New Suction effects on the residual shear strength of clays · 2017. 9. 3. · its applicability in...

Journal of Geo-Engineering Sciences 2 (2014) 17–37DOI 10.3233/JGS-141320IOS Press

17

Suction effects on the residual shear strengthof clays

Enrique Romero∗, Jean Vaunat and Vladimir MerchanDepartment of Geotechnical Engineering and Geosciences, Universitat Politecnica de Catalunya, Barcelona, Spain

Abstract. The paper presents an experimental study on the residual shear strength of different clayey soils at varying totalsuctions. In a first part of the paper some insight into the behaviour of residual shear strength of a filled rock discontinuityis presented to bring into light the sensitivity to hydraulic states of a clayey gouge material subjected to shearing along largedisplacements. An adapted Bromhead ring shear apparatus, in which the sample is enclosed in a controlled relative humiditychamber, has been used to control total suction during shearing. Afterwards, results on different types of clayey materials arepresented to discuss the importance of the plasticity of the clay on the residual friction angle changes. These changes showan important increase in the residual friction angle with imposed total suction that may reach 15◦ for medium plastic clay andwithout cohesion component. The reasons for this increase have been explained by the more granular character of the dry clay asa result of aggregate densification and desaturation during strong drying. The changes have been interpreted using a simple modelinspired in both macroscopic and microstructural observations, which is based on the stiffness of the soil (or aggregates) anddepends on the product of the total suction applied and the degree of saturation. A microstructural model, already developed totake into account microstructural aspects on water retention and following an equivalent behavioural response to the macroscopicshrinkage curve, has been used to estimate the degree of saturation at the microstructural level (inside aggregates). To highlightits applicability in geotechnical practice, the different parameters used in the water retention and residual shear strength modelshave been shown to depend on the plasticity index of the different clayey soils studied.

Keywords: Residual shear strength, clay, partial saturation, suction, microstructure

1. Introduction

The significance of residual shear strength of soils is well-recognised in geotechnical engineering, to cite but afew of them, in the reactivation of landslides along pre-existing slide surfaces [5, 30, 31], in the shear strength offilled discontinuities, residual shear stresses on shaft friction mobilisation of bored piles [16, 18], and foundationson stiff clays, natural slopes and earthworks [3]. Shear strength of soils is assumed to evolve towards a residual stateafter peak that is characterised by null cohesion and a residual friction angle, which provides the lowest envelopeas a consequence of the gradual realignment of clay particles along the shear plane. This residual shear strengthdepends on the level of normal stress [31, 32], soil grading [17, 30], bulky and platy-like particle mineralogy [24],dolomite content [2], calcite content [12, 23], rate of shearing [33] and on the chemical interaction between porewater chemistry and soil mineralogy [11, 22].

In contrast, available experimental information concerning partial saturation effects on residual shear strengthis more limited. This seems a consequence of at least two aspects: a) the reasoning that the mechanical effect of

∗Corresponding author: Enrique Romero, Departamento de Ingenierıa del Terreno, c/Jordi Girona 1-3, Campus Nord, Edificio D-2, UniversitatPolitecnica de Catalunya, 08034 Barcelona, Spain. Fax: +34 93 4017251; E-mail: [email protected].

ISSN 2213-2880/14/$27.50 © 2014 – IOS Press and the authors. All rights reserved

mailto:[email protected]

18 E. Romero et al. / Suction effects on the residual shear strength of clays

suction is due to the existence of water menisci that are hard to conceive across a sheared surface characterisedby large relative displacements (water menisci break and this contribution to strength is lost), and b) the difficultyof generating closed system conditions in conventional ring shear cells for suction application. In fact, only untilvery recently some efforts have been done to adapt an original Bromhead ring shear apparatus for testing partiallysaturates soils under controlled-suction status via axis translation or vapour equilibrium techniques [14, 20]. Hoyoset al. [13] also presented a fully servo/suction-controlled ring shear apparatus by using axis translation.

