rheological properties of wet soils and clays under steady

8/13/2019 Rheological Properties of Wet Soils and Clays Under Steady

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Rheological Properties of Wet Soils and Clays under Steadyand Oscillatory Stresses

Teamrat A. Ghezzehei and Dani Or*

ABSTRACT In engineering soil mechanics, it is very common todetermine stressstrain relationship of soils (under equi-Tilled agricultural soils are in a constant state of change inducedlibrium conditions) empirically from simultaneous mea-byvariations in soil strengthdue towetting anddryingand compaction

by farm implements. Changes in soil structure affect many hydraulic surements of stress and strain, assuming a certain rheo-and transport properties; hence their quantification is critical for accu- logical model applies to the particular soil deformation.rate hydrological and environmental modeling. This study highlights For example, theory of elasticity is used in Terzaghisthe role of soil rheology in determining time-dependent stressstrain theory of one-dimensional soil consolidation (Taylor,relationships that are essential for prediction and analysis of structural 1948); and the theory of viscoelasticity is applied forchanges in soils. The primary objectives of this study were (i) to study of creep phenomena in soils (McMurdie, 1963).extend a previously proposed aggregate-pair model to prediction of

Although very few stressstrain measurements havecompaction under external steady or transient stresses and (ii) to

been carried out at the so-called tillage range in agricul-provide experimentally determined rheological information for thetural soils, because of the inherent difficulty of obtainingabove models. Rheological properties of soils and clay minerals weremeasurements under field conditions (Keller, 1970), themeasured with a rotational rheometer with parallel-plate sensors.

These measurements,under controlledsteady shear stress application, above empirical methods are often applied for agricul-have shown that wet soils have viscoplastic behavior with well-defined tural soil mechanics with little modification (Koolen,yield stress and nearly constant plastic viscosity. In contrast, rapid 1983). The use of empirical stressstrain relationshipstransient loading (e.g., passage of a tractor) is often too short for for study of soil deformation, especially for agriculturalcomplete viscous dissipation of applied stress, resulting in an elastic soil mechanics, has several weaknesses. Primarily, the(recoverable) component of deformation (viscoelastic behavior). method is not useful for a priori prediction of magnitudeMeasured viscoelastic properties were expressed by complex viscosity

and mode of strain (Hillel, 1998). Secondly, the ap-and shear modulus whose components denote viscous energy dissipa-

proach is based on equilibrium state stressstrain rela-tion, and energy storage (elastic). Results show that for low watertions, while deformations in agricultural soils rarelycontents and fast loading (tractor speed), the elastic component ofreach equilibrium (Or, 1996), especially when transientdeformation increases, whereas with higher water contents, viscosity

and shear modulus decrease. Steady and oscillatory stress application and rapid loading by agricultural machinery is consid-to an aggregate pair model illustrates potential use of rheological ered. Finally, the method is applicable only for describ-properties towards obtaining predictions of strains in soils. ingbulkvolume changes, but it cannot be used to explain

pore-scale evolutionary processes that are very crucialin flow and transport processes.

S

oil compaction by externally applied stresses and A viable alternative approach that circumvents theseinternal capillary tension results in soil structure limitations is to develop pore-scale mechanistic models

modifications that are of wide interest because of the that are coupled with intrinsic soil rheological proper-influence of such changes on transport processes, root ties. Recently, we proposed energy balancebased for-growth, and soil mechanical strength. Soil deformation mulations that provide predictions of soil deformationinvolves time-dependent reorientation and displace- rates, at pore and bulk scales, induced by capillary forcesment of constituents at microscopic and macroscopic of water by considering nonequilibrium stressstrainlevels, and it is commonly characterized by the relative rate relations (Ghezzehei and Or, 2000; Or et al., 2000).deformation or strain. For agricultural and environmen- These models address soil deformation induced by inter-tal applications soil strain at pore scale is important nal capillary forces, where there is no particularly fa-[e.g., in the study of evolution of hydraulic properties vored stress direction. This omnidirectional stress is(Or et al., 2000)], while for geotechnical applications, quite different from external stresses that possess strongoverall strain and strength properties of the bulk soil directionality; usually vertical stresses are higher thanare required. Fundamental concepts of soil rheology, horizontal stresses. Moreover, stresses induced by mov-which describe the flow behavior of wet soils, are useful ing farm implements (e.g., tractor passage) have shortfor mathematical description of the time-dependent loading duration. As this study shows, there is a funda-stressstrain relationships under various loading condi- mental difference between soil deformation by farm im-tions (Mitchell, 1993; Vyalov, 1986). plements (oscillatory stress) and capillary induced

Soil strain is relatively large and nonuniformly distrib- strains (steady stress) rooted in the inherent soil proper-uted in space and time and is not easily predictable from ties, manifested in the form of frequency-dependenta given form and magnitude of stress (Hillel, 1998). rheological properties. Hence, the motivation for this

study was twofold: (i) to provide independently mea-Teamrat A. Ghezzehei and Dani Or, Dep. of Plants, Soils and Biome- sured rheological properties for the capillary-inducedteorology, Utah State Univ., Logan, UT 84322. Received 27 July 2000.*Corresponding author ([email protected]).

Abbreviations:CR, controlled shear rate; CS, controlled stress; OSC,sinusoidal (oscillatory) shear stress.Published in Soil Sci. Soc. Am. J. 65:624637 (2001).

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GHEZZEHEI & OR: RHEOLOGICAL PROPERTIES OF WET SOILS AND CLAYS 625

deformation models and (ii) to provide insights intostrain rates in externally loaded soils and the requiredrheological properties. Special emphasis is given to tran-sient loading by farm implements that involve morecomplex types of strains.

The primary objective of this study was characteriza-tion of soil rheological properties at several water con-

tent values and different stress conditions. The specificobjectives were (i) to provide rheological properties ofselected soils and clay minerals, and measurement guide-lines for soil characterization; (ii) to qualitatively corre-late the observed properties with microscopic propertiesof claywater systems; (iii) to demonstrate the potentialapplications of soil rheological data for prediction ofstrain conditions under external stresses (e.g., passageof farm implements).

THEORY

The theoretical section is organized as follows: first, basicrheological concepts are reviewed briefly, with special empha-sis on stressstrain conditionsthat exist in soils.Physico-chemi-

cal aspects of soil rheology at microscopic and molecular scalesare discussed subsequently. Finally, a simplified model of soilaggregates, used to demonstrate potential applications of therheological properties under different stress conditions, is pre-sented.

