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~)
Sedimentary rocks, associated with mineral extraction, come into a state of geostatic equilibrium following their deposition. Owing to stress relaxation, the lateral pressure coefficient X can be taken as unity, and the state of stress of the rock regarded as hydrostatic. In hydrostatic phenomena liquids and solids behave as if they were ideally elastic [1]. Thus, undisturbed native rock can be regarded as elastic, and the components of the stress at any point are governed by the weight of the superincumbent rock. The cutting of a working will cause changes in these stresses in the rock of the face.Let us consider a vertical shaft, of depth z, with a circular cross section of radius a, assuming that we know the mechanical properties of the rock and the nature of the circulating liquids filling it. We will take the lateral pressure coefficient X as unity [2]. (Note that this method can be used for any lateral pressure coefficient.) We have to determine the state of stress of the rocks at the bottom, and also the conditions of formation and propagation of the plastic zone in relation to depth and the mechanical properties of the rocks and the circulating fluids, allowing for the geological conditions.
Study of the effect of high pressures on the deformation properties of rocks has an important bearing on faster development of mineral deposits. The inadequacy of analytical methods of calculation, and of methods of simulating deformation processes for solving practical problems, is due to insufficient experimental research. Experimental data on the deformation properties of rocks are scanty and do not enable us to develop a schematic functional model of the medium being deformed [1][2][3]. In particular, the litmrature does not give correlating data on the effect of hydrostatic stress on the deformation and strength properties of the rocks of a sedimentary succession to which mined minerals belong. This paper gives data on the deformation properties of Mesozoic sandstones and siltstones under high pressures. Such investigations are important for developing effective schemes of rock breaking by drilling.The mechanical methods of breaking used in mining are based chiefly on driving tools into the rock. This is the basic process in percussive, chilled-shot, and roller-bit drilling. In roller-bit drilling, rotation of the rollers against the face is accompanied by indentation of the teeth into the rock; the axial load is transmitted via small contact areas.The partlcular characteristic ofexperimentalwork on the strength and deformation properties of in-situ rocks is the buLk characlmr of the stalm of stress. In research on drilling cores with the objective of simulating face conditions, a hydrostatic stress is created, and a cylindrical punch with a flat base is forced into a specimen of the rock. The fracture mechanism of the latter is determined by the stress field beneath the punch and by the properties of the rock itself. With the use of the sophisticated theory of elasticity for calculating the stress field, the rock is considered to a first approximation as an elastic uniform half-space.When the punch is driven into the rock, under conditions of volumetric stress a limiting sl~ess arises at a certain depthTills stressed state Is axially symmetric, and the distribution of radial, circumferential, and axial normal stresses o r, o0, and Oz, which are the principal stresses, may be expressed as follows [4]: ~r = ~o = 1/" a2 + z2 ~/a~ + z2 ; Z3
The driving of various types of mine workings for commercial mineral production involves the process of rock breaking. Roller-bit drills are the instruments most used to break rocks [1][2][3].In the operation of a roller bit, breakage occurs after single or repeated cyclic action of the teeth on the rock. An urgent problem [4][5][6][7] is the influence of the cyclic loading parameters, especially the amplitude and frequency of the dynamic load components, on the process of rock breaking at the face.In this article we shall suggest a method for quantitative estimation of the influence of the cyclic loading parameters on the process of rock breaking by roller bits at the face of a vertical working, with allowance for the time dependence of the strength and the mining-geological and technical fractors. 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]. We are to determine the number of cycles N before the rock breaks owing to the action of the roller teeth under given axial load and rotation speed.If the angular velocity of the roller about its axis is w = 2nn/60 x D/d, then the frequency of reciprocatory motion of the body of the bit for synchronous roiling of the rollers from tooth to tooth over the face will be wz. The period of longitudinal vibration of the body of the bit will be 2n/wz, which corresponds to the time of rolling of the rollers from one tooth to the next, and represents the duration of contact during a single event of interaction of a tooth with the rock The number of cycles to breakage, N, and the duration of contact of a tooth of the roller with the rock, t c, are linked with the time to complete breakage as follows: d 2,-:During drilling, as the angular speed of the bit increases, so do the number of blows inflicted on the face rock by the roller teeth in unit time, the speed of impact, and the dynamic component of the load. This increases the efficiency of rock breaking and the mechanical rate of advance.After a large number of cycles of loading by the roller teeth, as damage to the rocks increases, so does the probability of breakage of the rocks at the face of the working increase. Fatigue breakage is a result of the time dependence of the strength, and in this context the duration of action of the load is important [13][14][15].The rule of summation of damage for the long-term strength for time-dependent stress is as follows [16]. If we divide up the variable stress into a series of values acting during successive small time intervals, we can neglect stress changes and regard the stress as constant in each interval. Then if the duration of the action of load on the the rock is dt, owing to the irreversibility of the deloading process, the relative decrease in life is dt/t(o), where V. I. Lenin Dagestan State University, Makhac...
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