Results of residual failure envelopes of compacted soils have been reported by Hoyos et al. [13] and Velosa[36] at low suctions by applying axis translation, in which both an increase in friction angle and apparent cohesionhas been reported. In contrast, Vaunat et al. [34], Vaunat et al. [35] and Merchan et al. [19] focused on clayeysoils subjected to residual shearing at much higher suctions (typically above 10 MPa), which were controlled byvapour equilibrium technique. These authors reported a strong influence of total suction on the residual shearstrength of medium plasticity clay with an increase in friction angle up to 15◦ -at null cohesion intercept- duringdrying. This variation evidences an important interest in geotechnical practice for optimising designs in unsaturatedsoils (stabilisation of reactivated landslides, pile friction design, earthworks stability), as well as in analysing thesensitivity to reactivation of landslides in fissured rocks with dry clayey gouge that can undergo important shearstrength changes on wetting.

The present paper is devoted to a continuation of this study by presenting new and revisited results and is specifi-cally targeted to highlight its applicability in geotechnical practice by considering the dependence of parameters thatregulate these residual shear strength changes to conventional plasticity indices. Some insight into the behaviourof residual shear strength of filled rock discontinuities is first introduced in the paper to highlight the sensitivity todrying of an initially saturated clayey gouge material subjected to large displacement shearing. These data is com-plemented by presenting a variety of soils ranging from clayey silt to montmorillonite clay, in which shearing underresidual conditions was performed at different water contents starting from saturated conditions. Strong drying athigh suctions enhances aggregate densification and desaturation that makes the material behave in a more granularway with a high proportion of rotund and stiffer particles. The stiffness of these aggregates during desaturation canbe related to the total suction applied and to the degree of saturation at the microstructural level, inside aggregates,which defines an effective suction at aggregate scale [21]. To estimate the degree of saturation at the microstructurallevel, a model already developed to take into account microstructural aspects on water retention has been used [10,28, 29]. The microstructural model uses a volume change approach at aggregate scale equivalent to the macroscopicresponse of a shrinkage curve, in which loss of water content below a defined value does not result in any moremicrostructural (aggregate) volume reduction.

2. An experimental study on clayey gouge material of filled rock discontinuities

This section presents an experimental study on gouge materials occurring between the walls of filled rockdiscontinuities of a hydroelectric dam foundation located on the border of Mexico’s Nayarit and Jalisco westerncoastal states in Mexico [1]. Rock matrix is a highly weathered and fissured material of igneous rock (diorite andgranodiorite). Rock discontinuities are filled with dry greenish clayey gouge material, which can undergo watercontent changes during construction and operation stages. Two block materials B1 and B2 under relatively dryconditions excavated from a tunnel of the water deviation system and from an outcrop belonging to a former slidingzone were tested in a large direct shear box (300 mm × 300 mm) under different hydraulic conditions (saturatedand under dry conditions in equilibrium with the laboratory relative humidity 50% at a total suction s = 95 MPa).The block samples at different normal stresses were sheared along a discontinuity plane following a multi-stageprocedure at a displacement rate of 0.09 mm/min and to a minimum displacement of 100 mm in each stage. Figure 1shows the effects of the hydraulic state on the residual failure envelope of the two block samples that display nocohesion intercept. The influence of the rock walls and asperities is assumed negligible given the important thicknessof the clayey filling. As indicated in the figure, saturation has a marked influence on the residual friction angle byinducing a drop of 13◦.

To further investigate the effects of the hydraulic state on the clayey gouge material, the filling material wasremoved by scratching from the rock discontinuities. The mineralogy and index properties of its fine fraction are

E. Romero et al. / Suction effects on the residual shear strength of clays 19Ta

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Fig. 1. Residual shear strength envelopes at different suctions of filled discontinuities.

