Determining the unsaturated hydraulic conductivity of a compacted
sand–bentonite mixture under constant-volume and free-swell conditions
Y.J.Cui *,A.M.Tang,C.Loiau,P.Delage
吸附量
Ecole des Ponts-Paris Tech,U.R.Navier/CERMES,6et 8Avenue Blai Pascal,Champs-sur-Marne,77455Marne-la-Vallee Cedex 2,France
a r t i c l e i n f o Article history:
Available online 14October 2008Keywords:
Compacted sand/bentonite mixture Infiltration
Instantaneous profile method Constant-volume Free-swell
Unsaturated hydraulic conductivity
a b s t r a c t双曲线的基本知识点总结
Highly compacted sand–bentonite mixtures are often considered as possible engineered barriers in deep high-level radioactive waste disposals.In situ,the saturation of the barriers from their initially unsat-urated state is a complex hydro-mechanical coupled process in which temperature effects also play a role.The key parameter of this process is the unsaturated hydraulic conductivity of the barrier.In this paper,isothermal infiltration experiments were conducted to determine the unsaturated hydraulic con-ductivity according to the instantaneous profile method.To do so,total suction changes were monitored at different locations along the soil specimen by using resistive relative humidity probes.Three constant-volume infiltration tests were conducted showing,unexpectedly,a decrea of the hydraulic conductivity during infiltration.One test performed under free-swell conditions showed the opposite and standard trend.The obrvations were interpreted in terms of microstructure changes during wetting,both under constant-volume and free-swell conditions.
Ó2008Elvier Ltd.All rights rerved.
1.Introduction
In radioactive waste disposal at great depth,compacted expan-sive soils are sometimes considered as possible engineered barrier to be placed between the radioactive waste and the host rock.When
hydrated by the pore water infiltrated from the host rock,engineered barriers cannot swell,resulting in the development of swelling pressure,microstructure changes and related changes in hydraulic properties.A proper understanding of this particular sit-uation is necessary in the description of water transfers in a real storage condition.
The saturated hydraulic conductivity (k sat )of bentonite-bad buffer materials is often measured by hydrating the specimen un-der constant-volume condition with a constant inlet water pres-sure and by monitoring the water inlet and/or outlet flow.k sat is calculated using Darcy’s law.It has been obrved that k sat de-cread with incread dry density (Dixon et al.,1999),incread bentonite content (Komine,2004;Kenney et al.,1992)or decread temperature (in the range of 20–80°C,after Cho et al.(1999),Villar and Lloret (2004)).In addition,Pusch (1982),Haug and Wong (1992)and Loiau et al.(2002)obrved that water infiltration at constant-volume modified the soil microstructure,giving ri to k sat decrea.
The unsaturated hydraulic conductivity (k unsat )can be mea-sured in the laboratory by various methods among which unsteady
methods such as the instantaneous profile method (Daniel,1982)are the most suitable for clayey soil
s (Benson and Gribb,1997).For bentonite-bad buffer material,k unsat is often determined from infiltration tests in columns.In some cas,compacted soil cylindrical specimens are wetted from one end and the water con-tent profile is determined at a given time by cutting the specimen into slices (Börgesson et al.,2001;Kröhn,2003a ).Lemaire et al.(2004)performed an infiltration test in an oedometer cell and monitored the change in water content and dry density with time at different locations by using dual-energy c -ray measurement.Various methods have been applied to describe the water transfer obtained from infiltration tests:Among others,Lemaire et al.(2004)solved the common diffusion equation by using Boltzmann variable whereas Kröhn (2003b)considered both an advection model and a vapour diffusion model to fit his experimental data.This paper prents the experimental results obtained on com-pacted sand/bentonite mixture specimens by performing three infiltration tests under constant-volume conditions and one infil-tration test under free-swell conditions.The instantaneous profile method was ud to determine the unsaturated hydraulic conduc-tivity.The results from the two conditions were compared to ana-lyze the effect of microstructure changes on the hydraulic conductivity during wetting.2.Material and methods
The soil tested is a mixture of Kunigel-V1bentonite and Hostun sand with a respective proportion of 7/3in dry weight.According
1474-7065/$-e front matter Ó2008Elvier Ltd.All rights rerved.doi:10.1016/j.pce.2008.10.017
*Corresponding author.Tel.:+33164153550;fax:+33164153562.E-mail address:pc.fr (Y.J.Cui).Physics and Chemistry of the Earth 33(2008)
S462–S471
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to Komine (2004),the Kunigel-V1clay consists of 48%montmoril-lonite,resulting in high plasticity index (liquid limit w L =474%,plasticity index I p =447).The geotechnical properties of Kunigel-V1bentonite (after Komine,2004)are prented in Table 1.The particle size distributions of Hostun sand ud in the prent work is given in Fig.1.The solid unit weight of the sand/bentonite mix-ture is 2.67Mg/m 3.The mixture ud in this work is similar to that ud in the full-scale ‘‘tunnel aling experiment”(TSX test)con-ducted in Canada (Martino et al.,2007;Dixon et al.,2007).
