Resilient modulus of unsaturated subgrade soil ...



Comparisons between different suction control techniques by water retention curves: theoretical and experimental studies

Type of paper: Original Research Article

Authors: C. W. W. Ng, C. Zhou* and A. K. Leung

*Corresponding author

Information of the authors

Crown author: Dr C. W. W. Ng

Chair professor, Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong.

E-mail: cecwwng@ust.hk

Corresponding author: Dr C. Zhou

Visiting assistant professor, Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong.

E-mail: czhou@connect.ust.hk

Co-author: Dr A. K. Leung

Lecturer, Division of Civil Engineering, University of Dundee, Dundee, UK

E-mail: a.leung@dundee.ac.uk

Abstract

The axis-translation (ATT), osmotic (OMT) and vapour equilibrium (VET) techniques are widely used suction control techniques for investigating hydraulic and mechanical behavior of unsaturated soils in the vadose zone. Yet there is still debate in the literature regarding their validity and consistency. In this study, four purposely designed experiments have been carried out to measure the water retention curves (WRCs) of a compacted silty sand at different densities using the ATT and OMT. The four WRCs obtained from this study together with extensive existing data published in the literature are then analysed using newly derived thermodynamic equations. The aim and novelty of this study are to apply the thermodynamic theory to verify and explain the validity and consistency of WRCs obtained by the three commonly used experimental techniques. By allowing for some possible experimental errors, analysed results reveal that the WRCs obtained from the three techniques are remarkably consistent. These consistent results can be explained by the derived thermodynamic equations, which illustrate that the final soil water content at the thermodynamic equilibrium state must be the same regardless of the suction control technique used, even though the techniques involve different processes of moisture exchange.

Keywords

Thermodynamics, suction control technique, water retention curve

Introduction

Suction plays an important role in the hydraulic and mechanical behaviour of unsaturated soil. Total suction is generally recognised to have two components: matric suction and osmotic suction (Aitchison 1965). Various suction control techniques have been developed including the axis-translation technique (ATT) (Hilf 1956) and the osmotic technique (OMT) (Zur 1966) to control matric suction, and the vapour equilibrium technique (VET) (Tessier 1984) to control total suction (Agus and Schanz 2005; Ng et al. 2007; Tarantino et al. 2011; Laloui 2013).

The ATT is the most widely used for determining unsaturated soil properties such as the water retention curve (WRC) but it has been criticised for several reasons. Firstly, this technique artificially elevates the pore air pressure (ua) and hence it is not representative of field conditions where ua is generally under atmospheric conditions (Dineen and Burland 1995; Delage et al. 2008). The elevation of ua would increase the pore water pressure (uw) and eliminate the possibility of cavitation of pore water (Or and Tuller 2002; Baker and Frydman 2009). Secondly, the ATT may not be valid at the nearly saturated state because the application of ua would compress occluded air bubbles (Bocking and Fredlund 1980). Thirdly, some researchers have postulated that matric suction is attributed not only to capillary but also to adsorptive forces (Philip 1977; Tuller et al. 1999; Baker and Frydman 2009). Influence of the air pressurisation process on uw is not fully understood when water is held by adsorption mechanism (Baker and Frydman 2009).

To evaluate the validity and consistency of the ATT and OMT, previous researchers have compared WRCs of unsaturated soils measured using these two techniques (Zur 1966; Williams and Shaykewich 1969; Nam et al. 2010; Tarantino et al. 2011). Some have found that the equilibrium gravimetric water content (w) measured using the ATT is higher than that measured using the OMT by less than 10% at matric suctions ranging from 0 to 2000 kPa (Zur 1966; Williams and Shaykewich 1969; Tarantino et al. 2011), while others have shown that the equilibrium w measured using the OMT is higher than that measured using the ATT by less than 5% within the same range of matric suctions (Zur 1966; Nam et al. 2010). The observed differences might have been caused by experimental errors. For example, the test duration may not have been long enough for the soil specimen to reach the thermodynamic equilibrium state. On the other hand, Delage et al. (1998) found that WRCs determined using the VET and the OMT are very consistent. As far as the authors are aware, these previous studies all drew their conclusions based on the testing of one type of soil at one dry density, but the pore structure of unsaturated soil is complicated and dependent on various factors such as soil type and dry density (Tuller et al. 1999; Wheeler et al. 2003; Baker and Frydman 2009; Paz-Ferreiro and Vázquez 2014). Moreover, although the three suction control techniques have been compared by measuring WRCs in the literature, the experimental results have not been analysed theoretically and so the validity and consistency of these techniques are not fully understood.

