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Table of Contents
Acknowledgments
About the Author
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
2.3.1 Introduction
2.3.2 Inverse approach
2.3.3 Direct approach
2.3.4 Probabilistic approach
2.3.5 Fuzzy systems, Artificial Intelligence (AI), Neural network, etc.
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
4.8.1 Introduction
4.8.2 Numerical analysis methods
4.8.3 Critical strain methods
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
8.2.1 Introduction
8.2.2 Assumption of mechanical model
8.2.3 Mathematical formulation
8.3 Case study I (Washuzan Tunnels)
8.3.1 Exploration tunnel (work tunnel)
8.3.1.1 Introduction
8.3.1.2 Displacement measurements and back analyses
8.3.1.3 Design analysis of the main tunnels
8.3.2 Excavation of the main tunnels
8.3.2.1 Brief description with respect to the tunnels and instrumentation
8.3.2.2 Back analysis of measured displacements
8.3.2.3 Assessment of the stability of tunnels
8.4 Case study II (two-lane road tunnel in shallow depth)
8.4.1 Introduction
8.4.2 Brief description of the tunnel
8.4.3 Field measurements
8.4.3.1 Convergence measurements
8.4.3.2 Multi-rod extensometer and sliding micrometer measurements
8.4.4 Back analysis of measured displacements
8.4.5 Assessment of the stability of tunnels
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)
9.3.1 Tunnel configuration and instruments
9.3.2 Back analyses
9.3.3 Supporting mechanism of rock bolts, shotcrete and steel ribs
9.4 Modelling of support structures
9.4.1 Modelling of rock bolts
9.4.2 Modelling of shotcrete and steel ribs
10 Initial stress of rock masses determined by boundary element method
10.1 Introduction
10.2 Three-dimensional back analysis method
10.2.1 Mathematical formulation of the method
10.2.2 Computational stability
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
11.3.1 Maximum shear strain on the elasto-plastic boundary
11.3.2 Relationship between real and equivalent Young’s modulus
11.4 The method for determining the elasto-plastic boundary
11.5 Computer simulation
11.5.1 Procedure
11.5.2 An example problem and simulation results
12 Back analysis considering anisotropy of rocks
12.1 Introduction
12.2 Constitutive equations
12.3 Different modes of deformation
12.3.1 Spalling of joints
12.3.2 Sliding along joints
12.3.3 Plastic flow
12.4 Computer simulations
12.4.1 Spalling of joints
12.4.2 Plastic flow
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
14.2.1 Mohr?Coulomb failure criterion
14.2.2 Von Mises yield criterion
14.2.3 Nadai’s failure criterion and Drucker–Prager failure criterion
14.3 Anisotropic parameter and anisotropi...
