Damage In Brittle Rocks Research Articles

Statistical Assessment of the Effects of Grain-Structure Representation and Micro-Properties on the Behavior of Bonded Block Models for Brittle Rock Damage Prediction

The ability to predict the mechanical behavior of brittle rocks using bonded block models (BBM) depends on the accuracy of the geometrical representation of the grain-structure and the applied micro-properties. This paper evaluates the capabilities of BBMs for predictive purposes using an approach that employs published micro-properties in combination with a Voronoi BBM that properly approximates the real rock grain-structure. The Wausau granite, with Unconfined Compressive Strength (UCS) of 226 MPa and average grain diameter of 2 mm, is used to evaluate the effectiveness of the predictive approach. Four published sets of micro-properties calibrated for granites with similar mineralogy to the Wausau granite are used for the assessment. The effect of grain-structure representation in Voronoi BBMs is analyzed, considering grain shape, grain size and mineral arrangement. A unique contribution of this work is the explicit consideration of the effect of stochastic grain-structure generation on the obtained results. The study results show that the macro-properties of a rock can be closely replicated using the proposed approach. When using this approach, the micro-properties have a greater impact on the realism of the predictions than the specific grain-structure representation. The grain shape and grain size representations have a minor effect on the predictions for cases that do not deviate substantially from the real average grain geometry. However, the stochastic effect introduced by the use of randomly-generated Voronoi grain-structures can be significant, and this effect should be considered in future studies.

An analytical model of multi-stress drops triggered by localized microcrack damage in brittle rocks during progressive failure

Stress drops in stress–strain constitutive curves of intact brittle rocks under high confining pressure have great significance for evaluating the earthquake mechanism and the safety of deep underground engineering. Microcrack growth in intact rock strongly influences the stress drops. However, the theoretical model of microcrack growth-dependent multi-stress drops rarely is proposed in stress–strain curves of intact rocks. In this study, a constitutive model depending on the damage variable relating to microcrack growth and strain increment is proposed to explain the multi-stress drops in stress–strain curves including strain hardening and softening phases of intact rocks. This model is formulated by combining the wing crack growth model, the suggested relationship between axial strain and wing crack growth, and the stepping function of damage relating to axial strain. This stepping function of damage relating to axial strain approximately is used to simulate the developing process of the small individual shear bands caused by the local microcrack accumulation and coalescence. The effects of parameters in the suggested stepping function of damage on the stress–strain curves containing stress drops are discussed. The theoretical model qualitatively explains the experimental phenomena of multi-stress drops in the stress–strain curves, which provides an important implication for evaluating the earthquake mechanism and the safety of deep underground engineering.

Computational framework for analysis of contact-induced damage in brittle rocks

This paper presents a numerical approach for predicting damage in rock materials caused by contact loading. The rock material is modelled using a constitutive description that combines pressure dependent plasticity, for capturing shear deformation under high confining pressure, with an anisotropic damage model for capturing mode I cracking in tension. Material parameters for the model are taken from a recently performed investigation on a granite material. The model has been used to simulate two types of contact loading experiments from the literature, cyclic loading and monotonic loading up to fracture. In order to achieve accurate predictions, the model has been extended to account for small loaded volumes which occur at contact loading. The results show that the main damage mechanism at cyclic loading is crack propagation due to Hertzian stresses whereas in the monotonic experiments sub-surface cracks could initiate. All features measured in the contact loading experiments are captured by the model and hence, the modelling framework is judged to be able to capture contact damage if real stone geometries are studied in FEM.

Initial guidelines for the selection of input parameters for cohesion-weakening-friction-strengthening (CWFS) analysis of excavations in brittle rock

Recent studies on the behaviour of brittle rock under high stress around excavations have found that the use of a cohesion-weakening-friction-strengthening (CWFS) strength criterion in continuum models has provided excellent agreement with observations made in-situ, including fracture zone size, fracture zone shape, and ground displacement magnitudes. Despite continued success in the application of this strength model for brittle rock, the lack of rigorously established guidelines for CWFS model input parameter selection have limited the use of this approach. In this study, a review of published case studies using the CWFS strength models is provided, and parametric relationships are examined based on the most reliable data sets. Each model parameter is considered individually, and guidelines for parameter selection are provided. In addition, the process of numerical back analysis using the CWFS is discussed and a proposed back analysis methodology is outlined. The use of these guidelines, along with the suggested back analysis approach, will allow for an easier and more effective implementation of the CWFS strength model for numerical modelling of future case studies on brittle rock damage around highly stressed excavations.

