Convergence-Confinement Method for Tunnel Design

Foreword
Contents
1 Introduction
	1.1 Construction Methods
		1.1.1 Conventional Construction Methods
		1.1.2 Tunnel Boring Machines (TBM)
	1.2 Displacements Induced by Tunnel Construction
		1.2.1 Tunnel Convergence
		1.2.2 Pre-convergence and Extrusion
	1.3 Ground Instabilities and Failures in Underground Works
	1.4 Support Functions
	1.5 Time-Dependent Deformation
	1.6 Natural State of Stress
	1.7 Choice Tunnel Support and Lining
		1.7.1 Geotechnical Classifications for Tunnels
		1.7.2 Design Methods Based on the Analysis of the Ground Support Interaction
	1.8 Principles of the Convergence-Confinement Method
	Appendix: Rock Mass Classifications
		AFTES Classification
		Rock Mass Rating
		Q Quality Index
		Ground Strength Index (GSI)
	References
2 Methods of Support
	2.1 Unsupported Distance
	2.2 Normal Stiffness and Bending Stiffness of a Support
	2.3 Normal Stiffness and Bending Stiffness of a Circular Cylindrical Shell
	2.4 Timber Supports
	2.5 Steel Ribs
	2.6 Bolting
	2.7 Shotcrete
	2.8 Rings of Prefabricated Segments
	2.9 Yielding Elements
	2.10 Composite Supports
	2.11 Two-Phase Supports
	2.12 Support of the Face
		2.12.1 Support of the Face by Bolts and Shotcrete
		2.12.2 Ground Treatments Ahead of the Face
		2.12.3 Confinement of the Tunnel Face
	2.13 Presupport
	2.14 Lining
	References
3 The Convergence-Confinement Method for a Tunnel Driven in an Elastic Medium
	3.1 Displacements Field and Convergence of an Unsupported Tunnel
	3.2 Stress and Displacement Fields Around an Unsupported Tunnel
		3.2.1 Tunnel with Circular Cross Section Excavated in an Elastic Medium Under Isotropic Initial Stress State
		3.2.2 Tunnel with Circular Cross Section Excavated in an Elastic Medium Under Anisotropic Initial Stress State
	3.3 Application of the Convergence-Confinement Method
		3.3.1 Isotropic Initial Stress State
		3.3.2 Anisotropic Initial Stress State
	Appendix 1: Complex Variable Method for Solving Two-Dimensional Elasticity Problems
	Appendix 2: Stress and Displacement Fields Around a Tunnel with Circular Cross Section Excavated in an Elastic Medium with Transverse Isotropy
	References
4 The Convergence-Confinement Method for a Tunnel Driven in an Elasto-Plastic Medium
	4.1 Usual Plasticity Models
		4.1.1 Tresca Yield Criterion
		4.1.2 Mohr–Coulomb Yield Criterion
		4.1.3 Hoek and Brown Yield Criterion
		4.1.4 Other Usual Plasticity Criteria
	4.2 Development of a Plastic Zone
		4.2.1 Deconfinement Ratio at the Onset of Plasticity
		4.2.2 Stability Number
	4.3 Stress and Displacement Fields for an Elastic Perfectly Plastic Behavior of the Ground
		4.3.1 Tresca Yield Criterion
		4.3.2 Mohr–Coulomb Yield Criterion
		4.3.3 Hoek and Brown Yield Criterion
	4.4 Brittle Failure
	4.5 Effect of Gravity on the Stability of the Vault of the Tunnel
	Appendix: Tunnel with Circular Section Excavated in an Elastic Perfectly Plastic Medium with Mohr–Coulomb Yield Criterion. Axi-symmetric Case—Face Mode and Edge Mode
	References
5 Longitudinal Displacement Profile
	5.1 Longitudinal Displacement Profile for an Unsupported Tunnel
	5.2 Longitudinal Displacement Profile for a Supported Tunnel
		5.2.1 Method of Bernaud and Rousset
		5.2.2 Method of Nguyen-Minh and Guo
		5.2.3 Comparison of the Accuracy of the Implicit Methods and of the Empirical Expressions
	5.3 Taking into Account of a Pre-support or a Confining Pressure on the Face
		5.3.1 Taking into Account of a Pre-support
		5.3.2 Evaluation of the Deconfinement Ratio for TBM Excavation with a Pressurized Shield
	References
6 The Convergence-Confinement Method and the Time-Dependent Behavior of the Rock Mass
	6.1 Analysis of Convergence Measurements
	6.2 Excavation of Tunnel with a Circular Section in a Viscoelastic Rock Mass
	6.3 Excavation of Tunnel with a Circular Section in a Visco-Elastic–plastic Rock Mass
	6.4 Viscoplastic Models
	6.5 Taking into Account the Hydraulic Regime
		6.5.1 Ground Reaction Curve for a Poroelastic Medium
		6.5.2 Application of the Convergence-Confinement Method for a Poroelastic Saturated Medium
		6.5.3 Time to Establish the Steady-State Hydraulic Regime
		6.5.4 Excavation in a Saturated Poroplastic Medium
	References
7 Use of Numerical Models
	7.1 Background
	7.2 Numerical Modeling of Conventional Tunneling
	7.3 Numerical Modeling of TBM Tunneling
	7.4 2D Numerical Modeling for the Application of the Convergence-Confinement Method
		7.4.1 Principles of the Numerical Simulation
		7.4.2 Example
	7.5 Example of 3D Numerical Simulation
	References