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It is very important to predict the blasting fragmentation size of fractured rock mass. Based on the geological conditions of practical engineering rock mass, a plane analysis model of bench blasting in layered rock mass considering microcrack structure was established. And the distribution law of stress in the bench blasting of layered rock mass with different occurrence and layer thickness is analyzed by using the CDEM numerical simulation method. Combined with the theory of rock fracture mechanics and relevant test results, this paper quantitatively studied the change laws of the angle for the cracks to propagate, speed and crack initiation length at different particle points in bench blasting and realized the time history analysis of the crack development and rock fragmentation in bench blasting. And then, this paper derived the quantitative relationship between the post-expansion cranny ratio and the blasting fragmentation from a theoretical point of view, and proposed the prediction method of the median fragmentation in bench blasting of layered rock mass. Combined with the bench blasting productive test of Changjiu (Shenshan) limestone mine, the largest sand aggregate production mine in the world, the correctness of the theoretical results is verified. The test results demonstrate that in a vertically inclined rock bench, the degree of rock fragmentation intensifies in the horizontal direction, and the overall fragmentation effect can be optimized by adjusting the blasting hole spacing; the blasting fragmentation prediction method proposed in the paper can accurately predict the median fragmentation of layered rock, which provides a novel method for predicting the effects of bench blasting. Highlights: The prediction method for the median fragmentation of layered bench rock mass blasting is obtained The quantitative relationship between the post-expansion cranny ratio and the median fragmentation of bench blasting is theoretically derived The distribution law of microcracks in bench rock mass is simulated by discrete fracture network model. The internal force distribution characteristics are analyzed by continuous medium discrete element method The propagation law and rock breaking process of microcracks and layered cracks in bench blasting are studied At the same time, the correctness of the prediction method is verified by the field test and production of Changjiu (Shenshan) limestone mine [ABSTRACT FROM AUTHOR]

The method of backfill in underground mining is important for ground control as well as material recycling and energy efficiency. Even though extensive testing and field studies of backfill have been conducted, less is known about the detailed damage and fracturing that occurs directly at the rock/backfill interface. In this paper, cylindrical specimens containing an inner diameter of backfill and an outer diameter of rock (RB) were tested under triaxial compression. Acoustic emissions (AE) were used throughout testing, and X-ray computed tomography (CT) scanning was conducted before loading was applied and after the specimens had failed. The high-resolution CT images were then converted into point clouds to isolate the fractures and visualize them in three dimensions. The point clouds clearly show that fracturing occurred both in the rock and along with the contact between rock and backfill, while very little fracturing was found to occur in the backfill. Based on the point cloud and AE results, a unique evolution of fracturing is found to occur that includes two stages of shear fracturing in the rock, tensile fracturing along with the rock/backfill interface, and final tensile fracturing in the rock after delamination from the backfill, all of which contributed to the nonlinear stress–strain response. This paper presents a novel approach for investigating the initiation and propagation of 3D fractures in laboratory testing and can offer a useful reference for further studies on the mechanics of bi-material structures. [ABSTRACT FROM AUTHOR]

To accurately capture crack trajectory and failure morphology with continuum mesoscopic model-based methods in three-dimensional space, conventional global uniform refinement schemes may incur significant computational cost. This paper first presents a three-dimensional structured mesh refinement strategy to achieve the hierarchical discretization for the focused region. To deal with the mismatching problem caused by different-sized meshes, a coupling interface technique based on the discontinuous Galerkin framework is proposed. The validity and advantages of the present strategy are first verified by a benchmark example for elastic analysis. By strongly collaborating with the statistical meso-damage smear method, we further simulate the spatial crack growth (including a through-thickness crack, an embedded crack, and a surface crack) and the local failure process of a D-shaped tunnel. Great agreements between the simulation results and the available experiment or numerical reference results demonstrate that the present method can effectively simulate the rock fracturing process as well as save considerable computational time and memory storage. Highlights: A three-dimensional structured mesh refinement strategy is presented for the geometric and scale restrictions of rock meso-fracturing simulations. An effective coupling interface technique is introduced to accurately capture the interface effects and couple different-sized meshes. Different crack configurations, including a through-thickness crack, an embedded crack, and a surface crack are simulated. The present method can achieve an ideal trade-off between accuracy and computing effort. [ABSTRACT FROM AUTHOR]

In recent years, interest in the effect of positive temperatures on rock faces has increased, as evidenced by the extensive literature on the subject. The subsurface rock masses of rock slopes are submitted to uncontrollable natural temperature cycles which cause deformation, displacement, opening and closing of discontinuities and can lead to surface failure or more important rockfalls. In this paper we offer a review of the publications on this theme focusing on in situ observations and measurements. Measurements are described and analysed considering conditions of temperature and insolation, displacements, strains, focusing on two French sites (Les Rochers de Valabres and La Roque-Gageac). Mechanical analysis is then performed. The impact of temperature variation is studied from basic assumptions to much more complex ones. Thermoelasticity is first assessed, and analytical computation is suggested, fracture mechanism and fatigue are also considered. Finally, we outline some challenges to be addressed in the coming years. Highlights: The article reviews the accumulated knowledge on the effect of positive temperature changes on slope stability. Excluding the effect of water freezing and thawing. The different types of measurements are reviewed considering surface and in-depth measurements of temperature, displacements, fracture opening, and strain. Simple thermo-elastic analysis, alongside solutions from fracture mechanics are proposed. A focus is proposed on 2 French sites to illustrate interpretations. The conclusion summarizes the points of consensus, the aspects that are still under discussion among authors or should be more debated and open to pending challenges for the next years. [ABSTRACT FROM AUTHOR]

