Grounded in the principles of wave dynamics, this study employs the wave function expansion approach to mathematically describe how plane P- and SV-waves scatter around a composite tunnel lining embedded in an unbounded medium. To establish the transient analytical framework for the dual-layer structure subjected to blast excitations, we integrate Fourier integral transforms alongside the Heaviside step and Dirac delta functions. We systematically analyze how the tunnel’s transient dynamic stress concentration factor (DSCF) responds to variations in the shear modulus ratio, as well as the specific characteristics of the incoming waves (i.e., wave type and dimensionless pulse duration). Furthermore, a seismic mitigation strategy featuring a “soft-exterior, rigid-interior” configuration is theoretically explored. The analytical outcomes theoretically indicate that short-duration transient waves provoke severe dynamic stress concentrations within the lining, with SV-waves posing a markedly greater threat to structural integrity than P-waves. Analyses reveal that the peak dynamic stress concentration (DSCFmax) primarily localizes at the tunnel’s crown and invert. Interestingly, altering the pulse duration does not significantly shift this spatial distribution pattern. Ultimately, analytical results suggest that adopting the “soft-exterior, rigid-interior” design and optimizing the thickness of the primary support can substantially alleviate these stress concentrations, providing preliminary theoretical guidance for vibration attenuation.

To meet the demand for simulative materials exhibiting suitable hydraulic characteristics in geomechanical model tests, this research developed a type of simulative material using iron powder, quartz sand, and barite powder as aggregates, white cement as binder, and silicone oil as additive. An orthogonal experimental design L₁₆(4⁴) was employed to prepare 16 distinct mix proportions. Advanced statistical methods, including range analysis, residual analysis, Pearson correlation analysis, and multiple regression performed with SPSS 27.0.1, were applied to analyze the influence of four factors—aggregate-to-cement ratio (A), water–cement ratio (B), silicone oil content (C), and moisture content (D)—on physical and mechanical parameters such as density, uniaxial compressive strength, elastic modulus, angle of internal friction, and permeability coefficient. Range analysis results indicate that the aggregate-to-cement ratio serves as the primary controlling factor for density and elastic modulus; moisture content exerts the most significant effect on compressive strength and permeability; while the water–cement ratio is the dominant factor influencing the internal friction angle. Empirical formulas were established through multiple regression to quantitatively correlate mix proportions with material properties. The resulting similitude materials cover a wide range of mechanical and hydraulic parameters, satisfying the requirements of large-scale physical modeling with high similitude ratios. The proposed equations allow efficient inverse design of mixture ratios based on target properties, thereby supporting the rapid preparation of simulative materials for advanced model testing.

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.