PSI - Issue 18

Kostina A. et al. / Procedia Structural Integrity 18 (2019) 293–300 Author name / Structural Integrity Procedia 00 (2019) 000–000

295

3

k p

(      v g , ) f f 

(3)



  0   I



  σ

g ,

B f p p 



(4)





: T h    σ C ε ε ε ,

(5)

1 2

          ε u u , T

(6)

0 T s T T    ε I , ( )

(7)

ε

I .

0.09 (1 ) n  

(8)



h

In (1)-(8):  – effective density [kg/m 3 ], p c – effective heat capacity, [J/(kgꞏK)], T – absolute temperature, [K], t , p f c – specific heat capacity of fluid [J/(kgꞏK)],  – the Nabla operator, v – Darcy’s velocity, [m/s],  f p – pore pressure of fluid, [Pa], S – the fluid loss coefficient, vol  – volumetric part of the full strain tensor, g – acceleration of gravity, [m/s 2 ], k – permeability coefficient, [m 2 ],  – dynamic viscosity of the fluid, [Paꞏs], σ – Cauchy stress tensor, [Pa], C – stiffness tensor, [Pa], C –stiffness tensor, [Pa], which has two components bulk modulus K , [Pa], and shear modulus G , [Pa], B  – Biot coefficient, f p – initial pore pressure of fluid, [Pa], I – unity tensor, ε – full strain tensor, u – displacement vector, [m], T ε – thermal strain, s  – the thermal expansion coefficient, 0 T – initial temperature of the rock mass, h ε – strain induced by frost heave or thawing, n – porosity,  – phase indicator function. Expressions for the thermophysical, hydrodynamic and mechanical parameters are same as in (Panteleev et al. (2017)). The artificial freezing process of a rock mass is considered in a neighborhood of a freezing well. From the rock mass the three soil stratums with the most different material characteristics are chosen. The geometry of the problem (1)–(8) is presented in Fig 1. The problem is solved in axisymmetric configuration. The axis of symmetry coincides with the axis of the well. – time, [s], – effective thermal conductivity coefficient, [W/mꞏK], f  – fluid density, [kg/m 3 ],

Fig. 1. The computational scheme for the numerical simulation of processes of AGF and subsequent soil thawing

Initial and boundary conditions for the problem (1)-(8) is written as:

0 0 t T T   ,

(9)