# Experimental Study of the Dynamic Characteristics of PVA-Amended Expansive Soils
## 3 Analysis of Test Results
### Analysis of the Dynamic Triaxial Test Results
#### 3.2.3 Change Rule for the Damping Ratio  
Figure 11 shows the curves for the damping ratio \(\lambda\) versus the dynamic strain \(\varepsilon_{d}\) calculated by elliptic hysteresis curve fitting for different enclosing pressures. Figure 10: Curve for the initial dynamic modulus of elasticity \(E_{0}\) versus peripheral pressure \(\sigma_{3}\) and frequency \(f\). (**a**) \(E_{0}\) and \(f\) relation curve. (**b**) \(E_{0}\) and \(\sigma_{3}\) relation curve. The damping ratio \(\lambda\) of the soil reflects the proportion of energy dissipated due to the internal damping effect of the soil under dynamic loading and characterizes the ability of the soil to absorb energy and resist vibration. It can be observed from Figure 11 that the damping ratio \(\lambda\) of the soil increases with the development of the dynamic strain, and the growth rate is low at the beginning of the development of the dynamic strain (\(\varepsilon_{\rm d}\leq 0.4\%\)). When the dynamic strain continues to increase (\(\varepsilon_{\rm d}>0.4\%\)), the growth rate of the damping ratio \(\lambda\) first increases and then decreases and tends to stabilize with increasing dynamic strain. Under the same frequency conditions, the damping ratio gradually decreases with increasing confining pressure, and the development trend of the damping ratio \(\lambda\) under different confining pressures is more or less the same. In the early stage of dynamic strain development (\(\varepsilon_{\rm d}\leq 0.4\%\)), the proportion of elastic deformation in the deformation of the soil is greater, and the energy consumption for stress transfer is less. With the development of dynamic strain (\(\varepsilon_{\rm d}>0.4\%\)), relative sliding of the soil particles occurs, the proportion of plastic deformation gradually increases, the number of pores inside the specimen increases, and the work performed by the internal friction resistance increases, resulting in a drastic increase in the damping ratio. When the dynamic strain continues to increase, the internal structure of the specimen changes. Under the applied force, the pore space produced before is partially compacted, and the soil particles are rearranged to form a temporary stable state when the growth rate of the damping ratio begins to decrease. The damping ratio thus stabilizes with the development of dynamic strain. At a certain frequency, an increase in the circumferential pressure leads to a denser arrangement of internal particles in the specimen, and PVA can be better dissolved into the internal pores of the soil specimen. At this time, the pore space in the sample is reduced, and the contact area of the soil particles inside the sample is increased, which improves the efficiency of dynamic load transfer. The relative motion of soil particles inside the specimen under high-confining pressure is reduced, so the percentage of plastic strain is not as good as that for the specimen under lower confining pressure, so the damping ratio decreases with increasing confining pressure. The \(f\)-\(\varepsilon_{\rm d}\) curves for different frequencies are plotted in Figure 12. From Figure 12, it can be observed that the development trends for the \(\lambda\)-\(\varepsilon_{\rm d}\) relationship curves between the damping ratio and dynamic strain at different frequencies and confining pressures are basically the same, and the damping ratio grows less in the early stage of the development of the dynamic strain (\(\varepsilon_{\rm d}\leq 0.4\%\)); when the dynamic strain continues to develop (\(\varepsilon_{\rm d}>0.4\%\)), the rate of increase in the damping ratio first increases and then decreases. In addition, compared with Figure 12, when the frequency is the only variable, the damping ratio of the soil decreases with increasing frequency, and the difference in the damping ratio between neighboring circumferential pressures is greater than that between neighboring frequencies, which indicates that the frequency has a small effect on the damping ratio.