In this study, four purposely designed experiments have been carried out to measure the water retention curves (WRCs) of a compacted silty sand at different densities using the ATT and the OMT. The WRCs obtained using these two techniques are compared and analysed by employing a set of newly derived thermodynamic equations using the two independent stress state variables (i.e., net stress and matric suction). Moreover, a number of existing experimental data comparing different suction control techniques (i.e., the ATT, the OMT and the VET) are reinterpreted by using the new thermodynamic equations. The aim and novelty of this study are to apply the thermodynamic theory to verify and explain the validity and consistency of WRCs obtained by the three commonly used experimental techniques. It should be noted that these new thermodynamic equations are fundamental ones and so they can be applied to predict equilibrium water contents and WRCs of any soils such as clay and sand.

Theoretical considerations of soil moisture transfer

Thermodynamic theory was first introduced by Edlefsen and Anderson (1943) to study moisture transfer in unsaturated soil. In their study, the energy state of soil water is represented by free energy per unit mass (f) [SI unit: J/kg]. f controls water movement and phase transformation in unsaturated soil. Water flows from a region of higher f to a region of lower f, and transforms from a phase with a higher f to a phase with a lower f.

Free energy is equivalent to other widely used terminologies, for example, potential (( ) [SI unit: J/kg] (Sposito 1981). ( is defined as f - f0, where f0 is free energy per unit mass at a reference state. For simplicity, potential is used to describe the energy state of soil water in this study.

Figure 1(a) shows an idealized configuration of a representative unsaturated soil subjected to a confining pressure ((). Water in unsaturated soil can be present as liquid and gaseous phases, the latter of which is contained in pore air. The liquid phase and gaseous phase of soil water are termed pore water and pore vapour. Their potentials are denoted by (w and (v, respectively. To interpret suction effects on mechanical behaviour of unsaturated soil, pore water in this configuration was classified into meniscus water (see Figure 1(b)) and bulk water (see Figure 1(c)) (Wheeler et al. 2003). The energy state ((w) of these two types of water should be identical at thermodynamic equilibrium. Otherwise there would be water movement within the soil specimen. This implies that it is unnecessary to differentiate bulk water and meniscus water from energy state point of view.

Figure 1(b) and 1(c) show the air-water interfaces in unsaturated soil when pore air is continuous and discrete, respectively. At the thermodynamic equilibrium, there should not be any net mass transfer of soil water across the air-water interface between liquid and gaseous phases and (v is equal to (w. The potential of soil water can thus be controlled through either (w (ATT and OMT) or (v (VET). These two methods are equivalent as long as the thermodynamic equilibrium is achieved.

Figure 1 shows that the energy states of pore vapour and pore water (both bulk water and meniscus water) should be the same at the thermodynamic state. For the energy state of pore vapour, (v is related to partial vapour pressure (pv) through the following equation (Aitchison 1965):

[pic]

[1]

where R is the universal gas constant; T is absolute temperature; ωv is the molecular mass of water; pv0 is the partial pressure of water vapour in equilibrium with pure free water at a given pressure and temperature; and the ratio pv/pv0 is commonly referred to as relative humidity. Equation [1] suggests that (v is uniquely related to relative humidity under isothermal conditions. This is the principle of the VET, which imposes soil suction by controlling the relative humidity of pore air in unsaturated soil.

For the energy state of pore water, the variation in (w may be presented in the following incremental form (Sposito 1981):

[pic]

[2]

where(Sw is the specific entropy of pore water; ( is total mean stress; ua is pore air pressure; and(Vw is the partial specific volume of pore water, defined as the ratio of incremental soil volume to incremental water mass in the soil specimen. For a non-deformable soil specimen,(Vw is equal to 0. For a deformable soil specimen, (Vw is equal to 1/(w at saturated state and it decreases with a decrease in degree of saturation.

