The increase amplitude of residual strength of rock is larger than the rock peak intensity of rock with the increase of confining pressure. Gradually

residual strength becomes the main factor of complete stress-strain curve of rock at the stage after peak intensity. While establishing statistical damage constitutive model

it’s necessary to modify the residual strength. Based on the strain strength theory and hypothesis of rock particles intensity obeying Weibull random distribution

a statistical damage constitutive model for rock under triaxial compression，which can describe the characteristics of rock post-peak softening，is established by adopting Hoek-Brown criterion

and the residual strength to modify the damage parameter is considered. Then

all these model parameters analytic solutions are deduced according to the geometric features of rock complete stress-strain curve. On the basis of experimental results of granite specimens

the influences of Weibull distribution parameters on the rock damage constitutive model are studied. At the same time

the value of modified coefficient and the damage process of rock are discussed. Finally

the achieved theoretical curves by the damage model of rock under different confining pressures are comparatively analyzed with the results of conventional triaxial compression test of four kinds of rock: porphyaceous adamellite

fine-particle marble

sandstone and silty mudstone. The results indicate that this statistical damage constitutive model is able to provide an accurate description for complete stress-strain curve and residual strength for rock. All these are meaningful to the research of rock damage as well as to choose suitable measures to strengthen rock mass.