# Influence of Soil Particle Size on the Engineering Properties and Microstructure of a Red Clay
## 3 Results and Analysis  
### Analysis of Specific Surface Area and Pore  
#### 3.1.1 Specific Surface Area  
The features of the SSA of the soil are closely related to the macroscopic physical and mechanical properties of the soil. According to the law of adsorption of a gas on the surface of soil particles, the sum of the internal surface area and the external surface area of soil particle lattice per unit mass that the adsorbate molecules can reach is the SSA of the soil particles. The BET adsorption isotherm equation of the multilayer adsorption theory and the Langmuir adsorption isotherm equation is provided in Equations (2) and (3), respectively [22; 23]. \[\frac{P/P_{0}}{V(1-p/p_{0})}=\frac{C-1}{V_{m}C}\times P/P_{0}+\frac{1}{V_{m}C} \tag{2}\]  
where \(V\) represents the gas adsorption capacity, \(V_{m}\) represents the monolayer saturated adsorption capacity, \(P\) represents the adsorbate's pressure, \(P_{0}\) represents the saturated vapor pressure of adsorbate, and \(C\) represents the constant. \[\theta=\frac{V^{s}}{V_{ml}}=\frac{b\cdot P}{1+b\cdot P} \tag{3}\]  
where \(b\) represents the adsorption equilibrium constant, \(P\) represents the gas pressure, \(\theta\) represents the surface area coverage of solid surface occupied by adsorbed gas, \(V^{s}\) represents the volume of adsorbed gas per gram of solid, and \(V_{ml}\) represents the volume of adsorbed gas per gram of solid covered by a monolayer. The low-temperature nitrogen adsorption test (LT-NAT) measurement process is divided into two stages: adsorption and desorption. Take red clay with a particle size of 0.25 mm as an example. The adsorption amount of red clay during increasing and decreasing the relative pressure is illustrated in Figure 3. It is apparent that when the relative pressure is slight, the adsorption isotherm and the desorption isotherm coincide with each other. When the relative pressure is more extensive than 0.8 \(P/P_{0}\), the desorption isotherm is above the adsorption isotherm, indicating that red clay has a larger adsorption capacity during desorption than adsorption. The adsorption isotherms of red clay with different particle sizes are provided in Figure 4. These adsorption isotherms show a similar upward trend with the increase in relative pressure, and the curve is concave, indicating weak interaction. In addition, the adsorption isotherm can be divided into two stages: (1) Slow linear growth stage (when the relative pressure \(P/P_{0}\) is between 0 and 0.6, the adsorption isotherms of red clay with different particle diameters coincide with each other). (2) Rapid non-linear growth stage (when the relative pressure \(P/P_{0}\) is between 0.6 and 1.0, there is a slight difference between the adsorption isotherms of red clay with different particle sizes, and the adsorption quantity of red clay with a particle size of 0.5 mm is significantly lower than that with other particle sizes under the same relative pressure). Table 4 describes the SSA of red clay with different particle sizes, as calculated by Equations (2) and (3). As shown in Table 4, the SSA of the red clay obtained by the Langmuir adsorption isotherm equation is about 2.5 times that of the BET adsorption isotherm equation. The sum of the internal and external surface areas is the BET surface area, and the external surface area accounts for 93-95% of the total surface area. Additionally, the BJH adsorption cumulative surface area of the pores between 1.7 nm and 300 nm is smaller than the desorption cumulative surface area. With the increase in soil particle size, the SSA does not appear to decrease; instead, \(\text{SSA}_{(2,0)}>\text{SSA}_{(0.25)}>\text{SSA}_{(5,0)}>\text{SSA}_{(0.5)}\). The main reason for this is that the mass of red clay sample approximately between 0.5 g and 0.7 g is  
Figure 4: Adsorption isotherms of red clay with different particle sizes. Figure 3: Adsorption–desorption isotherm of red clay (0.25 mm).