Is Wetting Collapse an Unstable Compaction Process?Constance Mihalache, S.M.ASCE1; and Giuseppe Buscarnera, Aff.M.ASCE2

Abstract: This paper provides an interpretation of the phenomenon of wetting collapse in fine-grained soils based on principles of materialstability. For this purpose, classic experiments displaying the accumulation of irreversible compaction have been reinterpreted through a plas-ticity model for unsaturated soils. The resulting simulations have been inspected mathematically, with the goal of detecting a possible loss ofcontrol of the wetting process. The reanalysis of the experiments suggests that, if the wetting-induced deformations are interpreted as homo-geneous, the considered compaction events do not tend to be affected by a loss of material stability. As a result, such well-known phenomenahave been explained as controllable modes of plastic deformation. This feature has been found to be valid regardless of the mode of saturation(i.e., it is valid for both controlled suction removal and water volume injection). Indeed, parametric analyses have shown that the compactionprocess tends to become unstable only in the presence of highly water-sensitive media exposed to a drastic loss of suction (e.g., soaking orinjection), i.e., circumstances during which the soil undergoes large strains and suffers a marked deterioration of its mechanical properties.In these cases, the theory predicts a limit threshold of the water content at which the control of the injection process is lost, the applied stressis no longer sustainable, and even infinitesimal alterations of themoisture content can cause a sharp accumulation of compaction. Thesefindingsimpact the interpretation of wetting-induced settlements predicted via computational models, and are of general relevance for the design, main-tenance, and safety assessment of unsaturated earthen systems interacting with hydrologic processes. DOI: 10.1061/(ASCE)GT.1943-5606.0001226. © 2014 American Society of Civil Engineers.

Author keywords: Unsaturated soils; Collapse; Plasticity; Constitutive modeling.

Introduction

The accumulation of compactive strains during wetting has alwaysplayed a prominent role in unsaturated soil mechanics. Saturation-induced compaction is indeed a key design factor in arid climatesand/or in the presence of soils with complexmicrostructures (Farmerand Glynn 1990; Gasaluck and Veerasiri 2002). Such settlementscan be distributed across a site and have been identified as a cause ofdeterioration of shallow foundations (Houston et al. 1988; Phien-wejet al. 1992; Walsh et al. 1993), embankments (Lawton et al. 1992;Miller et al. 2001), and fill slopes (Brandon et al. 1990; Chen et al.2004). Wetting compaction is therefore detrimental to various typesof earthen systems, especially when their functionality is sensitive todifferential settlements (Houston 1988; Walsh et al. 1993; Charles2008). In these cases, the deformations accumulated during in-undation are a signature of site-specific soil properties. As a result,soil characterization is pivotal in the identification of violations ofthe limits of safety and/or serviceability, and their interpretationmust rely on a combination of monitoring techniques and mecha-nistic models.

For these reasons, the study of compactive strains upon wettinghas been a major driver for the formulation of constitutive theoriesand currently plays a critical role in virtually any mechanical model

involving unsaturated soils and their interaction with geotechnicalsystems. In particular, the limited success in capturing the phe-nomenology of wetting compaction has been advocated as evidenceof the lack of validity of the effective stress principle (Jennings andBurland 1962; Bishop and Blight 1963). This idea has inspired theuse of independent sets of constitutive variables (Fredlund andMorgenstern 1977) and the formulation of critical state models forunsaturated soils (Alonso et al. 1990), in which the most notablecomponent is the use of suction-dependent yielding to describe theonset of plasticity upon changes of the hydraulic state.

From that moment onward, the widespread use of suction-dependent properties in unsaturated soil plasticity has contributedto gaining a better understanding of wetting-induced compaction,pointing out that enhanced effective stress measures can also beused to capture these phenomena (Jommi 2000; Loret and Khalili2002; Wheeler et al. 2003; Khalili et al. 2004). Along these lines,Borja (2004) has combined an effective stress formulation with thestrain localization theory, elucidating the key role of suction anddrainage conditions on themechanics of failure of these soils.Morerecently, by combining a physically based effective stress measure(Lu et al. 2010) and a plastic failure criterion, Lu (2011) hasreinterpreted the collapse experiments by Jennings and Burland(1962), suggesting that the achievement of the strength threshold isa possible cause of the macroscopic compaction observed duringwetting. Similar approaches have emphasized the importance ofmechanical and hydrologic heterogeneities on strain localizationmechanisms (Borja et al. 2013), whereas other authors have useddifferent plastic models to study shear banding at the constitutivelevel (Schiava and Etse 2006; Peri�c et al. 2014). These workssubstantiate the notion that, in addition to an enhanced effectivestress definition, an appropriate plastic framework able to capturefailure events is pivotal for modeling the response of unsaturatedsoils subjected to hydrologic perturbations, thus corroborating theidea that wetting compaction must be interpreted as a plasticmechanism.

1Ph.D. Candidate, Dept. of Civil and Environmental Engineering,Northwestern Univ., 2145 Sheridan Rd., Evanston, IL 60208.

2Assistant Professor, Dept. of Civil and Environmental Engineering,Northwestern Univ., 2145 Sheridan Rd., Evanston, IL 60208 (correspond-ing author). E-mail: g-buscarnera@northwestern.edu

Note. This manuscript was submitted on March 24, 2014; approved onSeptember 23, 2014; published online on October 15, 2014. Discussionperiod open until March 15, 2015; separate discussions must be submittedfor individual papers. This paper is part of the Journal of Geotechnical andGeoenvironmental Engineering, © ASCE, ISSN 1090-0241/04014098(13)/$25.00.