Fig. 2. Water retention curve of gouge material (drying branch). Fitted curve and position of e∗m.

summarised in Table 1 (reference 1). Figure 2 shows its water retention curve in terms of water ratio ew alonga drying path starting from saturated states. Water ratio ew = Sr e is defined as the volume of water over solidvolume, where Sr is the degree of saturation and e the void ratio. Saturated samples prepared at ew = 0.530 wereallowed air drying following a multi-stage procedure up to ew = 0.054 (initial and final conditions are indicatedin Table 1). Samples at each stage were let to equilibrate before measuring total suction with a chilled mirrorpsychrometer. As a consequence of the initial water content, the clayey sample displays fully expanded aggregates

E. Romero et al. / Suction effects on the residual shear strength of clays 21

Fig. 3. Scheme of the experimental setup with ring shear cell, vapour transfer system and data acquisition [20].

leaving a small porosity between them, as observed by Merchan et al. [19] using environmental scanning electronphotomicrographs. At the total suctions indicated in the figure (above 2 MPa), water is mainly adsorbed insideaggregates and void ratio changes do not have an important effect [25, 26]. Thus, experimental data have been fittedto the following analytical expression describing the water ratio ew stored inside aggregates as a function of thetotal suction s [10, 28]:

ew = be∗m

ln(

smaxs∗m

)⎡⎣b + ln

(smaxs∗m

)

b + ln(

ss∗m

) − 1

⎤⎦ (1)

where e∗m is the water ratio corresponding to fully saturated micropores, s∗m is the suction corresponding to e∗

m,smax is the maximum suction attainable (for ew = 0), and b is a parameter describing the average slope of thecurve for high values of suction. Table 1 (reference 1) summarises the parameters for the water retention model. Atwater ratios ew < e∗

m, which is the range of interest for the test performed, the aggregates become desaturated. Thisinformation is further used to propose a relationship between the rate of friction angle increase with total suctionand the soil plasticity.

Merchan et al. [20] presented the adaptation, instrumentation and the calibrations undertaken on a commercialring shear apparatus (Bromhead type [6]) to study the shear strength properties under residual conditions of partiallysaturated clay in a wide total suction range. As shown in Fig. 3, the adaptation consisted of a glass chamber toisolate the sample from the laboratory environment and a forced convection system to transfer water vapour froma reference vessel, which allowed controlling the relative humidity of the air in contact with the soil and thus thetotal suction applied to the soil water. Relative humidity and temperature inside the chamber are registered during


Fig. 4. Residual shear strength envelopes at different total suctions of clayey gouge.

the entire test together with the vertical displacement of the upper box and the torque (associated with the shearstress acting on the sample).

Once the initially saturated and remoulded gouge sample is equilibrated at a relative humidity (or total suction),the shearing stage is started at different normal stresses and at a constant displacement rate of 0.09 mm/min (thisvelocity ensures drained conditions under saturated states). As observed in Fig. 4, which relates the residual shearstrength to the normal stress, linear shear strength envelopes are obtained and the increase in residual shear strength isentirely associated with the change in the residual friction angle (the apparent cohesion remains zero for the differentfailure envelopes). Such an increase has been interpreted in terms of the aggregated microstructure that prevailsat elevated suctions, as observed by Merchan et al. [19] during drying using scanning electron photomicrographsand mercury intrusion porosimetry. This stiffer aggregated microstructure induces the clayey material to essentiallybehave as a granular and frictional one at high suctions. As previously indicated, at these elevated suctions wateris mainly stored inside these aggregates, which become stiffer with increasing suction. An important increase inthe residual friction angle is observed in the figure at s = 160 MPa (φr = 28◦) compared to the value determinedunder saturated conditions (φ′

r = 16◦). Nevertheless, the dry and saturated residual friction angles display valuesthat are slightly lower than those presented in Fig. 1 for approximately the same hydraulic states. Probably, despitethe important thickness of the gouge, the rock asperity contacts could have had some effect on the residual shearstrength.

