Rock creep model based on the theory of fractional derivatives
YAN Mengyuan
WANG Xiaojian
Abstract：Traditional creep models often fail to accurately describe the non-steady-state creep charac-teristics of rocks,especially the nonlinear behavior during the accelerating creep stage,which limits the applicability and precision of the models.To address this issue,this study replaces the traditional dashpot with a fractional-order dashpot based on the classical generalized Kelvin model and the Muray-ama body model.This leads to the proposal of an improved generalized Kelvin body and Murayama body model.Additionally,a new fractional-order creep model for rocks is introduced using the super-position principle.Based on this,creep equations under one-dimensional and three-dimensional stress states are derived.To verify the validity of the model,experiments were conducted on green schist,red sandstone,and sandstone.The results indicate that the fractional-order creep model offers signifi-cant advantages in describing rock creep behavior.Compared to the traditional Nishihara creep model,the fractional-order creep model provides a more precise fit to experimental data,especially in the nonlinear phase,where the fitting accuracy is significantly improved.This confirms the rationality and accuracy of the model.
Keywords：fractional-order derivativerock creepaccelerated creepmurayama bodycreep model
Publication Date：2025-12-31
Online Publishing Date：2025-11-25(First online date of this platform, not the publication date of the document)
Pages：6( 89-94 )