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Within this context, the inelastic nature of wetting-inducedcompaction is often regarded as a signature of metastable structure(Barden et al. 1973), interpreting the increase in moisture content asa source of deterioration of both near-surface sediments (Assallayet al. 1997; Muñoz-Castelblanco et al. 2011) and compacted soils(Lawton et al. 1991; Pereira and Fredlund 1997). These argumentshave promoted the widespread use of the term wetting collapse, anexpression that suggests that large compaction may occur uponsmall changes in the hydraulic conditions (as it would do in anunstable system susceptible to wetting). It is readily apparent that,under this scenario, prediction of the timing, location, and proba-bility of occurrence of collapses becomes a critical task, especiallyif the performance of geotechnical systems must be monitoredover time to guarantee compliance with the design requirements.Nevertheless, despite the technical importance of wetting collapsemechanisms, the connection between saturation-driven compactionand the loss of stability of the deformation process has never beenverified from a continuum mechanics perspective. In particular, it isnot yet clear which criteria should be used to differentiate con-trollable compaction (i.e., strains gradually taking place upon sat-uration) from unstable processes causing sharp changes in thespatial/temporal dynamics of the deformation pattern. Given theimportance of wetting-induced compaction for unsaturated soilengineering, it is arguable that an incomplete understanding of themechanics of this phenomenon can hinder the interpretation ofexperiments, the characterization of soil properties, and the for-mulation of physically sound constitutive theories.

This paper aims to provide such a missing mechanical in-terpretation by addressing two key questions: (1) Should wettingcollapse be considered an unstable event in a proper mechanicalsense? and (2) What are the conditions that exacerbate the potentialinstability of soils subjected to wetting? For this purpose, a series ofwell-known wetting tests on fine-grained soils that have exhibitedirreversible compaction (Jennings and Burland 1962; Maswoswe1985) were simulated through a plasticity model (Buscarnera andNova 2009). Such simulations were interpreted with a criterion ableto detect instabilities in unsaturated soils (Buscarnera and Nova2011; Buscarnera and di Prisco 2012), thus assessing from a con-tinuum mechanics standpoint the mechanical nature of these widelystudied deformation processes.

Theoretical Background

Control Variables in Unsaturated Soil Testing

The representation of wetting collapse as a plastic process impliesthat its numerical simulationmay be affected by a loss of uniquenessand/or existence of the computed response (Buscarnera 2014).These circumstances reflect a loss of strength and depend signifi-cantly on the imposed conditions (e.g., stress versus strain control).Indeed, compared with most engineering materials, soils displaya wide range of failure modes (Lade 2002; Borja 2006). As a result,the models used to predict their response are prone to violating thepostulates of existence and uniqueness (Klisinski et al. 1992), andnumerous studies have emphasized the crucial role played by thecontrol conditions imposed by laboratory devices (Imposimato andNova 1998; Buscarnera et al. 2011).

The concept of control is important also for the interpretation ofwetting collapse, because both hydraulic and mechanical conditionsmust be considered. The configuration used in the laboratory toexplore such compaction processes has been typically based onoedometer testing [Fig. 1(a)]. In this scenario, saturation paths areimposed by controlling fluid pressures at the boundaries, while

maintaining a constant vertical stress. By contrast, horizontalstresses are not controlled, but rather, are an outcome of constrainedradial deformations. In other words, from a mechanical point ofview. The oedometer imposes a mixed stress-strain loading mode,which affects the evolution of the state of stress during suctionremoval. As a result, prevented lateral strains cause a differencebetween the increment of radial and axial stresses (Fig. 2), thusaffecting the evolution of the stress ratio and the amount ofmobilizedplasticity.

From a hydraulic point of view, the usual tests postulate suctioncontrol (i.e., they assume that the variables controlled at theboundaries can be used to infer the response of eachmaterial unit inthe specimen). Although this hypothesis is convenient for con-ceiving experiments and simulating the soil response, it can beconsidered valid only at equilibrium or during very slow saturationpaths. As a result, it does not reflect the mechanics of soaking,where a sharp front inundates the specimen from a boundary, im-posing a drastic loss of suction concurrently with the injection ofthe fluid (Lu 2011). To account for both cases, two contrastingwetting scenarios are distinguished here: (1) suction control (hereincorporated by considering suction to be a control variable) and(2) water content control (which will be used to approximate fluidinjection and to mimic the loss of suction associated with soaking).As stressed in the following discussion, these two scenarios can beinterpreted as the hydrologic counterparts of stress control andstrain control. Indeed, by analogy with mechanical analyses, inwhich it is important to identify a stress threshold at which theresponse can no longer be controlled [e.g., the loss of stress controlin Fig. 1(c)], here the limit thresholds will be defined in terms ofgeneralized hydraulic variables [e.g., jw in Fig. 1(d)], with thepurpose of identifying the conditions at which the control of suchvariables (e.g., suction or water content) is no longer admissible(i.e., even small changes of their value would cause a sharp ac-cumulation of compaction).

