# Modified Equation of Shear Strength with Respect to Saturation
## 4 Results and Discussion
### Comparison with Experimental Data
Then, a failure shear stress circle was plotted, with the shear stress as the vertical axis and normal stress as the horizontal axis, which can be obtained to calculate the shear strength parameters (Figure 10b). In the plot, the circles were around \((\sigma_{1}~{}+~{}\sigma_{3})/2\) with a radius of \((\sigma_{1}~{}-~{}\sigma_{3})/2\) at failure. For this experiment, a total of 84 tests carried out with four different confining pressures, three different dry densities, and seven different initial saturations (\(4\times 3\times 7\)). Hence, 84 circles were displayed in the final diagram. Then, the cohesion and angle of friction were obtained by measuring the intercept and slope of the failure envelope. The stress-strain curve of the soil with the dry density of 1.6 t/m\({}^{3}\) and the confining pressure of 150 kPa under the saturation of 30%, 40%, 50%, 60%, and 70% is shown in Figure 11. The curve with a saturation of 70% and confining pressure of 150 kPa under the dry density of 1.5 t/m\({}^{3}\), 1.6 t/m\({}^{3}\), and 1.7 t/m\({}^{3}\) is plotted in Figure 12. If the specimen is made up of saturated soil, the shear strength is constant under different cell pressures. Consequently, the failure envelope will be parallel to the horizontal axis because the angle of friction is zero. The other situation is that if the specimen is not saturated, the shear strength will increase as the confining pressure increases. When the result was plotted, it can be seen that the size of the circles increased and the failure envelope was an inclined line. Figure 11: Stress–strain curve under various saturations (\(\rho_{\rm d}=1.6\) t/m\({}^{3}\), \(\sigma-\mu_{\rm a}=150\) kPa). Figure 10: The schematic diagram of the soil shear strength parameter calculation. (**a**) Stress–strain curve. (**b**) Mohr’s circle. Figure 13 shows the relation between cohesion and saturation. There was a peak of cohesion at various dry densities when using the traditional test method of compaction. When the saturation was less than 40%, the cohesion showed an upward trend with an increasing degree of saturation, because a remolded soil sample made by dry soil and water was compacted in layers. The absorption between the soil layer and particles is weak and it is easy for a soil sample to be broken, especially in the link between two layers. When the saturation degree increases, the absorption between the soil layer and particles increases, so the cohesion increases. When the saturation is more than 40%, the thickness of the mucosa between the soil particles increases, the effective stress declines as a result, and the cohesion showed a downward trend. In addition, when the dry density increased, the distance between the soil particles became smaller, the absorption became stronger, and the cohesion became stronger. Figure 14 shows that the internal friction angle declined with climbing saturation. It is generally acknowledged that the total internal friction is made up of sliding friction, which is related to the mineral composition of the soil, the friction caused by dilatancy as well as friction caused by broken particles or the rearrangement of particles. When the water content increases gradually, the combined water film around the soil particles thickens; as a result, the amount of free water increases, then lubrication increases, and the friction between soil particles declines. This is why the internal friction angle showed a downward trend. In addition, when the dry density increased, the original structure became tighter. Then, the friction increased, which led to an increase in the internal friction angle. Figure 15 shows that shear strength dropped gradually with the degree of saturation. Measured values of the shear strength at higher dry density were greater than those measured in specimens with a lower dry density. The relationship between shear strength and degree of saturation at various net normal stresses is shown in Figure 16. As the net normal stress (\(\sigma-\mu_{a}\)) became higher, the shear strength became higher.