Information on the initial state of stress in undisturbed rocks in various regions, particularly those with enhanced tectonic activity, is of great importance for solving problems in the calculation, design, and construction of underground structures.In particular, the coefficient of lateral pressure of the rocks ~ = N2/N~ (equal to the ratio of the initial horizontal stresses to the vertical stresses) largely determines the distribution, over the cross-sectional perimeter, of the normal and tangential loads on a support operating in conjunction with the solid rock in the presence of mutually interfering deformations. To design the support (at the present level of the theory) we need a certain generalized value of the lateral pressure coefficient ~ typical of the ambient rocks as a whole, not just at individual points around the working; this sometimes impedes the use of measurements obtained, e.g., by the relief method, if they are insufficient for statistical processing.Acknowledging the overriding importance of the development of methods of direct measurement of the initial stresses in the solid rock and according them preference, of course, to extend the possibilities of obtaining information on the initial stress field we have made an attempt to estimate the state of stress of the rocks indirectly from its manifestations, i.e., to use for determining the generalized value of ~ the data of field measurements previously performed for other purposes, namely the results of measurements on the supports of mine workings and underground structures.This article gives a method for processing the data of field measurements of normal loads on supports of arbitrary cross section, permitting determination of the lateral pressure coefficient of rocks in order to use it for calculation and design of supports under similar geological conditions. The method is based on solution of the plane contact problem of elasticity theory concerning the equilibrium of a ring of arbitrary shape supporting a hole in a linearly deformed uniform isotropic medium with different deformation characteristics, having an initial stress field N, = --yHe*, N2 = --lyH~*, where ~* is a correcting factor allowing for the fact that the support lags behind the advancing working, for inelastic deformation of the rocks, and for other imperfections of the calculation scheme, determined, as in the case of ~, by measurements.The problem is posed as the inverse one and reduces to determination of the values of and a* at which the theoretical distributions of the normal contact stresses Op approximate most closely to the measured ones (o~), i.e., minimal standard deviation.The solution of this problem for a noncircular supportWis greatly complicated by the fact that the initial solution of the direct contact problem of elasticity theory is not a closed one, but reduces to a certain system of linear equations for a number of coefficients in the stress equation.As a result of the solution of the contact problem of elasticity theory for a ring of arbitrary shape ...
Currently, in the design of roof bolting there is extensive use of design schemes in which the tie is considered as a rod securing (suspending) broken rock to unbroken rock or forming a supporting rock-~le structure. These schemes do not take account of the reaction of ties with rock mass deformed during tunnel building and they do not reflect modern ideas about the operation of roof bolting.Consideration of the combined deformation of a set of ties around a tunnel with the rock mass makes it possible to consider the effect of a delay in tie installation both in time and space after rock exposure, the effect of the inltlal stress field in the rock mass, shape of the tunnel cross sectlon and technology for building It, and finally it makes it possible to use more fully the supporting capacity of the rock mass itself. The rock mass is considered as a welghable, llnearly deforming material exhibiting the property of llnear hereditary creep weakened by a cylindrical cut-out having the shape of the tunnel cross section.The set of ties is installed both in intact rock mass and with some delay after rock exposure. Ties could have initial (prellminary) stresses. Each tie experiences only longltudlnal strains. Reaction of a tie with the rock mass is represented in the form of two equal and oppositely directed forces, one of which is resultant stress applied to the surface of the blasthole (borehole) in the lock Joint of the tie, and the other is resultant stress over the surface of the support plate.The condition is fulfilled for combined displacement of the tie ends and corresponding points of the rock mass.It should be noted that slippage of the tie lock relative to the blasthole wall can in principal be considered within the framework of the method proposed.Forces Qi in the i-lh tie depending on relative displacements of its ends are described by the expression Q, = +where c~E~Fo/l is longitudinal tie stiffness; Ea, rod material elasticity modulus; Fa, rod cross-sectlonal area; ~, tie length;A~, relative displacement of the tie ends as a result of prior adjustment; ~i, relative movements for the tie ends as a result of combined deformation with the rock mass.Let a set of n ties be prescribed in a given tunnel section, and tie length ~, distance between ties u, and distance between section u I be known. After moving the face from the place where the ties are installed they are loaded and, a resultant strain field is formed in the rock mass which may be represented in the form of the sum of strains for the linearly deformed matez-lal with a cylindrical cut-out from the action of the natural weight of the rock 8" and from the action of forces at the tie ends 8~ .Thus, relative movements for the tie ands during their combined deformation with the rock mass may be represented in the form AI--A~.Ai----" "Owing to linear arrangement of the problem where ~ik are coefficients for the effect of loads Qk applied to the ends of the k-th tie by movement of the ends of the i-th tie.
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