An Improved Bingham Model and the Parameter Identification of Coal (Rock) Containing Water Based on the Fractional Calculus Theory

Abstract

The rheological properties of coal (rock) containing water cannot be characterized by the traditional Bingham model. This problem was addressed in this study through theoretical analysis and experimental research. Based on fractional calculus theory, a fractional calculus soft element was introduced into the traditional Bingham model. An improved Bingham model creep equation and a relaxation equation were obtained through theoretical derivations. Triaxial creep experiments of coal (rock) with different moisture contents were conducted. The parameters of the improved Bingham model were obtained by the least-squares method. Conclusions are as follows: (1) in the improved Bingham model, the stage of nonlinear accelerated creep could be characterized by the creep curves of the soft element; (2) with the increasing moisture content of the coal (rock), the transient strain and the slope of the steady creep stage increased and the total creep time showed a decreasing trend; and (3) the parameters of the creep model were obtained by nonlinear fitting of experimental data, and the fitted curve could better describe the whole creep process. The rationality of the improved creep model was verified. It can provide a theoretical basis for the study and engineering analysis of coal (rock).