Abstract：The finite-cover-based element-free method developed by the authors is briefly illustrated. The method takes the individual merits of both manifold method based on finite cover technique and the element-free method based on Galerkin weak form. In the method，the whole domain is overlaid by a series of overlapped mathematical covers. While being cut by joints，interfaces of different media，and physical boundaries，a mathematical cover may be divided into two or more completely disconnected physical covers. A cover weight function defined on each physical cover in conjunction with the multiple weighted moving least square approximation is used to determine shape function of a point under consideration. Afterwards，discrete equations of the boundary-value problem with discontinuity can be established by using variational principles. Then，the proposed method is extended to numerical simulation of fractural behavior and crack development process of rock masses with initial cracks. Two key techniques are used with the capability of automatically simulating crack propagation effectively：one is arbitrary small increment size of crack propagation and another is near-crack-tip stress releasing procedure. The proposed algorithm that is numerically implemented can be used for the evaluation of rock structures with stability of crack and automatic simulation of crack propagation，cutting-through and interaction of two adjacent cracks. Since a crack can propagate in a very small size of increment，the trajectory of the crack propagation is stable and does not manifest any sensitivity to choice of the increment size；and example analyses of fractural behavior of the rock mass with single crack are made. The numerical results are compared with the available theoretical or numerical solutions to verify the applicability of the method to fracture and discontinuous deformation analysis problems. Then，the stress intensity factor and crack propagation process of rock mass with multiple cracks are numerically simulated. It is shown that the proposed method is superior to the manifold method and the element-free Galerkin method.
