Coupled model for water, vapour, heat, stress and strain fields in variably saturated freezing soils

A Coupled Thermal‐Hydraulic‐Mechanical Approach to Modeling the Impact of Roadbed Frost Loading on Water Main Failure

“…This over‐consolidation is mainly caused by: (a) the accumulation of ice, which gradually occupies pore space and squeezes soil particles downward because of the upper fixed boundary; (b) the movement of soil water (moisture) toward the freezing front feeding the ice growth resulting in an increase in negative pressure (suction pressure) and effective stress in the unfrozen zone (e.g., Huang & Rudolph, 2021); (c) the additional moisture adds to the unit weight of soil in the frozen zone, and simultaneously, (d) induces shrinkage of the soil volume in the unfrozen zone. This results in significant consolidation below the freezing front were also observed in lab and field experiments (e.g., Ono, 2002; Tiedje & Guo, 2011) and simulation studies (e.g., Huang & Rudolph, 2021; Thomas et al., 2009). Therefore, in the transitional areas between the silt and sand, the large displacement differential resulting from the variable soil ice formation during freezing has the potential to damage buried infrastructure such as water mains.…”

“…The energy conservation law of thermal fields in freezing soils can be expressed as (e.g., Bense et al, 2009;Huang & Rudolph, 2021):…”

“…The energy conservation law of thermal fields in freezing soils can be expressed as (e.g., Bense et al., 2009; Huang & Rudolph, 2021): $$${C}_{e}\frac{\partial T}{\partial t}-{L}_{f}{\rho }_{l}{v}_{f}=\nabla \cdot \left[{\lambda }_{e}\nabla (T)\right]-{C}_{l}{q}_{l}\cdot \nabla T$$$ where $${q}_{l}$$ is the water flow rate ($$=K\left({\theta }_{l}\right)\nabla {\varphi }_{h}$$); effective heat capacity $${C}_{e}$$ is calculated as a volumetric weighted mean of the heat capacities of water $${C}_{l}$$, ice $${C}_{i}$$, air $${C}_{a}$$, and soil grains $${C}_{soil}$$; while effective thermal conductivity $${\lambda }_{e}$$ is calculated as a weighted geometric mean (e.g., Huang & Rudolph, 2022) from thermal conductivities of water $${\lambda }_{l}$$, ice $${\lambda }_{i}$$, air $${\lambda }_{a}$$, and soil grains …”

“…For this study, the built‐in modules within the Comsol platform porous media fluid flow, heat transfer, linear elastic geomechanical behavior and the equation‐based interface for the ice volumetric content are used for simultaneously solving the governing equations (Comsol, 2017). Comsol has been demonstrated to be good at simulating these complex, multiple‐coupled processes (e.g., Huang et al., 2019; Huang & Rudolph, 2021, 2022; Lai et al., 2009). We assumed isotropic ice growth under the two‐dimensional plane strain condition.…”

“…Soil freezing resulting from the downward propagation of cold winter temperatures along the upper surface of the roadbed may result in the development of variable degrees of strain within the subsurface depending on soil type, initial water (moisture) content, and availability of additional water in the subsurface. Additional soil water may be drawn toward the freezing front through cryosuction (e.g., Huang & Rudolph, 2021; Williams & Smith, 1989). In the case of a paved road surface (concrete or asphalt), the roadbed may restrict the upward deformation of the subsurface soil profile as freezing advances and the soil expands due to ice growth.…”