Abstract:Based on some principal rules of brittle rocks¢ polyaxial tests and previous researches,three controlling failure types for brittle rock are obtained. The first type represents the brittle failure controlled by extension microcrack under the condition of lower hydrostatic pressure;the second represents the ductile failure controlled by friction sliding action under the condition of higher hydrostatic pressure when microcrack is close;and the third represents brittle-ductile failure type controlled by multiple factors mentioned above under the condition of high hydrostatic pressure when some microcracks are open and others are close. On the basis of the achieved result and the effect of stress such as minor principal stress,intermediate principal stress,hydrostatic pressure,stress Lode degree,a generalized hyperbolic failure function adapted naturally with the envelope form of Mohr-Coulomb criterion is proposed for brittle rocks;and a smooth failure function acquired by Yu Maohong is also presented. Thus,a generalized polyaxial strain energy(GPSE) strength criterion is created. The criterion is similar to hyperbolic strength criterion including uniaxial compression strength and uniaxial tensile strength,which is an extended form of Griffith-Murrell criterion essentially under the condition of polyaxial stress when hydrostatic pressure is lower,and it represents the first failure type. However,the criterion is similar to generalized Mises criterion when hydrostatic pressure is higher,and it represents the second failure type. The transition part between the two criteria represents the third failure type when hydrostatic pressure is high. Finally,the GPSE strength criterion for rock is verified by polyaxial test data of brittle rocks. The strength criterion for rock can be widely used to brittle rocks and allows for a good description of the several effects of stresses mentioned above,nonlinear characteristics of strength and marked difference for tensile strength and compression strength.