Rheological ConceptsFig. 1. Rheological curves of ideal materials: (a) Stressstrain rela-

tions of ideal Hookean solid and flow curve of ideal plastic materialClassical mechanics deals with idealized objects, for exam-with distinct yield stress (y ). Spring and slider are mechanicalple, perfect solids, fluids, or plastics. An ideal Hookean (elas-analogs of ideal elastic and plastic solids, respectively. (b) Flowtic) solid deforms instantaneously when subjected to stress,curves of idealNewtonian fluidand Bingham viscoplastic body, and

and the energy invested in deforming the solid is fully stored.their respective mechanical analogs, dashpot and dashpot-slider.

When the stress is removed, the original shape is restored(deformation vanishes), while the energy is recovered in full. In Fig. 1a, an ideal plastic material is shown by the curveThe extent of elastic strain is linearly related to the stress of zero-strain below the yield stress (y ) and vertical line (con-

applied stant stress) beyond yielding, and the slider is an ideal mechan-ical analog of perfect plastic material. G [1]

Many real bodies, including soil, exhibit mixed behaviorswhere is tangential shearing stress, is shear strain, and the of elasticity, viscosity,and plasticity. Forbetterphysical under-constant of proportionality,G, is shear modulus. The stress standing of the equations of state of real materials, it is some-strain relationship of an ideal elastic is shown graphically in times easier to visualize them in terms of combinations ofFig. 1a, by the straight line passing through the origin and, analogous mechanical systems (e.g., springs, dashpots, or slid-mechanically, is analogous to a perfect spring. ers). In the following subsections, soil rheological properties

An ideal Newtonian fluid is characterized by the resistance under two important deformation processes and their mechan-of itselemental particlesto motionwith respect to oneanother, ical analogs will be discussed.and the energy invested in deforming viscous material is dissi-pated entirely. Newtonian flow is induced by any shear stress Soil Deformation under Steady State Stressgreater than zero,and progressesat constant velocity (shearing

Reduction of porosity in wet soil aggregates subjected torate), d/dt constant, which is directly proportional tosteady-state stresses involves welding at interaggregate contactthe stress (). The rheological equation of state of a Newtonianarea (Kwaad and Mucher, 1994). Micrographic study of aggre-

fluid is given by gate welding process indicates that flow of soil is initiated only [2] when the stress acting upon the interaggregate contact exceeds

a critical yielding point (Day and Holmgren, 1952; McMurdiewhere the constant of proportionality,, is coefficient of vis-and Day, 1958). Beyond the yield stress, soil aggregates flowcosity. In Fig. 1b, the straight line passing through the originin a manner similar to viscous material at a rate proportionalrepresents the behavior of ideal viscous fluid, and its mechani-to the stress in excess of the yield stress (Ghavami et al.,cal analog is a perfect dashpot.1974; Keller, 1970). This combination of plastic and viscousIn a perfectly plastic body, deformation can be initiatedbehaviors is commonly referred to as viscoplasticity.only when the tangential (shear) stress attains a critical stress

Upon close examination of experimental stressstrain ratevalue y, called the yield stress. The yield stress is also therelationships of several soils, Vyalov (1986) concluded that amaximum stress that can be set in a prefect plastic material.simple linear model of viscoplasticity,the Bingham rheologicalThe equation of state for perfectly plastic material is given bymodel, can describe soil deformation under steady-state stress.The equations of flow of Bingham body are given bymax y constant [3]


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626 SOIL SCI. SOC. AM. J., VOL. 65, MAYJUNE 2001

0, y [4a] osin(t ) [6a]

d

dt o cos(t ) [6b]

y

p, y [4b]

The coefficient of proportionality,p, is analogous to New- where o, is the strain amplitude. The phase shift angle, ,tonian viscosity and is commonly referred to as the coefficient sometimes called the mechanical loss angle (Dealy, 1982), isof plastic viscosity (Vyalov, 1986). Graphical representation described shortly. The time axis is scaled by the frequency

of Bingham viscoplastic material is shown in Fig. 1b by the (angular velocity) of loading, and is expressed in units of de-shifted viscous curve. Mechanical analog of Bingham visco- greesplastic material is the parallel arrangement of dashpot andslider. (t)

180

[7]

Soil Deformation under Cyclic StressesRecall from Eq. [1] and Fig. 1a that shearing stress appliedupon purely elastic material results in proportional and instan-Unlike steady-state stress, transient stresses (e.g., passagetaneous strain. Therefore, if ideal elastic material is testedof farm implement) act upon soil for a short duration. Forunder oscillatory stress, the stress function Eq. [5] and theexample, rear wheels of a typical tractor operating at 2.2 mstrain function Eq. [6a] must be exactly in phase; hence, thes1 (5 mph) apply stress on the soil bed for 0.2 s (Harris,phase shift angle in Eq. [6a] and [6b] vanishes ( 0) (thin1971). The amount of input energy that dissipates by viscousline in Fig. 3b). For purely viscous materials, Eq. [2] statesflow of soil during the short time of stress application is con-that the shearing stress is linearly related to the shearing rate.strained; thus, part of the energy input is stored in elasticThen, if the material tested under oscillatory stress is an idealstrain. The viscous component of the strain is permanent,viscous material, the oscillatory stress function Eq. [5] and thewhile the elastic part is restored when the stress is removed

strain rate response Eq. [6b] must be in phase, while the stress(after the tractor passes). The partitioning of strain to recover-and strain are out of phase with 90 (dashed line in Fig.able and nonrecoverable components during transient loading3b). In other words, the time dependence of viscous shearingof loessal Luvisol by tractor is illustrated in Fig. 2 (Horn andresults in peak strain delayed by one-half cycle from theBaumgartl, 1999). The curves represent location of a referencepeak stress.point, initially located at 100 mm below ground surface. The

Many natural materials, including soil, exhibit intermediateoverall strain path, including viscous and elastic deformations,behavior between ideal elastic solids and ideal viscous fluidsis represented by the position of the observation point. The(dotted line in Fig. 3b), and the phase shift angle is intermedi-strain reaches maximum while the tractor weight is still acting.ate (0 90). It is more convenient and compact toAfter the tractor has passed, however, strain that involvedrepresent the complementary viscous and elastic propertiesviscous flow is sustained permanently, while the remaining(viscoelastic) in a complex plane system, as shown below,portion of strain that involved elastic energy storage is recov-

The stress and strain amplitudes (o and o in Eq. [5] andered. Note also that similar trends of deformation occur later-[6a], respectively) can be related by an equation of elasticityally at lower magnitude.similar to Eq. [1]We now consider deformation of ideal materials under cy-

clic stresses. Experimental setup that can be used to conducto G*o [8]

such measurements will be discussed in the Materials andMethods section. Consider a homogeneous sample that is sub- where G* [(G)2 (iG)2] is a complex shear modulus.jected to sinusoidal shearing stress () of angular velocity The real component of the modulus G G*cos() indicates2f(where f is frequency), and stress amplitude o (Fig. 3a),

osin(t) [5]

The oscillatory shearing stress induces periodic shear(strain) and shear rate, which can be written in general formas

Fig. 3. (a) Stress function and (b) strain responses of ideal elasticFig. 2. The loci of observation points, initially 100 mm below theground surface, during passage of the front and rear wheels of a (solid), ideal viscous (dashed), and real viscoelastic (dotted) ma-

terials.tractor. Adapted from Horn and Baungartl (1999).


