the smallest possible error. In process modelling, the back-propagation algorithm is the most common learning rule applied for training multilayer ANNs [Rashidian and Hassanlourad, 2013]. Back-propagation learning algorithm includes two phases: forward and backward. In the forward phase, a training data set is presented to the network and fed forward until a prediction is generated. The final output is then compared with target value and an error signal is generated through subtraction. In the backward phase, the error signal is back propagated in the network from output layer to input layer and the appropriate weight changes are calculated using a mathematical criterion that minimizes the sum of squared errors [Rashidian and Hassanlourad, 2013]. The propagation of information in ANNs starts at the input layer where the network is presented with a historical set of input data and the corresponding (desired) outputs. The actual output of the network is compared with the desired output and an error is calculated. Using this error and utilizing a learning rule, the network adjusts its weights until it can find a set of weights that will produce the input/output mapping that has the smallest possible error. This process is called “learning” or “training”. Once the training phase of the model has been successfully accomplished, the performance of the trained model has to be validated using an independent validation set. [Shahin, et al., 2002].

5

DATA ACQUISITION

EDZ and input parameters’ data are collected from an excavation and a bore drilled in Iran, and analysis is performed between the data of input parameters chosen to predict excavation damaged zone for near bore area by constructing a new relationship for EDZ estimation. The testing for EDZ values were carried out by the Rock Mechanics Laboratory staff of the Department of Mining Engineering at Tehran Science and Research Branch of Islamic Azad University. Collected data were used to correlate data of perimeter powder factor, rock mass quality, tensile strength, density, wave velocity, vibration propagation coefficients and explosive detonated per delay, as input parameters of artificial neural networks with excavation damaged zone data as network targets. Selection of input parameters is based on a vast literature review in this area. 965

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DATA ANALYSIS

In this study, a feed-forward back-propagation network with three layers is used. The optimal model geometry was determined utilizing a trial-and-error approach. Layer 1 contained 10 sigmoid hidden neurons, and the second layer contained one linear output neuron. The input elements are perimeter powder factor, rock mass quality, tensile strength, density, wave velocity, vibration propagation coefficients and explosive detonated per delay, and the target parameter is excavation damaged zone. The network was developed, trained, validated and tested using data sets of input parameters and EDZ data. The chosen training algorithm was Levenberg-Marquardt. In order to develop ANNs, collected data were divided into three parts of training (70%), validation (15%) and testing (15%) data. MATLAB Toolbox for artificial neural networks is used using the instructions published by Demuth, et al. (2007). The results of the ANN model showed a high accuracy in estimation of EDZ values, due to the fact that appropriate R value near to one (0.97) was obtained in testing data analysis, and mean squared error (MSE) of near to zero (0.0003856) was reached. These results confirm the accuracy and potential ability of ANNs in prediction of EDZ values using selected input data.

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CONCLUSIONS

The purpose of this research was to predict the excavation damaged zone based on selected parameters data. To obtain continuous prediction of EDZ along the drilled bore, ANN based relationships were developed between EDZ and affecting parameters including perimeter powder factor, rock mass quality, tensile strength, density, wave velocity, vibration propagation coefficients and explosive detonated per delay. It is observed in this paper that EDZ predicted values by neural networks are very close with real data, which is concluded by analysis of network performance results including mean squared error and correlation coefficient. It is also concluded in this study that input parameters which are chosen in this study, have deep effects in EDZ prediction studies, and should be considered in other scientific studies. Conclusions show that using artificial neural networks to predict EDZ of rocks in borehole drilling around the world, would ease EDZ estimation, optimize drilling plans and decrease costs. REFERENCES Asadi, A., (2015). Application of adaptive neuro-fuzzy inference system for the assessment of excavation damaged zone using uniaxial compressive strength data. In: Proceedings of the ISRM Regional Symposium EUROCK 2015 & 64th Geomechanics Colloquium—Future Development of Rock Mechanics, Schubert, W. & Kluckner, A. (eds), Salzburg, Austria, 7–10, October 2015, pp. 291–296. Austrian Society for Geomechanics: Salzburg. Demuth, H., Beale, M., Hagan, M., (2007). Neural Network Toolbox 5 User’s Guide, Math Works Inc., USA. Dinis Da Gama, C., Navarro Torres, V., (2002). Prediction of EDZ (Excavation Damaged Zone). From Explosive Detonation in Underground Openings, ISRM, International Symposium on Rock Engineering for Mountainous Regions – EUROCK 2002 Funchal, 2002, November 25–28. Fattahi, H., Shojaee, T., Ebrahimi Farsangi, M.A., (2013). Application of Adaptive Neuro-Fuzzy Inference System for the Assessment of Damaged Zone Around Underground Spaces, International Journal of Optimization in Civil Engineering. Int. J. Optim. Civil Eng., 2013; 3(4):673–693. Rashidian, V., Hassanlourad, M., (2013). Application of Artificial Neural Network for Modeling the Mechanical Behavior of Carbonate Soils, International Journal of Geomechanics, February 22, 2013, (ASCE) GM.1943-5622.0000299. Shahin, M.A., Jaksa, M.B., Maier, H.R., (2002). Artificial Neural Network-Based Settlement Prediction Formula for Shallow Foundations on Granular Soils, Australian Geomechanics, September 2002. Shahin, M.A., Jaksa, M.B., Maier, H.R., (2001). Artificial Neural Network Applications in Geotechnical Engineering, Australian Geomechanics – March 2001.

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Using large-scale geotechnical modelling to solve mining tasks at a gold-copper mine Ivan Avramov, Tsvetomir Velkov & Iliya Garkov Dundee Precious Metals Chelopech EAD, Chelopech, Sofia District, Bulgaria

Dragomir Stefanov University of Mining and Geology, Sofia, Bulgaria

Ivan Georgakiev Dundee Precious Metals Chelopech EAD, Chelopech, Sofia District, Bulgaria

ABSTRACT: Map 3D geotechnical software is used at Dundee Precious Metals Chelopech EAD to study and understand the ground conditions prior to commencing any mining works. The mine uses the Long Hole Stoping with Fill mining approach. New production stopes are adjacent either to backfilled stopes or to fault areas. This article discusses largescale geotechnical modelling of two orebodies with a fault zone between them. It demonstrates the model development method and stages, the stability of the rock mass surrounding the planned stopes by monitoring certain key ground stability parameters. The model of the fault between the two orebodies is run for three scenarios: the first one is a wireframe solid model featuring lower strength and deformation properties and elastic behaviour; the second one is the same as the first one but with elastic/plastic behaviour; and the third one is a surface with zero cohesion, a fraction angle of 25° and elastic behaviour. After solving the model, the locations for installation of Multi-Point Borehole Extensometers (MPBX) are selected to monitor deformations for model verification. Keywords:

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geotechnical modelling, model development, fault behaviour, stability parameters

INTRODUCTION

Dundee Precious Metals Chelopech develops a gold-copper mine deposit, which comprises of massive steep-dipping orebodies. The current mine design comprises four vertical shafts and two declines that provide the main access to about 800 m below surface. The mining rate is 2.2 Mtpa @ 0.8–1.0% Cu and 3–4 g/t Au. The ore is mined using Long Hole Open Stop (LHOS) mining method with fill, where the open primary and secondary stopes are backfilled with paste fill. The stopes are 25–30 m long, 15–20 m wide and 30–90 m high. Production blastholes are 35–40 m long. The combined top-down and bottom-up mining sequence requires mining on several sublevels. The current stopes are designed near previously mined-out and backfilled stopes in under-mined and over-mined ground. Mining often takes place near fault structures of various ranks or in the crown pillars left behind between the historical cave zone and the underlying ore bodies where LHOS is employed (Stefanov, D. 2016). Mining in such a complex geotechnical environment requires prior study and understanding of the ground conditions to ensure safe, efficient extraction of the reserves. This is particularly important in the case where mining is scheduled in adjacent crown pillars in two orebodies with a fault zone between them. In this situation, modelling of a couple of stopes and the ground surrounding them is not sufficient; it requires large-scale geotechnical modelling of 967

both orebodies with the fault zone between in the horizontal direction, and the historical cave above and the underlying mined-out and backfilled stopes in the vertical direction (Stefanov, D., I. Garkov, 2016). Only in this way can it be guaranteed that the critical zones of high stress concentrations, the ground support requirements and the Factor of Safety will be determined providing a solid basis for the final designs.

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CURRENT STATUS

Mining practice and underground construction have reported cases where the proximity of a fault to capital development or production stopes can affect normal operation. T. Wiles (Wiles, T. 2014) analysed the behaviour of a fault that intersected the X41 shaft at Mount Isa Mines at a depth of about 725 m. The extraction of the orebody triggered a slip along the fault resulting in deformation to the shaft barrel, which in turn resulted in deformation to the shaft steelwork (cage guides) thus creating an emergency situation in the mine. Another example, which was studied and analysed by Wittke (Wittke, W. 2014), demonstrated the impact of a fault on the construction of an underground power plant generator room. The fault ran close to the bottom corner of the room and as the room excavation continued, a wedge formed between the fault plane and the wall of the room. The stress analysis showed that the excavation had an unloading effect on the wedge, which could slide under its own weight towards the room unless it was supported and stabilised. We have a similar issue at Chelopech mine. Mining occurs in two neighbouring orebodies (Block 150 and Block 151) at the same time. The area is intersected by a number of geological features of various rank (Figure 1), but the fault running between the block raises the greatest concerns because it is quite large in both dip and strike directions. The fault zone in question separates the silica envelopes of the blocks and therefore it is interpreted as the boundary between these orebodies. It is a deformation zone whose width varies and comprises of a group of interconnected faults with varying orientation and grinding zones in the hanging wall of the fault on the hanging wall side of Block 151. Based on its substantially lower strength properties and potential instability, and on the examples from practice, it is assumed that the fault zone, being a zone of instability, could be affected by the extraction of the orebodies. The reverse assumption—that the fault zone could affect the stability of the nearest stopes—is also valid (Villaescusa, 2014). That requires assessment of its likely behaviour during stope extraction. It is possible that delamination process may occur in the fault zone and extend upwards creating zones of reduced horizontal field strengths on both sides. This would reduce the overall ground stability and affect future extraction of the stopes in the crown pillar of Block 151.

