# Experimental Studies of Scale Effect on the Shear Strength of Coarse-Grained Soil
###### Abstract
[12] support that the internal friction angle \(\varphi\) increases with the improvement of \(d_{\text{max}}\). On the contrary, [PERSON] [13] and [PERSON] et al. [14] believe that the maximum particle size \(d_{\text{max}}\) has little effect on the peak internal friction angle \(\varphi\). [PERSON] et al. [15], [PERSON] et al. [16], and [PERSON] et al. [17] found that the internal friction angle increases with the reduction of content of fine particles, and [PERSON] et al. [18] observed that when the fine particle content is relatively low, the internal friction angle is stable at a certain level; however, after that, it decreases rapidly with increasing fine-particle content. Besides physical experiments, the discrete element method (DEM) was also a significant approach used to investigate the scale effect on the mechanical properties of CGS [19; 20]. Since [PERSON] et al. [21] first applied the DEM in geotechnical engineering, many scholars use DEM software to explore the scale-induced effect in the shear strength of coarse-grained soil. For example, [PERSON] et al. [22] analyzed and summarized numerous test data according to the similarity theory of particle crushing strength, and deduced the strength envelope under various maximum particle sizes. Hence, they verified the existence of the influence of the scale effect on the mechanical properties of CGS from a theoretical point of view. [PERSON] et al. [23] investigated the impacts of particle shape on the mechanical properties of rockfill based on the discrete element method and observed that the shear strength increases with the improvement of the particle aspect ratio. [PERSON] [24] studied the influences of maximum particle size, particle gradation, and structure on the mechanical behaviors of granular materials through a discrete numerical method. Although the DEM method has advantages in exploring the meso mechanism of the scale-induced effect on mechanical characteristics and tracking the evolution law of meso fabric of CGS, numerical simulation results still need to be verified by laboratory tests. Scaling methods for the gradation structure of CGS include similar grading methods, equivalent substitution methods, elimination methods, and mixing methods [2]. However, [PERSON] et al. [25] found that no matter which scaling method is adopted, the gradation structure of CGS after scaling significantly varies from in situ CGS. In particular, the elimination method removes some ultra-fine particles of CGS, which may increase the content of fine particles. In contrast, the equivalent substitution method (ESM) maintains the coarse particle content of the original gradation structure, but the particle size range of the gradation structure becomes smaller and the uniformity increases after scaling. The similar grading method (SGM) maintains the relative size between particles and the curvature coefficient of the non-uniformity coefficient. By analyzing the scaling methods, [PERSON] et al. [26] found that SGM is used to reduce the graded particle size according to a certain proportion in the mixing method, and then ESM is used to scale samples. However, it is necessary to use the empirical index \(P_{5}\) content to control the gradation structure of CGS (\(P_{5}\) is the relativeness with the scale ratio or the maximum particle size of the scaled material). The mixing method is essentially an empirical method, and the accuracy of the test results is insufficient and unconvincing. In conclusion, owing to the influence of scaling methods, gradation structure, sample preparation densities, and other factors, the relationship between the mechanical properties of scaled and in situ CGS is still difficult to describe quantitatively [4]. Most of the studies of scale effect on the shear strength consider the effect of maximum particle size and coarse-grain contents, which obviously cannot accurately represent the effect of scaled gradation on shear strength.