Formation and growth of multiple, distinct ice lenses in frost heave

Abstract

This paper presents a fully coupled thermo‐hydro‐mechanical (THM) model which simulates frost heave in fully saturated soils. The model is able to simulate the formation and growth of multiple distinct ice lenses. The basic equations of the system were derived using the continuum theory of mixtures, nonequilibrium thermodynamics, and fracture mechanics, considering skeleton deformation, water flow and heat transport. Central to this model is the coupled transport of mass due to the temperature gradient across the frozen fringe, which acts as the main driving force of the phenomenon. The model is formulated in terms of measurable physical properties and thus no ad hoc parametrization is required. In an ice‐lens‐free state, the system is solved as a continuum using the finite element method (FEM). It is then locally treated as a discontinuous system upon the formation of ice lens, by enriching the elements carrying the embedded ice lens(es) using the extended finite element method (X‐FEM). The accuracy and efficiency of the proposed model has been verified using several laboratory tests on Devon silt samples at different overburden pressures and thermal boundary conditions. Shut‐off pressures have been also estimated and compared with the experimental results.

Numerical simulation of frost heave of saturated soil considering thermo‐hydro‐mechanical coupling

“…Referring to Gao et al, 22 the difference of pressure between ice and water in frozen soil can be denoted as the cryogenic suction (positive value) due to the ice-water interface tension, 𝑠 cryo 𝑠 cryo = 𝑝 i − 𝑝 w (8) Combining Equations ( 7) and ( 8), 𝑠 cryo can be calculated by the temperature and ice pressure as…”

“…According to Equation (22), water flow in frozen soils is related to temperature due to cryogenic suction. Equation ( 22) also implies that temperature gradient cannot directly drive water flow in unfrozen zones because of the absence of waterice interface.…”

“…In conclusion, Equations ( 40) and ( 42) provides an approach to describe the growth of ice lens, while Equation (42) describes the mechanical behavior of freezing soil. According to Equations ( 16) and ( 42), the water flow and phase change in the frozen soil without ice lens can change the effective stress, then affect the ice pressure, leading to the reduction of the water flow due to the change of the pressure gradient in Equation (22). However, if an ice segregation takes place, the ice pressure will decrease to the total stress and remain unchanged according to Equation (42), leading to the continuous water flow to the ice lens.…”

“…Water was freely available at the base, that is, p = 0, while the top is impermeable, which means the water flux is zero. It should be noted that the soil samples are regarded as saturated during freezing tests, 22,32 even if it can be slightly unsaturated due to the movement of pore water. In other words, the unsaturated behavior and vapor flow are neglected.…”

“…Different types of mechanical boundary conditions, for instance, displacement boundary conditions may not be easily implemented in the model. Gao et al 22 presented THM coupling models using the extended finite element method, which is able to describe the growth of the ice lens as a crack in the soil. However, in their model the water can freely flow towards the segregated zones, the effect of the stress of ice lens on water flow is neglected, which might not in accordance with the actual physics when the overburden load reaches a high value.…”