After excavation of tunnel and so on

the surrounding rock mass of them usually generates a lot of persistent cracks which directly affect the stability of surrounding rock mass. It is important for reinforcement of surrounding rock mass to study the strength and failure modes of the rock mass with persistent cracks. On the basis of Coulomb strength criterion

the strength and failure modes of rock mass are studied based on the location relationship of strength curve of cracks and rock in - coordinate system by setting up the mathematical model. The relationships between strength of rock mass and the dip

cohesion

internal friction angle of cracks are explored. The relationships between strength of rock mass and the cohesion

internal friction angle of rock are also studied. The related judgment of failure modes of rock mass with persistent cracks is obtained. Numerical results show that the model can predict the strength and failure modes of the rock mass with persistent cracks under any minor principal stress along any loading and unloading paths. In order to judge the failure modes of rock mass

the traditional method usually need to compare the location of strength curve of cracks

strength curve of rock and Mohr’s circle of stress in - coordinate system. Compared with traditional method

the method of the model is more effective. The conclusion is more intuitive. So the model can better provide technical support for engineering design and reinforcement of rock mass.