# 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
#### 3.1.2 Porosity  
The pore size distribution principle is based on the capillary condensation phenomenon and the volume equivalent exchange rule [24]. The amount of liquid nitrogen permeated in the red clay particles is equal to the volume of the pores. Based on the Kelvin equation, the relationship between the partial pressure of adsorbate and the pore size of capillary condensation is described in Equation (4). The cumulative pore volume curves of BJH adsorption and desorption are given in Figures 5 and 6, respectively, and the pore volume of red clay with different particle sizes is shown in Table 5.  
\[R_{k}=-\frac{0.414}{\log(P/P_{0})} \tag{4}\]  
According to the size of the pore radius, the pores on the solid surface can be divided into three categories: (1) micropores with a radius less than 2 nm; (2) mesopores with a radius between 2 and 50 nm; and (3) macropores with a radius greater than 50 nm. According to Figures 5 and 6, it is evident that the BJH adsorption and desorption cumulative pore volume of the red clay gradually decreases with the increase in the pore size, implying that the pores of the red clay are primarily tiny (main mesopores with the pore size ranging from 1.7 to 15 nm). Moreover, the pore volume ranges from 0.008 to 0.08 cm\({}^{3}\)/g, and the minimum pore volume during desorption is 0.072-0.08 cm\({}^{3}\)/g, while that during adsorption is 0.061-0.066 cm\({}^{3}\)/g. The red clay with the smallest particle size of 0.25 mm shows a more remarkable relative change than the others by comparing the desorption and adsorption processes. The pore volume is the largest during the adsorption process, and the volume of small pore size equals the pore volume of the red clay, with a particle size of 2 mm; however, during the desorption process, the pore volume of the red clay with a particle size of 0.25 mm was significantly reduced compared with clays with different particle sizes.  
According to Table 5, the internal pore volume of soil particles is the smallest when the particle size is 0.5 mm, with the internal pore volume of other particle sizes remaining proportional to the particle size. The BJH adsorption and desorption cumulative volumes change little with the particle size, and the cumulative volume of desorption is larger than the cumulative volume of adsorption. The average pore sizes of BJH adsorption and BJH desorption are equal to 4 times the pore volume within the SSA, which might generate significant errors when the soil mass is unevenly distributed.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Grain Size (mm)**} & \multirow{2}{*}{**BET Surface Area (m\({}^{2}\)/g)**} & **Langmuir Surface Area (m\({}^{2}\)/g)** & **Internal Surface Area (m\({}^{2}\)/g)** & **External Surface Area (m\({}^{2}\)/g)** & **BJH Adsorption Cumulative Surface Area (m\({}^{2}\)/g)** \\  & & **(m\({}^{2}\)/g)** & **(m\({}^{2}\)/g)** & **(m\({}^{2}\)/g)** & **(m\({}^{2}\)/g)** \\ \hline
0.25 & 45.6956 & 116.2331 & 2.8895 & 42.8061 & 46.950 & 48.4585 \\
0.50 & 42.7188 & 109.0909 & 2.0696 & 40.6492 & 44.268 & 45.6784 \\
2.00 & 45.8130 & 117.7344 & 2.9162 & 42.8968 & 47.143 & 48.8844 \\
5.00 & 44.7118 & 113.1781 & 2.9628 & 41.7489 & 45.700 & 47.5564 \\ \hline \end{tabular}
\end{table}
Table 4: The SSA of red clay with different particle sizes.