Analysis of Stress around Tunnel by Conformal Mapping

One of the powerful methods in tunneling design in rock mechanics and geotechnical engineering is analytical method. Among the analytical models the best model is the use of complex potential functions one. The complex potential method applies conformal mapping. Applications of conformal mappings are made to two-dimensional boundary value problems involving rock mechanic, soil mechanic, heat flow, electrostatics and ideal fluids. Of particular interest is the ability of conformal mappings to map regions with a complicated boundary shape onto regions with a simple boundary shape McMahan (2008). This is because such mapping can be used to solve two-dimensional boundary value problems for the elasticity equations in regions of complicated shape. The required solution follows directly from the fact that conformal mappings map one analytic function into another one.