The flexible joints and segmental lining serve as effective seismic measures for tunnel in high-intensity seismic area. However, the tunnel axial deformation at flexible joints has not been fully incorporated into analytical models. This study presents a novel mechanical model for flexible joints that considers tension (compression)shear-rotation deformations, replacing the traditional shear-rotation springs model. An improved semi-analytical solution has been developed for the longitudinal response of a tunnel featuring a three-way flexible joint mechanical model subjected to fault movement. The nonlinear elastic-plastic foundation spring, the soil-lining tangential interaction, and the axial force of tunnel lining have been considered to improve the applicability and precision of proposed method. The proposed solution is compared with existing models, such as short beams connected by shear and rotation springs, by examining the predictions against numerical simulations. The results indicate that the predictions of the proposed model align much more closely with the outcomes of the numerical simulations than those of the existing models. For the working conditions selected in 4, neglecting the tension-compression deformation at flexible joints an 81.8% error in the peak axial force of the tunnel and a 20.2% error in the peak bending moment. The reason is that ignoring the axial deformation of these joints results in a larger calculated axial force on the lining, which subsequently leads to increased bending moment and shear force. Finally, a parameter sensitivity analysis is conducted to investigate the effect of various factors, including flexible joint stiffness, segmental lining length, and the length of the tunnel fortification zone.

Tunnels that cross active faults will inevitably be severely damaged, and there are mainly five fault types. There are five main fault types: strike-slip fault, normal fault, reverse fault, and oblique-slip fault (normal or reverse strike-slip fault). However, there is no calculation method of tunnel longitudinal mechanical analysis for all fault types, and the calculation accuracy is reduced by the assumptions used in the existing calculation models to simplify the solution of complex differential equations. In pursuit of this objective, this study presents a novel semi-analytical model that accounts for five distinct types of faults and analyzes complex mathematical problems via the finite difference method, thereby circumventing the need to derive intricate analytical solutions. Additionally, an unconventional iterative approach is suggested for the computation of the nonlinear interaction between the tunnel and soil. This method exhibits exceptional efficiency, requiring less than one second per calculation on a laptop. Furthermore, when compared to a numerical model based on finite elements and varying fault displacements, this model demonstrates that the longitudinal forces and displacements are quantitatively in good approval, even when massive fault displacements are considered. Finally, this model is utilized to assess the longitudinal displacements, forces, and safety factors of the Daliang tunnel under faulting, and the failure range and failure modes are consistent with the actual situation. The suggested approach addresses a gap in the existing literature and is valuable for quickly, cost-effectively, and stably analyzing and designing tunnels intersecting with active faults.

Tunnels subjected to active fault dislocation may experience significant damage. This paper establishes a novel methodology and solution procedure for analyzing the mechanical response and failure characteristics of tunnels subjected to active fault dislocation based on an elastic foundation beam model. The proposed methodology includes axial, transverse, and vertical soil-tunnel interaction terms, in addition to geometrical nonlinearity and axial force terms in the governing equation. This approach has a significantly extended application range, effectively addressing the problems encountered in tunnels crossing active faults with diverse crossing angles, dip angles, and fault types. The proposed methodology is verified by comparison to a 3D FEM model with various fault types, experimental tests, and on-site case, and the results are in excellent quantitative and qualitative agreement with the numerical, experimental, and on-site results. When fault displacement is below 0.5 m, disregarding geometric nonlinearity results in calculation errors of approximately 10% to 17% for peak axial force (Nmax), 18% to 22% for peak shear force (Vmax), and 20% to 30% for peak bending moment (Mmax). Finally, the responses caused by different factors, i.e., fault type, fault displacement, tunnel stiffness, and tunnel diameter, are investigated in detail to better understand tunnels crossing active faults. The results show that amongst the various fault types, the Vmax and the Mmax experienced by tunnels subjected to oblique slip-fault dislocation surpass those of other fault types, accompanied by the most extensive failure range. The augmentation of fault displacement, tunnel stiffness, and tunnel diameter precipitates a corresponding escalation in the Nmax, Vmax, Mmax, and failure range. Under oblique-slip fault dislocation, the tunnel undergoes an initial phase of shear failure, followed by tension-bending failure, delineated by distinct fault displacement thresholds of 0.1 m and 0.2 m, respectively. The proposed methodology provides the advantage of reliable stability analysis and design of tunnels crossing active faults.

In practical scenarios, tunnels may unavoidably cross active fault zones, leading to potentially severe damage by active fault displacement during earthquakes. Previous studies have failed to clearly establish an analytical method that considers both compressive and frictional behavior between tunnels and the soil that surrounds them, hindering the understanding of the tunnel -soil interaction. To address this, a finite element model (FEM) has been developed in this study to investigate the compressive and frictional characteristics of the tunnel -soil interaction of a reverse active fault -crossing tunnel. The model identifies six distinct zones of tunnel -soil interaction, namely, two active zones, two passive zones, and two separation zones. Building on these findings, the active fault -tunnel system was divided into three equivalent sub -systems, and an analytical method was established by creating and then combining equations for each sub -system. By applying the Pasternak Elastic Foundation Beam theory and Elastic theory, an analytical method is introduced that can simultaneously consider the distributed non-linear compressive interactive stress and non-linear frictional interactive stress. The results of the analytical method were validated with the FE results under three series of geological conditions. Through a quantitative examination of the similarity ratio and length of influence, the analytical results were seen to effectively reflect the characteristics of the soil -tunnel interaction and exhibit a good agreement with the FE results. It is concluded that the analytical model will serve as a computational reference for the design of reverse active fault -crossing tunnels.

Tunnels crossing active faults are susceptible to severe damage. This study establishes an improved semianalytical methodology for analyzing the mechanical responses of tunnels subjected to active fault dislocation. The methodology incorporates nonlinear axial, transverse, and vertical soil-tunnel interactions, shear effects, and geometric nonlinearity within its governing equations. Compared with existing methods, the proposed method has a significantly extended application range with improved accuracy, and the solution procedure demonstrates exceptional computational efficiency, with each case typically being solved in less than 1 s. The proposed methodology demonstrates outstanding qualitative and quantitative agreement with 3D FEM results across various fault types, as well as with the results obtained from the model test. Additionally, neglecting shear effects results in approximately 1.11 to 1.20 times higher bending moments and 1.13 to 1.19 times higher shear forces of the tunnel. Finally, a parametric analysis was conducted based on the proposed methodology to investigate the influence of critical parameters, such as fault displacement, buried depth, tunnel diameter, soil cohesion, and soil friction angle, on the tunnel response under fault dislocation. The results suggest that the tunnel responses positively correlate with the fault displacement, buried depth, and soil cohesion. Increasing the fault displacement amplifies the vertical shear force and bending moment asymmetry while increasing buried depth reduces this asymmetry. An increase in the tunnel diameter and soil friction angle is associated with a decrease in the peak axial force and an increase in the vertical shear force and bending moment. Additionally, variations in the friction angle do not exert a significant effect on the transverse shear force and bending moment.