Based on the thermodynamic theory, Houlsby (1997) showed that a complete description of unsaturated soil behaviour requires at least two stress-state variables. To enable rigorous yet simple interpretation of experimental data, this study adopts the most commonly used two independent stress state variables (Jennings and Burland 1962), namely net stress[pic] [pic] ((-ua) and matric suction (ua-uw). Equation [2] can thus be rearranged as follows:

[pic]

[3]

The first term on the right-hand side of equation [3] suggests that (w increases linearly with ua. This term is equivalent to the gas potential defined by Aitchison (1965). The second term represents the effects of net stress (( – ua) on (w and hence WRC of unsaturated soil. It should be pointed out some recent studies have shown that WRC is not only dependent upon matric suction (ua - uw), but it is also governed by net stress, which is one of the stress-state variables governing unsaturated soil behaviour (Coleman 1962). The water retention ability of unsaturated soil generally increases with an increase in net stress (Ng and Pang 2000; Ng and Menzies 2007; Ng and Leung 2012; Zhou and Ng 2014). The third term describes the change in (w with water content and it is governed by the water retention ability of soil specimen. It is important to note that this term is expressed using (-ua instead of ( to align with the framework of two stress-state variables. The last term represents thermal effects on the energy state of soil water. Equation [3] can be rewritten to describe the incremental water content of unsaturated soil:

[pic]

[4]

At a constant net stress and temperature, equation [4] can be simplified as follows:

[pic]

[5]

The numerator on the right-hand side of this equation is a function of (w and ua, where the denominator [pic] depends on the relationship between (w and w. Equation [5] is derived to describe soil moisture exchange in soil pores. It is applied later to analyse the WRCs obtained using different suction control techniques.

Test Program and Apparatus

To compare different suction control techniques in determining WRCs, four compacted specimens of a silty sand were prepared at two different initial dry densities. At each initial dry density, the WRCs of two specimens were measured using the ATT and the OMT. Details of each test are summarised in Table 1.

Figure 2 (a) shows a schematic diagram of the volumetric pressure plate for measuring the WRC with the ATT (Ng and Pang 2000). During a test, ua is controlled through an air pressure line. To prevent the soil from drying by evaporation, a vapour saturator is used to saturate the in-flow air to the airtight chamber. Soil water exchange is monitored by a ballast tube having a precision of ±0.01 mm3. Figure 2 (b) shows a schematic diagram of the apparatus adopted for the OMT. The basic principle of the osmotic technique has been described by Delage and Cui (2008). In this application, as shown in the figure, two flexible tubes were used to connect PEG solution and the base of test apparatus. Any water exchange between soil specimen and polyethylene glycol (PEG) solution was continuously monitored using an electronic balance having a precision of ±0.01 g by measuring the weight of PEG solution. The weight change rather than the absolute weight of PEG solution is of interest in this study. The presence of the two tubes, therefore, has no effect on the measurement of water exchange. It should be pointed out that these two apparatuses monitor the changes of soil water content using ballast tube and electronic balance, respectively. The accuracies of these two methods are almost the same (i.e., ±0.01 g) considering that water density is equal to 1000 kg/m3.

If necessary, both apparatuses can be used to control net stress and monitor soil deformation through a dial gauge having a precision of ±0.002 mm. According to equation [3] and experimental results reported in the literature (e.g., Ng and Pang (2000); Ng and Menzies (2007)), the equilibrium water content of unsaturated soil is dependent not only on suction but also on net stress. It is therefore that the apparatuses in Figures 2(a) and 2(b) were designed to control net stress and monitor any suction-induced volume change. In order to decouple the effect of net stress from that of suction on soil water content, no external load was applied during the tests in the current study for simplicity (the net stress resulting from top cap was negligible, less than 0.5 kPa).

Test soil and specimen preparation

The material used in this study is a yellowish brown completely decomposed granite (CDG) obtained from Hong Kong. It is classified as coarse-grained soil and silt (SW) according to the Unified Soil Classification System (ASTM 2006). The soil was pulverized using a rubber hammer and those particles larger than 2 mm in size were discarded by dry sieving. Figure 3 shows the particle size distribution of the test material determined in the sieve test (BSI 1990).

