Expansive bentonite–sand mixtures in cyclic controlled-suction
drying and wetting
E.E.Alonso,E.Romero *,C.Hoffmann,E.Garcı´a-Escudero
Department of Geotechnical Engineering and Geosciences,Universitat Polite `cnica de Catalunya,
UPC,c/Jordi Girona 1-3,Building D-2,08034Barcelona,Spain
Available online 11August 2005
Abstract
Expansive clay buffers in radioactive waste disposal designs experience cyclic drying and wetting paths during different stages of their design life.Clayey soils subjected to the process develop swelling and shrinkage deformations,which give ri to the accumulation of compression or expansion strains during suction cycles.Experimental studies were undertaken using oedometer tests on an artificially prepared bentonite–sand mixture (80%bentonite by dry mass).In order to study the process and to identify the most important features controlling soil behaviour,veral wetting–drying
cycles with suctions ranging between 130and 4MPa were applied using vapour equilibrium technique and covering a wide range of over-consolidation ratios (OCR).The tested samples showed cumulative shrinkage strains along the successive cycles,which became more significant at increasing vertical net stress (low OCR values).However,no accumulation of expansion strains was detected at elevated OCR values.Test results were interpreted and predicted within the context of an elastoplastic model propod by Alonso et al.,1999,[Alonso,E.E.,Vaunat,J.,Gens,A.,(1999).Modelling the mechanical behaviour of expansive clays.Engineering Geology,54,173–183.]which takes into account the accumulation of strains.A good correspondence between measured soil respon and model predictions was obrved.The paper also prents the methodology to derive the constitutive parameters.
D 2005Elvier B.V .All rights rerved.
Keywords:Swelling;Shrinkage;Suction;Expansive clay;Model
1.Introduction
Soils are naturally subjected to cyclic and strong drying and wetting paths due to natural environmental fluctuations.Buffers constructed using clays of expan-sive nature in radioactive waste
disposal designs also experience stress and suction cycles during different stages of their design life.In a general ca,stress and suction paths are far from being a simple monotonic
0013-7952/$-e front matter D 2005Elvier B.V .All rights rerved.doi:10.2005.06.009
*Corresponding author.Geotechnical Laboratory,Departamento de Ingenierı´a del Terreno,Jordi Girona 1-3,Edificio D-2,Universi-tat Polite `cnica de Catalunya,08034Barcelona,Spain.Tel.:+34934016888;fax:+34934017251.
E-mail -morales@upc.edu (E.Romero).Engineering Geology 81(2005)213
–226
/locate/enggeo
process.Clayey soils undergo an increa in volume
during water uptake,but also experience an important襄阳隆中
amount of shrinkage on water removal,which give
ri to the accumulation of compression or expansion
strains during suction cycles.Several studies were
undertaken in the past;however,few experimental
studies have been reported in the literature with
respect to water transfer in vapour form under con-
trolled-suction conditions.In fact,vapour transfer
plays a major role in buffers of radioactive waste
disposal designs becau of the existing strong ther-
mal gradients.In addition,bentonite-bad buffers
develop very large suctions,which cannot be tested
using conventional techniques with liquid water trans-
fer,such as the axis translation and osmotic techni-
ques.Furthermore,the respon of expansive soils
against suction cycles is a key information required
to understand its constitutive behaviour.
Experimental results describing the volume change
respon of expansive soil expod to cyclic wetting
and drying have been reported by Dif and Bluemel
(1991)and Al-Homoud et al.(1995),who detected
d fatigu
e T o
f swelling(shrinkage accumulation)that increas at higher vertical stress.This behaviour
was explained in terms of a continuous rearrangement
of soil particles,leading to a less active microstruc-行户
ture.On the other hand,Obermeier(1973),Popescu
(1980)and Pousada(1984)obrved an opposite
effect,in which the amount of swelling incread
with the number of cycles.Day(1994)and Basma
et al.(1996)reported cumulative shrinkage or expan-
sive strains,depending on the suction reached during
the drying paths.
The objectives of the rearch prented in this
paper are focud on the investigation and prediction
of the volume change respon of an artificially pre-
pared mixture of bentonite and sand subjected to
veral wetting and drying cycles in the high suction
range.To achieve the first objective,an experimental
programme was designed in which veral controlled-
suction wetting and drying cycles,with suctions ran-
ging between130and4MPa,were applied using
vapour equilibrium technique.Oedometer tests were
performed under different values of constant vertical
net stress covering a wide overconsolidation(OCR)
range.To address the cond objective,the volume
change respon of the mixture is discusd and inter-
preted within the context of the elastoplastic model propod by Alonso et al.(1999)(BExM:Barcelona Expansive Model).Comparisons are provided between the experimental results and the predicted results.Bad on the studies model parameters are derived.
