Stability Analyses of Large Structures Founded on Rock An Introductory Study Fredrik Johansson Licentiate Thesis Division of Soil and Rock Mechanics Department of Civil and Architectural Engineering Royal Institute of Technology Stockholm, Sweden 2005 TRITA-JOB LIC 2008 ISSN 1650-951X Contents CONTENTS ACKNOWLEDGEMENTS……………………………………………... v SUMMARY………………………………………………………………. vii SYMBOLS AND NOTATIONS................................................................ ix 1. INTRODUCTION…………………………………………………….. 1 1.1 Introduction…………………………………………………………… 1 1.2 Objectives……………………………………………………………... 3 1.3 Disposition of the thesis………………………………………………. 3 1.4 Extent and limitations............................................................................. 4 2 LITERATURE STUDY……………………………………………….. 5 2.1 Introduction…………………………………………………………… 5 2.2 Fundamental principles of stability analyses………………………….. 6 2.2.1 Introduction…………………………………………………… 6 2.2.2 Total factor of safety………………………………………….. 7 2.2.3 Probability of failure………………………………………….. 9 2.2.4 Limit state analyses with partial factors of safety…………….. 10 2.2.5 Acceptance requirements……………………………………... 12 2.3 Rock mass material models…………………………………………… 14 2.3.1 Introduction…………………………………………………… 14 2.3.2 General definitions regarding stress-strain response………….. 15 2.3.3 Failure criteria…………………………………………............ 17 2.3.4 Modelling a continuum material………………………............ 24 2.3.5 Modelling a discontinuum material……………………........... 29 2.4 Parameters to model rock masses……………………………………... 34 2.4.1 Introduction…………………………………………………… 34 2.4.2 Intact rock……………………………………………………... 35 2.4.3 Discontinuities………………………………………………… 39 2.4.4 Rock masses…………………………………………………... 47 2.4.5 Pore pressure………………………………………………….. 52 2.5 Calculations methods………………………………………………….. 54 2.5.1 Introduction…………………………………………………… 54 2.5.2 Analytical methods for bearing capacity failure………............ 55 2.5.3 Analytical methods for sliding failure…………………............ 62 2.5.4 Analytical methods for overturning…………………………... 72 2.5.5 Numerical methods for continuum material………………….. 72 2.5.6 Numerical methods for discontinuum materials………............ 75 2.6 Verification and follow-up of predictions...…………………………... 76 2.7 Laws, regulatory rules, and guidelines……………………………...… 78 2.7.1 Introduction…………………………………………………… 78 2.7.2 Eurocode………………………………………………............ 79 2.7.3 The Swedish bridge design code, BRO 2004…………………. 80 i Stability analyses of large structures founded on rock – an introductory study 2.7.4 The Swedish power companies guidelines for dam safety, RIDAS………………………………………………………………. 81 2.7.5 Regulatory rules and guidelines for concrete dams in other countries……………………………………………..……………… 84 2.8 Conclusions…………………………………………………………… 87 2.8.1 Introduction…………………………………………………… 87 2.8.2 Fundamental principles of stability analyses…………………. 87 2.8.3 Rock mass material models……………………………............ 88 2.8.4 Parameters to model rock masses…………………………….. 88 2.8.5 Calculation methods…………………………………………... 90 2.8.6 Verification and follow-up of predictions…………………….. 92 2.8.7 Laws, regulatory rules and guidelines…………………............ 92 3. REFLECTIONS ON FOUNDATION STABILITY OF THE ARCH DAM AT KROKSTRÖMMEN………………………………… 95 3.1 Introduction…………………………………………………………… 95 3.2 Notations of reaction forces…………………………………………… 96 3.3 Geology……………………………………………………………….. 97 3.4 Construction of the reinforcement slab……………………………….. 100 3.5 Previous calculations and measurements…………………………....... 101 3.5.1 Introduction…………………………………………………… 101 3.5.2 Calculations and measurements in the 1950’s (Reinius 1954).. 101 3.5.3 Finite element analysis (Johansson and Palmgren 1996)….….. 103 3.5.4 Analytical stability calculations (Stille et al. 2002)….……...... 104 3.5.5 Conclusions……………………………………………............ 105 3.6 Instrumentation and measurements………………………………….... 106 3.6.1 Introduction…………………………………………………… 106 3.6.2 Temperature measurements…………………………………... 107 3.6.3 Pore pressure measurements………………………….............. 108 3.6.4 Measurements of vertical deformations with extensometers..... 109 3.6.5 Measurements of horizontal deformations with deflectometers 112 3.6.6 Measurements of arch dam deformations with theodolite…..... 117 3.6.7 Conclusions……………………………………………............ 119 3.7 Back calculation of the modulus of elasticity for the rock mass……… 120 3.7.1 Introduction…………………………………………………… 120 3.7.2 Input to the back calculation………………………….............. 120 3.7.3 Methodology………………………………………….............. 122 3.7.4 Results………………………………………………................ 122 3.7.5 Discussion and interpretation of results………………............. 123 3.7.6 Conclusions……………………………………………............ 124 3.8 Analytical model for estimation of horizontal rock deformations…..... 