To clarify the regulatory laws of the fines content (FC) and particle size ratio (SR) on the mechanical properties of sand–fines mixtures and reveal the underlying microscopic mechanical mechanisms, this study takes sand–fines mixtures composed of natural river sand and silt as the research object. It systematically investigates the macro-mechanical behaviors and micro-interaction mechanisms of the mixtures by combining laboratory triaxial tests and discrete element method (DEM) simulations. First, through conducting triaxial drained shear tests on mixtures with three particle size ratios (SR = 9.1, 18.7, and 39.7) under seven fines contents (FC = 0%, 10%, 20%, 30%, 50%, 70%, and 100%), it is found that both the peak friction angle (φ_ps) and critical-state friction angle (φ_cs) of sand–fines mixtures show a “first increase, then decrease” trend with the increase in FC. The peak inflection points of their variation curves are the threshold fines content related to SR; meanwhile, a fines content below this threshold has an inhibitory effect on dilatancy, while that above this threshold exerts a promotive effect on dilatancy. Subsequently, by exploring the microscopic contact behaviors of sand–fines mixtures, it is observed that, under the fines content corresponding to the highest peak strength, the strong contact network and weak contact network inside the material form an optimal coordination between efficient load-bearing and stable support. This coordination enables the macro-strength of the mixture to reach the peak at this fines content. In addition, by modifying the weight coefficient of fabric anisotropy, a unique linear relationship between the fabric anisotropy of strong contacts and the stress ratio can be established, confirming that the strong contact network plays a core mechanical role in mixtures with different FC values.

This paper introduces an analytical method for passive earth pressure calculation based on a rigorous stress field analysis within the sliding wedge. Unlike traditional horizontal layer methods, this approach directly solves for the stress state at any point within the wedge by analyzing the equilibrium of 2D differential soil elements under appropriate boundary conditions, eliminating the need for a priori assumptions about the soil arch shape. The method yields the passive earth pressure distribution on the retaining structure and derives the soil arch shape analytically from major principal stress trajectories. This derived arch shape differs notably from conventional circular or parabolic assumptions, especially at higher soil–wall friction angles. Parametric studies show that the passive earth pressure coefficient increases with internal friction angle and surcharge. However, a key finding is the non-monotonic dependence of the passive earth pressure coefficient on the soil–wall friction angle, contrasting with many existing theories. Comparisons show predictions by the proposed method align well with experimental data, particularly offering a better representation of pressure distributions in the lower regions of retaining walls compared to Coulomb theory and other existing methods.

To accurately investigate the stress and deformation behavior of support structures during mechanical shaft construction, this study proposes an analytical method for active earth pressure calculation based on limit equilibrium theory, incorporating both the radial variation of the circumferential stress coefficient and the spatial arching effect. Considering the entire sliding soil mass behind the shaft wall as the analytical object, the inclination angle of the sliding surface under active limit conditions is derived. Subsequently, by incorporating interlayer shear forces, a horizontal layer analysis is employed to establish the vertical and radial force equilibrium equations, leading to the formulation of an active earth pressure model for circular shafts. Furthermore, based on elastic mechanics theory, a corresponding method is developed to calculate the internal forces of the shaft structure. The theoretical predictions show good agreement with existing model test results and field monitoring data, demonstrating the accuracy and reliability of the proposed approach. The findings provide a theoretical basis for optimizing the design of circular shafts and assessing the structural stability of shaft walls.