Dynamic deformation behavior of rock based on fractional order calculus

In order to describe the dynamic strain of rock better, lateral-axial strain fractional dashpot and viscoelastic lateral-axial strain combined models are put forward on the basis of viscoelastic stress-strain combined model theory. The fractional lateral-axial strain relationship and the fractional volume strain model are proposed based on the fractional order calculus, and the corresponding equations under dynamic loading and cyclic loading are derived. The analytic solution for the model of lateral-axial strain relationship is given theoretically. Moreover, a multi-functional material testing set-up is employed to measure the lateral-axial strain of a variety of rock, concrete and gypsum samples under the dynamic loading and cyclic loading. The parameters of the lateral-axial strain model are determined by fitting to the experimental results of lateral-axial strain of rock. In addition, a sensitivity study for the analytic solution of the lateral-axial strain model is carried out, showing the effects of confining pressure, strain level, fractional derivative order and model coefficient on axial strain of rock samples. Furthermore, it’s found that the new model can describe the volume strain phenomenon of negative and positive dilatancy and the variation law of deformation under dynamic loading and cyclic loading in rock.