Microstructure‐based effective stress for unsaturated frozen soils

Abstract

Current knowledge on unsaturated soils suggests that the effective stress should be related to soil microstructures, by which the immobile water attached to the soil solid in micropores and the free water mainly governed by capillary effects in relatively large pores can be distinguished. Paying attention to this knowledge, the micro-and macroscopic degrees of saturation to separate micro-and macropores occupied by the equivalent water (ice and liquid water) are used and the microstructurally based effective stress for unsaturated frozen soils is proposed using the first law of thermodynamics and the mixture theory. The formulated

Finite element modeling of thermal‐hydro‐mechanical coupled processes in unsaturated freezing soils considering air‐water capillary pressure and cryosuction

“…Such application is valid when there is a pore water pressure balance between macropores and micropores. More detailed microstructure‐based derivation for the equivalent pore pressure for unsaturated porous media is presented by Yin et al 49 . The simulated total pore pressure changes during the numerical test are obtained and displayed in Figure 10A.…”

“…where ∇ = ⟨ 𝜕∕𝜕𝑥 𝜕∕𝜕𝑦 𝜕∕𝜕𝑧 ⟩ represents the gradient operator and "⋅" denotes the dot product. According to Yin et al, 49 the total stress can be approximated using the effective stress and pore pressure components:…”

“…Equation (29) represents the conservation of linear momentum in the porous media, which states the balance between the divergence of the total stress tensor ( σ ) and body force ( b ): $$$$\begin{equation}\nabla \cdot {{\bm \sigma }} + {{\bf b}}\ = \ 0\end{equation}$$$$where $$\nabla \ = \langle { \def\eqcellsep{&}\begin{array}{*{20}{c}} {\partial /\partial x}&{\partial /\partial y}&{\partial /\partial z} \end{array} } \rangle \ $$ represents the gradient operator and “⋅” denotes the dot product. According to Yin et al., 49 the total stress can be approximated using the effective stress and pore pressure components: $$$$\begin{equation}{\bm{\sigma \ }} = {\bm{\sigma ^{\prime}\ }} - {S}_w{P}_w{{\bf I}} - {S}_g{P}_g{{\bf I}} - {S}_i{P}_i{{\bf I}}\end{equation}$$$$where $${\bm{\sigma ^{\prime}}}$$ is the effective stress. Thus, in Equation (30), saturations of individual components (fluid water, air, and ice) are used as weight coefficients for their pore pressure components.…”