An Analytical Solution for Stress and Displacement Field for Arbitrarily Positioned Twin-Tunnel Excavation at Great Depth

Abstract

In this study, an analytical solution for the stress and displacement field for arbitrarily positioned twin-tunnel excavation at great depth is proposed. The twin-tunnel is subjected to equivalent loads on the tunnel periphery and uniform loads at infinity. The analytical continuation of the complex variable method is used for stress “stair”, owing to the equivalent loads of the tunnel support. Subsequently, the Schwarz alternating method and Cauchy integral formula are used. The redundant surface forces on the periphery are expanded into Laurent series in the sequence of iterations, and a reasonable series truncation is adopted. Comparing with several existing solutions covering special cases from different perspectives, it is found that the proposed solution meets accuracy requirements for tunnel center distance greater than 2.2 times tunnel radius after 1.5 iterations. The proposed solution is fast and yields reference value to tunnel engineering.