Elasto-plastic ground settlement response and stability of single and twin circular unsupported and supported tunnels

An attempt has been made to examine numerically, based on an elasto-plastic finite elements (FE) analysis, soil unit weight-ground displacement response due to laying of single and twin circular tunnels which are supported by an internal isotropic pressure (sigma(i)); the case sigma(i) = 0 implies an unsupported tunnel. The soil mass has been assumed to be linearly elastic and perfectly plastic obeying the Mohr-Coulomb (MC) yield criterion and an associated flow rule. The stability numbers, corresponding to ultimate collapse, based on lower and upper bound finite elements limit analysis (FELA) have also been separately evaluated. The effects of cover (H) to diameter (D) ratio, spacing (S) to diameter ratio of the tunnels and soil internal friction (phi) angle on the results have been examined in detail. The study clearly reveals that the value of the non-dimensional loading parameter, gamma D/c + sigma(i), corresponding to given surface vertical settlement (s(v)) and that at ultimate collapse, with an assumption that the elastic and plastic material parameters do not vary with depth, increases continuously with an increase in the values of S/D as well as phi, but decreases with an increase in the magnitude of H/D. The obtained computational results were found to compare well with the data reported in literature. It is expected that the study will be useful for stability evaluation and estimating vertical ground settlements for single and twin tunnels.