mechanisms for soil-water retention and hysteresis at high ...soil-water content in unsaturated soil...

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Mechanisms for Soil-Water Retention and Hysteresis at High Suction Range Ning Lu, F.ASCE 1 ; and Morteza Khorshidi, S.M.ASCE 2 Abstract: Conventional conceptual mechanisms for the hysteresis of soil-water retention are the ink-bottle pore neck and the solidliquidair-contact angle. However, these mechanisms fail to explain hydraulic hysteresis for matric suction greater than 10 MPa. A conceptual model, based on hydration-water retention, is provided in this paper. Two hydration mechanisms, namely, particle-surface hydration and crystalline cation hydration, are distinguished to explain hydraulic hysteresis. The former is mainly involved in water retention by anions of oxygen and/or hydroxyls on particle surface, leading to reversible water adsorption and desorption. By contrast, cation hydration is con- trolled by both exchangeable cations and the intermolecular forces such as Coulomb attraction and London dispersion, leading to hysteretic water-retention behavior. Based on this hysteresis model, the highest total suction for any soil can be identified. From the isotherms of various soils at 25°C, it is found that the highest total suction varies from 475 to 1,180 MPa. This value depends on soil types and can be uniquely related to the BET adsorption constant, which represents the energy needed to change soil water from gas phase to liquid phase. DOI: 10 .1061/(ASCE)GT.1943-5606.0001325. © 2015 American Society of Civil Engineers. Introduction The total energy change in a unit volume of soil water relative to that of free water is called total potential and is measured in Pascal. There are a few well-known mechanisms responsible for the total potential of soil water under unsaturated conditions: gravity, osmo- sis, and matric potential. Mathematically, the total potential can be written as the sum of each component u t ¼ u g þ u o þ u m ð1Þ where u t = total potential, u g = gravitational potential (equal to the work needed to elevate a unit volume of soil water above a refer- ence point), u o = osmotic potential due to the dissolution of solutes in the soil water, and u m = matric potential. Two physical processes determine the matric potential in unsaturated soil, namely, capillar- ity and adsorption (e.g., Philip 1977; Nitao and Bear 1996; Tuller et al. 1999; Frydman and Baker 2009). Capillarity involves the in- teraction of airwater or airwatersolid. Adsorption involves the watersolid interaction. Historically, matric potential has been well captured by the YoungLaplace (YL) equation u m ¼ 2T s κ ð2Þ where T s = surface tension and κ = mean curvature of the airwater interface. The negative sign of matric potential signifies that soil- water potential is lower than that of free water, which is generally referenced to a value of zero. Because of the involvement of the airwater interface, Eq. (2) dictates that pore pressure has to be present. Therefore, the matric potential u m is commonly considered equal to u w u a , with the quantity u a u w defined as matric suction in the literature. Strictly speaking, however, the situation when matric suction is equal to u a u w is only valid in unsaturated soil above the soil-water cavitation pressure. Although the cavitation pressure of soil water is known to be lower than that of free water [approximately 100 kPa (e.g., Likos and Lu 2006)], the exact value has not been well established. Frydman and Baker (2009) suggested that the soil-water cavitation pressure is between approx- imately 100 and 400 kPa. Below the cavitation pressure, there will be no capillary water and the common definition or conception of matric suction equal to (u a u w ) is incomplete. In unsaturated soil, matric potential as low as 1.0 GPa has been measured and theorized (e.g., Croney and Coleman 1961; Richards 1965). Thus, in general, the definition of matric suction needs to include both capillarity and adsorption. Matric suction should be defined as the negative of matric potential or u m , which has been cast in the augmented YoungLaplace (AYL) equation (e.g., Philip 1977; Nitao and Bear 1996) u m ¼ 2T s κ þ AðhÞ¼ matric suction ð3Þ where h = thickness of the adsorbed water film on the particle sur- face. The second term in Eq. (3) states that the energy associated with the adsorption process is a function of the formation of the water-film thickness h. Like the first term, the second term also is generally negative, thus indicating a lower energy state for adsorbed water compared with free water. In the soil matrix, the adsorption process involves several complex intermolecular force interactions, most notably including van der Waals attraction, electric double-layer interaction, etc. (e.g., Derjaguin et al. 1987; Tuller et al. 1999). The energy-equilibrium condition between matric potential and soil-water content in unsaturated soil can be defined by the soil- water-retention curve (SWRC; e.g., Brooks and Corey 1964; van Genuchten 1980). Because the SWRC is characteristically de- pendent on a soils pore-size distribution and interface properties, it is also called the soil-water-characteristic curve (SWCC) (e.g., Fredlund and Xing 1994). Ideally, the SWRC defines a unique relation between soil-matric potential [in terms of relative humidity (RH), suction head, or matric suction] and soil-water 1 Professor, Dept. of Civil and Environmental Engineering, Colorado School of Mines, Golden, CO 80401 (corresponding author). E-mail: [email protected] 2 Graduate Student, Dept. of Civil and Environmental Engineering, Color- ado School of Mines, Golden, CO 80401. E-mail: [email protected] Note. This manuscript was submitted on September 15, 2014; approved on February 26, 2015; published online on April 9, 2015. Discussion period open until September 9, 2015; separate discussions must be submitted for individual papers. This paper is part of the Journal of Geotechnical and Geoenvironmental Engineering, © ASCE, ISSN 1090-0241/04015032 (10)/$25.00. © ASCE 04015032-1 J. Geotech. Geoenviron. Eng. J. Geotech. Geoenviron. Eng. Downloaded from ascelibrary.org by Colorado University At Boulder on 04/26/15. Copyright ASCE. For personal use only; all rights reserved.

