Mechanical Performance Investigation of the Effective Longitudinal Torsional Stiffness Ratio in Rectangular Shield Tunnels Under Combined Loadings

Rectangular shield tunnels demonstrate significant advantages in underground space utilization due to their optimal cross-section efficiency and enhanced spatial functionality. Furthermore, their shallow overburden construction capability minimizes environmental impact and preserves subsurface resources. However, compared with circular shield tunnels, rectangular configurations exhibit greater susceptibility to longitudinal differential torsional deformation under asymmetric external loading. This deformation mechanism may induce excessive stresses in segments and connecting bolts, potentially causing joint offsets at tunnel rings that compromise structural integrity. This paper proposes a computational method for determining the longitudinal equivalent torsional stiffness of rectangular shield tunnels under combined compression–bending–torsion loading based on an equivalent continuum model. The proposed novel theoretical solutions were systematically validated against numerical simulations through comparative analysis. Parametric studies revealed that the effective ratio of longitudinal torsional stiffness increases proportionally with segment width-to-height ratio and bolt quantity while exhibiting inverse correlations with segment thickness and bolt equivalent shear length. The effective ratio of longitudinal torsional stiffness is directly correlated with compression–torsion ratios and bending–torsion ratios, with different load combinations significantly influencing torsional performance. Consequently, design optimizations incorporating increased bolt pre-tension forces or pre-stressed segment structures are proposed to improve torsional performance in rectangular shield tunneling systems.