PSI - Issue 32

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

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7

the ratio of the weight and height of the pillar; and *

f k is the form factor of the pillar determined when b=b * .

Fig. 3. Changes of the subsidence increase of the earth surface with an increase in the degree of loading of the pillar due to dissolution.

The correction of the loading degree of the pillars, by taking into account their dissolution, makes it possible to cons truct the corresponding graphs of the subsidence increase at the earth’s surface. Let the graphs η(t) and η * (t) represent the subsidence increase of the earth surface in conditions of complete undermining at the initial loading degree С, until an instant of time t 1 and after flooding t > t 1 , when C * >C (Fig.3а). Depending on the degree of loading value of the inter-chamber pillar, the subsidence at time t 1 is calculated using formulas (9) or (10). Then, the time during which the same subsidence is achieved with an increased degree of loading of the pillars due to degradation is estimated from the ratios: * 1/ 

   

   

* * 1 ( ) t



*

0.32 *  C and

when

100

t





1

  ok

   

   

* ok t 1 ( ) 



* 1

0.32 *  C .

500

t





when

If the graph * 1 1 ** t t t   , it is possible to build a generalised curve of the subsidence increase over time, taking into account the dissolution of the salt rocks: ( ) t  when 1 t t  and ) ( ** * t t   when 1 t t  (Fig. 3b). Within the proposed rheological approach [Baryakh et al.,(2005)], this information represents the main parametric support for the mathematical modelling of the stress-strain state changes in the undermined rock mass, reflecting the degradation of the pillars due to dissolution. ( ) * t  is moved to the right by the time difference

Fig. 4. The predicted subsidence of the earth’s surface (mm) at the time of the complete elimination of a potentially dangero us area: (a) is the planned flooding; (b) is the emergency breakthrough of the freshwater.