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Keywords:

  • Hydromechanical coupling;
  • unsaturated soil;
  • volume change behavior;
  • anisotropy;
  • effective stress

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Stresses and Strain Variables
  5. 3. Experimental Investigation: Material, Equipment and Procedures
  6. 4. Experimental Evidence of Initial and Strain-Induced Anisotropy
  7. 5. Constitutive Modeling
  8. 6. Numerical Simulation of the Isotropic Test Data
  9. 7. Oedometer Tests: Experimental Data and Numerical Simulations
  10. 8. Summary and Conclusions
  11. Acknowledgments
  12. References
  13. Supporting Information

[1] Volume changes of natural and compacted soils induced by changes in their water content have many practical implications in the service life of earth dams, river and canal embankments, and waste disposal facilities. An insight into the overall strain response of a clayey soil upon gradual wetting and drying is provided here. Experimental data coming from oedometer and isotropic tests under suction and net stress control are presented for a compacted clay with an initial anisotropic fabric, highlighting the relevant role played by the hydraulic path on collapse, swelling, and shrinkage strains. Irreversible strains could be observed after wetting-drying paths and the subsequent drying-wetting cycle. Both stress and hydraulic histories play a role in the evolution of the directional fabric of clayey soils. The experimental data could be reproduced with a rather simple elastic-plastic constitutive model with a mixed isotropic-rotational hardening, previously conceived for saturated soils. The model is extended to unsaturated conditions by substituting the saturated effective stress with a measure of the average stress acting on the soil skeleton and by introducing generalized hardening rules governed by both plastic strains and degree of saturation. Coupling between the mechanical and the hydraulic behavior is provided by the water retention curve, in which degree of saturation is adopted as a useful measure of the soil water content.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Stresses and Strain Variables
  5. 3. Experimental Investigation: Material, Equipment and Procedures
  6. 4. Experimental Evidence of Initial and Strain-Induced Anisotropy
  7. 5. Constitutive Modeling
  8. 6. Numerical Simulation of the Isotropic Test Data
  9. 7. Oedometer Tests: Experimental Data and Numerical Simulations
  10. 8. Summary and Conclusions
  11. Acknowledgments
  12. References
  13. Supporting Information

[2] The determination of strains induced in natural and compacted soils by changes in their water content is of relevant importance in the analysis of many engineering constructions, like dams, river and canal embankments, waste disposal facilities, railway and road embankments [Pereira and Fredlund, 2000; Lim and Miller, 2004; Alonso et al., 2005a]. Enhancing the tools for a reliable prediction of the expected strains under environmental actions should help in the design of safer and cheaper earth constructions.

[3] It may be recognised that a drying process is always accompanied by a reduction of the soil volume, which may be associated both with shrinkage of the soil aggregates and with an increase in the average volumetric stress acting on the soil skeleton as a consequence of increasing suction. These processes may be only partly reversible, as irreversible strains observed in drying and wetting cycles at constant stress demonstrate [Dif and Bluemel, 1991; Fleureau et al., 1993; Day, 1994; Alonso et al., 2005b].

[4] On the contrary, clayey soils undergoing a wetting process may either expand or experience a volume reduction – collapse – due to different competing deformation mechanisms, which may in turn prevail one on the other as a function of stress level, stress history and hydraulic history [Maswoswe, 1985; Gens et al., 1995; Kato and Kawai, 2000; Sun et al., 2004; Jotisankasa, 2005]. Expansion may be due to swelling of the clay aggregates themselves due to water uptake. In this case, the amount of expansion observed at the macroscopic level depends mainly on the soil activity, although increasing the total stress will reduce the possibility for the soil to swell. Besides, an increase in water content is accompanied by a reduction of suction, which results in a decrease of the average volumetric stress acting on the soil skeleton, with a consequent elastic volumetric expansion. On the other hand, it is well known that wetting may induce softening of the macrostructure formed by the aggregates, whose stability may be ensured temporarily by the action of suction. Destructuration of the macrostructure induced by a reduction of suction manifests itself through an abrupt irreversible decrease of volume. Soils compacted dry of optimum at low dry density are well recognised to undergo collapse when wetted under constant total stress [Booth, 1977; Lawton et al., 1989, 1992; Noorany, 1992], but recent experimental investigations show that fine grained soils even compacted at optimum conditions or wet of optimum may experience collapsible behavior at high stresses, if they undergo drying before the wetting process [Gens et al., 1995; Suriol et al., 1998]. The experimental data clearly suggest that the whole coupled hydromechanical history of the soil should be analysed to interpret correctly the volumetric behavior of unsaturated soils.

[5] As many compacted soils, as well as natural soils, have an initial anisotropic structure due to the compaction operations or to the preferential depositional direction, respectively, the amount of volumetric strain alone is not expected to be an exhaustive measure of the strains experienced by soils undergoing drying or wetting. Distortional effects are expected to accompany volumetric strains of an anisotropic soil, even when undergoing generalised isotropic loads like drying or wetting processes. Moreover, the directional fabric of an anisotropic soil is expected to be affected by the development of irreversible strains, irrespective of the external agent that causes this irreversibility, hence even in simple drying and wetting cycles. The evolution of the initial anisotropic fabric affects in turn swelling and collapse response, as well as stiffness and water permeability tensor.

[6] In spite of its practical relevance, the role of initial anisotropy, and its evolution in processes involving water content changes, has not received much attention in the past. Zakaria et al. [1995], by measuring axial and radial strains independently in axisymmetric triaxial tests, reported a significant initial anisotropy due to the one-dimensional compaction procedure adopted for the preparation of the samples. Further, they observed that an isotropic loading stage was able to erase the initial anisotropy created during compaction. Cui and Delage [1996] showed experimental results substantiating the development of an anisotropic fabric on oedometer compaction, and provided some information on the associated irreversible strains. More recently, Romero et al. [2003] compared the collapse behavior under constant isotropic net stress of two different statically compacted soils, one axially strained and the other prepared by isotropic compaction. A clear anisotropic evolution of collapse strains was detected in the sample compacted in oedometer as opposed to the isotropically compacted one. Estabragh and Javadi [2006] presented further experimental data supporting the evidence of the anisotropic fabric due to compaction and suggesting that the degree of anisotropy was a function of the stress history of the soil.