Figure 1.

Blocks 150 and 151 and the fault zone between them on Level 360.

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Obviously, it is necessary to make a good forecast of the likely behaviour of the fault as extraction of both orebodies continues. Dundee Precious Metals Chelopech uses geochemical modelling tools to achieve this goal. An adequate model of both material environments—the ore and the fault—is generated. It encompasses a large portion of the mine—the two orebodies, the mined-out areas above and below the pillar and the fault zone between the orebodies.

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MODELLING

Geotechnical modelling utilises the Map3D software, which is an integrated 3d tool for model building, visualisation and analysis. Using the Map3D modules, we model environments with different mechanical and strength properties such as hard inclusions, soft ore zones, backfilled volumes and non-linear zones. A number of discrete faults or structures, which are moving, slipping or being extracted, are simulated in the ground that is scheduled for mining. The model development continues by clarifying the geotechnical parameters that will be monitored, how the results will be controlled and monitored, and what method will be used to process the data. The model benefits from the ability of the software to clean up detected errors automatically, e.g. overlapping or intersecting planes. This optimises the time taken to build the model, which gives engineers more time to focus on analyses and in situ studies, and on operational issues. The geomechanical engineer who is building the model forecasts the likely future behaviour of the various planes that are being modelled—stope or development walls, boundaries between materials with different properties, fault planes, etc. If they will be static, i.e. not moving relative to one another, they are modelled using FF (fictitious force) elements. Otherwise, DD (displacement discontinuity) are used if relative motion is expected. The criteria against which stability will be evaluated are selected—Hoek-Brown, Mohr-Coulomb, Drucker-Prager. Depending on the criteria, the rock properties inputs for each development/ stope and surrounding ground are entered. Depending on the criterion selected, the software requires a friction angle, peak and residual unconfined compressive strength of core samples, Poisson’s ratio, elasticity modulus, Hoek-Brown material constants, etc. The type of behaviour of the environment is set to elastic or elastic-plastic. Then the stress field parameters are set including magnitude and orientation, depth from surface at the measuring point, and depth gradient. Thus the geometrical model becomes a geotechnical model. The next modelling stage inputs the mining steps, i.e. the sequence of mining operations. Each stope, cross-cut, blast ring or structure can be shown as excavated, backfilled or

Figure 2. The model of Block 150, Block 151 and the fault zone in the resulting surface.

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supported in a separate step, and be active or inactive depending on the requirements. Multiple scenarios with different geometry of the production spaces, location in space, primary and secondary stopes, are run. The critical structures in the direction of stope advance are entered. The locations of the resulting views are set at the discretion of the geotechnical engineer who is constructing the model. These are plan and section views—vertical, horizontal and at an angle—for which the software computes the values of the geotechnical parameters that are incorporated in the assessment of the ground conditions. Normally these include vertical planes for assessment of the condition of stope walls and horizontal planes for assessment of the impact of mining operations on the excavations on the same level. The last step in the modelling process is the model solving. This is the most time-consuming operation of all the stages, which depends on the way the model is constructed, the number of planes/surfaces to be solved, the capabilities of the computer system, the solution environment, and the number of mining steps. The fault-slip/collapse geotechnical model of the fault zone between Block 150 and Block 151 has been constructed as above. The model cross section view is shown in Figure 2.

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FAULT BEHAVIOUR FORECASTING

The discussion of the likely behaviour of the fault is based on the fact that the limits of the mineralisation of Block 151 and limits of the fault overlap at many points along their strike and dip, which means that the stopes will either border on the fault or some of them may well extend into it. Practically, this means that the fault will be undercut and part of the stope roofs or walls will be into the fault material. The only way to avoid contact is to leave behind an ore pillar, which means loss of valuable ore. If it is proved that the fault is tightly locked (i.e. stuck) and won’t become unstable until the stope is backfilled, this loss can be avoided. The likely behaviour of the fault as the mining advances towards it has been considered on the basis of two assumptions. The first one is slip and the second one is lamination extending upwards and resulting in a chimney failure. The first assumption is based on the possibility that a slip surface can be created by induced stresses from the approaching stoping operations. Although there is no evidence of such developments in the past, i.e. that this option is plausible, we believe it is worth verifying it. Such a slip would compromise the stability of the area under study and the consequences of this are hard to foresee. The second assumption is based on the possibility to extend part of the stope roof into the fault, which, due to the reduced stability of the exposed surface of the material that makes up the fault, would result in a hanging-wall collapse extending above the crown pillar. This event would reduce the horizontal maximum principal stress in elevation and increase it in the stoping zone, which is not desirable, either. However, the possibility of having a slip does not determine the behaviour of the fault and it is not known in advance what state of stress would trigger it. The only thing that is certain is that the induced stresses will increase as the stoping operations approach the slope. Then comes the question: ‘What behaviour of the fault building material is most likely to trigger a slip?’ According to the software capabilities and the above-mentioned study at Mt. Isa Mines, there are several potential models of the fault behaviour. The first one is to simulate a surface in an elastic mode. In this model, the shear stresses increase with the advance of stoping to such an extent that they start exceeding the elasticity limits, the material is subjected to plastic deformations and relies only on residual strength, which is low and the result is motion. The second model features plastic behaviour of the fault (as it is most commonly accepted), which is stable at a certain value of shear stress applying across the fault; however, with the advance of stoping the tangential stresses exceed the shear strength, which triggers a slip. There is a third possibility: The fault is in a limit state equilibrium and very sensitive to changes in the induced stresses. Any increase would upset the equilibrium and trigger motion. The models in which the fault is simulated as a surface in an elastic and a plastic mode cannot be constructed at a friction angle that maintains the fault stable until commencement of stoping and slipping occurs as stoping advances. 970

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ANALYSIS

Following the conclusions of similar studies (Wiles, T., 2014), the stability modelling has been run for three scenarios under the above conditions at Chelopech. The first scenario is in an elastic environment and the fault zone is represented as a DD surface with zero cohesion and a friction angle of 25 degrees. In the second scenario, the fault zone is simulated as a solid displaying elastic behaviour and lower strength and deformation properties compared to the silica envelopes of the two orebodies. In the third and last scenario, the zone has the same lower properties but in an elastic-plastic environment. The conclusion drawn on the basis of the modelling results is that the model that represents the zone as a DD surface confirms the results from the study of T. Wiles that no single value for friction angle could be found such that the fault is stable prior to mining but slips with advancing mining. Based on those observations and the observations of the actual site conditions, it has been accepted that a fault slip response is very unlikely. The more likely scenario is that advancing mining could induce upward caving of the rock mass. This gives confidence to accept that the models representing the fault as a solid are more accurate, and more precisely, to select the model in which the environment is elastic. The same result is obtained using the elastic-plastic model; the difference, however, is that the elastic model requires less computing time and a less powerful computer system. In this model, the mining sequence is represented by 11 mining steps, which are representative of actual site conditions—the SLC caved zones above, the LHSF mined stopes below and the planned production stopes in the pillar between them near the fault zone. The analysis covers five resulting surfaces, which best show the displacements around and in the fault zone, the stresses that are induced and their impact on capital development and the stopes. Based on all the analyses and comparisons from the modelling and to confirm the obtained results, and to calibrate the model if needed, we have planned to install multi-point borehole extensometers (MPBX) at the locations where the tectonic zone intersects the main capital development, as well as in the zones where the B-151 stopes are in immediate proximity to the fault zone because these areas will be actively mined. The largest loads from the maximum principal stress are between the fault zone and Block 150, and in the area between Levels 165 and 195 below the mined areas, as shown in Figure 3a. Also the largest values for the shear stress shown in Figure 3b are seen again in the south-western contact of Block 150 in the crown pillar and in the areas close to the tectonic zone. The analysis of the displacement along the three axes x, y and z, and the total displacement showed in Figure 4 – δx, δy, δz and δtot, respectively—opposite to the zones of stress concentration, shows that displacement is directed towards Block 151. It is evident that the rock mass is trying to move in the direction of the voids, but Block 151 takes the upper hand in the zone between the two blocks and displacement is in its direction. The reason could be a combination of its larger footprint and the direction of the principal stress. It is observed that no slip response occurs at the boundaries where the tectonic zone starts and ends, which indicates that its impact does not contribute to the increase of displacement; on the contrary, it acts as a “brake”.

Figure 3.

a) Maximum principal stress σ1, MPa. b) Maximum shear stress τmax, MPa.

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Figure 4. Total displacement.

Figure 5.

Factor of safety.

The factor of safety (FoS), which is the general stability criterion, augments the information about the behaviour of the tectonic zone. Figure 5 shows that the zones of lower FoS are above the pillar, around the stopes in Block 150 and on the lower levels and the row of stopes between Levels 195 and 225 in Block 151. These areas, however, are relatively away from the contour of the zone, which indicates that they are the result of some local re-distributions and not affected by the zone itself. Note the different values in the rocks in and around the tectonic zone. The most plausible explanation is the different rock properties inputs in the two environments. It is reminded that the rock parameter values in the tectonic zone are more conservative.