2.Experimental programme
2.1.Tested material
Tests were performed on statically compacted ben-tonite–sand mixtures.This material was lected
due to the following favourable properties:significant volume changes on suction cycles and an appropriate water permeability,which allowed the time required for equalisation to be kept within reasonable bounds. Bentonite powder was mixed with silica sand to achieve a dry mass ratio of80%bentonite and20% sand.Ca-bentonite powder passing ASTM No.40 (FEBEX bentonite,ENRESA,2000)prents a liquid limit of93%,a plastic limit of47%,45%of particles less than2A m and a density of solid particles of2.70 Mg/m3.The uniform sand passing ASTM No.16pre-nts a uniformity coefficient of C u=2and an effec-tive size of D10=0.21mm.
The mixture in powder form was allowed to equi-librate at an average relative humidity of55%(suction of s=80MPa)to achieve a hygroscopic water content of10.5%.Specimens(30mm in diameter and8mm high)were then statically and one-dimensionally com-pacted at a displacement rate of0.2mm/min and constant water content to a target dry density of around1.5Mg/m3.The initial degree of saturation was around35%.
A complementary test programme under oed-ometer conditions was also performed to obtain addi-tional constitutive information on the mechanical behaviour of the as-compacted state.The tests include wetting at constant volume(swelling pressure tests)and loading–unloading paths at constant suc-tion.Bad on the results compressibility para-meters and yield properties of the material were
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estimated.Fig.1shows the oedometer loading–unloading test performed at constant suction s=80 MPa(as-compacted state).A clear pre-and post-yield respon is detected,defining a preconsolidation stress at around5MPa.Fig.2reprents the swelling
E.E.Alonso et al./Engineering Geology81(2005)213–226 214
pressure test performed under constant volume condi-tions.Imbibition of the sample was performed by liquid transfer at constant head.Water inflow was registered by a burette and vertical net stress evolution was monitored by a load cell.Time evolution of vertical net stress and degree of saturation changes on wetting are indicated in Fig.2.Different patterns of behaviour are obrved during this suction reduction path.The swelling pressure increas in the early transient stage to compensate for the swelling strain caud by the suction reduction,but eventually the
含有杏花的诗句sample yields.From the yield point on,the collap tendency is compensated for by the expansion of the swelling microstructure,and the vertical stress reduces to maintain the constant volume condition.In this way,swelling stress reaches a maximum controlled by the LC yield surface,as explained by Alonso et al.(1990),and then decreas on subquent wetting following approximately the yield locus at constant volume.The swelling pressure test results can be ud to determine the s
生命如此脆弱>基本事实
aturated vertical preconsolidation stress r vo *=0.65MPa (point B in Fig.2),as well as the initial yield point on the LC curve at r vo =1.05MPa (point A in Fig.2).This yield point is reached at an approximate degree of saturation of 70%(refer to Fig.2).This degree of saturation is associated with a suction of s =10MPa,which was measured with transistor psychrometers (Woodburn et al.,1993)on another sample undergoing the same fabrication and wetting process.
Bad on this information,the LC yield locus,which reprents the increa of preconsolidation stress with suction r vo (s ),is qualitatively depicted in Fig.3in conjunction with the stress paths previously described.
2.2.Controlled-suction technique and experimental tup
The vapour equilibrium technique was implemen-ted by controlling the relative humidity of a clod system.In this way,soil water potential was applied
0.01
0.1
1
10
100
1000
Time (hours)
0.10.30.50.70.91.1
V e r t i c a l n e t s t r e s s , σv (M P a )
2040
60
80
100
D e g r e e o f s a t u r a t i o n , S r (%)
Fig.2.Swelling pressure test.
V
Fig.3.Stress paths followed.Estimated LC yield locus for the as-compacted state.
100
1000
10000
Vertical net stress, σV (kPa)
1.50
1.60
1.70
1.80
S p e c i f i c v o l u m e
, (1+e )
Fig.1.Loading–unloading test at constant suction s =80MPa on the as-compacted sample.
E.E.Alonso et al./Engineering Geology 81(2005)213–226215
by means of the migration of water molecules through the vapour pha from a reference system of known potential and mass to the soil pores,until hydro-mechanical equilibrium was achieved.The relative humidity of the reference system was controlled by varying the chemical potential of different types of aqueous solutions.
