Study on statistical constitutive model and determination of parameters of rock based on normal distribution

Based on an existing new damage model for rock,firstly,according to the law that micro-unit strength of rock was in accordance with normal distribution and the energy theory of damage for rock,a statistical constitutive model for softening and hardening damage of rock under the specific confining pressure that could simulate the full stress-strain process reflecting the characteristic of strain softening and hardening for rock was established.Secondly,by discussing the characteristics of the full stress-strain curve of rock under the specific confining pressure and the relationship between the characteristic parameters(the stress and strain at the peak-stress point),the way for determining the parameters of the constitutive model was set up,and then,a unified statistical constitutive model for softening and hardening damage of rock was developed,which could adequately reflect the full stress-strain process of softening and hardening for rock.There were few parameters in the model and they were easy to be determined,and the present model could synchronously reflect the characteristics of strain softening or hardening of rock,moreover,the way of determining the parameters indicated the physical meaning of the parameters of model.Finally,The rationality of the proposed model was demonstrated with comparative analysis between theoretical and experimental results.