This study analyzes the fracture patterns generated from the high-energy release caused by commercially available explosives and the current capability of numerical methods to replicate this. The mechanics of rock fracture and fragmentation are first studied using the Hybrid Stress Blasting Model (HSBM) at the lab-scale through comparison with experimental results available in the literature. Following this, an in-house experimental blast campaign was undertaken with a detailed examination of an unconfined, 605 mm diameter cylindrical sample and a pressurised (confined), 700 mm diameter cylindrical sample. The post-blast samples were dissected and fractures were visually mapped before comparing the fracture intensity results to the output of the HSBM, which captures stress-wave-induced damage but not gas loading, for these test cases. This paper makes contributions to the literature in three fundamental areas. Firstly, the capability of numerical methods to capture the phenomenology of blasting on rock fracture and fragmentation was validated and the limitations were discussed when looking to use this as a design tool for practical blasting operations. Secondly, the experimental campaign provides detailed insights into the response of cementitious grout materials to internal, blast-induced loading that can be applied in various fields such as mining and construction. Finally, the impact of confining pressure on blast damage was investigated and details were provided for how this can be captured in numerical predictions. It was found that certain aspects of the material response can be well predicted through numerical analysis, namely, the damage radius and the number of dominant fractures. However, it also indicated a shortcoming in the explicit comparison of fracture intensity measures such as P21, with the use of damage metrics appearing more appropriate. The grout-based testing methodology discussed in this work provides an efficient means for gathering data on the impacts of individually controlled aspects of a blast in both unconfined, and confined environments. Highlights: Development and outline of the methodology associated with a novel experimental setup for confined blasting tests. Investigated state-of-the-art numerical methods' ability to capture the phenomenology of blasting on rock fracture and fragmentation. Discussion of existing limitations of numerical modelling when considering industrial blasting applications. Experimentally and numerically studied the impact of confining pressure on material response to provide insight into in-situ blast conditions. Explicit comparison of experimental and numerical fracture patterns induced by blasting. [ABSTRACT FROM AUTHOR]

Crack initiation, propagation, and coalescence are important for the understanding of rock mass behavior. In this paper, we use an improved numerical manifold method (NMM) that can stimulate the initiation, propagation, and coalescence of many cracks simultaneously to model the continuous–discontinuous deformation of granite under uniaxial and confined compression. This new simulation method couples subcritical crack growth (SCG) theory and the Mohr–Coulomb strength criterion with tension cut-off to consider the propagation of virtual and real cracks, respectively, and uses a statistical Weibull distribution to study the influence of elastic modulus inhomogeneity on crack propagation and rock failure. The mechanical behavior and failure modes of the models are in good agreement with experimental data. Increasing elastic modulus inhomogeneity decreases strength and the strain required for macroscopic failure. The stress corrosion index (n) and crack growth constant (C) also have a strong influence on uniaxial compressive strength. Indeed, higher values of C and n result in faster virtual crack speeds, a lower uniaxial compressive strength, and a lower axial strain upon failure. Confining pressure also exerts an influence on crack propagation, compressive strength, and failure mode. Our study shows that the improved NMM code combined with the virtual crack model is therefore an effective and reliable method to simulate crack initiation, propagation, and coalescence in granite under uniaxial and confined compression. Highlights: A virtual crack approach combined with subcritical crack growth theory is implemented in numerical manifold method to simulate the initiation of multi-cracks. The Mohr–Coulomb criterion with tension cut-off coupled with subcritical crack growth theory is incorporated into numerical manifold method to simulate the propagation of micro-and macro-cracks. Three types of crack intersection are identified in numerical manifold method to allow the model to accurately simulate the propagation and coalescence of multi-cracks and large displacement. [ABSTRACT FROM AUTHOR]

This paper presents a numerical study on the effects of microwave irradiation on the mechanical properties of hard rock. More specifically, the weakening effect of microwave heating induced damage on the uniaxial compressive and tensile strength of granite-like rock is numerically evaluated. Rock fracture is modelled by means of a damage-viscoplasticity model with separate damage variables for tensile and compressive failure types. We develop a global solution strategy where the electromagnetic problem is solved first separately in COMSOL multiphysics software, and then provided into a staggered implicit solution method for the thermo-mechanical problem. The thermal and mechanical parts of the problem are considered as uncoupled due to the dominance of the microwave-induced heat source. The model performance is tested in 2D finite element simulations of heterogeneous numerical rock specimens subjected first to heating in a microwave oven and then to uniaxial compression and tension tests. According to the results, the compressive and tensile strength of rock can be significantly reduced by microwave heating pretreatment. [ABSTRACT FROM AUTHOR]

Proppant embedment is a serious issue that reduces fracture width and conductivity. The paper presents the results of experiments on embedment phenomena on a shale rock from the region of the Baltic Basin, which is regarded as an unconventional gas deposit. A novel laboratory imaging procedure was implemented to the proppant embedment visualization. The tests were performed for conditions corresponding to the average reservoir conditions occurring in the studied deposit formation. The parameters characterizing damage of the surface of the fracture faces by the grains of proppant material, after the application of axial compressive stress to two shale core samples with proppant placed in between, are presented. The tests were carried out for rock samples pre-saturated with fracturing fluid. The obtained results of relatively low total effective penetration depth of proppant grains into the walls of the fracture (0.293 mm), and high effective width of fracture with proppant material after hydraulic fracturing (87.9%), indicate the proper selection of proppant and fracturing fluid for the properties of the rock and the reservoir conditions. The results of the experiments present a range of embedment parameters, that have not been widely described before. The test procedure presented in the article is a good method for assessing the vulnerability of a deposit rock to embedment phenomenon. [ABSTRACT FROM AUTHOR]

Based on the research background of the damage of high-temperature jointed rock masses, this paper studies the mechanical properties of jointed granite under high-temperature conditions and analyzes the failure law of jointed rock masses with increasing temperature, decreasing temperature and types of joints. The results have important scientific and engineering value. The main research results are as follows: (1) high-temperature conditions change the mechanical properties of granite, especially when the temperature is higher than 400 °C, and the peak stress of granite decreases sharply; the change rate of the mechanical parameters of granite under the condition of water cooling is higher than that under the condition of natural cooling. (2) The uniaxial compressive strength of jointed granite increases with increasing angle α between the joint and the maximum principal plane, and the peak strength of intact granite is higher than that of jointed granite with either conjugate or echelon joints (referred to as conjugate or echelon jointed granite here). (3) The conjugate jointed granite exhibits three failure modes, in which the fractures are all tensile fractures; the echelon jointed granite exhibits three failure modes, most of which include tensile and shear fracturing. [ABSTRACT FROM AUTHOR]