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Page 1: Mechanisms for Soil-Water Retention and Hysteresis at High ...soil-water content in unsaturated soil can be defined by the soil-water-retention curve (SWRC; e.g., Brooks and Corey

Mechanisms for Soil-Water Retention and Hysteresis atHigh Suction Range

Ning Lu, F.ASCE1; and Morteza Khorshidi, S.M.ASCE2

Abstract: Conventional conceptual mechanisms for the hysteresis of soil-water retention are the ink-bottle pore neck and the solid–liquid–air-contact angle. However, these mechanisms fail to explain hydraulic hysteresis for matric suction greater than 10 MPa. A conceptualmodel, based on hydration-water retention, is provided in this paper. Two hydration mechanisms, namely, particle-surface hydrationand crystalline cation hydration, are distinguished to explain hydraulic hysteresis. The former is mainly involved in water retention by anionsof oxygen and/or hydroxyls on particle surface, leading to reversible water adsorption and desorption. By contrast, cation hydration is con-trolled by both exchangeable cations and the intermolecular forces such as Coulomb attraction and London dispersion, leading to hystereticwater-retention behavior. Based on this hysteresis model, the highest total suction for any soil can be identified. From the isotherms of varioussoils at 25°C, it is found that the highest total suction varies from 475 to 1,180 MPa. This value depends on soil types and can be uniquelyrelated to the BET adsorption constant, which represents the energy needed to change soil water from gas phase to liquid phase. DOI: 10.1061/(ASCE)GT.1943-5606.0001325. © 2015 American Society of Civil Engineers.

Introduction

The total energy change in a unit volume of soil water relative tothat of free water is called total potential and is measured in Pascal.There are a few well-known mechanisms responsible for the totalpotential of soil water under unsaturated conditions: gravity, osmo-sis, and matric potential. Mathematically, the total potential can bewritten as the sum of each component

ut ¼ ug þ uo þ um ð1Þwhere ut = total potential, ug = gravitational potential (equal to thework needed to elevate a unit volume of soil water above a refer-ence point), uo = osmotic potential due to the dissolution of solutesin the soil water, and um = matric potential. Two physical processesdetermine the matric potential in unsaturated soil, namely, capillar-ity and adsorption (e.g., Philip 1977; Nitao and Bear 1996; Tulleret al. 1999; Frydman and Baker 2009). Capillarity involves the in-teraction of air–water or air–water–solid. Adsorption involves thewater–solid interaction. Historically, matric potential has been wellcaptured by the Young–Laplace (YL) equation

um ¼ −2Tsκ ð2Þwhere Ts = surface tension and κ = mean curvature of the air–waterinterface. The negative sign of matric potential signifies that soil-water potential is lower than that of free water, which is generallyreferenced to a value of zero. Because of the involvement of the air–water interface, Eq. (2) dictates that pore pressure has to be present.Therefore, the matric potential um is commonly considered equal to

uw − ua, with the quantity ua − uw defined as matric suction in theliterature. Strictly speaking, however, the situation when matricsuction is equal to ua − uw is only valid in unsaturated soilabove the soil-water cavitation pressure. Although the cavitationpressure of soil water is known to be lower than that of free water[approximately −100 kPa (e.g., Likos and Lu 2006)], the exactvalue has not been well established. Frydman and Baker (2009)suggested that the soil-water cavitation pressure is between approx-imately −100 and −400 kPa. Below the cavitation pressure, therewill be no capillary water and the common definition or conceptionof matric suction equal to (ua − uw) is incomplete.

In unsaturated soil, matric potential as low as −1.0 GPa hasbeen measured and theorized (e.g., Croney and Coleman 1961;Richards 1965). Thus, in general, the definition of matric suctionneeds to include both capillarity and adsorption. Matric suctionshould be defined as the negative of matric potential or −um, whichhas been cast in the augmented Young–Laplace (AYL) equation(e.g., Philip 1977; Nitao and Bear 1996)

um ¼ −2Tsκþ AðhÞ ¼ −matric suction ð3Þ

where h = thickness of the adsorbed water film on the particle sur-face. The second term in Eq. (3) states that the energy associatedwith the adsorption process is a function of the formation of thewater-film thickness h. Like the first term, the second term alsois generally negative, thus indicating a lower energy state foradsorbed water compared with free water. In the soil matrix, theadsorption process involves several complex intermolecular forceinteractions, most notably including van der Waals attraction,electric double-layer interaction, etc. (e.g., Derjaguin et al. 1987;Tuller et al. 1999).

The energy-equilibrium condition between matric potential andsoil-water content in unsaturated soil can be defined by the soil-water-retention curve (SWRC; e.g., Brooks and Corey 1964;van Genuchten 1980). Because the SWRC is characteristically de-pendent on a soil’s pore-size distribution and interface properties, itis also called the soil-water-characteristic curve (SWCC)(e.g., Fredlund and Xing 1994). Ideally, the SWRC defines aunique relation between soil-matric potential [in terms of relativehumidity (RH), suction head, or matric suction] and soil-water

1Professor, Dept. of Civil and Environmental Engineering, ColoradoSchool of Mines, Golden, CO 80401 (corresponding author). E-mail:[email protected]

2Graduate Student, Dept. of Civil and Environmental Engineering, Color-ado School of Mines, Golden, CO 80401. E-mail: [email protected]

Note. This manuscript was submitted on September 15, 2014; approvedon February 26, 2015; published online on April 9, 2015. Discussion periodopen until September 9, 2015; separate discussions must be submitted forindividual papers. This paper is part of the Journal of Geotechnical andGeoenvironmental Engineering, © ASCE, ISSN 1090-0241/04015032(10)/$25.00.

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content (in terms of the degree of saturation, gravimetric water con-tent, or volumetric water content). The SWRC of a soil provides aquantitative way to link soil-water energy level to soil-water con-tent, as illustrated in Fig. 1. This link plays governing roles inassessing water flow (e.g., Richards 1928), moisture distribution(e.g., Gardner 1986), and effective stress variation in unsaturatedsoil (e.g., Lu and Likos 2004).

