Displacements and stresses around a circular tunnel in an elastic medium with pseudo-static horizontal earthquake body forces

Abstract

This manuscript presents an analytical solution based on the complex variable approach for computing displacements and stresses around a single circular tunnel in a linear elastic medium in the presence of pseudo-static horizontal earthquake body forces. The solution has been obtained with the imposition of uniform as well as non-uniform radial displacement boundary conditions along the tunnel’s periphery taking the ground volume loss (GVL) as a governing input parameter. The non-uniform radial displacements’ boundary condition along the tunnel periphery has been modelled by using the Gaussian distribution function. The effects of the distribution of the tunnel’s peripheral displacements, Poisson’s ratio of the continuum and the depth to radius of the tunnel on the results have been examined. Necessary validation exercise, in the presence of horizontal earthquake acceleration, has also been carried out by comparing the obtained results with that computed on the basis of the finite element method. The results were also compared with that reported in literature. It was observed that with an increase in the pseudo static acceleration, there is (i) a significant increase in the horizontal displacements, (ii) a generation of non-symmetric displacement and stress pattern, (iii) an increase in the shear stresses, and (iv) the development of high deviatoric stress zones around the tunnel periphery.