# Experimental Study of the Dynamic Characteristics of PVA-Amended Expansive Soils
## 3 Analysis of Test Results
### Analysis of the Static Triaxial Test Results
#### 3.1.2 Shear Strength Index  
The shear strength of soil indicates the ultimate ability of soil to resist shear damage, and the shear strength index is an important calculation parameter for analyzing the stability of soil. Specimens with the same dosage of PVA were analyzed by plotting molar-stress circles for bias stress (\(\sigma_{1}\)-\(\sigma_{3}\)) and circumferential pressure (\(\sigma_{3}\)) under different circumferential pressures. The cohesion \(c\) for shear strength and the angle of internal friction \(\varphi\) of the soil were calculated based on the common tangent of [PERSON]'s circle (shown in Figure 3) and [PERSON]'s formula (1):  
Figure 2: Partial stress–strain relationship curves for amended soil with varying PVA dosage. (a) \(\sigma_{3}=100\) kPa. (b) \(\sigma_{3}=200\) kPa. (c) \(\sigma_{3}=300\) kPa.  
\[\tau=\sigma\tan\varphi+c \tag{1}\]  
where \(\sigma\) is the normal stress and \(\tau\) is the shear stress.  
According to the shear strength envelope diagram of PVA-amended expansive soil shown in Figure 3, the cohesion \(c\) and internal friction angle \(\varphi\) of the amended soil under different PVA dosages can be obtained, and the specific results are shown in Table 5. The relationship curve for the change in the shear strength index with respect to the PVA dosage is obtained, as shown in Figure 4.  
As shown in Figure 4, the angle of internal friction increases and then decreases with increasing PVA dosage, the angle of internal friction is greatest when the PVA dosage is 3%, and the cohesion c is not much different from that obtained for soil samples with a 4% PVA content at this time. Compared with those of the plain soil samples, the cohesion and angle of internal friction of the improved soil after mixing PVA were greater, indicating that PVA has a certain effect on the mechanical properties of the expansive soil and that the effect of improvement is greatest at a PVA mixing rate of 3%.  
Figure 3: Shear strength envelope for different PVA dosages. (**a**) PVA content 0% shear strength. (**b**) PVA content 1% shear strength. (**c**) PVA content 2% shear strength. (**d**) PVA content 3% shear strength. (**e**) PVA content 4% shear strength.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**PVA Dopant (\%)** & **0** & **1** & **2** & **3** & **4** \\ \hline \(c\) (kPa) & 50.8 & 55.6 & 60.5 & 66.5 & 65.8 \\ \(\varphi\) (\({}^{\circ}\)) & 16.42 & 16.59 & 16.86 & 17.45 & 17.29 \\ \hline \end{tabular}
\end{table}
Table 5: Adhesion cohesion \(c\) and angle of internal friction \(\varphi\) at different PVA dosages.  
This is because the internal cohesion of the specimen includes the original cohesion between the soil particles in the specimen, as well as the cohesion between the soil particles and PVA. The white colloid formed by PVA after dissolving in water increases the friction between soil particles, coagulating with water molecules in the specimen to form water-stable agglomerates [26]. This results in an increase in cohesion between PVA and soil particles, which is characterized by an increase in the cohesion \(c\) and the angle of internal friction \(\varphi\) of the improved soil with increasing PVA dosages. At a PVA content of 4%, the high concentration of PVA formed an overbonded clay film, which tightly bound the soil particles. This overbonding affects soil permeability, making it difficult for water to penetrate into the deeper layers of the soil, thus affecting the formation of aggregates. Furthermore, the bonding strength between the soils is reduced, and the occlusion between the soil particles is weakened, so the structural integrity of the improved soil with 4% PVA content is reduced, leading to a slight decrease in the improvement effect.