A characteristic and challenging feature of SWRC is its hyster-etic behavior. The SWRC is state or history dependent (e.g., vanGenuchten 1980; Fredlund and Xing 1994; Šimůnek et al.1999). This behavior is called hydraulic hysteresis hereafter. Thisimplies that the SWRC of a given soil is not unique, but rather de-pends on its wetting or drying state or history. Illustrated in Fig. 1are the principal drying SWRC (solid curves) and the principal wet-ting SWRC (dashed curves). The principal drying SWRC is definedhere as the trajectory local equilibrium where the water content de-creases (drying) with increasing matric suction, starting at the pointof saturation and zero matric suction. The principal wetting SWRCis defined as the trajectory for which the initial water content iszero, suction is a maximum that still is not well understood andis investigated in detail later in the paper, and therefore followsa wetting trajectory. A dominant phenomenon of SWRC hysteresisis that the water content at zero matric potential could significantlydiffer between the two principal SWRCs. Depending on soil type,the volumetric water content at zero matric suction could vary by asmuch as 35% between the two principal SWRCs (e.g., vanGenuchten 1980; Lu et al. 2013; Likos et al. 2014).

In the high total suction range (>10 MPa), some clayey soilssuch as montmorillonite typically exhibit high hydraulic hysteresis,whereas others such as kaolinite show small hydraulic hysteresis.Considering Wyoming montmorillonite for example (Fig. 2), at30% RH, the difference in the gravimetric water content betweenthe principal wetting and drying path is significant. The equilibriumwater content for the wetting is 2.2% and for the drying is 7%,leading to a difference of 4.8%. Contrastingly, for the SWRCsof Georgia kaolinite (Fig. 2), the hydraulic hysteresis is barely no-ticeable. For the context of this study, matric potential is studied at amuch lower range than that of the soil-water cavitation pressure, thegravitational potential, or the osmotic potential. Thus, the total po-tential measured as the equilibrium RH in the air phase is equal tothe adsorption component of matric potential. The AYL Eq. (3) canthus be reduced as follows:

um ¼ RT lnðRHÞvw

¼ AðhÞ ð4Þ

where R = universal gas constant, T = temperature in Kelvin, vw =molar volume of water, and RH = relative humidity.

To better capture hydraulic hysteresis, a fundamental questionhere is why some clay soil (e.g., montmorillonite) can exhibit suchsignificant hysteresis whereas some others do not (e.g., kaolinite)?The answers lie in understanding of the basic water-retention mech-anisms and how these mechanisms evolve under variably saturatedconditions. It is quite well-known that hydraulic hysteresis can beexplained by the ink-bottle pore neck mechanism (e.g., Cohan1938; De Boer et al. 1964; Morishige and Tateishi 2003) or thesolid–liquid–air-contact-angle mechanism (e.g., Johnson andDettre 1964; Joanny and De Gennes 1984; Likos and Lu 2004;

1E+00

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Soil water content(Scale depends on soil type)

Tightly adsorbed regime

Adsorbed film regime

Capillary regime

Highest soil suction

Air-entry suction

Saturated water-content adsorption

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Principal desorption SWRC

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Principal adsorption SWRC

Saturated water-content desorption

Air-expulsion suctionSoi

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Fig. 1. Soil-water-retention mechanisms for a full suction range with hysteretic behavior

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Wyoming montmorillonite

Denver claystone

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Fig. 2. Hysteresis of soil-water retention for three representative clays:Wyoming sodium montmorillonite, Denver claystone (mixed illite/smectite), and Georgia kaolinite

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Page 3: Mechanisms for Soil-Water Retention and Hysteresis at High ...soil-water content in unsaturated soil can be defined by the soil-water-retention curve (SWRC; e.g., Brooks and Corey

Gao and McCarthy 2006). Many empirical SWRC models havebeen established to capture hydraulic hysteresis (e.g., Brooksand Corey 1964; van Genuchten 1980; Kool and Parker 1987;Parker and Lenhard 1987). Because both mechanisms are estab-lished on the basis of the existence of capillary menisci or filmsof water in soil pores, they cannot be used to explain hysteresisat low matric potential where adsorption-water-retention domi-nates. For the transition of water retention between adsorptionand capillarity states, Tuller et al. (1999) provided a slit model thatcan be used to explain hysteresis due to surface adsorption, involv-ing a spontaneous capillary condensation (adsorption) or cavitation(desorption). Although many empirical SWRC models are devel-oped to cover a full range of soil suction (e.g., Kool and Parker1987; Parker and Lenhard 1987; Fredlund and Xing 1994), datafor matric suction greater than 10 MPa are rare. The validity ofthese models in the high suction range (>10 MPa) is thusuncertain.

Water-Retention Mechanisms

Previous studies on soil-water-retention mechanisms (e.g.,McQueen and Miller 1974; Lu and Likos 2004) have shown thatthere exist three water-retention regimes: capillary, adsorbed film,and tightly adsorbed, as shown in Fig. 1. Some of the boundariesamong these three regimes and their bounds are clear, whereasothers remain somewhat blurry. For the capillary regime, the high-est matric potential (or lowest matric suction) is not zero unless theinitial water content is at full saturation, as shown in Fig. 1. For asilty soil, Lu et al. (2015) showed that an unsaturated state couldexist for matric potential equal to 9.8 kPa. For finer soils, the high-est matric potential could be much higher. Although the lowest ma-tric potential where capillary water could exist is unclear, it appearsto be approximately −100 kPa, depending largely on water chem-istry and soil composition (e.g., Koorevaar et al. 1983). The highestmatric suction at which capillary water can exist is highly related tothe physical-phase transition point called cavitation or bubbling.Thermodynamically, because soil water is generally at a lower en-ergy state than free water, its cavitation pressure could be lowerthan that of free water, which is approximately −100kPa matricpotential. Frydman and Baker (2009) suggested that the soil-watercavitation pressure could be as low as −400 kPa.