A TIME-DEPENDENT THERMO-MECHANICAL CREEP MODEL OF ROCK

A coupled thermo-mechanical creep model of brittle rocks under constant temperatures is proposed based on the theory of rock deformation and thermodynamics. In the model, the heterogeneity of the rock is incorporated. Both the maximum tensile stress criterion and Mohr-Coulomb criterion are used to control tensile damage and shear damage in brittle rocks, and finite element formulation is implemented into COMSOL Multiphysics. A series of numerical simulations are performed and the numerical model is validated against experimental data. Numerical simulations show that the proposed model well captures the typical three creep stages, i.e., primary creep, secondary creep, and tertiary creep of rocks under different constant temperatures. Moreover, numerically simulated cumulative AE counts is consistent with the trend in axial strain of rock, and there are clusters of AE counts during the initial primary creep stage and the tertiary creep stage.

3D random Voronoi grain-based models for simulation of brittle rock damage and fabric-guided micro-fracturing

A grain-based distinct element model featuring three-dimensional (3D) Voronoi tessellations (random poly-crystals) is proposed for simulation of crack damage development in brittle rocks. The grain boundaries in poly-crystal structure produced by Voronoi tessellations can represent flaws in intact rock and allow for numerical replication of crack damage progression through initiation and propagation of micro-fractures along grain boundaries. The Voronoi modelling scheme has been used widely in the past for brittle fracture simulation of rock materials. However the difficulty of generating 3D Voronoi models has limited its application to two-dimensional (2D) codes. The proposed approach is implemented in Neper, an open-source engine for generation of 3D Voronoi grains, to generate block geometry files that can be read directly into 3DEC. A series of Unconfined Compressive Strength (UCS) tests are simulated in 3DEC to verify the proposed methodology for 3D simulation of brittle fractures and to investigate the relationship between each micro-parameter and the model's macro-response. The possibility of numerical replication of the classical U-shape strength curve for anisotropic rocks is also investigated in numerical UCS tests by using complex-shaped (elongated) grains that are cemented to one another along their adjoining sides. A micro-parameter calibration procedure is established for 3D Voronoi models for accurate replication of the mechanical behaviour of isotropic and anisotropic (containing a fabric) rocks.

Dynamic Ruptures on a Frictional Interface with Off-Fault Brittle Damage: Feedback Mechanisms and Effects on Slip and Near-Fault Motion

The spontaneous generation of brittle rock damage near and behind the tip of a propagating rupture can produce dynamic feedback mechanisms that modify significantly the rupture properties, seismic radiation, and generated fault zone structure. In this work, we study such feedback mechanisms for single rupture events and their consequences for earthquake physics and various possible observations. This is done through numerical simulations of in-plane dynamic ruptures on a frictional fault with bulk behavior governed by a brittle damage rheology that incorporates reduction of elastic moduli in off-fault yielding regions. The model simulations produce several features that modify key properties of the ruptures, local wave propagation, and fault zone damage. These include (1) dynamic generation of near-fault regions with lower elastic properties, (2) dynamic changes of normal stress on the fault, (3) rupture transition from crack-like to a detached pulse, (4) emergence of a rupture mode consisting of a train of pulses, (5) quasi-periodic modulation of slip rate on the fault, and (6) asymmetric near-fault ground motion with higher amplitude and longer duration on the side with reduced elastic moduli. The results can have significant implications to multiple topics ranging from rupture directivity and local amplification of seismic motion to near-fault tremor-like signals.

A nonlinear creep damage model for brittle rocks based on time-dependent damage

Many experiments conducted under the three-dimensional stress condition reveal that damage of brittle rocks shows obvious deformational and time-dependent effect. Based on triaxial rheological test results, the creep behaviours and creep rupture characteristics of metamorphic volcanic fine conglomerate were investigated. It is found that the test results agree well with numerical curve, and the relationship between creep damage variable and loading time can be fitted by an exponential function. By analysing the tertiary creep, a new nonlinear viscoplasticity model on the basis of creep damage was proposed, and then, the three-dimensional nonlinear creep damage constitutive equations were deduced and validated by tests. Comparisons between numerical predication and test data show that this nonlinear creep damage model is valid and reasonable. Therefore, it can better describe the complete creep phases of the metamorphic volcanic fine conglomerate, which include primary creep, secondary creep and tertiary creep.

