Modeling of Damage, Permeability Changes and Pressure Responses during Excavation of the TSX Tunnel in Granitic Rock at URL, Canada

This paper presents numerical modeling of excavation-induced damage, permeability changes, and fluid-pressure responses during excavation of the TSX tunnel at the underground research laboratory (URL) in Canada. Four different numerical models were applied, using a wide range of approaches to model damage and permeability changes in the excavation disturbed zone (EDZ) around the tunnel. Using in situ calibration of model parameters the modeling could reproduce observed spatial distribution of damage and permeability changes around the tunnel, as a combination of disturbance induced by stress redistribution around the tunnel and by the drill-and-blast operation. The modeling showed that stress-induced permeability increase above the tunnel is a result of micro and macrofracturing under high deviatoric (shear) stress, whereas permeability increases alongside the tunnel as a result of opening of existing microfractures under decreased mean stress. The remaining observed fracturing and permeability changes around the periphery of the tunnel were attributed to damage from the drill-and-blast operation. Moreover, a reasonably good agreement was achieved between simulated and observed excavation-induced pressure responses around the TSX tunnel for 1 year following its excavation. The simulations showed that these pressure responses are caused by poroelastic effects as a result of increasing or decreasing mean stress, with corresponding contraction or expansion of the pore volume. The simulation results for pressure evolution were consistent with previous studies, indicating that the observed pressure responses could be captured in a Biot model using a relatively low Biot-Willis coefficient, {alpha} {approx} 0.2, a porosity of n {approx} 0.007, and a relatively low permeability of k {approx} 2 x 10{sup -22} m{sup 2}, which is consistent with the very tight, unfractured granite at the site

Fundamentals of discrete element methods for rock engineering : theory and applications

This book presents some fundamental concepts behind the basic theories and tools of discrete element methods (DEM), its historical development, and its wide scope of applications in geology, geophysics and rock engineering. This book includes coverage of both explicit and implicit DEM approaches, namely the Distinct Element Methods and Discontinuous Deformation Analysis (DDA) for both rigid and deformable blocks and particle systems, and also the Discrete Fracture Network (DFN) approach for fluid flow and solute transport simulations. The latter is actually also a discrete approach of importance for rock mechanics and rock engineering. In addition, brief introductions to some alternative approaches are also provided, such as percolation theory and Cosserat micromechanics equivalence to particle systems, which often appear hand-in-hand with the DEM in the literature. Fundamentals of the particle mechanics approach using DEM for granular media is also presented

Numerical modelling of jointed rock masses by distinct element method for two- and three-dimensional problems

The mechanical behaviour of a jointed rock mass is strongly, and sometimes dramatically, affected by the behaviour of the discontinuities present in jointed rock mass. In many cases, preferential failures are dominated or defined by the natural discontinuities present in the neighborhood of engineering engineering works. Closed form solutions rarely exist in general problems and numerical methods must therefore be used. The constitutive models for discontinuities, therefore, play an essential part in the successful application of any numerical techniques. In this thesis, two new constitutive models, one twodimensional and one three-dimensional, for the mechanical behaviour of rock discontinuities are developed according to the experimental results obtained from shear tests under cyclic shear sequences. Fifty concrete replicas of natural rock joints are made and tested in different shear directions under different constant normal stresses. The results obtained confirm that the anisotropy in both the angle of friction and shear stiffness are significant properties of rough joints which have been ignored in the past time. In addition, the shear stiffness and friction angle depend on the normal stress. Based on these results, the behaviour of rock joints under two or three-dimensional loading conditions and undergoing cyclic shear sequences was generalized. This generalized behaviour forms the physical background for the development of the new constitutive models. The two-dimensional constitutive model for rock joints is a generalization of Plesha's original model. The theory of non-associated plasticity was used to formulate the model in which both pre- and post-peak shear stress regions are considered, by using empirical laws for workhardening and work-softening. The most basic aspects of the rock discontinuities, for example, the appearance of peak and residual shear stresses during shearing, the increase in the magnitudes of both shear, and normal stresses under constant normal displacement condition, nonlinear dilatancy during shearing under constant normal stress condition, surface roughness degradation and the dependence of stiffness parameters on the normal displacement and normal stress are reflected in the model. The second law of thermodynamics is used to restrict the values of some of the model parameters so that entropy production of the system is non-negative. The three-dimensional model is formulated in the same manner as its two-dimensional counterpart with special interest in the anisotropic nature of both the angle of friction and shear stiffness. Empirical laws for work - hardening, surface degradation, stiffness changes due to normal stress and normal displacement, are all considered. The path dependence of the shear stress components in the shear plane is highlighted. An asperity ellipse and a shear stiffness ellipse are constructed to represent the anisotropy in the friction angle and shear stiffness. The second law of thermodynamics is also used to restrict some model parameters to secure a non-negative entropy production of the system during shearing. The newly developed constitutive models are validated against well known test results published in the literature and the test results obtained by the author's own test results. The predictions from the models concurs well with the test results. The models are implemented into existing distinct element method programs, UDEC and 3DEC, respectively. Three examples of application of the new joint models are presented. The first is a simulation for plate movements in the Earth's crust to investigate the mechanisms of intraplate earthquakes with the new two-dimensional constitutive model. The second is an equilibrium analysis of three-dimensional rock slope with anisotropic friction angle and the third one is a study on sensitivity of stability of underground mining stopes on the anisotropy of friction angle. The new three-dimensional constitutive model is used in the last two examples and a large computational model is used in the third example to test the performance of the new model under complex geometrical and mechanical loading conditions. It is concluded in this thesis that the behaviour of rock joints under cyclic shear tests is more complex than that under monotonic shear tests and contraction becomes important. Under three-dimensional loading conditions, the anisotropy in friction and stiffness properties of rock discontinuities should be considered. The path dependence in the shear plane is significant feature which has not been studied adequately in previous time. In order to deepen our understanding of the mechanical behaviour of rock joints under three-dimensional loading conditions, a truly threedimensional test machine is needed. Recommendations for future research are provided at the end of the thesis.Godkänd; 1990; 20070429 (ysko