This paper investigates fragmentation in an aggregate quarry in the light of the fragmentation-energy fan concept. Six blasts were monitored, located one behind the other in the same quarry area. The rock structure was blocky, the water level and the usage of explosives were variable within and between the blasts; however, the distribution of explosive energy in the blocks was relatively uniform and the performance of both explosives per unit mass appeared to be similar. The powder factor above grade was between 0.28 and 0.44 kg/m3. Fragmentation of the plant feed was measured using an online digital image analysis system and three belt scales in the crushing plant. The oversize material that was not directly fed to the plant after the blast corresponds to 3-9.3% of the total. Data from image analysis was used to build the size distribution in the coarse range (fragments above 120 mm), and the passing fractions at 120 and 25 mm obtained from belt scales data were used in the range 120-25 mm. The non-dimensional percentile sizes between 10 and 90% for each blast are described through power functions of the powder factor above grade; the model coefficients (i.e. nine prefactors and nine exponents) are statistically significant. From them, using the principles of the fragmentation-energy fan and the Swebrec distribution properties, the fragmentation can be expressed in terms of the powder factor by means of five parameters: the fan focus coordinates and the three parameters of a function of the exponents versus the percentage passing. The model shows a good capability to describe fragmentation from 10 to 90 percentile sizes, with an expected error below 6% and a maximum likely error less than 15%. [ABSTRACT FROM AUTHOR]

In laboratory fracture toughness studies, the crack growth resistance of rock materials may be influenced by different factors such as specimen geometry, loading conditions, and also the type of pre-notch cut in the test sample. In this paper, a large number of mode I fracture toughness experiments are conducted on an Iranian white rock “Harsin marble” with six different mode I specimens. The selected test specimens are in the shape of cylindrical rod, rectangular beam, and circular Brazilian disk containing either chevron notch or straight crack. The effect of specimen geometry and pre-notch type was investigated statistically, and it was found that the average fracture toughness values of notched specimens were higher than those of the similar specimens but containing straight crack. Meanwhile, the scatters of fracture toughness data for chevron notched specimens were smaller than those for the straight cracked samples. For each set of experimental fracture toughness results, probability of fracture was investigated using two- and three-parameter Weibull statistical distributions. Comparison of the Weibull fitted curves for chevron notched and straight cracked samples with the same geometries demonstrated that the discrepancy between the corresponding curves can be described with a good accuracy by a simple shift factor. In addition, using the extended maximum tangential strain criterion which takes into account the influence of both KI and T-stress terms, the statistical fracture toughness data of chevron notched specimens were predicted in terms of the Weibull distribution parameters of the straight cracked specimens. [ABSTRACT FROM AUTHOR]

In this paper, a cohesive fracture model is applied to model P-wave propagation through fractured rock mass using hybrid continuum-discrete element method, i.e. Universal Distinct Element Code (UDEC). First, a cohesive fracture model together with the background of UDEC is presented. The cohesive fracture model considers progressive failure of rock fracture rather than an abrupt damage through simultaneously taking into account the elastic, plastic and damage mechanisms as well as a modified failure function. Then, a series of laboratory tests from the literature on P-wave propagation through rock mass containing single fracture and two parallel fractures are introduced and the numerical models used to simulate these laboratory tests are described. After that, all the laboratory tests are simulated and presented. The results show that the proposed model, particularly the cohesive fracture model, can capture very well the wave propagation characteristics in rock mass with non-welded and welded fractures with and without filling materials. In the meantime, in order to identify the significance of fracture on wave propagation, filling materials with different particle sizes and the fracture thickness are discussed. Both factors are found to be crucial for wave attenuation. The simulations also show that the frequency of transmission wave is lowered after propagating through fractures. In addition, the developed numerical scheme is applied to two-dimensional wave propagation in the rock mass. [ABSTRACT FROM AUTHOR]

This paper deals with numerical modelling of rock fracture under dynamic loading. For this end, a combined continuum damage-embedded discontinuity model is applied in finite element modelling of crack propagation in rock. In this model, the strong loading rate sensitivity of rock is captured by the rate-dependent continuum scalar damage model that controls the pre-peak nonlinear hardening part of rock behaviour. The post-peak exponential softening part of the rock behaviour is governed by the embedded displacement discontinuity model describing the mode I, mode II and mixed mode fracture of rock. Rock heterogeneity is incorporated in the present approach by random description of the rock mineral texture based on the Voronoi tessellation. The model performance is demonstrated in numerical examples where the uniaxial tension and compression tests on rock are simulated. Finally, the dynamic three-point bending test of a semicircular disc is simulated in order to show that the model correctly predicts the strain rate-dependent tensile strengths as well as the failure modes of rock in this test. Special emphasis is laid on modelling the loading rate sensitivity of tensile strength of Laurentian granite. [ABSTRACT FROM AUTHOR]

Determination of the cracking levels during the crack propagation is one of the key challenges in the field of fracture mechanics of rocks. Acoustic emission (AE) is a technique that has been used to detect cracks as they occur across the specimen. Parametric analysis of AE signals and correlating these parameters (e.g., hits and energy) to stress-strain plots of rocks let us detect cracking levels properly. The number of AE hits is related to the number of cracks, and the AE energy is related to magnitude of the cracking event. For a full understanding of the fracture process in brittle rocks, prismatic specimens of granite containing pre-existing flaws have been tested in uniaxial compression tests, and their cracking process was monitored with both AE and high-speed video imaging. In this paper, the characteristics of the AE parameters and the evolution of cracking sequences are analyzed for every cracking level. Based on micro- and macro-crack damage, a classification of cracking levels is introduced. This classification contains eight stages (1) crack closure, (2) linear elastic deformation, (3) micro-crack initiation (white patch initiation), (4) micro-crack growth (stable crack growth), (5) micro-crack coalescence (macro-crack initiation), (6) macro-crack growth (unstable crack growth), (7) macro-crack coalescence and (8) failure. [ABSTRACT FROM AUTHOR]

