## 3 Indoor Vibration Reconsolidation Experimental Study
### Analysis Method for Vibration Reconsolidation Test Results  
Consider a test scenario where a soil specimen undergoes initial consolidation under a static load \(P\) and then is subjected to a sinusoidal vibration load with a frequency \(f\) and \begin{table}
\begin{tabular}{c c c c c c c c c} \hline Consolidation pressure, \(p\) (kPa) & 12.5 & 25 & 50 & 100 & 200 & 400 & 800 & 1600 \\ \hline Void ratio of undisturbed soil, \(e\) & 1.419 & 1.389 & 1.344 & 1.258 & 1.121 & 0.985 & 0.849 & 0.722 \\ \hline Void ratio of remolded soil, \(e\) & & 1.132 & 1.059 & 0.968 & 0.867 & 0.778 & 0.678 & \\ \hline \end{tabular}
\end{table} 
Table 4: Relationship between void ratio and consolidation pressure of undisturbed and remolded soil. Figure 14: \(e\)-lg\(p\) relationship curve of undisturbed and remolded soil. Figure 13: Schematic diagram of static-dynamic consolidation apparatus. amplitude \(P_{1}\), resulting in a reconsolidation settlement \(s\). If, after the initial consolidation under the static load \(P\), the soil specimen is subjected to a static load increment \(\Delta P\) instead and the reconsolidation settlement is also equal to \(s\), then \(\Delta P\) is called the equivalent static load increment of the vibration load with frequency \(f\) and amplitude \(P_{1}\) for the soil consolidated under static load \(P\). In general, the larger the equivalent static load increment \(\Delta P\) corresponding to the vibration load for a soil specimen consolidated under a certain static load, the more significant the vibration reconsolidation phenomenon. By analyzing the relationship between the equivalent static load increment \(\Delta P\), the static load \(P\), the vibration load frequency \(f\), and the vibration load amplitude \(P_{1}\), some regularities of the vibration reconsolidation phenomenon of soft clays can be obtained. The calculation method for the equivalent static load increment \(\Delta P\) is as follows: The initial water content \(\omega_{0}\) and specific gravity \(G_{\text{s}}\) of the remolded soil are known. The initial void ratio \(e_{0}\) is calculated as follows:  
\[e_{0}=\omega_{0}G_{\text{s}} \tag{6}\]  
Assume the initial height of the soil specimen in the test is \(H\) and the applied static load is \(P\). Let the void ratio of the soil specimen after consolidation under the static load \(P\) be \(e_{P}\) (obtained from the \(e\)-l\(\text{g}p\) relationship curve of the remolded soil in Figure 14), and the height after consolidation is \(H_{P}\). Then, we have  
\[H_{P}=\frac{e_{P}+1}{e_{0}+1}H \tag{7}\]  
Let the reconsolidation settlement under the vibration load with amplitude \(P_{1}\) and frequency \(f\) be \(s\). Then, the void ratio of the soil after reconsolidation under this vibration load is  
\[e_{1}=e_{P}-\frac{s}{H_{P}}(e_{P}+1) \tag{8}\]  
Let the consolidation pressure corresponding to the void ratio \(e_{1}\) in the \(e\)-l\(\text{g}p\) relationship curve of the remolded soil be \(\hat{P}\). If the static load is increased to \(\hat{P}\) after the soil specimen in this test group is consolidated under the static load \(P\), the soil specimen will undergo an additional consolidation settlement of \(s\). According to the definition of the equivalent static load increment, the equivalent static load increment for the vibration load with frequency \(f\) and amplitude \(P_{1}\) in this test group is  
\[\Delta P=\hat{P}-P \tag{9}\]  
The vibration reconsolidation effect can also be illustrated as follows: Consider a soil specimen that has completed consolidation under a static load \(P\). The soil is in state A in Figure 15, with a void ratio of \(e_{P}\). Apply a vibration load with frequency \(f\) and amplitude \(P_{1}\). After vibration reconsolidation, the soil's void ratio changes to \(e_{1}\). Since the vibration load has no compressive or tensile tendency, the soil is now in state B. From a void ratio perspective, this corresponds to state C on the \(e\)-l\(\text{g}p\) curve of the remolded soil, with a corresponding static load of \(\hat{P}=P+\Delta P\).