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Finite element modeling of thermo-hydro-mechanical coupled processes in clay soils considering bound water dehydration

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Abstract

This paper presents a new finite element method (FEM) model to simulate the thermo-hydro-mechanical (THM) responses of water-saturated clay soils. The model can account for the effects of temperature variation on bound water dehydration and the corresponding thermo-poromechanical strains. The governing equations, including mass balance, momentum balance, and energy balance, are derived based on the principles of continuum mechanics for porous media. The impact of bound water dehydration on THM behavior is incorporated into the coupled THM equations. The model is equipped with an unconventional plasticity for more accurate description of elastoplastic behavior. To solve the nonlinear system of equations, a modified Newton–Raphson method is employed. The model is validated using laboratory tests on various clay soils with different geological origins, and reasonable agreement is achieved. The thermally induced contraction behavior of clay soils at a low overconsolidation ratio and thermally induced expansion behavior at a high overconsolidation ratio are well simulated. During heating, the effect of bound water dehydration on the generation of excess pore pressure in clay soils is highlighted in our numerical results.

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Data availability

The original data that support the findings of this study are available from the corresponding author, BL, upon request.

Abbreviations

\(c_{{\text{s}}}\) :

Specific heat capacity of solid

\(c_{{\text{f}}}\) :

Specific heat capacity of free water

\(c_{{\text{b}}}\) :

Specific heat capacity of bound water

\(F_{0}\) :

Preconsolidation pressure

g:

Gravity

H :

Hardening parameter

\(h_{{\text{e}}}\) :

Maximum element length of the mesh

\({\mathbf{k}}\) :

Intrinsic permeability

\(\overline{N}\) :

Normalized outward normal of the subloading surface

n :

Soil porosity

\(n_{{\text{s}}}\) :

Volume fractions of the solid phase

\(n_{{\text{f}}}\) :

Volume fractions of the free water phase

\(n_{{\text{b}}}\) :

Volume fractions of the bound water phase

\({\mathbf{n}}\) :

Outward normal direction

\(P^{{\text{f}}}\) :

Pore water pressure

\(P_{{\text{e}}}\) :

Local Peclet number

\({\mathbf{q}}\) :

Volumetric flow rate per unites of surface area

\(\overline{q}^{{\text{f}}}\) :

Water flux at the boundary

\(\overline{q}^{{\text{T}}}\) :

Heat flux at the boundary

R :

Similarity ratio

\(s_{{\text{f}}}\) :

Degree of saturation of free water

\(s_{{\text{b}}}\) :

Degree of saturation of bound water

T :

Temperature

\(T_{{{\text{Ini}}}}\) :

Initial temperature

\(T_{{\text{e}}}\) :

Temperature of the surrounding environment

\({\overline{\mathbf{t}}}\) :

Traction boundary condition

u :

Material parameter

\(v_{{\text{s}}}\) :

Soil particles velocity

\(v_{{\text{f}}}\) :

Free water velocity

\(w_{{\text{b}}}\) :

Bound water content

\(w_{{{\text{b}},{\text{Ini}}}}\) :

Bound water content at the initial temperature

\(\alpha_{{{\text{bf}}}}\) :

Constant that controls the conversion of bound to free water per each unit rise in temperature

\(\beta_{{\text{s}}}\) :

Thermal expansion coefficient of the soil phase

\(\beta_{{\text{f}}}\) :

Thermal expansion coefficient of the free water phase

\(\beta_{{\text{b}}}\) :

Thermal expansion coefficient of the bound water phase

\(\beta_{{\text{T}}}\) :

Equivalent thermal expansion coefficient

\(\gamma_{t}\) :

Thermal softening coefficient

\(\varepsilon\) :

Total strain

\(\varepsilon^{e}\) :

Elastic strain

\(\varepsilon^{p}\) :

Plastic strain

\(\varepsilon^{T}\) :

Thermal elastic strain

\(\kappa\) :

Slopes of the unloading–reloading line

\(\lambda_{{{\text{eff}}}}\) :

Effective thermal conductivity

\(\lambda_{{\text{s}}}\) :

Thermal conductivity of solid

\(\lambda_{{\text{f}}}\) :

Thermal conductivity of free water

\(\lambda_{{\text{b}}}\) :

Thermal conductivity of bound water

\(\lambda\) :

Slopes of the normal consolidation line

\(\overline{\lambda }\) :

Positive proportionality factor

\(\lambda_{{\text{e}}}\) :

Thermal conductivity of the surrounding environment

\(\mu_{{\text{f}}}\) :

Dynamic viscosity of water

\(\rho_{{\text{s}}}\) :

Density of soil particles

\(\rho_{{\text{f}}}\) :

Density of free water

\(\rho_{{\text{b}}}\) :

Density of bound water

\(\rho_{{{\text{eff}}}}\) :

Bulk density of the solid bound water–fluid mixture

\(\left( {\rho c} \right)_{{{\text{eff}}}}\) :

Effective heat capacity

\({{\varvec{\upsigma}}}\) :

Total Cauchy stress tensor

\({{\varvec{\upsigma}}}^{{\mathbf{\prime }}}\) :

Effective Cauchy stress tensor

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Acknowledgements

The authors would like to acknowledge the fund provided by NSERC Discovery Grant Canada (NO. RGPIN-2017-05169). Comments from two anonymous reviewers are beneficial for this manuscript.

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  1. Department of Building, Civil & Environmental Engineering, Concordia University, Montreal, QC, Canada

    Mohammadhossein Sojoudi, Biao Li & Emad Norouzi

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  1. Mohammadhossein Sojoudi
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Correspondence to Biao Li.

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Sojoudi, M., Li, B. & Norouzi, E. Finite element modeling of thermo-hydro-mechanical coupled processes in clay soils considering bound water dehydration. Acta Geotech. (2024). https://doi.org/10.1007/s11440-024-02262-7

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