A series of stepwise cyclic tests and short-term creep tests were conducted on Beishan granite to quantify the separated effect of stress corrosion and friction degradation during cyclic loading. An opti-acoustic monitoring platform that combined digital image correlation and acoustic emission techniques was utilized to monitor the rock deformation and fracturing at both the micro- and macro-scale simultaneously. In addition, a micromechanical model was built to study the crack growth of rocks exposed to cyclic and creep loads. Experimental and theoretical results indicated that both the repeated and constant loads play a great role in deformation localization, micro-fracturing, and damage accumulation. A similar law was observed in the evolution of the AE b value and distribution of frequency-amplitude in granite under cyclic and creep loading. However, cyclic loads induced a greater AE count rate in granite than constant loads at low loading levels, while constant loads stimulated a greater AE count rate than cyclic loads at high loading levels. Moreover, cyclic loads promoted more strain localization bands than constant load; so, more macro-cracks, branching, and debris were observed in granite during cyclic loading. These similarities and differences indicated that both the stress corrosion and fatigue mechanisms were highlighted to be responsible for the sub-critical crack growth of rocks during cyclic loading. The development of sub-critical crack growth and the evolution of stress intensity factor at the crack tip within rocks under cyclic and constant loads were well described by the micromechanical theoretical model. Highlights: Laboratory experiments were conducted to distinguish stress corrosion and reciprocating wear from rock fatigue. Real-time observation of rock deformation and fracturing was achieved using opti-acoustic technology. A micromechanical theoretical model was built to characterize the sub-critical crack growth in rocks. [ABSTRACT FROM AUTHOR]

Understanding the poroelastic effect on anisotropic organic-rich mudstones is of high interest and value for evaluating coupled effects of rock deformation and pore pressure, during drilling, completion and production operations in the oilfield. These applications include modeling and prevention of time-dependent wellbore failure, improved predictions of fracture initiation during hydraulic fracturing operations (Suarez-Rivera et al. Presented at the Canadian Unconventional Resources Conference held in Calgary, Alberta, Canada, 15-17 November 2011. CSUG/SPE 146998 ), improved understanding of the evolution of pore pressure during basin development, including subsidence and uplift, and the equilibrated effective in situ stress (Charlez, Rock mechanics, vol 2 ; Katahara and Corrigan, Pressure regimes in sedimentary basins and their prediction: AAPG Memoir, vol 76, pp 73-78 ; Fjær et al. Petroleum related rock mechanics. 2nd edn ). In isotropic rocks, the coupled poro-elastic deformations of the solid framework and the pore fluids are controlled by the Biot and Skempton coefficients. These are the two fundamental properties that relate the rock framework and fluid compressibility and define the magnitude of the poroelastic effect. In transversely isotropic rocks, one desires to understand the variability of these coefficients along the directions parallel and longitudinal to the principal directions of material symmetry (usually the direction of bedding). These types of measurements are complex and uncommon in low-porosity rocks, and particularly problematic and scarce in tight shales. In this paper, we discuss a methodology for evaluating the Biot's coefficient, its variability along the directions parallel and perpendicular to bedding as a function of stress, and the homogenized Skempton coefficient, also as a function of stress. We also predict the pore pressure change that results during undrained compression. Most importantly, we provide values of transverse and longitudinal Biot's coefficients and the homogenized Skempton coefficient for two important North American, gas-producing, organic-rich mudstones. These results could be used for petroleum-related applications. [ABSTRACT FROM AUTHOR]

During the past decade, numerous research has been conducted to evaluate the effectiveness of microwave treatment in improving rock fragmentation. While these studies focused on investigating the effect of microwave treatment on rock parameters, the current research approaches the problem from another perspective by studying the applicability of mode I fracture toughness parameters to evaluate the effectiveness of the microwave treatment as a rock pre-conditioning method based on energy analysis. Different rock sizes are investigated, and it is shown that for the basalt rock used in this study, the minimum required diameter for the fracture toughness experiments is 70 mm. In a novel approach, a finite element based numerical model is employed to maximize the energy absorption of the sample in the cavity. It is shown that optimizing the location of the rock sample in the cavity can increase the heat over microwave efficiency (HOME) and weakening over microwave energy (WOME) by more than 40% and 30%, respectively. Furthermore, it is concluded that although increasing the exposure time results in more KIC value reduction, it decreases the WOME value by more than 50% in some cases. Finally, the applicability of fracture toughness experiments in evaluating the effectiveness of microwave treatment is discussed in detail. Highlights: The energy efficiency of microwave treatment as a rock pre-conditioning method is improved by applying the numerical results in the experiments. A novel discussion concerning the preparation of fracture toughness samples before and after microwave treatment is provided. The efficiency of the microwave treatment method is experimentally investigated based on energy analysis. The appropriateness of using the mode I fracture toughness experiments in evaluating the efficiency of the microwave treatment is discussed. [ABSTRACT FROM AUTHOR]

The progressive brittle failure of high-stress hard surrounding rock masses caused by layered excavation severely threatens the stability of large underground caverns. We summarize the stress path in the potential failure zone of the Shuangjiangkou underground powerhouse during layered excavation, and then design the multistep unloading confining pressure test and the cyclic loading–unloading test with multistep unloading confining pressure. The deformation, strength, acoustic emission, and failure characteristics of granite, as well as the evolution of critical stress thresholds and mechanical parameters are analyzed based on experimental results under different stress paths. The peak strength of the rock significantly depends on the stress path and the amount of unloading confining pressure. The rock failure process under multistep unloading confining pressure is divided into stable and unstable crack growth stages, with the failure mode shifting from tensile cracks to mixed tensile–shear cracks. The evolution modes of critical stress thresholds, cohesion, and internal friction angle with amount of unloading confining pressure differ significantly from that with the equal plastic strain. The former is nearly linear, while the latter is exponentially nonlinear. The evolution of the deformation modulus, cohesion, and internal friction angle confirms the rationality of the cohesion-weakening–friction-strengthening model with degraded deformation modulus for the stability analysis of surrounding rock masses under layered excavation. The experimental methods for obtaining the evolution of rock mechanical parameters using a single specimen under unloading confining pressure are also discussed. The results imply that the layered excavation-induced nonlinear deterioration of the deformation modulus and strength parameters of high-stress hard surrounding rock masses should be considered in the stability analysis of large underground caverns. Further, the timely compensation of the excavation-induced confining pressure loss is critical to ensure the stability of high-stress hard surrounding rock masses under layered excavation. Highlights: A stress path was designed to reflect the stress evolution characteristics for rock masses of the large underground cavern under layered excavation; The deformation, strength, acoustic emission, and failure characteristics of granite under the layered excavation stress path were analyzed; The evolution of rock mechanical parameters with unloading confining pressure and the equivalent plastic strain were obtained; An experimental method for obtaining the evolution of rock mechanical parameters using a single specimen under unloading confining pressure was discussed. [ABSTRACT FROM AUTHOR]

