## 1 Introduction
### Background of an \"Estimation Procedure\"  
#### 1.1.1 Soil Section and Soil Water Characteristic Curve  
A commonly used method to relate suction and the changing degree of soil saturation is the soil water characteristic curve (SWCC), as shown in Figure 1. This curve represents a model of the pore water distribution as a function of soil texture, particle size distribution, and void ratio [4], providing a better understanding of the soil water energy system through direct or indirect measurements of suction and saturation. Matric suction and osmotic suction are the components of total suction \(\psi\)[5], which are mathematically represented in Equation (1):  
\[\psi\ = (u_{\mathrm{a}}-\ u_{\mathrm{w}})+\pi \tag{1}\]  
where:  
\((u_{\mathrm{a}}-\ u_{\mathrm{w}})\) = matric Suction [kPa]; \(u_{\mathrm{w}}\) = water pore pressure [kPa]. \(\pi\) = osmotic Suction [kPa]; \(u_{\mathrm{a}}\) = air pore pressure [kPa]. The suction values of both its components and the total suction, as well as its gravit-metric water content or degree of saturation, can be determined in the laboratory using direct and indirect tests. Table 1 summarizes some of these methods. With respect to the variation in the degree of soil saturation of SWCC, important zones were identified, as shown in Figure 1. In the boundary zone, the soil pores are saturated and small air bubbles may become trapped, resulting in negligible suction values. When desaturation occurs, the soil enters the transition zone where air begins to enter the soil pores and drains capillary water [9]. This gradually reduces the capillary effect of water in the pores, with both the liquid and gas phases present continuously. The air-entry value corresponds to the suction at which air first enters the soil pores, indicating a change in soil behavior [10]. Once a certain degree of saturation is reached, the capillary effect of water on the soil skeleton becomes negligible and large suction values are attained [11]. This \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Device** & **Measurement Type** & **Suction Component Measured** & **Comment** \\ \hline Axis Translation Technique & Direct & Matric & The air pressure in the chamber at water flow equilibrium and negative pressure in high-air-entry disc were measured. The difference between pressures is the soil suction [6]. \\ \hline Tensiometers & Direct & Matric & Low and high suction values can be measured using two different tensiometer devices [7]. \\ \hline Psychrometers & Direct & Total & It is not recommended for field measurements because it requires strict control of the ambient temperature. \\ \hline Thermal Conductivity Sensors & Indirect & Matric & The sensors used are sensitive to ambient temperature, and, therefore, corrections are required depending on the type of sensor. \\ \hline Filter paper & Indirect & Matric/Total & Hysteresis can affect the filter paper calibration. The process to obtain suction in soil (wetting or drying) must be consistent with the calibration process. \\ \hline \hline \end{tabular}
\begin{tabular}{c c c} \hline \hline
**Squeezing Technique** & Indirect & Osmotic & It uses the electrical conductivity of the salts dissolved in the free water of the soil to relate it to the osmotic suction they generate. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of suction measurement methods. saturation degree corresponds to a suction value known as residual suction, indicating a transition from the transition zone to the residual zone. Under field conditions, soil usually undergoes alternating wetting and drying processes, which lead to variations in its suction state, ranging from the air-entry value to the residual suction, thereby generating a hysteresis loop [13]. A noticeable difference exists between the suction trajectories of the same soil, depending on whether it undergoes wetting or drying [14], as illustrated in Figure 2(a).