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2014 | Buch

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Modelling Rock Fracturing Processes

A Fracture Mechanics Approach Using FRACOD

verfasst von: Baotang Shen, Ove Stephansson, Mikael Rinne

Verlag: Springer Netherlands

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This text book provides the theoretical background of rock fracture mechanics and displacement discontinuity methods used for the modelling of geomechanical problems. The computer program FRACOD is used to analyse the fracture problems, assessing fracture initiation and propagation in tension (Mode I), shear (Mode II) and mixed mode I and II of solid intact or jointed geomaterials. The book also presents the fundamentals of thermo-mechanical coupling and hydro-mechanical coupling. Formulations of multiple regional mechanical, thermal and hydraulic functions, which allow analyses of fracture mechanics problems for structures made of brittle, rock-like materials, are provided. In addition, instructive examples of code verification and applications are presented.

Additional material: The 2-D version of the FRACOD program, a manual on the program and a wealth of verification examples of classical problems in physics, mechanics and hydromechanics are available at http://extras.springer.com. A large number of applications related to civil, mining, petroleum and environmental engineering are also included.

- The first textbook available on modelling of rock fracture propagation

- Introduces readers to the fundamentals of rock fracturing

- Uses a modern style of teaching with theory, mathematical modelling and applications in one package

- The basic version of the FRACOD software, manual, verification examples and applications are available as additional material

- The FRACOD program and manual enable the readers to solve fracture propagation problems on their own

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Ki-Bok Min, Department of Energy Resources Engineering,

College of Engineering, Seoul National University, Korea

“Challenging rock engineering applications require extreme conditions of stress, temperature and hydraulic pressure resulting in rock fracturing to a various extent. The FRACOD is one of few computer codes available in engineering rock mechanics that can simulate the initiation and propagation of fractures often interacting with natural fractures. Its capability has been significantly enhanced to include the hydraulic and thermal fracturing with concerted interaction from multi-national research and industry partners. My experience with the FRACOD is very positive and I am certain that its already-excellent track record will expand further in the future."

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

Understanding the long-term behaviour of a rock mass and the coupled hydro-thermal-mechanical processes is crucial for geological radioactive waste disposal, geothermal, mining, LNG underground storage, and CO₂ geosequestration. Rock fracture initiation and propagation are the key mechanism for rock mass instability.

The ability to predict and realistically reproduce rock mass behaviour using a numerical model is a pivotal step in solving many rock engineering problems. Although several existing numerical codes can model the behaviour of jointed or fractured rock mass, most do not consider the explicit fracture initiation and propagation—a dominant mechanism, particularly in hard rocks.

The FRActure propagation CODe (FRACOD) presented here is a two-dimensional computer code designed to simulate fracture initiation and propagation in elastic and isotropic rock mediums. This book focuses on the theories and numerical principles behind FRACOD, providing examples where the numerical method is applied to solve practical problems.

Baotang Shen, Ove Stephansson, Mikael Rinne

Chapter 2. Introduction to Rock Fracture Mechanics

Abstract

This chapter provides the basic theories and principles behind rock fracture mechanics. It starts with introducing the Griffith flaws and energy balance theory, which is the foundation of the modern fracture mechanics. Then the concept of stress intensity factor for linear elastic fracture mechanics is introduced, followed by a description of the criteria for fracture propagation. Also described in this chapter is the subcritical crack growth which dominates the time-dependent long term stability of a fractured medium.

Baotang Shen, Ove Stephansson, Mikael Rinne

Chapter 3. Numerical Method

Abstract

The FRACOD code is based on Boundary Element Method principles. It utilizes the Displacement Discontinuity Method (DDM), one of the three commonly used boundary element methods. In the FRACOD code, a fracture criterion, the F-criterion, is incorporated into the numerical method for simulating fracture propagation. This chapter describes the numerical method DDM, the F-criterion and modelling the initiation and propagation of fractures.