Non-volatile solutes (CuSO 4)and volatile solutes (acid solutions of H 2S04)were ud in the experimen-tal programme.CuSO 4solutions were ud under saturated conditions of dissolution,which allowed suctions ranging between 4and 6MPa to be attained.This procedure was ud for the wetting paths.On the other hand,acid solutions were employed under par-tially saturated conditions of dissolution.In this ca,a specified solute quantity was lected to achieve a target relative humidity of 40%(suction of s =130MPa),which was ud in the drying paths.However,the acid concentration was not fixed due to the fact that the soil exchanged vapour on drying with the reference system.A densimeter with a readability of 0.0005Mg/m 3was ud to measure the equilibrated density of the solution after each drying path and at the controlled temperature of the laboratory.Fig.4shows the suction achieved as a function of the acid solution density and temperature.This plot is bad on aqueous solution properties and the psychrometric law,which translates relative humidity values to suctions at a given tem-perature (Fredlund and Rahardjo,1993).In addition,
every new density was ud to approximately deter-mine,at a constant temperature,the amount of water lost by the soil on drying.Further details of this technique are prented in Romero (2001).
Each equalisation step was maintained until the rate of straining had reduced to an axial strain rate o
f 0.1%/day.Each drying–wetting step required a typical duration of 12days,which resulted in a total test duration of approximately 4months.
Fig.5shows the oedometer cell and the different elements of the controlled-suction technique.A forced convection system,driven by an air pump,was ud to transport the vapour from the reference solution (desiccator in Fig.5)to the soil pores.Mass exchanges were monitored by weighing the desiccator with an electronic balance with a resolution of 10mg.Two procedures were followed to transfer the vapour:the vapour was either circulated along the boundaries of the sample (top and bottom porous stones indicated in Fig.5)or it crosd the specimen.This last proce-dure of vapour transport through the sample (valves A and B clod,D and C open),which was ud at low degrees of saturation,is more efficient but it is limited to soil states that prent continuity of air.On the other hand,at higher degrees of saturation,the alter-native procedure was followed (valves A and C clod,B and D open;or alternatively valves A,B and C open and D clod).2.3.Stress paths followed
The different stress paths followed in this test programme are shown in Fig.3where tests are indi-1.34
1.36
1.38
1.40
桂花一年开几次花Density of H 2SO 4 (Mg/m 3)
100
110
120
130
140
S u c t i o n , s (M P a )
Fig.4.Values of suction applied as a function of H 2SO 4density and temperature.
coar porous stone
Fig.5.Experimental tup of vapour equilibrium technique using a forced convection system.
E.E.Alonso et al./Engineering Geology 81(2005)213–226
216
cated in the(r v,s)plane.The drying–wetting paths were lected taking into account the position map
ped for the LC curve from the auxiliary tests performed.Applied vertical stress were in all cas lower than the yield stress for saturated conditions, r vo*.The main reason for this,was to investigate the yield behaviour of the soil in the d swelling region T far from the collap mechanism,described by the LC curve.Three cyclic drying–wetting tests were performed at vertical net stress of98,196and 396kPa respectively.
Once the sample was compacted in the oedometer cell,the lected vertical load was applied.Suction was maintained at a value of s=80MPa.Once equilibrium was reached the first wetting cycle was applied.Suction was reduced in a single step,to a value in the range4–6MPa.Subquent drying–wetting reversals were then applied once equilibrium was reached.Suction was changed in a single step from a low value of4–6MPa to a high value of 120–135MPa.The exact suction depended on the room temperature and the concentration of the solu-tion ud.Five to six cycles were applied for each vertical stress.
The constitutive model that was ud as a reference framework is prented prior to discussing the test results in more detail.
3.Expansive model.Theoretical framework for isotropic states
3.1.Elastic behaviour
Two structural levels are distinguished in the fabric of an expansive soil:micro and macro(Gens and Alonso,1992).The microstructural level describes the aggregates of active clay minerals and is asso-ciated with the lower range of soil pores.Its volume is given by the microstructural void ratio,e m.Clay fabric at this level is assumed to react in a pure volumetric and elastic manner against changes in iso-tropic stress and suction(Alonso et al.,1999):
d e e vm¼dˆp
K m
ð1Þ
where d e vm e=Àd e m/(1+e m)is the elastic microstruc-tural volumetric strain,K m is a compressibility coeffi-cient and pˆis a generalid microstructural effective stress,defined as:
ˆp¼pþS a
rmic
sð2Þwhere p is the mean net stress(excess of average total mean stress over air pressure),s is the suction,S rmic is the degree of saturation of the microstructural level (which depends on s)and a is a constitutive coeffi-cient.When a=0,saturated effective stress is recov-ered.When a=1,pˆcorresponds to Bishop’s mean stress.