The analysis of wetting compaction under a range of potentialcontrol scenarios may also include other forms of soil failure [e.g.,shear banding as shown in Fig. 1(b)]. Indeed, given the transientnature of the infiltration process and the important role of the actualrate of wetting, the previously mentioned material point schemesare just approximations of the global responses affected by bound-ary conditions, initial and process-induced heterogeneities, andlocalized strain patterns (Borja et al. 2013; Bruchon et al. 2013;Nikooee et al. 2012). Nevertheless, for the sake of simplicity,wetting compaction is analyzed here as a homogeneous response.The purpose of this paper is, in fact, to disclose whether suchdeformations, typically hypothesized to be a peculiar constitutiveproperty of unsaturated soils, are actually affected by a loss ofmaterial stability. It must be noted, however, that although strainheterogeneities during wetting are deliberately disregarded, themethods discussed hereafter can be adapted to identify the con-ditions at which strain localization may take place (Buscarnera anddi Prisco 2011, 2013). In this way, the assessment of controllabilityconditions can be conducted as a shear band analysis, therebyallowing the simultaneous inspection of different forms of failure(Mihalache and Buscarnera 2014).

Second-Order Energy Input and Loss of Control

The interplay between soil failure and loading constraints can becaptured by the concept of controllability (Imposimato and Nova1998; Buscarnera and Nova 2011; Buscarnera et al. 2011). Thisconcept implies a link between the second-order energy input andthe loss of strength of a specimen subjected to an external per-turbation. To apply this methodology to unsaturated soils,

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Buscarnera and di Prisco (2012) have recently proposed an ex-pression of second-order energy input accounting for changes inapplied stresses, as well as perturbations to pressures and/orvolume fractions of the fluid phases

d2W ¼ 12

�_sij2 Sr _uwdij2 ð12 SrÞ _uadij

�_ɛij2

12½nð _ua 2 _uwÞ� _Sr

(1)

where sij 5 total stress; uw 5 pore water pressure; ua 5 air pres-sure; Sr 5 degree of saturation; _ɛij 5 strain rate; n 5 porosity; dij5 Kronecker’s delta; and a superposed dot indicates an increment.With appropriate rearrangements, Eq. (1) can also be written as

d2W ¼ 12_snetij _ɛij 2

12

_s _ew1þ e

(2)

where _snetij 5 net stress rate; s5 suction; e5 void ratio; and ew 5 Sre

5 water ratio (representing the water volume per unit of solid

volume). The main advantage of Eq. (2) is the ability to express thesecond-order energy input in terms of variables that are directlycontrolled and/or measured in usual laboratory experiments, thusallowing a straightforward interpretation of the stress-strain-suctionresponse.

It is therefore possible to identify in analytical terms the con-ditions at which a specimen is no longer able to sustain the imposedstate of stress under the action of an external energy supply. Suchconditions can be derived by identifying an incremental relationbetween the control variables ( _f) and the corresponding responsevariables ( _c), as follows:

_f ¼ X _c (3)

whereX is a constitutive operator reflecting the response of the soilfor a specific set of control conditions. It is possible to demonstratethat, whenever X is singular, that is, when

detX ¼ 0 (4)

the soil is susceptible to a sharp change of its incremental responseeven for a vanishingly small energy input (i.e., the imposed per-turbation is not controllable under the considered conditions).

Controllability criteria can be specialized to wetting paths in anoedometer by expressing the constitutive response as follows:

_s ¼

8><>:_sneta

_snetr

_s

9>=>; ¼

Daa Dar Daw

Dra Drr Drw

Dwa Dwr Dww

264

3758>>><>>>:

_ɛa

_ɛr

2_ew

1þ e

9>>>=>>>;

¼ D _ɛ (5)

where subscripts a, r, and w 5 axial, radial, and hydraulic com-ponents, respectively. It can be readily shown that the first state atwhich a loss of control is possible coincides with the singularity ofthe symmetric part of the constitutive matrix in Eq. (5)

Fig. 1. (a) Control conditions in an oedometer subjected to imposed axial stress increment ( _sa), constrained radial strains ( _ɛr 5 0), and an appliedchange in suction ( _s5 _ua 2 _uw); (b) potential development of localized deformation zones during oedometric testing; (c) loss of control during loading(e.g., loss of stress control at peak); (d) hydraulic analog of loss of controllability (i.e., loss of control of generalized hydraulic variable, jw)

Fig. 2. Stress state evolution from unsaturated conditions (solid line)to saturated conditions after wetting (gray lines); difference betweenwetting under radial stress control (solid gray line) and wetting underprevented radial strains (mixed control conditions; dashed line) is shown

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detDs ¼ 0 (6)

where Ds 5 ðD1DTÞ=2. This circumstance corresponds with thefirst moment at which the quadratic form defining the hydrome-chanical energy input is no longer positive definite, thus indicatingthe existence of at least one mode of deformation that can be ac-tivated at zero energy input (Buscarnera and di Prisco 2012). In otherwords, Eq. (6) marks the first potential loss of hydromechanicalstability of the considered soil.