[7] The aim of the work presented in this paper is to provide a contribution to a sounder understanding of the strain history of anisotropic clayey soils undergoing hydraulic loads. A laboratory investigation was designed to study the strain response of a one-dimensionally compacted soil upon wetting and drying. Part of the testing program was carried out using a controlled-suction axisymmetric triaxial cell, in which volumetric and shear strains were monitored with local axial and radial transducers. The development of distortional strains accompanying volumetric strain during gradual wetting could be successfully examined under constant isotropic external stress. Besides, more traditional one-dimensional wetting and drying tests were run in a controlled-suction oedometer to verify the influence of the stress level on the sign and the amount of volumetric strain.

[8] The triaxial data presented clearly highlight the change of the direction of the plastic strain increment vectors occurring along wetting paths, which strongly suggests that a constitutive model allowing for the effects of anisotropy should be adopted to describe the observed behavior correctly.

[9] In the second part of the paper the experimental tests are numerically simulated with a simple elastic-plastic constitutive model, which proves able to capture the relevant features of the experimental data. The model is built following the conceptual approach proposed by Jommi and di Prisco [1994], who extended a model with a mixed isotropic-kinematic hardening rule, previously conceived for saturated sands [di Prisco, 1992; di Prisco et al., 1993], to unsaturated states.

2. Stresses and Strain Variables

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Stresses and Strain Variables
  5. 3. Experimental Investigation: Material, Equipment and Procedures
  6. 4. Experimental Evidence of Initial and Strain-Induced Anisotropy
  7. 5. Constitutive Modeling
  8. 6. Numerical Simulation of the Isotropic Test Data
  9. 7. Oedometer Tests: Experimental Data and Numerical Simulations
  10. 8. Summary and Conclusions
  11. Acknowledgments
  12. References
  13. Supporting Information

[10] All the experimental data presented herein refer to axisymmetric test conditions and a full description of the soil state may be accomplished by adopting triaxial stress and strain variables. The total stress state is described by total mean stress, p = (σa + 2σr)/3, deviator stress, q = σaσr, and suction, s = uauw, where ua and uw are the air and the water pressures. As for the strain variables, volumetric strain, ɛv = ɛa + 2ɛr, and shear strain, ɛs = 2 (ɛa − ɛr)/3, will be adopted throughout the paper. Subscripts a and r refer to axial and radial strain components, respectively.

[11] Houlsby [1997] presented a clear demonstration that different variables may be conveniently adopted in the description of the constitutive behavior, provided the variables chosen were work conjugate with the strain variable increments. During experimental tests, total stress and fluid pressures may be controlled or measured. In the experimental program presented herein air pressure was held constant throughout the tests, hence the net stress is the more natural choice to represent the experimental data. In the following, mean net stress, p″ = (σa + 2σr)/3 − ua, and deviator stress, q = σaσr, will be adopted in the presentation of the experimental data.

[12] Besides, a measure of the average stress acting on the soil skeleton may provide some advantages in the development of comprehensive constitutive models [see, e.g., Jommi, 2000; Sheng et al., 2004; Nuth and Laloui, 2008]. Hence, in the formulation of the model presented herein, the mean skeleton stress, equation image = [(pua) + Srs] = p″ + Srs, is adopted as constitutive stress, together with the deviator stress, q. Sr stands for the degree of saturation.

[13] For the description of the amount of pore water, both gravimetric water content, w, and degree of saturation, Sr, will be adopted. The gravimetric water content is the more natural choice when presenting the experimental data, while the degree of saturation is useful in the development of models for the retention curve.

3. Experimental Investigation: Material, Equipment and Procedures

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Stresses and Strain Variables
  5. 3. Experimental Investigation: Material, Equipment and Procedures
  6. 4. Experimental Evidence of Initial and Strain-Induced Anisotropy
  7. 5. Constitutive Modeling
  8. 6. Numerical Simulation of the Isotropic Test Data
  9. 7. Oedometer Tests: Experimental Data and Numerical Simulations
  10. 8. Summary and Conclusions
  11. Acknowledgments
  12. References
  13. Supporting Information

[14] The soil used for the study is Boom clay from Mol (Belgium), which has been extensively investigated in relation to radioactive waste disposal facilities. This moderately swelling clay (20%–30% kaolinite, 20%–30% illite and 10%–20% smectite) has a liquid limit of wL = 56%, a plastic limit of wP = 29%, a density of solid particles of ρs = 2.70 Mg/m3 and 50% of particles smaller than 2 μm.

[15] The data presented hereafter refer to samples obtained by static compaction under oedometer conditions, on the dry side of optimum, at water content w = 15% and dry density ρd = 1.40 Mg/m3. In Figure 1, the as-compacted state is compared on the conventional Proctor plane with different compaction data obtained by both static and dynamic procedures. The relatively high initial void ratio (e0 = 0.93) and low initial degree of saturation (Sr0 = 0.44) - i.e., on the dry side of optimum - were chosen to allow for collapse to occur on wetting and to study how water content deficit with respect to optimum could affect the behavior of the soil. It is worth noting that in field practice dry density is usually more controlled than mixing water content, which often simply depends on the construction season. The dry density chosen for the compacted soil for this experimental investigation is not far from the optimum standard Proctor value.

image

Figure 1. As-compacted state of Boom clay. Static and dynamic compaction curves.

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[16] The constant water content loading path to prepare the soil samples (path AB in Figure 2) and the following unloading path prior to testing (path BC in the same figure) were performed at an approximately constant suction of 1.9 MPa, which was determined from psychrometer readings, up to a maximum vertical net stress of 1.2 MPa. An oedometer cell with an active lateral stress system [Romero, 1999] was used for the preparation of the soil sample. Lateral stress measurement showed that the maximum vertical net stress was achieved under a relatively constant horizontal to vertical net stress ratio K0 = 0.37.

image

Figure 2. Stress paths followed on sample preparation and hydraulic cycles at constant mean net stress (static compaction ABCD, isotropic loading DE, and wetting/drying/wetting cycle EFGH).

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[17] After preparation, some samples were reloaded at constant water content in a controlled-suction oedometer cell schematically shown in Figure 3, up to four different vertical net stresses, namely 0.085, 0.30, 0.60 and 1.2 MPa. Wetting was then carried out using axis translation technique with four equalisation stages (s = 0.45, 0.20, 0.06 and 0.01 MPa). Afterwards, a multi-step drying, up to s = 0.45 MPa, and a subsequent wetting path were performed at the same vertical net stresses, following the same equalisation stages. Air pressure was maintained constant at 0.5 MPa throughout the wetting-drying-wetting process.

image

Figure 3. Controlled-Suction oedometer cell used in the experimental investigation.

