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Tensile failure, hybrid failure (combined tension and shear) and shear failure are the three basic failure types of brittle rock. For a long time, little attention has been paid to the first two failure types except for the failure strength of direct/indirect tension, and the deformation characteristics and failure criterion of rock in triaxial extension (herein "triaxial extension" denotes axial tension/unloading-tension in confining pressure P c) are still unclear. This paper proposes a simple auxiliary apparatus to implement triaxial extension tests of cylindrical rock specimens combined with a servo-controlled MTS machine. Subsequently, the mechanics behaviors of sandstone in triaxial extension tests under different constant confining pressures (P c = 0, 5, 10, 15, 20, 30, 40, 50 and 60 MPa) are experimented and analyzed in detail, including the fracture angle, the failure surface morphology, the deformation and strength. With the increase of confining pressure, the failure type of sandstone presents a continuous transition from tensile failure to hybrid failure and to shear failure as a whole. The changes of failure morphology, elastic modulus, Poisson's ratio, maximum strain and failure strength with increase in P c show significant difference among three failure types. For the tested sandstone, the partitions of confining pressure between tensile failure and hybrid failure and between hybrid failure and shear failure are approximately at 20 MPa and 40 MPa, respectively. Hoek-Brown criterion with a tension cut-off and Fairhurst criterion are applicable to fitting the failure strength of triaxial extension test, and the latter presents a satisfying continuous transition from tensile failure to shear failure. [ABSTRACT FROM AUTHOR]

In recent decades, numerous geotechnical hazards, including landslides, foundation settlements, and tunnel collapses, have been linked to block-in-matrix rock (bimrock), resulting in substantial damage. The investigation and analysis of the engineering properties and mechanical behavior of both the rock and soil have become increasingly intriguing research areas. However, analyzing bimrock remains a formidable challenge due to its inherent heterogeneity. In this study, to investigate the tensile behavior of the bimrock, the numerical method that couples discontinuous deformation analysis (DDA) and smoothed particle hydrodynamics (SPH) is improved. First, a tension damage model is implemented in SPH for simulating the tensile behavior of the soil. The effectiveness of the presented model is verified through the direct tensile test model and the Brazil disc split model as an indirect tensile test. The contact algorithm of DDA-SPH is then modified by adding a tensile contact spring to introduce tensile strength at the interface between the matrix and the rock in the bimrock. Through a simple pulling numerical model, the accuracy of this modification has been verified, and the appropriate tensile contact stiffness is discussed. Furthermore, using the proposed method, the overall tensile strength of the bimrock with respect to the interface tensile strength is investigated. Finally, the proposed numerical method is applied to the simulation of geoengineering problems, demonstrating the capacity to analyze the stability and large deformation of bimrocks. • A tension damage model is added to the soil-particle based SPH method for simulating the tensile behavior of the matrix. • The contact algorithm of DDA-SPH is then modified by adding a tensile contact spring to introduce tensile strength at the interface. • The overall tensile strength of the bimrock with respect to the interface tensile strength is investigated. • The proposed method is applied to analyzing the bimrock slope and bimrock shallow tunnel. [ABSTRACT FROM AUTHOR]

The ground stability of gateroads is a major concern in underground coal mines, especially when the surrounding strata are weak and fractured. This paper presents a novel numerical modelling technique for gateroad stability analysis based on a case study conducted at Zhaogu No. 2 mine, China. Considering the occurrence of fracturing and its weakening effect on the stiffness of the rock mass, a tension-weakening model is implemented into FLAC3D, whereby the stiffness of the rock mass is progressively decreased with the failure state. A relationship between the intensity of fractures and the residual strength of the rockmass is built in the numerical model. A parametric study of the tension-weakening model is carried out, and the results are compared to elastic-perfectly plastic and strain-softening models. It is shown that the tension-weakening model exhibits noticeable effects on ground deformation and rock support loading, which are observed from field measurements. Thus, the tension weakening model offers a more realistic simulation of the gateroad behavior than elastic-plastic and strain softening models. The proposed model can be utilized for other applications involving rock reinforcement of mine openings under similar geotechnical conditions. [ABSTRACT FROM AUTHOR]