For practical purposes, however, it is important to customize theloss of control criterion for the conditions imposed by an experi-ment. For example, if wetting is imposed by reducing the value ofsuction under constant axial net stress and zero radial strain in-crement, the compaction process can be considered to be no longercontrollable when

detXsOED ¼ DaaDww2DawDwa ¼ 0 (7)

A similar criterion can be derived for the case of water injection(i.e., when ew is controlled instead of s). This alternative caseemerges naturally from Eq. (2), where ew is the work-conjugatecounterpart of s. Indeed, the duality between suction control andwater content control corresponds to the duality between stresscontrol and strain control in mechanical analyses, making the studyof both suction and water content control scenarios necessary fora complete analysis. The loss of controllability for an oedometric testsubjected towater content control can be shown to be associatedwiththe following condition:

detXwcOED ¼ Daa ¼ 0 (8)

Conditions in Eqs. (7) and (8) can be derived from Eq. (5) byfollowing the strategy proposed by Buscarnera and di Prisco (2011).The fact that different expressions are found for suction control andwater content control indicates that the mode by which saturation isimposed plays a prominent role in whether the resulting compactionprocess is unstable. Such differences can be explained by observingthat suction governs the deterioration of the soil during wetting. Infact, whereas suction-driven saturation implies that the deteriorationof the soil is controlled from the boundaries (similar to imposingstrain control on a strain-softening medium), in the case of watercontent control, such deterioration becomes a function of the entirehydromechanical response of the soil (Buscarnera and di Prisco2013).

For the sake of generality, it is also possible to derive loss ofcontrollability conditions for wetting paths imposed under an iso-tropic state of stress. Under decreasing suction and constant meannet stress, the isotropic incremental response can be expressed as

�_pnet

_s

�¼

�Dpp Dpw

Dwp Dww

�8<:

_ɛv

2_ew

1þ e

9=; (9)

where _pnet 5mean net stress rate; _ɛv 5 volumetric strain rate; andDij

5 partitions of the constitutive matrix associated with such a load-ing configuration. Based on Eq. (9), the condition for a loss ofcompaction control under suction removal is expressed as

detXsISO ¼ DppDww 2DpwDwp ¼ 0 (10)

whereas the loss of controllability condition for water injection isgiven by

detXwcISO ¼ Dpp ¼ 0 (11)

Constitutive Modeling of Wetting Compaction

Constitutive Formulation

The assessment of possible violations of the stability criteria requiresa constitutive model able to simulate wetting paths. Here, the elas-toplastic law for unsaturated soils proposed by Buscarnera andNova(2009), which is formulated in terms of the following stressmeasure,is used:

sij9 ¼ sij2 Sruwdij2 ð12 SrÞuadij (12)

which can be seen as a specific case of Bishop’s stress calculated forxðSrÞ5 Sr. Although more sophisticated stress definitions based onthe effective degree of saturation can improve the performance ofmodels for fine-grained soils (Alonso et al. 2010; Lu et al. 2010),the stress measure in Eq. (12) is preferred here to give a simplerstructure to the model, while reproducing at the same time a suction-dependent shearing resistance. It must be noted, in fact, that thechoice of a specific effective stress is not critical for the current study,because the criteria discussed in the previous section are valid re-gardless of the constitutive framework and are applicable to themainclasses of plasticity models available in the literature (Buscarnera2014). As a consequence, the efficacy of Eq. (12) should be assessedsolely on the basis of its performance in reproducing the experi-mental data sets available for the specific soils under consideration.

The elastic strains caused by loading and/or wetting are com-puted by incorporating Eq. (12) into the hyperelastic law proposedby Borja et al. (1997), whereas the relationship between suction anddegree of saturation is modeled via an uncoupled van Genuchten(1980) soil water retention curve (SWRC), as follows:

Sr ¼ 1�1þ �

avgsnvg�mvg

(13)

Plastic deformations are reproduced using the expressions ofyield surface and plastic potential proposed by Lagioia et al. (1996)[Eqs. (16)–(20) in Appendix], as well as by the isotropic-hardeningrule used by Nova et al. (2003). As is customary in plasticity modelsbased on generalized effective stresses (Jommi 2000; Wheeler et al.2003; Sheng 2011), the inelastic effects caused by hydrologicprocesses are tracked through hardening rules enriched with non-mechanical contributions. Here, the only plastic internal variable ofthe model, ps, evolves according to the following incrementalrelation:

_ps ¼ 1Bp

ps _ɛ pv 2 rswps _Sr (14)

where ps is associated with the size of the elastic domain (whichevolves with both the plastic volumetric strain increments, _ɛ p

v , andthe rate of the degree of saturation, _Sr). The model constant Bp

controls the plastic compressibility,whereas rsw dictates the extent ofhardening or softening caused by changes in the degree of saturationduring drying/wetting. The constitutive parameters of the modelhave been calibrated to capture the response measured in classicalwetting compaction experiments available in the literature (Jenningsand Burland 1962; Maswoswe 1985). Hereafter, the calibrationstrategy used to quantify the hydromechanical properties of theconsidered soils is detailed. The values of all the model constants

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used for the study, aswell as the physicalmeaning of each parameter,are given in Table 1.

Simulation of Tests by Maswoswe (1985)

Maswoswe (1985) performed numerous wetting experiments underoedometric and isotropic conditions. Such tests were performed onthe Lower Cromer Till (LCT), a natural sandy clay of low plasticitythat has been used by numerous authors to validate constitutivemodels for both saturated (Gens1982; Gens and Potts 1982) andunsaturated (Alonso et al. 1990) soils. The natural samples testedin the aforementioned work were characterized by an initial de-gree of saturation Sr 5 45%, corresponding to a water content ofw5 11%.

To calibrate the parameters, the compression responsemeasured ina series of oedometric tests was considered. Although the modelallows the incorporation of nonnormality, for simplicity an associatedflow rule was used. This simplification has two main benefits: (1) it iscustomary for basic plasticity models for fine-grained soils, allowingone to reduce the number of model constants; and (2) it allowed thefocus to be on the interplay between hydromechanical coupling andsoil stability, thus isolating the effect of solid-fluid interactions fromthe well-known detrimental effects of nonnormality.

