This book mainly focuses on the adaptive analysis of damage and fracture in rock, taking into account multiphysical fields coupling (thermal, hydro, mechanical, and chemical fields). This type of coupling is a crucial aspect in practical engineering for e.g. coal mining, oil and gas exploration, and civil engineering. However, understanding the influencing mechanisms and preventing the disasters resulting from damage and fracture evolution in rocks require high-precision and reliable solutions. This book proposes adaptive numerical algorithms and simulation analysis methods that offer significant advantages in terms of accuracy and reliability. It helps readers understand these innovative methods quickly and easily. The content consists of: (1) a finite element algorithm for modeling the continuum damage evolution in rocks, (2) adaptive finite element analysis for continuum damage evolution and determining the wellbore stability of transversely isotropic rock, (3) an adaptive finite element algorithm for damage detection in non-uniform Euler–Bernoulli beams with multiple cracks, using natural frequencies, (4) adaptive finite element–discrete element analysis for determining multistage hydrofracturing in naturally fractured reservoirs, (5) adaptive finite element–discrete element analysis for multistage supercritical CO2 fracturing and microseismic modeling, and (6) an adaptive finite element–discrete element–finite volume algorithm for 3D multiscale propagation of hydraulic fracture networks, taking into account hydro-mechanical coupling. Given its scope, the book offers a valuable reference guide for researchers, postgraduates and undergraduates majoring in engineering mechanics, mining engineering, geotechnical engineering, and geological engineering.

(4). The next three papers extend these views by taking a closer look on parameters that govern hydraulic diffusivity in sandstones and other types of rocks. Specific targets addressed are the influence of differential stress on permeability (5), imaging of the fracture geometry (6), and pressure induced variations in the pore geometry (7). Contributions no. 8 to 10 cover investigations of permeability-porosity relationships during rock evolution (8), of the formation, propagation, and roughness of fractures in a plexi-glass block (9), and pressure oscillation effects of two-phase flow under controlled conditions (10). The subsequent four articles focus on diverse modeling approaches. Issues considered are how the geometry and the mechanical behavior of fractures can be characterized by mathematical expressions (11), how the evolution of permeability in a microcracking rock can be expressed by an analytical model (12), deviations from the cubic law for a fracture of varying aperture (13), and the numerical simulation of scale effects in flow through fractures (14). Three further papers refer to in situ observations, being related to topics as the assessment of in situ permeability from the spatio temporal distribution of an aftershock sequence (15), to the scale dependence of hydraulic pathways in crystalline rock (16), and to the significance of pore pressure - stress coupling in deep tunnels and galleries (17).

The analysis of crack problems through fracture mechanics has been applied to the study of materials such as glass, metals and ceramics because relatively simple fracture criteria describe the failure of these materials. The increased attention paid to experimental rock fracture mechanics has led to major contributions to the solving of geophysical problems. The text presents a concise treatment of the physics and mathematics of a representative selection of problems from areas such as earthquake mechanics and prediction, hydraulic fracturing, hot dry rock geothermal energy, fault mechanics, and dynamic fragmentation.

Porous Rock Failure Mechanics: Hydraulic Fracturing, Drilling and Structural Engineering focuses on the fracture mechanics of porous rocks and modern simulation techniques for progressive quasi-static and dynamic fractures. The topics covered in this volume include a wide range of academic and industrial applications, including petroleum, mining, and civil engineering. Chapters focus on advanced topics in the field of rock’s fracture mechanics and address theoretical concepts, experimental characterization, numerical simulation techniques, and their applications as appropriate. Each chapter reflects the current state-of-the-art in terms of the modern use of fracture simulation in industrial and academic sectors. Some of the major contributions in this volume include, but are not limited to: anisotropic elasto-plastic deformation mechanisms in fluid saturated porous rocks, dynamics of fluids transport in fractured rocks and simulation techniques, fracture mechanics and simulation techniques in porous rocks, fluid-structure interaction in hydraulic driven fractures, advanced numerical techniques for simulation of progressive fracture, including multiscale modeling, and micromechanical approaches for porous rocks, and quasi-static versus dynamic fractures in porous rocks. This book will serve as an important resource for petroleum, geomechanics, drilling and structural engineers, R&D managers in industry and academia. Includes a strong editorial team and quality experts as chapter authors Presents topics identified for individual chapters are current, relevant, and interesting Focuses on advanced topics, such as fluid coupled fractures, rock’s continuum damage mechanics, and multiscale modeling Provides a ‘one-stop’ advanced-level reference for a graduate course focusing on rock’s mechanics

Several recent works have demonstrated that phase-field methods for modeling fracture are capable of yielding complex crack evolution patterns in materials. This includes the nucleation, turning, branching, and merging of cracks subject to a variety of quasi-static and dynamic loadings. What follows will demonstrate how phase-field methods for fracture can be applied to problems involving materials subject to electromechanical coupling and the problem of hydraulic fracture. Brittle fracture is a major concern in piezoelectric ceramics. Fracture propagation in these materials is heavily influenced by the mechanical and electrical fields within the material as well as the boundary conditions on the crack surfaces. These conditions can lead to complex multi-modal crack growth. We develop a continuum thermodynamics framework for a damaging medium with electromechanical coupling subject to four different crack-face boundary conditions. A theory is presented to reproduce impermeable, permeable, conducting, and energetically consistent crack-face boundary conditions, the latter of which requires a finite deformation formulation. A primary application of hydraulic fracturing involves the injection of fluid into a perforated wellbore with the intention of fracturing the surrounding reservoir and stimulating its overall production. This process involves the coupling of fluid flow with material failure, which must account for the interactions of several cracks, both natural and man-made. Many of the questions on the effects these interactions have on the performance of the frac treatments are unanswered. We develop a continuum thermodynamics framework for fluid flow through a damaging porous medium in order to represent some of the processes and interactions that occur during hydraulic fracturing. The model will be capable of simulating both Stokes flow through cracks and Darcy flow through the porous medium. The flow is coupled to the deformation of the bulk solid medium and the evolution of cracks within the material. We utilize a finite deformation framework in order to capture the opening of the fractures, which can have substantial effects on fluid pressure response. For both models, a fully coupled non-linear finite element formulation is constructed. Several benchmark solutions are investigated to validate the expected behavior and accuracy of the method. In addition, a number of interesting problems are investigated in order to demonstrate the ability of the method to respond to various complexities like material anisotropy and the interaction of multiple cracks.

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 --------------------------- 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."