Back Analysis in Rock Engineering

This book provides practicing engineers working in the field of design, construction and monitoring of rock structures such as tunnels and slopes with technical information on how to design, how to excavate and how to monitor the structures during their construction. Based on the long-term engineering experiences of the author, field measurements together with back analyses are presented as the most powerful tools in rock engineering practice. One of the purposes of field measurements is to assess the stability of the rock structures during their construction. However, field measurement results are only numbers unless they are quantitatively interpreted, a process in which back analyses play an important role. The author has developed both the concepts of “critical strain” and of the “anisotropic parameter” of rocks, which can make it possible not only to assess the stability of the structures during their construction, but also to verify the validity of design parameters by the back analysis of field measurement results during the constructions. Based on the back analysis results, the design parameters used at a design stage could be modified if necessary. This procedure is called an “Observational method”, a concept that is entirely different from that of other structures such as bridges and buildings. It is noted that in general, technical books written for practicing engineers mainly focus on empirical approaches which are based on engineers’ experiences. In this book, however, no empirical approaches will be described, instead, all the approaches are based on simple rock mechanics theory. This book is the first to describe an observational method in rock engineering practice, which implies that the potential readers of this book must be practicing engineers working on rock engineering projects.

1 Introduction 1.1 Aims and scope 1.2 Field measurements and back analyses 2 Back analysis and forward analysis 2.1 What is back analysis? 2.2 Difference between back analysis and forward analysis 2.3 Back analysis procedures 2.4 Brief review of back analysis 3 Modelling of rock masses in back analysis 3.1 Modelling of rock masses 3.2 Back analysis and modelling 3.3 Difference between parameter identification and back analysis 4 Observational method 4.1 What is observational method? 4.2 Design parameters for different types of structures 4.3 Difference between stress-based approach and strain-based approach 4.4 Strain-based approach for assessing the stability of tunnels 4.5 Displacement measurements in observational method 4.6 Back analysis in observational method 4.7 Flowchart of observational methods 4.8 Hazard warning levels 5 Critical strains of rocks and soils 5.1 Definition of critical strain of geomaterials 5.2 Scale effect of critical strains 5.3 Simple approach for assessing tunnel stability 5.4 Hazard warning level for assessing crown settlements and convergence 5.5 Uniaxial compressive strength and Young’s modulus of rock masses 6 Environmental effects on critical strain of rocks 6.1 Critical strain in triaxial condition 6.2 Effects of confining pressure 6.3 Effects of moisture content 6.4 Effects of temperature 7 General approach for assessing tunnel stability 7.1 Critical shear strain of geomaterials 7.2 Hazard warning levels in terms of maximum shear strain 7.3 How to determine the maximum shear strain distribution around a tunnel 8 Back analyses used in tunnel engineering practice 8.1 Introduction 8.2 Mathematical formulation of the proposed back analyses 8.3 Case study I (Washuzan tunnels) 8.4 Case study II (two-lane road tunnel in shallow depth) 9 Universal back analysis method 9.1 Introduction 9.2 Mathematical formulation considering non-elastic strain 9.3 Case study (tunnel excavated in shallow depth) 9.4 Modelling of support structures 10 Initial stress of rock masses determined by boundary element method 10.1 Introduction 10.2 Three-dimensional back analysis method 10.3 Case study 11 Back analysis for the plastic zone occurring around underground openings 11.1 Introduction 11.2 Assumptions 11.3 Fundamental equations 11.4 The method for determining the elasto-plastic boundary 11.5 Computer simulation 12 Back analysis considering anisotropy of rocks 12.1 Introduction 12.2 Constitutive equations 12.3 Different modes of deformation 12.4 Computer simulations 12.5 Case study (underground hydropower plant) 13 Laboratory experiments 13.1 Absolute triaxial tests (true triaxial tests) 13.2 Conventional triaxial compression tests 13.3 Simple shear tests 14 Constitutive equations for use in back analyses 14.1 Fundamental theory of constitutive equations for geomaterials 14.2 Failure criteria 14.3 Anisotropic parameter and anisotropic damage parameter 14.4 Proposed constitutive equation for geomaterials 14.5 Applicability of the proposed constitutive equation 14.6 Conclusions on the results of the numerical simulation 14.7 Forward analysis vs. back analysis 15 Cylindrical specimen for the determination of material properties 15.1 Introduction 15.2 Constitutive equation for cylindrical coordinate systems 15.3 Numerical simulation 16 Applicability of anisotropic parameter for back analysis 16.1 Physical model tests in laboratory 16.2 Excavation of the tunnels and strain distributions around them 16.3 Back analysis for simulating the maximum shear strain distributions 16.4 Results and discussion 17 Assessing the stability of slopes 17.1 Factor of safety of slopes 17.2 Paradox in the design and monitoring of slopes 17.3 Difference between the factor of safety of tunnels and slopes 17.4 Factor of safety for toppling of slopes 18 Back analysis of slopes based on the anisotropic parameter 18.1 Mechanical model of rock masses 18.2 Laboratory experiments for toppling 18.3 Numerical analysis of toppling behaviours 18.4 Applicability of the anisotropic parameter to simulation of various deformational modes 18.5 Factor of safety back-calculated from measured displacements 19 Back analysis method for predicting a sliding plane 19.1 Introduction 19.2 Procedure of the method 19.3 Accuracy of the method 20 Back analysis of landslides 20.1 Introduction 20.2 Finite element formulation 20.3 Applicability of the proposed method (forward analysis) 20.4 Case study of landslide due to heavy rainfall (back analysis) 21 Back analysis for determining the strength parameters 21.1 Introduction 21.2 Back analysis procedure 22 Application of back analysis for assessing the stability of slopes 22.1 Cut slope 22.2 Slope of open-pit coal mine 23 Monitoring of slope stability using GPS in geotechnical engineering 23.1 Introduction 23.2 Displacement monitoring using GPS 23.3 Practical application of GPS displacement monitoring 23.4 Back analysis in GPS displacement monitoring

Prof. Sakurai studied Civil Engineering at Kobe University (B.E) and at Kyoto University (M.E), and finally at Michigan State University USA (Ph.D). He also received his Dr Eng. degree from Nagoya University, Japan.Prof. Sakurai worked at Kobe University as Professor of rock mechanics, and of structural mechanics, and then worked at the Hiroshima Institute of Technology as President. He is now Professor Emeritus of Kobe University, and also Professor Emeritus of Hiroshima Institute of Technology. Professionally, Prof. Sakurai has been involved in various types of Rock Mechanics projects (hydropower, nuclear power, pumped storage, compressed air energy storage schemes, highway and railway tunnels, slopes etc.) in Japan and abroad.His research interests have been connected to numerical analysis particularly back analysis and field measurements. The aim of these research activities is mainly concerned with building a bridge between theory and practice.