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The post-peak behaviors of rocks significantly impact safety assessments and structural designs in underground civil engineering. However, accurately quantifying these behaviors remains challenging due to the complex nature of modeling rock shear-cracking processes. This paper focuses on quantifying the post-peak mechanical behaviors of rocks exhibiting type-I, type-II, and mixed fractures within continuum mechanics. Our study introduces a novel approach quasi-state-based peridynamics to facilitate concurrent computation of the force density function and bond stress tensor. The force density function determination involves characterizing deformation within horizontal, vertical, and inclined bonds, adaptive allocation of directional components, and correction for volume loss. Fracture criteria, guided by the bond stress tensor, facilitate crack propagation description, incorporating the maximum tensile stress criterion and Mohr–Coulomb criterion to distinguish between tensile and shear fractures. In addition, a single linear fictitious crack model simulates the gradual weakening behavior of brittle rocks. The analysis employs an improved volume correction factor and volumetric method, validated through various numerical tests and experiments. These include fundamental tests, shear tests on specimens with prefabricated cracks, and uniaxial tests on specimens with three inclined cracks. Results unequivocally demonstrate the method's effectiveness in accurately modeling post-peak fracturing across various fracture types while maintaining high precision and minimizing computational costs. This research establishes a theoretical framework for diverse fracture criteria and fictitious crack models in rock cracking using peridynamics. It serves as a valuable reference for applying bond-based peridynamics in simulating tensile and shear fractures on a rock mass scale, offering a significant contribution to understanding rock behavior at reduced computational expenses. Highlights: Quasi-state-based peridynamics with stress and strains are developed to model the post-peak fracturing process of rocks in compression and shear. Force density and stress tensor are introduced in peridynamics to quantify the mechanical behaviors of brittle rocks during fracturing. Type-I, -II, and the mixed fractures in rocks are simulated at high accuracy and low computing cost. Numerical results agree well with experimental data on different types of rock cracks. [ABSTRACT FROM AUTHOR]

The occurrence of various types of disasters in deep underground engineering is related not only to the strength of the rock mass but also to the crack propagation capacity (CPC) under corresponding stress conditions. The deep-seated rock mass is generally in the stress state of σ1 > σ2 > σ3, and the CPC under differential stress is very important to evaluate the brittle failure of rock. Therefore, based on the deformation characteristics of Baihetan (BHT) basalt under true triaxial compression (TTC), the evaluation index (IP) of the CPC is established, which considers the characteristics of stress-induced deformation anisotropy and the propagation angle of volumetric strain. The evaluation indexes of JP marble, BS granite and BHT basalt under TTC are analysed and compared. When the stress exceeds the crack initiation stress, the evaluation index of the CPC decreases with the increase of σ2, but increases with the increase of σ3, and the effect of σ3 on the CPC index is greater than that of σ2. Under TTC, the CPC of JP marble is the largest, followed by that of BS granite and BHT basalt. The analysis shows that the evaluation index (IP) proposed in this study is also suitable for conventional triaxial compression and uniaxial compression conditions. In addition, the test result shows that there is divisibility between the failure mode and IP under TTC. The relationship between IP and the failure mode of BHT basalt shows that splitting failure occurs when IP < 0.3, that shear failure occurs when IP > 0.4, and mixed failure occurs when IP is between these values. The evaluation index of the CPC proposed in this paper can provide a theoretical reference for evaluating the failure of surrounding rock near the opening boundary of deep underground rock engineering. [ABSTRACT FROM AUTHOR]

Large deformations often occur during and after the construction of deep roadways, particularly in fractured hard rock. With persistent deformation, there may be mechanistically unexplained, repeated failure phenomena—they are difficult problems to analyse and address. One strategy is to analyse the failure characteristics of roadways and internal cracking characteristics of the surrounding rock which can be analysed with a digital borehole televiewer and three-dimensional laser scanning equipment. Here, we used this approach combined with research on geostress, joint information, and mechanical properties of rock to reveal the preliminary large deformation mechanism of deep fractured roadways. Based on a cracking-restraint method for engineering design, a control technique is proposed to prevent and control large deformations. The depth and degree of cracking are considered to design parameters and determine the appropriate installation time of the support system. To test this approach, the proposed control technique was applied to a roadway project more than 700 meters deep. The monitoring results demonstrated that this control strategy effectively restrained the cracking of surrounding rocks, improved the quality index of the rock mass, and reduced surface displacement. In addition, due to the improved deformation capacity of the bolt structure, an anti-deformation and energy-absorbing bolt can bear large deformations, preventing premature bolt failures in mining environments. [ABSTRACT FROM AUTHOR]

Deep rock masses are in true triaxial stress (TTS) fields, and few studies have examined the brittleness evaluation of rock under TTS thus far. In particular, research has not been conducted on the brittleness evaluation index and the effect of TTS. Therefore, based on a summary and analysis of pre-existing brittleness indexes, this paper proposes a brittleness index of rock under TTS that considers both stress-induced anisotropy and energy conversion characteristics during Class I behavior and Class II behavior. Meanwhile, the studied brittleness index is analyzed and verified. The brittleness of rock was found to increase with increasing σ2 while σ3 is constant; when σ2 is constant, the rock brittleness decreases with the increase in σ3. When σ3 is high, the increase in the rock brittleness amplitude with increasing σ2 is large; conversely, when σ3 is low, the amplitude is small. For the same σ3 (σ3 = 5 MPa), the order of brittleness of the three rocks is basalt > granite > marble. Finally, this paper shows that the proposed brittleness index can be applied to conventional triaxial and uniaxial stresses. In addition, under different TTS, a brittleness threshold of σ2/σ3 = 5 was found for the rocks, and when σ2/σ3 < 5, the rock brittleness enters a stress sensitive zone. The research results in this study can provide a relevant basis and guidance for the study of the brittle fracture process and the brittleness of rock under TTS. [ABSTRACT FROM AUTHOR]

