## 4 Results and Discussion
### Effect of Saturation on the Electrical Resistivity of Single Size Fraction of Calcareous Sand  
[PERSON] and [PERSON] [12] noted that soil saturation is one of the key parameters affecting the resistivity of unsaturated soil. To study the effect of saturation on the resistivity of single size fraction of calcareous sand, a series of electrical measurement tests were conducted on calcareous sand samples with different saturation levels. The experiment was conducted at the same temperature (20 \({}^{\circ}\)C), relative density \(D_{\mathrm{r}}\) = 0.6, and saturation \(S_{\mathrm{r}}\) = 20%-100% using three size fractions of calcareous sand. Before configuring the calcareous sand sample, the pore water (20 \({}^{\circ}\)C, tap water) resistivity was tested to 35.316 \(\Omega\cdot\)m. The resistivity test results of calcareous sand with different saturations are shown in Figure 10.  
Figure 10 shows that within the tested saturation range, the resistivity of the calcareous sand of the three size fractions decreased with increasing saturation, and the relationship between them was a power function. When the saturation reached a certain value, the rate of resistivity decline gradually decreased. When calcareous sand was fully saturated, its resistivity reached the minimum, which was similar to that of quartz sand [25]. When the three types of calcareous sand were at low saturation, the resistivity values of loose, medium dense, and dense calcareous sand all differed significantly. Especially when the saturation was between 20% and 40%, the decrease in resistivity value was the largest, and the decrease in resistivity decreased with increasing saturation. When the saturation was low, increasing the saturation of calcareous sand improved the connectivity of pore water, resulting in a significant decrease in soil resistivity with increasing saturation. When the saturation exceeded a certain value (60% in this experiment), the connectivity of pore water in calcareous sand reached a good state. The continued increase in saturation of calcareous sand had little effect on the connectivity of pore water. Therefore, a decrease in the resistivity of calcareous sand was relatively small as the saturation continued to increase, indicating that the change in the saturation of calcareous sand  
Figure 10: Relationship between resistivity and saturation of single size fraction of calcareous sand: (**a**) 1–1.5 mm; (**b**) 1.5–2 mm; and (**c**) 2–2.5 mm. Figure 9: Relationship between NaCl solution concentration and resistivity test values of calcareous sand. had little effect on its resistivity. This was because an increase in pore water simultaneously led to an increase in the number of charges and enhanced mobility, and a reduction in resistance caused by the continuous water film compared to the initial stage. [PERSON] [8] proposed the concept of the structure factor in the process of studying soil resistivity, which is defined as the ratio of soil resistivity to pore liquid resistivity. The soil structure factor \(F\) was used to analyze the test results, and the results shown in Figure 11 were obtained. There was a power function relationship between the structure factor \(F\) and saturation \(S_{\mathrm{F}}\). \[F=AS_{r}^{-p} \tag{5}\]  
In Formula (5), \(A\) and \(p\) are the fitting parameters related to soil properties (excluding saturation), and the structure factor \(F\) is the ratio of the resistivity of calcareous sand to the pore water resistivity. Here, the fitting parameter \(p\) was taken as the fitting average, with values of 1.9722, 1.9900, and 1.9137 for 1-1.5 mm, 1.5-2 mm, and 2-2.5 mm, respectively. According to the model proposed by [PERSON] [8] and [PERSON] et al. [12], the relationship between fitting parameter \(A\) and porosity \(n\) is as follows:  
\[A=B\cdot n^{-m} \tag{6}\]  
In Formula (6), \(B\) is the fitting parameter. The relationship curve between fitting coefficient \(A\) and porosity \(n\) was drawn, as shown in Figure 12, and a power function was used for fitting.