125 3.8.1 Introduction…………………………………………………… 125 3.8.2 Derivation of the model………………………………............. 125 3.8.3 Input to the calculations………………………………............. 127 3.8.4 Methodology………………………………………………….. 128 3.8.5 Results…………………………………………………............ 128 3.8.6 Discussion and interpretation of results…………………......... 132 3.8.7 Conclusions……………………………………………............ 132 ii Contents 3.9 Two dimensional finite element analysis…………………………....... 133 3.9.1 Introduction…………………………………………………… 133 3.9.2 Definition of load cases……………………………….............. 133 3.9.3 Input to, and construction of, the finite element models............ 135 3.9.4 Methodology………………………………………….............. 146 3.9.5 Results…………………………………………………............ 149 3.9.6 Discussion and interpretation of results………………............. 157 3.9.7 Conclusions…………………………………………................ 162 3.10 Discussion and reflections on the stability of the foundation............... 163 3.11 Conclusions………………………………………………………...... 172 4. GENERAL CONCLUSIONS………………………………………… 173 5. SUGGESTIONS FOR FUTURE WORK……………………………. 179 6. REFERENCES………………………………………………………... 181 APPENDIX A. Design of the reinforcement slab………………………………………. I B. Temperature measurements …………………………………………… III C. Pore pressure measurements…………………………………………… VII D. Vertical deformations measured with extensometers.............................. XI E. Horizontal deformations measured with deflectometers…...................... XV F. Measurements of arch dam deformations with theodolite……............... XIX G. Estimation of vertical stresses from the load of the reinforcement slab.. XXIII H. Calculation of temperature variations in the arch dam………................ XXXI I. Estimation of long term modulus of elasticity for the concrete................ XXXVII J. Results from the finite element analysis………………………………... XLIII K. Calculation of resistances in the rock foundation………........................ LV iii Stability analyses of large structures founded on rock – an introductory study iv Acknowledgements ACKNOWLEDGEMENTS First of all, I would like to express my gratefulness to my supervisor Professor Håkan Stille; for his invaluable advices, patience and encouragement throughout this work. Special thanks are also acknowledged to M. Sc. Karl Rytters who initiated the project. Without him, this project would not have been realized. This project has been financed by a number of participants. I would like to express my appreciation to SveBeFo and Tomas Franzén who has had the overall responsibility for the administrative work and financing. I am also most grateful to the other financiers, who are the Swedish power company’s research and development organisation, ELFORSK, the Swedish construction industry’s organisation for research and development, SBUF, the Swedish nuclear waste management, SKB, and the technical consultant firm SWECO VBB. During the work with this project, the work has been followed by a reference group, consisting of persons competent in the subject. The group has assisted with valuable comments and discussions. A debt of gratitude is acknowledged to the persons in this group, which are: − Tomas Franzén, SveBeFo − Anders Gutafsson, SWECO VBB − Carl-Olof Söder, SWECO VBB − Karin Hellstadius, SwedPower − Rolf Christiansson, SKB − Tommy Flodin, FORTUM Throughout the work with the arch dam at Krokströmmen, Lasse Persson and Kent Allard at Geometrik have helped out with valuable information and knowledge about the instrumentation equipment. Together with Geometrik, the instrumentation was performed by 1:st instrument maker Elis Svensson and research engineer Per Delin at the department of soil and rock mechanics. The author is thankful for their work. Thanks are also given to Mikael Söderholm for retrieving data from the instrumentation, and to Per Erik Froom for his detailed surveying of the arch dam deformations. Appreciation is also acknowledged to Gösta Johansson and Andreas Halvarsson at the technical consultant firm WSP, who have contributed with previous investigation materials about the arch dam at Krokströmmen and the reinforcement slab. v Stability analyses of large structures founded on rock – an introductory study I would also like to thank my colleagues and staff members at the department of soil and rock mechanics for their stimulating and interesting discussions and support. Finally, I would like to express my greatest gratitude to my dear Camilla, my parents and my sister for their support. Fredrik Johansson Stockholm, October 2006 vi Summary SUMMARY Previous investigations of Swedish and international dams have shown difficulties to assess the safety against failure in rock foundations. The problem was also given additional interest in connection to the recent construction of the new bridge at Traneberg