True triaxial short-term and long-term tests were conducted on three different types of hard rocks, namely, marble, basalt and granite. During true triaxial long-term creep tests, the crack evolution information was collected by using an acoustic emission system. The micro-structures before and after creep tests were analysed by scanning electron microscopy and polarising microscopy. The time-dependent propagation of cracks in hard rocks is affected by applied stress and the mineral composition. The high axial stress makes the cracks propagate with time development during creep stage. When the axial stress exceeds the damage stress, the AE signals intensity have increased significantly. The damage stress values determined through short-term and long-term tests are different, but the difference is small so that the former can be used efficiently to test the damage stress in terms of long-term strength analysis. Accumulation of extensile cracks induced by high applied axial stress eventually can cause creep failure of hard rocks; however, the time-effect seems to only increase the micro-cracking inside the rock. The ultimate macroscopic failure surface of the rock sample appears to only be affected by the difference between σ2 and σ3. The time-dependent dilatancy of Jinping marble and Baihetan basalt exceeded that of granite specimens. Under creep loading, calcite and pyroxene, which have lower hardness values, are more prone to crack time-dependent expansion than feldspar and quartz, which have higher hardness values. [ABSTRACT FROM AUTHOR]

Rocks with a layered structure (bedding or foliation) usually exhibit different levels of anisotropy in terms of deformation, strength, and failure mode under multiaxial stress conditions. This anisotropy is influenced by the spatial relationship between the internal layered structure and the principal stresses; however, relatively few experimental studies have been conducted due to various limitations, resulting in insufficient knowledge of the failure mechanism of layered rocks. A series of true triaxial compression tests for a gneiss were carried out considering the orientation of schistosity. The results show that the orientation of schistosity has a significant impact on the strength and failure of this gneiss. More specifically, under the same intermediate principal stress σ2, the strength of specimens increases as the angle (ω) between the strike of schistosity and the direction of σ2 increases. The greater the angle ω, the more sensitive the strength varies with σ2. When σ2 is low, the schistosity plane acts as a weak plane to control the failure of the specimen, and the main failure plane is parallel to the schistosity. As σ2 increases, the weakening effect of schistosity decreases, and the influence of σ2 on the failure is enhanced. In this case, the failure of cutting through the rock matrix more commonly occurs, and the failure plane dips toward σ3 and strikes parallel to σ2. [ABSTRACT FROM AUTHOR]

A remotely triggered rockburst is a typical engineering geology disaster that occurs during the excavation of hard rock at depth. Damage in the rock mass naturally exists and will also be induced by the construction of underground excavation. These damages, in turn, influence the occurrence and intensity of a rockburst. However, this problem, which draws significant public attention, remains unsolved. In the present study, the effect of the initial damage on a triggered rockburst of granite is investigated. Rectangular prismatic rock specimens with different initial damage D (0, 0.2, 0.3, 0.4, 0.6, and 0.7) are prepared by using heat-treatment (25, 200, 300, 400, 500, and 600, respectively). The initial damage is determined by the ratio of the P wave velocity of the specimen heat-treated at a specific temperature to that without heat-treatment. Then, remotely triggered rockburst simulations are conducted on the specimens with coupled static-dynamic loads exerted using an improved true-triaxial testing machine. The failure mode, deformation characteristics, fracture features, and kinetic energy of the ejected fragment of the tested specimen are systematically investigated. The experimental results indicate that for a given initial damage, a threshold of static stress exists, and beyond this threshold, a dynamic disturbance can trigger a rockburst. Additionally, it is found that a dynamic disturbance can much more easily induce a triggered rockburst as the level of initial damage increases. However, the kinetic energy of ejected fragments increases to a peak and then decreases as the initial damage increases. The maximum kinetic energy appears at an initial damage D = 0.3. Therefore, another interesting finding is a specific initial damage can induce the most violent triggered rockburst. [ABSTRACT FROM AUTHOR]

5.2 HT ht 13 HT ht Based on Eq. (1), the maximum sin I i SB I b i sb can be obtained when HT ht . 15 HT ht. [Extracted from the article]

Energy principles, which can favorably explain the complete rock failure process, are one of the most reliable analysis approaches in rock mechanics and engineering. In this study, a strain energy approach under true triaxial compression (TTC) is proposed. On this basis, the energy evolution characteristics and variations of different failure behavior types (Class I, Class II and ductile failure) under TTC are analyzed. The variations of the strain energy characteristics of Beishan granite with σ2 and σ3 under TTC are studied. The results indicate that the total strain energy U and the elastic strain energy U e of Beishan granite increase with the increasing σ2 or σ3. The dissipated strain energy U d rapidly increases when the value of ε1/ε1peak is approximately 0.6–0.8. The influence of σ3 on the rock failure mode and energy evolution characteristics is greater than that of σ2. In highly brittle rocks, the tensile cracking of the rock microstructure is dominant, and the rock has a high strain energy storage capacity and a low strain energy dissipation capacity. The cumulative acoustic emission (AE) count rate curve shows the same trend as the total dissipated strain energy U d curve. The research results show that the proposed strain energy analysis method for TTC can explain the macroscopic failure behaviors, microscopic failure mechanism and AE characteristics of Beishan granite under TTC, thereby providing new ideas and methods for investigating the behaviors of deep underground hard rock. [ABSTRACT FROM AUTHOR]

A new, high-efficiency technology for fracturing and breaking rocks is required. Due to various advantages including high efficiency, energy-saving, and having no secondary pollution, the technology of microwave-induced fracturing of hard rock has been considered as a potential method for rock fracturing and breaking. Aiming at the realisation of two engineering applications: microwave-assisted mechanical rock breaking and stress release from rock masses in deep underground engineering works to prevent geological disasters caused by high-stress concentrations such as rockbursts, a novel (open-type) microwave-induced fracturing apparatus (OMWFA) for fracturing hard rocks was developed. On this basis, the two modes of microwave-induced subsurface fracturing and microwave-induced borehole fracturing of hard rocks were proposed. Due to removal of the restraint of the microwave cavity, OMWFA can be used to fracture large-size rock samples and engineering-scale rock masses. Using the apparatus, the fracturing effects of the two fracturing modes on different dimensions of cuboidal basalt samples were investigated. By combining the microwave-induced fracturing apparatus with a press machine to explore the influence of unidirectional stress on the fracturing effect of microwave treatment on basalt. Moreover, field tests were carried out on rock masses encountered in underground engineering works at Baihetan Hydropower Station in Sichuan Province, China, and the fracturing effects were evaluated by applying a digital borehole televiewer and conducting acoustic wave testing. The results show that the apparatus had favourable fracturing effects on the subsurface and borehole samples of basalt. When no stress was applied, the cracks radially expanded from the approximate centre of the radiant surface and unidirectional stress promoted fracturing. The number and depth of cracks increased with prolonged microwave exposure. After microwave treatment, the P-wave velocity of the samples declined, and the longer the microwave exposure, the more significant the reduction in P-wave velocity was. The results of field test reveal that borehole fracturing can exhibit a favourable effect around boreholes. The sound velocity around the borehole and between the boreholes both declined to some extent. Microwave-induced hard rock fracturing offers guiding significance to those exploring and developing new rock breaking and tunnelling methods, and generally enhances construction safety in deep underground engineering works. [ABSTRACT FROM AUTHOR]

