# Shear Strength of Sand: Integrated Analysis of Initial Porosity and Stress Effects
## 1 Introduction
This means that the higher the initial compaction of the soil sample, the greater the increase in soil volume during shearing and the greater the peak angle in relation to the critical soil friction angle. Conversely, for initially loose soil samples, a progressive decrease in sample volume was observed during shearing, and the peak soil friction angle was equal to or slightly (up to 4 degrees) greater than the critical friction angle value. The slope of the relationship between soil sample height during shearing and horizontal displacement determined the dilation angle defined by [PERSON] [13]. In this approach, the peak internal friction angle was the sum of the critical internal friction angle and 80% of the dilation angle value. This relationship was verified and used in [3; 4; 8], obtaining similar dependencies. There are many studies aimed at explaining what affects the value of the internal friction angle. Factors such as initial compaction, water content, roughness, grain size, grain uniformity, fine fraction admixtures, and grain crushing were studied. The peak internal friction angle increases with initial soil compaction [14]. Ref. [15] shows that both increased water content and fine particle content reduce soil strength. In studies of the relationship between the measured internal friction angle and the sand grain uniformity index, it is indicated that soil strength defined by the internal friction angle increases with the uniformity coefficient [16]. Further studies provided solid evidence that the critical internal friction angle does not depend on grain size but on grain shape [17], and the commonly accepted practical relationship between the internal friction angle and soil uniformity index is more an attribute of variable grain shape than variable grain size. Direct shear tests of coarse-grained materials showed that the ratio of peak strength to strength determined at a given deformation increased exponentially with the increase in the equivalent grain diameter \(d_{50}\)[18]. This meant that grain size affected the rate of increase in shear stresses during shearing. During soil shearing, despite low stresses ranging from 0 to 400 kPa, grain crushing occurred due to significant contact stresses reaching up to 15 MPa [19]. The greatest impact of grain crushing on shear strength was observed at high effective stresses in the soil. As studies [20] showed, it is grain destruction that causes a significant reduction in strength after reaching peak strength. Grain destruction also caused less change in volumetric deformations of the sample during shearing. The roundness of soil grains was also an important factor, primarily affecting the critical internal friction angle, as demonstrated in [21]. The linear Coulomb-Mohr criterion, which involves two geotechnical parameters--the internal friction angle and cohesion--is widely used in geotechnics. However, experimental studies indicated that the development of soil strength had a nonlinear relationship with respect to normal stresses. This nonlinearity was particularly evident at low normal stresses to the shear plane [22; 23]. In studies conducted on sands over a wide range of stresses, including low stresses below 50 kPa, it was observed that both the peak and critical internal friction angles increased with decreasing normal stress [24] and could reach up to 50 degrees. Similar studies confirmed these relationships and additionally noted that soil dilation was more pronounced with larger grain sizes. It was also observed that the peak strength value of soils with larger grain sizes was achieved at greater deformations, which could be explained by the greater distance needed to be overcome in relation to grain diameter [25]. In further studies on direct shear testing at low normal stresses, it was found that the more rounded the sand particles, the smaller the decrease in strength after reaching the peak value for low stresses ranging from 4 kPa to 50 kPa [26].