Many sedimentary rocks are transversely isotropic bodies, the deformation properties of which are characterized by independent constants: E z and E z) the Young's modulus for extension -compression in the plane of isotropy and normal to it; g z3) the Poisson ratio which characterizes contraction in the plane of iso=opy during compression in it; g12) the Poisson ratio characterizing contraction in the direction of the y axis, perpendicular to the plane of isotropy, during compression in the direction of the x or z axis; andGt2) the shear modulus for planes normal to the plane of isotropy.In this system of coordinates, the generalized Hooke's law is written as [1]: 1 e~ = ~ (~ --~2~y --~t~%);
When a working is cut in the solid rock, stress redistribution takes place. The new state of stress is governed by the initial stress state of the rock, the shape and position of the working, the mechanical properties of the rock, and the mechanical characteristics of the supports used [1]. If we are considering a long working deeper than five times its radius, we can base our calculations on a weightless plane weakened by a hole with the same shape as the cross section of the working, the stresses at infinity being equal to those in the undisturbed rock before the working is cut, at the center of the space which it will occupy.There are three hypotheses concerning the state of stress in the undisturbed rock: 1) a horizontal stress o x = k ill, where k < 1; 2) o x = ~,H, the hydrostatic case; and 3) o x = kyH, where k > 1. At the points of greatest concentration the stresses exceed the strength of the rock, and then plastic zones arise and may encompass the whole periphery of the working or part of it, according to the mechanical properties of the rock and the size, shape, and depth of the working. The methods of calculation of the stress field for regions of elastic deformation differ from those for inelastic deformation, and therefore we must justify their use in any particular case.Let us consider the instantaneous stress distribution at the periphery of the working (for example, during formation of a cavity by drilling and blasting) in relation to the depth of the working, for three values of k, namely 0.5, 1.0, and 2.0, and for circular, elliptical, and square workings.For a working of given cross section, in rock with given mechanical properties, the stresses on the periphery of the hole, other conditions being constant, will depend on the depth of the working below the surface. At some depth H I the greatest s=ess existing at some part of the periphex'y wiU reach the limiting value for the given rock, Oli m, and plastic deformation will begin to develop at this point. At a depth H z >> H l the srnallest stress on the periphery will also be Oli m, and then the whele periphery will be plastically deformed. To find the values of H 1 and H z we need to know the greatest and least stresses on the periphery of the working.For a biaxial state of stress in which the stress at infinity is a tension (compression) with values k),H and yH in directions making angles a and a + Ir/2 to the x axis, respectively, the stress on the periphery was determined in [2]. Then for an eUiptical cross section,
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.