• Fully coupled thermo-hydro-mechanical model for hydraulic fracturing. • Fracture propagation in mixed tensile and shear failures for 3D modeling. • Thermally induced secondary fractures for the enhancement of hydraulic stimulation. • Anisotropic model for rock deformation, fluid-heat flow, and thermal expansion. Commercial development of enhanced geothermal systems in low-permeability rocks relies on fracturing treatments to create complex-fracture networks and an appropriate circulation strategy to maintain high flow rates at sufficiently high temperatures. However, it remains challenging to model complex-fracture propagation and heat energy extraction as a whole. This paper develops a fully coupled thermo-hydro-mechanical model to simulate reservoir stimulation and heat production in naturally fractured geothermal reservoirs. The proposed model is validated against a widely used model, TOUGH2, concerning heat sweep in a vertical fracture. This model is then applied to study multi-staged fracturing and geothermal extraction related to a doublet of horizontal wells. The hydro-geomechanical properties are chosen from the Soultz geothermal reservoir at a depth of approximately 3600 m. Numerical results demonstrate that: (1) mixed tensile and shear fracturing can constitute an important stimulation mechanism for naturally fractured geothermal reservoirs; (2) well interlinked, zigzag artificial fractures between injection and production wells readily lead to channeling flow; (3) keeping a segment of horizontal wells open and placing them further apart are beneficial to the formation of sufficiently diffuse flow pathways; (4) increasing well spacing tends to improve thermal performance; however, for the case of a one-stage opening, the improvement of heat sweep efficiency is not significant; and (5) an alternating circulation scheme could achieve superior thermal performance. This study establishes an effective modeling workflow for the design and optimization of naturally fractured geothermal reservoirs, and provides an integrated modeling framework for evaluating recoverable energy potential from geothermal reservoirs. [ABSTRACT FROM AUTHOR]

Microwave energy can be used to assist mechanical rock breakage for civil and mining engineering operations. To assess the industrial applicability of this technology, microwave heating of basalt specimens in a multi-mode cavity (a microwave chamber) at different power levels was followed by conventional mechanical strength and fragmentation effect tests in the laboratory. X-ray diffraction and scanning electron microscopy/energy-dispersive X-ray spectroscopy were used to determine the mineral composition and distribution of the basalt, to aid interpretation of crack propagation patterns and the associated strength reduction mechanism. These analyses demonstrated that cracks mainly occurred around olivine grains, primarily as intergranular cracks between olivine and plagioclase grains and intragranular cracks within olivine grains. Strength reduction during microwave fracturing of basalt is driven by heat from enstatite (a microwave-sensitive mineral) and volumetric expansion of olivine (a thermally expansive mineral). Uniaxial compressive, Brazilian tensile, and point load strengths all decreased with increasing microwave irradiation time at rates that were positively related to the power level. For a given power level, mechanical strength reduction can be estimated from linear relationships with irradiation time. On the other hand, a power function best described burst time (the irradiation time at which the specimen burst into fragments) vs. power level (for a given specimen size) and burst time vs. specimen size (for a given power level) relationships. Microwave-induced hard rock fracturing can be an integral part of new methods for rock breakage and tunnel excavation. [ABSTRACT FROM AUTHOR]

• Underground engineering instability is associated with rock damage evolution. • The progressive fracturing in intact and jointed marble is studied. • The irreversible strains and dissipated energy are computed as damage variables. • The influence of the intermediate principle stress and joint are quantified. Rock masses in underground engineering, such as mining and deep tunnelling engineering, are often repeatedly loaded and unloaded. Here, a series of true triaxial multi-level single cyclic loading tests (σ 1 > σ 2 > σ 3) were carried out on intact and jointed marble (50 × 50 × 100 mm3) to investigate the influence of the stress state and the absence or presence of a joint on the progressive damage process. The test results show that rock damage is directional and anisotropic. The irreversible strains in the σ 1 and σ 3 directions change linearly with cumulative damage, whereas the irreversible strains in the σ 2 direction decrease nonlinearly. The dissipated energy is appropriately linearly related to the equivalent irreversible strains. The damage variables based on the irreversible strains and dissipated energy are closely correlated, as determined by their similar fitted parameters. The stress state (σ 2 and σ 3), the absence or presence of a joint and the brittleness play a vital role in the rock damage evolution. More specifically, the parameter a has a logarithmic relationship with σ 3 and a linear relationship with σ 2. The relationship between the parameter a and the joint dip angle β can be fitted by a Gaussian distribution. In addition, the fitted parameter a decreases with increasing brittleness. [ABSTRACT FROM AUTHOR]

The purpose of this ISRM Suggested Method is to introduce a guideline on determining deformation and failure characteristics of rocks subjected to true triaxial compression on different stress path. The true triaxial testing apparatus was reviewed by means of the function and engineering application. Some key techniques, such as stress and strain measurements, and reduction of end effect between specimen and metal platens, preventing metal platens interference, were stated and suggested in detail. Methodology of specimen processing, specimen shape, and testing procedure are characterized. There is an explanation of the experimental data processing on stress–strain curves, strength, and fracture mode. [ABSTRACT FROM AUTHOR]