Stress-dependent mechanical properties and bounds of Poisson’s ratio for fractured rock masses investigated by a DFN-DEM technique

Supplement title: Proceedings of the ISRM SINOROCK 2004 SymposiumStress dependent mechanical properties and bounds of Poisson’s ratios for fractured rock masses are investigated using the Distinct Element Method (UDEC-BB), based on the geometry constructed by the Discrete Fracture Network approach (DFN-DEM technique). Results on a simple model with one fracture set show that mechanical properties are highly dependent on the magnitudes of stresses, and the Poisson’s ratio can be well above 0.5, the upper limit for the isotropic case. Numerical experiments with ten realistic DFN models suggest that elastic modulus of fractured rock masses increases substantially with the increase of stress magnitudes. A simple empirical equation relating the stress (s) and rock mass elastic modulus (Em) is proposed in the following form, 1/Em=1/Ei+1/(Sm×s), which fitted well with the calculated results. The calculated Poisson’s ratios generally decrease with the increase of stress magnitudes. The Poisson’s ratios obtained from realistic DFN models are also well above 0.5, which suggest that the common practice of assuming the Poisson’s ratio as 0.2 - 0.3 needs to be carefully re-evaluated for fractured rocks.K.-B. Min and L. Jinghttp://www.elsevier.com/wps/find/journaldescription.cws_home/256/description#descriptio

Anisotropy of strength and deformability of fractured rocks

Anisotropy of the strength and deformation behaviors of fractured rock masses is a crucial issue for design and stability assessments of rock engineering structures, due mainly to the non-uniform and non-regular geometries of the fracture systems. However, no adequate efforts have been made to study this issue due to the current practical impossibility of laboratory tests with samples of large volumes containing many fractures, and the difficulty for controlling reliable initial and boundary conditions for large-scale in situ tests. Therefore, a reliable numerical predicting approach for evaluating anisotropy of fractured rock masses is needed. The objective of this study is to systematically investigate anisotropy of strength and deformability of fractured rocks, which has not been conducted in the past, using a numerical modeling method. A series of realistic two-dimensional (2D) discrete fracture network (DFN) models were established based on site investigation data, which were then loaded in different directions, using the code UDEC of discrete element method (DEM), with changing confining pressures. Numerical results show that strength envelopes and elastic deformability parameters of tested numerical models are significantly anisotropic, and vary with changing axial loading and confining pressures. The results indicate that for design and safety assessments of rock engineering projects, the directional variations of strength and deformability of the fractured rock mass concerned must be treated properly with respect to the directions of in situ stresses. Traditional practice for simply positioning axial orientation of tunnels in association with principal stress directions only may not be adequate for safety requirements. Outstanding issues of the present study and suggestions for future study are also presented

Shear enhanced nonlinear flow in rough-walled rock fractures

Nonlinear flow in 3D rough-walled rock fracture models are simulated by solving the Navier-Stokes equations in this paper. The emphasis is on the impacts of shear caused aperture changes (variable apertures and asperity contacts) and flow conditions (inertial term) upon nonlinear flow behaviors in 3D rough-walled rock fractures. In order to compare shear effects, two 3D fracture models, with and without shear process, were established with the identical initial rough-walled surfaces tomography of a realistic rock sample. Five groups of simulations with different inflow boundary conditions of flowrates/Reynolds numbers (Re) were conducted to demonstrate shear enhanced nonlinearity of flow fields and limitations of local cubic law (LCL) approach. The flow results clearly show channeling flow along the preferential fluid paths, transverse flow around the contact spots and eddy flows behind contact spots with increasing Re numbers, which cannot be observed in 2D models. The effective transmissivity of the 3D fracture model was calculated from the modeling results of velocity and pressure fields. The results showed that the effective transmissivity is a function of local apertures with important uncertainties even when Re is small (i.e. Re = 0.4 in this study), thus the validity of the transmissivity evaluation using LCL approach for nonlinear flow in 3D rough-walled rock fractures is questionable. The mechanical effects, i.e. stress and shear caused aperture space changes and asperity contacts should be considered for modeling flow and mass/energy transport processes in rough-walled fractures in 3D.QC 20161010</p