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storage (elastic) modulus that is related to the recoverable subsequent brief review of microscopic shearing mechanismsin clay systems will aid in elucidation of macroscopic rheologi-deformation. The imaginary component G G*sin() de-

notes the loss (viscous) modulus representing the irrecover- cal properties measured in this study.Clay minerals are generally classified into two major groupsable deformation. Note that for perfectly elastic material (

0), the imaginary component (viscous) vanishes, and the stor- based on the arrangement of their basic unit layers (platelets):expansive and nonexpansive (Chenu and Tessier, 1995). Theage (elastic) modulus equals the complex shear modulus. The

terms loss and storage refer to the fact that energy input for interlayer spacesof expansiveclays(e.g., smectitesand vermic-ulites) can be hydrated; hence, the thickness of these claydeformation dissipates if it is viscous and is stored if it is elastic.

Similarly, the stress and strain rate amplitudes (oand o minerals is dependent on water content. The extent of permis-sible expansion is mainly determined by the charge densityin Eq. [5] and [6b], respectively) can be related by an equation

of viscosity similar to Eq. [2] of the dominant adsorbed cations. In smectites, containing Mgand Ca as exchangeable cations, or containing Na at high salt

o *o [9] concentration, the unit clay sheets are closely spaced due tostrong electrostatic attraction between the cations and thewhere * [()2 (i)2] is complex viscosity. The imagi-negatively charged clay surfaces (Keren and Shainberg, 1984).nary component *sin() G/indicates the loss (dy-As a result, these smectites have interlayer hydration limitednamic) viscosity and the real component *cos() to one to three molecular layers of water, and most of theG/denotes storage (elastic) viscosity. For perfectly viscouswater contained in the soil is located between clay clustersmaterial ( 90) the real component (storage) vanishes, and(as compared with the interlayer space) (Chenu and Tessier,the complex viscosity equals the loss viscosity. In summary,1995). The close fitting of the water molecules in the interlayerthe complex viscosity,*, (or complex modulusG*) containsspace results in relatively stable structure of the quasi-crystals.the information necessary for the description of both viscous

In smectites containing Na, Li, or K in the exchange sites atand elastic strains, and the relative contribution of each islow salt concentration, the adsorbed ions have large hydrationrepresented by the phase shift angle ().

radii and form a wide diffused double layer; thus the electro-static attraction between clay platelets are weak, forming losePhysico-Chemical Aspects Affecting Soil Rheology and dispersed tactoids. The interlayer spaces are very expan-

sive and accommodate a large proportion of the total waterAlmost all soil flow and deformation processes evolve fromcontained in these clays.molecular or microscopic interactions (Chenu and Tessier,

The interlayer spaces of nonexpansive clay minerals (e.g.,1995; Collins and McGown, 1974). Consequently, mechanicalkaolinite) are anhydrous. Because of the strong interlayerprocesses that govern macroscopic soil rheological propertiesattraction, these minerals have discrete, coarse, and plate-are determined by arrangement of constituent componentslike particles (domains) with very high rigidity. The overalland the nature and magnitude of bonds among them (Vyalov,physical stability of these clays is very low because of small1986). To facilitate a theoretical discussion pertaining to physi-interparticle (interdomain) contact areas resulting from thecal and chemical aspects of soil rheology at microscopic scale,rigidity of the particles (Ben-Ohoud and Damme, 1990).we usea generalized schematicmodel of a natural soil element,

The microrheological properties of claywater systems areas shown in Fig. 4 (Hueckel, 1992). Assemblage of clay plate-primarily determined by the water content because the weaklets, due to several forms of adhesive forces, creates clay do-cohesive forces between water molecules result in yieldingmains (kaolinite) and quasi-crystals (smectite). The domainsto applied stress prior to clay clusters that is, water reduces

and quasi-crystals along with silt and fine sand grains, in turn, solidsolid friction by actingas a lubricant. A number of exper-form microaggregates with an essentially regular network ofimental and theoretical studies have shown that water mole-micropores (intraaggregate pores) filled with liquid water and/cules held close to clay surfaces are subject to short- andor water vapor (Stepkowska, 1990). Because the silt grainslong-range forces that result in strong ordering and increasedare mostly interconnected by clay domains and quasi-crystalsviscosity of the molecules relative to their counterparts in bulk(as depicted in Fig. 4) (Collins and McGown, 1974; Dudley,state (Israelachvili and Adams, 1978; Schoen et al., 1987).1970; Mitchell, 1956), mechanical graingrain interactions areThese modifications of liquid behavior are the most likelyalso governed by properties of the clay bridges. The foregoingcandidates to describe the macroscopic viscoplastic and visco-suggests that soil deformation properties are primarily deter-elastic properties of claywater systems.mined by shearing properties of the clay fraction. Hence, the

In experiments by Israelachvili and Adams (1978) two micasurfaces were sheared under different normal forces and withdifferent velocities for a variable number of molecular layersof water. These experiments showed that sliding is initiatedafter a critical shear stress (yield stress) is reached, similar toplastic materials (see discussions in previous subsection). For

a given liquid and clay surface, the yield stress decreased withthe number of molecular layers, for example, two molecularlayers of water require twice as much stress as required forthree molecular layers to shear. Similar trends were reportedusing water (Kemper, 1964) and nonaqueous liquids (Gee etal., 1990). Numerical simulations of fluids contained betweenparallel plates, carried out by means of Monte-Carlo and mo-lecular dynamics method (Schoen et al., 1987, 1989; Skipperet al., 1991), showed an abrupt transition of interlayer waterfrom liquid- to solid-type flow by formation of block-like or-dered structures when the thickness was reduced to less thansix molecular layers. Values of yield stress of bound waterFig. 4. Schematic model of claysiltwater system depicting different

formsof porespaces andpore water. Adapted fromHueckel(1992). from the simulations were similar to experimental.