Underground rock mass conditions are often complex, crack propagation and coalescence results in a reduction in rock strength and can cause brittle failure. We study the influence of the fluid pressure and the lateral pressure on the propagation process of parallel flaws, the failure mechanism of rock bridges and the rock failure modes, respectively. A lateral pressure loading device and a water injection system are designed for experimental analysis. A fracture-damage model is introduced in the continuous discontinuous discrete element method to describe the crack propagation process. The following conclusions are obtained: compared with the specimen without fluid pressure in the flaws, the fluid pressures (0.5 MPa, 1 MPa and 1.5 MPa) affect the rock bridge coalescence modes, strength characteristics and failure forms under uniaxial compression. With the increase of fluid pressure, the failure form of the rock bridge changes from tensile shear failure to tensile failure. Without fluid pressure in the flaws, tensile shear failure occurs in the rock bridge under uniaxial compression. With the increase in the lateral pressure coefficient (30%), wing crack growth is restrained, and shear cracks appear in rock bridges, causing the failure mode of the rock bridge changes from tensile shear failure to shear failure. Compared with the specimen without fluid pressure in the flaws, with the increase of fluid pressure, the tensile stress at the flaw tips increases, and the shear stress at the rock bridges decreases , which promotes the growth of tensile cracks and decreases the peak strength of the specimen. Especially, high-pressure fluid promotes the coalescence of rock bridges and cause tensile failure occurs in the specimen, resulting in more obvious brittle failure characteristics of the specimen than the specimen with low fluid pressure and without fluid pressure. Highlights: The propagation process of parallel flaws and the failure mechanism of rock bridges under different fluid pressures were investigated. The rock brittle failure characteristics and the initiation stress of the parallel flaws under the fluid pressure were analyzed. The improved fracture-damage model in the CDEM can well simulate crack propagation process under hydromechanical coupling. [ABSTRACT FROM AUTHOR]

Aiming at geological disasters triggered by fracture zones in the surrounding rock mass during the excavation of deep railway tunnels, deformation and failure of the surrounding rock mass triggered by sudden changes of rock quality encountered in a tunnel excavation project were investigated. This research conducted an analysis of a field case: the Daliang Tunnel on the Gansu–Qinghai section of the Lanzhou–Urumuqi second double-track railway in China. The deformation profiles of the surrounding rock mass at different distances from the fracture zone was evaluated. The deformation of the surrounding rock mass in and around the fracture zone was explored by combining in-situ measurement, theoretical research, and numerical simulation. Furthermore, relationships of deformation of the surrounding rock mass in the section of the fracture zone with the materials and length of advanced support as well as the excavation advance rate behind the fracture zone were elucidated. Analysis of the results indicated that there is an inflection point on the deformation curves of the surrounding rock mass far ahead of the fracture zone; however, it is difficult to observe the inflection point on deformation curves of the surrounding rock mass in engineering practice as the rocks have undergone substantial deformation before being exposed. A combination of material properties and length of advanced support is conducive to controlling the deformation of the surrounding rock mass in the fracture zone. Highlights: Deformation curves of surrounding rocks exposed ahead of a fracture zone have an inflection point. The efficiency is optimal when the length of advanced support is twice the width of the fracture zone. Fitted lines of deformation of support for surrounding rocks in the fracture zone pass through the origin. [ABSTRACT FROM AUTHOR]

Time-dependent rock deformation caused by the initiation and growth of fractures leads to the weakening of the rock mass. Understanding the fracturing mechanisms involved in the time-dependent behavior in brittle rocks is very important and to achieve this goal, a systematic series of three types of experiments was performed on double-flawed prismatic Barre granite specimens under unconfined compression. The first series aimed to identify the failure mechanism in the short-term failure mode under monotonic loading, the, second series involved multistage relaxation (constant strain) experiments to analyze the damage at different strain levels, and the third series explored the fracture propagation under multistage creep (constant load) experiments. The spatial and temporal evolution of cracking mechanisms were evaluated using the acoustic emission (AE) and two-dimensional digital image correlation (2D-DIC) techniques to observe the whole crack growth process as well as the accumulated inelastic strain at the specified region of interest. Results suggest that in the case of multistage creep experiments, the time to failure was less compared to the multistage relaxation, when loaded above the crack damage threshold (CD) estimated from the monotonic testing. The frequency magnitude distribution of the AE events generated in the three loading conditions followed the Gutenberg Richter model. A relatively lower b-value was obtained for the creep experiments, indicative of high energy AE events and faster crack growth. In addition, the AE and DIC results also revealed high evolution of tensile cracks at-different stages of creep and relaxation compared to shear and mixed-mode cracks. Highlights: Fracturing mechanisms under multistage relaxation and creep experiments were identified. AE and DIC results showed high evolution of tensile cracks as compared to shear and mixed-mode cracks. Frequency-magnitude distribution illustrated a lower b -value in case of multistage creep as compared to multistage relaxation. [ABSTRACT FROM AUTHOR]

