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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The results of the numerical calculation of the degradation of the inter-chamber pillars over a potentially dangerous area for various flooding scenarios are shown in Fig. 1. This information is the starting point for geomechanical predictions of the consequences of eliminating a potentially dangerous area. 3. Geomechanical Analysis of Flooding Consequences of a Potentially Dangerous Area The geomechanical model reflected the entire set of geological (layering, hypsometry of strata, rock properties) and mining conditions (depth of mining, parameters of the mining system, the degree of material filling in the chambers), as well as a group of factors associated with the dissolution of the salt rocks (width reduction of the inter-chamber pillars due to their leaching, a change in their loading degree, etc.) [Baryakh et al.,(2018)]. The modelled domain of the isolated area was divided into computational blocks of seams with similar mining parameters and dissolutionintensity. The numerical implementation of the mathematical modelling of the stress strain state of the undermined rock mass in a three-dimensional formulation was based on a modified semi-analytic finite element method, which allowed the reduction of the three-dimensional problem to a set of two-dimensional ones, by expanding the sought displacement vector in Fourier series [Zienkiewicz,(1971)]. To analyse the deformation of the undermined rock mass over time, including the flooding process, a rheological approach was used, based on the mathematical description of the graphs of the increased subsidence of the earth’s surface [Baryakh et al., (2005)] and their implementation according to the scheme of alternating deformation moduli [Amusin,(1974)]. At each time step, the analysis of the stress-strain state of the undermined rock mass was made in the elastoplastic formulation. It helped to localise the areas of plastic deformation which, in the physical sense, were interpreted as the salt strata zones of the human-induced disturbances, due to the development of shear and opening mode fractures. As a strength (plasticity) condition for the three-dimensional stress state, a criterion was used that took into account the combined action of two types of destruction: shear due to shear stresses and opening mode fractures under normal stresses [Baryakh et al.,(2017)]. The elastoplastic problem was solved using the method of initial stresses [Malinin,(1974);Fadeev,(1987)]. The influence of the salt rock dissolution on the nature of the deformation processes was based on the proposed rheological approach, in terms of ensuring correspondence of the calculated and predicted subsidence of the earth surface. The predicted graphs of the increased subsidence depend on the degree of loading of the inter-chamber pillars С , which is determined by the ratio of the effective load to its bearing capacity [Instructions,(2014)]:

(8)

f m bk a b H  (   

0 )

С



where  is the coefficient that takes into account the load changes on the pillars due to various mining factors;  is the bulk weight of the rocks; H 0 is the maximum distance from the earth surface to the roof of the pillars; f k is the form factor of the pillars; m  is the strength of the rocks in the mass; and a , b are the initial widths of the chambers and pillars, respectively. For the salt rocks, the form factor is specified by the ratio:

   

2

0,5 0,5

when when



 

 

k





  

f

1





0

m

where  = b / m , m is the pillar height; 1.06  m  are the approximation parameters. The predicted graphs of the subsidence increase in the earth surface are characterised by an empirical relationship (Instructions 2014):       /100 ( ) t t ok   , when 0.32  C , (9) (10) Parameters  and  vary depending on the loading degree of the pillars. In Table ; ok  is the maximum 0.654, 0   100 ( ) 0.2 t t ok    , when 0.32  C