Four soil specimens, 70 mm in diameter and 20 mm in height, were statically compacted in an oedometer ring at a water content of 16.1%. After compaction, the initial dry density of two specimens was 0.71, while that of the other two specimens was 0.58. The compacted soil specimens were then submerged in de-aired water inside desiccators and subjected to a small vacuum of 2-3 kPa for about 72 h for saturation. More details of sample preparation are available from Ng and Pang (2000).

Calibration of Osmotic Pressure of PEG Solution

Figure 4 shows the relationship between the concentration of the PEG solution and osmotic pressure. In this study, the calibration was carried out using an osmotic pressure cell introduced by Ng et al. (2007) under a room temperature of 25(1℃. PEG 20000 (molecular weight value = 20000) and Spectrum 14000 semi-permeable membrane (molecular weight cut-off value = 14000) were adopted. As expected, the osmotic pressure increases with the PEG concentration. The calibration results obtained using two other methods (a psychomotor and an IC suction probe) are also shown in this figure for comparison. Imperial College (IC) suction probe is a miniature high-capacity tensiometer that is able to measure matric suction up to 1500 kPa (Ridley and Burland 1993). At PEG solution concentrations below 20%, the calibration curves obtained using the three methods are consistent. At higher PEG solution concentrations, however, the curves are noticeably different likely due to the membrane effect (Dineen and Burland 1995; Ng et al. 2007; Delage and Cui 2008). In the calibration using an osmotic pressure cell and an IC suction probe, equilibrium is achieved through water flow. Some PEG molecules may cross the semi-permeable membrane due to degradation of the membrane. The diffusion of PEG molecules reduces the gradient of PEG concentration across the membrane. When that happens, the osmotic pressure of the PEG solution is likely to be underestimated.

Test Procedures

The WRCs of two compacted specimens at different densities (ATT-Loose and ATT-Dense) were determined using the ATT. After sample preparation, these two specimens were saturated and dried to different suctions. The following suction stages were adopted: 0.1, 1, 5, 10, 50, 100, 200, 300, 400 and 450 kPa. The suctions of 0.1 and 1 kPa were controlled by placing a ballast tube below the soil specimen and atmospheric pore air pressure was maintained. The suctions ranging from 5 to 450 kPa were applied by controlling the ua and uw independently. To obtain accurate measurements, the test duration must be long enough for the specimen to reach the thermodynamic equilibrium state. Not only water content but also the volume of unsaturated soil change during the stage of suction equalization was measured. In a test using the ATT, the changes of soil water content and volume were measured using ballast tube and dial gauge respectively, providing a guideline for the termination of suction equalization stage. Suction was considered to be equalized when water flow was less than 0.01 ml and soil deformation was smaller than 0.002 mm within 24 h. These criteria were selected based on the resolution of the ballast tube and the dial gauge. For the specimens tested, the estimated relative errors of measured volumetric water content and volumetric strain were both smaller than 0.15%. Typically, it took 4-10 days for the specimens to reach equilibrium at a given suction. The soil water content at a given suction was deduced from burette readings (see Figure 3(a)).

The OMT was employed to measure the WRCs of the other two specimens (OMT-Loose and OMT-Dense). The suction stages of each test were 0.1, 1, 5, 10, 46, 93, 172, 334 and 450 kPa (the calibration curve by using osmotic pressure cell is used). It should be pointed out that suctions less than 10 kPa were controlled by placing the ballast tube below the soil specimen without adopting OMT, while the other suctions were controlled using the OMT. The same suction equalization criterion as in the ATT was adopted in the OMT. In a test using the OMT, the changes of soil water content and volume were monitored by a balance and a dial gauge respectively. When the water flow and soil deformation were less than 0.01 g and 0.002 mm within 24 h respectively, soil specimen was considered to have reached suction equalization. At the end of each suction stage, each specimen was weighed on an electric balance to determine its water content. The semi-permeable membrane was replaced after each suction stage as it is sensitive to bacteria attack. As suggested by Tarantino et al. (2000), the performance of each semi-permeable membrane was checked before and after use to ensure no leakage of PEG solution during tests.

