In recent years，some progresses are achieved in the research of rock mesoscopic failure，but elastic damage model cannot be adopted simply in many practical projects. Therefore，most important influences of mesoscopic local plastic deformation of rock on strength and stability of rock mass should be considered. An elastoplastic damage mesoscopic model is deduced based on the theory of strain space. The failure elements deleting method is put forward to simulate the crack propagation. If the degree of damage elements equals 1，the code deletes these elements automatically in order to explicitly show how cracks propagate in rock. High-performance parallel calculation is adopted to realize 3D numerical simulation of rock fracture process. The failure processes of marble three-point bending specimens with modes I and I–II cracks are numerically simulated. By setting crystal in crack-tip，transgranular fracture and intergranular fracture are studied. The initiation and propagation of cracks and the failure shapes of the specimens are given. The influence of mesoscopic heterogeneity on rock macroscopic failure mechanical behaviors is analyzed. The calculation results show that the rock mass stability considering mesoscopic local plastic deformation is better than that without consideration of local plasticity. The results of simulation and physical tests accord each other well，which illuminates the validity of the elastoplastic damage failure model. Failure pattern of transgranular fracture and intergranular fracture depends on the intension of crystal. The failure elements deleting method solves the difficult problem of FEM to simulate propagation. The model and method may be valid in practical projects.

Anisotropy and strength nonhomogeneity are common phenomena for clay foundation. However，the existing theories of bearing capacity calculation are mainly applicable to isotropic and homogeneous soils. Upper bound method is used to calculate the bearing capacity of rough strip foundations on clay with anisotropy and nonhomogeneity. The failure mechanism employed in the upper bound method has already been verified by other scholars to be the best one in multi-block upper bound method to calculate the bearing capacity of rough strip foundations on isotropic and homogeneous soils. To examine the proposed method，various calculations have been carried out. The results are compared with those of the characteristic method and other upper bound methods. It can be found that the proposed method gives the best calculation results among the existing upper bound methods in the literaturs. The effects of the anisotropy and strength nonhomogeneity on the values of the bearing capacity are then discussed. Failure envelopes can be obtained in the upper bound limit analysis and the mechanism for the influence of soil anisotropy and nonhomogeneity on the bearing capacity of foundation can be revealed. From the calculation results，it can also be found that the anisotropy and nonhomogeneity of soil affect not only the bearing capacity of foundation but also the location and shape of the failure envelopes.