PSI - Issue 32

I S Lomakin et al. / Procedia Structural Integrity 32 (2021) 117–123 I S Lomakin, A A Tsayukov / Structural Integrity Procedia 00 (2019) 000 – 000

119

3

ൌ

(3) where isthe normal stiffness of the contact. When ൐ Ͳ , the contact was considered to be open and in (3) it was assumed that ൌ Ͳ . Fortheshearstresses ( ) acting along the clay contact line, the relation with the shear strain ( ) was found with the three-link piecewise linear approximation (Baryakh et al. 1992): ൌ ǡ ℎ Ͳ ൏ ≤ − − ǡ ℎ ൏ ≤ ∗ ∗ ǡ ℎ ൐ ∗ where istheshearstiffnessofthecontact; istheshearstiffnessofthecontactat the softening region; is the peak strength of the contact; ∗ is the residual strength. The ultimate shear resistance (peak strength) was calculated according to the Coulomb equation: ൌ ൅ where  isthe adhesion factor of the contact; φ  is its inner friction angle. When the tensile stresses acted on the contact, it was assumed that its shear strength was decreased to zero ( ൌ ൌ Ͳ ). The numerical implementation was carried out by the finite element method in displacements (Zienkiewicz et al. 2013) with discretization of the considered region into triangular elements of the first order. The finite element solution of the elastoplastic problem was based on the method of initial stresses (Fadeev 1987). As a criterion for the rock caving in the interlayer, the following condition was taken: the outcropping of the zone of action of tensile stresses (the mass - chamber boundary) and reaching the lamination zone of the clay contacts by the zone of shear jointing (Baryakh et al. 2011).

Table 1. Parameters of the mining system.

Computation

Layer

Combine

Chamber width (а), m

Pillar width (b), m

Pillar height (m), m

Loading, С

upper lower upper lower

Combine 1 Combine 1 Combine 2 Combine 1

5.1 5.1 3.1 5.1

6.0 6.0 8.0 6.0

3.1 5.0 3.1 5.0

0.336 0.383 0.252 0.383

1

2

The basic geomechanical calculation scheme is shown in Fig. 1. Two variants for the goaf formation were considered. In the first case (Fig. 1, a), the upper productive zone was mined by a combine with a cross-sectional area S = 15.7 m 2 (Combine 1). In the second case (Fig. 1, b), the section was S = 8.7 m 2 (Combine 2). In both cases, the lower productive layer was mined by a combine of the first type. The geometry of the stopings corresponds to the cross-sectional diagram of the mine covered by the combiners taking into account the parameters of the mining system presented in Table 1. The thickness of the interlayer was 3.9 m. According to the regulation about protecting mines from flooding, made for enterprises operating within the VSD, the determination of the loading degree of interchamber pillars is carried out regardless of the number of working layers and is based on the Turner - Shevyakov method (Tournaire 1884; Shevyakov 1941) modified by taking into account the results of the experimental studies performed at the VSD: ൌ ሺ ൅ ሻ Ͳ