The available data set includes a loading-unloading test on a fullysaturated sample (Test LCT1), a compression test performed atconstant water content on an unsaturated specimen (LCT2), and

a wetting test at constant vertical net stress, snet1 5 414 kPa (LCT3).

The last test was performed until full saturation and then loaded andunloaded oedometrically. With reference to a similar experiment(modeled by LCT4),Maswoswe (1985) also provided the stress pathdata for oedometric loading conditions,whichweremeasured duringboth the loading stage and the wetting phase. In addition, thecompression response measured during wetting under constantisotropic net stress (pnet 5 297 kPa) was available (Test LCT5) andwas used here to validate the parameter calibration strategy.

Data on the evolution of void ratio with applied net stress forTests LCT1eLCT3 are reported in Fig. 3(a), whereas the stress pathdata for LCT4 in terms of both effective stress and net stress areshown in Fig. 3(b). Data points from the recorded evolution ofsaturation and fluid pressures during the wetting step of LCT4 areplotted in Fig. 4 and were used to calibrate the retention curve of thetestedmaterial. The evolution of void ratio with applied net stress forthe isotropic loading path (LCT5) is shown in Fig. 5.

To model the initial state of the samples, a drying path at con-stant net stress was simulated at low confinement (p0 5 1 kPa)until reaching a value of Sr 5 45%, after which axial stresses wereapplied. This procedure generates an initial state of stress and suctioncorresponding to those used in the tests, aswell as an initial void ratiocorresponding to that reported at the beginning of the experiments.The parameters controlling the compression response under saturatedand unsaturated conditions (i.e., k̂, Bp, and rsw in Table 1) weredetermined from the compression curves of Tests LCT1eLCT3

Table 1. Model Parameters Calibrated against Measured Data from Jennings and Burland (1962) and Maswoswe (1985)

Type of parameter Description Symbol Jennings and Burland (1962) tests Maswoswe (1985) tests

Elastic constants Logarithmic elastic compressibility k̂ 0.003 0.008Shear modulus G0 15,000 kPa 13,000 kPaReference mean stress pr 1 kPa 1 kPa

Hardening constant Logarithmic plastic compressibility Bp 0.015 0.045Yield function parameters Shape parameters af 0.63 0.63

mf 0.99 0.99Mc 1.10 1.23Me 1.00 1.10

Hydromechanical parameters Suction-hardening parameter rsw 2.7 5.5SWRC shape parameters avg 0.05 0.06

mvg 0.26 0.053nvg 1.6 5.6

Fig. 3. Comparison between model simulations and data from Maswoswe (1985): (a) evolution of void ratio with applied net stress for three tests onLCT soil; (b) stress paths plotted in terms of saturated mean effective stress (p2 uw) and mean net stress (pnet) for Test LCT4

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[Fig. 3(a)]. Yield surface parameters were chosen to capture the stresspath from Test LCT4 [Fig. 3(b)]. In particular, the shape parametersaf and mf were selected to obtain a nearly elliptical yield surface,which allowed the stress path to be captured accurately. In ad-dition, the good performance in capturing both the compressionresponse and the stress evolution corroborates the initial choice ofan associated flow rule.

The performance of the calibrated model is shown in Fig. 3. Asexpected, upon wetting, the void ratio of Test LCT3 approached thecompression curve of the saturated sample at the corresponding levelof stress (LCT1). Using the same calibration, the isotropic test inFig. 5 was also predicted satisfactorily, because the simulationagreed well with the compression data and correctly predicteda decrease in void ratio similar to that discussed for the previousexperiments.

Simulation of Tests by Jennings and Burland (1962)

The model was calibrated to reproduce the wetting compactionbehavior observed in classical experiments performed by Jenningsand Burland (1962). The tests were performed on pure quartz silt.Dry silt wasmixedwithwater to form a saturated slurry of 35%watercontent. Unsaturated samples with low degrees of saturation

(Sr 5 19%)were obtained via air drying. One slurry sample and foursamples of reconstituted unsaturated silt (RUS) were then loadedunder oedometric conditions (i.e., vertical loading with no radialdisplacement). The unsaturated samples were eventually soaked atvarious levels of constant vertical net stress. A significant decrease invoid ratio was observed in all samples as the state of the specimenstended to converge to the normal compression line of the saturatedslurry [Fig. 6(a)].

The model parameters were calibrated by fitting the simu-lations against the measurements from the aforementionedexperiments (Table 1). The slurry was modeled as normallyconsolidated, and its compression behavior was used to define thevalues of k̂ and Bp. The tests on unsaturated samples were sim-ulated by using the same compression properties of the slurry,whereas the parameters of the SWRC of the unsaturated silt werecalibrated using data reported by Jennings and Burland (1962)[Fig. 6(b)]. Because the stress paths during loading and/or wettingwere not available, the same yield surface shape as that determinedfor LCT was used. In addition, as in the previous calibrationexample, an associated flow rule was adopted, and the value of thesuction-induced hardening parameter, rsw, was chosen to re-produce the decrease in void ratio recorded during the wettingstage.

