## 4 Materials and Results  
### Data and Model Implementation  
To verify the reliability and rationality of the model proposed, in this paper, a series of sample data of untreated and lime-treated expansive clays was obtained from the foundation treatment area of Hefei Xinqiao International Airport [10]. The measured values of samples are listed in Table 2. Each parameter in Table 2 was obtained based on at least six sets of experiments. The data in Table 2 are taken from the measured data in the engineering implementation design stage; i.e., the significance level \(\alpha\) was assigned 0.05 based on the engineering practice experience, and \(t_{\alpha}\) was obtained at 1.645 according to the \(t\) distribution table. The corresponding reliability of the evaluation index of each case was obtained by Equation (8). However, it is difficult to calculate the coefficient of variation \(\delta\) and the reliability through Equation (8) when the mean value is 0; i.e., for the case discussed above, with the sampling numbers \(K\), the theory of hypothesis testing is used to calculate the reliability of the index, i.e.,  
\[p=\exp[\ln(1-C)/K]. \tag{18}\]  
Here, the confidence probability \(C=0.95\) and \(K=6\); thus, \(p=0.6070\). The obtained reliability of sample data is listed in Table 3. Then, according to the above discussion step 3, a membership limitation interval with the limitations of reliability was built to generate the corresponding matrix as follows:  
\[\mathbf{M}= \begin{bmatrix}[0.9976,1]&[0.8410,1]&[0.9832,1]&[0.9346,1]&[0.9089, 1]\\ [0.9933,1]&[0.7849,1]&[0.9849,1]&[0.9078,1]&[0.9372,1]\\ [0.9988,1]&[0.7937,1]&[0.9876,1]&[0.9271,1]&[0.8413,1]\\ [0.9563,1]&[0.9181,1]&[0.8455,1]&[0.9000,1]&[0.5214,1]\\ [0.9975,1]&[0.8322,1]&[0.9437,1]&[0.9275,1]&[0.8266,1]\\ [0.9968,1]&[0.8361,1]&[0.9875,1]&[0.9057,1]&[0.6070,1]\\ \end{bmatrix} _{. }\]  
Based on the classification standard interval in Table 1, the grades for measured index values were identified. According to the discussed step 2, the index weight vector was assigned as \(\mathbf{w}=[0.1912,\,0.2132,\,0.1912,\,0.2132,\,0.1912]\). Subsequently, the integrated membership interval was obtained as shown in Table 4. From Equations (12)-(15), the numerical characteristic values of the connection cloud for the \(j\)-th indicator at grade \(i\) can be determined. For instance, the obtained numerical characteristics of the connection cloud for grade I are listed in Table 5. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Case** & **Soil Type** & **Liquid** & **Total Shrinkage-** & **Plasticity** & **Natural Water** & **Free Expansion** \\  & & **Limit C1/\%** & **Swelling Rate C2/\%** & **Index C3** & **Content C4/\%** & **Rate C5/\%** \\ \hline A & Untreated expansive clay & [44.7,48.2] & [0.26,0.44] & [23.6,24.8] & [20.4,26.5] & [44.3,62.3] \\ B & 4\% lime-treated & [45.6,46.7] & [\(-0.76,-0.33]\) & [20.3,21.5] & [16.3,22.7] & [14.0,18.0] \\ C & 6\% lime-treated & expansive clay & [43.2,43.4] & [\(-0.73,-0.27]\) & [15.3,16.0] & [16.5,22.5] & [6.0,11.0] \\ D & 7\% lime-treated & expansive clay & [43.4,50.0] & [\(-0.15,-0.20]\) & [15.0,23.0] & [14.0,23.0] & [0.8,9.3] \\ E & 8\% lime-treated & expansive clay & [43.3,43.7] & [\(-0.763,-0.33]\) & [13.5,16.0] & [16.0,22.5] & [2.5,4.5] \\ F & 10\% lime-treated & expansive clay & [44.3,44.8] & [\(-1.08,-0.61]\) & [12.3,16.0] & [16.2,22.8] & [0.0,0.0] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Measured data of samples.