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.