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there is no proof that the theory of rate processes describessoil deformation correctly, parts of the theory were success-fully tested experimentally (e.g., Feda, 1989; Mitchell et al.,1969).

Simplified Soil Aggregate Model

One of the potential applications of soil rheological mea-

surements is prediction of soil strain deforming under appliedsteady or cyclic stresses. For illustrative purposes we use asimple model of a pair of equal-sized, spherical aggregates(radius a ), in contact as shown in Fig. 5. The objective ofthe modeling framework is to predict strain induced to theaggregate pair when subjected to either internal capillaryforces or external stresses. The core of the model is equatingthe net rate of work done by the applied forces to the rate ofenergy dissipation due to coalescence of wet aggregates. Themain factors determining the magnitude and rate of strain arethe rheological properties of the soil and the stress conditions.Details of the model and its underlying assumptions for aggre-gate coalescence under quasi-steady capillary forces (or chang-ing at a slow rate compared with the deformation rate) aregiven by (Ghezzehei and Or,2000). In the following, extension

of the model for aggregate deformation under external steadyand oscillatory stresses will be considered.

Aggregate Coalescence under Steady External Force

The mechanisms governing deformation underexternal andFig. 5. Aggregate pair model for aggregate coalescence: (a) variableinternal steady stresses are identical. The major differencedefinition in viscoplastically strained aggregate pair, (b) aggregatebetween the two modes of stresses is steady capillary forcespair model before strain, (c) aggregate pair model under Hertzianacting upon aggregate pair induce equal stresses in all contactsstrain, and(d) aggregate pairmodel under modified Hertzianstrain.regardless of their spatial orientation, provided the aggregateshave identical geometry and are at equal capillary pressure

In summary, adsorption of water molecules onto internal (Ghezzehei and Or, 2000), while external steady stresses haveand external clay surfaces of clay minerals induces ordered strong dependence on orientation.molecular layering and significant resistance to shearing. The Consider an aggregate pair subjected to a constant externalvery slow flow (time-dependent) of adsorbed water molecules forceF, and the aggregates coalesce at their contact while theresults in time-dependent viscoelasticbehavior of clays at mac- material forming the contact region flows outward. As a result,roscopic scale (Hueckel, 1992). Finite shearing of these or-

the centers of the aggregates move towards the contact planedered molecules occurs only when the stress exceeds a yield by h, and the axial strain is given by h/a. The radiuspoint, beyond which the water layers are sheared at higher (x ) of the resulting circular contact area, at time t, can beviscosity that decreases exponentially away from the clay sur- approximated byfaces (Low, 1976; Or and Wraith, 1999) and approaches the

x(t)2 2a2(t) [10]properties of the bulk water at about seven to ten molecularlayers (Hueckel, 1992). Then, the axial stress () acting upon the contact area is

Apart from the microscopic flow processes of adsorbedwater molecules, soil rheological properties at macroscopic

(t) F

2 a2 (t)[11]scale are further influenced by relative arrangement of clay

clusters and silt grains. As the results of this study show, theBecause the stress changes at a relatively slow rate, comparedeffect of solidsolid interactions becomes more pronouncedto the strain rate, we assume the deformation obeys Binghamwith the decrease in thickness of liquid film (water content)law Eq. [4] (i.e., entirely viscoplastic),separating the solids.

The theory of rate processes (Eyring, 1936; Glastone et al.,1941) has been adapted to describe some aspects of macro- (t)

F

2 a2 (t) p

d(t)

dt y [12]

scopic, time-dependent soil deformation, and creep phenom-ena (e.g., Abdel-Hady and Herrin, 1966; Anderslan and Doug- The coefficient of plastic viscosity in compression [p las, 1970; Feda, 1989; Mitchell, 1993). The basis of the rate 2p(1 ) (Vyalov, 1986)] and the yield stress in compressionprocess theory is that movement of flow units (atoms, mole- (y y/2) are determined from rheological measurements,cules, or particles) relative to each other is constrained by where is Poissons ratio. Analytical solution to Eq. [12],energy barriers separating adjacent equilibrium positions. Dis- subject to the initial condition(t 0) o(initial strain), isplacement of flow units to new positions requires investing of given byactivation energy sufficient to surmount the barrier, and thedeformation process is viewed as sequence of displacements (t)

1

Q1 ProductLogof individual flow units. At any instant, only some of the

activated flow units may successfully cross the barrier (signi-fying viscous flow), while others fall back to their original (Qo 1) exp(Qo 1) exp Q y tp [13]positions (denoting transient elastic deformation). Although


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whereQ (2a2y/F). The special function ProductLog(z ) v(t)2

Fo

2 2a2f(1 cos[t]) 2o [17]is the solution to the nonlinear expressionz e (Abra-

mowitz and Stegun, 1974). In the illustrative examples section,application of Eq. [13] along with viscoplastic-rheological where 2(1 ) is the loss component of the complexproperties of soil will be presented. viscosity Eq. [9]. The overall axial strain is given by the sum

of the elastic Eq. [16] and viscous Eq. [17] components

Aggregate Deformation under Cyclic (t) e(t) v(t) [18]Force Application

The applications of soil viscoelastic rheological properties andUnlike the case considered above, where the energy inputthe above models Eq. [18] in solving soil mechanics problemsby external loads has sufficient time to dissipate (via viscouswill be demonstrated in theIllustrative Examples section usingflow), cyclic (transient) loads offer only limited opportunityan example that mimics the effects of fast and slow passagetime for viscous deformation. Hence, part of the energy inputof a tractor.that does not dissipate in viscous flow is temporarily stored

in elastic deformation. Traditionally, the contact area of twospherical bodies resulting from an entirely elastic deformation

MATERIALS AND METHODSis modeled by Hertz theory (Mavko et al., 1998). Accordingto this model, the strain results in only the flattening of the Measurement Apparatuscontact areas without affecting large portions of the spheres

Rheological instruments developed for characterization of(Fig. 5c). Considering that flow of soil material at the contactother materials (e.g.,polymer melts, food materials) have beeninvolves viscous dissipation (as discussed above), we proposeused for determination of soil properties with some success.an alternative energy-conserving mechanism to account forFor example, rotary viscometers were applied to determinethe elastic strain in viscoelastic spheres. We consider elasticsoil plasticity and yield stress of clay mud (Koenigs et al.,deformation of a soil aggregate pair results in bulging of the1976) and super soft clays (Fakher et al., 1999).aggregates without permanent flow (rearrangement) of soil

