Comparison of vacuum consolidation with surcharge load induced consolidation of a two-layer system

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Chai, J.-C., Matsunaga, K., Sakai, A. & Hayashi, S. (2009). Geotechnique 59, No. 7, 637641 [doi: 10.1680/geot.8.T.020]

637

TECHNICAL NOTE

Comparison of vacuum consolidation with surcharge load inducedconsolidation of a two-layer system

J . - C . C H A I * , K . M A T S U N A G A , A . S A K A I * a n d S . H A Y A S H I *

Laboratory consolidation tests for a two-layer soil sys-tem under oedometer conditions were conducted underboth vacuum pressures and surcharge loads. The effectsof the order of soil layers on the behaviour of vacuumconsolidation of the two-layer soil system have beeninvestigated by comparing vacuum pressure and sur-charge load induced consolidations. Under one-way drai-nage conditions, for both a surcharge load and avacuum pressure, the order of soil layers only influencesthe rate of consolidation but not the final settlement.

When a layer with a relative lower value of hydraulicconductivity (k) is located immediately adjacent to thedrainage boundary, the consolidation rate is slower.However, for vacuum pressure applied under two-waydrainage conditions, the order of the soil layers not onlyinfluences the rate of consolidation but also the magni-tude of settlement.

KEYWORDS: consolidation; laboratory tests; settlement

Des tests de consolidation en laboratoire pour un sys-teme de sol a deux couches, avec un oedometre, sonteffectues en presence de pressions sous vide et desurcharges. On examine les effets de lordre descouches de sol sur le comportement de la consolidationsous vide du systeme a deux couches en comparant lesconsolidations induites par pression sous vide et sur-charge. Avec un drainage unidirectionnel, et aussi bienavec pression sous vide et surcharge, lordre descouches de sol ninflue que la vitesse de consolidation,

et non pas le tassement final. Lorsquon releve unecouche presentant une conductivite hydraulique (k) avaleur relative inferieure en un point adjacent a lalimite de drainage, la consolidation se deroule pluslentement. Toutefois, en cas dapplication de la pressionsous vide avec un drainage bidirectionnel, lordre descouches de sol influe non seulement sur la vitesse deconsolidation, mais egalement sur la magnitude dutassement.

INTRODUCTIONVacuum consolidation as a preloading method has received

attention recently (Bergado et al., 1998; Tang & Shang,2000; Tran et al ., 2004). Chai et al . (2005a; 2005b)discussed the characteristics of vacuum consolidation usingthe results of a laboratory odometer test with a uniformsoil layer under both vacuum pressures and surcharge loads.The response of a layered depositnatural deposits areoften layeredunder a vacuum pressure has not yet beenthe subject of comprehensive experimental and theoreticalinvestigation. Hence, in order effectively to design avacuum consolidation system, there is a need to clarify thecharacteristics of vacuum consolidation of a two-layer soilsystem.

A series of laboratory tests involving vacuum pressureand surcharge load induced consolidation under oedometer

conditions were conducted to investigate the fundamentalbehaviour of vacuum consolidation of a two-layer soilsystem. The effects of drainage condition (one-way ortwo-way) and the relative hydraulic conductivity (k) ofthe soil layer immediately adjacent to the boundary wherevacuum pressure is applied were studied with reference tothe amount of settlement and the rate of the consolida-tion.

A BRIEF DISCUSSION ON THE CHARACTERISTICS OFVACUUM CONSOLIDATION

Vacuum consolidation for a uniform soil layerChai et al. (2005b) reported the laboratory oedometer test

results for a uniform soil layer with both surcharge load andvacuum pressure. The conditions adopted can be found fromChai et al. (2005b), and the main findings are as follows.

(a) Settlements induced by vacuum pressure under one-waydrainage conditions. For vacuum consolidation, ifinward lateral displacement occurs, the settlementinduced by a vacuum pressure will be less than thatof a surcharge load with the same magnitude. Chaiet al. (2005b) defined a stress ratio kr as follows

kr vac

vac 9v0

(1)

so that, if kr< k0 (k0 is at-rest horizontal earth pressurecoefficient), there will be no lateral displacement andvice versa. Under oedometer conditions, Svac/Sl denotesthe settlement ratio of the final settlement induced by avacuum pressure (Svac) to that by a surcharge load withthe same magnitude (Sl). Fig. 1 (modified from Chai etal., 2005b) shows the relationship between the stressratio kr and the settlement ratio Svac/Sl obtained fromthe oedometer test results. It can be seen that whenkr. k0, Svac/Sl increases almost linearly with decreasingkr value. When kr< k0, Svac/Sl is very close to unity.

