## 5 Discussion
### Geoelectric Field Response Mechanism of Disaster Source Development
When the rock and soil are unsaturated, the resistivity \(\rho_{t}\) can be expressed as:  
\[\rho_{t}=\frac{{{a_{f}}\rho_{wf}}}{{\varphi_{f}^{{m_{f}}}}{S_{wf}^{{n_{f}}}}}+ \frac{{{a_{i}}\rho_{wi}}}{{\varphi_{i}^{{m_{i}}}}}+\frac{{{a_{c}}\rho_{wc}}}{{ \varphi_{c}^{{m_{c}}}}} \tag{15}\]  
\[S_{w}=\frac{{{\varphi_{f}}S_{wf}^{{n_{f}}}}+{{\varphi_{i}}}+{{\varphi_{c}}}}{{{ \varphi}}} \tag{16}\]  
where \(\rho_{wf}\), \(\rho_{wi}\) and \(\rho_{wc}\) are the resistivities of free water, microcapillary water and clay water, respectively (\(\rho_{wf}=\rho_{wi}\)), \(\rho_{t}\) is the resistivity of the unsaturated rock and soil mass, \(a_{f}\), \(a_{l}\) and \(a_{c}\) are the lithology coefficients corresponding to the conductive network, \(\varphi_{f}\), \(\varphi_{i}\) and \(\varphi_{c}\) denote the pore ratios of the three types of water and the total porosity of rock and soil, m\({}_{t}\), m\({}_{i}\) and m\({}_{c}\) are the cementation index values corresponding to the three types of water, \(S_{wf}\) is the free water saturation in the pores in the unsaturated state, \(n\) is the saturation index, and \(S_{w}\) is the total saturation [46]. When the rock and soil mass are saturated, \(S_{w}=1\) and the resistivity \(\rho_{w}\) can be expressed as:  
\[\rho_{w}=\frac{{{a_{f}}\rho_{wf}}}{{\varphi_{f}^{{m_{f}}}}}+\frac{{{a_{i}}\rho _{wi}}}{{\varphi_{i}^{{m_{i}}}}}+\frac{{{a_{c}}\rho_{wc}}}{{\varphi_{c}^{{m_{ c}}}}} \tag{17}\]  
The three-water model indicates that the distribution state and conductive path of free water, microcapillary water and clay water differ, and the conductive mechanism also differs. They all follow [PERSON]'s equation. The model structure shows that the resistivity of water-bearing rock and soil is negatively correlated with the saturation and porosity. The conductivities of free water and microcapillary water are the same, which is related to the salinity of water. Clay water is less notably affected by salinity, and its conductivity is mainly due to the formation of hydration ions after the residual negative charge adsorbs cations in water, which is related to the temperature change. Both microcapillary water and clay water occur in the bound state, which is collectively referred to as bound water [46,47]. The three-water model was applied to describe the change in resistivity of the rainfall-affected slope. The behavior of rainfall-affected slopes can be regarded as a process of the mutual replacement of air and free water in slope pores (cracks). According to the three-water model, at the initial stage of rainfall seepage, the saturation of the rock and soil mass is low, and the aqueous solution enters the pores and is adsorbed onto the particle surface to form bound water, resulting in interface polarization. The dielectric constant rapidly increases with increasing saturation, and the slope resistivity abruptly decreases. With increasing saturation, free water increases and both the interface polarization phenomenon and the rock and soil mass conductivity further increase until water molecules enter the pores after exceeding the critical saturation, thus forming free water and subjecting the water molecules to polarization. Moreover, the increase in the dielectric constant decreases, \begin{table}
\begin{tabular}{c c c} \hline
**Three Water Model** & **Rock** & **Soil** \\ \hline Free water & Gravity water & Gravity water \\ Clay water & Bound water on clay surface & Bound water \\ Microcapillary water & Capillary water and bound & Capillary water \\ \hline \end{tabular}
\end{table} 
Table 5: Relationship of state between water in the water model and water in rock and soil masses. and the resistivity gradually stabilizes. Therefore, the apparent resistivity decline and mutation after the 5 th and 76 th rainfall events in this test could be explained as follows: the slope body was formed at the corresponding depth under the action of bound water in the rainfall seepage process; the apparent resistivity of the saturated rock and soil slowly decreased, which is mainly affected by free water.