Damage to the overlying soil caused by fault misalignment poses a significant threat to the structural safety of buried pipelines crossing faults, which is a non-negligible factor in the design of underground pipelines in complex environments. Existing research rarely involves analytical solutions for the force and deformation of pipeline structures under normal and reverse fault movements, and theoretical studies on fault-pipeline interactions often treat the pipeline structure as continuous, with little consideration for the influence of pipeline joints. Firstly, soil displacement curves for both normal and reverse faults are derived using the erf and erfc functions, based on a simplified SSR (stationary zone, shearing zone, rigid body zone) soil deformation model. Secondly, the deformation and internal force of the buried pipeline structure are solved using the two-parameter Pasternak foundation model and the finite difference method. Finally, the theoretical analytical solution is compared with existing experimental and 3D numerical simulation results, showing good agreement. In addition, sensitivity analyses are conducted for key physical parameters, including fault dip, fault-pipeline inter location, and joint rotation stiffness. The results show that fault dip will change the position of the pipeline displacement curve and axial stress curve, but the maximum displacement and maximum axial stress are basically identical. The inter of the fault and the pipeline will not only change the shape of the pipeline displacement curve and axial stress curve, but also alter the maximum axial stress. With the increase of joint rotation stiffness, the maximum axial stress value of the pipeline increases. When the joint rotation stiffness is large enough, the jointed pipeline can be calculated as if it is continuous.

Accurate prediction of excavation deformation and stress affects the safety of excavation engineering and the surrounding environment. However, the traditional calculation method ignores the influence of soil shear action and its nonlinear deformation characteristics. Therefore, this paper proposed a coupled analytical method for braced excavation considering the continuity of soil deformation and nonlinear pile-soil interaction. A nonlinear Pasternak two-parameter foundation model was developed based on the Pasternak foundation model and nonlinear p-y curves. The control differential equations for the excavation in the critical and embedded sections were derived. Also, the numerical solutions of excavation deformation and force under different boundary conditions were obtained by the finite difference method and Newton's iteration method. Further, the excavation calculation procedure considering the construction process and nonhomogeneity of soil was suggested. Through finite-element (FE) and engineering case analyses, the traditional calculation method overestimated the excavation deformation and internal force, while the proposed methods were consistent with the measured results. Finally, the effects of soil shear stiffness and initial foundation reaction modulus on the excavation were discussed, and we found that the two parameters had more significant impact on the wall bending moment than displacement. The results provide some reference for the design calculation of braced excavation.