Study on constitutive model of coal rock damage under graded cyclic loading and unloading

Taking coal as the research subject, the damage mechanical properties of coal were studied by grading cyclic loading and unloading tests. Using the Weibull statistical distribution and the introduction of damage variable D, a damage constitutive model suitable for coal at loading and unloading stages was established, which conforms to Mises yield criterion based on the coal microelement strength. According to the test data, the model parameters of each cycle grade were determined by nonlinear fitting method, and the physical significance of the model parameters was analyzed. The results show that the damage constitutive model based on Mises yield criterion can reflect the stress-strain relationship of coal under grading cyclic loading and unloading accurately. With the increase of loading and unloading levels, the residual strain accumulates, and the elastic modulus increases first and then decreases gradually. The hysteresis loop shape shows the characteristics of “fat”-“thin”-“fat”. The constitutive model p