A numerical investigation of brittle rock damage model in deep underground openings

The excavation of underground openings generally causes damage to the rock in the vicinity of the openings. The dominant causes of irreversible rock deformations are damage process and plastic flow. Most of the existing elastic–plastic models employed in the analysis and design of rock structures only consider the plastic flow and ignore the full damage process. The common approach used to model the rock failure, does not model the rock realistically and often the important issues such as stiffness degradation, softening, and significant differences in rock response under tensile and compressive loadings are ignored. Therefore, developments of realistic damage models are essential in the design process of rock structures. In this paper, the basic concepts of continuum damage mechanics are outlined. Then, a more clear and accurate definition of the damage function is established. In the definition of rock damage function, many authors considered only the tensile stress condition. Since quasi brittle materials such as rock degrade under tensile and compressive stress fields, separate tensile and compressive damage functions are introduced. The proposed damage functions are formulated in the framework of a damage model which was coded and implemented into a commercial code. Accordingly, the developed algorithm was applied to the simulation of brittle rocks behavior. Using field measurements from the AECL’s (Atomic Energy of Canada Limited) Mine-by Experiment tunnel, the new developed damage model was calibrated and validated for its ability to reproduce the shape and size of excavation damage zone (EDZ) around the Mine-by test tunnel.

Brittle Deformation of Solid and Granular Materials with Applications to Mechanics of Earthquakes and Faults

Crustal fault zones are complex regions of localized deformation with fractured, cataclastic and pulverized rocks having evolving geometries and altered rheological properties from those of the host material. At some level of fracture density (damage) the cohesive matrix of the material is destroyed and the associated volume becomes granular. The occurrence of seismic ruptures, and healing phases in the interseismic periods, continually modify the damage and granularity. This produces evolution of the elasticity, permeability and geometry of the actively deforming regions. The evolution of fault zone structures leads, in turn, to changes in the properties of dynamic earthquake ruptures, seismic radiation, inter- and post-seismic deformation, and local seismicity patterns. Many fundamental aspects of brittle deformation in crustal rocks remain unsolved. Basic examples include: What are the proper metrics to characterize brittle rock damage and the transitions between damaged rock and granular material? What are the main similarities and differences between the dynamics of damaged rocks and granular media? What are the characteristics of nonlinear stress–strain behavior of damaged rocks and how can they be modeled quantitatively? How much slip is localized on main rupture surfaces and how much is distributed in the bulk for various fault environments? The 16 papers in this volume provide recent theoretical and observational perspectives that address the above and related issues. Topics include damage rheology models, high-resolution measurements of nonlinear evolving elasticity, high-resolution experiments on frictional instabilities and dynamic ruptures, theoretical and observational results on different dynamic regimes of sheared solids and granular materials, effects of fluids and roughness on fault zone rheology, seismic radiation near fault kinks, and geological and laboratory characterizations of fault surfaces and damaged rocks.

Postseismic deformation induced by brittle rock damage of aftershocks

Large earthquakes are commonly followed by abundant aftershocks that are densely located around the coseismic rupture zone. Laboratory experiments indicate that “microscopic” brittle rock failures (acoustic emission) are associated collectively with a “macroscopic” damage‐related inelastic relaxation. Utilizing basic relations between local brittle failures and gradual inelastic strain in a viscoelastic damage rheology model, we develop connections between aftershock decay rates and the aftershocks‐induced component of geodetic deformation. The discussed mechanism is relevant for postseismic relaxation produced by sources located within the seismogenic zone, and especially in regions that overlap locations of high aftershocks activity. Assuming the Omori‐Utsu decay rate for aftershocks, we find that the temporal decay of the damage‐related postseismic relaxation follows a generalized power‐law relation with the standard Omori‐Utsu law as a limit case. The results provide a way for estimating the separate contributions to observed postseismic displacements that stem from brittle failures in the seismogenic zone (aftershocks) and other (aseismic) processes. Using the obtained theoretical expectations, we analyze postseismic displacements measured by GPS stations around the North Anatolian fault ∼3 months following the 1999 M7.4 İzmit earthquake. We find that the observed postseismic displacements decay slower than the aftershock seismicity. Based on our theoretical results, we conclude that up to 50% of the measured surface displacements at near‐fault sites can be attributed to aftershock‐induced inelastic deformation in the seismogenic zone. The remainder postseismic deformation can generally be explained by relaxation in the deeper ductile substrate.