(b) Effect of drainage boundary condition. In the case oftwo-way drainage, at the bottom of the sample the

excess pore pressure is fixed at zero and effectively novacuum pressure can be applied. It is obvious thereforethat vacuum consolidation involving two-way drainageshould result in less settlement than one-way drainage.

Manuscript received 16 May 2008; revised manuscript accepted14 November 2008. Published online ahead of print 17 March2009.

Discussion on this paper is welcomed by the editor.* Saga University, 1 Honjo Saga 840-8502, Japan Chuoh Consultants (formerly Saga University), 6-1-1 Arado,Chuoh-ku, Fukuoka, Japan


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Under a vacuum pressure, for both one-way and two-way drainage conditions, water is drained out of a soilsample only at the boundary where the vacuumpressure is applied. Therefore, for both the cases, therate of consolidation should theoretically be the same.

General discussion on the characteristics of vacuumconsolidation for two-layer soil system

Generally, the effect of initial stress (9v0) in a soil sampleon the characteristics of consolidation of a two-layer soilsystem with a vacuum pressure should be similar to that of

a uniform soil layer. However regarding the effect of drai-nage boundary condition, it is strongly affected by the orderof soil layers relating to the boundary where the vacuumpressure is applied.

(a) One-way drainage. The final state will be a uniformvacuum pressure in the soil layers and no flow in thesystem. The order of soil layers will therefore notinfluence the final settlement. It will, however, influencethe rate of consolidation. Under the condition of nolateral displacement occurring, when a layer with arelative lower k value is located at the drainageboundary, the consolidation rate will be slower; this isthe same for a surcharge load case (e.g. Pyrah, 1996).

(b) Two-way drainage. Under a two-way drainage condition

with a vacuum pressure, the final state involves asteady water flow towards the boundary where thevacuum pressure is applied. In a two-layer soil system,to satisfy the flow continuity at steady state, thefollowing equation must be hold

i1 kv1 i2 kv2 (2)

where i1 and i2 are the hydraulic gradients of layer-1and layer-2, and kv1 and kv2 are the vertical hydraulicconductivities of layer-1 and layer-2, respectively. Ascan be seen from equation (2), a layer with a lower kvalue must have a higher i value in order to maintainthe continuity of flow. Then, changing the order of thesoil layer will not only influence the rate of consolida-

tion, but also the distribution of vacuum pressure in thesystem as illustrated in Fig. 2. The final settlement willbe a function of both the relative k values and thecompression indexes of the soil layers (Cc).

LABORATORY TEST PROGRAMME FOR TWO-LAYERSOIL SYSTEM

The equipment used was a Maruto multiple oedometerapparatus (manufactured in Tokyo, Japan) (Chai et al .,2005b). The equipment has five consolidation cells, whichcan be used either as individual consolidation cells orconnected to form a 5-layer system. Each sample is 60 mmin diameter and typically 20 mm in thickness. In this studytwo cells were connected to form a two-layer soil system asillustrated in Fig. 3. For the case of an applied surchargeload, the same amount of load was applied at the tops ofboth layer-1 and layer-2. For the case of a vacuum pressureloading, however, the desired amount of vacuum pressurewas only applied at the top of layer-1. The soil preparationprocedure, initial stress and boundary conditions, and themagnitude of the load applied are the same as that of thetests for a uniform soil layer (Chai et al., 2005b). To make adirect comparison between a surcharge load and a vacuumpressureinduced consolidation for both one-way and two-waydrainages, only cases where 9v0 80 kPa were tested. Asshown in Fig. 1, for 9v0 80 kPa (kr 0.5), no or veryminimal lateral displacement is expected for a vacuumpressure increment of 80 kPa.

Two types of soil were used. One was reconstituted Ariakeclay, and another was reconstituted mixed soil consisting of

50% Ariake clay and 50% sand (passing 2 mm sieve) by dryweight. The grain size distribution curves of the Ariake clayand the sand used are given in Fig. 4. Some of the physicaland mechanical properties of the soils are listed in Table 1.The values of k and Cc were deduced from the standardoedometer test results. The k values listed represent averagevalues in the normally consolidated region. At an averageeffective vertical stress of 100 kPa, the coefficient of con-solidation (Cv) of the mixed soil sample is about 4 times ofthat of the Ariake clay sample. The tests conducted arelisted in Table 2.