In this study,a rotational (torsional) rheometer with a paral-material around the contact (Fig. 5d), with the magnitude oflel-plate sensor system (RheoStress RS75, Thermo Haake,the axial strain being equal to the Hertzian strain. Conse-Karlsruhe, Germany) was employed. The instrumental setupquently, when an aggregate pair is subjected to oscillatoryis shown in Fig. 6. The soil sample is placed between thestress, the resulting elastic and viscous strains happen at sepa-rotary plate (top) and stationary plate (bottom) at a specifiedrate locations; that is, the aggregates undergo elastic bulgingconstant spacing (2 mm) between the plates. The shaft of thewhile the material forming the contacts flows viscously. Therotary plate is equipped with sensors that measure torque andelastic deformation is instantaneous while the viscous flowangular velocity, and the computerized driver translates themtakes place at a rate dictated by wet soil viscosity.to average shear stress () and shear strain (), respectively,Now, consider a pair of perfectly elastic spheres in contactusing geometrical relations. Two basic alternatives are avail-shown in Fig. 5b; collinear forces are applied so as to press theable to use the above geometry as an absolute rheometer: (i)two spheres together. According to Hertz theory, the elasticcontrolled stress () input and determining the resulting shearspheres deform temporarily at their mutual contact region,rate ( ) (CS mode) or conversely (ii) a controlled shear rateforming a circular contact area of radiusx (Fig. 5c) given by

input () and determining the resulting shear stress () (CRmode). When CS- or CR-mode measurements are conducted

under steady stress or shear rate applications, respectively,x

3

3

2(1 )a F

G1 3

[14]the resulting flow curves can be used to determine viscosity( or p ) and yield stress (y ) of ideal viscous or viscoplastic

whereGis shear modulus of the spheres. An oscillatory input materials, as discussed above. The CS- or CR-mode measure-forceF(e.g., induced by passage of tractor) may be given by ments conducted under sinusoidal (oscillatory) shear stress

(CS-OSC) or shear rate (CR-OSC) application, respectively,F Fosin(t) [15] can be used for viscoelastic characterization.

Forproper application and interpretation of rheometric testThen, the resultant elastic strain (e ) at any timetis obtained results, the following assumptions must be considered (Dealy,by substituting Eq. [14] and [15] in Eq. [10]

1982; Thermo Haake, 1994):

1. The shear stress applied must be transmitted fully frome(t) 3 95121

a2 G2

[Fo sin(t)]2 3 [16]

the moving plate to the sample (no slippage). Poor cohe-sion between the steel plate and soil sample can cause

substantial slippage at low shear stresses or high waterFor viscoelastic soils with storage and loss components ofcontent. Slippage was reduced in our experiments byelasticity, the storage shear modulus (the real componentGlining the rheometer plates with fine-grain sandpaperof the complex modulus G* Eq. [8]) is responsible for the(0.08 mm) (Banfill and Kitching, 1991).elastic strain Eq. [16]. The resulting Hertzian strain in the pair

2. Because soil density and confining pressure are impor-of spheres is shown schematically in Fig. 5c. For the proposedtant factors in determining rheology, they should be keptelastic bulging of soil aggregates (modified Hertzian elasticat a constant magnitude to avoid unaccounted variationsstrain Fig. 5d), the major and minor axes of the resultingin the measurement results. Forthese reasons, the exper-ellipsoidal aggregate are obtained from the Hertzian strain byiments were conducted at constant sample volumea(1 e ) and a/(1 e )

2, respectively.(plateplate spacing of 2 mm) and zero vertical stress.The deformation (flow) at the interaggregate contact is

3. It is assumed that the properties of the test materialconsidered entirely viscous as stated by Eq. [12], without yield(soil) have no intrinsic dependence on direction, and thestress (i.e.y 0). The solution to Eq. [12], with time-depen-

dent input force Eq. [15], is given by material reacts to applied stress uniformly. Test results


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Soils and Clay Minerals Tested

Rheological measurements were conducted on two naturalsoils [Millville silt loam (coarse-silty, carbonatic, mesic TypicHaploxerolls) and Fraternidad clay soil (fine, smectitic, iso-hyperthermic Typic Haplusterts)], and three clay minerals (ka-olinite, Ca-montmorillonite, and Na-montmorillonite). Therheological properties of the natural soils may be directly

linked with processes occurring in agricultural soils. The clayminerals, however, are intended to aid in understanding thefundamental flow behaviors of soil in the absence of heteroge-neity and interference by silt and sand fractions. Selectedphysical and chemical properties of the samples are given inTable 1. The soil samples were sieved through 1.0-mm meshsize. Different water content levels were established for allsamples by mixing air-dried soil or clay with an appropriatemass of water and allowing the mixture to equilibrate for 48to 72 h.

Measurement Procedures

Steady Controlled-Stress Tests

Enough soil or clay samples to fill the 2-mm gap betweenthe parallel plates were placed between the plates. For eachsample, new (unused) circular discs of sand paper were affixedto the parallel plates using two-sided adhesive tape, with therough surface facing the soil. Measurements of stress, strain,and strain rate were conducted at 100 stress points, incre-mentedin logarithmic scale during a total measurement periodof 3 min. During pilot tests, two criteria were used in selectingthe stress range appropriate for each soil or clay and watercontent. First, adequate points are required near the yieldpoint for better distinction of the yield stress, and secondly,at the maximum stress (strain rate) the soil sample shouldremain intact within the plateplate spacing (at higher strainrate, failure results by high centrifugal forces). At each stresspoint the computerized driver conducts measurements in trip-

Fig. 6. Rotational rheometer used in this study. (a) complete setup, licate and reports averaged data. The entire procedure was(b) sensor system during measurement, and (c) arrangement of repeated three to five times, for each soil or claywater con-sand paper and soil sample in sensor system. tent combination.

reflect average properties of the sample and not of indi-Oscillatory Controlled Stress Tests

vidual flow components.4. All physical and chemical properties affecting the rheol- Sample handling and placement for oscillatory measure-

ment are identical to steady stress measurements. The oscilla-ogy of the sample must be kept constant during measure-ment. To reduce loss of soil water by evaporation, the tory measurementswere conductedin thestress range selected

for the corresponding steady stress measurements. For everyduration of the measurements was limited to 3 to 15 min.The maximum reduction in water content occurred in stress point (amplitudeo ), the stress was applied as full-sine

cycle (Fig. 3), and the corresponding strain was recorded. Thesamples with high water content (26 kg kg1 ), but waslimited to1%. The temperature of the plates was kept instrument used has the capability of recording stress and

strain values at a resolution of one point for every degree ofconstant by circulating water.

