Analytical solution for estimating surface settlements induced by multiple tunnel excavation

The derivation of an approximate explicit analytical solution was presented to calculate three-dimensional surface settlements due to the excavation of either single or multiple tunnels in a homogeneous elastic soil.This solution was based on the integrated form of Mindlin’s equations and Taylor’s series expansions.Surface settlements due to the construction of tunnels with an arbitrary orientation during the tunnel advancement with and without supporting pressure could be modelled by using a stress relief coefficient.The derived analytical solution was verified by carrying out a three-dimensional finite element analysis of a single tunnel excavation.The discrepancy between the simplified approximate solution and the finite element analysis was less than 9%.The usefulness of the simplified approximate analytical solution was demonstrated by analyzing two parallel and two cross tunnels.