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CONCLUSION

Usually, the fault zones are less studied than the mineralised zones and therefore they can give rise to critical situations. The large-scale geotechnical modelling used at Chelopech to evaluate the behaviour of the fault between two orebodies, the methods used and the analysis of the results demonstrate that in our case there will be no threat to the mining operations in its vicinity. The three scenarios used to validate the behaviour of the fault confirm that the models in which the fault is represented as a solid in an elastic environment provide the most realistic predictions.

REFERENCES Stefanov, D. Assessment of the Potential to Mine Reserves in Proximity to Historical Cave Zones and in Undermined Areas. Report. Sofia. Dundee Precious Metals Chelopech Fund. 2016. Pp. 46. Stefanov, D., I. Garkov. Underground Ore Miniung - 2. Sofia, Avangard Prima, 2016. Pp. 224. Villaescusa E. Geotechnical Design for Sublevel Open Stoping, CRC Press, Taylor & Francis Group, 2014, pp. 93–102. Wiles, T., Three ways to assess mining-induced fault instability using numerical modelling. 6th South African Rock Engineering Symposium SARES 2014. Pp 1–8. Wittke, W. Felsmechanik. Springer Verldg. Berlin-Heidelberg-Tokio. 1984. Chapter 9.

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Geotechnical data management and visualization systems: Meeting the data challenge of the 21st century and maximizing value for open pit mines Neil Bar Gecko Geotechnics, Cairns, Australia

Sam Nicoll Newcrest Mining Limited, Brisbane, Australia

Mark Reynolds Newcrest Mining Limited, Lihir Island, Papua New Guinea

Dinella Bran Newcrest Mining Limited, Port Moresby, Papua New Guinea

ABSTRACT: Since the turn of the century, advances in the computing, information technology and telecommunication sectors have empowered geotechnical engineers to collate vast and large amounts of data on a daily basis. More recently, with instability in commodity prices, most mining companies have been reluctant to proportionally increase staffing levels. Effectively and logically storing this wide array of data, and moreover, enabling the validation, analysis and subsequent presentation of the data are paramount in an ever faster paced mining environment where we aim to proactively manage emerging risks and uncertainty. Geotechnical databases for open pit and underground mining operations have been created on a combination of the acQuire Geoscientific Information Management System and Navstar Geoexplorer. The purpose of these systems is to establish and maintain a central source of data that is easily collected, entered, analyzed, visualized or exported by relevant stakeholders. This paper presents an overview of the system capability and flexibility to meet geotechnical engineers ‘requirements at unique and complex mining operations. Through system upgrades and the training of personnel, the output from geotechnical sections has markedly increased while staffing levels have remained relatively constant over last three years.

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INTRODUCTION

The modern mining industry needs to provide stakeholders with guarantees that the promised return on investment will be realized. It also needs to ensure that personnel and equipment are kept safe during the mining process. This means that the company identifies hazards that can impact on production, assesses the associated risks and provides controls to manage the risks (Hamman et al. 2017). Geotechnical engineers are tasked to manage one of the biggest risks in a mine—unpredicted and uncontrolled ground movement. In order to optimize a geotechnical design and mine plan that incorporates a certain level of risk, the geotechnical engineer should follow a systematic, traceable design process and an implementation plan and risk mitigation strategy. Both of these require a robust structure or system such that the

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foundation is always reliable data. This data can be collected, stored in, and analyzed with geotechnical databases. Geotechnical databases have developed from spreadsheets to Microsoft Access and now SQL-based systems with improved reliability for data integrity and data security over the last 20 years. The integration and transformation of different databases to common systems has also become ever more possible. Technology for data collection is constantly improving and datasets are getting larger and acquired more quickly and more frequently. For example, in the 1990s deformation monitoring was practicable with the manual surveying of a few survey prisms on a weekly or monthly basis. Today, automated robotic total stations can survey 200 prisms every 90 minutes or so without the need for a surveyor. Similarly, mapping of geological structures on slopes or in underground excavations with a geological compass in the 1990s was the only option and it took several hours if not days to obtain a statistically valid dataset for analysis. Today, with laser scanning and digital photogrammetry, digitally mapping structure orientations can be undertaken for very large areas, very quickly. Of course, mapping is still required for understanding the geomechanical properties of the geological structures and validation of the digital data. A major challenge faced by many geotechnical engineers in the 21st century is collecting, storing and analyzing large volumes of data. Another challenge is being able to readily and easily access, interrogate and visualize these large volumes of data. Figure  1 illustrates the (simplified) role of data management within the geotechnical engineering discipline and the mining environment. Data collection aspects vary in complexity depending on the specific task or monitoring instrument. Similarly, both data analysis and the feedback of processed information to the geotechnical engineer as well as the hazard management process with mine operations and management varies in complexity depending on the specific data and situation. However, in both instances, several manual tasks from data collection to data processing can be avoided, reducing time, cost and potential for human error.

Figure 1.

Database process or workflows.

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GEOSCIENTIFIC DATA MANAGEMENT AND VISUALIZATION

The acQuire Geoscientific Information Management System is commonly used by geology teams in the mining industry and has been proven to be a suitable platform for geotechnical data management. Pere et  al. (2011) utilized it for logging of drill core and borehole televiewer geophysical surveys. Several similar, and equally sophisticated geoscientific data management software are available including Centric or Maxwell Datashed. In this instance, acQuire was selected as the most cost-effective options since the mining company already used the system in their geology teams. The geoscientific databases can integrate well with mine modelling software such as Vulcan and Minesight as shown in Figure 2. The acQuire geoscientific database was set up to capture geologic, geotechnical, geothermal and hydrogeological data directly or ‘live’ in the field using laptop or tablet computers through either a wireless network in the pit or offline and synchronizing when returning to the office. The use of a handheld GPS and live data capture enabled geotechnical engineers to carry out inspections of pit slopes, waste dumps and provide up-to-date information to coworkers and the management team in the office. The system was set up with data collection and report generation functionality with inbuilt QA/QC features to ensure reliable data capture and presentation. The data is viewable in the database itself or in 3D-space through connected mine modelling software.  The  following components have been successfully implemented at multiple operations: Engineering geological data from drill core logging for rock and soils, face mapping and photogrammetry on slopes or in underground excavations. Report generation included statistics of collected and calculated parameters including RMR and Q. Geomechanical laboratory and field test work data for rock and soils. Routine inspection and risk assessments of pit slopes, underground excavations, waste dumps, stockpiles, tailings and water storage dams. Example of data entry from a tablet PC in the field or in the office and report generation shown in Figure 4.

Figure 2. Example of part of the streamlined geothermal outburst and geyser risk management process from field data collection using a tablet PC (A) directly into the geoscientific database (B) and automated visualization capability in mine modelling software (C).

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Figure  3. Example of a geological fault model (purple wireframe) being validated with geological mapping and photogrammetry data (represented as scaled, oriented circular disks). Each disk represents an individually recorded orientation of a structure.

Figure 4. Example of data entry into geoscientific database for pit inspections (A) and automatically generated individual (B) and multiple (C) reports.

Geotechnical hazard management and fall of ground reporting (identifying new and updating the status or changes in existing geotechnical hazards such as rock fall risk zones, potential landslides or fall of ground areas). Trigger-action-response-plan (TARP) management. Slope depressurization drilling management. Probe drilling and hole temperature logging for geothermal outburst and geyser risk areas or for potential subsidence or void zones where historic underground workings are present below. Drill, blast and final wall excavation performance management (blast design verification for desired fragmentation and wall control). 976

The process of updating geological and structural models can be facilitated by field data collection in the form of pit wall mapping (and drill core logging) directly to the geoscientific database on a tablet computer and visualizing the data in a mine modelling software (e.g. BasRock GEM4D as illustrated in Figure 3). The automation of the data management process enables engineers and geologists to view and even make adjustments to geological and structural models in the field and, of course, in the office.

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MONITORING DATA MANAGEMENT AND VISUALIZATION

The Navstar Geoexplorer database and visualization package was utilized to capture deformation and groundwater data in real-time, at set-intervals or manually from an array of field instruments. Alarms can be created for each instrument for system downtime, deformation or groundwater pressure and levels to generate emails, SMS or visual warnings to relevant stakeholders. It facilitates warnings from all available monitoring instrumentation through a single system that can provide warning to geotechnical engineers, mine supervisors and managers of impending risks when mining geotechnically hazardous areas. It allows the integration of all data sources and the simple and easy generation of reports. For example, a group of survey prisms, vibrating wire piezometers and rainfall gauges can be selected and simply ‘dragged’ into a report that remains ‘live’ while open and continues to update as new data can become available. The following instruments have been successfully integrated at a large open pit mine in Papua New Guinea: 6 automatic, robotic total stations surveying over 1,700  individual survey prisms on pit slopes, waste dumps and stockpiles, cofferdam and culturally sensitive heritage areas. 3 slope stability radars for high risk areas (1x IDS IBIS-FM and 2x Groundprobe SSR-XT). >330 vibrating wire piezometers and pumping well head pressure gauges with a combination of manually entered or uploaded data and connection to loggers with telemetry. 5 tip-bucket rainfall intensity gauges. Pit water levels (linked to acQuire where manual survey data is routinely entered).