Micromechanical modelling of anisotropic damage in brittle rocks and application

The present study deals with the formulation of a new micromechanical model for anisotropic damage in brittle rocks and its numerical implementation and application. The basic idea is to integrate Eshelby solution-based homogenization approaches into the standard thermodynamics framework for the description of inelastic deformation contributed by microcracks; the anisotropic damage is coupled with frictional sliding which occurs on closed cracks. The identification of the micromechanical model requires only six parameters, each with a clear physical meaning. Comparisons of the model's predictions with experimental data are performed on both conventional and true triaxial compression paths, respectively, for two granites. The proposed model is implemented into the finite element software Abaqus. Its application to an underground excavation problem shows that the proposed model is able to describe general responses and damaged zone evolution due to excavation.

Modeling of anisotropic damage and creep deformation in brittle rocks

A new constitutive model is proposed for the description of induced anisotropic damage in brittle rocks. The formulation of the model is based on relevant results from micromechanics consideration. The distribution of microcracks is approximated by a second-order damage tensor. The effective elastic properties of damaged material are derived from the free enthalpy function. The evolution of damage is directly related to the growth of microcracks in different space orientations. The volumetric dilatancy due to sliding crack opening is taken into account. The model is extended to the description of creep deformation in brittle rocks. The time dependent deformation is seen as a consequence of the sub-critical propagation of microcracks due to stress corrosion process. The proposed model is applied to a typical brittle rock, the Lac du Bonnet granite. A general good agreement is obtained between numerical simulations and experimental data.

Modelling of anisotropic damage in brittle rocks under compression dominated stresses

AbstractA new model for describing induced anisotropic damage in brittle rocks is proposed. Although phenomenological, the model is based on physical grounds of micromechanical analysis. Induced damage is represented by a second rank tensor, which is related to the density and orientation of microcracks. Damage evolution is related to the propagation condition of microcracks. The onset of microcrack coalescence leading to softening behaviour is also considered. The effective elastic compliance of the damaged material is obtained from a specific form of Gibbs potential. Irreversible damage‐related strains due to residual opening of microcracks after unloading are also captured. All the model's parameters could be determined from conventional triaxial compression tests. The proposed model is applied to a typical brittle rock. Comparison between test data and numerical simulations shows an overall good agreement. The proposed model is able to describe the main features related to induced microcracks in brittle geomaterials. Copyright © 2002 John Wiley & Sons, Ltd.

Microstructural approach in damage modeling

A microstructural approach is proposed for the modeling of brittle rock damage. The basic idea of this approach is to model, not directly the mechanical response of the rock but the changes in crack geometry. The term `crack geometry' is used in the sense of Oda et al. (cf. Oda, M., Yamabe, T., Kamemura, 1986. A crack tensor and its relation to wave velocity anisotropy in jointed rock masses. Int. J. Rock. Mech. Min. Sci. 23 (6), 387–397). It therefore implies both a crack density and a spatial crack organization. As Kanatani, K. (1984. Stereological determination of structural anisotropy. Int. J. of Eng. Sci. 22, 531–546.) has shown, if the P L stereological parameter is known, the accumulated crack length may be calculated in any direction, which in turn makes it possible to calculate the crack induced deformation for any given stress. Hence, our approach consists in formulating some laboratory-based laws for the evolution of P L as a function of applied stress as well as the criterion for crack initiation and for macroscopic failure. Some of the laboratory tests used to elaborate and validate this approach are described in detail in the accompanying paper. The parameters of the proposed model are calculated for a granite and the results of the running simulations are in good agreement with laboratory tests.

Broadband acoustic emission observations during fracture propagation in rock-like material

This paper is devoted to the study of time dependent damage of brittle rocks. Laboratory investigations, including triaxial tests and fracture mechanics tests, have been conducted on a granite. These tests allowed to determine the main damage related properties of the material, such as damage initiation and evolution, dilatation, induced anisotropy, failure mode and time dependent sub-critical propagation of microcracks. A continuous damage model has been proposed. A tensorial damage variable related to microcrack propagation is used to model anisotropic behaviour of damage. This model can describe stress induced ‘instantaneous’ damage and time dependent sub-critical damage. After the calibration of the model, a application example is given in the field of nuclear waste storage.

Time dependent continuous damage model for deformation and failure of brittle rock

Abstract This paper is devoted to the study of time dependent damage of brittle rocks. Laboratory investigations, including triaxial tests and fracture mechanics tests, have been conducted on a granite. These tests allowed to determine the main damage related properties of the material, such as damage initiation and evolution, dilatation, induced anisotropy, failure mode and time dependent sub-critical propagation of microcracks. A continuous damage model has been proposed. A tensorial damage variable related to microcrack propagation is used to model anisotropic behaviour of damage. This model can describe stress induced ‘instantaneous’ damage and time dependent sub-critical damage. After the calibration of the model, a application example is given in the field of nuclear waste storage.