AssessMent of the InDIvIDuAl rIsK of fAtAl Injury to coAl MIne worKers DurInG collApses purpose. To develop an effective model for assessing occupational risk due to rock caving in the country's coal mines. Methodology. A mathematical model based on the maximumlikelihood method is presented, which makes it possible to assess the probability of a rockfall. The use of Bayes theorem for assessing the individual risk of fatal injuries of coal mine workers is justified. The complex method for effective control of mountain pressure is illustrated by application of the developed methodol ogy of computer modeling of geomechanical processes, instrumental and geophysical methods for protection and maintenance of mine workings at development of a coal seam of the Barentsburg field. findings. The work demonstrates the relationship between the key statistical indicator that affects the accident rate and the value of professional risk. A key statistical indicator, the value of which is determined using the multifunctional systems of safety, is substantiated. originality. The development efficiency of the multifunctional safety system installation in coal mines to monitor the condition of the rock mass is analyzed. practical value. The model developed by the authors will make it possible to determine the predicted value of the individual risk of fatal injury to personnel during rock collapse more accurately compared to the existing methods.
WEAKENINGWeakening (postlimiting deformation) undergone by elements of massive rock or contacts between blocks and strata plays an important part in the behavior of the rock round a working. This must be taken into account in determining the supporting capacity of pillars, the pressure on the supports, and the danger of shock bumps [1]. However, except for the simplest cases of a uniform state of stress, axial or spherical symmetry, or a thin layer, these problems cannot be solved in analytical form, and require numerical methods such as the method of finite elements (MFE), boundary integral equations (BIE), etc. Most of these methods involve discretization of the problem, i.e., the region (in the MFE) or its boundaries (in BIE) are represented in the form of a set of discrete elements. The peculiar features of the problems of weakening, consisting in the possibility of loss of stability in connection with physical but not geometrical nonlinearity, are reflected in the feature that with critical combinations of parameters the matrices representing the linear operators cease to be positive definite.There is another important feature: Each of the discrete elements after reaching the limiting load can undergo either active irreversible deformation or load relaxation. As shown in [2], to choose between these possibilities we must invoke the method of quadratic programming (MQP).In problems of mining geomechanics, applications of the MQP to discretized problems are only just beginning. So far we know of only one article [3] in which a combination of the MFE and MQP is used for the case of an ideally plastic medium and a piecewise-linear load surface. There are no applications to weakened rocks or to cases in which the decay diagrams reflect not the properties of volumes of the medium but rather the contact conditions. Some of these applications are described below; for the MFE we turn attention to the possibility of specific loss of stability not infrequently caused by the choice of unduly small finite elements.1. The solution in steps with the aid of the MFE and MQP is effected as follows. Let the transition from the initial state of equilibrium to the final state be divided into several steps of increment of the external loads and displacements. These increments can be regarded as proportional to some monotonically increasing parameter t, e.g., the physical time. Then referring the increments of all the quantities to the increment of this parameter, we get the velocities (which we shall denote by a dot above the appropriate symbol). The increments of the quantities themselves in the next step are obtained by multiplying the velocities by the increment of the parameter t in this step.In terms of velocities, in the next step we must find where $i are the rates of change of the bulk forces (if the latter are constant, ~;i =0); and ~rui0, ~Ii0 are the given rates of change of the loads and displacements at the boundary.The third group of relations in (1) represents the relationships between the rates of stressing and de...
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