A cross-anisotropic constitutive model considering bedding plane spacing effect and its applications to tunnel cavity analysis in layered rock mass

Abstract

Tunnel cavities are often excavated in layered rock mass characterized by the pronounced cross-anisotropic behavior. To simulate these kinds of problems, a new cross-anisotropic constitutive model is developed to represent both the stiffness and strength anisotropy of layered rock mass, with the aid of a cross-anisotropic elastic compliance matrix and a proposed generalized anisotropic stress tensor, respectively. By formulating the constitutive model in second-order cone programming (SOCP) format, the SOCP optimized finite element method (FEM-SOCP) is established and applied to tunnel cavity analysis involving cross-anisotropic rock mass. The proposed generalized anisotropic stress tensor with three stress scaling factors endows the FEM-SOCP framework with promising feasibility, flexibility and practical applicability in simulating the cross-anisotropic rock mass. By introducing five independent elastic constants into the cross-anisotropic elastic compliance matrix, the bedding plane spacing can be taken into account in cross-anisotropic rock mass. Based on the analyses of three examples, namely an unsupported tunnel, a cylindrical cavity expansion and a tunnel in layered rock mass, it is found that the implicitly modeling FEM-SOCP can capture the deformation behavior and failure mode of cross-anisotropic rock mass induced by tunnel cavity, being consistent with those simulated by the explicitly modeling discrete element method (DEM).

Keywords

tunnel / cross-anisotropic rock mass / bedding angle and spacing / stress scaling factor / second-order cone programming-optimized finite element method / discrete element method

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