Energy criterion for the stability of a mine working

Abstract

Of great practical importance is the problem of the stability of rock weakened by a deep cylindrical hole. This problem has not been discussed in the literature, although it LS very pressing in mining technology, being associated with the drilling of oil and gas wells, mineshafrs, tunnels, etc.[1].We wiU give an energy criterion for the stability of rock exposed by vertical cylindrical workings in terms of the stress distribution and mechanical properties of the rock.Naturally stratified rock subjected to hydrostatic pressure can accumulate large reserves of elastic energy. Any working will alter the stress distribution in the rock, leading to displacement or even c011apse of the walls. The sudden release of elastic energy may cause shock bumps.An isolated vertical working may be regarded as a cylindrical hole in a homogeneous, continuous, isotropic rock mass with internal radius a and infinite external radius, filled with a liquid which does not penetrate the rock [1, 2]. From within, the walls of the hole undergo pressure from the filler liquid, Pl = 71 z, and from without, lateral pressure from the rock, Pz = kTzz. For a spatial stress distribution in the rock, as a criterion of their stability we take only that part of the potential energy which is due to the change of shape [2, 3].If the counterpressure from'the filler liquid is sufficiently low, there will be large stresses in the sides of the working, and the potential energy of shape may become so great that the rock becomes plastic. Transition beyond the yield point causes irreversible deformations in the rock which lead to loss of stability in the walls which thus move or collapse. Thus loss of stability means brittle fracture or the onset of plastic flow of the rock of the borehole walls.According to the energetic theory of change of shape, the condition for stability of the wall rock [2, 3] is (~r --~t~ ~ +. Ot --~)2 + (~ _ ~F < 2 ~.(1)Owing to the axial symmetry of the load, there are no tangential stresses on areas/_u the radial, tangential, and axial directions, and the principal stresses will be the normal stresses o r, o t, o z.Let us now determine the normal stresses. We assume that the solid rock around the working is in a state of plane deformation, and therefore 1 ~: = -~-[% -~ (a, --~t)] = 0.(2)In the theory of elasticity, the equation of eqnilibdum in cylindrical coordinates for a state of plane deformation is d er ar --~t --dr r ": 1-:g -7;-, § -2;-, + =tffil+~' r+l--2~kdr + ; ~z = ~. (~r + at). From Eqs. (41 and (3), we get a differential equation which determines the displacement (movement): where C~)

Analytical estimation of cyclic fracture of rocks during drilling

“…According to [17], the integral in the left-hand part of (9) is a zero-order Bessel function of the imaginary argument Io(aod), Therefore the number of cycles N before disintegration is readily determined from (9).…”

“…The problem can be formulated as follows. Suppose we have a vertical mine working with internal diameter D and depth L, filled to its mouth with unfiltered wash liquid, the parameters of which are given in [8,9]. We also know the mechanical properties and stress-strain state of the face rocks lying at depth L [10,11].…”