To replicate the drying process performed in the experimentsprior to oedometric compression, a suction increase stage wassimulated up to Sr 5 19%. Suction-controlled loading was thensimulated, eventually modeling four wetting tests at different valuesof vertical net stress [Fig. 6(a)]. Using this calibration, the simulatedwetting stage predicted compaction of the samples up to a final statelocated in the proximity of the compression curve for the saturatedslurry, as observed in the experiments.

Interpretation of Model Simulations

The stability of simulated compaction events can be assessed viacontrollability criteria based on the second-order work equation.Here, both suction control and water content control were consid-ered. For this purpose, the simulated response for wetting pathsRUS2 (pure silt) and LCT3 (sandy clay) were inspected in detail inFigs. 7(a) and 8(a), respectively. Based on the simulations, the voidratio decreased during suction removal, whereas the water ratioincreased up to complete saturation (e5 ew). The computed second-order work is always positive, suggesting that these wetting pathswere in fact stable.

This result can be interpreted in light of energy criteria. If thesecond-orderwork iswritten as in Eq. (2), constant vertical net stressand constrained radial strains cause the first component of d2W to bezero. As a result, the energy supply during a wetting test dependsonly on the changes in suction andwater content. The stability of theprocess can thus be inferred from the rate of these hydrologicvariables. From Figs. 7(a) and 8(a), it is apparent that the water ratio(ew) consistently increases with decreasing suction, thus implyinga positive second-order work throughout the wetting stage. Hence,the simulated change in configuration during suction removal isassociated with a positive energy input, which suggests that externalwork is needed to modify the degree of saturation and inducedeformations in the sample.

A similar analysis can be performed using the second-order workexpression given in Eq. (1). Under constant net stress, because ofdecreasing suction and increasing volumetric strains (i.e., compac-tion), the first component of Eq. (1) is negative. On the other hand, thesecond component of d2W is positive, because under decreasingsuction, the degree of saturation steadily increases in accordance with

Fig. 4. Measured soil water retention curve (data from Maswoswe1985) and model calibration

Fig. 5. Isotropic compression data from Maswoswe (1985) and cor-responding model simulation (LCT5)

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Fig. 6. Comparison between model simulations and data from Jennings and Burland (1962): (a) compression response for saturated and unsaturatedspecimens and compaction upon wetting for four tests (RUS1e4); (b) soil water retention curve

Fig. 7. Controllability analysis of wetting test on RUS soil (simulated wetting path at 380 kPa confining pressure, RUS2): (a) predicted evolution ofvoid ratio, water ratio, and second-order work upon decreasing suction; (b) controllability indices for suction control (detXs

OED), water content control(detXwc

OED), and lower bound of controllability (detDs); to facilitate comparison, controllability indices were normalized by their initial values at theonset of wetting

Fig. 8.Controllability analysis of wetting test on LCT soil (simulatedwetting path LCT3): (a) predicted evolution of void ratio, water ratio, and second-order work upon decreasing suction; (b) controllability indices for suction control (detXs

OED), water content control (detXwcOED), and lower bound of

controllability (detDs); to facilitate comparison, controllability indices were normalized by their initial values at the onset of wetting

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the adopted retention behavior. Again, in this situation, the hydrauliccomponent of the second-order work

d2W½ �H ¼ 212½nð _ua2 _uwÞ� _Sr ¼ 2

12n _s _Sr . 0 (15)

dominates and causes positive values of d2W [Figs. 7(a) and 8(a)].Although positive values of second-order work suggest a stable

wetting path, the effect of the control conditions must also be ex-plored. In particular, it is necessary to compute controllabilityindices for suction control (detXs

OED) and water content control(detXwc

OED), as well as the index associated with the positive defi-niteness of the energy input (detDs). These results are presented inFigs. 7(b) and 8(b). In accordance with the sign of second-orderwork, the evolution of detXs

OED and detXwcOED during the RUS2

simulation indicates that both modes of saturation are admissible.A similar result was obtained for the simulated LCT3 specimen, forwhich the computed values of detXs

OED and detXwcOED were posi-

tive during the wetting stage. Steadily increasing water ratio andvolumetric strainwith decreasing suctionwere also computed for theremaining RUS tests and the isotropic wetting path LCT5, and thecorrespondingmaterial stability analyses arepresented inFigs. 9 and10,

respectively. As in the previous cases, both second-order work andcontrollability indices indicate that the observed wetting-inducedcompaction can be interpreted as a stable/controllable process. Theevolution of detDs for the unsaturated silt and the LCT specimens,however, indicates differences between the wetting responses of thetwo soils. Although consistently positive values of detDs were-computed for RUS2 [Fig. 7(b)], the prediction for Test LCT3 revealsan interval of suction values with detDs , 0 [Fig. 8(b)]. As a result,whereas the oedometric wetting of the unsaturated silt (RUS)is always predicted to be controllable regardless of the mode ofloading, the model suggests that there exists a set of control con-ditions for which the response of LCT may not be controllable. Inother words, during the inspected simulation, the state of LCT ispredicted to come across a region of potentially noncontrollableresponse. Such a potential for instability increases during wetting,until it disappears when the specimen approaches full saturation. Asdiscussed by Buscarnera (2014), such instability potential is con-trolled by the material constants that govern the hydromechanicalcoupling. As a result, a parametric analysis is required to identify theproperties that exacerbate the tendency of the soil to transit fromcontrollable wetting compaction to an unstable collapse caused bysaturation.