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[18] Another soil sample was removed from the compaction mould, releasing both axial and lateral stresses (path CD in Figure 2), and mounted in a controlled-suction triaxial cell. The sample was then compressed isotropically (path DE in Figure 2) at constant water content up to a mean net stress p″ = 0.6 MPa. Afterwards, the sample underwent a wetting path EF with the same four equalisation stages as before (s = 0.45, 0.20, 0.06 and 0.01 MPa), at constant mean net stress. At the end of the first wetting path, the multi-step drying and wetting cycle FGH was performed at the same mean net stress up to s = 0.45 MPa, following the same equalisation stages.

[19] The triaxial equipment used in the investigation is schematically depicted in Figure 4. Suction control was provided to the sample (76 mm high and 38 mm in diameter) by axis-translation technique applied to both ends. Top and bottom platens included a combination of two porous stones: a peripheral annular coarse one connected to a constant air pressure of 0.5 MPa (7 in Figure 4) and an internal high air-entry value ceramic disc connected to varying water pressure (6 in Figure 4). Double drainage ensured a significantly shorter equalisation stage, an important advantage when testing low-permeability unsaturated soils. Axial strains were measured locally using two diametrically opposite miniature LVDTs, which were directly mounted on the specimen (2 in Figure 4). Radial strains were also measured locally with a non-contact system that uses two electro-optical laser sensors mounted on two opposite external columns (3 in Figure 4). This system can be used as radial displacement scanner by moving the sensors throughout the sample height. In this way, the whole profile of the sample from the base to the top cap could be measured and the average radial strain determined. This approach is best suited for the determination of the degree of saturation of the sample and when the specimen tends to deform non-uniformly because of end restraint effects.

image

Figure 4. Controlled-Suction triaxial apparatus used in the experimental investigation.

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[20] More details on the experimental equipments may be found in the works by Romero et al. [1997], Romero [1999] and Barrera et al. [2000].

4. Experimental Evidence of Initial and Strain-Induced Anisotropy

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Stresses and Strain Variables
  5. 3. Experimental Investigation: Material, Equipment and Procedures
  6. 4. Experimental Evidence of Initial and Strain-Induced Anisotropy
  7. 5. Constitutive Modeling
  8. 6. Numerical Simulation of the Isotropic Test Data
  9. 7. Oedometer Tests: Experimental Data and Numerical Simulations
  10. 8. Summary and Conclusions
  11. Acknowledgments
  12. References
  13. Supporting Information

[21] As suggested by Mitchell [1972] and Hueckel and Pellegrini [1996] deviation from isotropic behavior can be conveniently analysed in isotropic loading and unloading paths. In the following, the results of the controlled-suction wetting-drying-wetting cycle performed under constant isotropic net stress will be presented and discussed, to highlight the role played by the initial anisotropic structure of the compacted soil on its strain response, and to show how suction induced plastic strain will affect the degree of anisotropy.

[22] Figure 5 plots the time evolution of axial, ɛa, radial, ɛr, shear, ɛs, and volumetric, ɛv, strains, as well as water content, w, and degree of saturation, Sr, changes, that the sample underwent upon applying a suction change from s = 1.9 MPa to 0.45 MPa at p″ = 0.6 MPa. Strain ratio, ɛar, is also indicated for a complementary description of sample distortion on wetting. In the figure, ɛr evolution plotted with solid line corresponds to mid-height readings. Average global ɛr values, measured on the sample height at specific elapsed times, are indicated with dashed lines. Systematically lower average ɛr values have been calculated because of end restraint effects, which affect the development of collapse strains at the contact with the loading caps. The figure also shows in dashed lines ɛs and ɛv strains calculated on radial strain average basis.

image

Figure 5. Time evolution of strains, water content, and degree of saturation. Suction step of path EF: 1.9 to 0.45 MPa.

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[23] As expected for the one-dimensionally compacted sample, a clear development of shear strain ɛs on wetting is observed, tending to ɛs = −0.65%, that corresponds to ɛar = 0.6. The transversally isotropic fabric provides greatest stiffness in the axial direction, leading to the development of smaller collapse strain in this direction. The volumetric strain ɛv describes a monotonic collapse of the sample. While radial strain ɛr monotonically decreases throughout the suction step, some small expansion is recorded by the axial displacement transducers before detecting collapse. This initial strongly anisotropic response will be further discussed in the light of the constitutive model and the numerical simulations presented in the next sections.

[24] Figure 6 shows the time evolution of the same quantities for the suction step from s = 0.20 MPa to 0.06 MPa. The nearly equal evolution of ɛa and ɛr components indicates that the material anisotropy was progressively erased on saturation and suction-induced plastic straining. As observed in the figure, minor differences are detected between mid-height and average ɛr values.

image

Figure 6. Time evolution of strains, water content, and degree of saturation. Suction step of path EF: 0.20 to 0.06 MPa.

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[25] The evolution of strain, water content and degree of saturation in the drying step s = 0.20 MPa to 0.45 MPa are plotted in Figure 7. Both ɛs and ɛar evolutions show a clear isotropic shrinkage. No important degree of saturation changes are observed, indicating that the air-entry value of the soil has not been surpassed in this drying step, hence suggesting that the water retention properties were affected by the previous wetting path.

image

Figure 7. Time evolution of strains, water content, and degree of saturation. Suction step of path FG: 0.20 to 0.45 MPa.

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[26] Figure 8 summarises the variation of ɛa, ɛr, ɛs and ɛv, as well as w and Sr changes, underwent by the sample throughout the whole wetting-drying-wetting at constant p″ = 0.6 MPa (path EFGH in Figure 2), as a function of suction. Under the assumption that local equilibrium between liquid and vapour phases were reached during the transient wetting stage, at least as an average, knowing the water content and the sample volume, degree of saturation and suction could be calculated at any time.

image

Figure 8. Evolution of strains, water content, and degree of saturation in the wetting, drying, and wetting paths EFGH.

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[27] The evolution of shear strain clearly shows that the response on wetting is definitely anisotropic in the first stage of the wetting episode, and that the degree of anisotropy reduces as suction-induced plastic volumetric strains accumulate and the degree of saturation increases. Finally, the response on subsequent drying is nearly isotropic.

[28] Plastic flow direction was further examined by plotting the evolution of plastic strain increments dɛsp/dɛvp as a function of s along the wetting stages. Figure 9 shows this variation for the following suction stages: s = 1.9 MPa to 0.45 MPa, 0.45 MPa to 0.20 MPa and 0.20 MPa to 0.06 MPa. In order to derive plastic strains from experimental data, elastic strains due to suction changes were evaluated from the elastic moduli determined along the reversible wetting path GH. The figure shows that the evolution of the plastic strain increments, measured by the ratio dɛsp/dɛvp, rapidly tends to zero, highlighting erasure of the initial anisotropy of the as-compacted material.

image

Figure 9. Evolution of dɛsp/dɛvp along the wetting path EF. Experimental results.

