An analytical solution to account for the earthquake body force for twin circular tunnels in elastic media using complex variable approach

By using the complex variable approach, an analytical solution for non-uniformly deforming twin circular tunnels has been determined for a linear elastic weighty medium under the influence of earthquake pseudo-static inertial force. The non-uniform radial displacements along both the tunnels' peripheries have been imposed by using the Gaussian distribution function keeping the ground volume loss (GVL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\it {\text{GVL}}$$\end{document}) as the basic input parameter. By using the Schwarz iterative technique, the effect of interference of the twin tunnels on stresses and displacements' patterns has been explored. The analytical solution satisfies (i) the prescribed non-uniform displacement boundary conditions along the tunnels' peripheries, (ii) the existence of buoyant and pseudo-static earthquake inertial forces due to the formation of tunnels, (iii) the geostatic stresses in the presence of horizontal earthquake (inertial) forces in a zone far away from the tunnels, and (iv) the stress-free ground surface. The ground displacements and stresses in the domain have been determined and presented in terms of a number of contour plots showing the effect of spacing, orientation and size of the tunnels for a given magnitude of pseudo-static earthquake acceleration. The results obtained from the analytical approach have been found to compare well with the solution separately determined on the basis of the finite element analysis.