Research on the Mechanical Model of the Tunnel Supporting Structure Shell Based on the Modified Ellipsoid Theory

Accurate assessment of tunnel lining deformations and stress distributions critically governs structural integrity, while miscalculations may trigger construction delays and budget overruns. A mechanical shell model for tunnel supports was developed, integrating the modified ellipsoid theory to analytically resolve vertical displacements and internal stresses. Numerical validation through finite element simulations confirmed model efficacy. The influence of key geometric and material parameters encompassing height-to-width ratio, burial depth, lining thickness, and elastic modulus on tunnel support displacement and stress distributions was systematically investigated. Parametric analysis revealed that vertical displacement exhibited greater sensitivity to height-to-width ratio variations compared to burial depth. Longitudinal distributions demonstrated similar trends axial force and vertical displacement, with bending moments and shear forces exhibiting analogous behavioral patterns. Transver sely, axial forces and vertical displacements adopted a symmetrical trough (U-shaped) profile, while bending moments and shear forces formed a bimodal (M-shaped) distribution with attenuated gradients near the crown region. This computational model establishes a practical analytical tool for evaluating post-support tunnel deformation and structural load distributions.