Modified Effective Stress Theory for Rate-Dependent Frozen Soil With Phase Transitions From Pre-Melting Thin Film to Composite

Abstract

We propose a modified mixture theory and a corresponding dual-skeleton constitutive law that captures the multi-temporal-scale rate-dependent response of frozen soil under phase transitions. We hypothesize that the transport of ice crystals surrounded by a thin water film may halt during freezing once the ice crystals grow to a size comparable to that of the pores. Since ice crystals may bear the load with the solid skeleton when stuck in the pores, the shear and tensile strength of the ice–solid skeleton increases. This transition of the role of ice crystals during the freezing and thawing from inducing cryo-suction to being a constituent of a two-phase composite is captured via a dual-skeleton theory. Consequently, we modify the effective stress theory to capture the kinematics transition between the fluid-like transporting ice crystals and solid-like ice crystals. This transition is considered separately from the ice–water phase transition in the field theory. This setting, in return, allows us to derive a dual-solid-skeleton constitutive theory where the rate-dependent constitutive response of the fully frozen soil is obtained via those of the unfrozen solid matrix and the ice crystals that exhibit creep at different time scales. THM mixed finite element simulations are conducted on laboratory samples under freeze–thaw cycles from hours to days. The numerical results show good consistency with experimental records at both scales. The numerical model provides insights into the rate-dependent processes involved across temporal scales and allows controlled parametric studies to identify different coupling mechanisms at various stages of the freeze–thaw cycles.