Baotang Shen, Ove Stephansson, Mikael Rinne

Chapter 4. Iteration Process in FRACOD

Abstract

This chapter describe the iteration process used in FRACOD. Boundary element methods (including DDM) are implicit numerical methods. This means that the numerical calculation will only provide a final solution at given stress or displacement boundary conditions, ignoring the linearity of the process that reaches the final solution. For elastic problems, the implicit method is the most efficient and straightforward way to get the final solution because of the linear stress–strain relation. However, for plasticity problems caused by joint sliding and fracture propagation, the implicit method can give false results if the process to reach the final solution is non-linear. Final solutions will then depend on the path of loading. Iteration process is an effective method to consider the path dependent problem.

Baotang Shen, Ove Stephansson, Mikael Rinne

Chapter 5. Modelling Time Dependency

Abstract

This chapter describes the theories of sub-critical crack growth and numerical procedures implemented in FRACOD. Classical fracture mechanics postulates that a fracture tip with a stress intensity equal to the material’s critical fracture toughness will accelerate to speeds approaching the elastic wave speed in a medium. However, in cases of long-term loading, fractures can grow at stress intensities significantly lower than the critical values. This process is called subcritical fracture growth (SCG); SCG and propagation velocities can vary over many orders of magnitude as a function of stress intensity. In FRACOD the subcritical crack growth is modelled by considering the crack length as a function of time. Using the subcritical crack growth function, the time-dependent stability of fractured rock masses can be modelled.

Baotang Shen, Ove Stephansson, Mikael Rinne

Chapter 6. Simulation of Multiple Region System

Abstract

Rock mass may have different properties in different regions of its structure. An example is a shaft where three different regions (concrete lining, Excavation Disturbed Zone (EDZ), and in situ rock mass) must be considered.

For application in this case, FRACOD needs to simulate the multiple regions with different material properties. Because FRACOD is a boundary element code based on the mathematical solutions in an elastic, homogeneous, isotropic medium, it is not a trivial task to extend FRACOD to handle multiple region problems. New approaches must be found. This chapter presents the mathematical formulations and their implementation in FRACOD for multiple region problems.

Baotang Shen, Ove Stephansson, Mikael Rinne

Chapter 7. Solving Gravitational Problems

Abstract

Many practical rock-engineering problems involve gravitational stresses. Rock slope stability and shallow tunnel stability are two examples where the gravity stresses cannot simply be ignored or simplified as far-field in situ stresses. In such cases, uneven gravitational stresses at different depths of the rock mass must be explicitly considered.

Modelling gravitational stresses with boundary element (BE) methods is not as straightforward as in finite element (FE) method where the mass and weight of the rock are distributed into each element. Because the elements in BE methods are only located at the boundaries, they are not able to directly represent the gravitational force inside the rock body. To effectively represent this gravitational force, we need to: (1) account for the uneven gravitational stresses at the centre of all boundary elements; (2) superposition the gravitational stresses at any point inside the rock. This chapter provides the formulations to consider the effect of gravitational forces.

Baotang Shen, Ove Stephansson, Mikael Rinne

Chapter 8. Sequential Excavation Function

Abstract

FRACOD as a boundary element code works best for problems with predefined boundaries. If the model boundary is not completely fixed at the beginning, this creates difficulties for boundary element modelling. An example of such a case is the sequential excavation of two adjacent boreholes in a rock mass. One borehole is excavated first, resulting in deformation and failure (fracturing) in the borehole wall. The second borehole is then excavated in an already disturbed stress field, and it may create new fractures and/or further propagate existing fractures in the surrounding rock mass. Because of the problem encountered above, a method to manage sequential excavation has been developed in FRACOD. This chapter describes the principles and numerical procedures of this method.

Baotang Shen, Ove Stephansson, Mikael Rinne

Chapter 9. Thermo-Mechanical Coupling

Abstract

This chapter provide the theoretical formulations and numerical procedures involved in thermo-mechanical coupling function in FRACOD. Coupling between thermal loading and mechanical process can occur either when the temperature change in rock mass causes thermal stresses or when stress change in the rock mass causes a temperature change. Although heat transfer can result in significant changes in volumetric stress, influences of rock matrix deformation on the temperature field are usually negligible. This means that thermal flux and temperature can be calculated separately without the consideration of mechanical stresses. In this discussion, thermo-mechanical coupling refers only to cases where the heating of rock increases volumetric stresses.

