A Meshless Manifold Method And Test Scheme For Fractured Rockmass

The background of the researches in this paper is the fractured rock mass of the hydropower underground group (rock high slope). Based on numerical manifold method and meshless methods, some numerical methods are presented to simulate the discontinuous domain and the stress field at the tip of a crack for fractured rock mass. And the corresponding tests are done.At first, in the paper, the numerical manifold method based on the method of weighted residuals (MWR) is presented. The solving equations of the numerical manifold method (NMM) were formed by the minimum potential energy principle before. But for many practical problems, it is very difficult to find the functional of the governing equations, and then the minimum potential energy principle or the variational principle can't be used to obtain the solving equations of the numerical manifold method. As a matter of fact, we must choose a general method to obtain the solving equations of NMM. The paper studies how to obtain the solving equations of NMM from the MWR. And the potential problem is solved by the method in the paper. The method in this paper enriches the mathematical foundation of NMM and extends the applied fields of the method.In order to simulate the real failure process of rockmass, for the local problems at the tip of the discontinuity, the extended numerical manifold method is presented based on the partition of unity method. The local trial functions at the tip of the discontinuity are enriched with the analysis solution at the tip. So the method in the paper can solved the problems of the fractured rockmass and the localization with continuity and discontinuity. At the same time, the method can enhance the precision of the numerical result to discontinuous and its tip.To simulate the discontinuous growth in the fractured rockmass, a meshless manifold (MM) method is presented based on the numerical manifold method and the partition of unity method. The method can conquer the disadvantages of the remesh technique treating with the discontinuous growth problems in the NMM method. In the meshless manifold method, the finite cover technology is applied. And some difficulties in the meshless methods, such as the trial function due to the discontinuity in the displacement, are avoided. The meshless manifold method is a meshless method, which are well suited to problems involving crack propagation due to the absence of any predefined manifold element connectivity.When the discontinuity lies in a cover in the solving domain such as the tip of crack, the meshless manifold (MM) method use the visibility criterion at the tip of crack to divide a cover into two irregular sub-covers. The method may bring some errors in the result. So the enriched meshless manifold method is presented. The method perfects meshless manifold method.The meshless manifold method is also used to analyze transient deformations of the dynamic fracture mechanics for failure rule of the fractured rockmass. So the Meshless manifold method of the dynamic fracture mechanics is presented in the paper. The method forms the shape function by the partition of unity and finite cover technology, so the shape functions cannot be effected by discontinuous in the domain. And dynamic fracture mechanics problems can be solved well.In order to show that the numerical methods in the paper is correct and the full process of crack growth, the CT tests are done. A loading system corresponding to CT machine is designed. The resemble material is used, and the specimens with single crack including hydraulic pressure and no hydraulic pressure are under triaxial compression. When the meshless manifold method is used to analyze the crack growth of the rock samples, the validity and accuracy of the meshless manifold method are illustrated by a numerical example. The numerical results agree to the test ones. At the same time, the curves of the stress and displacement fields at the tip of crack are given.The crack propagation of the fractured rockmass is simulated by the meshless manifold method.