# Analysis of Soil-Water Characteristic Curve and Microstructure of Undisturbed Loess
## 3 Results and Discussion
### Response of SWCCs to Pore Structure  
In unsaturated soil, a pressure difference exists at the air-water interface, often conceptualized using an equal diameter capillary model, as depicted in Figure 10. Capillary midpoints 1 and 2, situated at the radius of curvature \(R\), have identical water pressures. The pressure differential at the interface can be expressed as:  
\[u_{a}-u_{w}=\frac{2T_{s}}{R}=\frac{2T_{s}\cos a}{R} \tag{2}\]  
where \(u_{a}\) is the pore-air pressure (kPa); \(u_{w}\) is the pore-water pressure (kPa); \(u_{a}-u_{w}\) is the matric suction (kPa); \(T_{s}\) is the surface tension of the liquid phase; and \(a_{ww}\) is the wettability contact angle. The curvature radius \(R\) is determined using the constraint radius \(r\) and the liquid-solid contact angle \(a\); \(a\) is an intrinsic property, with a wetting contact angle \(a_{sw}\) for soil-water that is often taken as 0\({}^{\circ}\)-90\({}^{\circ}\), while \(a_{sm}\) for soil-mercury is a repulsive contact angle, often taken as 130\({}^{\circ}\)-140\({}^{\circ}\). Assuming that the matric suction in soil is generated by capillary action, and the pore radius is equal to the capillary radius, the matric suction can be calculated by the pore radius. The relationship between the PSD and SWCC can be elucidated by converting the pore radius to matric suction using Equation (2). This conversion allows for an analysis in the same coordinate system, facilitating comparison. In Figure 11, there is a notable alignment between the PSD and SWCC for the five undisturbed loess samples. The inflection point of  
Figure 10: Schematic diagram of equilibrium in capillary. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Sample** & **Sample Burial** & **Dry Density \(\rho_{d}\)** & **Porosity\% (\%)** & **Effective Porosity** & **Mercury Intrusion** \\  & **Depth (m)** & **(g/cm\({}^{3}\))** & & \(n_{e}\) (\%)** & **Efficiency \(\varphi\) (\%)** \\ \hline NO. 1 & 3.4 & 1.27 & 53.33 & 50.69 & 95.04 \\ \hline NO. 2 & 8.5 & 1.30 & 52.21 & 47.50 & 90.99 \\ \hline NO. 3 & 13.2 & 1.50 & 44.65 & 40.47 & 90.64 \\ \hline NO. 4 & 25 & 1.48 & 44.28 & 39.59 & 89.41 \\ \hline NO. 5 the PSD corresponds to the air entry value (AEV) of the SWCC, while the first dominant peak section of the pore density corresponds to the steep decline segment in the SWCC. Conversely, the low valley section of the pore density aligns with the gentle section of the SWCC. This correspondence reflects the dynamic process of water occupying the pores during desaturation. As the matric suction increases, water gradually discharges from the pores, with larger pores losing water more rapidly. Upon reaching the AEV, capillary action dominates in small pores and mesopores, leading to a rapid decrease in the volumetric water content. Capillary action in this zone is inversely proportional to the capillary radius: smaller pores exhibit a stronger capillary action, slower water loss rates, and higher water holding capacities. Consequently, the soil enters the unsaturated residual zone, where the pore water mainly exists as bound water due to strong bonding with soil particles. Here, the volumetric water content is minimally affected by matric suction. This analysis underscores the intricate relationship between the pore structure, capillary action, and water retention properties in unsaturated soils. It demonstrates how changes in matric suction impact water movement and storage within soil pores, highlighting the importance of understanding the soil's pore structure for predicting the water behavior in various environmental conditions. Figure 11 illustrates that the total area of the pore size distribution (PSD) curve and the X-axis governing the upper boundary of the soil-water characteristic curve (SWCC). A larger area indicates a higher saturated volumetric water content. Notably, the saturated volumetric water content decreases with an increasing burial depth for the five undisturbed loess samples. Moreover, the dominant pore range dictates the range of the transition zone in the SWCC.