Thermo–Hydro–Mechanical Behavior of Unsaturated Loess Considering the Effect of Porosity and Temperature on Water Retention Properties

Data Availability Statement

Acknowledgments

Notation

b

dimensionless smoothing parameter;

C

specific moisture capacity;

C_eff

effective volumetric heat capacity of unsaturated loess;

C_p

volumetric specific heat of particles;

C_w

volumetric heat capacity of water;

D

gravitational potential;

e

void ratio;

e_ref

reference void ratio;

G

shear modulus;

g

gravitational acceleration;

g

value of gravitational acceleration;

H_p

soil water potential;

K

hydraulic conductivity;

k₀

initial intrinsic permeability;

k_c

constitutive parameter representing the increase of strength due to matrix suction;

k_r

relative water conductivity;

M

slope of the critical state line;

m, n, α

parameters in simplified van Genuchten expression;

n

outward normal unit vector of the boundary;

n_p

current porosity;

n_p0

initial porosity;

Ρ

equivalent density of loess matrix;

P₀

model parameter measured at a reference void ratio of e₀;

p

mean total stress;

$\overline{p}$

mean net stress ( $\overline{p}$ = p − u_a);

p₀

yield stress of positive suction;

p_atm

atmospheric pressure;

p_ref

reference pressure;

S

storage coefficient of the soil;

S_e

degree of saturation;

S_r

residual degree of saturation of liquid phase;

S_s

maximum degree of saturation of liquid phase;

s

suction (s = u_a − u_w);

s_y

yield value at current suction;

s₀

yield suction during the shrink;

T

temperature;

T_ref

reference temperature;

u_a

pore air pressure;

u_w

pore-water pressure;

ν

specific volume (ν = 1 + e);

v

velocity of the moisture;

Φ, φ, n_1, m₁

parameters in state surface expression for S_e;

β_e

model parameter;

β_T

linear thermal dilatation coefficient;

θ_p

volumetric content of the loess particles;

θ_w

current volumetric content of the water;

λ(0)

slope of the virgin compression line for saturated conditions;

λ(s)

slope of the compression line corresponding to suction s;

λ₀, β, and r

parameters in BBM for describe the virgin compression line for different suction;

λ_eff

effective heat conductivity of the loess;

λ_p

heat conductivity for the soil particles;

λ_s

slope of the virgin compression line in terms of suction increase;

λ_w

heat conductivity for the free water;

κ

elastic constant;

κ

swelling index;

κ_s

swelling index for changes in suction;

μ

kinematic viscosity of water;

ρ_s

densities of loess particles;

ρ_w

water density;

σ

surface tension at current temperature;

σ

total stress tensor; and

σ₀

surface tension at reference temperature.

References