In double-shield TBM tunnel construction, grouting plays a vital role in consolidating the gravel backfill and maintaining the integrity of the segmental lining. To investigate the permeation behavior of grout within the pea gravel layer, a fluid dynamics model was developed in this study. The model directly simulates the flow of grout through the porous medium by solving the Navier–Stokes equations and employs the level set method to track the evolving interface between the grout and air phases. Unlike conventional continuum approaches, this model incorporates particle-scale heterogeneity, allowing for a more realistic analysis of grout infiltration through the non-uniform pore structures formed by gravel packing. Three different grouting port positions and two boundary conditions are considered in the simulation. The results indicate that under pressure boundary conditions, the grout flow rate increases rapidly in the initial stage, and then decreases and stabilizes, with the flow rate peak increasing as the grout port moves upward. Under velocity boundary conditions, the injection pressure grows slowly in the early stage but accelerates with time. Additionally, the rate of pressure change is faster when the grout port is located lower in the backfilling layer. Through theoretical analysis, the existing analytical formula was extended by introducing a gravitational correction term. When the grouting port is near the upper part of the tunnel, the analytical solution aligns well with the numerical simulation results, but as the grout port moves downward, the discrepancy between the two increases.

This study aims to assess and select shield tunnel segment configurations and assembly angles based on the characteristics of circumferential internal force distribution. Based on the multi-hinged circular ring method and considering the diversity of assembly angles and segment configurations in practical engineering, a fundamental equation is established to calculate the contact forces at the longitudinal joints of a single shield segmental ring under arbitrary segment configurations and assembly angles. In addition, formulas for calculating internal forces are derived, and the corresponding coefficient matrix and constant vector are obtained, which significantly simplifies the process of solving the equation. Results from an actual project show that the calculated internal-force distributions are consistent with the expected mechanical response, while the calculated longitudinal-joint contact pressures show reasonable agreement with field measurements, supporting the reliability of the proposed method under the investigated engineering conditions. For the investigated circular segmental ring, the segment configuration and assembly angle significantly affect the distribution of internal forces. Moreover, appropriate configurations and assembly angles can effectively reduce bending moments and shear forces within the segments. When the segment configuration and assembly angle are fixed, external loads have a greater impact on the magnitudes of internal forces but less influence on their distribution. The selection of the segment assembly angle should be based on specific engineering objectives, such as structural performance and joint waterproofing requirements. The proposed method provides a basis for the assessment and selection of segment configurations and assembly angles, as well as for the design of longitudinal-joint waterproofing measures in practical engineering.