# Shear Strength of Sand: Integrated Analysis of Initial Porosity and Stress Effects
## 4 Conclusions  
Soil shear strength, the most important soil property in geotechnical engineering calculations, was investigated by a direct shear testing of a cohesionless soil sample. The research presented in this paper did not investigate the influence of roughness, soil grain roundness, grain size distribution, and water content as these were constant values in each study.  
The main components analysed by the laboratory tests were the influence of initial porosity index and state of stress on the values of peak and critical internal friction of soil.  
The following major conclusions were drawn based on the investigated sample:  
* Considering the soil friction angle, it is important to specify whether it is the peak or critical soil friction angle because they apply to different deformation ranges and, in many cases, especially in dilative soils, they differ considerably.
* The peak soil friction angle increased with decreasing initial soil porosity index.
* The critical soil friction angle was independent of the initial porosity index.
* Both the peak and the critical soil friction angle depended on the stress state. The lower the stress, the larger the soil friction angle. This might have been due to the lower energy required to induce shear deformation of the specimen, which was also indicated by the decreasing critical porosity index with increasing stress. At high stresses, grain breakage became more important, which also resulted in a reduction in the strength described by the internal friction angle.  
Figure 11: Shear strength of soil and friction angle in relation to normal stress in soil sample \(e_{0}=0.54\). Critical shear strength and critical friction angle determined (**a**) under low normal stress conditions and (**b**) under high normal stress conditions.  
The analysis and conclusions were drawn based on a studied sample of cohesionless soil and could not be directly applied to describe the behaviour of all soils, including cohesive soils. Additional experiments should be carried out on sand with different grain size distribution, roughness, and roundness to draw more general conclusions.  
Conceptualization, K.Z. and R.B.; methodology, K.Z. and R.B.; validation, K.Z. and R.B.; formal analysis, K.Z. and R.B.; investigation, K.Z. and R.B.; resources, K.Z.; data curation, K.Z.; writing--original draft preparation, K.Z. and R.B.; writing--review and editing, K.Z. and R.B.; visualization, K.Z. and R.B.; project administration, R.B. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Data Availability Statement: Data are contained within the article. The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare no conflicts of interest.
Figure A5: Shear stress \(\tau\) and \(u_{y}\) vs. \(u_{x}\) for (**a**) zg-1-\(C\), \(\sigma=14.75\) kPa and (**b**) zg-2-A, \(\sigma=4.87\) kPa.  
Figure A6: Shear stress \(\tau\) and \(u_{y}\) vs. \(u_{x}\) for (a) szg-2-B, \(\sigma=9.81\) kPa and (b) szg-2-C, \(\sigma=14.75\) kPa.