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5. Constitutive Modeling

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Stresses and Strain Variables
  5. 3. Experimental Investigation: Material, Equipment and Procedures
  6. 4. Experimental Evidence of Initial and Strain-Induced Anisotropy
  7. 5. Constitutive Modeling
  8. 6. Numerical Simulation of the Isotropic Test Data
  9. 7. Oedometer Tests: Experimental Data and Numerical Simulations
  10. 8. Summary and Conclusions
  11. Acknowledgments
  12. References
  13. Supporting Information

[29] The development of constitutive modelling of unsaturated soils in the framework of elastoplasticity originated from the first generalised hardening model proposed by Alonso et al. [1990]. The term generalised is adopted here to highlight that hardening of unsaturated soils depends not only on plastic strains, but on variables describing water content too. Following Alonso et al. [1990], suction is adopted most frequently for the description of the hardening mechanisms, but other choices may be equally acceptable [Gens, 1996; Gens et al., 2006]. Moreover, suction itself is not sufficient to describe an unsaturated state for a given soil. To complete the description, a measure of the soil water content must be provided, at least in between the state parameters of the soil [Wheeler, 1996]. Besides, the role of hysteresis of the water retention mechanisms on the mechanical behavior of unsaturated soils should be considered [Tamagnini, 2004; Sheng et al., 2004; Nuth and Laloui, 2008].

[30] Notwithstanding the many developments in constitutive modelling of unsaturated soils, only few efforts were devoted to the study of the shape of the yield function and of the plastic potential of anisotropic compacted soils. To this respect, the work by Cui and Delage [1996] must be mentioned. To model the initial anisotropic fabric of a compacted silt, they proposed an analytical expression for the yield function, in the mean net stress – deviator stress plane, describing an elastic limit centred on an axis rotated with respect to the hydrostatic axis. Suggestion of a non-associated flow rule was motivated by the elaboration of the experimental data in the superposed net stress – plastic strain increment planes. The mechanical behavior of the compacted soil was then modelled only by assuming a change in the dimensions of the yield locus as a function of volumetric plastic strains and suction, with no further modification of the inclination of the initial rotated yield surface.

[31] An elastic-plastic model with generalised isotropic and rotational hardening depending on plastic strains and on degree of saturation was proposed by Jommi and di Prisco [1994]. Rotational hardening was a basic capability of the original model previously conceived by di Prisco [di Prisco, 1992; di Prisco et al., 1993] for saturated sands, but Jommi and di Prisco did not exploit this feature of the model, as at that time no experimental data were available to appreciate the relevance of anisotropy on the strain response. Anyway, to the authors' knowledge, no other model allowing for rotational hardening has been published so far for unsaturated soils.

5.1. Conceptual Basis of the Coupled Elastic-Plastic Model

[32] In the model presented in the following, the analytical expressions of the yield function and of the plastic potential, the hardening laws and the number of parameters were kept as simple as possible. Its conceptual bases stem from the proposal by Jommi and di Prisco [1994]. A modified Cam Clay model, with associated flow rule, was adopted instead of the original non-associated di Prisco's [1992] model, to simplify its calibration for Boom clay. Although simple, modified Cam Clay usually proves to be an effective choice as reference model for compacted clayey soils in saturated conditions, and only four parameters, coming from conventional saturated tests, are needed for its calibration.

[33] As in the original proposal by Jommi and di Prisco [1994], the yield function and the plastic potential for unsaturated conditions are analytical functions of the skeleton stress. This choice allows for a few advantages in formulating the constitutive model, as discussed by Jommi [2000] and most recently by Nuth and Laloui [2008]. Among them, the most important one is that the effects of hysteretic water retention mechanisms may be built naturally into the constitutive formulation. To the latter aim, the hysteretic retention curve proposed by Romero and Vaunat [2000] is introduced in the coupled hydromechanical model, in order to reproduce cyclic wetting and drying paths correctly [Tamagnini, 2004]. A hysteretic retention curve will prove to be quite important in modelling the mechanical response of the soil undergoing drying and wetting paths, as the following numerical simulations will demonstrate with reference to the experimental data discussed.

[34] A mixed isotropic-rotational hardening law depending on plastic strain and degree of saturation is introduced to model the soil structure evolution. Again, simple choices were made for the analytical functions adopted, to limit to a minimum the number of new parameters introduced to describe the behavior of the compacted soil in unsaturated conditions.

5.2. Hydraulic Model: The Water Retention Domain

[35] Recent trends in the interpretation and modelling the coupled hydromechanical behavior of unsaturated soils suggest that knowledge of the water retention properties of a soil is of vital importance not only to describe properly the changes in its water content, but also to complete the description of its actual stress state in unsaturated conditions [Jommi, 2000; Sheng et al., 2004; Nuth and Laloui, 2008].

[36] Both literature data [Ng and Pang, 2000; Kawai et al., 2000; Gallipoli et al., 2003b; Tarantino and Tombolato, 2005] and the experimental data presented in the previous section show that irreversible strains undergone by a soil along different hydromechanical stress paths affect its water retention properties. Nevertheless, as a first approximation, in the following it will be assumed that the water storage capacity of the soil investigated could be described by a unique hysteretic retention curve in the suction-degree of saturation plane.

[37] As the dependence of the water retention characteristics on irreversible strains is disregarded, the retention properties of the soil samples may be described by means of data coming from different data sets. Figure 10 shows the main wetting and drying branches of the water retention domain of the soil based on experimental data obtained for a constant void ratio of e0 = 0.93, hence with reference to the as-compacted condition. Data points at s > 3 MPa were obtained from different samples using vapour equilibrium technique. Data points at s ≤ 0.45 MPa were determined using axis translation technique under constant volume conditions [Romero, 1999].

image

Figure 10. Water retention curves fitted to equation (1) for Boom clay compacted to a dry density 1.4 Mg/m3.

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[38] Water retention data may be fitted to a modified form of van Genuchten [1980] expression for the degree of saturation, Sr, as a function of suction, s, [Romero and Vaunat, 2000]:

  • equation image

Parameters n, m and α describe the shape of the retention functions, as in the original van Genuchten's expression. Hysteresis is introduced by defining two different sets of parameters for the main drying branch and the main wetting branch of the retention domain, respectively. The inverse of parameter αD (for main drying) is related to the air-entry value of the soil in a drying path, while the inverse of αW (for main wetting) is related to the air occlusion pressure in a wetting path. The original van Genuchten's expression is not adequate to fit retention data for clayey soils at high values of suction. For this reason, the expression was modified by a correction function C(s), which makes the curve tend to a linear relationship between the logarithm of s and Sr in the high-suction zone, with intersection parameter a at Sr = 0.

