Complex variable solutions for shallow twin tunnelling in visco-elastic geomaterial considering buoyancy effect and equivalent three-dimensional effects of tunnel faces

Abstract

Shallow twin tunnels are commonly encountered in urban metro construction. Twin tunnel excavation causes buoyancy effect in geomaterial and the interaction between twin tunnels significantly redistribute stress and displacement around twin tunnels. At the same time, twin, and tunnelling causes three-dimensional effects around tunnel faces. To explore the problems, this paper proposes complex variable solutions for shallow twin tunnelling in visco-elastic geomaterial under the initial stress field, considering the buoyancy effect, as well as the equivalent three-dimensional effect of tunnel faces. The proposed solutions are applicable to two common scenarios: (a) newly constructing twin tunnels, and (b) a newly constructing single tunnel near an existing one. The Schwarz alternating method is applied to the proposed solutions to reduce the half-plane twin tunnel problem into several connected half-plane single tunnel problems. During the alternating procedure, a separation technique is applied to reduce the mixed and complicated numeric-symbolic calculation into a simple numeric one to lower the threshold of the algorithm performed on computers of moderate computation capacity and considerably save the required running time. Additionally, a symmetrical modification method is applied to eliminate the displacement singularity at infinity of shallow twin tunnelling to obtain reasonable displacement in nearby and far-field geomaterial. The proposed analytical solutions are elaborately verified through a comparison with a corresponding numerical solution, which reveals good agreements between both solutions. A subsequent parametric investigation is performed to study the influence of twin tunnel geometry (including twin tunnel spacing, depth, relative size, and relative angle), lateral stress coefficient, preconvergence, and excavation sequence on stress and displacement in geomaterial. The proposed analytical solutions exhibit high accuracy in quickly obtaining the stress and displacement fields, and thus, is a feasible alternative in the preliminary design stage of shallow twin tunnels.