the pronounced settlement issues in overlying structures. Therefore, a comprehensive understanding of the mechanical behavior of cohesionless soils is a critical prerequisite for ensuring the safety of underground engineering in such geotechnical environments. Significant progress has been made in the study of the strength behavior of cohesionless soil [1; 2; 3; 4; 5]. [PERSON] et al. [6] conducted an experimental investigation into the stability of tunnel excavation faces in sandy soil strata using a self-developed simulation test device. They obtained the specific failure modes of tunnel excavation faces in sandy soil strata. Based on the Kirsch indoor model test, [PERSON] et al. [7] elucidated the instability mechanism of shield tunnel excavation faces in sandy soil from a microscopic perspective and proposed an improved wedge analysis model for calculating the ultimate support force of the excavation face. Despite these advancements, the quantitative relationship between the variables influencing the strength factors of cohesionless soil and the strength behavior has not been fully established in these studies. Investigating the influence of each mesoscopic parameter (internal variable) on the mechanical properties of cohesionless soil is essential for developing a quantitative strength index that comprehensively reflects the contributions of these internal variables. [PERSON] et al. [8] demonstrated that the fine particle content of sand significantly affects the stability of the surrounding rock in sandy tunnel, and the internal friction coefficient does not increase with the increase of sand density. [PERSON] et al. [9] employed PFC software to conduct numerical experiments on triaxial specimens with different gradations, revealing significant differences in the internal friction angles among specimens with different particle gradations. [PERSON] [10] and [PERSON] [11] showed that particle shape has a substantial impact on both crushing strength and shear strength. Specifically, particles with greater irregularity are more prone to fracture. [PERSON] et al. [12; 13; 14; 15] further established that the gradation of granular materials affects their density, strength, and stability in various ways. Optimizing particle gradation can enhance the performance of engineering materials. Through investigation into the strength characteristics of materials under diverse arrangements, [PERSON] et al. [16; 17] concluded that exploring particle arrangement is instrumental in elucidating the interaction mechanisms among particles. This understanding can facilitate better control over material behavior and properties. Particle size is a critical internal variable that significantly influences the mechanical behavior of cohesionless soil. Recent research has extensively explored this relationship [18; 19; 20; 21], revealing both consistent and contrasting findings. For instance, [PERSON] [22], [PERSON] [23], and [PERSON] [24] demonstrated, through laboratory and simulation tests, that shear strength is positively correlated with average particle size in circular gravel fillers and sand. Similarly, studies by [PERSON] [25], [PERSON] [26], [PERSON] [27], and [PERSON] [28] showed that the internal friction angle increases with the maximum particle size. However, [PERSON] [29], [PERSON] [30], [PERSON] [31], and [PERSON] [32] reported contrasting results, finding that the internal friction angle decreased with increasing maximum particle size in large-scale triaxial tests of rockfill materials. These findings highlight the complexity of the relationship between particle size and the mechanical properties of cohesionless soil. The inherent coupling between granulometric characteristics and other particulate attributes, such as particle morphology and surface texture, poses challenges in isolating the independent influence of particle size on shear strength development.