[39] Inside the domain delimited by the main wetting and the main drying branches, the hydraulic behavior is assumed to be reversible, with a simple linear relationship between suction and degree of saturation. The slope of the scanning curves, ∂Sr/∂s = l, is given a constant value. Fitted parameters for the description of the water retention domain of Boom clay are listed in Table 1.

Table 1. Parameters of the Retention Curves According to Equation (1)
ParameterWetting BranchDrying BranchScanning Curves
a (MPa)300400
α (MPa−1)19.31.40
n1.120.95
m0.200.41
l (MPa−1)0.02

5.3. Mechanical Model: Plastic Potential, Yield Function and Hardening Laws

[40] The experimental program was mainly devoted to the study of the strain response of Boom clay under drying and wetting paths. No attempts were made to determine the actual shape of the current yield locus. Hence modelling was concentrated primarily on the evolution of plastic potential. In the development of models with rotational hardening for saturated clays some authors adopted associated flow rules [see, e.g., Dafalias, 1986; Korhonen and Lojander, 1987; Wheeler et al., 2003], while others suggested different analytical functions for the plastic potential and the yield locus [see, e.g., Newson and Davis, 1996; Dafalias et al., 2003, 2006]. In the absence of specific experimental data on compacted Boom clay, and following a common choice in unsaturated soil modelling, the yield function was assumed to coincide with the plastic potential. This choice may pose some limitations to the capabilities of the present model. Nevertheless, normality could be easily removed conceptually if the need for distinguishing between yield function and plastic potential should arise.

[41] Although some degree of anisotropy is expected for the elastic behavior too, the adoption of an isotropic elastic law is rather common in constitutive modelling of anisotropic soils [see, e.g., di Prisco et al., 1993; Wheeler et al., 2003; Dafalias et al., 2006]. This choice is usually justified by the assumption that elastic strains are small with respect to plastic strains, and do not affect the overall strain response in a relevant way. Here the classical non-linear elastic law adopted in critical state models, described by the logarithmic compliance, κ, and a constant shear modulus, G, is introduced.

[42] By just substituting the soil skeleton stress for saturated effective stress in the original form of modified Cam Clay [Roscoe and Burland, 1968], a convenient isotropic yield function for an unsaturated clayey soil may be written in the form:

  • equation image

In the previous equation, equation image0 is the preconsolidation pressure in unsaturated conditions, and parameter M, describing the slope of the critical state line, is assumed to be independent of suction. Although the latter assumption is still a matter of debate, many experimental results suggest that it can hold true (see, e.g., the data collection presented by Nuth and Laloui [2008]).

[43] To allow for the description of an anisotropic response, a rotation of the axis of the yield surface and plastic potential must be introduced. The proposal by Dafalias [1986] was followed here and the analytical expression of the yield surface and of the plastic potential adopted finally reads:

  • equation image

In equation (3), Mα represents the inclination of the current rotated yield surface with respect to the equation image axis.

[44] The two internal variables, equation image0 and Mα, govern the isotropic and rotational hardening, respectively, provided convenient hardening laws are defined. Figure 11 shows the shape of the rotated yield surface in the triaxial skeleton stress plane together with the geometrical interpretation of the two internal variables. In the figure, the plastic strain increment vector associated with an isotropic stress state at yield is drawn. The direction of the vector clearly shows that even adopting an associated flow rule, due to the rotation of the axis of the yield surface, a shear strain increment will be predicted for a purely isotropic stress increase at null deviator stress. Hence the previous choices, although rather simple, allow for modelling the distortional strain observed along an isotropic loading as a consequence of the anisotropic soil behavior.

image

Figure 11. Rotated yield surface and plastic strain increment vector for an isotropic stress state in the triaxial skeleton stress plane.

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[45] Taking advantage of the suggestion by Gallipoli et al. [2003a], the preconsolidation pressure in unsaturated conditions, equation image0, is defined as the sum of the preconsolidation pressure in saturated conditions, p*0, depending on volumetric plastic strains, plus a term also depending on the degree of saturation:

  • equation image

In the previous expression, b1 and b2 are model parameters ruling the dependence of preconsolidation pressure on the degree of saturation. For p*0, the classical critical state evolution law is adopted:

  • equation image

where λ and κ are the elastic-plastic and elastic logarithmic volumetric compliances, respectively, and e is the void ratio.

[46] Rotational hardening is assumed to be governed by the angle between the current obliquity, equation image = q/equation image, and the current inclination Mα of the yield surface:

  • equation image

as originally proposed by Dafalias [1986]. The dimensionless constant, c, governs the rate of evolution of Mα, while ξ controls the target value of Mα for a given obliquity, i.e., dMα = 0 when ξ = equation image/Mα.

[47] Although more advanced evolution laws have been proposed in the last years – an updated review is provided by Dafalias et al. [2006] –, the assumed rotational law has the advantage to allow for a direct calibration of the constants on the basis of relatively simple laboratory tests.

5.4. Mechanical Model: Calibration of the Parameters

[48] The model is defined in terms of eight material parameters. Four of them, M, λ, κ and G, describe the behavior of the isotropic soil under saturated conditions, and may be calibrated on the basis of conventional laboratory tests performed on saturated samples.

[49] The parameters M and G could be obtained from standard triaxial tests on saturated samples. A collection of values for the two parameters for various samples of Boom clay is presented in the report by Horseman et al. [1987]. The elastic shear modulus does not play a prominent role in the overall behavior. A value of G = 40 MPa was adopted based on experimental data from Coop et al. [1995]. As for the slope of the critical state line, a collection of consolidated-undrained triaxial data coming both from Horseman et al. [1987] and from tests run at Universitat Politècnica de Catalunya, on undisturbed samples of Boom clay from Mol, is presented in Figure 12. Two limit envelopes are shown in the figure for the data set. The lowest one, with a slope of M = 0.87, was adopted, as it is thought to be more representative of the behavior of Boom clay at critical state.

image

Figure 12. Undrained triaxial stress paths on different samples of saturated Boom clay. Data from Horseman et al. [1987] and Universitat Politècnica de Catalunya.

