Cover refinement of numerical manifold method for crack propagation simulation

A cover refinement method is proposed for the numerical manifold method (NMM) to simulate crack propagation in brittle materials. New mathematical covers are defined for manifold elements near a crack tip. The refinement is done for corresponding mathematical covers of the selected manifold elements. The updating process of mathematical cover with respect to different boundary conditions is introduced in detail. When a mathematical cover is updated, the corresponding physical covers and manifold elements are updated accordingly. Furthermore, the loops of the considered domain are updated as well. Three numerical examples are analyzed to validate the proposed cover refinement method. The numerical results are all in good agreement with those results in the existing studies. It is demonstrated that the proposed cover refinement method has higher accuracy for crack propagation simulation comparing to the traditional numerical manifold method which has a consistent mathematical cover system. The proposed cover refinement method also does not significantly change the manifold elements at the vicinity of the crack tips. A rock slope model with a bilinear failure mode is simulated and progressive failure process of the rock slope is obtained, which demonstrates the applicability of the proposed method in practical rock engineering.