Samples were prepared by compacting a mixture made up of clay powder and sand grains with an initial water content of 4.2%.Prior to compaction,the mixture was put in three airtight chambers at three different relative humidities (RH )controlled by using saturated saline solutions.At equilibrium,final water con-tents were,respectively,equal to 6.5±0.1%(Mg(NO 3)2solution,RH =55%,suction s =82MPa);8.0±0.3%(NaNO 2solution,RH =66%,suction s =57MPa);and 10.0±0.3%(Z
nSO 4solution,RH =90%,suction s =12.6MPa).The mixture was then compacted statically in a metallic cylinder of 50mm diameter at a dry unit mass q d =2.0Mg/m 3.Loiau et al.(2002)determined the water retention curves (suction s versus gravimetric water content w )of the mixture compacted at w =7.7%and q d =2.0Mg/m 3.The re-sults obtained along the wetting path under free-swell and no vol-ume changes conditions are prented in Fig.2.
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In order to determine the unsaturated hydraulic conductivity of the compacted sand/bentonite mixture by using the instantaneous profile method,infiltration tests were performed under two condi-tions:constant-volume and free-swell.The device ud for the
infiltration test at constant-volume conditions is prented in Fig.3.The soil specimen (50mm in diameter,250mm high)was directly compacted in the metallic cylinder (50mm in inner diam-eter,80mm in outer diameter).Four resistive RH nsors (Elcowa)were installed in small holes made into the sample through the four ports in the wall of the cylinder.The two ends of the cylinder were covered by two metallic discs of 40mm thickness.The bot-tom of the cell was connected to a water source while the upper end was connected to an air source under atmospheric pressure.Porous stones were placed in both bottom and upper ends.One RH probe was installed in the upper disk to monitor the RH on the top of the soil specimen.The device enables RH monitoring
Table 1
Geotechnical parameters of Kunigel-V1clay (after Komine,2004).Type
Sodium bentonite Particle density (Mg/m 3) 2.79Liquid limit (%)474Plastic limit (%)27Activity
6.93Clay (<2l m)content (%)64.5Montmorillonite content (%)
48Cation exchange capacity (meq./g)0.732Exchange capacity of Na +(meq./g)0.405Exchange capacity of Ca 2+(meq./g)0.287Exchange capacity of K +(meq./g)0.009Exchange capacity of Mg 2+(meq./g)
0.030
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继续教育会计Fig.3.Schematic diagrams of the infiltration test with no volume changes.
Y.J.Cui et al./Physics and Chemistry of the Earth 33(2008)S462–S471
S463
at five different distances from the wetted end (h =50,100,150,200,and 250mm).
The infiltration test with swelling allowed is schematically de-scribed in Fig.4and a picture is prented in Fig.5.In this system,the cylindrical compacted soil specimen (50mm in diameter,
100mm high)was wrapped by a deformable neoprene membrane (0.3mm thick)and placed horizontally on a bed made up of glass balls in order to reduce friction between the sample and its support during swelling.Four RH probes were embedded into the sample at distances h =10,40,65,and 95mm from the wetting end.The con-necting wires went through the membrane and air-tightness was ensured by putting silicon glue between the membrane and the wire.Four displacement transducers (0.001mm accuracy)were also ud to monitor the local radial swelling of the soil specimen at distances h =9,36,71.5and 96.5mm from the wetted end.A displacement transducer was also installed on the top of soil spec-imen to monitor the total axial swelling.In order t
o better visualize the soil swelling,a grid (2Â2cm)was plotted on the membrane.The volumes of inlet water and expelled air were equally moni-tored using graduated fine tubes.