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[50] The logarithmic elastic and elastic-plastic compliances, κ and λ, were determined from experimental data coming from a wider experimental investigation on compacted Boom clay [Romero, 1999]. Values for the two compliances as a function of suction are presented in Figure 13. As in the present model the values for saturated conditions are needed, λ = 0.125 and κ = 0.014 were chosen.

image

Figure 13. Logarithmic elastic and elastic-plastic compliances for Boom clay as a function of suction.

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[51] As for the parameter ξ, the experimental data associated with static compaction under oedometer conditions (path AB in Figure 2) could be exploited, following a similar way of reasoning as in the study of Wheeler et al. [2003]. Knowing the initial suction, s0, the initial degree of saturation, Sr0, and the net stress coefficient of earth pressure at rest, K0, from the experimental data, the obliquity equation image0 at the end of compaction in the (equation image, q) plane could be easily calculated and was found to be equation image0 = 0.509. Assuming that, at least at the end of compaction, plastic strain increment could be assimilated to total strain increment, the initial value of the rotational parameter, Mα0, could be determined on the basis of the stress dilatancy law obtained by derivation of the plastic potential (equation (3)), and observing that under oedometer conditions the ratio between volumetric and deviatoric strain increments must be equal to 3/2:

  • equation image

A value of Mα0 = 0.343 was determined. Finally, by assuming that at the end of compaction, the direction of plastic strain increments were not changing any more, hence dMα0 = 0, from equation (6), the value of ξ = equation image0/Mα0 = 1.484 could be determined.

[52] Only the two parameters b1 and b2, strictly related to the evolution of the preconsolidation pressure with degree of saturation, need experimental data coming from tests run on samples in unsaturated conditions for calibration. To this aim, the experimental data presented in the study of Romero [1999] were exploited to determine possible ranges for the two parameters. Afterwards, they were optimised by numerical simulation of the isotropic experimental test (Figure 8) on the basis of the evolution of volumetric plastic strain along the first wetting path alone.

[53] In principle, parameter c, ruling the velocity of rotational hardening, could be determined with reference to saturated samples too. As no experimental data from saturated samples were available for calibration, the material parameter c was calibrated on the basis of the data presented in Figure 8, by minimising the difference between observed and simulated deviatoric strains (as shown in Figure 15).

[54] The complete set of parameters adopted in the simulations presented in the next paragraphs is listed in Table 2.

Table 2. Material Parameters Adopted in the Numerical Simulations
equation imageG (MPa)λMξb1b2c
0.014400.1250.871.4840.118.2136

6. Numerical Simulation of the Isotropic Test Data

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Stresses and Strain Variables
  5. 3. Experimental Investigation: Material, Equipment and Procedures
  6. 4. Experimental Evidence of Initial and Strain-Induced Anisotropy
  7. 5. Constitutive Modeling
  8. 6. Numerical Simulation of the Isotropic Test Data
  9. 7. Oedometer Tests: Experimental Data and Numerical Simulations
  10. 8. Summary and Conclusions
  11. Acknowledgments
  12. References
  13. Supporting Information

[55] The model was implemented in a numerical driver, and the constitutive equations were integrated with a refined explicit algorithm. The tests run to simulate oedometer compaction, unloading and isotropic reloading up to an isotropic net stress of 0.6 MPa are not reported here, as the attention is focused on the strain response of the material upon wetting. Nonetheless, it is worth noting that these simulations allowed for initialisation of the preconsolidation pressure, equation image0, and for verification of the initial value of rotational hardening parameter, Mα0.

[56] The initial state at the beginning of the first wetting phase (point E in Figure 2) is described by equation image = p″ + s Sr = 1.43 MPa, q = 0, equation image0 = 1.69 MPa, Mα0 = 0.343. The stress point image lies on the yield surface; hence, elastic-plastic straining is expected from the very beginning of the wetting phase. Given the initial values of the rotation hardening parameter, the initial direction of the plastic strain increment vector gives a ratio between shear and volumetric plastic strain increments of dɛsp/dɛvp = −0.90. If the ratio between the axial and radial plastic strain increment is calculated starting from this inclination, a value of dɛap/dɛrp = −0.72 is found. On the onset of the first wetting stage, the axial incremental plastic strain is smaller than the radial one and of opposite sign.

[57] In Figure 14 the numerical predictions of axial and radial strains are compared with the experimental findings. At the beginning of the first wetting stage (point E in the figure) the two incremental strain paths coincide. Contraction in the radial direction is observed, while a first expansion in the axial direction is evident, followed by a definite contracting behavior throughout. The final values of both axial and radial strains are well caught, although the model predicts a slower strain rate than observed in the first wetting stages. The qualitative predictions along the following drying and wetting stages (paths FG and GH in the figure) are pretty good.

image

Figure 14. Evolution of ɛa and ɛr along the stress paths EFGH. Comparison between experimental results and model simulation.

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[58] In Figure 15 the evolution of the numerical predictions of shear and volumetric strains are depicted and compared to the experimental data. Again, one can observe that the qualitative predictions are very good for both components. Relevant shear strain is accumulated along the first wetting path, as a consequence of the initial anisotropic fabric of the soil. At the end of this first step the shear strain reaches almost its final value, while in the following steps its increment is negligible. Because of the assumption of constant shear modulus, G, no shear strain will be predicted in the subsequent isotropic drying and wetting stages (along paths FG and GH). The evolution of volumetric strains shows that the model correctly reproduces a volumetric collapse from the very beginning of the wetting stages.

image

Figure 15. Evolution of ɛs, ɛv, w and Sr along the stress paths EFGH. Comparison between experimental data and model simulation.

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[59] The final amount of collapse is obviously caught, as the material parameters ruling the preconsolidation pressure were calibrated on the basis of this experimental datum, but it is interesting to notice that even the small increase of volumetric strain in the following drying and wetting cycle FGH is also well caught. At least in part, the latter result is a prediction of the model, as the evolution of the preconsolidation pressure in the drying path is no longer ruled by the wetting branch of the water retention curve but by its drying branch. Apparently, the material parameters calibrated with reference to a wetting path do work well also for the following drying branch. This point will be further discussed in the next section with reference to oedometer tests performed at different stress levels. The behavior along stress path FGH in Figure 2 is merely isotropic, as the plastic strains accumulated in the previous wetting path erased the initial anisotropic fabric.