Interpretations of experimental results

Comparison between the ATT and the OMT

Figure 5(a) compares the WRCs of CDG (silty sand) obtained by using the ATT and the OMT. At a given suction, the gravimetric water content is defined as the ratio of water mass and soil solid mass. In the ATT, the soil water content at the end of each suction stage was determined from burette readings (see Figure 2(a)). In the OMT, soil specimen at each suction stage was weighed by an electric balance to determine its water content. For both the looser specimen and the denser specimen, the WRCs obtained using these two techniques are remarkably consistent. The maximum percent difference in equilibrium w at any given suction is less than 5%. It should be pointed out that there is no data point at suctions of 200 and 400 kPa for “OMT-Loose”, since leakage of PEG solution was identified at the suction of 200 kPa during the test.

The WRCs of other coarse-grained soils (Natania sandy loam and Columbia fine sandy loam) obtained using the same two techniques are presented in Figure 5(b). The Natania sandy loam and the Columbia fine sandy loam were both tested by Zur (1966). For both types of soil, the WRCs obtained using the ATT and OMT also show good agreement over a wide range of suctions from about 50 to 2000 kPa. Given the possible existence of experimental errors, the consistency between the two techniques in determining WRCs is remarkable. For example, Figure 4 illustrates that the relationship between PEG concentration and osmotic pressure is affected by calibration method. The experimental errors associated with the calibration of the PEG solution may lead to more scattered WRCs. Note that the WRCs are presented as the relationship between suction and w rather than the volumetric water content and degree of saturation, as volume changes during Zur’s (1966) tests reported in Figure 5 (b) are not available.

As discussed in the Introduction, some researchers argued that the artificial elevation of ua in the ATT may alter the water retention ability of unsaturated soil (Or and Tuller 2002; Baker and Frydman 2009). However, it is clear from Figure 5 that WRCs obtained using the ATT and the OMT are remarkably consistent, implying that the artificial increase of ua in the ATT does not noticeably affect the equilibrium w at a given suction. Hence, the term [pic]in equation [5] could be simplified to [pic]. Equation [5] can be further reduced to the following equation:

[pic]

[6]

Figure 6 compares the WRCs obtained using the ATT and the OMT of three different fine-grained soils, including Aylon clay (Zur 1966), Wellwood clay (Williams and Shaykewich 1969) and a mixture of sand and clay (Tarantino et al. 2011). For Aylon clay and Wellwood clay, the WRCs measured using the two techniques are quite consistent. The difference is less than 5% in terms of gravimetric water content. These consistent results can be explained by equation [6], which reveals that the final w at the thermodynamic equilibrium must be the same regardless of the suction control technique used. For the mixture of sand and clay, the WRCs cover a wide range of w (i.e., from 0.1 to 0.7). At w below 0.2, WRCs obtained using the ATT and the OMT are quite consistent. At w above 0.2, however, an obvious difference in the measured WRCs is observed. The maximum difference is about 10% in terms of gravimetric water content. The observed difference at higher w is likely caused by experimental errors. As suggested by Tarantino et al. (2011), at the nearly saturated state, occluded air bubbles may exist in the unsaturated soil. These air bubbles would be compressed when ua is artificially increased in the ATT, resulting in an overestimated w at transient states (Marinho et al. 2008). When the thermodynamic equilibrium is reached, however, the equilibrium w should not be affected by the artificial elevation of ua significantly. To minimize experimental errors, the test duration should be long enough for the soil specimen to achieve the thermodynamic equilibrium (Gee et al. 2002).

Some previous researchers have proposed that pore water in fine-grained soil is held not only by capillary forces but also by adsorptive forces. The capillary component develops at cylindrical pores with various sizes, depending on the curvature of liquid-gas interface. The adsorptive component is a result of various long-term and short-term forces (e.g., electro-static forces and van der Walls forces), depending on the distance of pore water from soil particle (Philip 1977; Tuller et al. 1999; Baker and Frydman 2009). So far, the influence of the air pressurization process in the ATT on the uw is not fully understood when soil water is mainly held by the adsorptive force. Baker and Frydman (2009) therefore argued that the ATT is not valid when adsorptive force is relatively important. However, the experimental data provided in this study show that for both coarse-grained and fine-grained soils, over a wide range of w, no significant discrepancy can be observed between measured WRCs using the ATT and the OMT. The observation made in this current study seems to echo the view expressed by Gens (2010) that although it is useful to differentiate adsorptive and capillary mechanisms for conceptual understanding, the importance of the differentiation should not be overstressed. No matter whether pore water is held by capillary forces or by adsorptive forces, the energy states of different types of water should be identical at the thermodynamic equilibrium. Otherwise there would be water movement within the soil specimen, as illustrated in the section of “theoretical considerations of soil moisture transfer”.