Fig. 9.Controllability analysis for four wetting tests performed on RUS soil by Jennings and Burland (1962) (RUS1e4 at 187, 380, 760, and 1,513 kPavertical net stress, respectively): (a) second-order work; (b) controllability indices for suction-controlled loading (detXs

OED) and water content-controlled loading (detXwc

OED)

Fig. 10. Controllability analysis for isotropic wetting test performed byMaswoswe (1985) (simulation LCT5): (a) second-order work; (b) normalizedstability criteria for suction-controlled (detXs

ISO) and water content-controlled (detXwcISO) loading

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Because the suction-hardening parameter, rsw, is the constantthrough which hydromechanical coupling is incorporated, theeffect of this parameter was explored in greater detail. As shownin Eq. (14), rsw dictates the extent of hardening or softeningcaused by changes in the degree of saturation. As a result, largevalues of this constant are expected to deteriorate the size of theyield surface during a wetting path, thus exacerbating the po-tential for inelastic compaction (Buscarnera and Nova 2009).

To study this effect, the wetting path in LCT3 was resimulated forincreasingvaluesof rsw,whereas the remainingmodel parameterswerekept unchanged (Fig. 11). As rsw increases, the values of computedsecond-order work decrease, until becoming negative before completesaturation. This result indicates that wetting of a water-sensitive soil(i.e., a soil characterized by large values of rsw) may be susceptible toa loss of control of the wetting stage. To corroborate this statement,controllability indices for both suction control and water contentcontrolwere plotted in Fig. 11(b).Although suction-controlledwettingis predicted to be stable throughout the wetting path (i.e., detXs

OED. 0, as in the previous analyses), the index for water content controlreaches zero for large values of rsw. The points of instability associatedwith detXwc

OED5 0 in Fig. 11 (gray circles) correspond to the onset ofnonpositive second-order work [Fig. 11(a)], as well as to a peak inwater ratio [ _ew 5 0 in Fig. 11(c)]. These results indicate that, for theselected range of parameters, the wetting path becomes non-controllable under a water injection scenario [i.e., a threshold for thewater content is attained, similar to the sketch in Fig. 1(d)].

In other words, the model suggests that even a negligible in-crement of water content can produce a sharp accumulation ofcompaction. Similar results were obtained if the value of rsw waslikewise increased in the other simulated wetting paths on RUS andLCT soils. Although these results are not shown here for the sake ofbrevity, the increase in the instability potential is always obtainedwith magnified values of water sensitivity (i.e., for values of rswlarger than those calibrated for the two soils considered in this study).It should also be noted that larger values of rsw also cause a loss ofpositive definiteness of the constitutive operators of RUS and LCTsoils [i.e., negative values of detDs (Fig. 12)], further emphasizingthat high water sensitivity has detrimental effects on the state ofstability of soils subjected to wetting.

Because a loss of controllability is amenable to a failure event(i.e., a loss of strength), it is useful to compare the preceding pre-dictionswith typical interpretations based on failure envelopes in thestress space. Indeed, although the controllability analysis cap-tures loss of strength under stress control [i.e., it recovers failureenvelopes as a particular case (Buscarnera et al. 2011)], it alsoencapsulates the effect of nonstandard control conditions (e.g.,partial strain control, as in an oedometer), as well as changes indrainage (Buscarnera and Whittle 2013).

Consider theMohr circles associated with the RUS2 wetting path[Fig. 13(a)], plotted on theMohr plane for a failure line characterizedby friction angle, f5 28� (back calculated from the values inTable 1). Conditions at the initial state (point A), at the onset of

Fig. 11. Effect of increasing values of suction-hardening parameter, rsw, on the controllability of the wetting path LCT3: (a) second-order work;(b) normalized controllability indices for both suction control (solid lines) andwater content control (dashed lines); (c) water ratio; (d) volumetric strain,plotted against suction

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wetting (point B), and at the postwetting state (point C) are con-sidered. All stress states lie below the failure line, and hence do notviolate the boundaries of limit strength associated with frictionalfailure. In addition, they also satisfy the controllability criteria, asidentified in Fig. 7. The same analysis can be considered for theLCT3 wetting path [Fig. 13(b)], where a friction angle of 31� wasselected in accordance with the data reported byMaswoswe (1985).Again, the states never reach the failure line, and at the same time donot contradict the energy-based stability analysis discussed throughFig. 8.

The same analysis was repeated for wetting paths modeled forsimulated soils with greater water sensitivity (i.e., larger values ofrsw), whichwere previously shown to be not controllable underwatervolume injection. The stress states for the RUS2 wetting path weresimulated with rsw 5 30 [Fig. 14(a)], and the stresses correspondingto the onset of instability (detXwc

OED 5 0 and d2W5 0) are repre-sented by a dashed circle. It is readily apparent that, although thecontrollability is predicted to be lost for a soaking path, the stressstates are still strictly inside the failure domain. Similarly, if suction-induced hardening is alsomagnified in the LCT3 simulation (e.g., byusing rsw 5 9:5), the states at the onset of instability (B) and at

saturation (C) both remain below the failure line [Fig. 14(b)].Therefore, controllability methods are needed for a correct me-chanical interpretation, because they include the effect of imposedloading constraints and can capture losses of strength duringwettingthat would otherwise be overlooked by classical failure criteria.

