Analytic approximant of elastic stress around noncircular shallow-buried tunnels under general loading conditions

Abstract

This study proposes a novel procedure for obtaining analytic approximant of elastic stresses around noncircular shallow-buried tunnels under general loading conditions. The solution is regarded as a superposition of two parts: one induced by gravity and/or tectonics, surcharge loads on the ground and reinforced loads acting within the outer region of tunnel (Model A), the other yielded by the release stresses due to excavation, together with supporting forces on the tunnel boundary (Model B). The elastic stresses for Model A are analytically obtained by the theory of elasticity. The stresses for Model B can be further divided into another two components: one in a half-plane without a tunnel subjected to virtual tractions along the ground surface (Model B1), which has analytical solutions, and the other in an infinite plane with a tunnel loaded by virtual tractions along its boundary (Model B2), which can be analytically approximated by using a method recently presented by the authors. An iterative procedure is proposed for computing the two sets of virtual tractions resulting in stresses in Model B. The present method gives analytic approximant of elastic stress solutions of tunnels, sufficiently approaching the exact ones to high degree of accuracy. Example studies shows that such solutions agree well with those by the finite element and boundary element methods in the whole region from the viewpoints of practical engineering. Moreover, the present method can accurately determine stresses even in the region at a distance of 10-13 times the characteristic size of tunnel from the corner. More investigations, using this method, are performed into the influence of supporting force and buried depth on stress distribution around shallow-buried tunnels.