## 4 Discussion
### Evaluation of Disintegration Rate  
To further elucidate the disintegration evolution of the stabilized soil, the average disintegration rate can be calculated by using the disintegration ratio. This rate does not directly represent the actual disintegration rate but serves as a measure of the speed at which the soil disintegrates within a defined time period, as expressed by the following equation [33]:  
\[\overline{v_{t}}=\frac{A_{t}^{i+1}-A_{t}^{i}}{t_{i+1}-t_{i}} \tag{12}\]  
where \(A^{i+1}\)\({}_{t}\) and \(A^{i}\)\({}_{t}\) are the disintegration rate of the specimen at \(t_{i+1}\) and \(t\), respectively. The average disintegration rate reflects the speed of the disintegration ratio from the initiation to the completion of the disintegration process. By substituting the maximum disintegration time \(t_{\text{max}}\) of the disintegrated specimen into Equation (12), the variation in average disintegration rate with the total amount of stabilizer added during the disintegration process could be obtained for the stabilized soil. The increase in lime content significantly reduced the average disintegration rate of the stabilized soil (Figure 18a). The average disintegration rate of untreated soil was \(6.6\times 10^{-3}\%/\text{s}\) under 90% compactness, while the average disintegration rate of lime-stabilized soil at the lime additions of 8% decreased to \(3.9\times 10^{-3}\%/\text{s}\). This reduction exhibited a basic linear trend for soil under both 90% and 100 compactnesses, with an increase in 1% lime content leading to a decrease in the disintegration rate by about \(3\times 10^{-4}\%/\text{s}\). This suggested that the lime stabilizer is effective in improving the disintegration performance of silty clay. Compared with lime-stabilizer soil, the lower average disintegration rate of lime- + cement-stabilized soil implies better disintegration resistance under the same compactness and stabilizer content, as shown in Figure 18b. However, the soil sample using the larger combined additions presents a higher marginal effect, such that the effect of reducing the average disintegration rate is weakened. This once again demonstrated that the appropriate content of stabilizer needs to be investigated for application in engineering, and the addition of 6% may be a better scheme for soils stabilized by lime and cement. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline \multirow{2}{*}{**Stabilizer Content**} & \multicolumn{2}{c}{**90\% Compactness**} & \multicolumn{5}{c}{**100\% Compactness**} \\  & \(d\) & \(k\) & \(R^{2}\) & \(d\) & \(k\) & \(R^{2}\) \\ \hline
4\% lime & 0.5752 & 2.4582 & 0.9989 & 0.6726 & 3.2293 & 0.9975 \\
6\% lime & 0.6086 & 2.6464 & 0.9978 & 0.6902 & 3.2729 & 0.9959 \\
8\% lime & 0.6575 & 2.9838  
The average disintegration rate fails to capture the variation in the instantaneous disintegration rate in the disintegration process. Given that the disintegration evolution of the stabilized silty clay could be characterized by the Weibull distribution model, the instantaneous disintegration rate was calculated using the first derivatives of Equation (8) in combination with Equation (9):  
\[v_{i}=\frac{dP_{i}}{dt}=ke^{-(\frac{t}{t_{\max}\cdot d})^{k}}t^{k-1}(t_{\max} \cdot d)^{-k} \tag{13}\]  
With the corresponding Weibull parameters substituted into Equation (13), the instantaneous disintegration rate of the stabilized silty clay was obtained, as shown in Figures 19 and 20. Compared with the average disintegration rate, the instantaneous disintegration clearly describes the evolution process of the disintegration rate of the stabilized silty clay. Specifically, the disintegration rate demonstrates a parabolic growth with the disintegration time, reaching a peak at about half of the disintegration process and then decreasing continuously. In addition, the peak disintegration rate is basically twice the average disintegration rate. Figure 19: Instantaneous disintegration rate of silty clay stabilized by lime: (**a**) 90% compactness; (**b**) 100% compactness.