Figure 5. Navstar Geoexplorer: Pit terrain model overlain with deformation data from three slope stability radars (left); inset: IBIS-FM radar data combined with scaled vectors for individual survey prisms showing direction and magnitude of deformation around a historic landslide back scarp; photograph: historic landslide back scarp and failure debris continuing to deform.

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Routine inspections of pit slopes, underground excavations, waste dumps and stockpiles. Inspection photographs (camera and aerial unmanned vehicle—UAV) with annotations, and even reports can be stored at specific geographic locations related to their content. Figure 5 presents a sample of Navstar Geoexplorer data collection, analysis and visualization for the two types of slope stability radar and survey prisms (ATS).

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DISCUSSION

The data management challenge in the 21st century is expected to get bigger and more difficult to deal with as technology continues to rapidly advance. It is now possible to integrate several data capture systems and manage data more effectively and efficiently in various SQL-based databases. There are many such systems currently available in industry, and it is not the intention of this paper to promote one system over another. Prospective users are encouraged to investigate various options, particularly since the technology continues to rapidly improve. Geotechnical engineers are at the forefront of technological improvements in the mining industry since unwanted or unforeseen geotechnical events have the potential to significantly impact upon safety and the economic value of a mine. Benefits of implementing the geoscientific and monitoring data management systems have so far included: Elimination of hundreds of complex spreadsheets and dozens of stand-alone access databases. A centralized location for viewing and comparing data from different data sources and provision for flexible visualization. Elimination of human error (e.g. Navstar Geoexplorer automatically reports via email, SMS and visual alerts when any of the connected monitoring systems are down; geotechnical data collection is automatically validated upon entry into acQuire). Reduced reliance on human resources and repetitive manual labor (e.g. transferring data from paper to computer systems and then into modelling packages is removed; logger units and telemetry systems remove the need for repetitive field work collecting monitoring data). Improvements in safety and awareness. Reduction in rework by site teams and consultants—cost reduction. Allows for work to be done at the right level (i.e. data collection, analysis and interpretation can be done by site teams). Systems have the capacity to grow with increasing mine complexity and size. Less engineers are required to manage and analyze more data from more systems. The data management systems presented in this paper meet the needs of complex, modern mining operations. However, it is very difficult to predict or foresee how data management requirements will evolve over the next 20 years with further technological advancements.

ACKNOWLEDGEMENTS The authors acknowledge the efforts of Frank Pothitos, Erin Sweeney, Steven Graham and John Davis for their contributions to the successful implementation of the systems. REFERENCES Hamman ECF, du Plooy DJ, Seery J (2017) Data management and geotechnical models. Proc. Deep Mining 2017: 8th Deep & High Stress Mining Conf. Perth, ACG: 461–487. Pere V, Seery J, de Graaf P, Mould R (2011) Development of an acQuire Based Geotechnical Data Management System. Proc. 8th Int. Min. Geol. Conf. Queenstown, 22–24 August 2011: 353–359.

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On sinkhole formation at the site of fresh water breakthrough into salt mine* A.A. Baryakh Perm Federal Research Center of Ural Branch of Russian Academy of Science, Perm, Russia

S.Y. Devyatkov & A.K. Fedoseev Mining Institute of the Ural Branch Russian Academy of Sciences, Perm, Russia

ABSTRACT: Salt deposits development is always associated with the risk of waterproof stratum failure resulting in hazardous fresh water inflow in mine openings. Due to high solubility of salts this could lead to flooding and collapse of mine as a result of uncontrollable water inflow increase. Process of flooding is usually accompanied by increased subsidence rate and sinkhole formation on earth surface. Estimation of negative consequences of mine flooding is based as a rule on earth surface subsidence surveys and a priori expected evaluations of rocks dissolution. Depending on different assumptions and taking into consideration actual data from geophysical research complex (seismic prospecting, gravity measurements, electrical exploration etc.) the results obtained could differ greatly. Geomechanical model that describes the process of salt covering rocks failure during accelerated deformations associated with rock dissolution of upper part of salt strata is presented in the paper. The conditions of subsidence transformation into dynamic phase with sinkhole formation on earth surface are considered for the case of First Berezniki Potash mine flooding.

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INTRODUCTION

The basic feature of salt and potash deposit underground mining is the necessity of waterproofness maintenance of sedimentary unit called waterproof stratum (WPS) which lies between the roof of upper layer extracted and bottom boundary of first (counting upwards) water-bearing horizon. This feature sufficiently complicates deposit exploration and mining, requiring the use of methods that exclude the possibility of water intrusion in mine. If the integrity of WPS is violated fresh or brackish waters erode fractures by dissolving salt rocks which leads to increasing of water inflow and flooding of mine. Fresh water breakthrough results in intensification of earth surface deformations (Prugger, 1991, Baryakh A. A., Samodelkina N. A., 2017, Shiman, M. I., 1992) up to sinkholes formation of hundreds meters of depth during dynamic phase (Whyatt,  J, 2008, Rauche,  H, 2000). That of course presents a real danger for buildings and civil engineering infrastructure objects on earth surface (M. Van Den Eeckhaut, 2007, Waltham T., 2011, Gutiérrez F., 2014 and many others). Hazardous water inflow into First Berezniki mine, which is situated directly within boundaries of Berezniki town, was recorded at the 17th of October 2006 (Krasnoshtein A.E., 2009). Initial approximate brine output was about 300–400 m3/h. Chemical analysis of brine composition left no doubt that the water inflow into the mine openings was from the strata above salt bed which unambiguously indicated that integrity of WPS was violated. ∗This work has been financed by the Russian Scientific Foundation (grant No. 15-05-04988 A).

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At the 28th of October the increase of water inflow up to 1200 m3/h was registered. Due to such high output brine pumping was ceased, mining terminated—the process of mine flooding became uncontrollable. One of the main prompt tasks of accident aftermaths minimization was directed at initial consequences estimation of increased water inflow due to salt rocks eroding in upper parts of WPS that could lead to cave formation and create danger of overlying rocks failure or sudden subsidence. That threatened nearby federal railway and mine technical structures functioning.

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GEOMECHANICAL ESTIMATION OF SINKHOLE SIZE OVER THE SITE OF WATER BREAKTHROUGH INTO MINE

To forecast possible sizes of sinkhole on earth surface over supposed site of brine inflow into mine openings mathematical modelling of rocks overlying salt bed failure process due to eroding of upper parts of WPS was carried out. The scheme used is presented on Fig. 1. It was supposed that cavern could grow laterally until overlying rocks caving occurs. During mathematical modelling two cases were considered: elastic behavior of all rocks and plastic deformation of salt-marl strata. Failure pattern of rocks overlying salt bed was evaluated according to strength and deformation criteria. To define the possibility of cracks appearance for elastic problem statement the following criteria were used: R=

τ max

(

+

) ⎡⎣ 2σ t − 2

t(

t+

⎤ c ) + σc ⎦

≥ 1 − in compressive stress zone,

(1)

and

σ 1 > 0 − in tensile stress zone,

(2)

where τ max (σ − σ ) 2 ,σ = (σ + σ ) 2 , σ1, σ3 − main stresses, σc − compressive strength, σt − tensile strength. For plastic problem statement (1–2) also indicated the beginning of plastic flow. Propagation of fractured area or plastic deformation zone through all strata overlying salt bed was recognized as criterion for the possibility of sinkhole formation for both variants of calculations.

Figure 1.

The scheme used for calculation of sinkhole size on the earth surface.

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Figure 2. Estimation of strata overlying salt bed rocks failure in elastic (a) and plastic (b) problem statements.

The calculation of rock mass stress-strain state alteration during karst void growth in conditions of overlying rocks dynamic caving was carried out iteratively using the finite element method. If tensile stress arose in elements in the cave roof those elements were eliminated from further iterations by nullifying their mechanical properties. Analysis of rock stress-strain state in the vicinity of karst voids showed that their stability scarcely depends on their height if strength of surrounding rocks is high enough. That means that for given rock properties and WPS depth of burial the main parameter defining the width of a possible sinkhole would be the lateral size of the void. According to the results of calculation for elastic problem statement the sinkhole over karst void is formed when the width of washout zone in upper part of salt bed reaches 250 m. The diameter of possible sinkhole on surface in that case would be about 450 m which could be used as an upper estimate. Results reflecting plastic deformations development in saltmarl rocks show the possibility of sinkhole formation for karst void length about 150 m; its size on the earth surface is estimated at 260 m. Due to high risks for important objects situated at hazardous area possible sinkhole anticipated size on the earth surface was assumed to be from 400 to 450 m. The crater contour was drawn from surmised spot of water breakthrough. At the end of July of 2007 at the assumed site of water breakthrough into mine openings sinkhole on the earth surface was formed. Initially it was of 80 m length and 55 m width. In the first months after the formation the sinkhole actively propagated—its growth speed reached 80 m/month. The situation became stable only after complete flooding of the mine at the end of 2008 with the lateral sizes of the crater 440 × 320 m. At present the sinkhole is completely filled with underground waters. Further evolution of the approaches suggested at the time of the accident made it possible to develop methodology of determining sizes of possible sinkhole on earth surface for different geological conditions of karst genesis (Baryakh A.A., Fedoseev A.K., 2011). However, the geomechanical models proposed don’t allow to predict the dynamic patterns of sinkholes genesis on the earth surface and the time ranges of their formation.

