# The Size Effect of Shear Bands in Dense Sands--A Discrete Element Analysis
## 5 Conclusions and Prospects  
In the context of soil mechanics, the shear band is an important concept, as it helps explain the behavior of granular materials under various loading conditions and the failure of slopes, dams, etc. Although the shear band is a narrow region, it is responsible for the overall macroscopic behavior at the failure. In this study, the shear band characteristics and in particular the size effect are mainly focused on. The major conclusions are as follows.  
1. As specimen size increases, the residual strength of the specimen decreases. A clear size effect was observed in the stress-strain relationship after the peak strength point. Such a size effect decreased as isotropic confining stress increased, and it was observed for both biaxial compressive and biaxial tensile tests.  
Figure 12: The development of porosity during compression.  
Figure 13: The porosity at an axial strain of 10%: (**a**) the porosity outside the shear band; (**b**) the porosity inside the shear band.  
2. The increase in the specimen size has less impact on the angle of the shear band. Compared with [PERSON]'s theory and [PERSON]'s theory, [PERSON]'s theory gave the best estimation of the angle of the shear band for the dense sand.
3. A possible explanation of the size effect was found by instigating the development of displacement and porosity within the shear band. Although the width of the shear band increased to some extent with the size of the specimen, the ratio of the shear band in the whole specimen decreased. Accordingly, the concentration of strain became more obvious for a large specimen.
4. The size effect reduces as the isotropic confining stress increases. Meanwhile, the specimen tends to give a cross-type shear band at a low isotropic confining stress level. The latter could be a possible reason that the size effect is influenced by the magnitude of isotropic confining stress.  
Currently, only one particle distribution was considered throughout this paper. Further study should consider more soils for general conclusions.  
Conceptualization, Z.M. and L.Z.; Formal analysis, Z.M.; Funding acquisition, N.Z.; Methodology, L.Z. and N.Z.; Validation, L.Z. and L.C.; Writing--original draft, Z.M. and N.Z. All authors have read and agreed to the published version of the manuscript.  
This study is supported by the National Natural Science Foundation of China, grant number 42302331, and the Qinghai Province Science and Technology Department Project, grant number 2024-ZJ-973.  
Not applicable.  
The datasets generated during the current study are available in the following repository. [[https://github.com/NingZhangQh/rawDataPublic_zn](https://github.com/NingZhangQh/rawDataPublic_zn)]([https://github.com/NingZhangQh/rawDataPublic_zn](https://github.com/NingZhangQh/rawDataPublic_zn)) (accessed on 13 March 2024). In addition, the data are available from the first author and the corresponding author on request.  
Author [PERSON] was employed by the company China Building Technique Group Co., Ltd. and author [PERSON] was employed by the company China Railway Design Corporation. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.