Figure 5 shows a series of shear stress – displacement curves obtained at a normal stress of σn = 100 kPa andequilibrated at different total suctions (including the saturated state) along varying resting periods at constant normalstress. The enhancement with total suction increase of the brittleness during shearing at low displacements is clearlydetected, which has been discussed by Vaunat et al. [35]. In the case of total suction at 160 MPa, the equalisationperiod was the largest one (144 hours) and this could have also affected–besides total suction–the higher peakobserved. Such kind of peak response has been reported in the literature for saturated materials and is usuallyattributed to the work required to reorient particles in the direction of shearing (see for instance [17, 31]). In thecase of drying, this transition from ductile to strain softening response can also be associated with the progressivefusing of initially soft aggregates during suction increase, which induces some kind of healing effect along theresting period at constant normal stress. This suction-induced healing effect has important consequences on thereactivation along pre-sheared surfaces, in which progressive failure phenomenon can be again reactivated.


Fig. 5. Shear stress vs. displacement curves at constant σn = 100 kPa of clayey gouge. Samples dried to different total suctions before shearing.

3. Residual shear strength properties of clayey soils subjected to drying

Different clayey soils ranging from clayey silt to montmorillonite clay have been studied to analyse the influenceof the plasticity index on the residual shear strength properties. Main properties of these soils are summarised inTable 1 (references 2 to 4), which cover plasticity indices ranging from 16% (clayey silt) to 49% (predominantlydivalent bentonite). Activity values (ratio of plasticity index to fine fraction <2 �m) have been also included inTable 1, but this index has shown to be less sensitive since it ranged between 0.54 and 0.80.

Figure 6 presents the water retention curve along a drying branch of the clayey silt starting from an initialew = 0.43 (initial and final conditions are summarised in Table 1, reference 2). A multi-stage drying was followedusing psychrometer measurements. The high suction zone presented has been fitted to the microstructural waterretention curve described by Equation (1) and Table 1 summarises the parameters used.

Once equilibrium is reached after a drying path on the clayey silt, shearing at a displacement rate of 0.09 mm/min iscarried out. Again, a consistent a pattern is detected in Fig. 7 regarding the linear shear strength envelopes displayingnull apparent cohesion and increasing residual friction angles with total suction. Nevertheless, the increase in thefriction angle with total suction in this clayey silt is more limited (from 22◦ at saturation to 26◦ at s = 135 MPa).The evolution of shear stress with displacement is depicted in Fig. 8 for the tests at σn = 300 kPa and equilibratedat different total suctions (including the saturated state). As the soil becomes drier, the ductile response observedunder saturated condition progressively disappears and the peak values increase–associated with the fusing/healingof initially soft aggregates and the work required for the reorientation of the stiffer aggregates. At s = 135 MPa thesoil displays a brittle response, in which the shear stress increases rapidly to a peak around 240 kPa at a displacementof the order of 5 mm. Shear stress then decreases sharply to the residual value around 145 kPa at a relatively smalldisplacement and consistent with the low plasticity of the clay. Vaunat et al. [34] observed that the ductile responsein saturated conditions was associated with a compression of the sample, whereas peak development in unsaturatedconditions took place at the transition between sample contractancy and dilatancy, the latter enhanced with suctionas a consequence of the stiffening of the aggregates.

Figure 9 presents the water retention curve on a multi-stage drying branch on illitic-kaolinitic clay (Boomclay, reference 3 in Table 1) starting from the initial conditions indicated in the table and using psychrometermeasurements. Fitted parameters of the water retention curve are reported in Table 1. Figure 10 plots the residualshear strength envelopes of this clay at different total suctions. As a consequence of drying, again an important


Fig. 6. Water retention curve of Barcelona clayey silt (drying branch). Fitted curve and position of e∗m.

Fig. 7. Residual shear strength envelopes at different suctions of Barcelona clayey silt (updated from [34]).

increase in the residual friction angle is observed at a total suction of 152 MPa (φr = 27◦) compared to the valuedetermined under saturated conditions (φ′

r = 12◦).Residual stress ratios τ/σn for the different clayey soils indicated in Table 1 are compiled in Fig. 11 as a function

of total suction. These results indicate that suction plays an important role in the residual shear strength of clayeymaterials undergoing drying and that this effect is highly conditioned by the plasticity of the clay. The rate of increasewith total suction is particularly high for the bentonite (Febex bentonite, reference 4 in Table 1), and systematicallyreduces with decreasing plasticity index. Despite starting from different τ/σn values at saturation – see Table 1 –, on


Fig. 8. Shear stress vs. displacement curves at constant σn = 100 kPa of Barcelona clayey silt (updated from [34]). Samples dried to differenttotal suctions before shearing.

