Twin tunnel stability and support requirements: Insights from limit analysis

Urban tunnels are often built in multiples, yet the influence of surface structures on their support demands is frequently overlooked, highlighting the need for refined design under realistic loading. This study addresses this gap by examining the response of a uniformly loaded strip footing above twin horseshoe tunnels with structural linings. A non-dimensional Footing Stability Improvement Factor (I_f), defined as the ratio of ultimate bearing capacity with and without lining to that of a footing on intact rock—is evaluated using adaptive finite element limit analysis. The effects of normalized vertical depth of tunnel, normalised horizontal spacing of tunnel, and lining-thickness factor are examined, providing key insights into foundation–tunnel interaction and support optimization. This study finds that, for unlined twin tunnels, footing–tunnel interaction becomes negligible when embedment exceeds four times of footing widths and tunnel spacing surpasses eleven times of footing widths, beyond which additional support is unnecessary. For lined tunnels, the tunnel-lining thickness required to maintain footing stability equivalent to that on intact rock decreases rapidly with embedment depth. At a tunnel spacing equal to one-half of the footing width, the critical lining-thickness ratio is about six percent of the footing width at a tunnel depth of half the footing width, reducing to approximately five, four, and three percent at depths of one, one-and-a-half, and two footing widths, and asymptotically approaching nearly one percent for embedment depths exceeding two-and-a-half footing widths. Additionally, rock mass parameters exhibit minimal impact (±2%) on I_f. The results show that failure mechanisms in footing–tunnel systems are primarily governed by tunnels-positional parmeters, and lining thickness. The study presents a mechanistic framework that delineates the critical depth–spacing–thickness regimes controlling twin-tunnel behavior, providing engineers with clear design boundaries and performance-based lining guidelines to improve the stability of both tunnels and overlying foundations.