TEST RESULTS FOR TWO-LAYER SOIL SYSTEM

One-way drainageThe settlement/time curves under one-way drainage are

compared in Figs 5 and 6 for the surcharge load and thevacuum pressure cases respectively. It can be seen that with9v0 80 kPa, the settlements induced by the vacuum pres-sure are almost the same as those induced by a surchargeload of the same magnitude. Also, the order of the soillayers did not have an influence on the final settlement. Both

10

09

08

07

06

04

Stressratio,

/(

)

kr

vac

vac

v0

05

Assumed valuek0

06 07 08 09 10 11

Settlement ratio, /S Svac l

Fig. 1. Stress ratio kr plotted against ration Svac/Sl (modifiedfrom Chai et al., 2005b)

Flow direction

Drained

Layer-1 ( )k1

Layer-2 ( )k2

Vacuum applied

Drained vac

Layer-2 ( )k2

Layer-1 ( )k1

Drained

Vacuum applied

Drained vac

k k2 1

(a) (b)

Fig. 2. Illustration of vacuum pressure distribution in two-layersoil system: (a) layer-1layer 2; (b) layer 2layer 1

Layer-1 Layer-2

Tubeconnection

Fig. 3. Two-layer system

638 CHAI, MATSUNAGA, SAKAI AND HAYASHI


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figures show, however, that the order of the soil layers didhave an obvious effect on the rate of consolidation. The casewhere the mixed soil sample was located at the drainageboundary (V-2 and S-2 in Table 2) had a faster consolidationrate. For the vacuum consolidation case, the time for 50% ofthe final settlement reached (t

s50) for C+M case was about

37 min and for M+C case was about 28.5 min, and thesetimes will be compared later with those for the two-waydrainage cases.

The measured excess pore pressures at the bottoms oflayer-1 (u1) and layer-2 (u2) are given in Figs 7 and 8 forthe surcharge load and the vacuum pressure cases respec-tively. It can be seen that u1 dissipated much faster in theM+C case (S-2 and V-2) than in the C+M case (S-1 andV-1). For the surcharge load cases, at the interface of layer-1and layer-2, the time for u1 to reduce to 40 kPa (half of theapplied surcharge load) was 9 min for the M+C case (S-2)and 62 min for the C+M case (S-1). For the case of vacuumpressure, the time for u1 to reach 40 kPa was about 5 minand 35 min for the M+C (V-2) and the C+M (V-2) cases,

respectively. Obviously, the vacuum pressure propagatedfaster than the dissipation of the surcharge load inducedexcess pore pressure at the early stages of consolidation.The reason considered is the possibility of very small inward

lateral displacement occurring in the upper soil sample(layer-1) under the vacuum pressure, which could form

micro-gaps between the confining ring and the soil samplecausing an apparent increase in the hydraulic conductivity ofthe sample. In layer-1 and layer-2, the average hydraulicgradients (i) can be estimated as u0 u1j j=h and

100

80

60

40

20

0

Percentfinerbyweight

0001 001 01 1 10 100

Diameter: mm

Ariakeclay

Sand

Fig. 4. Grain size distribution curves

Table 1. Physical properties of the soil samples

Soil particles: % Unit weight,t: kN/m

3Liquid limit,

Wl: %Plasticity

limit, Wp:Void ratio,

e0

Compressionindex, Cc

Hydraulicconductivity, k:

Clay:,5 m

Silt Sand % 109 m/s

Ariake clay 31.0 67.8 1.2 13.9 116.6 57.5 3.63 0.88 1.44Mixed soil 18.1 1.11 0.21 3.13

Table 2. Summary of the tests conducted

No. Sample condition Drainage condition Consolidation pressure Remarks

Soils 9v0: kPa Type Magnitude: kPa

V-1 C+My 80 One-way Vacuum pressure 80 Two-layer V-2 M+C 80V-3 C+M 80 Two-wayV-4 M+C 80S-1 C+M 80 One-way Surcharge load 80S-2 M+C 80

S-3 C+M 80 Two-way

9v0 is initial vertical effective stress.yC+M: the first layer is the Ariake clay and the second layer is the mixed soil; M+C: reverse the order of the soil layers.

