The state of stress in solid rock with a horizontal working with stowing

Abstract

The results in [1][2][3] form the basis for many solutions to the problem of the stress-deformation state in rock with an extraction working. Mikhlin [1] considers a working in the absence of rock fracture. If we imagine two symmetrical workings formed from a single one [1] with sufficient width, such that the floor and roof meet smoothly (the effect of caving is eliminated) and such that w e can neglect their mutual influence, then we can consider one of them. This problem was discussed by Barenblatt and Khristianovich [2]. Both these papers assume the seam to be absolutely rigid and the tangential stresses at the seam-rock contact m be zero, O~u~-0.An elastic seam-rock system in natural interaction was discussed by us in [4,5].For solving various practical mining problems, an experimental-analytical approach has been devised for the restoration of the stresses in a half-plane [3]; the first boundary condition is based on field measurements of the normal component of the displacement, while the second is given by one of the two hypotheses u = 0, Oxy = 0 or Oxy = koyy over the whole boundary of the half-plane.This article is in a sense an extension of the above papers [1,2,3]. On the one hand, the formulations in [1, 2] can be obtained as special cases; on the other, as in [3], we can use field displacement measurements, but those obtained from a finite section I. As in our previous articles [4,5], the rock mass is modeled by the system seam -rock, but here the seam receives only the normal load in the additional stresses; i.e., it is modeled by a setof preeompressed springs. With this representation, only the Young's modulus E 2 of the seam is involved in the calculation. where gl(x) = %(x) is the normal component of the displacement, and ga(x) = O~y is the normal component of the stress (in particular, the stresses found experimentally).Thus for the lower half-plane (rock), the boundary conditions at y = 0 take the form ~---~0, --oo<x<oo;

Effect of nonuniformity of a rock mass on contact pressure and its distribution

“…Figure 1 gives the p(x) values obtained by solving system (33) in [6] for 2n = 20 [the highest power of x retained in expansion (29)] and X 0 = 0.0335, 0.08375, 0.1675, 0.335, 0.8375, and 1.675, to which curves 1-6, respectively, correspond. In particular, these curves may be regarded as independent of the ratios EH/E = 0.2, 0.5, 1, 2, 5, and 10, assuming that h/a = 0.1 and v H = 0.25.…”

“…(4), putting k = 1 and E(x) = const, we get an equation similar to gq. (12) in [6], where instead of k 0, we must put…”

“…

In solving the problem of the stress-strain state in the vicinity of a working, the rock mass is usually simulated by two identical uniform isotropic half-planes adjoining the seam as a uniform isotropic band [1][2][3][4][5][6]. However, in a real rock mass, on the one hand the seam has nonuniform thickness and natural variable elastic parametees [E(x, y), v(x, y)], and on the other hand the adjoining rocks are markedly nonuniform.

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“…It is therefore of interest to investigate the effect of the above factors on the stress-strain state of a rock mass. Our paper deals with this effect in terms of the variable elastic constants of a rock mass.As in our previous communication [6], the rock mass is modeled by the system seam-rock, but here we assume that EB, v B and E H, v H are different elastic constants of the upper and lower half-planes adjoining a seam of thickness 2tl with a Young's modulus E = E(x. y).The elastic constants of the upper and lower half-planes are different, but in view of the fact that, in accordance with the model in [6], the seam receives only a normal load and is regarded as a uniform elastic layer, p (x) at the contacts y = 0 and y = 2h will be the same. Therefore, the functions r and ~(z) [6], characterizing the stress-strain state of the upper and lower half-planes, have the same form, and the ratio of the displacements of the half-plane boundaries is…”

“…Therefore, the functions r and ~(z) [6], characterizing the stress-strain state of the upper and lower half-planes, have the same form, and the ratio of the displacements of the half-plane boundaries is…”