Fig. 9. Water retention curve of Boom clay (drying branch). Fitted curve and position of e∗m.

suction increase the materials tend to level-off at a value close to 0.5 at the driest states. As previously indicated, thisbehaviour may be related to the aggregation capacity of the clayey particles on drying inducing stiffer and rotundaggregate arrangements. Cafaro & Cotecchia [8] also observed reduction in clay fraction during drying processon Montemesola clay. Kenney [15] recognised the importance of the proportions in a mixture of clay particles tomassive, rotund and rigid particles that are difficult to align. A plasticity index around 25% has been suggestedas a transition to separate platelike particles able to realign from stiffer and rotund particles [3, 17]. This is better


Fig. 10. Residual shear strength envelopes at different suctions of Boom clay (updated from [20]).

Fig. 11. Variation of τr /σn with total suction for the different soils tested.

observed in Fig. 12, in which residual friction angles at saturation and at the driest states are plotted with clayfraction and plasticity index. Upper and lower bounds for a wide range of clayey materials obtained by severalauthors and reported in Lupini et al. [17] have been also added for reference. Points corresponding to saturatedstates are close to the lower bounds proposed by Binnie et al. [4] and Bucher [7], while points corresponding tothe driest states are tending to a value close to 30◦ and that lie over the proposed upper bounds–particularly at thehighest clay fractions and plasticity indices.


Fig. 12. Relationship between residual friction angle and clay fraction (at the top), and plasticity index (at the bottom) for the different soilstested. Upper and lower bounds, as well as Bucher’s domain, were obtained from plots reported by Lupini et al. [17].


Fig. 13. Shrinkage curves of the different soils tested starting from the initial conditions reported in Table 1.

4. Macroscopic and microstructural insights into the residual shear strength properties

The previous results have reinforced the concept of the stiffening of aggregates during strong drying, a microstruc-tural phenomenon that becomes more important with the increase in plasticity index. Figure 13 shows the volumechanges undergone by three clayey materials–in terms of void ratio e – during drying and starting from elevatedwater ratios (refer to Table 1 for the initial and final conditions). The shrinkage curve at full saturation initiallyfollows a slope 1 : 1, before tending to lower shrinkage deformations below the shrinkage limit when the mate-rial undergoes desaturation. Table 1 summarises the shrinkage limits and void ratios at this limit of the differentmaterials.

Sensitivity of the pore size density PSD functions on drying paths is exemplified by the data presented in Fig. 14for the same clayey soils. This information has been derived by mercury intrusion porosimetry performed on freeze-dried samples [27]. As observed in the figure, the saturated materials (state ‘A’ in Fig. 14) display monomodal poresize distributions with dominant pore modes at approximately 700 nm, 1.6 �m and 300 nm, for the gouge material,Barcelona clayey silt and Boom clay, respectively. The materials at these high water contents are formed by soft andexpanded aggregates leaving a minimum pore volume between them, as detected by the microstructural observationswith environmental scanning electron microscopy presented by Merchan et al. [19] on Febex bentonite preparedat the liquid limit and Romero et al. [28] on saturated Boom clay. On drying (state ‘B’ in Fig. 14) the dominantpore mode is shifted towards lower values associated with the shrinkage of the intra-aggregate pore volume (insideaggregates). Monomodal pore size distributions result after shrinkage on the gouge material and Boom clay, whichare consequences of the denser aggregates formed during drying that leave minimum inter-aggregate pore volume


Fig. 14. Evolution of the pore size density functions of the different soils tested along a drying path (A: saturated; B: dried): (a) gouge material,(b) Barcelona clayey silt and (c) Boom clay.


