## 1 Introduction  
Expansive soil is one typical special soil that is very sensitive to the change in moisture content, which is widely distributed around the world [1]. Such soil swells and shows the considerable volumetric deformation in response to changes in moisture content [2]. Consequently, expansive soil causes serious damage and distortion to structures, particularly for light buildings and pavements [3,4]. As a result, the swelling behavior of expansive soil is closely related to the safety and stability of engineering structures [5,6]. Free swelling ratio, swelling pressure, and swelling percent are usually identified as three important swelling characteristics which are required for the assessment of safe and economical designs of engineering structures resting on expansive soils. However, in the process of engineering design and construction, it is conventionally considered that expansive soil is a homogeneous material that the swelling behavior is the inherent property and consistent along the depth of the soil layer. In fact, the parameters such as moisture content, void ratio and swelling indexes of different soil layers in the active zone are not the same under actual field conditions. Hence, their swelling behavior is different even under saturated state. In this respect, the results of numerous laboratory and field tests on black cotton soil from MRBC 76 reported by [PERSON] and [PERSON] [7] are noteworthy. It was found that the lower black cotton soil layer will not produce excessive swelling deformation though the swelling pressure (224 KPa) is far greater than the weight stress of the upper soil layer under saturated conditions. In particular, when the thickness of the upper black cotton soil layer reaches 1.2 m, the swelling of the lower black cotton soil can be completely inhibited, and its moisture content, void ratio, dry density and shear strength remain unchanged. This finding indicates that the black cotton soil at different depths has an obvious swelling difference during the saturated process [7; 8]. Previous studies revealed that the types and concentrations of cations in soil solution have significant influence on the potential of soil surface and its electrochemical properties [9; 10]. In the soil-water-electrolyte system, as a kind of particular clay soil that contains a certain amount of montmorillonite and carries negative charges, the surface of clay particles is absorbed by the cations, so that a very high ion concentration is induced surrounding it [11]. Consequently, it can be speculated that the swelling difference of expansive soil at different depths is closely related to its electrochemical properties and may depend largely on the type and concentration of electrolyte in pore solution. Several scholars have pointed out that different kinds and concentrations of electrolyte can cause the expansion of swelling clays to varying degrees [12; 13; 14; 15]. It was demonstrated that different pore solutions have a significant effect on the swelling characteristics of bentonite [16; 17; 18; 19; 20; 21]. [PERSON] et al. [17] demonstrated that the swelling pressure of Ca-bentonite is distinct from that of Na-bentonite, and this difference depends on the concentration of electrolyte, which can be ascribed to changes to the thickness of diffuse double-layer (DDL) or cation exchange [22]. According to DDL theory, the DDL thickness decreases as the concentration of solutions increases, resulting in a decrease in the swelling pressure. Additionally, one cation with lower valence can be replaced by another with higher valence. So, when Na-bentonite is infiltrated with calcium solutions, sodium will be replaced by calcium [23; 24], resulting in a reduction in the swelling potential. Therefore, when the cation concentration of bulk liquid in expansive soil changes, the electrochemical properties of expansive soil will also change, which finally affects its macroscopic swelling characteristics.