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RANGE ESTIMATION OF SINKHOLE FORMATION CONDITIONS

As a result of WPS integrity violation at least one water conducting channel is formed in salt strata. At the initial stage of flooding due to free brine outflow from the site of water breakthrough into mine free water flow through the channel takes place. Because of salt rock dissolution the channel radius is constantly increasing. At the same time due to water outflow and piping a “weak” zone is formed in the overlying strata directly over the channel. This zone becomes a reason for high earth surface subsidence gradient at a relatively small district. During geomechanical calculations sizes and localization of the “weak” zone and also the degree of mechanical properties decreasing in it are adjusted so that calculated subsidence would comply with surveyed data (Baryakh A. A., Devyatkov S.Y., Samodelkina N. A., 2016). 981

Thereby during mathematical modelling of stress-strain state of the mined area the actual values of subsidence and its velocity could be achieved by increasing water conducting channel radius, by decreasing mechanical properties values in the “weak” zone and as a result of interchamber pillar deformation and degradation during mine flooding. Principal geomechanical calculation scheme that takes into account all those aspects is presented on Fig. 3. To derive the influence of water conducting channel on the state of strata overlying salt bed mathematical modelling of the channel widening was performed. The state of rock mass at the moment of the leak discovering was used as initial condition for modelling. The “weak” zone was introduced into the overlying strata to make it possible to achieve the actual subsidence as a result of calculation. The location of water conducting channel was chosen at the spot of highest subsidence gradient, i.e. at the place where WPS integrity violation occurrence is most probable. The process of the overlying strata failure during water conducting channel widening is presented on Fig. 4. At that stage of calculation the width of the channel is simply assumed value and not derived from the dissolution rate and pattern observed in the field. According to the results of calculation at the moment of water breakthrough no anthropogenic failure zone is formed that goes all the way through the overlying strata (Fig. 4 a). So, at the initial stage of mine flooding there were no prerequisite for sinkhole formation. With widening of water conducting channel fracturing of rocks in overlying strata occurs. With the channel radius of 2 m discontinuous failure zones appear directly over the channel (Fig. 4 b). When the channel radius reaches 3 m those zones become connected and continuous anthropogenic failure area is formed in the lower part of the overlying strata (Fig. 4 c). The fractured area reaches earth surface when the channel radius is about 5 m. (Fig. 4 d). According to the used assumptions that means that conditions for sinkhole appearance on the earth surface are met. As the time from the beginning of water inflow into the mine openings to the sinkhole formation on the earth surface is known (284 days), and mathematical modelling provided the necessary channel radius value (5 m), it is possible to estimate the rate of the channel growth – 1.76 cm/day. Of course, as the water inflow during the mine flooding wasn’t constant the rate obtained is average for calculated period. The calculated channel growth rates are in range of theoretical (about 20  cm/day) and laboratory (less than one centimeters per day) estimations of salt rock dissolution rate. The rates calculated are closer to laboratory data and could be used as parametric support for further salt rock dissolution calculations and sinkhole growth forecast. Taking into account the obtained water conducting channel growth rate and surveyed subsidence of the earth surface the mathematical modelling of stress-strain state genesis during the period of time from water breakthrough into the mine up to the moment of sinkhole formation was carried out. Rock mass anthropogenic failure pattern at the moment of water breakthrough is presented on Fig. 5 a. According to the performed estimations straight-through anthropogenic

Figure 3.

Principal geomechanical calculation scheme.

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Figure 4. Pattern of anthropogenic integrity violation of mined rock mass for radius of water intrusion through WPS channel: 0.1 m (a), 2.0 m (b), 3.0 m (c) and 5.0 m (d).

Figure 5. Pattern of anthropogenic integrity violation of mined rock mass at the time of water breakthrough in October of 2006 (a) and at the moment of sinkhole formation in July of 2007 (b).

failure zone is registered in WPS. It is within this zone where the channel of water intrusion from the overlying strata into the mine openings could be formed. This zone is located at the subsidence trough edge where high subsidence gradients are observed. Thereby all conditions for water conducting channel appearance are fulfilled. The further increase of the earth surface subsidence due to decompaction of the overlying rocks inevitably leads to the formation of fractured zone in them and to the possibility of subsidence transferring into dynamic phase with sinkhole appearance on the earth surface. The state of the rock mass at the moment of sinkhole formation is presented on Fig. 5 b. As it can be seen fractured zones are located in every part of geological profile, but it is possible to distinguish sections where areas of anthropogenic failure stretch from mine opening up to the earth surface. This is considered as a possibility of sinkhole formation. It’s worth mentioning that the sinkhole appearance occurred not at the point of maximum subsidence where they had 983

increased by 1.1 m, but at the subsidence trough edge, at the slope with highest subsidence gradient. There the vertical displacement increased only by 0.35 m over the same period of time. The results of mathematical modelling showed that the sinkhole formation becomes possible when strength and deformation properties in the “weak” zone in the overlying strata are decreased by a factor of 2.6 and by a factor of 6 directly at the site of maximum subsidence. That level of softening could be used as a quantitative criterion of transition of static deformation into dynamic phase with further sinkhole formation in case of the void existence in WPS. The sinkhole formation becomes possible when the water conducting channel radius reaches 5–10 m with its average growth rate of 2–5 cm per day. On the base of these assumptions that are in accordance with the sinkhole observations at the moment of its appearance and with experimentally obtained values of salt rock dissolution rate it is possible to estimate the period of time from the water breakthrough to the sinkhole formation at 100–500 days. Of course in general water conducting channel radius value that leads to sinkhole formation and its growth rate depend on particular mining and geological conditions (rock properties, overlying strata thickness etc.) Thereby for the specific accident conditions an additional geomechanical analysis is necessary.

4

CONCLUSION

With the use of mathematical modelling methods spatial localization of straight-through anthropogenic failure zone in WPS layers is carried out. The forecast of characteristic sizes and growth rate of water conducting channel in salt strata due to water breakthrough and salt rock dissolution is fulfilled. The possibility for range estimation of sinkhole formation moment is shown. The results of numerical calculations are in accordance with patterns of accident at First Berezniki Potash mine.

REFERENCES Baryakh A. A., Devyatkov S. Y., and Samodelkina N. A. Theoretical explanation of conditions for sinkholes after emergency flooding of potash mines//Journal of Mining Science, 2016, Vol. 52, Issue 1, pp. 36–45. Baryakh A. A., Samodelkina N. A. Geomechanical estimation of deformation processes intensity over flooded potash mine//Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh. – 2017. – 4. – pp. 33–46. Baryakh A.A., Fedoseev A.K. Sinkhole Formation Mechanism//Journal of Mining Science, 2011, vol. 47, Issue 6, pp. 404–412. Gutiérrez, F., M. Parise, J. De Waele, H. Jourde. A review on natural and human-induced geohazards and impacts in karst//Earth-Science Reviews. – 2014. – vol. 138. – pp. 61–88. Krasnoshtein A.E., Baryakh A.A., Sanfirov I.A. Mine anthropogenic accidents: flooding of the First Berezniki Potash mine//Herald of Perm scientific center of Ural branch of Russian Academy of Sciences. – 2009. – 2. – pp. 40–49. Prugger F.F., Prugger A.F. Water problems in Saskatchewan potash mining—what can be learned from them?//CIM Bulletin. – 1991. – Vol. 84, 945. – P. 58–66. Rauche  H. Sinkhole Formation over Flooded Potash Mines—Case Studies from the Motherland of the Potash Industry // Fall 2000 Meeting SMRI, San Antonio, Texas, USA, October 15–18, 2000/ Solution Mining Research Institute. – 2000. – P. 161–162. Shiman, M.I. Predotvrashchenie zatopleniya kaliinykh rudnikov (Potash Mine Flooding Prevention). Moscow: Nedra – 1992. Van Den Eeckhaut, M., J. Poesen, M. Dusar, V. Martens, Ph. Duchateau. Sinkhole formation above underground limestone quarries: A case study in South Limburg (Belgium)//Geomorphology. – 2007. – vol. 91, Issues 1–2. – pp. 19–37. Waltham, T., H.D. Park, J. Suh, M.H. Yu, H.H. Kwon, K.M. Bang. Collapses of old mines in Korea// Engineering Geology. – 2011. – vol. 118, Issues 1–2. – pp. 29–36. Whyatt, J., Varley F. Catastrophic Failures of Underground Evaporite Mines//Proceedings of the 27th International Conference on Ground Control in Mining, 2008, Morgantown, West Virginia – 2008. – P. 113–122.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Experimental and theoretical studies of undermined strata deformation during room and pillar mining A. Evseev, V. Asanov, I. Lomakin & A. Tsayukov Mining Institute of the Ural Branch of the Russian Academy of Sciences, Perm, Russia

ABSTRACT: The research object is the Upper Kama potash salt deposit. It is one of the biggest potash and magnesium salt deposits in the world. Two contiguous sylvinite layers are being developed at the depth of 250–400 m. The mining structure is characterized by a great water content of the overlying terrigenous and carbonate rocks which may result in a flooding of the mined-out area. The impermeable rib pillar which separates the industrial strata from the water-bearing layers provides safe mining conditions. The decrease of the deformation value of the impermeable strata and preservation of its water-resisting properties is ensured by the use of the room and pillar method with a rigid rib pillar. Comparative studies have been carried out to establish the relation between the deformations of the room and pillar elements and earth surface subsidence. The earth surface subsidence was determined using the geodetic measurements according to the ground reference points. The vertical and transverse deformations of the pillars, the stratification of the parting and the roof of the top layer were measured by the experimental stations using the tape extensometer along the contour and depth reference marks. The research results which had been carried out in various mining and geological conditions made it possible to establish a relation between the processes of the ribs’ deformations, their loading rates and ground subsidence. Based on the results of the experimental work, the theoretical description of the chamber deformation processes using the mathematical modeling methods was made. Keywords:

1

monitoring; room and pillar; saliferous rock; deformation; roof; pillar; stability

INTRODUCTION

The research object is the Upper Kama potash-magnesium salt deposit that is one of the biggest deposits in the world. The deposit is notable for the mining of a series of superimposed sylvinite layers. The depth of mining operations ranges from 250 to 400 m. The structure of the deposit is unique due to a considerable amount of water content of overlying rocks, which can result in the flooding of underground mine openings. For safety purposes, mining operations are carried out under the protection of an impermeable pillar that separates industrial strata from water-bearing formations. The reduction of deformations of waterblocking formation and the preservation of their water-resisting properties are achieved by using the room and pillar method and leaving rigid interchamber pillars (RIPs). In order to monitor mining operations and their safety on the earth’s surface, a network of profile lines is formed. The state of an undermined mass is judged by subsidence and horizontal displacements of ground reference marks. One main problem of this approach consists in delayed processes of displacement of the earth’s surface from the time when rib pillars start to fracture in the mine, which hinders a duly application of necessary measures to preserve water-blocking formation.

