Prediction of Frozen Soil Deformation Characteristics Using Fractional Derivative Creep Model

Abstract

To investigate the temperature susceptibility and nonlinear memory effects of artificially frozen soil creep behavior, this study conducted uniaxial step-loading creep tests under controlled temperatures ranging from -10℃ to -20℃. The transient creep characteristics and steady-state creep rates of artificially frozen soils were systematically examined with respect to variations in temperature and stress. Experimental results demonstrate that decreasing temperatures lead to a decaying trend in the steady-state creep rate of silty frozen soil, confirming that low-temperature environments significantly inhibit plastic flow while enhancing material stiffness. Based on fractional calculus theory, a fractional derivative creep model was established. By incorporating temperature dependencies, the model was further improved to account for both stress and temperature effects. The model predictions align closely with experimental data, achieving over 91% agreement (standard deviation ± 1.8%), and effectively capture the stress-strain behavior of artificially frozen soil under varying thermal conditions. This research provides a reliable theoretical foundation for studying deformation characteristics in cold-regions engineering.