Due to the time dependency of heat conduction, the changes of thermal stress fields are transient processes. It should be noted that for rocks with low permeability, heat conduction dominates the heat transfer process. Heat convection can usually be neglected because of the extremely low heat flow velocity in rocks. This chapter is concerned with low permeability rocks like shale and granite, so effects of heat transported by convection are neglected, and linear thermal conductive behaviour is assumed in the thermo-elastic analysis.

Baotang Shen, Ove Stephansson, Mikael Rinne

Chapter 10. Hydro-Mechanical Coupling

Abstract

This chapter provide the theoretical formulations and numerical procedures involved in hydro-mechanical coupling function in FRACOD.

An explicit iteration approached is used in FRACOD to solve the coupled fracturing – hydraulic flow processes. The mechanical calculation (including rock deformation and fracture propagation) is completed using the Displacement Discontinuity Method (DDM) with an iteration scheme for modelling fracture propagation processes. The fracture fluid flow calculation is conducted through the time-marching iteration based on the Cubic Law.

Baotang Shen, Ove Stephansson, Mikael Rinne

Chapter 11. Anisotropic Rock Strength Function

Abstract

In rock engineering, anisotropic rock masses are often encountered and cannot be simplified as an isotropic problem in numerical models. Hence an anisotropic function in the numerical model is required.

Rock anisotropy includes strength anisotropy and modulus anisotropy. Developing the anisotropic function in FRACOD requires significantly different complexity for strength anisotropy and modulus anisotropy. The strength anisotropy function alone does not require any alteration in the way FRACOD calculates the rock stress and displacement, and therefore it is relatively straightforward. The modulus anisotropy function, on the other hand, will require the modification of the fundamental equations of stress and displacement, and hence will be much more complex and difficult. In actual rock engineering, the strength anisotropy is often considered to be much more pronounced and important than the modulus anisotropy, and it dominates the stability and failure pattern of the rock mass.

This chapter discusses work related to the development of the strength anisotropy in FRACOD. This function has been developed for modelling the rock fracturing behaviours at the Finnish URL for high-level radioactive waste disposal where the host rock of gneiss is highly foliated and anisotropic.

Baotang Shen, Ove Stephansson, Mikael Rinne

Chapter 12. Rock Properties for FRACOD Modelling

Abstract

Modelling of rock fracturing problems with FRACOD requires some physical and mechanical rock properties not commonly used in traditional rock mechanics. This chapter gives a short description and references to testing methods and data for properties in the following areas:

Mechanical properties
- Intact rock
- Joint
- New fracture
Fracture mechanics properties
Thermal properties

Baotang Shen, Ove Stephansson, Mikael Rinne

Chapter 13. FRACOD Verification Tests

Abstract

This chapter describe several verification tests using FRACOD to model some simple problems from single fracture propagation to coupled fracturing process. The tests cases are designed to demonstrate the functionality of FRACOD, and they include:

Propagation of a single fracture under pure tension;

Propagation of a single fracture under pure shear;

Multiple region model of a shaft with concrete lining;

Subcritical crack growth – Creep – model of a single tensile fracture;

Gravitational problems involving a tunnel in shallow ground;

Thermo-mechanical coupling – a single heat source in rock mass;

Dynamic fluid flow in a single fracture;

Hydraulic fracturing in rock mass with pre-existing fractures.

Baotang Shen, Ove Stephansson, Mikael Rinne

Chapter 14. Application Case Studies

Abstract

This chapter provides five representative case studies employing FRACOD, including 1) Borehole Breakout; 2) Tunnel EDZ; 3) LNG Underground Cavern; 4) Pillar Spalling; and 4) UCS and Brazilian Test. These cases cover various aspects of modern rock mechanics and aim to demonstrate the effectiveness of the fracture mechanics approach.

Baotang Shen, Ove Stephansson, Mikael Rinne

Backmatter

Titel: Modelling Rock Fracturing Processes
verfasst von: Baotang Shen
Ove Stephansson
Mikael Rinne
Verlag: Springer Netherlands
Electronic ISBN: 978-94-007-6904-5
Print ISBN: 978-94-007-6903-8
DOI: https://doi.org/10.1007/978-94-007-6904-5