Table 1. Selected physical and mineralogical properties of soils (clays) used in this study.

Texture

Sample Source Sand Silt Clay Clay composition Surface area CEC

% m2 g1 cmol kg1

Millville silt loam Logan, Utah 29 55 16 Kaolinitic montmorillonitic 73 NAFraternidad clay Lajas Valley, PR 18 31 52 Montmorillonitic NA 40.5Kaolin-well ordered Washington Co, GA 0 0 100 SiO2(43.9%); Al2O3(38.5%) 23.5 3.3Ca-montmorillonite Gonzales Co, TX 0 0 100 SiO2(70.1%); Al2O3(16.0%) 83.79 84.4Na-montmorillonite# Wyoming 0 0 100 Wyoming bentonite (100%) NA NA

Or and Wraith (1999). EGME method (Carter et al., 1986). Gierbolini (1979). N2 method (Olphen and Fripiat, 1979).# Maycoban Drilling Fluids Services, Dresser Industries, Houston, TX.


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scaled time () or better. The phase shift angle () and strain- passing through the origin, signifying an elasticdeforma-amplitude (o ) were computed from duplicate measurements tion regime (Fig. 1a). According to Eq. [1], the inverseat each stress point. Because measurements take longer dura- slope of the stressstrain function denotes the sheartion at every stress point, only 15 stress increments were used. modulus (G). The second linear segment of Fig. 7a,The frequencies reported in this paper are: 0.0681, 0.6810, and

with a slope of above unity (in log-log scale), indicates3.160 Hz.

a linear relationship between the derivative of the strain(strain-rate) and stress (Fig. 7c), and suggests a viscous

RESULTS AND DISCUSSION flow (see Fig. 1b). In line with Eq. [4b], the inverseslope of the stress vs. strain-rate relationship representsViscoplastic Properties of Unsaturated Soilthe coefficient of plastic viscosity (p ) of the soil sample.

The steady-state, CS measurements (conducted on The stress at which transition from the elastic to thethe different soil types and water contents) provide rela- viscous segment occurs indicates yielding of the soiltionships of shearing stress () vs. shear strain () and sample (yield stress y ). One can also notice higher non-shearing rate ( ). A typical test result for Millville silt linear strain-rate beyond the viscous range, where theloam soil (at 0.28 kg kg1 water content) is depicted in sample could not be contained between the plates (fail-Fig. 7. The stressstrain relationships, plotted in log- ure). In summary, viscoplastic soil flow behavior for alog scale (Fig. 7a), are divided into two distinct linear given water content can be described by three parame-segments. The first segment with a unit slope (in log- ters: shear modulus (G), yield stress (y ), and coefficientlog scale) indicates a linear stressstrain relationship. of plastic viscosity (p ).In linear-scale (Fig. 7b), this segment fits a straight line Viscoplastic parameters of the different soils and clay

minerals are shown in Fig. 8. Discussions on effects ofstress magnitude, water content, and clay mineralogyon viscoplastic parameters are given below.

Fig. 7. Typical measurement results for steady state CS measurement(Millville silt loam soil at 0.28 kg kg1 water content). (a) Stress

Fig. 8. Viscoplastic parameters of different soil and clay types as func-strain relation in log-log scale, showing the distinct differentiationof the deformation to elastic and viscous types; (b) elastic range tion of water content by weight. (a) Yield stress, (b) coefficient of

plastic viscosity and, (c) shear modulus. Each point in the plotsin linear scale; and (c) viscous range in linear stressstrain ratecurve (flow curve), and definition of Bingham model. denotes mean of three to six independent replicates.


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The Effect of Stress Magnitude coplastic properties observed in this study, as detailedbelow.The division of the flow behavior into elastic and

A decrease in water content is accompanied by anviscous regimes (as shown in Fig. 7a) is typical for allexponential increase in yield stress, shear modulus and

the soils and clay tested. Low applied stress can be ac-viscosity of all the soils tested (Fig. 8), principally due

commodated with small and temporary bending of solidto a decrease in the number of water molecular layers

matrix or stretching of bonds between water moleculescoating clay domains and quasi-crystals, and reducedwithout substantial rearrangement of water molecules ad-mobility of the molecules. In addition, decrease in watersorbed on surfaces of clay domains and quasi-crystals.content leads to reduction of the intergranular spacing.

If the stress is relieved, the strain usually recovers fully.This, in turn, may set off additional resistance to defor-

Yielding of the soil and subsequent viscous flow aremation by the enhanced solidsolid interactions.initiated when temporary bond stretching or bending

To further elaborate the effects of water content oncan no longer accommodate the applied stress. In termsviscoplastic properties, properties of Na-montmorillon-

of rate processes theory, the elastic regime is where theite clay were determined fora wider watercontent range

energy imposed on an average flow element is insuffi-(Fig. 9). The yield stress of the clay (Fig. 9a) decreased

cient to surmount an energy barrier, hence the deforma-exponentially with water content. This observation is intion is temporary and fully recoverable. Viscous defor-agreement with the plastic flow behavior of adsorbed

mation (flow) commences when the stress magnitudewater molecules (Israelachvili and Adams, 1978). In

reaches a point where it can cause a jump over thecontrast, there was an abrupt reduction in viscosity of

energy barrier of an average flow unit.the clay by about three orders of magnitude (Fig. 9b)when the water content was increased to more than 6

The Effect of Water Content kg kg1, signifying a macroscopic transition from solid-Experiments of molecular shearing of water held be- like to liquid-like behavior. The main reason for this

tween mica surfaces (Israelachvili and Adams, 1978) phenomenon could be that solid-like flow at lower waterhave shown that the tightly adsorbed water molecules content is dictated by the shearing of water held betweenhave yield stress that is independent of shear rate. Fur- clusters and quasi-crystals, whereas liquid-like flow atthermore, they have shown that the viscosity of one or higher water content is governed by the flow of liquidtwo molecular layers of water is five to seven orders of in micropores.magnitude higher than the viscosity of bulk water. Thesefindings were in qualitative agreement with soil vis- The Effect of Clay Type

The effect of clay type is directly related to thespecificsurface area, activity, and type of adsorbed cations. Ingeneral, the larger the internal surface area the largerthe liquid mass required to form one molecular layer

of water. Consequently, the change in viscoplastic prop-erties with increasing water content is more gradualfor Na-montmorillonite than Ca-montmorillonite andkaolinite, as shown in Fig. 8. Although the internal sur-face area of Ca-montmorillonite is equivalent to that ofNa-montmorillonite, the maximum amount of waterthat can be held in internal surfaces of Ca-montmoril-lonite is limited to one to three molecular layers. Theinternal surfaces of kaolinite are practically nonwetta-ble. Hence, large proportion of soil water in Ca-mont-morillonite and kaolinite clays is held in intercluster

Fig. 9. Viscoplastic parameters of Na-montmorillonite overexpanded Fig. 10. Typical measurement results of controlled stress oscillatorytest of Na-montmorillonite at frequency of 3.16 Hz and waterwater content range. (a) coefficient of plastic viscosity and (b) yield

stress. Each point in the plots denotes mean of three indepen- content of 4 kg kg1.dent replicates.


