1. When rocks or metals are to be broken up by dynamic loads, experiments show that It is necessary to take account of the time-dependent strength characteristics [5,6] imtead of the "static" characteristics [1][2][3][4]. The point of introducing these characteristics is that an important feature of the breakage process is the time of action of the load: the critical stress must act for a definite time, which increases as the load decreases.In studies of the fracture of many materials such as rocks and many metals and alloys, a metal has been suggested and extensive study has been made of the time-dependent strength characteristic over a wide range of "longevity" r (10"3-10 +T sec), and experiments have confirmed the rule of damage summation when the tensile values of the normal stress have different time dependences [5,6]. However, although this rule applies over a wide range of r values, the latter is very limited, and furthermore the method used to study the characteristic, or its analog, scarcely permits us to study small longevity values and correspondingly high stresses. A model experirnental-analytical method, which gives satisfactory results, is based on study of "scabbing" (splitting-off) phenomena in plates acted on by impact or explosion. There are exact solutions to the dynamic problem of the theory of elasticity concerning an impact on a plate; the analysis on the axis of symme~y is based on certain qualitative ideas about rear scabbing [7,8]. In addition, much experimental materialhas accumulated on the laws of variation of the state of stress in a real material and on the description of the physical pattern of possible fractures [9][10][11] and on the construction of the time-dependent strength characteristic [12].Calculation of the pattern of fracture on the basis of an approximate construction of the solution to the problem of the theory of elasticity in uhe neighborhood of the axis of symmetry wtl~ the aid of an exact solution on the axis itself, followed by correction for the real distribution of the action on the front surface of the plate with account of the real laws of damping, and also on the basis of a suitably-chosen fracture characteristic, can yield interesting data and may be regarded as the converse problem to correcting the strength characteristics of the materlal, the fracture parameters, and the laws of propagation of stress waves.In our experiments we used the scheme shown in Fig. 1. The testspecimens lwereof Steel 3 in the form of square plates, L = 200 mm on a side and b = 5-60 mm thick; they were installed on support 2 and acted on by the detonation of a cylindrical charge 3 of a TNT-Geksogen mixture (TG-50/50) with a density of p = 1.68 g/cm ~ and a detonation velocity of VD = 7800 m/sec. The diameter of the charge was d = 30 mm, and its height H was 10, 30 or 60 ram. It was initiated by electrical detonator 4 attached to the charge at the end opposite the specimen.If we calculate the total impulse Js with the aid of the formula suggested in [13], J, ~ 0.8p 9 vo 9 (H), (1) ...

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An investigation of the state of rocks in undisturbed form, and during disturbance by drivage of development workings and the working of seams or ore beds, is both important and also extremely complex in practice. The complete physical and mathematical formulation of the problem must take into account the complex geologlcal structure (allowing for tectonics) of the region, the mutual influence of the systems of workings, the change in the mechanical characteristics in the vicinity of the workings, etc. All these factors make it necessary to solve spatial problems with inclusions and workings of arbitrary form.The literature gives data on the stress in the rock in the vicinity of a working remote from the free surface (see, e.g., [1][2][3], in which there is a more detailed bibliography) and in its vicinity [4, 5]. However, the possibilities of an analytical investigation of the problem are limited to the simplest cases under conditions of plane deformation. Considerable success in the solution of problems of geomechanlcs has been attained using numerical methods, particularly the finite-element method [6][7][8][9], which enables us, without altering the algorithm, to change fairly rapidly and simply the outer and inner boundaries of the region and the properties of the medium, or to assign various boundary conditions.In this article we calculate the stress in the rocks around mlnlng-out and development workings during mining of the Talnakh and Oktyabr' deposits by the longwall sllcing system with stowing of the worked-out area.The Norilsk polymetallic deposits are nearly flat; the bedding angle reaches i0 ~ The seams are 20-40 m thick and relatively deep (H = 600-1500 m).The characteristics of the geological structure of the platform are such that the horizontal component of the stress of the undistrubed rock is greater than the vertical component 7H (7 is the bulk density of the medium) by a factor of 1.5-2. The principal system of working deposits under these conditions is recognized to be the lonswall slicing system with hardening stowage, the slices being worked in ascending, descending, or combined order. Figure 1 shows these schemes; the arrows show the directions in which the work is performed. The ore body, the hardening stowage, and the worked-out area correspond to regions I, II, and III; the adjoining rocks IV lie above and below the seam. In some cases the slices immediately belowthe roofs are extracted and reinforced-concrete canopies erected, followed by working of this sector of the deposit in strips over the whole thickness of the deposit. As characteristic dimensions we took Z = 4-8 m, Z, = 15 m, h, = 3-4 m, and ha = 6-8 m.It will be assumed that the conditions of plane deformation are satisfied. This approach is valid if the whole picture is similar in the perpendicular direction to the direction sketch (we have in mind not only the geometric dimensions of the undisturbed rock but also those of the workings). It will also be assumed that during working of the deposit and strengthening of the har...

The neighborhood of the free surface of a medium and the interfaces between different media are very liable to spalling fracture when they interact with stress waves. At present, owing to the increased popularity of drilling and blasting, it is becoming more and more urgent to study the breaking action of stress waves in a medium and to investigate the stability of the free surfaces of the solid rock -the contours of workings, the sides of quarries and pillars, etc. It is very important to know how to estimate the character and extent of the state of stress of the solid rock near such surfaces: this will enable us to preserve the contours of workings or to estimate correctly the possible fractures. The main features of these phenomena can be investigated by taking as an example a body with plane-parallel faces, the simplest case being a plate. The spallation of the backs of plates is of independent interest. The literature contains much experimental material on the laws of variation of the state of stress in a real material and on the actual pattem of possible breakage; there are various approaches to the analytical solution of the problem -the acoustic versions, quasistatic estimation, and exact solutions of the stress field [1][2][3]. This article gives a numerical investigation of the stress fields in an elastic plate and discusses the nature of the spallation in it.For a numerical solution of the problem it is convenient to adopt the following scheme [4,5]. From the equations of motion in the Cauchy form in cylindrical coordinates (r, O, z), ~9ar (rr --O0 Orrz := p c)~'u 0-7 + ~ + Oz ~7 ~' a6 z a~ tJTrz Tr....~z _--~ :: p Or + r or" (1) and from Hooke's law, 2it ()it. o~ --=).e + ' "o7' oo ..... ; oz-=...; Ou u am e:=a7 + -7-+ -aT, (au rr,=F -bE + 0r]'(3)(where X, p, and p are the Lam6 parameters and the density of the medium, o r , %, o z, rrz, and u and w are the components of the stress tensor and the displacement vector respectively, and t is the time) we eliminate the displacements. The equations must be differentiated with respect to r or z so that on the fight-hand sides of the superposition of the resulting relations we can formulate the second derivative with respect to time of any component of the stress tensor, as we find from Eqs.(2), (3), and (1). As a result we get the equation (T-' Crz = (~, -l-" " a2frz ~, o2ffr ~, O (o" r --o'0) [, ~ z~t)~ +_ Or" + 7 Or ~. do r 02rrz 2 (~, ;-It) Orrz (4) + r-~7 + 2 (~ + P) b-7"~ + r oz and similar ones for the other two normal components of the stresses. A distinguishing feature of Eq. (4) is that, as well as the second derivativeofo z with respect to time, it contains only the derivative of the same function with Institute of Mining, Novosibirsk.