We perform numerical studies on vertical fracture propagation induced by tensile hydraulic fracturing for shale gas reservoirs. From the numerical simulation, we find that tensile fracturing occurs discontinuously in time, which generates saw-toothed responses of pressure, the fracture aperture, and displacement, and that fracture propagation is sensitive to factors such as initial condition of saturation, a type of the injection fluid, heterogeneity, tensile strength, elastic moduli, and permeability models. Gas injection induces faster fracturing in shale gas reservoirs than water injection, for the same mass injection, because of high mobility of gas. However, water injection to highly water-saturated formations can contribute to fast pressurization and high mobility of water, resulting in large fracturing. For moderate initial water saturation, complex physical responses within the fracture result from strong nonlinear permeability and multiphase flow with gravity. Pressure diffusion and pressurization within the fracture are also affected by permeability. High intrinsic and high relative permeabilities result in fast fluid movement of injected fluid, followed by fast fracturing. High Young׳s modulus and high Poisson׳s ratio do not seem favorable to fracture propagation, although they are not significantly sensitive. For heterogeneity, a geological layer of high strength between near surface and above the shale gas reservoirs can prevent vertical fracture propagation, changing the direction of fracturing horizontally. [ABSTRACT FROM AUTHOR]

Discontinuities remarkably dominate in jointed or blocky media, yielding an assemblage of blocks, and the mechanical properties of joints can greatly affect the behavior of a blocky system. Discontinuous deformation analysis (DDA) is promising method to analyze the failure process of a blocky system. In three-dimensional (3-D) blocky systems, face-to-face contact between adjacent blocks is common, especially for an ideal rock block system at the very early stage. The accurate modelling of the face-to-face contact is critical. The original 3-D DDA adopts the concentrated spring face-to-face contact model, in which a face-to-face contact is simply converted as the combination of several dominant contacts each with a couple of normal and shear springs. However, such simplification is not always accurate and can yield unreasonable results when simulating the progressive tensile failure between blocks under asymmetrical tension conditions. To overcome this problem, a multi-spring face-to-face contact model incorporated into 3-D DDA is proposed. In the proposed model, multiple couples of normal and shear springs are applied for a face-to-face contact to simulate the distributed force induced between contacting blocks. Several verification examples involving tensile failure are studied to show the advantages of the improved 3-D DDA. The simulated results obtained from the improved 3-D DDA converge to the theoretical solutions or experimental results while the original 3-D DDA gets unreasonable results. Thus, the improved 3-D DDA can provide more reasonable results when analyzing the tensile failure problems. • Improved 3-D DDA by incorporating a multi-spring face-to-face contact model. • Showed limitations of the original concentrated spring face-to-face contact model. • Presented the advantages of the proposed contact model in 3-D DDA. • Improved 3-D DDA can more reasonably simulate tensile failure problems. [ABSTRACT FROM AUTHOR]

The behavior of transversely isotropic rock material was studied under Brazilian test conditions for nine different rocks (two sandstones, one shale, two slates, one schist, and three gneiss). Both the variation of the strength and the final fracture patterns induced by testing were examined as a function of the inclination angle of the weak planes. The combination of the observations for both parameters illustrated clearly the complexity of the failure of such rocks, which was summarized by assuming four different trends. The four trends for the variation of the strength as a function of the inclination angles range from little or no variation (trend 1, i.e., isotropic behavior for strength) to a sharp decrease of the strength from very small angles onwards, followed by a leveling off (trend 4). Trend 2 is characterized by a constant value between 0° and about 45°, followed by a linear decrease, while trend 3 corresponds to a decrease of the strength over the entire interval, but a rather systematic decrease, approximating a linear variation. Different variations were observed among these four trends in terms of the relative lengths of the respective fractures along the weak planes and in any other direction. For the rocks investigated, there is a cross-over from dominant fractures in directions other than the weak planes to dominant fractures along the weak planes. For the four trends, there are systematic changes in the position of this cross-over point, i.e., on average, at about an inclination angle of 75° for trend 1 and at about 15° for trend 4. For inclination angles larger than the cross-over point, the rock specimens failed primarily by splitting between both loading lines. [ABSTRACT FROM AUTHOR]

