The Use of the Three Dimensional Boundary Integral Equation Method for Determining Stresses at Tunnel Intersections

For some underground structures, the use of the plane strain assumption in stress analyses may not be justified. The finite element method and photoelasticity have been used to obtain complete 3-D solutions, but, for various reasons, neither method has found universal use. The boundary integral equation method (B.I.E.M.) can be more efficient and economical than the finite element method for 3-D problems involving large volume to surface area ratios. A B.I.E.M. program developed for calculating stresses and deformations in infinite elastic media has been used to determine the 3-D distributions of stress around T- and Y- junctions of circular tunnels in stress fields in which the ratios of horizontal to vertical stress are 0, 0.33, 1.0 and 2.0. For the T- junction considered,stress concentrations at the intersection are approximately twice the plane strain values. Except where horizontal field stresses are high, the stresses in both tunnels approximate the plane strain values at about two tunnel diameters from the point of intersection of the tunnel centre lines. The stresses in the two branches reach those for the corresponding plane strain, two parallel tunnel case two diameters from the point of intersection of thq inner tunnel walls. Very high stress concentra- tions occur in the pillar of rock between the inner tunnel walls near the point of intersection.