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S. V. Kuznetsov and B. N. Onopchuk, Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 2

(1974).

THE STATE OF STRESS OF THE SIDE ROCKS IN THE SLOT METHOD OF PROTECTING A WORKING V. I. Piskunov and G. A. Simanovich

UDC 622.261

The essence of the slot method of protection is that in driving a working, narrow slots are cut in its sides, promoting rapid formation of a zone of inelastic deformations, so that a region of reduced stress arises round the working. The low height of the slot ensures the necessary deformation of the side rocks without bed separation or loss of contact between strata. The slot method of reducing the stress concentration in the side rocks is an effective means of increasing the stability of mine workings [i]. The lack of solutions representing the stress distribution in the neighborhood of a working protected by this method is an obstacle to its extensive application and to the development of a theoretical method of determining the optimal parameters of the slot. In this article we give a solution to the first fundamental plane problem in the theory of elasticity for the case of the state of stress of the solid rock round an isolated horizontal working with slots in its sides (Fig. i). The state of stress in the undisturbed rock is taken to be

Artem Mining Institute, Dnepropetrovsk. Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 5, pp. 34-40, September-October, 1976. Original article submitted June 3, 1975. This material is protected b y copyright regLTtered in the n a m e o f Plenum PublLThing Corporation, 227 Wc~t J 7th Strett, N e w York, H. Y. I OOJ 1. N o part o f thLfpublication m a y be reproduced, ~ o r e d in a retrieval #y~rgera, or mansmit~ed, in any f o r m or b y any mean& electronic, mechanical, photocopying, microfglming, recording or otherlvite, w i t h o u t written permission o f the publ4~htr. A c o p y o f thl3 grglcle is available f r o m the publLfiter f o r $7.50.

487

~i 7 H

.__ItttltltlttltttltlIIItltlIttltttltL Fig. i. Scheme of calculation for determining stresses in side rocks in slot method of protection of working.

'

where H is the depth of the working below the surface, and y is the density of the rock. We neglect the weight of the rock within the zone of influence of the working. We assume that the rock is homogeneous and isotropic. The periphery of the working will be regarded as free from external forces. To solve the problem we used the powerful method of Academician N. I. Muskhelishvili [2], based on a complex representation of the stresses and displacements, with preliminary construction of a function which conformally maps the exterior of the unit circle in the ~ plane onto the exterior of a contour which is a polygon in the z plane (Fig. 2). This is effected by means of the so-called Christoffel-Schwartz integral, which in our case takes the form

z =

e (~)

=

c

~t2 I[

t--|

(~ --

a~

ai)~i-I ~" + c~

(i)

w h e r e t h e a i a r e p o i n t s on t h e u n i t c i r c l e c o r r e s p o n d i n g t o t h