Using the AYL equation and van der Waals interaction as theprincipal adsorption force, Tuller et al. (1999) suggested thatcapillary and adsorption could coexist starting at matric potentialon the order of −10 kPa. Below this value of matric potential andabove −10 MPa, soil-particle surface are likely covered by ad-sorbed water on mineral surfaces and by capillary water at concavecorners (e.g., particle contacts), shown as the adsorbed film regimein Fig. 1. Water can still move continuously in soil through filmat particle surfaces and menisci at particle contacts, but theadsorption-layer effect plays an important role in fluid flow. Theintermolecular forces such as electric double layer can operateup to a distance of 50 nm (500 Å) (Derjaguin et al. 1987), whereasvan der Waals and surface hydration forces can only be significantfor a distance less than 10 nm (100 Å) (e.g., Tuller et al. 1999). Inthis regime, both the ink-bottle and contact-angle models couldwell explain hydraulic hysteresis (e.g., Cohan 1938; De Boer et al.1964; Johnson and Dettre 1964; Joanny and De Gennes 1984; Orand Tuller 2002). Recently, a nondrainable semiopen pore modelhas been proposed by Revil and Lu (2013) to explain the waterhysteresis in the transitional process between adsorbed film andtightly adsorbed regime. This model has been implemented in aunified SWRC for clayey porous materials. Despite the excellent

fits for numerous clays, it cannot reproduce the wavy behavior ob-served in montmorillonites. The lower-limit matric potential for thisregime is where the water film becomes significantly discontinu-ous, and the precise value is yet to be established but some worksuggested it to be around −10 MPa (e.g., McQueen and Miller1974; Tuller et al. 1999; Lu and Likos 2004).

For matric potential below −10 MPa, it is likely that only ad-sorption water can exist in soil due to surface hydration and crys-talline cation hydration, shown as the tightly adsorbed regime(Fig. 1). Here water cannot flow in the liquid phase, and thus evapo-ration and condensation are the sole transport mechanisms forwater transport. Matric potential in this regime has been consideredas low as −1.0 GPa (e.g., Croney and Coleman 1961; Richards1965), although the precise limit or the lowest matric potentialhas yet to be defined. The intermolecular forces among exchange-able cations, anions at the particle surface, and water moleculescontrol matric potential in this regime. Hydraulic hysteresis in thisregime has been reported in the literature (e.g., Mooney et al. 1952;Keren and Shainberg 1975; Likos and Lu 2006). However, to date,no working hydraulic hysteresis mechanism has been proposed andtested for the tightly adsorbed regime. Because the water-retentionmechanisms in this regime are different from capillarity, thecommon hysteresis models such as ink bottle and contact angleare not applicable. The focus of this work is, therefore, (1) todevelop a conceptual hydraulic hysteresis model that can explainseveral characteristic behaviors of hydraulic hysteresis in the tightlyadsorbed water-retention regime, and (2) to explore the lowestmatric potential and its fundamental controlling factors.

Low-Matric-Potential Experimental Program

A total of 11 various natural silty and clayey soils were used. Thebasic physical and geotechnical properties of these soils are listedin Table 1. To examine the effect of different mineralogy on thehydraulic hysteresis behavior, mixtures of pure clay mineralswere also prepared. Four representative pure clays (>99% naturalsoils)—Wyoming montmorillonite, Denver montmorillonite,Denver claystone, and Georgia kaolinite—were used to preparethese mixtures. Wyoming montmorillonite (NaS) is predominantlysodium smectite (e.g., Keren and Shainberg 1975), Denver mont-morillonite (CaS) is mostly calcium smectite (Likos and Lu 2006),Denver claystone (Cs) is mainly illite/smectite mixture (Likos andLu 2006), and Georgia kaolinite (GaK) is mostly kaolinite (e.g.,Likos and Lu 2006). Natural silty soils included Bonny silt fromeastern Colorado (McCartney and Rosenberg 2011), BALT siltfrom the San Francisco area (Lu et al. 2013), Hopi silt fromnorthern Arizona (Lu et al. 2013), and Iowa silt from western Iowa(Lu et al. 2013). All specimens were prepared in oven-dried powderform. The SWRCs or isotherms in the high total suction range(7.1–440 MPa or 0.04 < RH < 0.95) for both drying (desorption)and wetting (adsorption) were measured by a vapor sorption ana-lyzer (VSA) manufactured by Decagon Devices (Likos et al. 2011).The basic working principle of VSA is to dynamically identify theequilibrium RH states by their dew points at the measured soil-water contents. The details of the working principle and testing pro-cedures of VSA can be found in Likos et al. (2011).

Hydraulic Hysteresis Mechanisms

To understand how and why hydraulic hysteresis occurs in the highmatric suction range, it is important to understand how hydrationoccurs in soils. As illustrated in Fig. 3, there are two distinct hy-dration mechanisms, namely, particle-surface hydration and cation

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hydration. Particle-surface hydration only occurs at the soil-particlesurface as depicted in Fig. 3(a). A good example is kaolinite(e.g., van Olphen 1963; Bathija et al. 2009). Because exchangeablecations such as aluminum are located inside the nonexpandablecrystalline structure, there is little change in crystalline structuredue to hydration of exchangeable cations (e.g., van Olphen 1963;Katti and Katti 2006; Bathija et al. 2009). This is because otherintermolecular forces forming the crystalline structure (one tetrahe-dron to one octahedron) are strong enough to restrain the hydrationcapability of aluminum cation. However, at the particle surface, thelast layer of oxygen and hydroxyl anions causes electric chargedipoles, attracting hydrogen anion of water toward them. There-fore, intermolecular attractive force of oxygen/hydroxyl anion andhydrogen cation governs the hydration mechanism for nonexpand-able minerals such as kaolinite. Contrastingly, in expandable min-erals such as montmorillonite shown in Fig. 3(b), hydration occurs

at the surface and around the cations (i.e., the surface hydration andcrystalline cation hydration). Here, in addition to oxygen/hydroxylanion hydration at the particle surface, the exchangeable cationssuch as sodium, calcium are able to attract water molecules intothe crystalline structure, owing to the weak restriction of the 2∶1crystalline structure (two tetrahedrons sandwich one octahedron;e.g., Katti and Katti 2006; Bathija et al. 2009). The result of ex-changeable cation hydration is the expansion of volume duringcation hydration. Note that the weak restriction of intermolecularforce would still play an important role in the hydraulic hysteresis,as described later.