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When carrying out mining operations, deformations of the room and pillar system’s structural elements are assessed visually and by means of instrumental measurements. Contour and deep reference marks are most frequently used for these purposes. The frequency of observations depends on the speed of deformation and research tasks. Monitoring are usually carried out with regard to each and every stratum. This helps to assess the stability of separate openings and deformation processes taking place in their vicinity. At the same time, it doesn’t make it possible to assess the influence of a simultaneous mining of two and more layers on the nature of deformation of an undermined mass in such conditions.

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EXPERIMENTAL STUDIES

In order to make a connection between deformations of the mining system’s elements and subsidence of the earth’s surface under the conditions of mining of the two superimposed sylvinite layers (KrII and AB), comparative studies of deformation processes and the nature of disintegration of pillars, a parting and a roof of stopes and the displacement of reference marks over an area to be mined were carried out. The studies were conducted in underground conditions and with the use of measuring stations that represented a system of contour and deep reference marks located in one section on both strata to be mined. Each measuring station had 10 contour and 17 deep reference marks (Fig. 1), which allowed monitoring the

Figure 1.

The structure of the measuring station in room block.

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vertical (longitudinal) deformation of pillars, their horizontal (cross) stratification, the movement of the parting’s rocks and the deformation of the upper stratum’s roof. The measuring diagram also includes the direct identification of the total vertical deformation of the whole stratum to be mined (a change in the distance between a deep reference mark in the upper stratum’s roof and a deep reference mark in the lower stratum’s floor). The measurement of the openings’ deformations was carried out by means of tape extensometers. The speed of subsidence of ground reference marks on the earth’s surface in the area where the measuring stations were located was monitored by high-precision levelling. The experimental areas covered different variants of parameters of mining operations: period of mining—from 2002 to 2013; depth—from 300 to 400  m; width of stopes—from 5 to 9  m; width of pillars— from 5.5 to 10 m; thickness of parting—from 3.6 to 8.2 m; speed of subsidence of earth’s surface—from 4 to 35  mm/year. This allowed assessing the mutual influence of the strata mining parameters on the state of the pillars and the displacement of the earth’s surface. The analysis of measurement results shows that the nature of deformation of the whole block to be mined depends on the extent of pillars loading rates at each stratum. With a similar loading rates on both strata, the pillars are deformed at the same time and approximately at the same speed. A considerable difference in the extent of loading of the pillars results in the intensification of deformation of the most loaded pillars, and the second stratum shows practically no deformation processes. In such conditions the most loaded stratum acts as a protective one. In order to establish a relationship between the deformation of the room block and the subsidence of the earth’s surface, the normalization of the experimental data was carried out and a dimensionless coefficient kη was determined. After it the analysis was conducted related to the change of this parameter depending on the time elapsed from the moment of the strata mining (Fig. 2). kη =

η , ε

(1)

where η – the speed of subsidence of the earth’s surface, ε – the speed of longitudinal deformation of the room block (or the total deformation of the pillars). The obtained dependence reflects the redistribution of deformations in the undermined mass and gives evidence of the delayed displacement of the earth’s surface starting from the moment when the disintegration of the pillars in the mine begins.

Figure 2. The dependence of the dimensionless coefficient kη on the time elapsed from the moment of mining of the room block.

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3

MATHEMATICAL MODELLING

The results of the field studies were used to correct the model of deformation of the dual room block that was located in the area of full undermining and was under the influence of mass forces (Fig.  3). Symmetric boundary conditions were set on the side boundaries where the horizontal displacements were considered to be equal to zero. Likewise, on the lower boundary the vertical displacements were considered to be zero either. On the upper boundary a surface distributed loading equal to the sum of the mass forces of the overlying strata was set. The numerical implementation was carried out by the displacement-based finite element method. The two-dimensional simplex elements were used as discretization subdomains. The solution area was broken by a free mesh, with the geometry of the openings’ section taken into consideration. In order to determine how the opening’s state was changed over time, the rheological approach based on the module variable method was used. The deformation of the pillars of the mined strata was determined according to the following formula: E (t ) =

E , 1 + Φ(t )

(2)

where Φ (t) is the creep function:

Figure 3. The principal computation scheme and location of the points corresponding to the measuring station’s reference marks.

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Φ( ) =

η( ) . v0

(3)

The values of the η(t) function were controlled by the data of the field observations on the vertical deformation of the pillars. The calibration of the mathematical model of the stressed-strain state of the generalized room block was carried out by comparing the room block deformation measurement results (obtained from the field observations) to the corresponding calculated values. Fig. 3 shows a scheme of points in a computational area corresponding to the measuring station’s reference marks by which the vertical convergence of the undermined strata (lines 1-1, 6-6), the longitudinal deformation of the pillars (lines 3-3, 5-5), as well as the vertical displacement of the room block were determined (line 7-7). The calibration was carried out in 4 stages. The first stage was intended to determine the stress-strain state (SSS) of an unmined mass. The second stage was to establish the SSS of the enclosing rocks after the mining of the AB stratum, and based on that the creep function was determined for the interchamber pillars (ICPs). Similarly, at the following stage, with both already mined strata, the SSS and the creep function for the ICPs of the KrII stratum were determined. The obtained stress-strain state was now a starting point for further calculations of the SSS of the mass around the stopes. In other words, this stage was to determine the SSS of the mass during the installation of the measuring station. Now, having in mind the SSS of the mass and the creep functions, and controlling them with the data of the field observations, the SSS for each date of measurements were calculated. According to the calculation results, the deformation graphs (Fig. 4) were constructed. The horizontal axis on the graphs sets out the number of months from the date of installation of the measuring station. As is seen from the figures, this geomechanical modelling stage succeeded in reaching a rather high level of quantitative consistency between the calculated and actual values of vertical deformation in the stope of the KrII stratum and in the room block in general. Some difference between the measured and calculated values of vertical displacements in the stope of the AB stratum is probably connected with the implementation of the roof stratification processes that are not considered in the model yet.

Figure 4. Vertical displacements: a) in stratum AB; b) in stratum KrII; c) of the room block; d) of the earth’s surface.

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For the purpose of comparing the change of the room block’s vertical deformations and the earth’s surface’s subsidence, relevant data were normalized to a unified time scale, which is seen in Fig. 4 (d). A reference point of the time scale and the registration of displacement of the earth’s surface correspond to the date of installing the measuring station. The analysis of the room block’s vertical displacement indicators and the earth’s surface’s subsidence suggests a connection between these values. The actually registered subsidences of the earth’s surface are less than the room block’s vertical displacements by no more than 30 mm. However, the qualitative consistency between the calculation and field subsidence increase graphs was obtained. Probably these quantitatively smaller values of the subsidences under study may give evidence of stratification processes taking place in the overlying rock strata, which was not taken into consideration in the course of modelling.

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CONCLUSION

The comparison of the room block’s deformation speeds to the instrumental measurement results taken on the earth’s surface shows a good repeatability of the determined parameters in every experimental area, which allows us to conclude that the obtained results are highly reliable. As a result of correcting the geomechanical model of mining of the dual room block according to the field observations, a rather acceptable level of consistency between the calculated and measured values of vertical deformations has been achieved. The conducted studies show a steady connection between the vertical deformations of the rocks around the room block and the subsidences of the earth’s surface. The numerical estimates of the subsidences appear to be slightly greater than those observed, which may give evidence of stratification processes in the overlying rock strata. The study of the salt mass deformation under different conditions of mining operations is still under way to increase the reliability of the experimental data. In addition to the obtained function of subsidence of the earth’s surface over time, the establishment of a connection between longitudinal and cross deformations of interchamber pillars is of special interest. This dependence will be used to develop a technique aimed at predicting the stability of the room and pillar system’s elements.

ACKNOWLEDGEMENT This study was conducted with the support from the grant of the Russian Foundation for Basic Research Nr. 17-45-590681.

