Discussion of constitutive relation of rocks based on correction factor

In order to establish a more realistic constitutive relation to the engineering rocks with original micro-failure，the relationship between the original damage part and the whole part of the rock was obtained by introducing the correction coefficient. Based on the Weibull random distribution and damage mechanics theory, and under the condition of Coulomb criterion, the combination of theoretical derivation and experimental verification were used to establish the damage constitutive relation of rock based on the correction coefficient. The rationality of the red sandstone was verified by the conventional mechanical properties test. The results show that the theoretical curve obtained by the model is in good consistent with the experimental curve, which can better reflect the characteristics of various rock deformation and failure stages. In the process of loading, the rock is further damaged on the basis of original damage, and ultimately completely failed; The changes of the model parameters m and F0 have an effect on the rock damage model. With the change of F0 , the elastic phase, the peak stress and the corresponding strain, and the strain just reaching the complete failure show a consistent change, affecting the brittleness and ductilityof the rock.As the change of m, the elastic phase and the peak point change but are not obvious, the peak stress and post-peak damage degree have a greater influence. With the change of correction coefficient , the stress corresponding to the same strain changes before and after the peak changes. However, the value of γ has no effect on the development trend of the theoretical curve, nor does it change the size and position of the peak point.