## 3 Levels of Analysis
### Significance Analysis Considering Interaction  
In the real state, the influence of frozen soil strength was not the result of single factors that were independently affected and then simply superimposed. The interactive influence of various factors could not be ignored. For example, the water content was the factor determining the volumetric ice content of frozen soil. However, an increase in the salt content reduced the freezing temperature of the water in the soil, making it difficult to freeze, and the volumetric ice content naturally decreased, thereby reducing the strength. At the same time, the application of a confining pressure caused the compression-thaw effect in the frozen soil, and the ice crystal cementation and melting affected the intensity. There were complex interactions between the various factors affecting the intensity. The above analysis results that did not consider the interaction between the factors could only be qualitatively analyzed to a certain extent. Hence, it was necessary to make the following significance analysis considering these interactions.  
According to the basic idea of the orthogonal experiment design, the L\({}_{32}\)(4\({}^{9}\)) orthogonal experiment table was used to design the experiment. The orthogonal experiment table head design was implemented in strict accordance with the experimental procedures. Due to many factors, the table head was too large, and the table head design is not presented herein. This study only considered the interaction between factors A, B, and C. Some of the 32 groups of effective tests were consistent with the test conditions listed in Table 3, and the test results could be used. Most of the remaining test results were calculated from Equation (2). The data obtained were analyzed for significance using the method described in Section 4.1. Table 8 presents the results.  
The test results showed that for the significance levels listed in Table 6, the effects of the confining pressure, water content, and intermediate principal stress coefficient \(b\) on the peak stress were all significant; the interactions A \(\times\) B, A \(\times\) C, and B \(\times\) C had different degrees of influence on \(\sigma_{1}\), and the significance of the three interactions exceeded the degree of influence of the salt content. When \(\Omega>0.01\), the influence of A \(\times\) B on the equivalent  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Factor** & **Sum of Squares** & **Degrees of Freedom** & **F Ratio** & **Significance** \\ \hline A & 5.286 & 3 & 2.259 & V \\ B & 46.950 & 3 & 20.064 & II \\ A \(\times\) B & 8.259 & 9 & 3.529 & IV \\ C & 2.340 & 3 & 1.000 & VIII \\ A \(\times\) C & 4.606 & 9 & 1.968 & VI \\ B \(\times\) C & 2.547 & 9 & 1.088 & VII \\ D & 81.744 & 3 & 34.933 & I \\ E & 18.564 & 3 & 7.933 & III \\ Error & 2.34 & 19 & 0.01 & \(\backslash\) \\ Sum & 173.296 & 31 & \(\backslash\) & \(\backslash\) \\ \hline \hline \end{tabular}
\end{table}
Table 8: Significance test of factors affecting the peak intensity \(\sigma_{1}\) when the interaction was considered.  
stress was significant, and its influence even exceeded that of the temperature. From the results listed in Table 8, we concluded that the order of significance of the influence of various factors on the peak stress was as follows: confining pressure D, water content B, intermediate principal stress coefficient \(b\), interaction A \(\times\) B, temperature A, interaction A \(\times\) C, interaction B \(\times\) C, and salt content C. Hence, when studying the strength of frozen soil, it was necessary to comprehensively consider the various factors and their interactions to more accurately characterize the mechanical behavior of frozen soil.