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Layered shales exist widely and are often encountered during shale gas development. However, the mechanical response of layered shales is significantly affected by the existence of beddings, resulting in the obvious anisotropy characteristics regarding deformation, strength and failure mode. To clarify the underlying mechanisms of shale anisotropy that control the safety of engineering projects, the numerical simulation and theoretical analysis were conducted. The results show that with the growth of confining pressure, the compressive resistance of shales gradually increases, the shear fractures govern the instability and the anisotropy index decreases. Furthermore, several strength criteria for layered rock masses were summarized, and the modified Jaeger strength criterion was proposed by introducing the anisotropic parameter Rcθ ${R}_{c\theta }$. It can effectively reflect the failure modes and strength features of layered shales under triaxial conditions with a higher accuracy. Besides, the variation of cohesion and internal friction angle of layered shale samples was comprehensively analysed under the triaxial conditions. Clearly, as the inclination angle of bedding planes increases, the cohesion of layered shales first decreases, but then increases under triaxial compression, showing the 'U'‐shaped changing trend. Additionally, the internal friction angle of layered shales gradually increases with the increase in the inclination of bedding planes. [ABSTRACT FROM AUTHOR]

Rocks are less resistant to tension than to compression or shear. Tension cracks commonly initiate compression or shear failure. The mechanical behavior of layered rocks under compression has been studied extensively, whereas the tensile behavior still remains uncertain. In this paper, we study the effect of layer orientation on the strength and failure patterns of layered rocks under direct and indirect tension through experimental and numerical testing (RFPA2D: numerical software of Rock Failure Process Analysis). The results suggest that the dip angle of the bedding planes significantly affects the tensile strength, failure patterns, and progressive deformation of layered rocks. The failure modes of the layered specimens indicate that the tensile strength obtained by the Brazilian disc test is not as accurate as that obtained by the direct tension test. Therefore, the modified Single Plane of Weakness (MSPW) failure criterion is proposed to predict the tensile strength of the layered rocks based on the failure modes of direct tension. The analytical predictions of the MSPW failure criterion agrees closely with the experimental and numerical results. In rock engineering, the MSPW failure criterion can conveniently predict the tensile strength and reflect the failure modes of layered rocks (such as shale, slate, and layered sandstone) with satisfactory accuracy. [ABSTRACT FROM AUTHOR]

Highlights • An anisotropic constitutive model of layered rock masses is proposed and numerically implemented. • The equivalent anchoring parameters for bolted layered rock masses are studied based on the proposed model. • The equivalent anchoring method for bolted layered rock mass is proposed. • The Huashang Road tunnel in Wuhan China is simulated by the equivalent anchoring method. Abstract Rock bolting has been widely utilized for reinforcing underground openings, such as tunnels and mining. To ease the complexity of numerically simulating of the bolted rock mass, a novel method for equivalent anchoring simulates the reinforcement effect of the bolts by considering the anisotropic characteristics of the layered rock mass. The jointed material model in ABAQUS is improved by incorporating the anisotropy through the programming language FORTRAN. Based on the improved jointed material model, the equivalent anchoring parameters of the bolted layered rock masses are studied through a series of numerical tests. The numerical outcomes reveal that the improved jointed material model can be used to simulate the anisotropic features of the layered rock mass by comparing the classic and analytic solutions. The degree to which the supporting parameters affect the equivalent reinforcement performance are different in anisotropic rock masses, and the sensitivity of their influence is bolt length > bolt spacing > bolt diameter. Furthermore, an equivalent anchoring model for bolted rock masses (the formula of the improved parameter between the ratio of bolt length to tunnel diameter and the ratio of bolt diameter to bolt spacing) is proposed through numerical results analysis by the multiple linear regression method. An application case shows the field monitoring agreed well with the predicted vertical displacement of the tunnel demonstrating the feasibility of the proposed simulation method for the bolted rock mass. The results show the proposed method in this study can be conveniently utilized for efficient simulation of the mechanical behavior of bolted rock masses. [ABSTRACT FROM AUTHOR]