Three tests were performed at constant-volume conditions with three initial water contents (w i =7.70%–Test T01,w i =6.45%–Test T02,and w i =9.95%–Test T03).The test performed with swelling allowed (Test T04)had w i =8.20%.
3.Experimental results
Fig.6prents the RH changes with time of the three tests per-formed at constant-volume conditions in the column of Fig.3.The initial RH value of Test T01(w i =7.70%)was 70±1%(suction equal to 49.5±1.5MPa).To reach this water content,the sand/bentonite mixture was previously hydrated in the vapour pha in an airtight chamber at RH =66%.The RH of the soil incread from 66%to 70%during subquent compaction.Once infiltration started,the RH value at h =50mm incread rapidly and reached a zero suction state (RH ffi100%)after 2500h.For other RH probes,the further the distance from the wetting face,the slower the rate of RH in-crea.For instance,RH at the upper end of the soil specimen (h =250mm)incread only from 70%to 73%after 2500h infiltration.
In Test T02(w i =6.45%),the compaction incread RH from 55%(value impod when hydrating the
mixture prior to compaction)to 62±2%after compaction.During infiltration,the value of RH at h =50mm incread rapidly and reached a zero suction state after 4000h.Afterwards,the signal of the RH probe at h =50mm was lost,becau resistive probes are known to fail at saturated relative humidity due to water vapour condensation.At h =250mm,RH incread from 63%to 73%after 7500h.
The wetter mixture ud in Test T03(w i =9.95%)was prepared at RH =90%and the initial RH measured in the column was 90±1%.The RH value at h =50mm incread rapidly from 90%to 98%after 1000h while RH at h =250mm incread from 89%to 93%after 2400h.As explained previously,the RH probe at h =50mm failed after 1000h once the humidity was saturated (RH =100%).
The total suction (s )was calculated from RH using the Kelvin’s law
s ¼Àðq w RT =M w Þln ðRH =100Þ
ð1Þ
where R is the universal (molar)gas constant (8.31432J/mol K);T is the absolute temperature (K);M w is the molecular mass of water va-pour (18.016g/mol)and q w is the water unit weight (1000kg/m 3)
.Fig.7prents the suction isochrones for Test T01with a time step of 200h.At t =0,the initial total suction of the compacted sample is approximately constant with a mean value of was 49.5±1.5MPa.After starting the infiltration,the suction at the wetting face (h =0)rapidly decread to zero.Note that this zero suction is an impod value and the real suction in the mixture in this level must took some time to decrea to zero.The total suc-tion at h =50mm rapidly decread to 4.1MPa at t =2200h
while
Fig.4.Schematic diagrams of the infiltration test with swelling
allowed.
Fig.5.Picture of the infiltration test with swelling allowed.
S464Y.J.Cui et al./Physics and Chemistry of the Earth 33(2008)S462–S471
the total suction at h=250mm remained high(s=45.5MPa at t=2200h).
The determination of the unsaturated hydraulic conductivity using the generalized Darcy’s law according to the instantaneous profile method is detailed in Fig.8.In Fig.8a,the suction profiles at t=200and600h are plotted.The hydraulic gradient(i)is calcu-lated as the slope of the isochrone(tangent of the suction profile at h and t)as follows:
i¼d s=d hð2Þwhere s and h are expresd in m.
In Fig.8a,the hydraulic gradients at h=50mm,at t=200and 600are,respectively,25,000and53,400.The volume of water passing through the area located at h=50mm in the time period comprid between t and t+d t is computed by integrating the dif-ference in the water content profiles at time t and t+d t.
In this work,the water content of the soil was calculated from the total suction bad on the water ret
ention curves obtained at constant-volume conditions on the same material by Loiau et al.(2002).The following empirical equation was derived from Fig.2:
w¼À5:9logðsÞþ17:7ð3ÞNote that the total suction measured by RH probe is ranging from4 to100MPa.The relationship between the logarithm of suction and water content obtained by Loiau et al.(2002)can be correlated with a linear function in this range of suction.For this reason,a lin-ear correlation was ud to calculate the water content from the suction measured.
