PSI - Issue 5

Plekhov A. et al. / Procedia Structural Integrity 5 (2017) 492–499 Panteleev I / Structural Integrity Procedia 00 (2017) 000 – 000

497

6

9 1.8 10  

9 1.4 10  

Pa – bulk modulus and shear modulus of ice.

i K

Pa ,

i G

where

T he Biot coefficient and the Biot tangent modulus was defined as: 1 d B K K    , 1 B n N K    , where d K – bulk modulus of the dry porous skeleton calculated by the formula:       3 1 1 2 1 2 1 d K K n n        , where 9 2( 3 ) 1 K G K     – Poisson ’ s ratio of soil particles. Thermal strain T  was determined according to the equation:   0 T s T T E     . Equations (1)-(17) are supplemented with the following initial and boundary conditions:   0 0 f p t   ,

(17)

(18)

  0 0 v t   ,   0 0 u t   ,

(19)

(20)

 T t i

 0 T   , i o

1... i n  ,

(21)

1... j m  ,

, 0 j x u    , l y u    , j 0 j

(22)

1... j m  ,

(23)

,

b u 

0  ,

(24)

,

b n  u n 

gz

(25)









,

gz

(26)









, , u b n q       , 0 l

(27)

0 n v      ,

(28) (29)

  1 , j T T t x   ,

  1 ,

1... j m 

1 T t T t x h T t     , ( ( ) pod ( )) ( ) obr pod

T t x

where i o T – initial temperature of the layer, i – layer number, n – number of layers, j – well number, m – number of wells, j  – well boundary, b  – lower boundary of the layer, u  – upper boundary of the layer, l  – boundary of the considered area of layered rock mass, l b u j       , pod T – temperature of coolant supply, obr T – coolant return temperature, 1 h – depth of freeze wells. It is assumed that pore pressure, Darcy’s veloc ity, initial displacement of the solid skeleton are zero, initial temperature of each layer is known from the geophysical investigations. Horizontal displacements and heat flux on the outer boundaries of the considered area are zero. Lithostatic pressure on the boundaries of the layers corresponds to the given depth. Zero horizontal displacements and linear temperature gradient are prescribed on the walls of the freezing wells. The temperature on the bottom of the wells is equal to the temperature of the coolant supply; the temperature on the wellhead is equal to the return temperature of coolant. The initial data were generated close to the real observed situation. Artificial freezing zone includes 41 freezing wells. Centers of these wells are located on the circle which has the diameter of 10.5 m and located at the distance of 1608 mm from each other. The diameter of the freezing well is 146 mm and its depth is 225 m. To simulate influence of the real geometry of the wells after drilling, the artificial inclinometer data were generated. Deviation of the bottom