When excavating a tunnel, the stresses are distributed asymmetrically along the tunnel cross-section. Other factors, particularly slope friction force and excavation speed, can also contribute to the deformation and displacement of a tunnel. Despite this, several authors have used the complex potential method to predict the ground deformation surrounding the tunnel. However, their applicability to the ground response caused by the asymmetric stress distribution around the tunnel wall is analysed in this context. This paper, therefore, proposes an approximate solution on the slope to predict the tunnel cross-section deformation. The solution is based on the complex potential method to predict analytically and numerically the ground deformation around the tunnel. However, two variables called the “complex potential functions” for the Laurent series expansion are used for the stress redistribution to the tunnel boundary conditions. Data from the Qijiazhuang tunnel case are used to justify the proposed analytical solutions. This solution is an essential guide for analyzing deformations in complex geological conditions and structures, such as steeper slopes.

This paper proposes analytical solutions to the soil deformation around a cylindrical cavity under drained conditions. Analytical procedures are used to predict the degree of interaction between cavities and ground surface loads based on mathematical theorems. The stresses applied at the boundary condition induce the ground motions around the cylindrical cavity wall. Additionally, the Airy stresses are obtained through mathematical derivatives and integrations by combining the Fourier analysis test with the Navier equations. Next, we established a schematic representation of the horizontal and vertical displacement related to the corrective shear model to obtain insight into the intensity and directions of ground stresses. The resulting transformations include displacement, shear, and deviatoric stresses applied to the cylindrical cavity wall. These data can be used as input parameters for numerical simulations to alternatively solve the groundmass redistribution problems and calibrate the horizontal stress of drained soil conditions.

Based on the analytical method of formation deformation caused by tunnel excavation proposed by Verruijt and Sagaseta, combined with the basic principles of soil mechanics and elastic mechanics, a method for determining the pending parameters required in the analysis process is proposed. This method does not require the actual measurement of deformation values in the field, and the required parameters can be determined from geological data, so as to obtain the deformation values of any points of the whole stratum. According to engineering examples, when the pending parameters are obtained by this method, the difference between the resolved value of maximum surface settlement and the measured value can be controlled within 5.0%, and the analytical results can splendidly reflect the formation deformation law caused by tunnel excavation. Further combined with the analysis of the numerical simulation results, the proposed approximation method has certain shortcomings and deficiencies, mainly in the lack of lateral constraints on the displacement. When the measured data in the field are insufficient, this method can be used to estimate the deformation, and the analysis results are slightly larger than the measured values, which is safer.

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.