## 1 Introduction  
Resistivity testing has the advantages of continuity, non-destructiveness, speed, and convenience. The electrical resistivity of soil is a basic parameter that characterizes the electrical conductivity of soil and is one of the inherent characteristic physical parameters of soil. Currently, the application of resistivity testing in the field of geotechnical engineering has attracted increasing attention from scholars. By continuously testing the resistivity during the deformation of soil, the microstructure deformation characteristics of soil can be accurately measured, thus achieving quantitative evaluation of soil microstructure [1; 2]. As one of the physical property indicators of soil, resistivity can reflect the structure and engineering characteristics of soil to a certain extent [1; 3; 4; 5] and is influenced by many factors, such as water content, soil structure, pore solution properties, and environmental temperature [6; 7; 8; 9]. When an electric current passes through rock and soil, the ions in the pore water of the rock and soil move under the action of the electric current, and the difficulty with which these ions pass through the pore system of the rock and soil under the action of the electric current determines the resistivity of the rock and soil [10]. The electrical resistivity of soil is actually the magnitude of the resistance that occurs when a current passes vertically through a cube of soil with a side length of 1 m. The unit of electrical resistivity is \(\Omega\cdot\)m. The resistivity of soil can be obtained by measuring the voltage drop \(\Delta V\) between two electrodes under a constant current. The soil resistance \(R\) is calculated according to [PERSON]'s law, and the resistivity of a sample \(\rho\) is determined as follows:  
\[\rho=\frac{RS}{L}=\frac{\Delta VS}{IL} \tag{1}\]  
For sandy soil, at a certain temperature, water content and pore water conductivity are the two determining factors of soil conductivity. The conductivity of saturated soil is composed of soil particle conductivity, pore water conductivity, and particle surface conductivity. For saturated sand, the surface of the particles carries no charge, so the surface conductivity of the particles is approximately zero [11]. [PERSON] [8] established a resistivity model of saturated sand according to the relationship between the structure factor and porosity of sand. \[\rho=\alpha\rho_{w}n^{-m} \tag{2}\]  
In Formula (2), \(\rho\) is the electrical resistivity of the soil; \(\rho_{w}\) is the pore water resistivity; \(\alpha\) is a soil parameter; \(m\) is the bonding coefficient; and \(n\) is the porosity. [PERSON] and [PERSON] [12] established a resistivity model for unsaturated sand based on the [PERSON] model and considered the influence of saturation. \[\rho=\alpha\rho_{w}n^{-m}S_{r}^{-p} \tag{3}\]  
In Formula (3), \(S_{r}\) is the soil saturation, and \(p\) is the saturation coefficient. There is relatively little research on the resistivity characteristics of calcareous sand. [PERSON] et al. [13] studied the relationship between the conductivity of calcareous sand, water content, and pore solution conductivity through on-site measurements and laboratory experiments and found a positive correlation. They also proposed a calculation model for the conductivity of calcareous sand. [PERSON] et al. [14] conducted laboratory experiments to study the changes in electrical conductivity of a single size fraction of calcareous sand with different dry densities, water contents, and pore solution concentrations but did not establish a relationship between them. This study systematically investigates the effects of factors such as pore water resistivity, test temperature, sample saturation, and relative density on the resistivity of calcareous sand samples through laboratory experiments and establishes a quantitative relationship between the resistivity of calcareous sand and the salt content and saturation of pore water.