Investigating the Constitutive Model of Frozen Supersulfate Saline Soil: Insights from Fractional Calculus

The study of the mechanical properties of frozen saline soil is one of the key issues in addressing the design of infrastructure in cold regions. This research focuses on the supersulfated saline soil of the Ningxia Yellow River Irrigation Area in China, conducting triaxial tests under negative temperatures (−5, −10, −15 °C, and − 20 °C) with varying water contents (12%, 16%, 20%). Based on fractional calculus theory and incorporating an exponential decay factor, this study proposes a novel fractional-order constitutive model for a unified description of the softening and hardening behaviors in frozen saline soil. The model treats frozen saline soil as a composite blend of ideal solids and ideal fluids in varying proportions, taking into account the material's inherent time-dependency and non-linear stress-strain relationships. Finally, the validity of the model is verified by the calculated values of the model and the triaxial tests. The results indicate that, based on preliminary judgment, due to the presence of salt solutes, a large amount of liquid water remains in the supersulfated saline soil at temperatures ranging from 0 to −10 °C, forming an unstable state called "warm frozen saline soil". The mechanical properties of frozen saline soil depend on the relative content of unfrozen water, ice crystals, and salt crystals and the formation of ice and salt crystals significantly enhances the strength of frozen saline soil. The computational results of the improved fractional constitutive model align well with experimental results, effectively describing the stress-strain relationship of frozen supersulfate saline soil. In the model, the parameter κ functions analogously to an elastic modulus and exhibits a linear relationship with temperature, and the parameter α characterizes the strain hardening of saline soil, while β describes its softening behavior. The proposed fractional constitutive model, with only three parameters having clear physical significance, is convenient for practical engineering applications.