PSI - Issue 28

5

A. Prokhorov et al. / Procedia Structural Integrity 28 (2020) 1579–1589 Author name / Structural Integrity Procedia 00 (2019) 000–000

1583

The radius of the specimen was 20 mm and height was 90 mm. Into the specimen four thermocouples were placed on the axial line at the same distance from each other for monitoring the freezing process.

3. Numerical model To simulate the process of freezing of water-saturated soil, a thermo-hydro-mechanical model was developed. This model considers a three-phase porous medium consisting of a dry skeleton, water and ice. The pore space is assumed to be completely saturated. The effect of water vapor is neglected. A dry skeleton is supposed to be a continuous, homogeneous, isotropic material that undergoes only elastic deformation during freezing. The description of heat and mass transfer is based on the model [32], which includes the law of energy conservation and the mass balance equations for moisture and ice content. Moisture migration is governed by a moisture gradient with diffusion coefficients dependent on moisture. Ice movement is neglected. Heat dissipation, changes in moisture and ice content during the phase transition are taking into account using volumetric sources. The stress-strain state is determined from the equilibrium equation. The relationship between stresses and strains is given by Hooke's law. The freezing process takes into account temperature deformations and deformations caused by the phase transitions of water into ice. The calculation of frost heave deformations is performed based on the current value of ice content. The mathematical formulation of the model is written as follows.   div grad i W D W Q t      , (1)

i I Q t 





,

(2)







div grad λ

T L ρ Q 

C T



sk

i

t



,

(3)

W W

t 

eq

Q



i

,

(4)

*

ρ  σ g ,

div

(5)

fh ) T    σ C ε ε ε , : (

(6)

T 1 (grad grad ) 2  u u

ε



,

(7)

0 T T α T T   ε I , ( )

(8)

fh 1 3 v ε  ε I

, (9) Thermophysical parameters and elastic properties of a saturated porous medium are determined according to the mixture rule. Volumetric deformations of the soil are specified as: