The use of the vertical shaft sinking machine (VSM) for shaft construction can effectively improve construction safety and efficiency. This study focused on analyzing the internal forces and deformation characteristics of a 50.3 m deep shaft constructed by the VSM method. Findings reveal that the external pressure of the shaft is positively correlated with the excavation depth, increasing as the depth grows. Pumping water inside the shaft disrupts the balance of the soil behind it, leading to a reduction in the external pressure of the shaft wall. During the excavation and sinking stage, the bottom connecting beam mainly endures compression. After water pumping, the coupling and restrictive effect between the bottom connecting beam and the shaft wall strengthens, significantly boosting the internal compressive stress. The stress states of the segments above and below the shaft vary: the upper segments are under pure compression, while the lower ones may experience uneven deformation due to multiple factors. Moreover, the cast-in-place piles and surrounding stratum show a “bulging” deformation pattern during sinking, greatly influenced by the shaft’s attitude deviation, whereas grouting at the shaft bottom and internal water pumping have minimal impact on the surrounding stratum.

Granular materials exhibit pronounced macroscopic irreversible deformations during shearing, which mainly contributes to frictional sliding dissipation in the conventional thermodynamic frameworks. This study aims to investigate the non-dissipative microscopic mechanisms governing macroscopic irreversibility of granular materials. Using DEM, a series of biaxial shear and reverse loading simulations are conducted on dense granular assemblies with different friction coefficients. The results show that continuous topological reconfiguration occurs through the transformation from lower-order to higher-order meso-loops, eventually reaching a statistical steady state at the critical state. Accompanying this topological evolution, elastic energy at contact level is continuously stored and released, providing a persistent non-dissipative energy exchange that sustains continuous shear alongside primary frictional dissipation. Based on the reverse loading analysis, topological reconfiguration is intrinsically irrecoverable, causing part of the free energy to remain locked within the reconfigured contact network as irrecoverable free energy. Meanwhile, another portion of the recoverable free energy is irreversibly dissipated through friction during unloading. Together, these two components constitute the irreversible free energy. The evolution of irreversible free energy with interparticle friction is consistent with those of the critical frictional dissipation and macroscopic volumetric strain, indicating that the macroscopic irreversible deformation of granular assemblies is governed not only by frictional dissipation but also by the irreversible evolution of free energy.

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.