Fractional derivative modelling for consolidation of multilayered saturated soils with interfacial thermal contact resistance subjected to time-dependent heating and loading

In this paper, the one-dimensional rheological consolidation characteristics of multilayered saturated soil foundations under time-dependent loading and heating are investigated by considering the semi-permeability and the interface thermal resistance. By introducing the fractional derivative model and the thermos-elastic theory, a thermo-mechanical coupling model is established to describe the rheological properties of saturated soils. Semi-analytical solutions for strain, temperature increment, pore water pressure and settlement were derived through the Laplace transform and its inverse. The accuracy of the solutions proposed in this paper has been verified by comparing with existing solutions. The effects of different thermal contact models of the interface on the rheological properties of saturated soils under semi-permeable boundary are discussed, and the effects of fractional derivative order, constitutive material parameters, and thermal conductivity of soil on the thermal consolidation process are investigated. The results show that: neglecting the thermal resistance effect can result in an overestimates of the impact of rheological properties on the thermal consolidation process of saturated soils under semi-permeable boundaries; As the thermal resistance coefficient increases, the influence of soil thermal conductivity on settlement decreases.