Fig. 2 presents the experimental results of the SWRC under bothadsorption and desorption conditions for three representative pureminerals: Wyoming montmorillonite (bentonite), Denver claystone(mixed illite/smectite), and Georgia kaolinite (kaolinite). Severalobservations can be made. First, the maximum water content for

Table 1. Summary of Mineralogical and Engineering Properties of the Test Soils

Soil Mineralogy Clay (%) LL (%) PL (%) PI (%) USCS classification

Georgia kaolinite K 35 44 26 18 CLWyoming montmorillonite Discrete S, trace Qtz. 100 485 353 132 CHDenver bentonite Discrete S, trace K, Qtz., K-Feld 90 118 45 73 CHDenver claystone Mixed layer I/S, trace K, Qtz., Gypsum 55 44 23 21 CLBonny silt — 14 25 21 4 MLBALT silt I — 14 26 19 7 CL–MLBALT silt II — 5 28 23 5 SMHopi silt I — 3 26 19 7 SC–SMHopi silt II — 2 — — — MLIowa silt I — 10 33 24 9 MLIowa silt II — 14 31 24 7 ML

Note: K = kaolinite; K-Feld = K-Feldspar; I = illite; Qtz. = quartz; S = smectite; USCS = Unified soil classification system.

Fig. 3. Conceptual illustration of soil-hydration mechanisms: (a) particle-surface hydration; (b) particle-surface and intercrystalline cation hydration

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these three clays is vastly different. At approximately 94% RH or85-MPa matric suction, bentonite can adsorb 23% gravimetricwater content, illite/smectite mixture can adsorb 8% gravimetricwater content, but kaolinite can only absorb 5.5%. Therefore, whatmakes the adsorbed water content so different for these pure clays?Second, there exists significant hydraulic hysteresis in bentonite,but only barely noticeable hysteresis exists in kaolinite. Why is thisso? Third, the wavy pattern is exhibited in the SWRCs of montmo-rillonite and this pattern in the desorption SWRC is much morepronounced than in the adsorption SWRC in bentonite. What isthe cause for such behavior and its variation between desorptionand adsorption processes?

A conceptual hydraulic hysteresis model is constructed here toanswer the aforementioned fundamental questions. As illustrated inFig. 4(a), if a soil consists of predominantly nonexpandable min-erals such as kaolinite, the sorption process is governed by the sur-face hydration mechanism. Because the particle surface is next tothe large gas-filled pore space, there is no other energy barrier thanthe energy required for the desorption (heat of evaporation) or ad-sorption (heat of liquefaction). Heat of evaporation here refers tothe energy needed to transfer sorbed water to water vapor and heatof liquefaction refers to the energy needed to transfer water vapor tosorbed water. Therefore, the adsorption and desorption processesare mostly reversible physical process and the hydraulic hysteresisis barely noticeable, as this can be evidenced in the SWRCs Geor-gia kaolinite shown in Fig. 2.

For a soil consisting of predominantly expandable minerals suchas montmorillonite, however, the sorption process is concurrentlycontrolled by two hydration mechanisms, as illustrated in Fig. 4(b).The surface hydration mechanism, like that which occurs in non-expandable soils, would not alter the spaces within crystallinestructure as the adsorbed water occurs most formerly gas-filled porespace. This is not the case for the interlayer cation hydrationprocess. As illustrated in Fig. 4(b) during the adsorption process,the initial water content is low and the interlayer distance is small,leading to strong van der Waals attractive forces between the

interlayers. If the prevailing environment outside the interlayer con-tains water vapor of higher potential, the exchangeable cations canovercome the resistance from the strong intermolecular attractiveforces between crystalline layers to attract water around them, lead-ing to volume expansion of the crystalline structure and the hydra-tion clay with high water potential. Because of the existence of thisstrong resistance from the interlayer attractive force, cation hydra-tion is more difficult to occur than dehydration, leading to a lesswavy behavior of the adsorption SWRC (Fig. 2). During thedesorption process [Fig. 4(b)], the initial water content is highand the hydrated clay is in a higher energy state than that in thedehydrated conditions. The interlayer space is larger and the inter-layer attractive force is weaker. If the prevailing environment iswith low water potential, the water surrounding the cations willdehydrate with an additional help from the weak attractive forcebetween the interlayers, leading to larger volume reduction andmore wavy or stepwise behavior shown in the desorption SWRCof Wyoming montmorillonite (Fig. 2).

Quantifying Hydraulic Hysteresis

Two new quantities to quantify the degree of hysteresis are pro-posed here: the local and average degrees of hysteresis. As illus-trated in Fig. 5, the local degree of hysteresis Dhi evaluates thehysteresis at a point (i) in the RH or matric suction space and isdefined as

Dhi ¼wdi − wwi

wmið5Þ

where wdi = water content at point i during drying or desorption,wwi = water content at point i during wetting or adsorption, wmi =average water content at point i between the wetting and dryingstates. Based on the localDhi, the average degree of hysteresis overthe space of RH or matric suction between data point j and point kcan be defined as

(a) (b)

Fig. 4. Conceptual illustration of mechanism for hysteresis in the high suction range: (a) adsorption (wetting) path; (b) desorption (drying) path

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Dh ¼P

i¼ki¼j

wdi−wwiwmi

k − jþ 1ð6Þ

Thus, a Dh value of 0.1 indicates that the average water contentdifference between the wetting and drying SWRCs is 10% of itsmean water content. Applying this definition to the measuredSWRCs for the three clays shown in Fig. 2, it is found that the

average degree of hysteresis for Georgia kaolinite is 0.11, the aver-age degree of hysteresis for Denver claystone is 0.52, and the aver-age degree of hysteresis for Wyoming montmorillonite is 0.89.Georgia kaolinite is a 1∶1 nonswelling clay with a specific surfacearea of 22.14 m2=g (Table 2), and the particle-surface hydration isthe predominant mechanism for sorption, leading to a relativelysmall Dh value (0.11). Denver claystone is a mixed illite and smec-tite with a specific surface area of 82 m2=g (based on the BETmodel and shown in Table 2), and both particle hydration and ex-changeable cation hydration are important, leading to a moderatevalue ofDh (0.52). Wyoming montmorillonite is well-known for itsstrong swelling capability with a large specific surface area of251.03 m2=g (Table 2). Therefore, both particle-surface andcation hydration are important, leading to a relatively largeDh (approximately 0.95).