To investigate the deformation and failure mechanism of rock influenced by initial stress and unloading rates, this study presents minimum principal stress unloading tests of Jinping marble under true triaxial compression conditions under various initial stresses and unloading rates based on the in situ stresses measured in the China Jinping Underground Laboratory Phase II (CJPL-II). The effects of initial stresses and unloading rates on the bearing capacity and the deformation and failure characteristics of Jinping marble were analysed. The relationship between the strains in the three principal stress directions and the unloading extent of σ 3 is defined using parameters such as the strain-unloading extent ratio and the unloading strain rate. With an increase in the initial σ 1 , the increase in strain-unloading extent ratio and unloading strain rate changed from linear to exponential earlier, and sample failure occurred with a smaller unloading extent. Meanwhile, the number of acoustic emission rings and the amount of cumulative energy increased, and the sample failure changed from tensile failure to a mixture of tensile and shear failure that showed more transgranular cracks in the microscopic images. With an increase in the initial σ 2 or σ 3 , the overall trend of the failure characteristics was similar to that with an increase in the initial σ 1 , but the sample failed with a larger unloading extent, and the increase in strain-unloading extent ratio and unloading strain rate changed from linear to exponential later. The influence of unloading strain rate shows that as unloading strain rate increased, the sample failed with a larger unloading extent and changed from a mixture of tensile and shear to tensile failure, and more transgranular cracks were observed in the microscopic images. • σ 3 unloading tests with different unloading rates and initial stress levels under true triaxial stresses were carried out. • The bearing capacity, deformation process, and failure mode of Jinping marble under σ 3 unloading condition were examined. • The relationships between strains along principal stress directions and unloading extent of σ 3 (Δσ 3) were established. • Failure mechanisms of Jinping marble were identified based on AE data and SEM pictures of fractures. [ABSTRACT FROM AUTHOR]

Abstract A weak interlayer zone (WIZ) is a rock mass system with poor mechanical properties, large-scale random distribution, water softening, causing an adverse effect on the safety of the construction and project progress. To investigate the fracture process and the mechanism of rock masses with WIZs in the intersecting chambers during the excavation process, in situ microseismic (MS) monitoring was carried out in the underground powerhouse on the right bank of the Baihetan Hydropower Station, China. During the monitoring, the spatio-temporal evolution process of the microseismicity of the rock masses around the intersecting chambers was obtained during the excavation unloading of multiple working faces. The spatial evolution of MS events illustrates the dynamic progressive characteristics of MS activities as they propagate and accumulate along the WIZ and finally form a cluster zone. The fracture mechanism of moment tensor inversion reveals the distribution and evolution of MS events with respect to different fracture types: Tensile fracture events are distributed near the free surface while non-tensile fracture events are far from the free surface. Finally, the study proposes support measures restraining fracture development in surrounding rock masses with WIZ. The effectiveness of reinforced support measures is verified by MS events and the deformation of surrounding rocks. The results of the study are particularly valuable for the stability analysis, excavation, and support optimization of similar engineering studies. Highlights • In situ microseismic (MS) monitoring is carried out in Baihetan Hydropower Station, China. • The spatio-temporal evolution process of MS events is obtained. • The moment tensor inversion is used to analyze the fracture mechanism of rock mass. • The study proposes support measures restraining fracture development in surrounding rock masses with weak interlayer zone. [ABSTRACT FROM AUTHOR]

Zonal disintegration refers to the phenomenon whereby fractured zones and intact zones appear alternately in surrounding hard rocks under high stress conditions. In this study, zonal disintegration within hard surrounding rocks of deep tunnels at the China Jinping Underground Laboratory Phase II (CJPL-II) was observed by using a digital borehole televiewer in pre-drilled boreholes. The results revealed that fractured zones within intact high-strength marbles were small and exhibited a higher degree of fracturing, whereas fractured zones within low-strength, low-integrity, marbles showed fewer, yet larger fractures. An evaluation method based on rock mass integrity index using digital borehole televiewer data (RMIBT) has been proposed for the analysis of zonal disintegration process in the deep hard rocks surrounding the tunnels. By using the method we were able to quantify the initiation and evolution of fractures during zonal disintegration. The formation mechanism of the second and third fractured zones induced by the existing fractures was further investigated using numerical analysis. The data provide an insight into the evolution of failures in, and a basis for support design and stability control of, deep engineering works in hard rock. [ABSTRACT FROM AUTHOR]

Large-scale columnar jointed basalt (CJB) developments have had serious adverse effects on the stability of the project in progress to create the diversion tunnels at the Baihetan hydropower station in China. An in situ microseismic (MS) monitoring experiment was carried out to help understand the fracturing process in the CJB rock mass as a result of tunnel excavation. MS monitoring performance (accuracy of location estimation and system sensitivity) is analyzed first. Then, the spatiotemporal evolution of the MS activity associated with the Baihetan CJB rock mass fractures along the tunnel axis and at the tunnel sidewalls during the entire excavation unloading process is obtained. Finally, the forms and opportunities to deploy appropriate support are suggested according to the characteristics of the CJB microseismicity. Meanwhile, the MS monitoring methods required for CJB or jointed hard rock engineering (e.g. sensor types, sensor spacing, sensor array forms, system protection, and selection of analysis regions) resulting from this exploration experiment are summarized. [ABSTRACT FROM AUTHOR]

Layered rock masses exhibit significant anisotropy in both the deformability and strength. Properties of this rock mass are largely affected by its bedding structure and also by the stress state change. For the purpose of characterizing these salient features using the equivalent continuum concept, an enhanced model is proposed in this paper based on the ubiquitous-joint model. In the enhanced model, the intact bedded rock is assumed to behave as a transversely isotropic elastic body. A modified anisotropic strength criterion is adopted to describe the direction dependence of the strength of intact bedded rock. In addition, stress-sensitive parameters are utilized for both the intact rock and bedding plane, among which the dilation angle and strength parameters of intact rock are influenced by confining pressure and loading history, whereas the stiffnesses of bedding planes are closely related to the current normal stress. The effect of layer thickness on the mechanical behavior of rock mass is reflected by continuously updating the global stiffness matrix after failure of bedding plane, and by conditions for conducting bedding plane related calculations determined by the relative scales between element size and layer thickness. Preliminary validation of this model is conducted by comparing with the closed-form solutions and with laboratory tests. Generally good agreements can be achieved between numerical simulations and theoretical/experimental results, which indicate that applicability of the enhanced model on underground engineering issues related to layered rock mass is promising. [ABSTRACT FROM AUTHOR]

In the process of underground engineering excavation, the adjustment of the stress field includes not only the magnitude of stress but also the direction of stress. The failure characteristics of Portuguese granite caused by interchange of the σ 2 and σ 1 directions are studied using a true triaxial testing system to investigate the effects of the interchange of principal stress directions on the failure characteristics of rock. After the interchange of the σ 2 and σ 1 directions, the bearing capacity of the rock increases, the anisotropic characteristics of deformation and fracture are interchanged, the macroscopic failure surface is deflected, and the brittleness of the rock is enhanced. When the rock failure degree increases upon the interchange of the σ 2 and σ 1 directions, the amplitude of the rock bearing capacity increases, the deformation difference decreases, and the number of deflection failure surfaces decreases. Based on the anisotropic characteristics of true three-dimensional stress-induced fractures, the reason for the change in failure mode induced by the interchange between the σ 2 and σ 1 directions is explained. By measuring acoustic emission parameters and performing scanning electron microscopy (SEM) observations, the tensile and shear fracture mechanism and fracture mode with interchange of the σ 2 and σ 1 directions are investigated. The effect of stress rotation on the rock strength and the reason for the change in the failure mode of deep hard surrounding rock excavated in underground engineering projects are discussed. [ABSTRACT FROM AUTHOR]