Fig. 15. (a) Scheme for the condition of partial saturation under fixed void ratio at the shrinkage limit (eSL on the left) and fixed microstructuralvolume (e∗

m on the right). (b) Shrinkage curves from macroscopic and microstructural viewpoints. Void ratio at the shrinkage limit (eSL) andequivalent microstructural void ratio (e∗

m).

between them. On the contrary, Barcelona clayey silt undergoes shrinkage of the intra-aggregate pore volume ondrying with some emergence of inter-aggregate porosity at approximately the same void ratio (from e = 0.50 atsaturated state ‘A’ to e = 0.40 at the driest state ‘B’). This is a consequence of the granular shielding skeleton of thematerial (rigid silty particles less sensitive to water content changes), which limits shrinkage of the soil as shownin Fig. 13.

As a result of the previous discussion, a key aspect when trying to incorporate microstructural features is theselection of an adequate criterion to split the porosity domain in intra-aggregate (inside aggregates) and inter-aggregate (between aggregates) pore volumes, which are evolving along the drying paths. Romero et al. [28] andDella Vecchia et al. [10] described a criterion based on the assumption that intra-aggregate pores are always smallerthan inter-aggregate pores – i.e., it assumes an aggregated structure even at high water contents. The conditionat high water content that promotes the most significant swelling of the aggregates–dominant pore size peaks atstate ‘A’ in Fig. 14 – represents the upper bound for the intra-aggregate porosity and the lower bound for the inter-


Fig. 16. Relationship between void ratios at the shrinkage limit (eSL) and equivalent microstructural void ratios (e∗m) and the plasticity index.

Fig. 17. Variation of τr /σn with Sr s. Parameters of the linear fits for the different materials.


Fig. 18. Variation of τr /σn with Smr s. Parameters of the linear fits for the different materials.

Fig. 19. Relationship between macroscopic and microstructural shear strength parameters and the plasticity index.


Fig. 20. Variation of τr / σn with total suction for the different soils tested. Experimental and model results.

aggregate pore domain at the same time. At this high water content state, the maximum intra-aggregate pore volumeis developed on swelling and the occluded inter-aggregate pore volume tends to its minimum. The intra-aggregatepore volume (defined in terms of the microstructural void ratio em, volume of intra-aggregate pore volume to volumeof solids) represents the area under the PSD curve for pore sizes smaller than the dominant pore size peak at state‘A’, as shown by the shaded area indicated in Fig. 14a for the gouge material.

Figure 15b shows a scheme of the shrinkage curve of a soil. Below a water ratio eSL no further soil volumedecrease occurs (eSL represents the void ratio at the shrinkage limit where the degree of saturation is still 100%),and the degree of saturation below the shrinkage limit can be calculated as Sr = ew/eSL (refer also to the schemein Fig. 15a on the left). A similar bi-linear pattern, resembling the trend of the shrinkage curve, has been observedby Romero et al. [28] and Della Vecchia et al. [10] for the evolution of the intra-aggregate pore volume with waterratio. This evolution has been also schematically depicted in Fig. 15b. At elevated water ratios, the fully saturatedem evolves linearly with ew on drying until the curve reaches the line 1 : 1 at e∗

m (a microstructural parameter thatemulates the void ratio at the shrinkage limit), which corresponds to a water ratio that is sufficient to saturate theaggregates and leaves the inter-aggregate pores empty. The evolution of the microstructural void ratio for waterratios above e∗

m can be described by a linear function with a slope that is linked to the plasticity of the clayey soil,as reported by Romero et al. [28] and Romero [29]. Below e∗

m, no appreciable microstructural void ratio changesare expected with water content, and only desaturation of this intra-aggregate pore volume is assumed.

All the residual shear strength data at elevated suctions reported in this paper develop at water ratios belowe∗m, within the desaturation regime of the microstructural pore volume. This fact allows defining a microstructural

degree of saturation Smr = ew/e∗

m, expressed as the volume of water inside the intra-aggregate pores over themicrostructural pore volume. Figure 15a on the right outlines this condition of partial saturation of the aggregatesunder fixed microstructural volume e∗

m.


