PSI - Issue 32

20 4

A.A. Baryakh et al. / Procedia Structural Integrity 32 (2021) 17–25 Baryakh A.A / Structural Integrity Procedia 00 (2021) 000 – 000

Fig. 1. Predicted damage to the pillars at the end of the flooding process of a dangerous section: (a) the planned flooding; (b) the emergency breakthrough. The current value of ǡ at each time step for each computation block was calculated from equation (4):

k

k

С

i j K S C

t

   

  

 

i j ( , )

i j ( , ) ( , )

n

k m i j

C



(5)

( , )

k

1

K S

t

k i i , 

The pillar damage (degradation of its side) at each time step

was found from the balance equation:





k

k m i j

k

i j ( , ) V C C   i j ( , )

M

( , )

i j ( , )

k

k

or

,

v

S



i j ( , ) 





i j ( , )

( , )

s i j





where k

k i j M ( , ) is the mass of the dissolved salt; ρ is the density of the

i j v ( , ) is the volume of the dissolved mineral;

( , ) s i j S is the total area of the contact of the dissolved mineral with the solution along the sides,

dissolved mineral;

soil and ceiling of the mines; ( , ) i j V is the total volume of the solution in the mines. Thus, the expression to calculate the damage increment to the pillars at each time step for each computational block is:   ( , ) ( , ) ( , ) ( , ) i j k m i j k i j k i j S C C      (6) The total value of the damage to the inter-chamber pillars in each calculation block is determined by a simple summation of the time steps:    k k i j i j ( , ) ( , )  (7) There is no possibility for such a damage calculation to the pillars in the PM8 software package. Therefore, in order to implement this procedure, a special program was developed, in which, at each time step, the matrices of the current concentrations in the calculation blocks were read and the actual damage was calculated.