Excavation-induced unloading fractures in the rock mass can easily cause rock engineering structural failure under high stress. This research work investigated the unloading fracture characteristics of the protective layer of the rock bench in Shuangjiangkou underground powerhouse in detail, thereby revealing the unloading fracture mechanisms via numerical simulation and true triaxial unloading tests, and proposed an optimal method for protective layer excavation. The study found that unloading cracking failure in the rock mass is asymmetric in Shuangjiangkou underground powerhouse, with the fracturing degree of rock mass on the downstream protective layer being greater than that on the upstream side. The dip angle of the unloading fracture plane in the downstream protective layer increased with the aspect ratio (k) of the protective layer and gradually coincided with the diagonal of the protective layer. The stress concentration in the downstream protective layer was caused by the tectonic stress, the stress changed in the form of multistep loading σ 1 and unloading σ 3 during layered excavation. Tensile-shear unloading cracks were formed in the rock under the excavation stress path, becoming steeper and denser, and gradually parallel to σ 1 as the unloading amount of σ 3 increased. As k increases, the σ 1 in the protective layer becomes steeper, causing the unloading fracture plane to steepen and eventually coincided with the diagonal of the protective layer. A formula for designing the protective layer width was proposed based on the relationship of the dip angle of the fracture plane with k. The findings lend themselves to implications to engineering geology in that engineers should consider the asymmetric failure characteristics of the tunnel caused by high tectonic stress, and formulate asymmetric excavation and support schemes during the construction process of rock benches or other similar structures. [Display omitted] • Unloading cracking characteristics of rockmass were investigated under multi-face unloading. • Tensile-shear unloading cracks were formed roughly parallel to σ 1 in the rock under the excavation stress path. • Dip angle of the fracture plane and σ 1 increase in aspect ratio of rockmass. • An optimal design of the rock engineering structure with multi-free faces were proposed. [ABSTRACT FROM AUTHOR]

We investigated the statistical characteristics and probability distribution of the mechanical parameters of natural rock using triaxial compression tests. Twenty cores of Jinping marble were tested under each different levels of confining stress (i.e., 5, 10, 20, 30, and 40 MPa). From these full stress-strain data, we summarized the numerical characteristics and determined the probability distribution form of several important mechanical parameters, including deformational parameters, characteristic strength, characteristic strains, and failure angle. The statistical proofs relating to the mechanical parameters of rock presented new information about the marble's probabilistic distribution characteristics. The normal and log-normal distributions were appropriate for describing random strengths of rock; the coefficients of variation of the peak strengths had no relationship to the confining stress; the only acceptable random distribution for both Young's elastic modulus and Poisson's ratio was the log-normal function; and the cohesive strength had a different probability distribution pattern than the frictional angle. The triaxial tests and statistical analysis also provided experimental evidence for deciding the minimum reliable number of experimental sample and for picking appropriate parameter distributions to use in reliability calculations for rock engineering. [ABSTRACT FROM AUTHOR]

The stability of high sidewalls of large-span underground powerhouses will be a major issue when the cavern axis forms a small angle to the steeply inclined rock strata. A synthetic test scheme composed of four experiments was performed on two rocks with clear bedding features, aiming at better understanding the otherwise confusing deformation behavior and failure patterns of bedded rocks. Bedding orientations with respect to stress direction impose significant effect on the mechanical behavior of bedded rocks. Excessive tensile strain is observed in the direction perpendicular to bedding or across material interface in uniaxial test. Under low confinement in true triaxial test, the σ angle mainly influences the deformation and fracture propagation but not strength. Deformation dependence of bedded rocks on two stress paths is thoroughly investigated. Confining pressure unloading leads to pronounced volumetric dilation accompanied by moduli drop. Samples with large bedding angle exhibit more obvious lateral dilation. Post-peak degradation of deformation parameters is confirmed by cyclic test. Fractures entirely or partly along bedding occurred under different stress states depend not only on the bonding strength between beds but on the anisotropic deformation field. Based on these observations, it is deduced that the possible reasons for the failure of steeply dipping rock mass after excavation are a combination of (1) the pervasive bedding planes, (2) the more pronounced deformation normal to bedding, and (3) the excavation-induced unloading of confinement. [ABSTRACT FROM AUTHOR]

High stress induced by excavation disturbance in deep hard rock engineering can cause rockburst accidents. Microwave-induced borehole fracturing of hard rock is a promising technique for preventing rockbursts, the principle of which is to reduce energy and stress concentration levels in rock mass through microwave heating. The characteristics and mechanism of microwave-induced borehole fracturing of hard rock under different true triaxial stresses were experimentally investigated. After microwave-induced borehole fracturing under different σ 1 and σ 2 conditions, a complex crack network dominated by tensile cracks was generated in the rock specimen, which is consistent with the results obtained by AF and RA. According to the P-wave velocity before and after the test, the degree of thermal fracture is positively linearly correlated with σ 1 and σ 2 as a whole, and has good consistency with the length and number of thermal cracks. The results show that the technique will have better applicability and higher fracturing efficiency in high-stress areas. The thermal fracture process of basalt specimens under different σ 1 and σ 2 conditions is similar, which can be divided into a silent period, quiet period, dense period, and persistent period. In addition, thermal fracture exerts a significant threshold temperature effect, and fracture rate increases rapidly when the temperature reaches 150–192 °C (average about 172 °C). The relationship between thermal fracture and stress provides guidance for parameter design. • Microwave-induced borehole fracturing of hard rock is a promising technique for preventing rockbursts. • Microwave-induced borehole fracturing tests are conducted under different true triaxial stress. • The characteristics and mechanism of microwave-induced borehole fracturing under different σ 1 and σ 2 conditions are investigated. • Microwave-induced borehole fracturing process is investigated by AE technique. [ABSTRACT FROM AUTHOR]

