Design of roof bolting as the solution of a contact problem

Abstract

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.