Following the conceptual model of hydraulic hysteresis shownin Figs. 3 and 4, soils with a greater expansive mass fraction shouldexhibit higherDh as the cation hydration becomes a more predomi-nant factor. This notion can be tested using well-prepared mixturesof Georgia kaolinite and Wyoming montmorillonite. Fig. 6(a)shows the measured complete loop of the SWRCs for different mix-ture ratios and Fig. 6(b) shows the calculated average degree ofhysteresis Dh for each of these mixtures. The average degree ofhysteresis Dh follows an increasing nonlinear trend as the fractionof montmorillonite increases, indicating the importance of cationhydration in hydraulic hysteresis. The computed average degreeof hysteresis for all the soils is listed in Table 2.

Quantifying the Highest Soil Suction

The current technology to control RH or total suction can only godown to RH of about 3–4%, which corresponds to total suction

Fig. 5. Definition of the degree of hydraulic hysteresis

Table 2. Calculated Parameters for Various Soils Based on the BET Model

Soil Xm (mgH2O=g soil) c Highest total suction (kPa) Specific surface area by BET (m2=g) Degree of hysteresis

100% GaK–0% NaS 6.14 5.95 4.7 × 105 22.14 0.1290% GaK–10% NaS 11.08 6.75 4.8 × 105 39.96 0.5980% GaK–20% NaS 17.87 4.55 5.2 × 105 64.44 0.7670% GaK–30% NaS 21.92 7.52 5.5 × 105 79.05 0.8260% GaK–40% NaS 26.97 9.22 5.5 × 105 97.26 0.7650% GaK–50% NaS 32.41 8.45 5.0 × 105 116.89 0.8140% GaK–60% NaS 37.37 9.34 6.1 × 105 134.79 0.8830% GaK–70% NaS 41.17 9.30 5.9 × 105 148.48 0.9620% GaK–80% NaS 51.26 6.84 5.4 × 105 184.88 0.9210% GaK–90% NaS 57.11 7.05 5.7 × 105 205.96 0.950% GaK–100% NaS 69.60 6.19 6.1 × 105 251.03 0.90100% CaS–0% Cs 109.98 20.98 9.7 × 105 396.66 0.2890% CaS–10% Cs 98.66 27.84 1.1 × 106 355.82 0.2580% CaS–20% Cs 93.43 22.64 9.7 × 105 336.95 0.2970% CaS–30% Cs 75.01 16.28 8.0 × 105 270.55 0.4160% CaS–40% Cs 67.71 13.87 7.7 × 105 244.19 0.3550% CaS–50% Cs 56.32 14.75 7.6 × 105 203.14 0.4940% CaS–60% Cs 48.49 13.83 7.1 × 105 174.90 0.4330% CaS–70% Cs 42.63 14.16 7.0 × 105 153.76 0.5220% CaS–80% Cs 34.16 15.53 7.5 × 105 123.19 0.4810% CaS–90% Cs 29.77 26.64 1.2 × 106 107.39 0.520% CaS–100% Cs 22.98 19.48 8.2 × 105 82.86 0.52Bonny silt 16.13 18.66 7.9 × 105 58.19 0.19BALT silt I 15.72 22.25 8.8 × 105 56.69 0.22BALT silt II 14.13 16.34 7.7 × 105 50.98 0.24Hopi silt I 18.20 32.73 1.1 × 106 65.63 0.14Hopi silt II 18.19 32.53 1.2 × 106 65.61 0.19Iowa silt I 17.69 13.62 7.4 × 105 63.79 0.14Iowa silt II 16.22 12.76 7.3 × 105 58.51 0.21

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from 440,000 to 480,000 kPa. Some previous studies have shownthat the highest total suction can definitely be much higher than thisrange (e.g., Campbell et al. 1993). Two fundamental questions canbe asked regarding the highest soil suction: (1) what is the highestsoil suction when the water content is decreasing to zero? and(2) what are the controls of the highest total suction for a givensoil? Understanding and quantifying the highest total suction haveboth theoretical and practical importance in developing properSWRC models and using them to solve engineering problems.Because there are accurate and continuous measurements of theSWRCs, the data can be used to project the highest total suctionalong the desorption SWRCs.

From the measured principal isotherms, the highest total suctionvalues inferred from the adsorption or desorption would bedifferent. As conceptualized in the previous section on hydration

hysteresis, because adsorption process would need to overcomemuch higher intermolecular forces than desorption process, forthe purpose of inferring surface and exchangeable cation-relatedproperties, it is more representative to use desorption or dryingSWRC (e.g., Mooney et al. 1952; Quirk 1955). The measureddesorption SWRCs of the mixtures of Denver smectite (CaS)and Denver claystone (Cs) are shown in Fig. 7(a) and the desorp-tion SWRCs of the mixtures of Wyoming smectite (NaS) and Geor-gia kaolinite (GaK) are shown in Fig. 7(b), along with the projectedhighest soil suction when the water content is zero. These figuresalso show the extrapolated trends in the drying-path SWRCs toidentify the maximum suction values. Note that some uncertaintyis encountered due to small fluctuations in the slope of the drying-path SWRCs at the maximum extent of the VSA. From such pro-jections, it is found that the highest soil suction for the calciumsmectite and illite mixtures is in the range of 700–960 MPa,and for the sodium smectite and kaolinite mixtures it is in the rangeof 475–610 MPa. As further illustrated in Fig. 8(a), the highest totalsuction for calcium smectite (CaS) is 960 MPa, the highest soil

