Non-isothermal soil-structure interface model basedon critical state theory


In energy geostructures, the soil-structure interface is subjected to thermo-mechanical loads. In this study, a non-isothermal soil-structure interface model based on critical state theory is developed from a granular soil-structure interface constitutive model under isothermal conditions. The model is capable of capturing the effect of temperature on sand/clay-structure interfaces under constant normal load and constant normal stiffness conditions. First, the developed model was verified for sand-structure interface in isothermal conditions. Then, it was calibrated for clay-structure interface under non-isothermal conditions. On one hand, a well-defined peak shear stress for the clay-structure interface and, on the other hand, the effect of temperature on the void ratio of the clay-structure interface were captured and reproduced by the model. The importance of interface thickness determination and some differences between the interface thicknesses of clay-structure and sand-structure interfaces are discussed in detail. The additional parameters have physical meanings and can be determined from laboratory tests. The modeling predictions are in good agreement with experimental results, and the main trends are properly reproduced.

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\(e (-)\) :

Void ratio

\(e_\mathrm{in} (-)\) :

Initial void ratio

\(e_\mathrm{in}(T) (-)\) :

Initial void ratio at temperature T

\(e_\mathrm{cs} (-)\) :

Critical state void ratio

\(\epsilon (-)\) :

Shear strain (in direct shear test)

W (mm):

Shear displacement (in direct shear test)

\(\xi (\mathrm{mm}^{-1})\) :

Controls the rate of void ratio evolution

\(k_{1}^{*} (\mathrm{mm}^{-1})\) :

Intensifies the initial contraction

\(k_{2}\) (kPa/mm):

Parameter of the model

K (kPa/mm):


t (mm):

Interface thickness

\(\Gamma (-)\) :

Initial critical void ratio

\(\lambda (-)\) :

Slope of the critical void ratio reduction with normal stress

\(\mu \) (kPa):

Elastic shear modulus

\(k_{t0}\) (kPa/mm):

Slope of the initial part of the \(\tau -w\) Curve

\(M (-)\) :

Slope of the \(\tau /\sigma _{n}\)

N :

Controls the peak and the strain softening

\(\psi \) :

Controls the rate of volumetric evolution

\(\alpha (^{\circ }C^{-1})\) :

Slope of the void ratio evolution with temperature

\(T (^{\circ }C)\) :


\(\beta (-)\) :

Controls the effect of normal stress


Constant normal load


Constant normal stiffness

\(\tau \) (kPa):

Shear stress

\(\sigma ^{'}_{n}\) (kPa):

Effective normal stress

U (mm):

Normal displacement

\(R_\mathrm{max}\) (mm):

Maximum surface roughness

\(\delta (^{\circ })\) :

Friction angle of interface

\(D_{50}\) (mm):

Mean diameter of soil particles

\(\rho _{s}\) \((\mathrm{g/cm}^{3})\) :

Grain density of soil particles

\(\rho _{dmax}\) \((\mathrm{kN/m}^{3})\) :

Maximum dry density

\(\rho _{dmin}\) \((\mathrm{kN/m}^{3})\) :

Minimum dry density

\(e_\mathrm{max}\) :

Maximum void ratio

\(e_\mathrm{min}\) :

Minimum void ratio

\(C_{u}\) \(=D_{60}/D_{10}\) :

Coefficient of uniformity

k (m/s):

Hydraulic conductivity

LL (\(\%\)):

Liquid limit

PL (\(\%\)):

Plastic limit

PI (\(\%\)):

Plasticity index

\(\lambda \) (W/mK):

Thermal conductivity

C \((J/m^{3}K)\) :

Heat capacity


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Maghsoodi, S., Cuisinier, O. & Masrouri, F. Non-isothermal soil-structure interface model basedon critical state theory. Acta Geotech. (2021).

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  • Constant normal stiffness (CNS)
  • Critical state theory
  • Energy geostructures
  • Non-isothermal model
  • Soil-structure interface
  • Temperature