The three-dimensional problem of the-theory of elasticity was solved for heterogeneous rock mass, subjected to abnormal primary state of stress, in driving the working along the seam of coal varying in thickness.
Le problème tridimensionnel de la theorie d"elasticite est resolu pour le massif rocheux heterogène soumis aux contraintes naturelles irregulières pendant l"excavation le long de la couche du charbon d"une epaisseur variable.
Die Lösung des raumlichen Problems nach-der Elastizitatslehre fuer den nicht homogenen Felsverband unter der Wirkung der abnormalen Primarspannung beim Vortrieb eines Hohlraums im Kohlenflöz, dessen Dicke veranderlich ist.
The monitoring and prevention of the gasodynamic events can be accomplished with the analysis of stress and strain distribution in the rock mass near the face. The rock mass featuring heterogeneous properties can be presented in the form of mathematical model with details of the specific structures, for example, its stratification. The stress and strain state of a homogeneous elastic rock mass has been studied well enough. Evaluation of the heterogeneous rock mass calls for use of the finite element method (FEM) which permits solving the problem in more simple manner. It is necessary to take into consideration the three-dimensional problem for calculation of the distribution stress and strain around the working face.
The three-dimensional solution of elastic problem was used in realization of the study. The weightless area in the form of cube was analyzed. The cube models the rock mass with the, working, drived along the seam of the coal. The sizes- of- analyzed area exceeded the length of working as much as 10 times which permits the influence of boundary to be neglected. The working did not have support and was modelled by the parallelepiped with the length of 4"a", where "a" is the height of the working. The width, of working is equal to its height. The origine of coordinates are connected with the geometric centre of the working (Fig. 1). The horizontal boundary of cube was subjected to distribution pressure (γ H) in form the weight (γ) of overlying (H) rock mass and vertical boundary- λγ H, where λ - the, coefficient of lateral pressure in rock mass. We tried assess how heterogeneity in the elastic properties of rock mass would influence the stress and strain state around the face. The coefficient B=ER/EC(ER,EC - the modulus of elasticity, the roof of the working of rock mass and seam coal respectively) are varied in the range from 2 to 10. The heterogeneity of rock mass has potential influence on the distribution of the stress and strain. So the heterogeneity tends to increase the strain of the seam and respectively reduce the stresses.
Analysis of strained state shows that in the rock mass under the compressing stresses the zone of tensile strains will form before the face (Ex), than in the back of working (Ey) and at last in the roof. The absolute value of strain and the sizes of the tension areas tend to grow with the increase the heterogeneity of the rock mass.