A novel microcrack damage theory for describing the time-dependent behavior of brittle rocks is proposed. Instead of using scalar or tensorial variables to approximate the effect of microcracks, the concept of directional damage is introduced by upscaling the directional distribution density of microcracks through the noninteracting homogenization scheme. The contribution of an individual crack on global strain is first derived from the crack-opening displacements including sliding, closure, and dilation. The model is then cast in the free energy form, and the range of parameters ensuring compliance with the second law of thermodynamics is derived rigorously. Considering that the subcritical propagation of microcracks is the dominant mechanism behind the time-dependent deformation and failure of brittle rocks, the driving force for directional damage is defined as the corresponding energy release rate, and the effect of time is introduced through a damage evolution law inspired from the kinetics of subcritical crack growth. The model is applied to simulate the behavior of basalt rock under various loading conditions. In addition to predicting the stress–strain–time response, the model offers enhanced resolution in representing the anisotropic characteristics of microcrack-induced damage in brittle rocks and their time-dependent evolutions. [ABSTRACT FROM AUTHOR]

Due to the low permeability of many shale reservoirs, multi-stage hydraulic fracturing in horizontal wells is used to increase the productive, stimulated reservoir volume. However, each created hydraulic fracture alters the stress field around it, and subsequent fractures are affected by the stress field from previous fractures. The results of a numerical evaluation of the effect of stress field changes (stress shadowing), as a function of natural fracture and geomechanical properties, are presented, including a detailed evaluation of natural fracture shear failure (and, by analogy, the generated microseismicity) due to a created hydraulic fracture. The numerical simulations were performed using continuum and discrete element modeling approaches in both mechanical-only and fully coupled, hydro-mechanical modes. The results show the critical impacts that the stress field changes from a created hydraulic fracture have on the shear of the natural fracture system, which in-turn, significantly affects the success of the hydraulic fracture stimulation. Furthermore, the results provide important insight into: the role of completion design (stage spacing) and operational parameters (rate, viscosity, etc.) on the possibility of enhancing the stimulation of the natural fracture network ('complexity'); the mechanisms that generate the microseismicity that occurs during a hydraulic fracture stimulation; and the interpretation of the generated microseismicity in relation to the volume of stimulated reservoir formation. [ABSTRACT FROM AUTHOR]

A recently developed unconventional fracture model (UFM) is able to simulate complex fracture network propagation in a formation with pre-existing natural fractures. A method for computing the stress shadow from fracture branches in a complex hydraulic fracture network (HFN) based on an enhanced 2D displacement discontinuity method with correction for finite fracture height is implemented in UFM and is presented in detail including approach validation and examples. The influence of stress shadow effect from the HFN generated at previous treatment stage on the HFN propagation and shape at new stage is also discussed. [ABSTRACT FROM AUTHOR]

The cracked chevron notched Brazilian disc method (CCNBD) recommended by the International Society for Rock Mechanics is a major method for measuring the rock fracture toughness. In the rock fracture mechanics, the micro-crack evolution behavior during Mode I fracture is of great theoretical significance. To fully understand the micro-crack evolution mechanism and fracture process zone evolution information of non-uniform sandstone, numerical simulation of CCNBD specimen under Mode I fracture condition was carried out using PFC3D. Combined with the box fractal dimension theory, the sandstone particle size and mineral composition were considered, and the non-uniform bonded particle model was built. By monitoring the evolution of micro-cracks in the interior and boundary of the cluster, the micro-crack evolution process of the numerical model was obtained. The results showed that the micro-fracture of CCNBD specimen during the cracking process was dominated by weak cementation plane and the contact of interstitial filling particles, while the micro-crack generated between detritus particles mainly concentrated in the CCNBD specimen with the peak stress range of 80–100% and the post-peak failure stage. Combined with the stress field analysis, the Mode I fracture experiment of the bonding between diagenetic mineral particles at the crack tip of CCNBD specimen was dominated by tension, while the bonding between interstitial filling particles is dominated by compression. The micro-crack evolution mechanism of the CCNBD specimen during Mode I fracture was obtained by experiments and numerical simulations. This study is expected to improve the understanding of the unstable fracture mechanism of the fractured rock mass. [ABSTRACT FROM AUTHOR]

Carbonate reservoirs accommodate a significant proportion of global hydrocarbon reserves. However they are often tight and permeability is therefore usually dependent on either flow through existing fractures or through those produced by hydraulic stimulation. Hence, understanding how fracture networks develop in carbonate reservoir rocks is key to efficient and effective production. However, despite their prevalence as reservoir rocks, there is a paucity of data on key fracture properties of carbonate rocks, particularly in more than one orientation. Here, therefore we report measurements of both the tensile strength and fracture toughness of Nash Point limestone in the three principal fracture orientations to determine what effect any mechanical anisotropy might have on fracture propagation. We find Nash Point limestone to be essentially isotropic in terms of both its microstructure and its fracture properties. When comparing the fracture toughness of Nash Point limestone with that of others limestones, we find that fracture toughness decreases with increasing porosity, although this dependency is not as strong as found in other porous rocks. Finally, as many so-called carbonate reservoirs actually comprise layered sequences, we extend our analysis to consider the layered sequence of limestones and shales at Nash Point. We find that the fracture toughness of Nash Point limestone is higher than Nash Point shale but that the fracture energy is lower. We therefore discuss how the implications of fracturing through multi-layered sequences could be explored in future work. [ABSTRACT FROM AUTHOR]