[60] In Figure 15 the evolutions of water content, w, and degree of saturation, Sr, with suction are depicted. Along path EF the numerical predictions follow the wetting branch of the retention curve adopted in the model. It is worth remembering that the function chosen for the retention curve was not specifically calibrated on the results of the experimental test presented herein, as already explained in section 5. Water content and degree of saturation are slightly overestimated at the end of the wetting stages, although the numerical predictions are still good. On the subsequent drying-wetting cycle the model predicts a hysteretic path along a reversible scanning curve until a value of suction of 0.05 MPa, followed by drying along the main drying branch until the maximum value of suction (0.45 MPa). Upon wetting from state G in Figure 2, a reversible behavior along a new scanning curve is predicted again, until a suction of around 0.08 MPa is reached. The last part of the wetting stage follows the main wetting branch of the retention curve.

[61] On the contrary, the experimental data show slight reversible changes of degree of saturation throughout the whole drying and wetting cycle, highlighting that the previous wetting path not only affected the mechanical behavior of the compacted soil but also its hydraulic retention properties. A significant shift of the air-entry value toward higher suctions is observed experimentally following the first wetting, which cannot be reproduced by the present model which assumes a fixed retention curve in the suction – degree of saturation plane, based on experimental data for a constant e = 0.93.

[62] In Figure 16 the projection of the initial yield surface is depicted together with the projections of the yield surfaces at the end of each wetting stage in the mean net stress, deviator stress plane (p″, q). The figure clearly highlights the rotation of the yield locus induced by plastic strains developed mainly during the first wetting stage. In the following steps, starting from a suction of s = 0.45 MPa, the main effect of wetting is a reduction of the size of the elastic locus in stress space. The image of the net stress point is fixed throughout the whole test, as total stress and air pressure are not changing.

image

Figure 16. Initial yield surface and yield surfaces at the end of the different wetting stages (path EF) in the triaxial net stress plane.

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[63] A scalar measure of the plastic potential rotation is provided in Figure 17, in which the theoretical evolution of the inverse of dilatancy, dɛsp/dɛvp, resulting from the numerical simulation is compared with the experimental data. Although the overall experimental trend is well caught by the model it may be observed that the hardening law adopted for Mα (equation (6)) predicts a rotation of the plastic potential and associated yield function initially slower and subsequently faster than that derived from experimental data. A complementary description of this aspects is provided in Figure 18, in which the incremental plastic strain vectors are shown superposed to the skeleton stress path in the (equation image, q) plane. In this plane, the stress path followed during the wetting stage EF lies on the equation image axis, and is directed toward the origin, due to the decrease of equation image with the product of suction and degree of saturation, Srs. The direction of the vectors representing the experimental plastic strain increments gradually change from the initial inclination at the beginning of the wetting path to nearly horizontal at saturation, highlighting once more that plastic strains induced by wetting at constant total stress and constant air pressure erased the initial anisotropic fabric of the as-compacted soil. The theoretical model catches this feature well although shear strain increment almost goes to zero already for a mean average soil skeleton stress equation image of about 1 MPa.

image

Figure 17. Evolution of dɛsp/dɛvp along the wetting path EF. Comparison between experimental results and model simulation.

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image

Figure 18. Direction of incremental plastic strain vectors along the wetting path EF. Comparison between experimental results and model simulation.

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7. Oedometer Tests: Experimental Data and Numerical Simulations

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Stresses and Strain Variables
  5. 3. Experimental Investigation: Material, Equipment and Procedures
  6. 4. Experimental Evidence of Initial and Strain-Induced Anisotropy
  7. 5. Constitutive Modeling
  8. 6. Numerical Simulation of the Isotropic Test Data
  9. 7. Oedometer Tests: Experimental Data and Numerical Simulations
  10. 8. Summary and Conclusions
  11. Acknowledgments
  12. References
  13. Supporting Information

[64] To provide a wider view on the overall behavior of compacted soils upon gradual wetting and drying, the experimental data of more conventional controlled-suction oedometer tests, in which samples of Boom clay were submitted to a wetting-drying-wetting cycle under different constant vertical net stresses, may be exploited. The data presented allow for analysing the influence of stress level on the volumetric strain experienced by the soil in the first wetting path, as well as in the following drying and wetting paths. The different competing strain mechanisms upon changes in water content may be appreciated analysing the experimental data.

[65] All soil samples were compacted one-dimensionally and then unloaded using the procedure described in section 3. Afterwards, each of them was reloaded up to a different vertical net stress, to final values ranging from 0.085 MPa to 1.2 MPa. The volumetric strain undergone by the different samples during the hydraulic cycle is presented in Figure 19 and in Figure 20 (lines with symbols). The experimental data are compared in the same figures with their numerical simulations (thick solid lines), in order to verify whether the model is able to capture, at least qualitatively, the main features of the observed behavior.

image

Figure 19. Wetting-Drying-Wetting cycle under oedometer conditions at σv = 0.085 MPa and σv = 0.3 MPa. Comparison between experimental data and model simulations.

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image

Figure 20. Wetting-Drying-Wetting cycle under oedometer conditions at σv = 0.6 MPa and σv = 1.2 MPa. Comparison between experimental data and model simulations.

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[66] The experimental data show that during the first wetting stages the compacted soil may experience a net increase or a net decrease of volume just as a function of the applied vertical net stress. At low vertical stress, σv = 0.085 MPa, the soil sample swells until suction reaches a value of s = 0.2 MPa (Figure 19). Afterwards, an inversion in the volumetric strain tendency is observed. A slight decrease in the soil volume may be appreciated for low suctions, but a total net increase of the soil sample volume is eventually associated with full saturation. The initial volume increase may be physically due to either or both swelling of the aggregates and unloading of the macrostructure formed by the aggregates. This aspect may be better appreciated comparing the experimental results with the numerical simulation of the test. The soil state at the beginning of the wetting phase is well inside the initial elastic domain. As suction decreases, the elastic domain shrinks but the stress state still remains inside it for a while. A suction decrease implies a reduction of the average vertical stress acting on the soil skeleton, and elastic swelling occurs as long as the stress state remains inside the elastic domain, until a predicted suction value of about s = 1.0 MPa. Afterwards, the total volumetric strains are the sum of elastic swelling and a small plastic collapse. In the numerical simulations elastic swelling prevails throughout the whole wetting path, and the collapse strains are of limited entity. The experimental data are qualitatively similar, although a higher swelling is observed on the onset of wetting and a more relevant collapse may be appreciated for low suction values. The final increase in volume is very well predicted by the model.