The microstructural void ratio e∗m becomes more relevant to the void ratio as the plasticity of the clay increases,

as suggested by Romero & Vaunat [26] and Romero et al. [28]. A good correlation between e∗m and the plasticity

index is detected in Fig. 16, which is based on data reported in this paper (Table 1) and on complementary dataon different soils with lower plasticity [29]. An expression to estimate e∗

m based on plasticity index is proposed inthe figure. Figure 16 also includes data of eSL for the different soils plotted against the plasticity index, in whichFebex bentonite and the gouge material attain the same value for the microstructural void ratio and the void ratio atthe shrinkage limit. As observed, the shrinkage limit does not display so good correlation with the plasticity index.Different macrostructural features, such as crack opening contribution and granular shielding skeleton effects, mayaffect the shrinkage limit – i.e., clay and soils containing it do not usually display the same shrinkage curve (see forinstance [9]).

The increase in stiffness of the soil (or of the aggregates) on drying is a consequence of two phenomena, namelythe reduction of void ratio towards eSL (or towards e∗

m when considering the micropore volume inside aggregates)and the desaturation of the soil (or of the aggregates). As a first insight into the problem, only desaturation effectshave been considered and the stiffness of the soil (or of the aggregates) have been related to the product of the totalsuction applied and the degree of saturation (or to the product of the total suction and the degree of saturation atthe microstructural level inside aggregates). This product defines an effective suction at macroscopic scale (soil) orat a lower microstructural scale (inside aggregates), which takes into consideration the effects of water availabilityand its distribution inside the porous medium – i.e., the capability of the soil or of the aggregates to sustain a giventotal suction without appreciable desaturation.

Residual stress ratios τ/σn for the different clayey soils are compiled in Figs. 17 and 18 as a function of thiseffective suction at macroscopic and microstructural scales, respectively. Stress ratios have been used to separatethe influence of the contact forces (normal stress) from the effects originating due to stiffening (effective suction).The data in both figures suggest linear trends in the increase in the residual stress ratio with the effective suction atboth macroscopic and microstructural scales, which can be expressed as

τr

σn

=(

τr

σn

)sat

+ a Sr s = tan (φ′r sat) + a Sr s

τr

σn

=(

τr

σn

)sat

+ am Smr s = tan (φ′

r sat) + am Smr s

(2)

where a and am are parameters at macroscopic and microstructural scales, respectively, which affect the effectivesuction. Shear strength parameters at both scales of the proposed model are included in Figs. 17 and 18, as well asin Table 1, for the different clayey materials tested. As observed in Fig. 19, parameters a and am are sensitive tothe plasticity of the material. At low PI (around 10%), parameters a and am vanish on a silty soil with rotund andstiff particles that are not able to store water (soil with low e∗

m). The parameters rapidly increase and level off at PI>23–26%, which coincides with the plasticity index around 25% that has been accepted as a transition to separateplatelike particles able to realign from stiffer and rotund particles [17]. Nevertheless, further research is needed topropose reliable correlations with consistency limits or the activity of clayey soils.

Merchan et al. [20] presented preliminary results on Boom clay in which the residual shear strength was notdependent on the initial water content and the total suction history, and essentially was controlled by the prevailingtotal suction during shearing. This means that the previous constitutive framework can be used either on wettingor drying paths and that total suction can be potentially considered as constitutive variable instead of the effectivesuction. Regarding the first aspect, no important hysteretic effects are expected in the high suction domain wherewater is adsorbed inside the aggregates that do not undergo significant volume changes (see for instance, Romeroet al. [25] and Romero and Vaunat [26]), and therefore approximately the same degree of saturation can be consideredfor a given total suction in both drying and wetting branches.