0

5

10

15

20

25

0 20 40 60 80 100

Gra

vim

etric

wat

er c

onte

nt (

%)

Relative humidity (%)

0% GaK – 100% NaS

20% GaK – 80% NaS

40% GaK – 60% NaS

60% GaK – 40% NaS

80% GaK – 20% NaS

100% GaK – 0% NaS

R2 = 0.95

0102030405060708090100

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 60 70 80 90 100

Ave

rage

deg

ree

of h

yste

resi

s

Wyoming montmorillonite mass fraction (%)

Georgia kaolinite mass fraction (%)

(a)

(b)

Fig. 6. Wetting and drying isotherms of mixtures of Wyomingmontmorillonite and Georgia kaolinite: (a) isotherms; (b) the degreeof hysteresis for different mixtures

1.0E+3

1.0E+4

1.0E+5

1.0E+6

1.0E+7

0 5 10 15 20 25 30

Tot

al s

uctio

n, k

Pa

Gravimetric water content (%)

100% CaS – 0% Cs

70% CaS – 30% Cs

30% CaS – 70% Cs

0% CaS – 100% Cs

(a)

1.0E+3

1.0E+4

1.0E+5

1.0E+6

0 5 10 15 20 25

Tot

al s

uctio

n, k

Pa

Gravimetric water content (%)

0% GaK – 100% NaS

30% GaK – 70% NaS

70% GaK – 30% NaS

100% GaK – 0% NaS

(b)

Fig. 7. Total suctions at zero water content from desorption isothermfor (a) mixtures of Denver montmorillonite and Denver claystone;(b) mixtures of George kaolinite and Wyoming montmorillonite

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suction for the illite and smectite mixture (Cs) is 810 MPa, and thehighest soil suctions for the mixtures are roughly between the twoend members. For GaK and NaS mixtures, the highest soil suctionsare between 610 MPa (the highest soil suction for NaS) and475 MPa (the highest soil suction for GaK).

In the literature, it has been considered that the highest total suc-tion is a unique value independent of soil types, with some authorsreporting 1.0 GPa (e.g., Croney and Coleman 1961; Richards 1965;Fredlund and Xing 1994), some 900 MPa (Cui et al. 2008), andsome defined as the suction at the oven-dry conditions to be106 J=kg (Ross et al. 1991; Campbell et al. 1993). The highest soilsuction has been used as the upper bound of the total suction ormatric suction in some SWRC models (e.g., Campbell et al.1993; Fredlund and Xing 1994). It is shown experimentally herethat this is not the case, as the variability of the highest total suction

is quite high (475–960 MPa) and less than 1 GPa. As illustrated inthe conceptual soil-water-retention and hydration mechanisms inFigs. 3 and 4, the fundamental controls on the highest soil suctiondepend on the type of hydration involved. The type of hydration isgoverned by the interplay of intermolecular forces among cationhydration, interlayer attractive forces, surface anions, and watermolecules. To provide further experimental evidence on thedependency of the highest total suction on soil types, nine differentnatural soils are used and the results of the highest total suction forthese soils are shown in Fig. 8(b). To test the repeatability and reli-ability of the VSA technique for SWRC and the projection strategyof extrapolation by the tangent line at the highest measured suctionpoint for the highest total suction, some of these soils are collectedfrom the same geographic locations. These soils are also from geo-graphically quite different locations in the United States (Iowa,Colorado, Arizona, and California). The highest soil suction forthese soils ranges from 730 to 1.18 GPa, with only soils fromone source (two specimens of Hopi silts from northern Arizona)exceeding 1.0 GPa.

4.0E+5

6.0E+5

8.0E+5

1.0E+6

1.2E+6

1.4E+6

1.6E+6

100%

CaS

– 0

% C

s

70%

CaS

– 3

0% C

s

30%

CaS

– 7

0% C

s

0% C

aS –

100

% C

s

100%

GaK

– 0

% N

aS

70%

GaK

– 3

0% N

aS

30%

GaK

– 7

0% N

aS

0% G

aK –

100

% N

aS

Tota

l suc

tion,

kP

a

(a)

4.0E+5

6.0E+5

8.0E+5

1.0E+6

1.2E+6

1.4E+6

1.6E+6

Den

ver

clay

ston

e

Den

ver

bent

onite

Bon

ny s

ilt

BA

LT s

ilt I

BA

LT s

ilt II

Hop

i silt

I

Hop

i silt

II

Iow

a si

lt I

Iow

a si

lt II

Tota

l suc

tion,

kP

a

(b)

Fig. 8. Highest total suction for mixtures of (a) Denver montmorillo-nite and Denver claystone, and Wyoming montmorillonite and Georgiakaolinite; (b) different soils

4.0E+5

6.0E+5

8.0E+5

1.0E+6

1.2E+6

1.4E+6

1.6E+6

4.0E+5 6.0E+5 8.0E+5 1.0E+6 1.2E+6 1.4E+6 1.6E+6

Mea

sure

d hi

ghes

t tot

al s

uctio

n, k

Pa

Predicted highest total suction, kPa

0% CaS – 100% Cs10% CaS – 90% Cs20% CaS – 80% Cs30% CaS – 70% Cs40% CaS – 60% Cs50% CaS – 50% Cs60% CaS – 40% Cs70% CaS – 30% Cs80% CaS – 20% Cs90% CaS – 10% Cs100% CaS – 0% Cs

R2=0.95

(a)

(b)