Using this correlation,the volumetric water content(h)can be calculated by
h¼w q d=q wð4ÞIn the infiltration test at constant-volume conditions,q d is assumed to be constant,q d=2.0Mg/m3.In Fig.8b,the volumetric water con-tent profiles at t=200and600h are calculated from the suction profiles and plotted.The shaded area corresponds to the volume of water passing through the point h=50mm during the time per-iod between200and600h.
The same procedures have been applied after various periods of time with a time increment of100h.The results in terms of water fluxes(q)and hydraulic gradients(i)are plotted in Figs.9and10, respectively,for distances from the wetted ends h=50,100,150,
Y.J.Cui et al./Physics and Chemistry of the Earth33(2008)S462–S471S465
and 200mm.The maximal measured flux q is equal to 1.8Â10À12m 3/s.Calculations show that huge values of hydraulic gradients are mobilid,with values of i at h =50mm increasing rapidly from 0to 54,000in the first 550h and subquently decreasing to 19,000at t =2250h.The huge values of hydraulic gradients are to be related to the significant changes in suction with respect to the distance to the wetted end that occur during hydration.
In Fig.11,the calculated flux q is plotted versus the hydraulic gradient i at distances h =50,100,150,and 200mm from the wet-ted end,according to the results prented in Fig.9.It can be ob-rved that various q Ài relationships are obrved depending on the position considered,with not simply linear shapes like in cas where Darcy’s law is respected (the hydraulic conductivity k being given by k =(q /i )/A ,where A is the cross-ctional area equal here to 0.00196m 2).
In Fig.12,the water flux q is plotted versus the hydraulic gradi-ent i for each value of suction (according to the results prented in Fig.11).It can be obrved that,for a given suction,the q Ài rela-tionship is bilinear with two slopes;the slope at high gradients being larger than that at low gradients.This bilinear relationship of q Ài has often been obrved when measuring the saturated hydraulic conductivity of clayey soils (Dixon et al.,1992).
S466Y.J.Cui et al./Physics and Chemistry of the Earth 33(2008)S462–S471
In Fig.13,the values of unsaturated hydraulic permeability k is plotted versus suction according to calculations made at various distances from the wetting point with h=50,100,150and 200mm.Different curves are obtained in different levels.This is the conquence of the bilinear relationship of qÀi obrved above(Fig.12),evidencing the effect of water gradient.To analy the waterflow using Darcy’s law,one of the possibilities is to u the term‘‘critical gradient”,i.e.,to consider
waterflow only when the linear gment at higher waterflux(Fig.12)is reached(more details about this method are prented in Dixon et al.(1992)). This analysis using critical gradient leads to a unique relationship, independent of the measurement level.This relationship refers to T01in Fig.13.It can be obrved that k decreas from 12Â10À14to3Â10À14when suction decreas from50to 25MPa.On the contrary,k slightly increas for further decreas in suction from25to15MPa.
Unlike in low plasticity unsaturated soils in which no significant strain is obrved during infiltration and in which the coefficient of permeability is increasing during infiltration,it can be obrved that the kÀs relationship is not unique in swelling soils with con-stant-volume conditions.This non unicity obviously add a degree of complexity when trying to model and calculate water transfers in this material.
Similar procedures were applied to determine the unsaturated hydraulic conductivity from tests T02and T03and all results are prented together in Fig.21.
The results obtained from the infiltration test T04in which swelling was allowed are prented in Figs.14and15.In Fig.14, the values of RH measured by each probe are plotted versus time t.The test was conducted during1600h with four RH probes embedded at distances h i=10(S1),40(S2),65(S3)a
nd95mm (S4)from the wetted end.In general,the shape of the curves is comparable with that of the constant-volume infiltration tests (e Fig.6).The RH measured by probe S1located clost to the wetting face(h i=10mm)incread quickly and reached a zero suction condition after only50h(the probe afterwards failed due to vapour condensation).Probe S2failed at800h and the Probe S3failed at1000h.
In Fig.15,the evolution of the axial and radial strain that were monitored by the displacement gages during infiltration are plot-ted at various times.After1400h,the radius at10mm from the wetted end incread from25to30mm(corresponding to a radial swelling strain e rs=20%)and the distance between S1and the wet-ting face(h)incread from10to18mm(80%).The total length of
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