## 2 Materials and Methods
### Quantification of the Degree of Influence of Each Factor  
The research in this section focuses on the degree of influence of seven factors (CMT, CMC, VSs, CTs, ATs, CC, and pH) on rock water content and water absorption velocity. According to the principle of orthogonal test analysis and the design of orthogonal table, the range analysis method is selected to analyze the degree of influence of various factors on rock water absorption [49]. The range values for all responses during water absorption process are calculated according to Equation (6), and the results are shown in Table 3.  
\[R=K_{max}-K_{min}, \tag{6}\]  
where \(R\) is the range value. The greater the value, the greater the impact. \(K_{max}\) and \(K_{min}\) are the maximum and minimum values within each factor of the representative \(t_{1}\), \(t_{2}\), \(w_{0}\) and \(b\) in the equation parameters in Table 2.  
From Table 3, the rock porosity (VSs) and the type of anions (ATs) in the solution have the greatest influence on the water absorption time (\(t_{1}\) and \(t_{2}\)), and the solution concentration (CCs) has the least influence on the water absorption time. The concentration of the solution had the greatest influence on the saturated water content (\(w_{0}\)), and the clay mineral type (CMT) had the least influence on the saturated water content. The clay mineral type has the greatest influence on the change rate of water absorption velocity (\(b\)), and the rock porosity has the least influence on the change rate of water absorption velocity.  
In order to eliminate the order of magnitude difference between the four parameters and facilitate the analysis, the range values are normalized and the degree of influence of the seven factors is drawn, and the overall degree of influence of each factor on the water absorption process is calculated (Figure 9, \(R_{n}\) is the normalized degree of influence of each factor on each parameter, and \(R_{t}\) is the sum of the degree of influence of each factor on the four parameters). It is found that seven factors have different effects on each parameter of the water absorption process. The total influence (\(R_{t}\)) of the seven factors on the water absorption process of soft rock is ATs, CMT, CMC, CTs, VSs, pH and CCs from the largest to the smallest. That is, the types of anions and cations in water solutions and clay  
\begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline \multirow{2}{*}{**Factor**} & \(\mathbf{t_{1}}\) & \multicolumn{3}{c}{\(\mathbf{t_{2}}\)} & \multicolumn{3}{c}{\(\mathbf{w_{0}}\)} & \multicolumn{3}{c}{\(\mathbf{b}\)} \\ \cline{2-9}  & **R** & **PDI** & **R** & **PDI** & **R** & **PDI** & **R** & **PDI** \\ \hline CMT & 4 & 5 & 1186 & 3 & 0.5 & 7 & 0.60 & 1 \\ CMC & 5 & 2 & 985 & 5 & 1.5 & 5 & 0.34 & 2 \\ VSs & 5 & 2 & 1268 & 1 & 2.0 & 4 & 0.13 & 7 \\ CTs & 4 & 5 & 1001 & 4 & 2.1 & 3 & 0.27 & 5 \\ ATs & 11 & 1 & 1248 & 2 & 2.5 & 2 & 0.15 & 6 \\ CCs & 0 & 7 & 278 & 7 & 3.3 & 1 & 0.29 & 4 \\ pH & 5 & 2 & 545 & 6 & 1.4 & 6 & 0.31 & 3 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Range value of the seven factors and degree of influence on the water absorption process of rocks. The larger the range value of the factor, the higher the priority of a factor’s degree of influence. PDI refers to the priority of degree of influence.  
mineral compositions in rocks have the greatest influence on rock water absorption process. Predecessors also studied the influence of these seven factors on rock water absorption, but did not use the water content model and water absorption velocity model to quantify its influence [37].