Stability analysis of rock blocks around tunnels

The mechanical response of rock blocks around tunnels is affected by factors such as the orientation and shear strength of the rock joints, the redistributed stresses, supportforces and other applied loads, and the shape and size of the tunnel. The safety of rock blocks can be studied by means of block theory. Since block theory ignores surface tractions arising from redistributed stresses, it tends to be over-conservative and may lead to uneconomical designs. When redistributed stresses are considered, however, the system of forces governing block safety becomes statically indeterminate. Indeterminacy in the mechanical response leads to uncertainty in determination of the safety conditions.This thesis presents an optimization method for the safety evaluation of two dimensional and three-dimensional rock blocks, which considers the effects of self weight,redistributed stresses, friction angles, and joint set orientations on the safety of the blocks around tunnels. To investigate safety requirements, a fictitious support force was introduced yielding two limiting values: the minimum support force for which safety can be achieved and the maximum support force for which the unsafe condition can occur. Linear Programming was used to determine these limiting values. Effects of friction angle, jointorientation, distributed stresses, and support pressure were studied. It was found that as the height or apical angle of the block increases, the block safety decreases. Block safety increases as horizontal stress ratio K, function coefficient p of the joints, or the tunnel depth increases.