Shear enhanced nonlinear flow in rough-walled rock fractures

Nonlinear flow in 3D rough-walled rock fracture models are simulated by solving the Navier-Stokes equations in this paper. The emphasis is on the impacts of shear caused aperture changes (variable apertures and asperity contacts) and flow conditions (inertial term) upon nonlinear flow behaviors in 3D rough-walled rock fractures. In order to compare shear effects, two 3D fracture models, with and without shear process, were established with the identical initial rough-walled surfaces tomography of a realistic rock sample. Five groups of simulations with different inflow boundary conditions of flowrates/Reynolds numbers (Re) were conducted to demonstrate shear enhanced nonlinearity of flow fields and limitations of local cubic law (LCL) approach. The flow results clearly show channeling flow along the preferential fluid paths, transverse flow around the contact spots and eddy flows behind contact spots with increasing Re numbers, which cannot be observed in 2D models. The effective transmissivity of the 3D fracture model was calculated from the modeling results of velocity and pressure fields. The results showed that the effective transmissivity is a function of local apertures with important uncertainties even when Re is small (i.e. Re = 0.4 in this study), thus the validity of the transmissivity evaluation using LCL approach for nonlinear flow in 3D rough-walled rock fractures is questionable. The mechanical effects, i.e. stress and shear caused aperture space changes and asperity contacts should be considered for modeling flow and mass/energy transport processes in rough-walled fractures in 3D.QC 20161010</p

Numerical determination of the equivalent elastic compliance tensor for fractured rock masses using the distinct element method

The purpose of this paper is to establish a methodology to determine the equivalent elastic properties of fractured rock masses by explicit representations of stochastic fracture systems, and to investigate the conditions for the application of the equivalent continuum approach for representing mechanical behavior of the fractured rock masses. A series of numerical simulations of mechanical deformation of fractured rock masses at different scales were conducted with a large number of realizations of discrete fracture networks (DFN), based on realistic fracture system information and using the two-dimensional distinct element program, UDEC. General theory of anisotropic elasticity was used for describing the macroscopic mechanical behavior of fractured rock masses as equivalent elastic continua. Verification of the methodology for determining the elastic compliance tensor was conducted against closed-form solutions for regularly fractured rock mass, leading to very good agreements. The main advantage of the developed methodology using the distinct element method is that it can consider complex fracture system geometry and various constitutive relations of fractures and rock matrix, and their interactions. Two criteria for the applicability of equivalent continuum approach were adopted from the investigations: (i) the existence of a properly defined REV (representative elementary volume) and (ii) the existence of an elastic compliance tensor. For the problems with in situ conditions studied in this paper, the results show that a REV can be defined and the elastic properties of the fractured rock mass can be represented approximately by the elastic compliance tensor through numerical simulations.http://www.elsevier.com/wps/find/journaldescription.cws_home/256/description#descriptio

Modeling of solute transport in a 3D rough-walled fracture-matrix system

Fluid flow and solute transport in a 3D rough-walled fracture-matrix system was simulated by directly solving the Navier-Stokes equations for fracture flow and solving the transport equation for the whole domain of fracture and matrix with considering matrix diffusion. The rough-walled fracture-matrix model was built from laser-scanned surface tomography of a real rock sample, by considering realistic features of surfaces roughness and asperity contacts. The numerical modeling results were compared with both analytical solutions based on simplified fracture surface geometry and numerical results by particle tracking based on the Reynolds equation. The aim is to investigate impacts of surface roughness on solute transport in natural fracture-matrix systems, and to quantify the uncertainties in application of simplified models. The results show that fracture surface roughness significantly increases heterogeneity of velocity field in the rough-walled fractures, which consequently cause complex transport behavior, especially the dispersive distributions of solute concentration in the fracture and complex concentration profiles in the matrix. Such complex transport behavior caused by surface roughness are important sources of uncertainty that needs to be considered for modeling of solute transport processes in fractured rocks. The presented direct numerical simulations of fluid flow and solute transport serve as efficient numerical experiments that provide reliable results for the analysis of effective transmissivity as well as effective dispersion coefficient in rough-walled fracture-matrix systems. Such analyses are helpful in model verifications, uncertainty quantifications and design of laboratorial experiments.QC 20161010</p