# Model Modification of the Soil-Water Characteristic Curve of Unsaturated Weak Expansive Soil
## 6 Correction of the Soil-Water Characteristic Curve by the Mercury Intrusion Test
### Correction of Soil-Water Characteristic Curves by the Capillary Principle  
According to the above analyses, SWCC test values were obtained, based on the pressure plate method and the filter paper method, as well as the SWCC theoretical calculation value based on mercury intrusion porosimetry, as shown in Figure 9. There is consistency in the theoretical calculation and test values of the expansive soil-water characteristics obtained using mercury intrusion porosimetry and the filter paper method, respectively. The soil-water characteristic curve corresponding to the area with high pore size distribution density is steep, while the soil-water characteristic curve corresponding to the area with low pore size distribution density is slow. Moreover, the SWCC trend has a step-like  
Figure 8: Profile of the fitting parameters on dry density.  
This phenomenon is attributed to the following reasons: Firstly, the MIP test does not generate all the pore volume of the expansive soil. In addition, the minimum equivalent pore size that can be measured is 6 nm, while the minimum pore size that the geotechnical test water molecules can fill is 0.3 nm. From Equation (2), it is evident that the soil's suction force of is inversely proportional to the pore size, that is, the suction value generated by this part of the pore itself is very large. Secondly, the pore shape of the soil body is not completely in line with the spherical pore hypothesis, and the pores in the actual cohesive soil often have complex flat shapes (rhomboid-shaped). Notably, an increase in mercury pressure causes a continuous increase in the pore mercury medium, although it cannot be filled (the mercury pressure P cannot be infinitely increased). [PERSON] et al. [22] analyzed the fractal dimension of a soil body and found that an increase in the dry density of the sample resulted in a more complex spatial distribution morphology of the pores of the mudstone, and the farther the morphological characteristics of the pore surface of the material in space deviated from the smooth surface. Consequently, the two curves deviate, and the degree of deviation increases with the increase in dry density.  
In order to realize the simultaneous analysis and evaluation of the microscopic properties and soil-water properties of soil using the mercury intrusion technique alone, the theoretical calculation of the SWCC was modified based on the filter paper method test value. Particularly, when the moisture content is \(\theta_{1}=\theta_{2}\), the theory should have \(\psi=\psi_{1}\). Therefore, the corrected matric suction \(\psi\) can be obtained as follows:  
\[\psi=\psi_{1}=e\Bigg{(}\frac{57.497-43.662\rho_{d}-(6.751-1.782\rho_{d})ln( \psi_{2}-18.348+12.581\rho_{d})}{-2.406-1.206\rho_{d}}\Bigg{)} \tag{18}\]  
The suction correction model of the mercury pressure method (capillary principle), based on the filter paper method, was obtained, as shown in Equation (18), while the correction curve is shown in Figure 8. This model allows efficient calculation and prediction of the suction of the soil matrix based on the microscopic pore structure, density state, and moisture content of a soil body