The face stability analysis of a longitudinally inclined shield tunnel using an analytical approach in water-rich areas is still a research gap. To solve this face stability problem, a numerical simulation based on the FLAC3D is first conducted to calculate the seepage field behind the inclined tunnel face. An improved rotational failure mechanism is developed to make it possible to investigate the face stability of inclined tunnels using analytical approaches. In the framework of the kinematic approach of limit analysis, the limit support pressures and corresponding failure surfaces of the inclined tunnel face are determined to analyze the face stability issue. The interpolation tool (griddata) in MATLAB is adopted to involve the obtained numerical values of pore water pressures into the analysis of the stability issue. The analytical solutions obtained from the proposed method are validated by comparisons with existing results from published literatures and numerical results. For a quick estimation of the inclined tunnel face stability in water-rich areas, a series of design charts are then presented for various soil strength parameters, water tables, and inclined angles. Finally, an application of the proposed method to a practical tunneling case is provided, which further illustrates the effectiveness of the proposed method.

This paper addresses stability challenges at excavation faces in shield tunneling through water-rich soil-rock formations, particularly focusing on partial failure caused by significant strength differences between soil and rock layers. A three-dimensional discrete rotational failure mechanism model is developed under the limit analysis upper-bound theorem, considering the influence of pore water pressure. This model leads to a novel method for calculating ultimate support pressure in complex strata, with its reliability confirmed through comparison with existing solutions. Key findings reveal a roughly linear positive correlation between soil layer proportion, water level, soil saturation weight, and ultimate support pressure. Conversely, cohesion, tunnel depth and friction angle demonstrate an inverse correlation. Notably, the relationship between soil layer proportion and ultimate support pressure exhibits significant nonlinearity. Cohesion and water level exert the most significant effects on ultimate support pressure, while the impact of soil layer proportion is notably complex. Additionally, a normalized design method is established using tunnel diameter and soil saturation weight, supported by design charts for varying normalized cohesion, normalized water level, and friction angles. A detailed example of a classic case is provided to illustrate the use of these design charts, aiding practical engineering applications.

Seismic activity on a tunnel damages the tunnel support systems. The extent of the tunnel damage depends on the soil type, the magnitude of the earthquake acceleration, and the tunnel cover depth. Hence, analyzing the stress induced by the seismic event from the surrounding ground on the tunnel facilitates a safe tunnel design. Based on the pseudostatic method, this study examined the seismic stability of square and rectangular tunnels placed in cohesive-frictional soil. The tunnel collapse load was found using the lower-bound theorem of limit analysis in combination with the finite-element method. From the distribution of stresses along the periphery, the normal stress at each tunnel node was calculated, and the maximum of stresses was reported as the support pressure. Thus, the systems safeguarding the tunnel against devastating lateral earthquake forces are expected to offer the ultimate resistance equal to the maximum normal stress on the tunnel periphery. With the increase in tunnel cover depth, aspect ratio, seismic acceleration coefficients, and a decrease in soil cohesion and friction angle, the support pressure was noted to enhance. The distribution of normal stresses around the tunnel periphery depends on the tunnel geometry, the soil's shear strength parameters, and the magnitude of earthquake acceleration. For a square tunnel, the magnitude of stress was maximum on the walls, followed by the roof and base, implying that collapse will be more prone from the side walls. However, the rectangular tunnels are noted to be susceptible to collapse from the roof, followed by walls and base.

Face passive failure can severely damage existing structures and underground utilities during shallow shield tunneling, especially in coastal backfill sand. In this work, a series of laboratory model tests were developed and conducted to investigate such failure, for tunnels located at burial depth ratios for which C/D = 0.5, 0.8, 1, and 1.3. Support pressures, the evolution of failure processes, the failure modes, and the distribution of velocity fields were examined through model tests and numerical analyses. The support pressure in the tests first rose rapidly to the elastic limit and then gradually increased to the maximum value in all cases. The maximum support pressure decreased slightly in cases where C/D = 0.8, 1, and 1.3, but the rebound was insignificant where C/D = 0.5. In addition, the configuration of the failure mode with C/D = 0.5 showed a wedge-shaped arch, which was determined by the outcropping shear failure. The configuration of failure modes was composed of an arch and the inverted trapezoid when C/D = 0.8, 1, and 1.3, in which the mode was divided into lower and upper failure zones.