A large number of non-circular tunnels are widely used in engineering practice. The application of these geometric structures not only makes the boundary conditions of mechanical problems more complex, but also makes the theoretical solution more difficult. The introduction of curvilinear coordinate system can easily transform the elliptical region into a circular region, and the physical relationship can also be adjusted accordingly. In the state space, the transformed problem can be solved by using the dual variables of Hamiltonian mechanics, and the special solution equation can be obtained. With regard to the non-homogeneous boundary conditions of general engineering problems, Fourier expansion is used to transform them into algebraic sums. According to the special solution equation, the relationship between the direction eigenvalues and the angle coefficients of each order of the expansion term is found. Then the analytical solution of the non-homogeneous problem is obtained by superposing the special solutions of the expansion terms of each order. By comparing the calculation results of the boundary stress around the elliptical tunnel, it can be seen that the results are completely consistent with the finite element calculation results, which verifies the correctness and reliability of the method in this paper. This paper analyzes the influence of internal pressure, lateral pressure coefficient and elliptical shape coefficient on the circumferential stress around the elliptical hole, and obtains the following conclusions: increasing the internal pressure of the elliptical hole can effectively reduce the circumferential compressive stress at the hole edge; when the lateral pressure coefficient approaches 1, the circumferential stress distribution around the elliptical hole tends to be uniform; the minimum value of the circumferential stress around the elliptical hole is independent of the shape coefficient, while the maximum value is closely related to the shape coefficient. The research results can not only provide specific theoretical guidance for the construction and construction of elliptical tunnel, but also expand the application scope of the symplectic elasticity method.

The double singularities including singular stress field and singular electric displacement field, in the tips of piezoelectric composite junctions, are analyzed by the interpolation matrix method (IMM). The double singularity analysis problem of piezoelectric composite junctions is converted into eigenvalue solution problem of ordinary differential equations with variable coefficients under corresponding boundary conditions. In numerical examples, the first couple of singularity orders and the corresponding characteristic angular functions of displacement and electric potential for the electromechanical coupling field are obtained and comparisons are presented to validate the accuracy of the proposed method. The singularity of the electromechanical coupling field at the tip of piezoelectric composite material junctions is closely related to the bonding angle and fiber direction. According to the numerical results, the best scheme can be configured for the combination of dissimilar materials.

This study experimentally investigated the stabilization mechanisms and structure formation models of high-water-content soft soils (>70%) treated with ordinary Portland cement, sulfur aluminate cement, gypsum, and lime. Fifteen single- and composite-stabilizer systems were evaluated using unconfined compressive strength (UCS) tests and microstructural analyses, including SEM, XRD, TG–DTG, and FTIR analyses. The results show that stabilized soils containing cementitious components exhibit significantly higher strength due to the formation of calcium silicate hydrate (C–S–H) gel, which effectively binds soil particles. The addition of sulfur aluminate cement, gypsum, and lime promotes rapid hydration and generates abundant ettringite (AFt) crystals with strong water absorption capacity, contributing to early strength development. Based on these findings, a composite stabilizer (ECS) combining cement with appropriate proportions of sulfur aluminate cement, gypsum, and lime is proposed, achieving substantial improvements in both early and long-term strength. The stabilization process proceeds in two stages: rapid AFt formation absorbs free water and fills large pores to form a three-dimensional network, and then C–S–H gel cementation integrates the soil–AFt framework into a dense and coherent structure. The study provides mechanistic insight and a theoretical basis for stabilizing high-water-content soft soils in coastal and riparian engineering applications.