A methodology to establish freezing characteristics of partially saturated sands
Introduction
When partially or fully saturated soils are subjected to sub-zero temperatures, ice starts to form because of the freezing of water present in the pores of the soil matrix. However, all the water in the pores of the soil matrix will not get converted into ice even if the temperature of the specimen is less than 0°C (Ting et al., 1983; Suzuki, 2004; Sun et al., 2012). The probable reasons for this observation are (i) suction acting on the water due to the formation of ice, (ii) adsorption forces acting on the water due to the physico-chemical interaction with the soil mineral and pore-water, and (iii) depression in the freezing point due to the curvature of water at the particle-water interfaces (Watanabe and Mizoguchi, 2002; Vugmeyster et al., 2017). As a result, freezing of partially or fully saturated soils at sub-zero temperatures would yield in the formation of a multiphase soil matrix that comprises of unfrozen and frozen water, air/ gas, and mineral(s). Needless to state, the thermo-hydro-mechanical (THM) properties of these soils are influenced significantly by the volumetric fractions of these individual phases (Sayles and Carbee, 1981; Arenson et al., 2004; Arenson and Sego, 2006; Arenson et al., 2007; Dongqing et al., 2016; Fu et al., 2018; Gao et al., 2020; Lin et al., 2020). Hence, to deal with the various geo-environmental engineering, soil physics and crop science problems related to the cold regions, it becomes vital to establish the soil freezing characteristics curve (designated as SFCC). Conventionally, SFCC describes the relationship between volumetric unfrozen water content (θuw) with temperature (T) (Lackner et al., 2008; Azmatch et al., 2012; Ma et al., 2017; Falak et al., 2018; Kadivar and Manahiloh, 2019; Xu et al., 2019). However, it has been realized that the variation of volumetric ice content (θi) with T, determined by employing a suitable method would also be necessary to define the state of the frozen soils for establishing their THM properties which are bound to alter with the extent of ice formation.
In this context, various techniques such as nuclear magnetic resonance (NMR) (Koopmans and Miller, 1966; Kleinberg and Griffin, 2005; Watanabe and Wake, 2009), gas dilatometry (Koopmans and Miller, 1966), calorimetry (Anderson and Tice, 1972; Handa et al., 1992; Kozlowski, 2016), acoustic methods (Dongqing et al., 2016) have been employed for determining θi (or θuw) of the soil mass at a specific temperature. However, apart from being expensive, these techniques are cumbersome to adopt and are not suitable for in-situ measurements and require calibration at each temperature. Also, if the soil consists of ferromagnetic particles/compounds, NMR would yield erroneous results (Patterson and Smith, 1980; Spaans and Baker, 1995).
To overcome these issues, techniques which utilize the high contrast between relative permittivity (ε) of liquid water (εw = 80) and ice (εice = 3.2), air (εa = 1), and soil minerals (εs= 2 to 8) have been developed for estimating porosity, saturation, fabric structure, the volumetric fraction of ice and water present in soil matrix (Rohini and Singh, 2004; Kleinberg and Griffin, 2005; Bhat et al., 2007; Watanabe and Wake, 2009; Zhou et al., 2014; Susha Lekshmi et al., 2016). Time-domain reflectometer (TDR) is one such technique where the travel time of an electromagnetic wave pulse through a TDR probe (i.e., waveguide), which is inserted in soil mass, is measured to compute ε of the soil mass. The frequency range of the electromagnetic wave is 0.5 to 1.5GHz, usually for TDR application. However, some studies have reported that TDR cannot be employed for simultaneous determination of θuw and θi because of the low relaxation frequency of ice (1 to 10kHz). In addition, in the frequency bandwidth of TDR, both ice and dry soil have approximately same relative permittivity (Bittelli et al., 2004). To this end, capacitive sensor-based technique is emerging as an effective technique for determining relative permittivity of the soils (Fen-Chong et al., 2004; Fen-Chong and Fabbri, 2005). The significant advantages of the capacitance-based method are that it: (i) is non-destructive, (ii) can be employed under in-situ and laboratory conditions and (iii) relies on the permittivity of each of the components of the specimen that would contribute to its effective dielectric permittivity, εmix (Bhat et al., 2007).
With this in view, in the present study, an experimental setup has been proposed to measure the relative permittivity of soil mass accurately by employing a capacitance-based technique at various sub-zero temperatures. A four-phase mixing model has been employed to obtain θi and θuw from the experimental measurement of relative permittivity of soils. Further, the proposed methodology was used to investigate the influence of initial moisture content on the SFCC of standard sands. In this regard, a set of experiments have been performed to develop the SFCC of standard sands for which the initial volumetric moisture content (θw0) was 6, 12, 18, 25 and 41%, over a temperature range of 25 to −15°C.
Section snippets
Specimen preparation
In this study, two standard sands, designated as S1 (coarse sand) and S2 (fine sand), were used to prepare the frozen sand specimen to determine the variation of θi with T. Specific gravity (Gs), mean grain size (D50), maximum voids ratio (emax), and minimum voids ratio (emin) of the soils were determined by following the guidelines suggested in ASTM-D6913 (2017), ASTM-D854 (2014), and ASTM-D4254 (2016), respectively and are presented in Table 1 along with the coefficient of uniformity (Cu),
Determination of relative permittivity of the specimen
The amount of ice/ unfrozen water content (i.e., θi and θuw) of frozen sands was estimated by measuring their relative permittivity (ε) at various temperatures (T) ranging from 25°C to −15°C. To this end, an easy-to-use capacitance-based technique was employed. The soil samples were prepared in the impedance cell (refer Fig. 2), which is a rectangular box made of perspex and dimensions 140 mm in height, 110 mm in length, and 30 mm in width. On the two opposite inner longer sides of the cell, a
Mixing model
This section presents an elaborate formulation of a dielectric mixing model to obtain θi from εmix. In this model, the relative permittivity of the specimen is denoted by εmix, and θs, θuw, θi and θa, represent volumetric fractions of sand grains, unfrozen water, ice, and air, respectively. The relative permittivity of sand grains, unfrozen water, ice, and air is denoted as εs, εuw, εi, and εa, respectively. It is well established that εmix would depend upon the volumetric fraction of each
Results and discussions
The variation of εmix of S1 and S2 sands with T is plotted in Fig. 5, where it is found that in unfrozen state of the specimen (i.e., T > 0°C) the εmix remains practically constant. However, in this state, εmix of specimen increases with θw0. This is mainly because with an increase in θw0, air (ε = 1) from the pore space gets replaced with water (ε = 81), which in turn increases the contribution of water on εmix according to Eq. 1. Interestingly, just below 0°C (−1 < T < 0°C), a sudden decrease
Conclusions
The current study briefly discusses and validates a simple to use cost-effective capacitance-based technique for establishing the soil freezing characteristic curve (SFCC) of fully saturated coarse- and partially saturated fine-sands by depicting the variation of θi with T. Further, the efficacy of the proposed methodology has been investigated with the help of three widely employed SFCC models viz., Anderson and Tice (1972) model, Kozlowski (2007) model and McKenzie et al. (2007) model.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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