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spaces, resulting in localization of the effective stress rameters can be derived from these (see the Theorysection for details).in few intercluster contacts. These contacts primarily

determine the viscoplastic properties of the clay. This Summarized viscoelastic properties (complex viscos-ity * and phase shift angle ) for Millville silt loam soil,also explains why the viscoplastic properties of both

Ca-montmorillonite and kaolinite change with water Fraternidad clay soil, kaolinite, and Na-montmorilloniteare presented in Fig. 11 and 12. The effects of stresscontent at the similar rates. However, the Ca-montmo-

rillonite curve is shifted to the right in Fig. 8 (more wet) magnitude, clay or soil type, water content, and loading

frequencyon viscoelastic parameters are discussedbelow.because the large quantity of water held in internalsurfaces of Ca-montmorillonite does not play as signifi-cant a role as the water held between clusters in the The Effect of Stress Magnituderheological properties. The same reasons also explain

During steady loading, elastic deformation and vis-the shifting of Fraternidad curves (higher surface area)cous flow occur under different stress magnitudes (seeto the right with respect to the Millville curves (lowerFig. 7). During cyclic loading, however, both elastic andsurface area).viscous deformations occur concurrently at any givenstress. The primary reason is that short loading duration

Viscoelastic Properties of Wet Soilsoffered by oscillatory stress limits the viscous flow and

and Clay Minerals allows for elastic strainrelaxation to take place.Considering the heterogeneity within a soil sample,Typical measurement output for Na-montmorillonite

(water content 4 kg kg1 ) at specified stress-ampli- at any given stress magnitude, part of the microscopicflow units (e.g., water molecules held between clay clus-tude (o 1390 Pa) and loading frequency (f 3.160

Hz) is shown in Fig. 10. The input sinusoidal stress ters and quasi-crystals) may be below their yieldingpoint, whereas others are under viscous state. Moreover,function [osin(t)] and resulting strain function areplotted as functions of scaled time (Eq. [7]), in the increasing stress magnitude would increase the propor-

tion of the flow units that are under viscous state. Thus,x-axis. All the viscoelastic properties are contained ineither the complex viscosity (*) or complex modulus two important consequences of increasing stress can be

noted for all the soils or clays and water contents tested(G*), and the phase shift angle (); the remaining pa-

Fig. 11. Summary of viscoelastic properties of Millville silt loam soil and Fraternidad clay soil. Each point in the plots denotes mean of threeindependent replicates.


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(Fig. 11, 12). First, the proportion of viscous deforma- The Effect of Loading Frequencytion (phase shift angle) increases, and second, the over- The effect of increasing loading frequency (fasterall viscosity decreases. The degree of change in viscosity tractor speed) is vividly shown in the decreasing viscos-and phase shift angle are directly related to the hetero-

ity for all soils and clays and stresses (Fig. 11, 12). Ingeneity of the samples tested. The change in viscosity

contrast, the relative proportion of viscous to elasticand phase shift angle with stress is more gradual for the

deformation (phase shift angle) decreases with fre-homogeneous clay minerals (kaolinite and Na-montmo- quency for most situations. These observations are re-rillonite) than the natural heterogeneous soils (Millville lated to the differences in loading duration provided byand Fraternidad). Similarly, the trend is more gradual different frequencies. Low frequency testing providesfor the relatively less heterogeneous Fraternidad clay longer loading time, allowing for more viscous dissipa-soil than the more heterogeneous Millville silt loam soil. tion (higher phase shift angle), and vie versa. Comparing

viscosity functions of different soils and clays, pure clayshave a similar rate of decrease in viscosity with stressThe Effects of Water Contentat all frequencies. However, natural soil (mixture of

At a microscopic scale, an increase in water contentdifferent clays and silt) shows a faster rate of decrease of

increases the spacing between clay domains and quasi-viscosity with stress when loaded at higher frequencies.

crystals, thereby reducing solidsolid interactions.These, in turn, decrease the complex viscosity and the

Illustrative Examplesproportion of elastic strain of the clay water under cyclicload. As a result, increasing water content is accompa- For detailed description of soil aggregate coalescencenied by lower viscosity and higher phase shift angle model and resulting evolution of soil pore-size distribu-

(decrease in elastic component), for all soils and clays tion, especially due to wetting and drying cycles, theand stress conditions. Other effects of water content reader is referred to Ghezzehei and Or (2000) and Orand wetting properties of different clay types discussed et al. (2000). These models consider viscoplastic defor-in the context of viscoplastic properties also apply to mation of spherical aggregates subjected to steady-state

capillary stresses. Because the stresses originate in thethe viscoelastic properties.

Fig. 12. Summary of viscoelastic properties of kaolinite and Na-montmorillonite clays. Each point in the plots denotes mean of three indepen-dent replicates.


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vicinity of individual contacts, the process of aggregate Ignoring all the interactions with neighboring aggre-gates, the strain induced by the stress is given by Eq.coalescence by capillary forces is nondirectional and

uniform with depth. In contrast, external forces have a [13]. In Fig. 13b, Eq. [13] is evaluated using viscoplasticproperties of Millville silt loam soil (0.28 kg kg1 wa-unique direction of maximum impact, and their effect

diminishes with depth as stresses are transmitted through ter content).The Bingham rheological model states that aggregateoverlying aggregates. In general, two forms of external

forces, namely, steady and cyclic, are expected. In the coalescence occurs only when the applied stress is greater

than the yield stress (y 612 Pa). Initially, when thefollowing examples, rheological properties of Millvillesilt loam soil at 0.28 kg kg1 water content will be used interaggregate contact area is nearly zero, the effective

stress acting upon the contacts is very high (Fig. 13a)along with the simplified models discussed above todemonstrate applications of the rheological properties. resulting in a rapid rate of aggregate coalescence (slope

of Fig. 13b). As the contact area increases with time, theThese presentations are concerned only with a singlecontact between identical spherical aggregates. Consid- effective stress, hence the rate of aggregate coalescence,

decreases. The coalescence ceases when the effectiveerations of different aggregate sizes, interaction be-tween adjacent aggregate pairs, and effect of depth are stress equals the yield stress. Further coalescence can be

initiated only if the water content is increased (therebyleft for forthcoming work.decreasing the yield stress) or the applied load (force)is increased.Soil Aggregate Deformation under Steady

State External Stress

Soil Aggregate Deformation underWeight of overlying soil layers (overburden) is anTransient Cyclic Stressesexample of steady external forces that exist in all soils.