[67] In the following drying path the soil shrinks considerably, and the data of the final wetting path show that the reduction of volume experienced in the first drying path is almost irreversible. The numerical simulation demonstrates that the constitutive model is able to reproduce this irreversible shrinkage quite well, although its final amount is a little underestimated. It is interesting to note that this irreversible shrinkage in the numerical model is due to volumetric strains developed as a consequence of a plastic loading process. In fact, a suction increase is translated in an increase of the mean skeleton stress, whose image point remains on the yield function during most of the drying process. The model predicts only a small elastic swelling along the second wetting path, and the experimental results seem to substantiate this possibility.

[68] Comparison between the experimental data on the same wetting-drying-wetting process at increasing vertical net stresses, allows for drawing the following conclusions. In all the tests run under vertical net stresses higher than 0.085 MPa, no swelling was detected upon first wetting. A vertical net stress of 0.3 MPa is sufficient to promote monotonic collapse strains throughout the whole wetting process. The amount of collapse increases with the vertical net stress applied before the wetting episode, but the maximum value is detected under a vertical net stress of 0.6 MPa. The collapse experienced by the soil sample loaded up to 1.2 MPa is comparable to the previous one or even slightly lower (Figure 20). On the contrary, the amount of irreversible shrinkage experienced in the following drying-wetting cycle decreases monotonically with increasing net stress.

[69] The numerical simulations show that all these qualitative aspects may be reproduced with the simple model proposed. From a quantitative point of view, the amount of volumetric strain in the different paths is well captured except for the last test. This could be expected as a maximum of collapse is not embedded in the theoretical model, which predicts a monotonic increase of the volumetric collapse with net stress.

[70] The model correctly predicts irreversible shrinkage along first drying, although the amount of final shrinkage is always a little underestimated. Nevertheless, the numerical predictions are quite good, except for the test run at 1.2 MPa. It is worth noting that monotonic decrease of the irreversible shrinkage after the drying-wetting cycle with increasing stress is correctly predicted.

8. Summary and Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Stresses and Strain Variables
  5. 3. Experimental Investigation: Material, Equipment and Procedures
  6. 4. Experimental Evidence of Initial and Strain-Induced Anisotropy
  7. 5. Constitutive Modeling
  8. 6. Numerical Simulation of the Isotropic Test Data
  9. 7. Oedometer Tests: Experimental Data and Numerical Simulations
  10. 8. Summary and Conclusions
  11. Acknowledgments
  12. References
  13. Supporting Information

[71] Anisotropy of the initial fabric created by one-dimensional compaction had already been highlighted previously by other researchers [Zakaria et al., 1995; Cui and Delage, 1996; Estabragh and Javadi, 2006]. The aim of this research was to emphasise the evolution of the initial fabric upon wetting and drying, ruled by the coupled action of plastic strains and changes in the degree of saturation. To achieve this scope, a specific testing program was carried out on one-dimensionally compacted samples using a controlled-suction axisymmetric triaxial cell and a controlled-suction oedometer. A selection of wetting and drying results under isotropic stress state, including time evolution of volumetric and shear strains and water content changes, as well as equilibrated states at the end of each suction step, was presented.

[72] The collapsible nature of the as-compacted soil was evidenced by the experimental data, although some swelling under low net stresses was also detected. Upon first drying the soil always experienced irreversible shrinkage, whose amount may be comparable with that of previous collapse strain. Total irreversible shrinkage decreased monotonically with increasing net stress.

[73] Besides, the study highlighted that the amount of volumetric strain is not an exhaustive measure of the strain response of a compacted soil, unless isotropic stress paths are followed starting from an isotropic initial fabric [see, e.g., Barrera et al., 2000]. The behavior of the one-dimensionally compacted soil on wetting under isotropic stress state was clearly anisotropic, although the degree of anisotropy reduced progressively with the development of plastic strains. As-compacted soils in the field are rarely isotropic, and the initial anisotropic structure is likely to undergo important changes under the combined action of external loads and wetting. As a consequence, reliable predictions of displacements under working conditions may be obtained only by taking into account the real stress and strain paths [see, e.g., Karstunen et al., 2006], as the strain components will evolve in different ways.

[74] Finally, the experimental investigation confirmed that plastic strains, besides governing the overall mechanical response, may also have an important effect on the water retention properties of compacted soils. The experimental data presented showed a clear evolution of the water retention domain following plastic strains. In the drying and wetting cycle after the first wetting steps water was exchanged reversibly, suggesting that the suction-saturation path was entirely contained inside a current reversible water retention domain. A sound interpretation of the mechanical behavior of unsaturated soils may take significant advantage from a reliable model of the hydraulic characteristics of the soil and of their evolution with irreversible strain.

[75] In order to simulate the experimental data, a rather simple constitutive framework was proposed, involving a generalised mixed isotropic-rotational hardening, governed by both plastic strain and degree of saturation. The model, calibrated on the basis of the experimental data coming from the isotropic test, proved to be able to reproduce correctly the main competing deformational mechanisms (swelling, collapse, shrinkage, elastic rebound) experienced by the soil at different net stress levels. Comparison between experimental data and numerical simulations clearly shows that taking into account correctly the hysteretic water retention properties will greatly enhance the modelling of the mechanical behavior of unsaturated soils.

[76] The changes in the direction of plastic strain increment vectors observed experimentally upon wetting in the triaxial test could be successfully simulated with the simple assumptions made in the development of the elastic-plastic model. Extension of the proposed anisotropic model to general three-dimensional stress and strain paths can be easily accomplished, following the criteria already suggested in the literature, so as to provide a valuable tool in the numerical analysis of earth constructions.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Stresses and Strain Variables
  5. 3. Experimental Investigation: Material, Equipment and Procedures
  6. 4. Experimental Evidence of Initial and Strain-Induced Anisotropy
  7. 5. Constitutive Modeling
  8. 6. Numerical Simulation of the Isotropic Test Data
  9. 7. Oedometer Tests: Experimental Data and Numerical Simulations
  10. 8. Summary and Conclusions
  11. Acknowledgments
  12. References
  13. Supporting Information
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Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Stresses and Strain Variables
  5. 3. Experimental Investigation: Material, Equipment and Procedures
  6. 4. Experimental Evidence of Initial and Strain-Induced Anisotropy
  7. 5. Constitutive Modeling
  8. 6. Numerical Simulation of the Isotropic Test Data
  9. 7. Oedometer Tests: Experimental Data and Numerical Simulations
  10. 8. Summary and Conclusions
  11. Acknowledgments
  12. References
  13. Supporting Information
FilenameFormatSizeDescription
wrcr11582-sup-0001-t01.txtplain text document0KTab-delimited Table 1.
wrcr11582-sup-0002-t02.txtplain text document0KTab-delimited Table 2.

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