Some researchers have postulated that pore water of unsaturated soil in the field is subjected to cavitation at suctions ranging from 100 to 400 kPa for both fine-grained and coarse-grained soils. The ATT eliminates the possibility of cavitation by transferring uw from the negative range to the positive range. On the contrary, the OMT does not have to elevate uw when controlling soil suction. The OMT is therefore considered closer to the field condition, allowing cavitation to take place (Or and Tuller 2002; Baker and Frydman 2009). This argument is, however, not supported by the newly derived theoretical equations and experimental evidence illustrated in this study. In Figures 5 and 6, the maximum matric suction (i.e., up to 2000 kPa) that was applied in the ATT and the OMT are much higher than the deduced range of cavitation pressure (i.e., 100 – 400 kPa). Within such a wide range of suctions, equilibrium w obtained using the ATT is found to be almost identical to that obtained using the OMT. Any difference associated with the suction control technique is less than 10%. The observed consistency suggests that cavitation does not affect the WRC of soil, no matter whether cavitation occurs or not in an unsaturated soil. This is because any occurrence of cavitation may alter the process of moisture exchange only (i.e., vaporization of air bubbles in pore water), but not w at the thermodynamic equilibrium.

Comparison between the OMT and the VET

To evaluate the consistency between the WRC determined using the OMT and that determined using the VET, some existing data in the literature were gathered for reanalysis. Figure 7 compares the drying WRCs of Foca7 clay measured using the OMT and the VET (Delage et al. 1998). The WRCs measured using the two techniques show smooth continuity and consistency. At a given suction, equilibrium w obtained using the OMT is almost identical to that obtained using the VET. The difference in measured water contents is not more than 5%. In fact neither WRC in this figure was obtained from a single soil specimen. Each data point was obtained from one recompacted specimen. Although all soil specimens were prepared to the same initial dry densities, the possible inconsistency in sample preparation may lead to more scattered WRCs. Tarantino et al. (2011) measured WRCs of a mixture of sand and clay using the OMT and the VET. Their experimental results are shown in Figure 7. Since the range of suctions controlled by the OMT and VET do not have any overlapping, WRCs obtained by the two techniques cannot be directly compared. However, it can be clearly seen that the WRCs measured using the two techniques show smooth continuity.

Moisture exchange between soil specimen and the solution occurs generally by liquid water transfer in the OMT and by vapour transfer in the VET. Experimental evidence suggests that these two techniques produce remarkably consistent WRCs of unsaturated soil at zero osmotic suction. This is because the energy states of pore water (liquid phase) and pore vapour (gaseous phase) should be identical at the thermodynamic equilibrium, as illustrated in Figure 1. Suction of unsaturated soil can be controlled through either the liquid phase or the gaseous phase. The change in w is independent of the form of moisture exchange (see equation [6]) as long as the thermodynamic equilibrium is achieved.

It should be pointed out that the three suction control techniques operate at different ranges (i.e., generally ATT: 0 – 1.5 MPa; OMT: 0 – 10 MPa; VET: 10 – 1000 MPa) (Ng and Menzies 2007). It is thus very difficult, if not impossible, to make direct comparison of WRCs measured at the same suction range by all three techniques, especially between the ATT and the VET. Since the range of suction controlled by the ATT and OMT has some overlapping, it is hence possible for one to make a direct comparison, such as those shown in Figures 5 and 6 for coarse-grained and fine-grained soils, respectively. Similarly, the OMT and the VET can have some overlapping of suction ranges and so they are compared in Figure 7. Using this approach, the validity and consistency of the three suction control techniques have been investigated. Based on the theoretical equations derived, it is clear that they are applicable to any soil type. This means that it is not necessary to use the same material to compare and verify the three suction control techniques.

Conclusions

Water retention curves of coarse-grained and fine-grained soil specimens obtained using the ATT, the OMT and the VET were compared and analysed over a wide range of suctions. At a given suction, the maximum difference in the equilibrium water contents is less than 10% between the ATT and OMT, whereas the maximum difference is not more than 5% between the OMT and VET. Considering possible experimental errors such as suction calibration in the OMT, analysed results reveal that the WRCs obtained from the three techniques are remarkably consistent. Based on the derived thermodynamic equations, the consistency between the experimental results obtained by different suction controlled techniques can be explained theoretically. This is because the final soil water content at the thermodynamic equilibrium state must be the same regardless of the suction control technique used, even though the techniques involve different processes of moisture exchange.