Abstract: A modified distinct element Voronoi method, which we refer to as “Trigon” logic, is proposed for use in both two and three-dimensional modelling. A rock material is represented by an assembly of triangular (in 2D) or tetrahedral (in 3D) blocks bonded through their contacts. To evaluate the ability of the proposed Trigon logic in simulating brittle fracture, a series of unconfined and confined compression and Brazilian tests is performed illustrating the sample failure mechanisms under two and three dimensional conditions. Typical failure fracture patterns (damage) experienced by brittle rock are explicitly simulated including axial tensile failure under unconfined compression, shear failure under confined compression, and tensile crack extension during indirect tension (Brazilian) testing. A ‘damage parameter’ D and a ‘damage intensity’ D 21 measure are proposed to allow the evaluation of the simulated rock damage in a more quantitative manner. At the mine opening scale, the process of roof shear failure is successfully captured using the Trigon logic. In comparison with the conventional Voronoi model, the proposed Trigon model is less mesh-sensitive and predicts both a more realistic friction angle and failure pattern under varied loading conditions. [Copyright &y& Elsevier]

Abstract: A 1-m-thick pillar was subject to coupled excavation- and thermal-induced stresses to induce brittle rock mass yielding. The yielding strength of the heterogeneous and fractured rock mass consisting of Äspö diorite was evaluated at eighteen discrete locations using data from the displacement, acoustic emission, and thermal monitoring systems. The average rock mass yielding strength was determined to be 0.59 of the uniaxial compressive strength. The onset of dilation in uniaxial laboratory tests, determined from strain gauge data, was found to occur at approximately 0.45 of the uniaxial compressive strength. It was shown that that the onset of acoustic emission events in situ also occurred when the tangential stress exceeded 0.43 of the uniaxial compressive strength. For sites with absence of in situ data it is recommended that this lower-bound value determined from laboratory data may be used for assessing the in situ rock mass yielding strength. Visual observation and displacement monitoring showed that extent of rock mass yielding is sensitive to small changes in the tangential stress magnitudes. It was determined using three-dimensional modelling that changes in the tangential stress magnitude of approximately 1MPa was sufficient to cause yielding of the pillar to propagate in what appeared to be intact rock. Observations suggest that without this small stress change yielding of the rock mass would not occur. In other words, there appeared to be a well defined boundary, and if the stresses reached this boundary yielding was observed. However, if stresses were only slightly below this boundary yielding or time-dependant processes were not observed over the monitoring period used in the experiment. [Copyright &y& Elsevier]

Abstract: There has been a debate in the rock mechanics community regarding the mechanisms causing what is known as core discing. This phenomenon occurs when diamond drill cores are retrieved from rock masses in which high in situ stresses relative to rock strength are present. The interest in that phenomenon is to use it to estimate the in situ stresses from the shape and frequency of the failures along the core axis. In the present paper we argue that discing is only an indicator of high stresses, and that estimating in situ stresses from fracture observations is much too inaccurate. As most of the literature found on the subject has tackled the problem using elastic numerical models, it is shown that the stress distribution in the core being formed obtained from such models does not exist once failure has been reached. Numerical analyses using Flac2D with an elasto-plastic cohesion softening friction hardening model show that for a given stress state, discing or core damage may involve tensile failure, a combination of shear and tensile failure, or only shear failure, depending on the stress state and ratio of tensile to shear strength of the rock. The numerical model used is validated by replicating core discing observed under controlled laboratory conditions. Parametric analyses involving changes in mesh density, deformability parameters, dilatancy, drill bit pressure, drilling fluid pressure and applied stress states are also performed. Finally, it is shown that drilling-induced core discing or damage store important residual stresses in the core which may explain why recovered core samples tend to show a deterioration of their mechanical properties with time. [Copyright &y& Elsevier]