Conclusions

Classic evidence of wetting-induced compaction (a phenomenon of-ten referred to as wetting collapse) has been reinterpreted throughmaterial stability criteria. The main goal of this study was to un-derstand whether these phenomena are a signature of an unstable soilresponse. For this purpose, it was hypothesized that the accumulationof strains during wetting is a plastic process, and its phenomenologywas described through a basic constitutive law for unsaturated soils.The parameters of themodel were calibrated for twofine-grained soilswidely studied in the literature, considering various test configurations(i.e., oedometric and isotropic compression) and loading/wettingmodes (e.g., suction-controlled loading, compression at constantwater content, water inundation). Despite the simplicity of the model,

Fig. 12. Controllability criteria for potentially unstable wetting paths with high rsw: (a) RUS2 with rsw 5 30 ; (b) LCT3 with rsw 5 8:5; normalizedcontrollability indices for suction control (detXs

OED) and water content control (detXwcOED) and lower bound of controllability (detDs)

Fig. 13. Evolution of stress states predicted for simulations: (a) RUS2; (b) LCT3; Mohr circles associated with stress conditions at initial loadingstage (A), at onset of wetting (B), and at saturation (C) are shown

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a satisfactory performancewas obtained in terms of both compressionresponse and predicted stress paths.

The good agreement between the data and the predictions cor-roborated the hypotheses about the plastic response of the soil, andinspired the inspection of the simulations through criteria able todetect a loss of stability of the wetting path. For this purpose, twodistinct wetting modes were considered: (1) suction-controlled sat-uration and (2) water volume injection. It was shown that thesescenarios constitute a hydraulic analog of the duality between strainand stress control. In fact, whereas for suction control the de-terioration of the soil is directly governed, in the case of watercontent control (e.g., water undrained compression or inundation viafluid injection) the degree of deterioration is no longer imposed, butrather, is a function of the soil response. In addition, the quadraticform associated with the energy input necessary to wet and/or de-form the soil was inspected with the purpose of determiningwhether other modes of deformation not encompassed by oedo-metric conditions could also become unstable during wetting(i.e., whether these modes could be activated by a vanishinglysmall energy input).

The analyses suggested that the oedometric wetting stage of thetwo considered soils was controllable regardless of the mode ofsaturation. In other words, the considered wetting experiments werenot characterized by a loss of stability. Nevertheless, the analysisrevealed that in one of the two soils, the boundaries of unconditionalcontrollability (i.e., the ability to sustain any type of deformation/loading mode) were crossed prior to full saturation. This circum-stance was predicted despite the enforcement of oedometric con-straints, which usually tend to hinder unstable mechanisms. Sucha prediction was explained as an outcome of the interplay betweenchanges in suction and inelastic strains (i.e., hydromechanicalcoupling). A parametric analysis corroborated this concept, showingthat noncontrollable compaction is, in principle, possible only in thepresence of a magnified water sensitivity. Such events have beenpredicted to occur strictly inside the frictional failure domain, andhence, cannot be anticipated by standard failure theories (i.e., theirprediction requires advanced interpretation strategies).

These results provide a novel interpretation of the concept ofwetting collapse, which for the first time was studied througha proper definition of controllable wetting path. This reinterpretationsuggests that typical fine-grained soils do not experience actualcollapses, but rather, stable forms of compaction driven by changes

in their hydrologic state. Nevertheless, the study has also pointed outthat hydromechanical coupling has detrimental effects on the state ofstability, and saturation paths may contribute to a progressive in-crease in the potential for noncontrollable deformations even underusually safe stress configurations (e.g., in an oedometer). The sim-ulations suggest that such circumstances are possible only in thepresence of highly water-sensitive soils exposed to a drastic loss ofsuction. In those cases, nonstandard analyses based on plasticitytheory and continuum mechanics are necessary to assess the po-tential for unstable compaction, because they can support the in-terpretation of wetting-induced settlements and the safetyassessment of unsaturated earthen systems interacting with hydro-logic processes.

Appendix. Yield Surface and PlasticPotential Expressions

The model proposed by Buscarnera and Nova (2009) adopts yieldsurface and plastic potential expressions proposed by Lagioia et al.(1996). Such a yield surface can be written as

f ¼ AK1f=Cf

f B2K2f=Cf

f p92 ps ¼ 0 (16)

where

K1f

K2f

�¼ mf

�12 af

2�12mf

16

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi12

4af�12mf

mf

�12 af

2vuut

264

375 (17)

Af ¼ 1þ 1K1f Mc

qp9

(18)

Bf ¼ 1þ 1K2f Mc

qp9

(19)

Cf ¼�12mf

�K1f 2K2f

(20)

where q5 deviatoric stress; p9 5mean effective stress; andMc,mf ,and af 5 shape parameters.

Fig. 14. Evolution of Mohr circles for wetting paths at high rsw values: (a) RUS2 simulated with rsw 5 30 ; (b) LCT3 simulated with rsw 5 9:5; stressstates at onset of wetting (B), at potential loss of stability (dashed line), and at end of wetting (C) are noted

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Nonassociated plastic flow can be incorporated by using a plasticpotential having the same equations but different shape parameters.In this paper, an associated flow rule was implemented, as is typicalfor fine-grained soils. The parameterMc therefore was computed onthe basis of the friction angle f of the considered soils, as follows:

Mc ¼ 6 sinf32 sinf

(21)

whereas the shapeparametersmf and af were chosen to obtain a yieldsurface close to an elliptic envelope, as is customary for fine-grainedsoils.

Acknowledgments

This work was supported by the U.S. National Science Foundation,Geomechanics and Geomaterials Program, under Grant Nos. CMMI-1234031 and CMMI-1443791.

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