Measurements indicate that the development of cracking is a key feature relating to the strength and collapse of a columnar jointed rock mass. In this context, a new support design method utilising rock cracking indices for columnar jointed rock mass under high stress is proposed to restrain the development of cracking in the surrounding rock mass. The method involves limiting the cracking evolution of the surrounding rock mass by designing the appropriate parameters and time of installation of the support system. Two indices are suggested: the allowable depth of the excavation damaged zone (EDZ); and the allowable damage extent of the rock mass in the EDZ. The method involves limiting the evolution of cracking in the surrounding rock mass by designing the parameters and time of installation of the support system. The support system should have a suitable stiffness and installation time so as to restrain the evolution of the depth and damage extent of the EDZ within the surrounding rock. Therefore, the depth and damage extent of the EDZ, as well as the axial stress in the anchor bolts, are calculated at different distances between the support location and the tunnel working face to find the appropriate stiffness and installation time of the support system. The method has been successfully adopted to determine the thickness of shotcrete, the arrangement and installation time of rockbolts, and other parameters, for five large diversion tunnels at the Baihetan hydropower station, China, which were excavated in columnar jointed rock masses. [ABSTRACT FROM AUTHOR]

The article discusses the method on the measurement of rock fractures observation through borehole digital optical televiewer. It considers the importance of fractures on rock masses over the study of rock mechanics and rock engineering issues such as rock mass geometry, analysis of the Excavation Damaged Zone (EDZ), and understanding rock mass behavior and response to excavation. It provides the feature of a digital borehole camera which records a continuous colour of the borehole wall.

Abstract: Rockbursts occurred frequently during the excavation of several parallel tunnels in the Jinping II hydropower station under a maximum overburden of 2525m over an average length of 17.5km. In order to investigate the nucleation and evolution mechanism of rockbursts, a comprehensive monitoring campaign consisting of a digital borehole camera, cross-hole acoustic apparatus, and sliding micrometer was undertaken for in situ measurements in two specially excavated test tunnels B and F. This paper presents the comprehensive monitoring methods applied, and results of numerical analysis applied to a typical rockburst that fortuitously occurred during the testing period. Precursory characteristics preceding rockbursts are: (a) abundant crack initiation, propagation and coalescence, (b) deformation of surrounding rock mass involving an accelerated deformation stage, quiescence stage and reaccelerated deformation stage, and (c) decrease of the characteristic elastic wave velocity of the rock mass. The nucleation and evolution of rockbursts discussed consist of four stages: a) stress adjustment, b) energy accumulation, c) crack initiation, propagation and coalescence, and d) fractured rock collapse and ejection. The results provide a direct case history to assist the prediction and support of rockburst disasters, and contribute to field excavation of deeply buried tunnels. [Copyright &y& Elsevier]

The paper aims at a numerical study of strength and deformation behaviors of rocks under different loading conditions in uniaxial compression with an elasto-plastic cellular automaton (EPCA2D) code. Two loading conditions, i.e. with and without considering frictions between loading platens and rock specimen's ends, are used in the failure processes of heterogeneous rocks. Rock specimens are assumed to be the same heterogeneity, i.e. the specimens with different sizes have the same probability of containing flaws. Under this condition, it is concluded that the strength and deformation behaviors of rocks are influenced by the heterogeneity a little. The mismatch of elastic properties of the platen and the rock in influencing the stress distribution at the ends of the specimen is the dominant cause for the so-called strength and deformation size effects, which in turn affects the final failure patterns of rocks. [ABSTRACT FROM AUTHOR]

The accurate picking of waveform arrival times is fundamental to microseismic (MS) monitoring technology and is related to the location accuracy of MS sources. An urgent requirement is an automatic and accurate method for picking up the MS waveform arrival times to realize automatic MS monitoring. In this work, a new arrival time picker has been designed to pick up the P- and S-wave arrival times of MS waveform automatically in tunnels. A control model for the arrival time quality of the S-wave (ATQS) is proposed to automatically identify waveforms with high ATQS values, and the S-wave arrival time of the waveforms is subsequently used in MS source location, to improve the automatic location accuracy. Many rock fracturing waveforms are used to construct a sample database. The experimental and engineering applications show that the P- and S-wave arrival time accuracies are 94.39% and 91.59%, respectively. The automatic location error of a rockburst event is reduced from 42.2 m to 15.3 m. The arrival time picker proposed in this paper demonstrates high accuracy, which ensures the automatic location accuracy of MS sources and lays a foundation for the realization of automatic MS monitoring. [ABSTRACT FROM AUTHOR]

The conventional (σ 1 > σ 2 = σ 3) multi-step creep test and true triaxial (σ 1 > σ 2 > σ 3) multi-step creep test of Jinping marble with rectangular shape were conducted. In this way, the effects of σ 1 , σ 2 , σ 3 and time on creep behaviour were compared and analysed. Unlike conventional creep tests, Jinping marble showed differential creep deformation and failure characteristics in σ 2 and σ 3 -directions under true triaxial stress. The crack time-dependent evolution was-directional, and the crack tip growth was nearly parallel to the σ 1 -direction with high stress and opened along the σ 2 and σ 3 -directions with low stress. Moreover, when σ 2 > σ 3 , the crack growth in the σ 2 -direction was inhibited, and the crack evolution mainly occurred along the σ 3 -direction. This difference eventually led to the macroscopic failure plane of Jinping marble generally acting parallel to the σ 2 -direction and along the σ 3 -direction. The larger the value of σ 2 , the steeper the macroscopic failure surface, and the failure mode of the rock samples changed from shear to near-splitting failure: however, increasing σ 2 can only cause closure of initial cracks opening along the σ 2 -direction, but did not change the number of initial cracks opening along the σ 3 -direction. The experimental data also showed that the differential creep deformation in the σ 2 and σ 3 -directions caused by true triaxial stress did not change with time and σ 1 , but was only affected by σ 2 and σ 3. The differential creep deformation in σ 2 and σ 3 -directions can be described by the formula DI = a (1-exp(b ((σ 2 -σ 3)/σ 3))). [ABSTRACT FROM AUTHOR]