REFERENCES Amusin, B.Z. Applying the variable modules for solving one kind of tasks of linear hereditary creep/ Amusin, B.Z., Linkov, A.M. // Izv. AS USSR. Mekhanika tverdogo tela (The mechanics of rigid bodies). - 1974. - No. 6. p. 162–166. Evseev, A., A. Baryakh, P. Butirin Remote Instrumental Monitoring of Interchamber Pillar Stability. Procedia Engineering. ISRM European Rock Mechanics Symposium EUROCK 2017. Vol. 191 (2017), 1218 p., pp. 962–966. Zienkiewicz, O.C. The finite element method in engineering science. – London, 1971. 521 p.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

Progressive damages in hard rock by utilising an oscillating undercut technology Morteza Ghamgosar The University of Queensland, Brisbane, Australia

Stephen Duffield Newcrest Mining Limited, Orange, Australia

Nazife Erarslan Adana University of Technology, Turkey

ABSTRACT: Rock cutting is a complex phenomenon that requires advanced and sophisticated techniques to predict fracture initiation and propagation under applied or induced mechanical forces. While conventional cutters apply compressive or impact forces to break a rock body, the idea of applying cyclic forces to rock has led to a novel system to break rocks under tension and fatigue mechanisms. Experimental and numerical models have shown that the oscillating disc cutter (ODC), as a new technology in rock cutting industries, can potentially enable more than 30% increase damage in hard rocks, which offers a profitable, safer and cheaper method to underground rock cutting operations. The various physical properties of the rock influence fracturing behaviour in the cutting process, including water content, dry density, porosity and temperature. In addition to the environmental and physical effects, the roles of microfractures and micro-damaging are deterministic, such as structural anisotropy, grain sizes, different mineral compositions, crack size, amplitude and frequency. A noticeable difference in the fracturing behaviour of monzonite specimens was observed under static and cyclic loading. Symmetrical fracture surfaces were seen under static failure, while excessive dust and crushed particles with no evidence of symmetrical fractures were determined under cyclic test. As the main mechanism in ODC is cyclic action at the cutter disc, therefore; this paper discusses laboratory and numerical results of microfractures propagation in Fracture Process Zone (FPZ) under the cyclic loading in order to utilise and optimise for the ODC technology. Keywords:

1

Oscillating undercut technology, cyclic and static failures, image process

INTRODUCTION

Many brittle rocks, like other engineering materials, may contain several micro- and macrofractures. Some mechanical parameters, such as friction angle and cohesion, are inherited, while others may be caused by engineering activities. The different orientations and distributions of microstructural geometry are the main causes of the anisotropy in rock. Overlapping of such micro- and macroscale inhomogeneity with the stress induced by engineering activity can cause rock behaviour to become more complex. Further, predicting failure load and prefailure responses of rock to applied static and dynamic loading is a crucial aspect of rock mechanics. In the rock failure process, microcracks and natural flaws coalesce, causing failure criteria to become more complex and it is sometimes difficult to describe the actual fracturing process (Argatov and Nazarov, 2000). In Linear Elastic Fracture Mechanics (LEFM), a crack initiates and propagates when stress intensity factors at the crack tip reach a critical value (Atkinson and Avdis, 1980). However, rocks are not perfectly isotropic or homogeneous; they will always exhibit nonlinearity before and after ultimate failure (Ghamgosar and 991

Erarslan, 2014). Some of researchers measured the amount of acoustic emissions before reaching ultimate failure; this may be an indirect way to detect fracture initiation and propagation prior to catastrophic breaking (Ghamgosar and Erarslan, 2014; Kahlen and Alber, 2008). Such indirect methods enable the application of stress analysis in larger scale problems; however, they cannot explain the initiation or formation of cracks, and they cannot be used to describe propagation of fractures (Hillerborg et al., 1976). Thus, Nonlinear Elastic Fracture Mechanics (NLEFM) have been proposed to investigate the plastic behaviour of the Fracture Process Zone (FPZ) in rocks (Erarslan and Williams, 2012). Many empirical and theoretical approaches have been proposed in fracture mechanics, including stress intensity analysis (Atkinson and Meredith, 1987), energy-based failure models (Xie et al., 2011), cohesive crack models (Planas et  al., 2003), the progressive microfractures model (Bazant and Oh, 1985; Eberhardt, 1998), and the isotropic and non-isotropic micro-damage model (Gambarotta and Lagomarsino, 1993). In all proposed models, fracture toughness is significantly influenced by initial cracks, natural flaws and microstructural properties (Ghamgosar and Erarslan, 2015). This study discusses experimental achievements in order to investigate the effect of cyclic loading tests on microfractures extension in the FPZ.

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OSCILLATING DISC CUTTER TECHNOLOGY

The principal mechanism in ODC cutter is the undercutting cyclic loading and attempts to break rocks under the tensile mode than the compression which is the current action in the most of pick cutters. Therefore, Oscillating Disc Cutter (ODC) provide less effort to break hard rocks. ODC cutter concepts as a new technology were initially proposed by David Sugden in 1971 (Karekal, 2003); oscillating disc cutter was introduced uses a different action to cause the cutting action. The first lab-scale porotype (Figure 1a) used a small amplitude (1.5–2.5 mm) with the range of moderate pressure associated with a water jet and equipped with a continuous flush out system to carry the crushed rock around the cutter span (Karekal, 2003), but the large-scale prototype can apply higher amplitudes and variable frequencies (Figure 1b). The oscillating frequency of the ODC has a significant influence on cutting force reduction, and unlike the drag cutting, the cutting force increase by increasing the tool velocity. The cutting force was found in a nonlinear trend related to the uniaxial compressive strength of tested rock. Therefore, the concept of the influence of cyclic loading effects was investigated in this study, and ultimately a new cyclic loading was proposed and evaluated to further achievements in hard rock crushing process. The crack initiation and propagation path can be determined by using the tensile force and rigorous fracture criteria. Therefore, the chips formation in ODC can be determined by fracture toughness test to simulate the crack tip in fracture process zone. According to the cutting action, there are two main methods can be governed by the fracture mechanics concepts, normal splitting action and parallel cutting

Figure  1. (JOY).

Lab-scale design of ODC (a) and large-scale prototype ODC (b) developed by Komatsu

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action (Hood and Alehossein, 2000). In the normal splitting operation, a thrust force incorporating with the tool movement perpendicular to the free surface at the contact point of ODC and rock. A crushed zone, which can be identical to the FPZ, is developed immediately beneath the cutter contact point with rock, which contains the first cracks at the boundary (contact line between the ODC and Rock) and secondary cracks are subsequently generated inside the rock (FPZ).

3

FRACTURE PROCESS ZONE IN CYCLIC DAMAGES

During the development of a crack in rock, the tip of the fracture propagates a plastic zone called the FPZ. The mechanical properties of rock, such as tensile and uniaxial compressive strength, elastic modulus, fracture toughness, and loading condition, play a significant role in FPZ development. Unique crack initiation from a crack tip is the most common method used to study the fracturing behaviours of rocks and used for validation of theoretical and practical applications. The mechanical concepts of the FPZ in mining applications have been investigated to accurately evaluate extension fractures from parting plane interfaces (Malan et  al., 1994). A previous study theoretically obtained principal stress distribution for a solid disc rock based on the Griffith criterion, and it investigated the effect of a different arc of contact on indirect tensile strength. Fracture toughness is the most important factor in evaluating fracturing behaviour and is used to characterise rock resistance against fracturing. The most appropriate experimental methods describe the propagation of a crack under static failure; however, few attempts have been made to describe cracks that develop under cyclic loading (Ghamgosar and Eraslan, 2016). Studies of progressing fractures under static loading shown that fracture toughness could be independent of the loading rate, whereas it is affected by amplitude and frequency under cyclic loading (Ghamgosar and Eraslan, 2016). Consequently, a brittle crack is defined as any separation in the rock body that has one dimension (i.e., in horizontal axes) propagated smaller than one-third of the other dimensions (i.e., in vertical axes), which is typically a width-to-length ratio of between 10−3 and 10−5 for most types of rock (Ghamgosar and Eraslan, 2016). Different laboratory techniques have been used to determine microfractures processing in brittle rocks. The morphology of microfractures is defined in two ways based on the connection of microfractures to the boundary of grains. If cracks are exposed totally within the grain, ‘intergranular’ or ‘intercrystalline’ cracks emerge, whereas cracks that grow from one-grain boundary across to another grain boundary are called ‘transgranular’ microfractures (Simmons and Richter, 1976). Temperature and higher confining pressure are also associated with induced and stressed microfractures, which cause dislocations in nucleating microfractures and influence rock fracturing behaviour (Ghamgosar and Eraslan, 2016). Figure  2(c) illustrates the morphology of microfractures in front of the chevron crack in the Cracked Chevron Notched Brazilian Disc (CCNBD) test (Figure 2 and 3) (Ghamgosar and Erarslan, 2016). The morphology and developing the shape of the FPZ in the numerical model (Figure 2b) can be utilised to simulate ODC performance (Figure 2a) based on LEFM concepts. However, the actual size and model of the FPZ is very different from current theoretical models in the literature. Further, little attention has been paid to quantifying the microfractures development in the FPZ of rock (Ghamgosar and Erarslan, 2016).

4

LABORATORY TESTING RESULTS

CCNBD specimens were used in this study with both the static and cyclic tests. The CCNBD geometry dimensions were selected according to the methods suggested by ISRM (Fowell et al, 1995) to attain reliable results (Figure 3). The chevron notch causes crack propagation to start at the tip of the V alignment and to proceed radially outwards in a stable fashion until the point at which the fracture toughness is calculated. A circular 40 mm diamond saw was used to cut the required notch. A specially designed jig suggested by ISRM (Fowell et al, 1995) was used to ensure that the chevron notches were exactly in the centre of the disc (Figure 3). Wave993

Figure 2. The concept of microfracturing in FPZ under cyclic loading in (a) ODC action (b) simulated FPZ in numerical model and (c) image processed of a tested CCNBD sample.

Figure 3.

CCNBD sample preparation (a), testing and monitoring process (b).

