Closed solutions to soil displacements induced by twin-tunnel excavation under different layout patterns

The existing theoretical researches on deformation of soils caused by twin-tunnel excavation are generally based on the linear superposition of single tunneling results and seldom consider the interaction effects between the two tunnels. Based on the displacement-controlled Schwarz alternating method and the complex variable function theory, and considering the oval deformation contraction boundary condition of tunnel opening, a method is proposed to analyze the deformation of the surrounding soils caused by twin-shield tunnel excavation in arbitrary position in order to reveal the interaction influences for the closed underground excavation. The method is based on the displacement boundary condition, which reflects the interaction between the twin tunnels during excavation. Through experiments and engineering cases, the theoretical solutions to the complex variable function based on the displacement-controlled Schwarz alternating method are obtained and compared with those of the linear superposition method and the measured data. The deformation influence laws of ground, which are caused by the variation of space between twin tunnels under two different layout patterns, horizontal and oblique, are acquired through parameter analyses. The results indicate that the surface settlement curve obtained by the complex variable function method based on the displacement-controlled Schwarz alternating method is in good agreements with the measured one, while the linear superposition method has a comparatively large error. Analysis of the laws of contour map indicates that