Tensile strength of rocks is an important parameter involved in the design and stability analysis of rock structures. The present paper is devoted to develop a new experimental method to investigate tensile strength, and the effect of confining pressure (P c) on tensile behavior of rocks in underground rock engineering. A triaxial direct tension (noted as TDT) apparatus was developed based on the conventional triaxial compression (noted as CTC) device with the inspiration of the glue on steel cap type of method. TDT tests were carried out on the Fontainebleau quartz sandstone specimens under four different confining pressures. CTC tests under nine confining pressures were also carried out in order to compare the tension and compression behavior of the tested quartz sandstone. Tensile stress-strain curves were obtained during the CTC and TDT tests. Post-failure specimen analysis was also carried out to identify the failure mode in TDT test. The triaxial tension failed surfaces was sampled and scanned with the optical microscopy to obtain three dimensional images to show the effect of the confining stress on the failed surface roughness. The relationship between tensile and compressive strength and the strength criteria were analyzed with the experimental data. The results show the failure mechanism under TDT loading is different from that under CTC. The inter-grain cement is the dominant factor that contributes to the triaxial tensile strength of the quartz sandstone although the increase of confining pressure can induce a decrease of the triaxial direct tensile strength. It is suggested that the direct tensile strength of rocks should be tested directly for underground structures that confining pressure exists since uniaxial tensile strength can induce overestimate of the triaxial tensile strength. [ABSTRACT FROM AUTHOR]

Dominant crack algorithm (DCA) is a statistical micromechanics model for the dynamic tensile response of brittle materials. In the DCA model, both microscopic and macroscopic material parameters are included to construct the constitutive relation, and the damage evolution is described by the growth of the dominant crack. In this study, the sensitivity analysis of the microscopic parameters (i.e. the characteristic volume size a , the initial crack size c 0 , and the crack velocity related parameter m) in the DCA model is conducted. The results demonstrate that the dynamic tensile strength is sensitive to the value of c 0 / a. Compared with the influence of the c 0 / a on the dynamic tensile strength, the dynamic tensile strength is less sensitive to the variation of the characteristic volume size a or the variation of the crack velocity related parameter m. Furthermore, the DCA model is applied to predict the dynamic tensile response of Laurentian granite (LG). A nonlinear regression method - Particle Swarm Optimization (PSO) - is utilized to optimize the values of the microscopic parameters. The results indicate that the dynamic tensile response of LG predicted by the DCA modeling has a good agreement with that obtained from the experiments. Therefore, the DCA modeling is valid and applicable to describe the dynamic tensile response and predict the dynamic tensile strength of rock-like materials. • The sensitivity of the microscopic parameters in the DCA model is analyzed. • The dynamic tensile strength predicted by the DCA model is sensitive to the value of c 0 / a. • The dynamic tensile strength predicted by the DCA model is less sensitive to the value of a and m. • The predicted and measured dynamic tensile responses of rocks are consistent. • The DCA modeling is valid to predict the dynamic tensile response of rocks. [ABSTRACT FROM AUTHOR]

To bridge the gap between elemental concentrations and rock mechanics, this paper proposed to predict a tensile failure using the weight concentrations of various elements. In this research, the Brazilian test was used to measure the indirect tensile strength of sandstones under different environmental conditions, i.e., oven drying, water immersion, and mud filtration. According to the mechanical test results of 37 sandstone specimens, the fracture patterns can be quite complicated due to an interaction of tensile fracture with shear fracture or bending fracture. To improve the prediction accuracy of the statistical analysis, a digital image correlation (DIC) technique was used to capture the dynamic fracturing process and to verify the validity of the Brazilian tests. Finally, only 15 specimens met the principle of the Brazilian test with a valid tensile failure. Using the energy-dispersive system (EDS), a distinct disparity of elemental concentrations was identified between those two sides of a fracture, such as the content contrasts of C, Mg, Al, Si, Ca, Ti, Fe, and Zn. These key elements can be used to identify the fracture positions and predict the rock mechanical properties, e.g., Brazilian test strength, Young's modulus, and Poisson's ratio. The excellent correlation performance, between rock strength parameters and elemental concentrations, proved it applicable to provide another potential function of the Elemental Capture Spectroscopy log in the evaluation of wellbore integrity. [ABSTRACT FROM AUTHOR]