Support Pressure for Undrained Stability of Horseshoe-Shaped Twin Tunnels with Semi-Elliptical Roof in Clay

Undrained stability of twin horseshoe-shaped tunnels with semi-elliptical roof in clay soil has been investigated by using lower bound finite element limit analysis with second-order conic programming (SOCP). The magnitude of support pressure is presented in normalized form (sigma(t)/c(u0)) for different combinations of soil cover depth ratio (H/B), tunnel roof height-to-its width ratio (2h/B), normalized spacing between twin tunnels (s/B), normalized soil overburden pressure (gamma B/c(u0)) and rho B/c(u0) where B, H, h(r) and s are the width, cover depth, roof height and spacing of twin tunnels, respectively, and c(u0), gamma, rho and sigma(t) are the undrained shear strength at ground surface, bulk unit weight of clay soil, rate of increase in shear strength with depth and peripheral support pressure, respectively. The analysis illustrated that the normalized support pressure (sigma(t)/c(u0)) (i) increases due to increase in H/B, h(r)/(B/2) and gamma B/c(u0) and (ii) decreases with an increase in rho B/c(u0). Although sigma(t)/c(u0) decreases due to increase in s/B, the value of sigma(t)/c(u0) has been increased with an increase in s/B for high value of gamma B/c(u0) and 1 <= s/B <= 6. The proximity of the stress state to failure under active collapse state is also studied.