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Matrix™ software with a six-channel data logger system was employed to apply cyclic loading and complied in Instron 8800. All samples were diametrically loaded to induce indirect tensile fracturing under static and cyclic loading, and the chevron inclination angle was 0°. Instron 8800series machine equipped with a fast tracking system was used for conducting a precise testing. The fast tracking console provides visual communication between the loading control functions and user controlling options. Moreover, the fast tracking system provides multiple controlling interfaces such that graphical control panels are available in a single data window (contains time and desired parameters) or in a multiple data screen (mixed mode of data control, i.e. load versus time, displacement), which integrated to display the summary of the testing results during the testing process. The WaveMatrix™ dynamic testing software was used to perform a wide range of the cyclic tests (also preferable for conducting dynamic, fatigue and quasi-static tests. The software is capable to support 24 channels at the same time and can control various loading types such as sinusoidal, square, triangle, trapezoidal, and the combinations of hold-ramp function facilitated by user defined turning points and data recording display modes. In this study, three different cyclic loadings were designed and performed on the CCNBD specimens; Stepped Cyclic Loading (SCL), and Continuous Cyclic Loading (CCL) as presented in Figure 4. SCL and CCL loads were defined as a combination of three loading levels in WaveMatrix™, which they are a new type of cyclic loading. The loading test should start with an initial ramp step from the original position to the desired amplitude of the cyclic loading and continued by a sinusoidal cyclic loading, and afterwards, a trapezoidal step returns the current cyclic load to the original (SCL), or to the particular level of compressive load (CCL). The CT scan processing images for CCL showed that a fraction of the cracks or damaged area was considerably parallel and contained notable major cracks that initiated in front of the embedded crack tip (Figure 5). However, there were few major fractures in the SCL

Figure  4. Cyclic-loading types created by WaveMatrix™ interface in Instron loading machine: (a) static, (b) (CCL) and (c) SCL loading tests.

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Figure 5. Image processing with CT scan for the monzonite CCNBD specimens tested under SCL, CCL and static loading.

model, while excessive microfractures were propagated (Figure 4). In addition, further analysis revealed that there was no specific difference between the fracturing behaviour with SCL and CCL outside the FPZ. The processed images imply that different cyclic loadings can have a significant effect in the FPZ.

5

RESULTS AND DISCUSSION

The aims of this research were to perform fundamental experiments, in order to analyse and discuss the fracturing behaviour of rocks by including the FPZ and the damage mechanisms of the tested rocks under various loading conditions. A fracturing process is a complex process but rigorous methodologies were proposed in this thesis to successfully characterise microfractures and micromorphology properties based on the experimental results, numerical analyses and image processing techniques. CT-scan observations were found helpful to enable the quantifying of damage in the FPZ that developed under cyclic and static loading. The incremental damage tests were done to investigate the effect of amplitude and frequency on evolution and accumulation of microfractures in FPZ. Results of cyclic loading tests showed that damage obtained with cyclic loading was found significantly dependent on amplitude more than frequency. CMOD results showed the accumulation of axial deformation was found to be greater than lateral deformation under cyclic loading. CT-scan and image processing results showed the same results. Two different cyclic loading tests, SCL and CCL, were designed and conducted in this thesis to assess the most damaging loading for the selected hard rock samples of monzonite and tuff. The results of these tests should be integrated into the ODC technology to achieve easier cutting in hard rock excavations. Laboratory tests showed that microfractures density is strongly related to the individual loading–unloading cycles that occur during the cyclic tests. Further detailed CT-scan results revealed that the main characteristic of the FPZ is related to the loss of strength or stiffness of the material under SCL more so as compared to the same under CCL. Consequently, the larger size FPZ was achieved with SCL due to the difference between the amount of damage that occurred during loading and unloading cycles. Particle size analysis of fractured samples showed the average percentage of passing rock fragments (identical diameters of crushed material from the FPZ) was between 1.59% and 12.8% with SCL and varied between 1.04% and 8.36% with CCL. Laboratory results showed that SCL produced approximately 30% more crushed particles than CCL. The achieved results would be useful in order to improve the ODC performance.

ACKNOWLEDGMENT Newcrest Mining Limited is acknowledged for a scholarship provided by the first author during the PhD research upon which this paper was partly based. Komatsu (Joy Global) is likewise acknowledged for providing the monzonite core samples from Cadia Valley Operation (CVO) that were used for testing purposes. Golder Associates is acknowledged for providing Brisbane tuff core samples from the CLEM7 tunnel project in Brisbane that were used for testing purposes. 996

REFERENCES Argatov, I.I. and Nazarov, S.A., 2002. Energy release caused by the kinking of a crack in a plane anisotropic solid. Journal of Applied Mathematics and Mechanics, 66(3), pp. 491–503. Atkinson, B.K. and Avdis, V., 1980, December. Fracture mechanics parameters of some rock-forming minerals determined using an indentation technique. In International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts (Vol. 17, No. 6, pp. 383–386). Pergamon. Atkinson, B.K. and Meredith, P.G., 1987. The theory of subcritical crack growth with applications to minerals and rocks. Fracture mechanics of rock, 2, pp. 111–166. Bažant, Z.P. and Oh, B.H., 1985. Microplane model for progressive fracture of concrete and rock. Journal of Engineering Mechanics, 111(4), pp. 559–582. Eberhardt, E., 1998. Brittle rock fracture and progressive damage in uniaxial compression. Saskatoon: University of Saskatchewan. Erarslan, N. and Williams, D.J., 2012. Experimental, numerical and analytical studies on tensile strength of rocks. International Journal of Rock Mechanics and Mining Sciences, 49, pp. 21–30. Fowell, R.J., Hudson, J.A., Xu, C. and Zhao, X., 1995. Suggested method for determining mode I fracture toughness using cracked chevron notched Brazilian disc (CCNBD) specimens. In International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts (Vol. 7, No. 32, p. 322 A). Gambarotta, L. and Lagomarsino, S., 1993. A microcrack damage model for brittle materials. International Journal of Solids and Structures, 30(2), pp. 177–198. Ghamgosar, M. and Erarslan, N., 2014. The effect of cyclic loading amplitude and notch crack inclination angle on the fracture toughness test on Brisbane tuff-multiple factorial analyses. Rock Engineering and Rock Mechanics: Structures in and on Rock Masses-Proceedings of EUROCK, pp. 303–8. Ghamgosar, M. and Erarslan, N., 2015, January. A Numerical Study on Oscillating Disc Cutting (ODC) Technology for Hard Rock Cutting. In 13th ISRM International Congress of Rock Mechanics. International Society for Rock Mechanics. Ghamgosar, M. and Erarslan, N., 2016. Experimental and numerical studies on development of fracture process zone (FPZ) in rocks under cyclic and static loadings. Rock Mechanics and Rock Engineering, 49(3), pp. 893–908. Hillerborg, A., Modéer, M. and Petersson, P.E., 1976. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and concrete research, 6(6), pp. 773–781. Hood, M. and Alehossein, H., 2000. A development in rock cutting technology. International journal of rock mechanics and mining sciences, 37(1), pp. 297–305. Kahlen, E. and Alber, M., 2008. Damage characterization of coal measure rocks under uniaxial compression. In 6th Int Symp Ground Support in Min Civ Eng Construct (pp. 369–379). Karekal, S., 2003. The Oscillating Disc Cutting Technology–Experimental, Analytical and Numerical Investigations (Doctoral dissertation, Ph. D thesis, Division of Mining and Minerals Process Engineering, The University of Queensland, Australia). Malan, D.F., Napier, J.A.L. and Watson, B.P., 1994, December. Propagation of fractures from an interface in a Brazilian test specimen. In International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts (Vol. 31, No. 6, pp. 581–596). Pergamon. Planas, J., Elices, M., Guinea, G.V., Gómez, F.J., Cendón, D.A. and Arbilla, I., 2003. Generalizations and specializations of cohesive crack models. Engineering fracture mechanics, 70(14), pp. 1759–1776. Xie, H., Li, L., Ju, Y., Peng, R. and Yang, Y., 2011. Energy analysis for damage and catastrophic failure of rocks. Science China Technological Sciences, 54(1), pp. 199–209.

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Geomechanics and Geodynamics of Rock Masses – Litvinenko (Ed.) © 2018 Taylor & Francis Group, London, ISBN 978-1-138-61645-5

An integrated geostatistical-geomechanical approach for predicting potential risk of failure in pit walls Nader Ghasempour, Kamran Esmaieli & Hesameddin Eivazy Lassonde Institute of Mining, University of Toronto, Toronto, Canada

ABSTRACT: Detailed information on the spatial variation of rock mass geomechanical properties is essential for pit slope design. This information can be used for an optimized slope design, and for more accurate identification of the high-risk zones (low quality rock mass zones) along the pit walls. Geostatistical techniques have been successfully used for modelling the spatial variability of rock mass geomechanical properties. The 3D geotechnical block models that are developed using the geostatistical techniques could model both the randomness and spatial structures of a geomechanical variable. Thus, the heterogeneity and anisotropy of geotechnical properties can be modelled. This paper presents the results of a geostatistical simulation method used to develop a 3D geotechnical block model of Rock Mass Rating (RMR) for an open pit iron ore mine in Canada. Geotechnical data from boreholes was used for the spatial modelling of the geomechanical attribute. Five realizations of the RMR block models were generated. The resulting 3D block models of RMR were used to track geotechnical risks in different pit configurations throughout the life of mine. The probability of weak/ very weak rock mass blocks (RMR  40, the slope stability is governed by the orientation and shear strength of discontinuities whereas for RMR