In the present study, a physical model test was used to investigate the cracking characteristics of the surrounding rocks of hydraulic tunnels under high geothermal conditions. Based on similarity theory, a similar material was developed to simulate the intact and hard rocks in thermo-hydro-mechanical (THM) coupling fields; this material was used to cast a large-scale model tunnel. A new loading system, including a temperature loading system and a water pressure loading system, was designed to improve upon conventional laboratory hydraulic tunnel testing and provide a means of better understanding the fracture behavior of solid media. An acoustic emission (AE) monitoring system, thermocouples and osmometers were used to reveal the real-time evolution of the temperature field, seepage pressure field and crack propagation. The test results showed that compared to a hydraulic tunnel without high geotemperature, the critical internal water pressure of the hydraulic tunnel under high geothermal conditions decreased significantly. After the initiation of main cracks was induced by hydraulic fracturing, due to THM coupling, a certain number of secondary cracks initiated and developed between the main cracks. In this process, the trend of the secondary crack tip deviated from the radial direction, resulting in a more developed and complicated evolution of cracks (including main cracks and secondary cracks). This was different from the cracking behavior of surrounding rocks without a high geothermal gradient, in which only a few main cracks due to hydraulic fracturing were observed. An obvious multifield THM coupling effect was observed under high-geotemperature conditions, and cracks propagated and damage increased in the surrounding rocks in a discontinuous and step-like manner. The number and source locations of the cracks recorded by the AE monitoring system were in good agreement with the evolution of the temperature field and seepage pressure field. In addition, FLAC3D numerical simulations based on the thermo-hydro-mechanics and damage (THMD) model revealed that high geotemperatures and in situ stresses significantly influenced on the cracking mode of the surrounding rocks of hydraulic tunnels under high geotemperatures. The results obtained in this study provide a better understanding of the cracking characteristics of the surrounding rocks of hydraulic tunnels under high geothermal conditions and are useful for the design of hydraulic tunnels. [ABSTRACT FROM AUTHOR]

Rock masses contain pre-existing cracks. These cracks are not usually considered when predicting the maximum injection pressure, i.e. the breakdown pressure, in hydraulic fracture stimulations. The conventional approach to predict breakdown pressure is to use the maximum tensile stress failure criterion to calculate the pressure when a point on the borehole wall reaches the tensile strength of the rock. In addition, a pre-existing crack intersecting a hydraulically pressurized section of a borehole may produce a non-planar crack propagation surface. It is important to predict these non-planar crack propagation surfaces to design productive hydraulic fracturing stimulations and to mitigate risks associated with uncertainties of the resultant crack propagation. To gain a better understanding of this problem, a series of hydraulic fracturing experiments were conducted to investigate the breakdown pressures and crack propagation surfaces of a pressurized circular crack represented by a thin notch, subjected to different external triaxial stresses. The results show that the breakdown pressures under the shear stress conditions studied can be estimated using only the resultant normal stress on the plane of the crack. As the material properties of the experimental specimens are well defined and the crack propagation surfaces were mapped, the experimental results presented in this study provide a very useful measured dataset for the validation of various modelling approaches. The propagation surfaces from experiments were found to align closely to the computational predictions based on the maximum tangential stress criterion. Finally, this study gives evidence in three-dimensions that via the hydraulic fracturing process, the propagation of an initially arbitrarily oriented crack will eventually realign to be perpendicular to the minor principal stress direction. [ABSTRACT FROM AUTHOR]

Salt rock is a polycrystalline material of interest for geostorage because of its low permeability and potential to self-heal by pressure solution at favorable stress and temperature conditions. It is often assumed that microcrack propagation and healing lead to isotropic stiffness changes. The goal of this study is to check this assumption and to gain a fundamental understanding of the mechanisms that control the accumulation of damage and irreversible deformation. Cyclic axial loading tests are performed under a confining pressure of 1 MPa on synthetic salt rock generated by thermal consolidation. The stress–strain curves and the microstructure images taken at key stages of the cycles reveal the formation of a complex system of sliding and wing microcracks, the orientation of which is loading dependent. We interpret the mechanisms that control the coupled evolution of crack families by a discrete wing crack elastoplastic damage (DWCPD) model. Crack propagation is controlled by Mode I and Mode II fracture mechanics criteria. Sliding "main" cracks grow if a cohesive frictional criterion is met, while the wing cracks propagate in tension. Displacement jumps at crack faces are related to the deformation of the rock representative elementary volume (REV). The DWCPD model can capture the nonlinear stress–strain relationship and the degradation of stiffness during the loading cycles. Simulations show that microcracks occur following two stages: (1) wing cracks initiate and main cracks do not propagate; (2) wing cracks and main cracks then propagate simultaneously. Higher friction at the crack faces leads to higher strength. With a larger cohesion, salt rock strength increases, damage development is delayed and exhibits a stick-slip evolution. At higher confinement, the initiation of wing cracks is delayed, which results in an increase of strength. The damage rate is higher in specimens that are damaged prior to compression than in the ones that are not. The proposed DWCPD model can be extended to any polycrystalline semi-brittle material, and can be applied to understand the formation of crack patterns in geostorage facilities. [ABSTRACT FROM AUTHOR]

To explore the differences in deformation failure and energy evolution and simulate the real excavation conditions of coal masses at different depths during the coal-mining process, an unloading failure experiment was conducted. The experiment included coal samples at different depths from the no. 15 coal seam of the Ji group in the Pingmei coal-mining area. The sample depths were 300, 600, 700, 850, and 1050 m. The in situ stress environment, physical rock properties, and excavation disturbance influence were considered in the analysis. The results show that as the depth increases, the peak strength and residual strength of coal samples increase nonlinearly and that the deformation capacity simultaneously increases. The elastic strain energy stored before the unloading of coal, the total energy input, the accumulated elastic energy, and the dissipated energy generated during failure all increase with increasing depth, and the ratios of these results for the 1050–300 m samples were 10.79, 3.75, 3.78, and 4.67, respectively. A prepeak stage energy evolution model was established for coal samples from different depths, and the energy transformation trends of the deformation and failure of coal were explored from the perspective of the energy evolution rate. The energy dissipation efficiency (ued) was defined to represent the energy dissipation generated per unit of energy input. When the energy input is mainly transformed to dissipation energy, the failure of coal occurs (ued > 0.5), and the energy is predominantly associated with crack growth at this point, so the coal is quickly destroyed. This conversion occurs earlier as the depth increases. The AE energy release trend exhibited a good correspondence with the increases in the energy dissipation, dissipation rate, and dissipation efficiency with depth during coal unloading failure, which indicates a more intense failure of the coal body at deeper depths. [ABSTRACT FROM AUTHOR]