For the in situ surrounding rocks of underground excavations, the radial stress corresponding to the minimum principal stress σ 3 varies with increasing distance away from the excavated boundary. To characterize the rock failure along the radial direction of an excavation, true triaxial compression tests with different σ 3 values (0.5, 5, 10, 15, 20, 25, and 30 MPa) were performed. The characteristic stresses (including the crack initiation stress σ i , crack damage stress σ d , and peak stress σ s) and failure mode of the tested specimen under different σ 3 conditions were systematically investigated. The experimental results indicate that with increasing σ 3 , the characteristic stresses increase monotonically and continuously. The increasing rate of the characteristic stresses with σ 3 ranging from 0 to 10 MPa is higher than that with σ 3 ranging from 10 to 30 MPa, indicating that low σ 3 impose a greater effect on the characteristic stresses than high σ 3. In addition, the failure mode of the tested specimen changes from tensile-shear failure mode I (with vertical tensile cracks and oblique tensile-shear cracks developing along the σ 2 direction) to tensile-shear failure mode II (with oblique tensile-shear cracks developing only along the σ 2 direction) to tensile-shear failure mode III (with oblique tensile-shear cracks along both σ 2 and σ 3 directions) as σ 3 increases. Then, the failure characteristic of the surrounding rocks of the underground excavation was characterized based on the obtained experimental results. When maximum radial stress σ r encountered near the excavated boundary is much smaller than the axis stress σ a , the surrounding rocks will exhibit a "Ternary failure characteristic", i.e., with an increase in the distance from the excavated boundary along the radial direction, the failure mode of the surrounding rocks after excavation changes from tensile/splitting failure mode to tensile-shear failure mode I and then to tensile-shear failure mode II. When the maximum σ r encountered near the excavated boundary approximates the original σ a , the surrounding rock masses will exhibit a "Quaternary failure characteristic". Specifically, the corresponding failure mode along the radial stress direction away from the excavated boundary changes from tensile failure mode to tensile-shear failure mode I then to tensile-shear failure mode II and finally to tensile-shear failure mode III. • True triaxial tests with different σ 3 are conducted. • Rock strength under different σ 3 condition are investigated • The influence of σ 3 on the rock failure mode is studied. • Rock failure near the boundary of underground excavations is characterzied. [ABSTRACT FROM AUTHOR]

The energy evolution processes and mechanisms between three hard rocks are studied using a strain energy analysis method under true triaxial compression (TTC). Using Beishan granite as an example, the change in the energy storage limit U max e , strain energy ratio and strain energy conversion rate for different σ 2 and σ 3 values is investigated. The research results indicate that within the scope of this study, the energy evolution processes and characteristics are largely similar at pre-peak, and notably different at post-peak. The energy storage limit U max e of the Beishan granite indicates an approximately slow increase with an increasing σ 2 , whereas its mean value shows a favorably linear increase with an increasing σ 3. The elastic strain energy ratio shows a reverse relationship with that of the dissipated strain energy during rock failure. For an increasing σ 2 , the conversion rates of the total elastic strain energy U e and the total dissipated strain energy U d of the Beishan granite demonstrate a poor relationship at both pre- and post-peak. For an increasing σ 3 , the mean values indicate a favorable linear change at both pre- and post-peak. The total strain energy and total elastic energy of the different hard rocks increase with increasing σ 2 or σ 3 values at pre-peak, whereas the total dissipated strain energy increases with an increasing σ 3 and decreases with an increasing σ 2 at pre-peak. When the external conditions are not considered, the difference in the elastic and plastic deformation capacities, which influence the energy difference in different rocks, is influenced by the mineral compositions and microstructures of the different rocks. • The strain energy evolution process and difference of three hard rocks are studied under true triaxial compression. • The change of energy storage limit U max e , strain energy ratio and strain energy conversion rate with different σ 2 and σ 3 are investigated. • The energy evolution mechanism under different σ 2 and σ 3 levels and the energy difference of different hard rocks are analyzed [ABSTRACT FROM AUTHOR]

With excavation during deep underground engineering, the rock mass near the sidewall changes from ductile behavior to brittle behavior. However, the ductility of the rock mass at a certain distance from the sidewall may increase due to the change in stress. Over time, the failure mechanism of the rock mass is not necessarily consistent. The aim of this study is to obtain a better understanding of creep mechanisms under 3-D stress states. To achieve this goal, six brittle creep and two ductile creep experiments on Jinping marble were conducted under true triaxial stress conditions (σ 1 > σ 2 ≥ σ 3). The test results show that creep deformation of rock decreases with increasing intermediate principal stress. Many micro-cracks were observed by scanning electron microscopy in the samples failed under the ductile creep. However, brittle creep and ductile creep present different crack expansion modes in microscopic terms, resulting in significant differences in macroscopic deformation behavior. The steady creep rate increases slowly with increasing σ 1 - σ 3 when brittle creep occurs. Meanwhile, when the stress reaches a certain value during ductile creep, the steady creep rate suddenly increases exponentially from 10−6 h−1 to 10−5 h−1. From the test results, we can deduce that the true triaxial stress and time effects play key roles in the creep behavior of rock masses in deep engineering projects. • Crack propagation modes are different during ductile and brittle creep. • Crack time-dependent expansion in microscopic terms, resulting in differences in macroscopic deformation. • The σ 2 can inhibit creep deformation. [ABSTRACT FROM AUTHOR]

Investigation of the strength, deformation and constitutive model of rocks under true three-dimensional stress is of much significance to scientifically and accurately predict the integrity of underground gas storage caprock. In general the intermediate principal stress and the minimum principal stress to which the caprock is subjected are not equal, and there is uncertainty in the in-situ stress test. In this study, the siltstone is taken from the caprock of the Hutubi gas storage in Xinjiang, with a buried depth of 3600 m. A series of true triaxial compression tests on siltstones were carried out using a true triaxial testing system for rocks, and the strength and deformation characteristics of siltstones under different intermediate principal stress conditions were studied. The elastoplastic constitutive model of rocks has been established: in the plastic part, the Mogi-Coulomb yield criterion has been modified so as to obtain the triple-mean-normal-stress yield function and triple-mean-normal-stress potential function suitable for rocks under the true three-dimensional stress state. The hardening law has been determined by fitting the relationship between the plastic deviatoric shear strain and the deviatoric stress in the true triaxial compression test. The constitutive model and the test data of siltstones have been verified by fitting. Finally, the influence of true triaxial stress on the permeability and breakthrough pressure of caprock siltstones has been discussed. The result indicates that with the increase of intermediate principal stress within a certain range, the peak strength of siltstones will also increase, and deformation in the direction of the intermediate principal stress will be restrained. Compared with the potential functions in other constitutive models, the triple-mean-normal-stress potential function proposed in this paper can accurately describe the plastic flow direction of siltstones under the true three-dimensional stress state. And the hardening law truly reflects the plastic deformation of siltstone specimens under different stress states during the loading process. The calculation result of the constitutive model is in good agreement with the test result. Under the true three-dimensional stress, the permeability of siltstones shows anisotropy. With the increase of the intermediate principal stress, the minimum value of siltstone permeability decreased by 8%, and the maximum value of breakthrough pressure increased by 4.3%. • The deformation and strength of rocks under the true three-dimensional stress are studied. • The triple-mean-normal-stress potential function proposed can truly describe the plastic flow direction. • A constitutive model emphasis on plastic potential and hardening law of rocks is established and verified. • The anisotropy of rock permeability is confirmed under the true three-dimensional stress. [ABSTRACT FROM AUTHOR]

