A Nonlinear Damage Creep Model with Time-varying Viscoelasticity Based on Fractional Theory for Rock Materials

Abstract

This study is aimed at introducing a nonlinear damage creep model with time-varying viscoelasticity, which is based on the Caputo fractional derivative with respect to the Mittag-Leffler (M-L) and damage functions. First, the M-L function was applied to the Caputo fractional calculus to describe the nonlinear creep behavior. A series of creep experiments of sandstone were performed and the mechanical behavior of the accelerating creep was depicted in detail. Second, the experimental data of sandstone and experimental data of salt rock and mudstone achieved from previous classical studies were used to confirm the reasonability and applicability of the proposed damage creep model. Finally, the proposed damage creep model was reported to be in excellent agreement with the obtained experimental creep data, and the accuracy between predicted data and measured data is analyzed.