Fractional derivative-based creep constitutive model of deep artificial frozen soil

A fractional derivative constitutive model of deep artificial frozen soil was established based on the Nishihara model by analyzing the triaxial creep and shear test results of deep artificial frozen soil under different confining pressures and temperatures. Considering the physical and mechanical properties of frozen soil, linear Newton equations were substituted with nonlinear Newton equations, and a flexibility matrix was derived for numerical calculations. A relevant constitutive finite element program was developed and used to simulate a deep artificial frozen curtain of a coal mine through a user subroutine of the ADINA commercial finite element software. The theoretical calculations agreed well with the experimental results of the triaxial creep tests, and the numerical simulation results were consistent with the field measurement data. This fractional derivative constitutive model was verified to describe the non-decaying creep deformation characteristics of deep artificial frozen soil under high confining pressures. It can also be applied to the design and calculation of artificial freezing in deep strata.