Abstract: A rock discontinuous cellular automaton (RDCA) was developed for modeling rock fracturing processes from continuous to discontinuous deformation under mechanical loading. RDCA is an integration of the following basic concepts: (1) representation of heterogeneity and strong discontinuity of rock material; (2) moving crack tracking with level set method; (3) the cellular automaton updating rule; (4) rock yield criteria and crack growth laws, etc. This model uses a local, “bottom–up” cellular automaton rule set and state input from neighboring cells to update the state of each cell in a stepped manner, avoiding the need to develop and solve large scale linear equations and the complexity therein. RDCA has the ability to simulate the non-linear and discontinuous deformation behaviors such as plastic yielding, crack initiation, propagation and coalescence etc., in the fracturing process of rocks. The theoretical background and numerical implementation of RDCA are introduced, and the associated numerical code is compiled in the C++ environment. Problems involving a central single crack, edge single crack propagation and three-point bending tests were numerically studied, and the results were compared with the analytical and experimental results to demonstrate the robustness of the method. [Copyright &y& Elsevier]

Both coal and uranium resources are found in the Dongsheng area which is located in the northern part of Ordos Basin, China with the coal seam below the uranium deposit. In this paper, we attempt to study the feasibility of co-exploitation of the coal seam and the uranium deposit. The permeability evolution in strata around the coal seam are selected as the key parameter indexing the separate and safe concurrent recovery of two deposits and a novel strain-dependent permeability model is proposed covering the full deformation range of rock. The proposed model is first verified with experimental data with good fitting of the results. Then an upscaled numerical model is established considering the geology conditions of Dongsheng area. This is implemented using COMSOL Multiphysics; and the interface of COMSOL with MATLAB is used to study the damage to the rock mass. We show that (a) compared with the stress-dependent permeability model, the strain-dependent permeability model proposed in this work has the advantage that each strain value is associated with a unique permeability value; (b) The feasibility of co-exploitation of the coal seam and the uranium deposit depends on the relative distance between two resources. When the caved and fractured zone encroaches on the uranium deposit the coal seam should be abandoned. Conversely, when the uranium deposit lays in the constrained zone, the recovery of the coal seam would benefit recovery of the uranium deposit; (c) The feasibility of the co-recovery of the two resources can be optimized by the choice of mining approach. The top-caving mining approach and room-and-pillar mining approach can reduce the height of the caved and fractured zones and make the co-exploitation of the uranium and coal feasible. This work provides a new approach to investigate the feasibility of co-exploitation of uranium and coal. [ABSTRACT FROM AUTHOR]

• An unconventional CA scheme is used to solve excavation induced dynamic response in rock mass. • A dynamic 3D elasto-plastic cellular automaton code (EPCA3D) is developed. • The Den Iseger algorithm is introduced to validate the numerical method. • The factors affecting dynamic responses in rock mass are investigated. The problem of transient excavation-induced dynamic response in rock mass is discretized on both spatial and temporal scales and is solved by using the cellular automaton (CA) technique and the Newmark scheme, respectively. Using this approach, a dynamic analysis version of 3D elasto-plastic cellular automaton (EPCA3D) is developed. The advantage of this method is it avoids the solution of large-scale linear equations since only the local CA rule is used for dynamic state updating. The Den Iseger algorithm is introduced to validate the numerical method. The evolution of stress and velocity for the transient excavation in rock mass under different conditions obtained by the EPCA3D and Den Iseger methods are in good agreement. The abilities of EPCA3D in the modeling of elasto-plastic dynamics of transient excavation in rock mass are well demonstrated. By considering different in situ stresses, excavation radiuses, unloading durations and unloading paths, the factors affecting nonlinear dynamic responses are investigated. It is found that the failure extent increases with the decrease of unloading time. When lateral pressure coefficient (σ x /σ y) equals to 1, the failure zone is evenly distributed around the tunnel. However, with the decrease of lateral pressure coefficient, the extent of failure localization increases. The fault around the tunnel makes the dynamic failure zone asymmetric distribution. The modeling helps to understand the major mechanism of rock mass damage for the transient excavation. [ABSTRACT FROM AUTHOR]

Strong unloading damaged zones at both slopes of the dam of a hydropower station in Southwest China have been attributed to the stress release. To study the deformation and failure mechanism of dacite (dam site material) under unloading conditions, three groups of true triaxial unloading tests were conducted on the rock sample with an initial minimum principal stress σ 3 0=5 MPa, and initial intermediate principal stresses σ 2 0= 10, 15, and 20 MPa. The experimental results indicate that the strain in the direction of σ 3 is the most sensitive to the unloading of σ 3 , whereas the three principal strains are further suppressed with increasing σ 2. Ductile deformation is a failure precursor of dacite under unloading conditions. Based on the analysis of the failure mode and acoustic emission monitoring data, it has been concluded that the unloading failure of dacite is caused by the initiation, propagation, and coalescence of microcracks, which form localized tension macrocracks. The observed anisotropic damage evolution is found to be determined by stiffness degradation and quantified the degree of fracture during the final unloading stage. The results indicate that damage is anisotropic under the true triaxial unloading conditions, and that the damage ω 3 is the most sensitive to the unloading stress σ 3. Therefore, the deformation or damage in the direction of σ 3 can be used as a guide in the design of engineering excavation plans. • The effects of unloading σ 3 on dacite is studied under true triaxial conditions. • The deformation in the direction of σ 3 is most sensitive to unloading. • The unloading failure of dacite is tensile cracks propagation in the direction of σ 1. • The evolution of damage is anisotropic under unloading conditions. [ABSTRACT FROM AUTHOR]