Abstract: To solve the mesh dependence of finite element method in simulating the failure of brittle rock， an improved microplane damage model was built based on the microplane model and regularization method. And the numerical simulations were compared with the experimental results under uniaxial compression test. Heterogeneous indexes were introduced for the damage process simulation of three points bending tests. The results showed that the damage area was more concentrated at the high heterogeneous index. In addition， the three points bending tests with different characteristic length were simulated by regularization based on higher-order deformation gradients. The results showed that the damage evolution of microplane damage models with regularization are analogous when the characteristic length is 1mm， while the microplane damage model without regularization has a significant mesh-dependence at different mesh size. Finally， the load-displacement relationship of normal model and regularization model was contrasted. Mesh density has little effect on the microplane damage model based on regularization with higher-order deformation gradients.

Key words: microplane model; heterogeneous; damage evolution; regularization; numerical simulation