Modeling of Shear Crack Propagation in Rock Masses Using Mesh-Free LRPIM

Qingbo Li,Nengxiong Xu,Weifeng Wan,Yazhe Li,Daniele Baraldi

doi:10.1155/2021/6654812

Abstract

The modeling of shear cracks in materials is critical in various engineering applications, such as the safety analysis of concrete structures and stability analysis of rock slopes. Based on the idea of Goodman element, the elastic-plastic constitutive model of the shear cracks is derived, and the elastic-plastic analysis of shear crack propagation is realized in the local radial basis point interpolation method (LRPIM). This method avoids the loss of accuracy caused by the mesh in the analysis of fracture propagation, and the crack propagation of rock brittle material is simulated. The investigation indicates that (1) the LRPIM results are close to the FDM results, which demonstrates that it is feasible to analyze shear cracks in rock masses. (2) Compared with the results of the built-in oblique crack model, when the LRPIM is used to analyze crack propagation, the results are close to the experimental results, showing that the LRPIM can model shear crack propagation in a rock mass. (3) The propagation path using the LRPIM is not sufficiently smooth, which can be explained as the crack tip stress and strain not being sufficiently accurate and still requiring further improvement.

Highlights

Rock masses are discontinuous media that contain many kinds of defects, such as cracks, bedding, and holes
(2) Compared with the results of the built-in oblique crack model, when the local radial basis point interpolation method (LRPIM) is used to analyze crack propagation, the results are close to the experimental results, showing that the LRPIM can model shear crack propagation in a rock mass. (3) e propagation path using the LRPIM is not sufficiently smooth, which can be explained as the crack tip stress and strain not being sufficiently accurate and still requiring further improvement
Considering the solid mechanics problem defined in domain Ω, the local weighted residual method is used for node I to satisfy the governing equation, and the local weak equation of the node is obtained. e form of the locally weighted residuals is defined on the local integral domain Ωq and the corresponding boundary Γq in the following form

Summary

Introduction

Rock masses are discontinuous media that contain many kinds of defects, such as cracks, bedding, and holes. Existing shear cracks have a substantial influence on the mechanical characteristics of rock masses. A rock mass with many defects is extremely sensitive to the action of forces. Erefore, it is necessary to analyze the influence of shear cracks and their propagation under the action of external forces. Considering the solid mechanics problem defined in domain Ω, the local weighted residual method is used for node I to satisfy the governing equation, and the local weak equation of the node is obtained. E form of the locally weighted residuals is defined on the local integral domain Ωq and the corresponding boundary Γq in the following form. Considering the solid mechanics problem defined in domain Ω, the local weighted residual method is used for node I to satisfy the governing equation, and the local weak equation of the node is obtained. e form of the locally weighted residuals is defined on the local integral domain Ωq and the corresponding boundary Γq in the following form

Methods

Results

Discussion

Conclusion