## 4 Results and Discussion
### Effect of Relative Density on the Electrical Resistivity of Single Size Fraction of Calcareous Sand  
The conductivity of soil increased with increasing porosity, and the effect of porosity on conductivity was independent of the type of soil. For saturated sand, an increase in porosity caused an increase in soil conductivity [11]. To study the effect of relative density on the resistivity of calcareous sand, a series of electrical measurement experiments were conducted on three types of saturated calcareous sand particles. The relative density \(D_{\mathbf{r}}\) of the experiment was 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9, the current frequency \(f\) was 1000 Hz, and the pore liquid was treated with tap water (with a resistivity of 35.316 \(\Omega\cdot\)m). The relationship between resistivity and relative density was plotted using the experimental results, as shown in Figure 13. From the figure, it can be seen that the resistivities of the three types of single size fractions of saturated calcareous sand gradually increased with increasing relative density; that is, the larger the porosity of calcareous sand was, the smaller the resistivity was. This was because the larger the pore ratio was, the better the connectivity of its pores was and the better the continuity of pore water was, which resulted in a decrease in the resistivity of calcareous sand. There was a \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Size Fraction** & **Relative** & \(A\) & \(n\) & \(B\) & \(m\) & \(R^{2}\) \\  & **Density \(D_{\mathbf{r}}\)** & & & & & \\ \hline  & 0.3 & 0.586 & 0.5609 & & & \\
1-1.5 & 0.6 & 0.758 & 0.5394 & 0.0358 & 4.893 & 0.9678 \\  & 0.9 & 0.886 & 0.5157 & & & \\ \hline  & 0.3 & 0.711 & 0.5666 & & & \\
1.5–2 & 0.6 & 0.804 & 0.5450 & 0.1211 & 3.116 & 0.9999 \\  & 0.9 & 0.921 & 0.5214 & & & \\ \hline  & 0.3 & 0.896 & 0.5714 & & & \\
2-2.5 & 0.6 & 0.947 & 0.5510 & 0.2313 & 2.4 & 0.9637 \\  & 0.9 & 1.079 & 0.5285 & & & \\ \hline \end{tabular}
\end{table} 
Table 4: Fitting results of porosity and fitting parameter \(A\) of calcareous sand with different size fractions. \begin{table}
\begin{tabular}{c c} \hline
**Size Fraction/mm** & **Relationship between Saturation and Structure Factor** \\ \hline
1–1.5 & \(F=0.0358\times n^{-4.893}\cdot S_{r}^{-1.9722}\) \\
1.5–2 & \(F=0.1211\times n^{-3.116}\cdot S_{r}^{-1.99}\) \\
2–2.5 & \(F=0.2313\times n^{-2.4}\cdot S_{r}^{-1.9137}\) \\ \hline \end{tabular}
\end{table} 
Table 5: Relationship between saturation of calcareous sand of different size fractions and structure factor. linear relationship between the resistivity and relative density of calcareous sand, and their linear fitting coefficients were not less than 0.94. The fitting parameters between the resistivity and relative density of calcareous sand are shown in Table 6. As shown in the table, the intercept of the fitting line between the resistivity and relative density of saturated calcareous sand increased with increasing particle size. Figure 14 shows the relationship between the resistivity and particle size of calcareous sand for the same relative density. The figure shows that the particle size has a certain impact on the resistivity of saturated calcareous sand, and there are certain differences in the resistivity of different particle sizes of calcareous sand. Under the same density conditions, the resistivity of calcareous sand tended to increase with increasing particle size, which was consistent with the variation pattern of saturated sand resistivity under the influence of the size fractionation studied by [PERSON] et al. [28]. \begin{table}
\begin{tabular}{c c c c} \hline
**Size Fraction/mm** & **1–1.5** & **1.5–2** & **2-2.5** \\ \hline Slope & 5.1 & 5.8 & 5.12 \\ Intercept & 46.806 & 48.299 & 50.776 \\ Fitting coefficient & 0.95 & 0.94 & 0.97 \\ \hline \end{tabular}
\end{table} 
Table 6: Linear data table for fitting the relative density and resistivity of single size fraction of saturated calcareous sand.