Some researchers postulated that the ATT changes the water retention ability of unsaturated soil as it elevates the pore air pressure and prevents the cavitation of pore water. This postulation is not supported by the derived theoretical equations and experimental evidence illustrated in this study. From the thermodynamic point of view, cavitation is a form of moisture exchange. No matter whether cavitation occurs or not in an unsaturated soil, it should not affect the equilibrium water content at the thermodynamic equilibrium state.

Acknowledgements

The research grant 2012CB719805 of 2012CB719800 provided by the Ministry of Science and Technology of the People's Republic of China through the National Basic Research Program (973 project) is gratefully acknowledged. In addition, the authors would like to thank the Research Grants Council of the Hong Kong Special Administrative Region (HKSAR) for providing financial support through the research grant HKUST6/CRF/12R.

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Notation

| f |free energy |

|w |gravimetric water content |

|(w |soil water density |

|[pic] |specific entropy of soil water |

|T |absolute temperature |

|[pic] |partial specific volume of soil water |

|[pic] |total stress |

|[pic] |pore air pressure |

|[pic] |net stress |

|[pic] |matric suction (potential) |

|[pic] |osmotic suction (potential) |

|[pic] |universal gas constant |

|[pic] |molecular mass of water or vapour |

|[pic] |partial vapour pressure |

|[pic] |partial pressure of water vapour equilibrium with pure |

| |free water at given pressure and temperature |

|[pic] |relative humidity |

|[pic] |total potential |

|[pic] |total potential of pore vapour |

|[pic] |total potential of pore water |

Tables and Figures

List of tables

Table 1. A summary of the test program for measuring WRCs of CDG

List of figures

Figure 1. Idealized configuration of an unsaturated soil: (a) Representative elementary volume of a soil-water-air system; (b) Air-water interface with continuous air phase; (c) Air-water interface with discrete air bubble

Figure 2. Schematic diagrams showing the apparatuses for determining WRCs using (a) the ATT; and (b) the OMT

Figure 3. Particle size distribution and index properties of CDG

Figure 4. Calibration relationship between osmotic pressure and the concentration of the PEG solution (modified from (Ng et al. 2007))

Figure 5. Comparisons of drying WRCs determined using the ATT and the OMT of coarse-grained soils: (a) new data from this study; (b) data from Zur (1966)

Figure 6. Comparisons of drying WRCs obtained using the ATT and the OMT of fine-grained soils

Figure 7. Comparisons of drying WRCs determined using the OMT and the VET

Table 1. A summary of the test program for measuring WRCs of CDG

|Specimen identity* |Suction control |Maximum suction |Initial dry |Initial void |

| |technique |applied (kPa) |density (g/cm3) |ratio |

|ATT-Loose |ATT |450 |1.53 |0.71 |

|OMT-Loose |OMT |330 |1.53 |0.71 |

|ATT-Dense |ATT |450 |1.65 |0.58 |

|OMT-Dense |OMT |450 |1.65 |0.58 |

[pic]

Figure 1. Idealized configuration of an unsaturated soil: (a) Representative elementary volume of a soil-water-air system; (b) Air-water interface with continuous air phase; (c) Air-water interface with discrete air bubble

[pic]

[pic]

Figure 2. Schematic diagrams showing the apparatuses for determining WRCs using (a) the ATT; and (b) the OMT

[pic]

Figure 3. Particle size distribution and index properties of CDG

[pic]

Figure 4. Calibration relationship between osmotic pressure and the concentration of the PEG solution (modified from (Ng et al. 2007))

[pic]

[pic]

Figure 5. Comparisons of drying WRCs determined using the ATT and the OMT of coarse-grained soils: (a) new data from this study; (b) data from Zur (1966)

[pic]

Figure 6. Comparisons of drying WRCs obtained using the ATT and the OMT of fine-grained soils

[pic]

Figure 7. Comparisons of drying WRCs determined using the OMT and the VET

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