Dynamic constitutive model for subloading surface of rock materials considering rate effect

In order to reflect the characteristics of the hysteresis loop under cyclic loading and the rate effect under dynamic loading of the rock materials, firstly, based on the theory of subloading surface, the stress-path model for the subloading surface considering Drucker-Prager criterion is proposed. Secondly, on this basis, the rate effect of rock materials is analyzed. The rate effect of stiffness is considered in the elastic modulus and the rate effect of strength is taken into account in the Drucker-Prager criterion, and then the dynamic constitutive model for subloading surface of rock materials is established. Finally, through the self-programming, the dynamic constitutive model for the sub-loading surface of the rock materials is implanted, and the mechanical response of the rock materials under dynamic loads is simulated. The results show that the stress path model, compared with the Drucker-Prager criterion, can describe the Massing effect and the ratchet effect of basalt under cyclic loading, and reveal the developmental pattern of basalt. Through the simulation of dynamic uniaxial loading and cyclic loading by using the dynamic model, it is found that the larger the strain rate is, the larger the elastic modulus is and the smaller the strain is, which is in accordance with the mechanical properties of the rock during dynamic loading. Under the seismic load, the stress-strain curve of the rock also exhibits the hysteresis loop and rate effect. The seismic load has the equivalent cyclic load and the form of dynamic load, and the dynamic constitutive model for subloading surface is feasible to simulate the mechanical properties of the rock materials under seismic loads.