A thermodynamic model to simulate the thermo-mechanical behavior of fine-grained gassy soil


Fine-grained gassy soil is a special kind of unsaturated soil, with the gas in the form of discrete big bubbles within the saturated matrix. These gas bubbles are sealed and considerably larger than the normal particle size. Based on the conceptual model of soil containing large gas bubbles proposed by Wheeler (Géotechnique 38(3):389–397, 1988a) and the granular solid hydrodynamics (GSH) theory, a thermodynamic model is presented to describe the mechanical properties and temperature effect of fine-grained gassy soil in this paper. The model assumes that the gas pressure is related to total stress and pore water pressure of soil, and the behavior of saturated matrix is controlled by “quasi-effective stress.” In addition, the effect of gas on the plastic deformation of soil skeleton is considered. Comparing with the experimental results, the ability of the model to describe the consolidation and undrained shear properties of fine-grained gassy soil is verified. What is more, the effect of temperature on fine-grained gassy soil considering the various responses for different drainage conditions and overconsolidation ratios is discussed and simulated by the proposed model. It is concluded that for fine-grained gassy soil with different overconsolidation ratios, the increase of temperature can increase the compressibility and thermal contraction under drained conditions, as well as the pore water pressure under undrained conditions, while the temperature effect on undrained shear properties depends on the initial conditions.

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S :


T :


S g :

granular entropy

T g :

granular temperature

I g :

granular entropy decay rate

R :

entropy production

R g :

granular entropy production

ρ :


ϑ :

specific entropy

ϑ g :

specific granular entropy

f k :

entropy flow

\( {f}_k^g \) :

granular entropy flow

ρ’ :

mass transfer

a :

solid and liquid phases

n a :

volume fraction

\( {\psi}_{ij}^a \) :

deformation rate

\( {v}_i^a \) :


ε ij :

deformation of soil skeleton

\( {v}_i^{LS} \) :

relative velocity

\( {\sigma}_{ij}^a \) :

Cauchy stress tensor

g :

gravity acceleration

e a :

specific energy

Q k :

energy flow associated with dissipative processes

π ij :

elastic stress

q k :

heat conduction

\( {\sigma}_{ij}^{v\mathrm{a}} \) :

viscous stress

Y ij :

plastic strain rate

Γ :

dissipative flow caused by temperature change

λ ijklg :

tensor form of granular level migration coefficient

λsg, λvg :

migration coefficients

\( {m}_i^a \) :


\( {\varepsilon}_{ij}^e \) :

elastic strain

\( {\varepsilon}_{ij}^p \) :

plastic strain

μ ca :

chemical potential

p L , u l :

pore water pressure

p S :

fluid pressure on soil particles

α LT :

conversion rate of bound water to free water

α v :

proportion of effective stresses borne by bound water

w e :

elastic potential energy density

B 0 :

hardness of the material

\( {\varepsilon}_v^{\mathrm{e}} \) :

elastic volumetric strain

\( {\varepsilon}_s^{\mathrm{e}} \) :

elastic deviator strain

ζ :

material parameter

e ij :

deviator strain

β T :

coefficient of thermal expansion

ΔT :

temperature gradient

c :

viscosity coefficient

Ke :

elastic volume modulus

G e :

elastic shear modulus

p’ :

mean effective stress

q :

shear stress

e :

void ratio

λ :

slope of compression curve

N :

special void ratio

η ijkl :

tensor form of migration coefficient

ηs, ηv :

migration coefficient


index parameter

w g :

energy density associated with the fluctuation motion of particles

b :

material parameter

T gg :

a form of granular temperature

e g :

gas void ratio

e l :

water void ratio

s r :

saturation degree

V :


μg :

gas pressure

a g :

proportion of total stress transferred to the gas phase

T s :

surface tension

R c :

radius of curvature

H :

Henry solubility coefficient

n mol :

mass of gas phase

p a :

atmospheric pressure

σ '' :

quasi-effective stress

n g :

gas volume fraction

l i :

circumference of the intercepted gas bubble

θ i :

contact angle between solid and liquid phase

σ m :

stress on saturated soil matrix

\( {\varepsilon}_v^G \) :

gas volume strain

τ v :

coupling coefficient

f :

gas bubbles volume fractions

c1, c2, c3, c4, c5 :

model calculation parameters


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The authors gratefully acknowledge the financial support provided by Beijing Natural Science Foundation (No.8182046) and National Natural Science Foundation of China (No.51878035, No.51678043).

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Correspondence to Bing Bai.

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Yang, G., Bai, B. A thermodynamic model to simulate the thermo-mechanical behavior of fine-grained gassy soil. Bull Eng Geol Environ 79, 2325–2339 (2020). https://doi.org/10.1007/s10064-019-01694-w

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  • Fine-grained gassy soil
  • Thermodynamic model
  • Gas pressure
  • Thermo-mechanical behavior