An improved Maxwell creep model for rock based on variable-order fractional derivatives

For describing the time-dependent mechanical property of rock during the creep, a new method of building creep model based on variable-order fractional derivatives is proposed. The order of the fractional derivative is allowed to be a function of the independent variable (time), rather than a constant of arbitrary order. Through the segmentation treatment, according to different creep stages of the experimental results, it is found that the improved creep model based on variable-order fractional derivatives agrees well with the experimental data. In addition, the fact is verified that variable order of fractional derivatives can be regarded as a step function, which is reasonable and reliable. In addition, through further piecewise fitting, the parameters in the model are determined on the basis of existing experimental results. All estimated results show that the theoretical model proposed in the paper properly depicts the creep properties, providing an excellent agreement with the experimental data.