Numerical simulation and field monitoring are conducted in this study to investigate rock deformation and failure behaviors during excavation of underground cavern group under high in situ stresses in Jinping I Hydropower Station. According to the numerical simulation, large deformation and damage in the surrounding rock mass result in anchorage cable overlimit. The traditional elastoplastic model only considers plastic yielding in rock mass and does not consider the evolution of damage in rock mass, i.e., initiation, propagation and coalescence of cracks. It is found from the numerical results that the damage behaviors of rock masses subjected to high in situ stresses are characterized by the formation of multi-fractured zones, i.e., the zonal disintegration. Theoretical basis, general rules and reinforcement method for zonal disintegration of the surrounding rock masses under high in situ stresses are proposed. The proposed methods are applied to strengthen support measures for construction of Jinping I Hydropower Station. [ABSTRACT FROM AUTHOR]

Triaxial compression experiments under confining pressures of 16 and 35 MPa were first carried out for hollow-cylinder sandstone specimens using a rock mechanics testing system. Four hollow-cylinder sandstone specimens were compressed to various deformation positions before or after the peak strength. Then, the compressed hollow-cylinder sandstone specimens were analysed using a three-dimensional X-ray micro computed tomography (CT) scanning system. Based on the horizontal and vertical cross-sectional CT images, the internal damage behaviour of hollow-cylinder sandstone specimens was evaluated. It can be seen that the crack system of hollow-cylinder sandstone specimens with higher compressed deformation after the peak strength are more complicated than those with lower compressed deformation close to the peak strength. In the present study, the hollow-cylinder sandstone specimens with lower compressed deformation are only dominated by some internal wall fractures resulting mainly from shear cracks, whereas the hollow-cylinder sandstone specimens with higher compressed deformation are mainly dominated by two shear fractures, as well as some tensile cracks. For the same axial stress level, hollow-cylinder sandstone under a higher confining pressure has a more complicated crack system than that under a lower confining pressure. The experimental results demonstrated that the three-dimensional cracks in the hollow specimen under triaxial compression are first initiated from the internal wall due to shear slippage, and then propagate towards the top or bottom boundary of the specimen in shear fracture mode. To better explain the internal crack evolution mechanism of hollow-cylinder sandstone during the entire loading, a conceptual model of hollow-cylinder sandstone material under the action of confining pressure is proposed. At the same time, the effect of the borehole size on the internal damage behaviour of the compressed specimen after the peak strength is also discussed. The investigated conclusions are significant for predicting the instability occurring around deep well bores in petroleum engineering and for ensuring the safety of deep excavation damage zones in tunnel engineering. [ABSTRACT FROM AUTHOR]

The crack initiation, growth, wrapping and coalescence of two 3D pre-existing cross-embedded flaws in PMMA specimens under uniaxial compression are investigated. The stress-strain curves of PMMA specimens with 3D cross-embedded flaws are obtained. The tested PMMA specimens exhibit dominant elastic deformation and eventual brittle failure. The experimental results show that four modes of crack initiation and five modes of crack coalescence are observed. The initiations of oblique secondary crack and anti-wing crack in 3D cracking behaviors are first reported as well as the coalescence of anti-wing cracks. Moreover, two types of crack wrapping are found. Substantial wrapping of petal cracks, which includes open and closed modes of wrapping, appears to be the major difference between 2D and 3D cracking behaviors of pre-existing flaws, which are also first reported. Petal crack wraps symmetrically from either the propagated wing cracks or the coalesced wing cracks. Besides, only limited growth of petal cracks is observed, and ultimate failure of specimens is induced by the further growth of the propagated wing crack. The fracture mechanism of the tested PMMA specimens is finally revealed. In addition, the initiation stress and the peak stress versus the geometry of two 3D pre-existing cross-embedded flaws are also investigated in detail. [ABSTRACT FROM AUTHOR]

Increasing fracture aperture by lowering effective normal stress and by inducing dilatant shearing and thermo-elastic effects is essential for transmissivity increase in enhanced geothermal systems. This study investigates transmissivity evolution for fluid flow through natural fractures in granodiorite at the laboratory scale. Processes that influence transmissivity are changing normal loads, surface deformation, the formation of gouge and fracture offset. Normal loads were varied in cycles between 1 and 68 MPa and cause transmissivity changes of up to three orders of magnitude. Similarly, small offsets of fracture surfaces of the order of millimeters induced changes in transmissivity of up to three orders of magnitude. During normal load cycling, the fractures experienced significant surface deformation, which did not lead to increased matedness for most experiments, especially for offset fractures. The resulting gouge material production may have caused clogging of the main fluid flow channels with progressing loading cycles, resulting in reductions of transmissivity by up to one order of magnitude. During one load cycle, from low to high normal loads, the majority of tests show hysteretic behavior of the transmissivity. This effect is stronger for early load cycles, most likely when surface deformation occurs, and becomes less pronounced in later cycles when asperities with low asperity strength failed. The influence of repeated load cycling on surface deformation is investigated by scanning the specimen surfaces before and after testing. This allows one to study asperity height distribution and surface deformation by evaluating the changes of the standard deviation of the height, distribution of asperities and matedness of the fractures. Surface roughness, as expressed by the standard deviation of the asperity height distribution, increased during testing. Specimen surfaces that were tested in a mated configuration were better mated after testing, than specimens tested in shear offset configuration. The fracture surface deformation of specimen surfaces that were tested in an offset configuration was dominated by the breaking of individual asperities and grains, which did not result in better mated surfaces. [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]

Summary  A discrete element approach was used in the simulation of rock fracture. The numerical synthetic material was made of rigid circular particles or cylinders that have interaction through normal and shear springs. The cylinders were bonded to each other at the contact points to withstand the applied loads. To characterize the microscopic properties of this synthetic material, a dimensional analysis approach was presented. It was shown that the dimensionless parameters and graphs obtained were useful tools for fast and efficient calibration of a synthetic material. This calibration method was employed for finding a numerical model for Pennsylvania Blue Sandstone. The numerical model could mimic many deformational and failure characteristics of the sandstone in both conventional and some non-conventional stress paths. [ABSTRACT FROM AUTHOR]