Estimation of the wetting scanning curves for sandy soils

Highlights

• Simulation of main wetting SWCC.

• Incorporating “rain-drop” effect.

• Incorporating “ink-bottle” effect.

• Estimation of wetting scanning curves.

Abstract

It is known that the soil-water characteristic curve (SWCC) of unsaturated soils is hysteretic. The engineering properties of unsaturated soils during the drying process are different from those during the wetting process, and the difference can be related to the hysteresis of the SWCC. Therefore, understanding the hysteresis of the SWCC is crucial in engineering practices. In this paper, both the “rain-drop” and “ink-bottle” effects on the hysteresis of the SWCC are quantified with mathematical equations. In the proposed equations, it is assumed that soil volume changes during the drying and wetting processes are negligible, which is a reasonable assumption for most sandy soils. Based on the proposed theory, the wetting scanning curves were estimated from the main drying curves. The results from the method proposed in this paper have been compared with experimental data from the published literature. Satisfactory agreements were found between the measured and estimated wetting scanning curves. Consequently, the method for estimating the wetting scanning curves from the fitting parameters of the SWCC by using the equations proposed in this paper is recommended.

Introduction

In engineering geology, the hydromechanical properties of soil are crucial for the evaluation of its potential value for practical applications. The soil-water characteristic curve (SWCC), which defines the relationship between the amount of water in soil and soil suction, is one of the hydraulic properties of soil. Due to the different forms of expressions for describing the amount of water in soil, the SWCC can be expressed in the form of the gravimetric water content, w-SWCC, volumetric water content, θ-SWCC, and degree of saturation, S-SWCC. The major difference between these three forms of the SWCC is the consideration of the soil volume change during changes in soil suction. Zhai and Rahardjo (2013) indicated that the fitting parameters of w-SWCC, θ-SWCC and S-SWCC should be the same if soil volume changes can be ignored. However, the fitting parameters for each form of the SWCC will be much different if the soil volume change is significant. In this paper, the soil volume change for sandy soil is considered to be negligible.

The SWCC is also reported to be hysteretic because the water content at a given suction in the wetting process is less than that in the drying process (Topp, 1969; Haines, 1930, and Pavlakis and Barden, 1972). Kim et al. (2018) showed the effects of the hysteresis of the SWCC on the hydromechanical properties of soil by using different SWCCs corresponding to the drying and wetting processes. Chung et al. (2019) demonstrated the different responses of time domain reflectometry (TDR) in measuring the soil moisture contents during the drying and wetting processes. As a result, it is crucial to understand the hysteresis behavior of the SWCC for practical engineering. To simulate the hysteretic characteristics of the SWCC, many models have been proposed by different researchers, such as Enderby (1955), Néel, 1942, Néel, 1943, Poulovassilis, 1962, Poulovassilis, 1970a, Poulovassilis, 1970b, Hanks et al. (1969), Poulovassilis and Childs (1971), Gillham et al. (1976), Poulovassilis and EL-Ghamry (1978), Scott et al. (1983), Jaynes (1984), Hogarth et al. (1988), Viaene et al. (1994), Braddock et al. (2001), Karube and Kawai (2001), Pham et al. (2003) and Pham et al. (2005), for estimating the hysteretic behavior of the SWCC. Pham et al. (2005) categorized these models into two groups: domain models and empirical models. Klute (1986) showed that the SWCC is primarily dependent on the texture or the particle-size distribution of soil and the structure or the arrangement of the particles (Salter and Williams, 1965; Richards and Weaver, 1944; Reeve et al., 1973; Sharma and Uehara, 1968; Croney and Coleman, 1954).

The hysteretic nature of the SWCC has been known for a long time and can be attributed to multiple factors, such as the “ink-bottle” effect, contact angle difference during the drying and wetting processes, entrapped air and thixotropic regain due to the drying and wetting history of the soil (Klausner, 1991). During laboratory measurement, normally only limited cycles of drying and wetting processes are conducted during SWCC tests. The effect of thixotropic aging on the hysteresis of the SWCC is insignificant for experimental data and is not considered in this study. In addition, entrapped air may not always be encountered in sandy soils (Talsma, 1970; Gillham et al., 1976; Yang et al., 2004). As a result, entrapped air is also not considered in this study. Bear (1979) demonstrated that the hysteresis of the SWCC results from the “ink-bottle” effect and “rain-drop” effects, which means that the contact angle at an advancing interface in the wetting process is different from that at a receding interface in the drying process, as shown in Fig. 1. Assuming that soil pores are connected to each other, the capillary water rise height is shorter in the wetting process than in the drying process. This phenomenon is called the “ink-bottle” effect. On the other hand, as shown in Fig. 1(b), the contact angle advancing interface, α₂, is higher than that in the receding interface, α₁, and this phenomenon is called the “rain-drop” effect. The experimental results from Reinson et al. (2005) show that water can only flow through the wet pores in soil and is blocked out from the dry pores by the air-water interface. In this case, dry pores in soil can block water flow and cause the saturation of soil in the wetting process to be less than that in the drying process.

Klute (1986) introduced the characteristics of SWCC hysteresis, as shown in Fig. 2. It is noted that S₀ is called natural saturation, S_r is called residual saturation and 1-S₀ is entrapped air. As shown in Fig. 2, the dotted lines represent the wetting scanning curves. These wetting scanning curves start from the points on the main drying curve and yield the main wetting curves. The main objective of this paper is to develop a method for estimating these wetting scanning curves, which are wetted from the points on the main drying curve.

In this paper, the “rain-drop” effect on the hysteresis of the SWCC is quantified by introducing an additional parameter, k, defined as the difference in the contact angle of the air-water interface and the surface of soil particles in the drying and wetting processes. The “ink-bottle” effect is also quantified by adopting the concept of the “pore-size distribution function” (PSDF) and the arrangement of dry and wet pores. A new equation is proposed to simulate the main wetting curve for sandy soils. Consequently, the wetting scanning curves are estimated from the proposed equation using the information from the main drying and main wetting curves. The estimated wetting scanning curves for sandy soil were verified with experimental data from the published literature.