In this example we consider a pair of identical soil aggre- The most common oscillatory stresses that occur ingates (radius 1 mm), initially with a very small initial natural agricultural soils result from passage of farmstrain (o 0.001). The line connecting the centers of implements. The force delivered by a tractor can bethe aggregates is parallel to the direction of the weight denoted by a half-cycle sine function Eq. [15]. Qualita-force (F 1.63 104 N). The compressive stress (Eq. tively, the frequency (f) of the sine function is propor-[11]) acting upon the contacts is shown in Fig. 13a. tional to tractor speed, and the force amplitude (Fo) is

proportional to the weight of the tractor.In the following example we consider a vertically up-

right aggregate pair (radius 1 mm), subjected to cyclicforce (Fo 1.63 10

4 N). Ignoring all interactionswith neighboring aggregates and effect of depth (stresspropagation), the strain induced by the passing tractoras a function of time is given by Eq. [18]. For the purpose

of comparing different frequencies of stress applicationthat last for different periods, the time (t) is scaled bythe frequency as in Eq. [7] and is expressed in units ofdegrees. The applied oscillatory force Eq. [15] is sym-metric about Fo as shown in Fig. 14a. The resultingoscillatory stress, however, is asymmetric (skewed tothe right) because it also depends on the increasingstrain magnitude. The total strains in a soil aggregatepair (Millville silt loam soil, water content 0.28 kgkg1 ) subjected to two cycles (analogous to front andrear wheel impacts) of slow (0.0681 Hz) and rapid(0.6810 Hz) cycles of stresses are depicted in Fig. 14b.

The viscous strain amplitude occurring at the interag-gregate contacts lags behind the stress amplitude by 90,

and the elastic bulging of the aggregates is in phase withthe stress curve as shown in Fig. 14b. The magnitudesof the strain components are determined by compoundeffects of the complex viscosity (*) and phase shiftangle (). In Fig. 14b and 14c, it is indicated that strainsat 0.681 Hz are lower than at 0.0681 Hz. Physically, thisimplies that longer loading time, during slow passageof a tractor, provides enough opportunity time for moreviscous straining to occur. The higher phase shift angle

Fig. 13. Stressstrain relationships in aggregate pair model (Millville () at lower frequency shown in Fig. 11 also suggests asilt loam soil at 0.28 kg kg1 water content) subjected to steady

more viscous strain (less elastic) component. In general,state stress. (a) Applied contact stress and yield stress functionsand (b) viscoplastic strain response as a function of real time. the increase in contact area with each additional loading


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agricultural soils. Steady-state stress occurs in naturalsoils in two forms: (i) directional overburden of overly-ing soil, and (ii) omnidirectional capillary forces. Oscil-latory stresses are induced by passing farm implements.Measurement results were modeled using simple me-chanical analogs (namely; spring, dashpot, and slider)to further assist mathematical analysis of the results.

The observed rheological properties and trends werequalitatively explained using soil and clay microstruc-ture and flow processes of claywater systems.

The main findings and conclusions of this study areas follows:

1. Rheological properties of soils are closely relatedto microscopic clay structure and flow behavior ofclaywater systems. There was qualitative agree-ment between observed macroscopic rheologicalproperties and expected theoretical and experi-mental evidence of rheology at microscopic scales.

2. Under steady stress, wet soils and clay mineralsexhibit viscoplastic properties characterized by a

well-defined yield stress and constant coefficientof plastic viscosity, both of which increase withdecreasing water content. These phenomena arerelated to confinement of liquid water betweenclay sheets and the resulting decreased ability ofwater molecules to flow freely, and solidsolidfriction.

3. Cyclic or transient loads applied to soil, for exam-ple, passage of a tractor, apply stress for only ashort duration insufficient for full dissipation ofthe applied energy, leading to partly recoverable(elastic) strains. This concurrence of viscous andelastic deformations is generally referred to as vis-

Fig. 14. Stressstrain relationships in aggregate pair model (Millvillecoelasticity.silt loam soil at 0.28 kg kg1 water content) subjected to two cycles

(0.0681and 0.681Hz) of oscillatory stress. (a) Applied cyclic force 4. Viscoelastic properties are expressed in compactand contact stress, (b) elastic and viscous strain components, and form using complex viscosity or shear modulus(c) total strain as functions of scaled time (in degrees). containing both viscous and elastic properties. The

relative proportion of each component is providedcycle decreases the effective stress. Consequently, the by the phase shift angle (0 for perfect elastic, 90degree of viscous strain also decreases with the number for perfect viscous, and intermediate for visco-of cycles. Practically, this implies that the damage in- elastic).curred by a tractor passing over aggregated soil de- 5. Frequency of loading (tractor speed), water con-creases with the number of passes. Thus, the particular tent, and stress amplitude are important factorsaggregate geometry and soil rheology define the maxi- that determine viscoelastic properties. High fre-mum strain level that can be causedby a given stresscon- quency (corresponding to fast tractor speed) anddition. lower water content result in a higher proportion

of elastic deformation and vice versa. High watercontent and/or high stress amplitude results in

SUMMARY AND CONCLUSIONS lower viscosity of all soils and clays.This study describes soil rheological properties under

The illustrative examples presented, considering sin-stress conditions that mimic actual field conditions. Thegle contact between a pair of spherical aggregates, dem-experimentally determined rheological properties gath-onstrate the potential usefulness of soil rheologicalered could be used in predicting soil strain and resultingproperties for prediction of time-dependent stresschanges in hydraulic properties during compaction ofstrain relationships, for a given stress condition and wa-agricultural soil. Soil rheological properties under steady-ter content. Upscaling of the model to multiple contactsstate and oscillatory stress conditions for different soilinvolving different soil aggregate geometries (e.g., dif-and clay types were measured using a rotational rheom-ferent sizes) and various packing mechanisms in ordereter with a parallel plate sensor system. The rationaleto provide quantitative prediction of strain and strainbehind the stress conditions studied (steady and oscilla-

tory) was motivated by stresses commonly occurring in rate of bulk soil are addressed in subsequent work.


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rheological properties of wet soils and clays under steady

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