4.0E+5

6.0E+5

8.0E+5

1.0E+6

1.2E+6

1.4E+6

1.6E+6

4.0E+5 6.0E+5 8.0E+5 1.0E+6 1.2E+6 1.4E+6 1.6E+6

Mea

sure

d hi

ghes

t tot

al s

uctio

n, k

Pa

Predicted highest total suction, kPa

Denver claystone

Denver bentonite

Bonny silt

BALT silt I

BALT silt II

Hopi silt I

Hopi silt II

Iowa silt I

Iowa silt II

R 2=0.92

Fig. 9. Correlation between the measured and predicted highest soilsuction for (a) mixtures of Denver montmorillonite and Denverclaystone; (b) different soils

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To examine the aforementioned fundamental controls of thehighest soil suction by the SWRC models, the well-known BETmodel (Brunauer et al. 1938) is used. The BET equation for theSWRC or isotherm quantifies the relation between the gravimetricwater content w and the prevailing RH

RHwð1 − RHÞ ¼

1

Xmcþ RHðc − 1Þ

Xmcð7Þ

where Xm = gravimetric water content when the first layer of sorp-tion is completed; and c = BET equilibrium constant of the soil thatcan be defined as

c ¼ exp

�E1 − EL

RT

�ð8Þ

where E1 = heat of adsorption for the first layer; and EL = heat ofadsorption for the second and higher layers and is equal to the heatof liquefaction. The difference between the two energy parametersin the exponent is the energy needed to transfer from adsorbed gasto liquid. For this reason, the correlation between the highest soilsuction and the BET constant needs to be identified.

Using Eq. (7) and the drying SWRCs of the soils listedin Tables 1 and 2, a least square fit is conducted to obtain theBET constant c and the water content at the completion of thefirst-layer sorption Xm for each of these soils. Typically, the iso-therm data for the RH less than 40% are used for the fitting. Com-paring the c values with the highest matric suction values shown inTable 2, the following simple relation for the highest total suctionumax is found:

umax ¼RT3vw

c ð9Þ

The performance of the Eq. (9) can be assessed in Fig. 9, whereFig. 9(a) shows the comparison between the measured highest totalsuction and the predicted highest soil suction by Eq. (9) for mix-tures of Denver smectite and Denver claystone, and Fig. 9(b) showsthe comparison for different natural soils. Good correlations arefound between the measured and predicted highest soil suction withthe coefficient of determination greater than or equal to 0.92.

Summary and Conclusions

The water retention in soil can be considered in three distinct re-gimes, starting from full saturation to oven dry: capillary, adsorbedfilm, and tightly adsorbed. Matric suction or matric potential in allof these three regimes can be unified and expressed by the AYLequation. In the capillary regime, matric suction varies from ap-proximately negative tens of kPa to several hundreds of kPa wherethe adsorption potential is zero and matric suction is deduced to thecommonly used definition, that is, the difference between the poreair and pore water pressure. Here the AYL equation is deduced tothe classical YL equation and the SWRC is greatly controlled bythe pore-size distribution and less so by soil mineralogy. In the ad-sorbed film regime, capillary and adsorbed water coexist and bothcapillarity and adsorption contribute to matric suction as describedby the AYL equation. Here matric suction could range from 100 to10 MPa and the tradition pressure concept may not be physicallyvalid. The SWRC in this regime is controlled by both soil miner-alogy and particle-size distribution. For matric suction greater than10 MPa, all soil water is in the form of tightly adsorbed water andthe SWRC is solely controlled by soil mineralogy. The upper limitof this regime is controlled by soil mineralogy, and is not a uniquenumber. This is experimentally shown so in this study.

A universal and objective way to quantify the degree of hy-draulic hysteresis is also mathematically defined and used to assessthe hydraulic hysteresis for the SWRCs of various soils. It is foundthat for soils with dominant particle surface hydration mechanismsuch as Georgia kaolinite, the average degree of hysteresis is 0.11or 11% between the principal wetting and drying SWRCs. By con-trast, for soils such as Wyoming montmorillonite, the hydration ismainly by interlayer exchangeable cation hydration mechanism andthe average degree of hysteresis between the two principal SWRCscould be as high as 0.95 or 95%.

Conventional conceptual mechanisms for the hysteresis of soil-water retention are the ink-bottle pore neck and solid–liquid–air-contact angle. These mechanisms fail to explain hydraulichysteresis for matric suction greater than 10 MPa. A conceptualmodel, based on hydration-water retention, is provided. Here twohydration mechanisms are distinguished to explain hydraulic hys-teresis: particle-surface hydration and crystalline or interlayer cat-ion hydration. The former is mainly involved in water retention byanions of oxygen and/or hydroxyls of particle surface, leading tomostly reversible water adsorption and desorption. By contrast,interlayer cation hydration is not only controlled by the exchange-able cations but also affected by the intermolecular forces such asCoulomb attraction and London dispersion, leading to the hyster-etic and wavy water-retention behavior.

To examine the conceptual model, different soils and theirmixtures are used and their SWRCs are obtained at the high totalsuction range under both wetting and drying conditions. The con-ceptual hysteresis model can successfully explain three character-istics in the fundamental behavior of soils in the high suction range:(1) why there exists little hydraulic hysteresis in nonswelling soilsuch as kaolinite, whereas there exists strong hysteresis in swellingsoil in which interlayer cation hydration dominates soil-water-retention behavior; (2) why there exists strong wavy behavior indesorption and much less so in adsorption SWRC for expansiveclays; and (3) why the highest total suction is not a unique valuebut depends on soil mineralogy.

Based on this hysteresis model, the highest total suction for anysoil can be experimentally identified and theoretically interpreted.From the isotherms of various soils, it is found that the highest totalsuction varies from 475 to 1,180 MPa, it depends on soil mineral-ogy, and it can be uniquely related to the BET sorption constant c,which represents the energy needed to change water from gas phaseto liquid phase. An important implication of this unique relation forthe highest total suction is that the SWRC or SWCC models shouldnot set the upper bound to a fixed value. The unique relation for thehighest soil suction discovered here should provide an importantbenchmark for developing new accurate SWR models in the highsuction range.

Acknowledgments

This research is funded by a grant from the National Science Foun-dation (NSF CMMI 1233063).

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