The coefficient K m is not a constant.It depends on the confining stress.A suitable expression for K m is derived from the classical logarithmic law of void ratio reduction for increasing stress:
K m¼
1þe m
ðÞˆp
j m
ð3Þwhere j m is the(constant)compressibility index of the microstructure.
Macrostructural strains describe the rearrangement of the soil structure.They imply changes in size of the largest pore sizes,characterid by a global volume measure(macrostructural void ratio e M;th
e void ratio is then given by e=e m+e M).Elastic and plastic macrostructural strains develop as stress and suction change.Elastic macro strains are given by the classi-cal expression of Alonso et al.(1990):
d e e VM¼
dp
K t
þ
ds
K s
ð4Þwhere
K t¼
1þe M
ðÞp
j
K s¼
1þe M
ðÞsþp atm
ðÞ
j s
ð5Þ
and j and j s are(macro)compressibility indexes against mean net stress and suction changes.
The total elastic strain can be calculated using
d e e v¼d e e vmþd e e vMð6Þ
3.2.Plastic behaviour
The variation of preconsolidation mean net stress with suction is given by an LC yield surface in the(p, s)plane:
p0¼p c
p*o
p c
k0ðÞÀj
ð7Þ
E.E.Alonso et al./Engineering Geology81(2005)213–226217
with
k s ðÞ¼k 0ðÞr þ1Àr ðÞe Àb s
ÂÃ
ð8Þ
where p *o is the saturated preconsolidation mean net stress,p c is a reference stress,k (0)is the slope of the vir-gin compression line and (r ,b )are model parameters.Eq.(7)describes the yield conditions of the macro-structure.Experimental evidence,reported in the Introduction of this paper,indicates that wetting and drying paths are also capable of inducing plastic strains.The plastic strains have their origin in the underlying microstructural deformations but,as reported previously,they em to be controlled also by the applied confining stress and by the density (alternatively,the intensity of compaction)of the material.The model describes the plastic straining by means of two additional yield curves (SI and SD,associated with suction increa and suction decrea,respectively),which are reprented in Fig.6.The yield curves are defined by the expressions p ˆÀs I =0for the SI yield curve and p ˆÀs D =0for the SD yield curve;s I ,s D being the hardening parameters.
When SI and SD yield curves are activated,plastic strains are induced,which in view of the above consid-erations have been given the following expressions:
d e p vM ¼f I d e e
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vm ð9Þd e p vM ¼f D d e e vm
ð10Þ
f I and f D are micro–macro couplin
g functions whic
h are made dependent on (p /p 0),p 0being the current
preconsolidation stress at the current value of suc-tion,as given by the LC yield curve.The nature of
the coupling functions will be discusd later when the experimental results are analyd.
It was also assumed that SI and SD hardening is
governed by d a 1=d e p vSI +d e p
vSD ,although a depen-dence on plastic strains induced by LC plastic loading may be suspected.LC hardening is assumed to depend
on d a 2=d e p vSI +d e p vSD +d e p vLC ,where d e p
vLC is the volu-metric plastic strain due to the activation of LC.Hard-ening laws are defined as follows (Alonso et al.,1999):
ds I ¼K m d a 1
f ¼ds D ð11Þ
dp T 0
p T 0
¼
1þe M ðÞd a 2k 0ðÞÀj ð12Þ
In Eq.(11)the function f is either f I or f D depend-ing on whether yielding is occurring on the SI or SD
curve.
4.Test results and interpretation 4.1.Complementary tests
In the remainder of the paper,the mean net stress p in the model will be replaced by the applied vertical net stress r v .Since horizontal stress were not mea-sured,application of a generalid model would not lead to significant advantages over the simpler approach adopted.
The swelling pressure test provides direct infor-mation on the value of the saturated preconsolidation stress r vo *and on the shape of the LC yield locus of the macrostructure.Gens and Alonso (1992)showed that the maximum swelling pressure is slightly above the current yield stress for the prevailing suction.In addition,the swelling pressure path for lower suction values follows approximately the LC yield curve.The recorded data given in Fig.2has been ud to plot the swelling pressure path in a (r v ,s )stress plane.Measured degrees of saturation (or alterna-tively,water content w )were related to suction through the following empirical relationship found by Villar (1995)for the water retention curve of the FEBEX bentonite:
w ¼36À5:5ln s ðÞ;w in %and s in MPa
ð13
Þ
Fig.6.Yield loci of expansive model.
E.E.Alonso et al./Engineering Geology 81(2005)213–226
218