Experimental data of the evolution of the residual stress ratio with total suction for the different soils are comparedto model results in Fig. 20, in which fairly good agreement can be observed. A key aspect when using the effectivesuction model is the correct determination of the water retention curve in the high total suction range together


with eSL and e∗m values, which allows defining the degree of saturation at both macroscopic and microstructural

scales. At high water ratios (ew > eSL for the soil, or ew > e∗m for the microstructure), the increase in the residual

stress ratio is entirely a consequence of the soil (or aggregate) stiffness increase associated with total suction sinceSr = 1 (or Sm

r = 1). As observed in the figure, at high total suctions (usually above 200 MPa) the effective suctionmodel predicts the decrease in the residual stress ratio, as a consequence of the loss of the aggregate stiffness at lowmicrostructural degree of saturation (low water availability). Preliminary results performed by the authors on verydry powder of Boom clay (ew < 0.15 at s > 70 MPa) and with small aggregate sizes suggest this hypothesis andstrengthen the use of the effective suction rather than total suction to describe the evolution of the stiffness effectson the residual shear strength. Nevertheless, further research is undergoing to verify this residual shear strengthresponse at very low water ratios and small aggregate sizes.

5. Summary and conclusions

An experimental investigation has been performed to highlight the relevance of the hydraulic state on the residualshear strength of different clayey materials. The tested clayey materials, which displayed a wide range of plasticityindices (from 16% to 49%), were clayey silt, illitic-kaolinitic clay, bentonite and clayey gouge material that wasremoved by scratching from volcanic rock discontinuities. An adapted Bromhead ring shear apparatus [20], inwhich the initially saturated and remoulded samples are enclosed in a controlled relative humidity chamber, hasbeen used to apply high total suctions along drying paths and to control the relative humidity during shearing alonglarge displacements. Total suctions ranged typically between s = 10 MPa and 160 MPa, which covered a wide rangeof relative humidity (between 90% and 30%). A key aspect is the definition of the water retention curve in thishigh suction range, in which water is mainly held inside aggregates and no important capillary effects are actingbetween them. Water retention results on drying of the different soils have been fitted to a microstructural waterretention curve [10, 28], which expresses the water stored inside aggregates as a function of the total suction andallows defining a microstructural degree of saturation. This information is further used to propose a simple modelfor the residual shear strength increase with suction.

The residual shear strength envelopes displayed null cohesion intercept on total suction increase. The residualshear strength increase was entirely a consequence of the systematic increase in the residual friction angle withimposed total suction. In the case of the illitic-kaolinitic material, this increase reached 15◦ between saturatedand dry states (s = 152 MPa). It has been explained in terms of the prevailing aggregate structure despite startingfrom saturated conditions – large soft aggregates were observed by Merchan et al. [19] on saturated bentonite withenvironmental scanning electron microscopy. On drying, these large aggregates shrink and undergo desaturation,which induces the increase in their stiffness and the development of a more granular/frictional character withrotund particles. This aggregate stiffening at elevated suctions also explains the enhancement of dilatancy duringshearing, which has been observed by Vaunat et al. [34]. Suction increase also enhances the brittleness duringshearing, which has been associated with the fusing/healing effect of initially soft aggregates during resting periodat constant stress and the work required for the reorientation of the stiffer aggregates. These variations are ofinterest in geotechnical practice for optimising designs in unsaturated soils (stabilisation of reactivated landslides,pile friction design, earthworks stability). The healing effect on drying and associated with an increase in brittlenesshas also an important consequence on the reactivation of progressive failure phenomena.

The increase in friction angle with total suction has been interpreted using a simple model inspired in bothmacroscopic and microstructural observations on drying (shrinkage curves), which is based on the stiffness increaseof the soil (or aggregates) during desaturation and depends on the product of the total suction applied and the degreeof saturation. This product defines an effective suction at the macroscopic scale (soil) or at a lower microstructuralscale (inside aggregates), which takes into consideration the effects of water availability and its distribution insidethe porous medium. This effective suction also allows for some reduction in the effect of total suction in the highrange (s > 200 MPa) at very low water ratios and small aggregate sizes. Parameters of the model proposed haveshown to depend on the plasticity index of the different tested clays, which makes more useful its applicability ingeotechnical practice.


Acknowledgments

Dr. Merchan was supported by the Programme Al�an, the European Union Programme of high level Scholarshipfor Latin America, scholarship No. E05D052296CO.

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