A full-stage creep model for rocks based on the variable-order fractional calculus

Abstract

An accurate characterization of rocks for the modelling of creep is an essential step toward ensuring the safety with respect to reliability of underground rock engineering. In this work, a novel variable fractional order rheological model is established to describe the full-stage creep behavior of rocks. With simpler form and fewer parameters, the proposed model is verified to have the ability for the description of trimodal creep behavior of rocks. The evolution of mechanical properties during creep is quantitatively described by the variable fractional order including the creep hardening, softening and the transition part between them. Moreover, the physical significance of fractional order is further explored by the commonly accepted competition mechanism of creep hardening and softening for brittle creep, which indicates that the mechanical property of rocks during creep is harder with lower water contents but softens faster with larger applied stresses. Furthermore, the linear form of the variable order function is determined by applying the new variable order fractional operator. It is shown that the slope of order function confirms the creep strain rate and the intercept of order function primarily affects the critical time for entering the nonlinear creep phase. Finally, the rising tendency of fractional order reveals that the accelerating creep is a continuous softening process of mechanical properties since the larger values of fractional order exhibits the property of rocks is more viscous.