Granular soil is a porous medium composed of particles with different sizes and self-similar structures, exhibiting fractal characteristics. It is well established that variations in these fractal properties, such as particle size distribution (PSD), significantly influence the mechanical behavior of the soil. In this paper, a three-dimensional (3D) Discrete Element Method (DEM) is applied to study the mechanical and critical-state behavior of the idealized granular assemblages, in which various PSD shape parameters are considered, including the coefficient of uniformity (C_u), the coefficient of curvature (C_c), and the coefficient of size span (C_s). In addition, the same PSDs but with different mean particle sizes (D₅₀) are also employed in the numerical simulations to examine the particle size effect on the mechanical behavior of the granular media. Numerical triaxial tests are carried out by imposing axial compression under constant mean effective pressure conditions. A unique critical-state stress ratio in p′-q space is observed, indicating that the critical friction angle is independent of the shape of the PSD. However, in the e-p′ plane, the critical state line (CSL) shifts downward and rotates counterclockwise, as the grading becomes more widely distributed, i.e., the increasing coefficient of span (C_s). Additionally, a decrease in the coefficient of curvature (C_c) would also move the CSL downward but with negligible rotation. However, it is found that the variations in the mean particle size (D₅₀) and coefficient of uniformity (C_u) do not affect the position of the CSL in the e-p′ plane. The numerical findings may shed some light on the development of constitutive models of sand that undergo variations in the grading due to crushing and erosion, and address fractal problems related to micro-mechanics in soils.

Metro foundation pits are important components of urban infrastructure projects. Dewatering and excavation are essential stages in foundation pit construction; however, this process can significantly induce groundwater drawdown, as well as diaphragm wall deformation and surface settlement. Based on a subway station foundation pit project, in this study, we employ three-dimensional numerical software to simulate the process of dewatering and excavation. A refined model is used to investigate groundwater seepage, the deformation of the retaining structure, and surface settlement under spatial effects. The finite element model accounts for stratified excavation and applied prestress conditions for the support system within the foundation pit. Its accuracy is validated through a comparison and analysis with measured data from the actual foundation pit. The results indicate that foundation pit excavation leads to significant groundwater drawdown around the pit and the formation of a characteristic “funnel-shaped” drawdown curve. Moreover, extending the diaphragm wall length contributes to maintaining a higher external groundwater level surrounding the foundation pit. The horizontal displacement of the diaphragm wall increases progressively during dewatering and excavation, and the bending moment of the diaphragm wall exhibits a trend consistent with its horizontal displacement. Surface settlement decreases as the length of the diaphragm wall increases.