00

05

10

15

2001 1 10 100 1000 10000

Elapsed time: min

M C, one-way (S-2)

C M, one-way (S-1)

Two-way (S-3)

Settlement:mm

Fig. 5. Settlement/time curves (two-layer, surcharge load)

00

05

10

15

2001 1 10 100 1000 10 000

Elapsed time: min

C M, one-way (V-1)

C M, t

M C, two-way (V-4)

M C, one-way (V-2)

wo-way (V-3)

Settlement:mm

Fig. 6. Settlement/time curves (two-layer with one-way drainage,vacuum pressure)

COMPARISON OF VACUUM CONSOLIDATION WITH SURCHARGE LOAD INDUCED CONSOLIDATION 639


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u2 u1j j=h (h is the thickness of the layer, and u0 is 0 forthe surcharge load case and 80 kPa for the vacuum pres-sure case). It can also be observed that during the wholeconsolidation process, for the C+M case, the differencebetween u2 and u1 is very small, which implies that therewas a higher hydraulic gradient (i) in the clay sample thanthat in the mixed soil sample. For the M+C case with asurcharge load, when the elapsed time was longer than about60 min, u2 u1j j became larger than u0 u1j j (Fig. 7), thatis, the i values became larger in the clay sample (layer-2)than in the mixed soil sample, and for the vacuum pressurecase when the elapsed time is longer than about 30 min,u2 u1j j became larger than u0 u1j j (Fig. 8), the i values

in the clay sample were larger or almost equal to those inthe mixed soil sample.

Two-way drainageUnder a surcharge load with two-way drainage, the order

of the soil layers should have no influence on both themagnitude of settlement and the rate of consolidation. Onlyone test (S-3 in Table 2) was therefore conducted, whichrepresents both the C+M and the M+C cases. The settle-ment/time curve for this case is also given in Fig. 5. Therate of consolidation is much faster, and the final settlementis almost the same when compared with that of the one-way drainage. Under vacuum pressure with two-way drain-

age, however, the order of the soil layers not only influ-enced the rate of consolidation but also the magnitude ofsettlement. The settlement/time curves are included in Fig.6. The M+C case (V-4) had a faster consolidation rate and

a larger final settlement. The final settlement was 0.80 mmfor the C+M case (V-3) and 0.94 mm for the M+C case (V-4), and the values of ts50 were 43.3 min and 28.5 minrespectively. The values of ts50 are comparable with thecorresponding values of a two-layer soil system under one-way drainage conditions as discussed previously (37.0 minand 28.5 min accordingly), and it supports the statementthat under vacuum pressure, the rates of consolidation for

one-way and two-way drainage should be the same if thecoefficient of consolidation of soil sample is a constantduring the consolidation. The measured u1 variations aregiven in Fig. 9. It can be seen that M+C case had a muchhigher u1j j values than that of C+M case. At the elapsedtime of 48 h (2880 min), the measured u1 values were19.0 for the C+M case (V-3) and 45.6 kPa for the M+Ccase (V-4) (52.0 kPa at time t 60 min and increased to45.6 kPa at t 2880 min). Using equation (2), the ratiosof hydraulic conductivity of the mixed soil sample (km) tothat of the clay sample (kc) (km/kc) are about 3.2 for theC+M case and 1.9 for the M+C case (using u1 of -52.0 kPa). All these numbers are comparable with the ratioof 2.2 obtained using the k values given in Table 1.Theoretically, if k

cand k

mare constants, the k

m/k

cratios

for both cases should be the same. There are two reasonsto explain the difference in km/kc ratios. First, the k valueof a soil relates to its void ratio (e), and a reduction invoid ratio will result in a reduction of k value (e.g. Taylor,1948). Compressions of the clay samples for both the C+Mand the M+C cases are compared in Fig. 10(a). This figureshows that the clay sample had more compression (morevoid ratio reduction) in the C+M case (V-3) than that inthe M+C case (V-4), and therefore a smaller kc value forthe C+M case. Further, the compression of the mixed soilsample in the C+M case was less than that in the M+Ccase (Fig. 10(b)), and therefore a larger km value for theC+M case. Consequently, the C+M case had a larger km/kcvalue. Second, for the M+C case, there was a possibility of

leakage of vacuum pressure for t. 60 min owing to thepossible vacuum pressure induced inward lateral displace-ment of the samples, which tends to reduce the km/kc ratio.The mixed soil sample (M) may have a larger internalfriction angle (9) than the Ariake clay sample (C), whichpossibly implies a smaller at-rest earth pressure coefficient,ko. The condition for inward lateral displacement to occurcan be written as follows (Chai et al., 2005b)

vac .ko9vo

1 ko(3)

Assuming 328 for the mixed soil sample, andko 1 sin9, with 9vo 80 kPa, equation (3) yields a

80

60

40

20

0

Excessporepressure:kPa

101

100

101

102

103

Elapsed time: min

u1 (S-1)

u2 (S-1)

u1 (S-2)

u2 (S-2)

u0

u1

u2

Fig. 7. Measured excess pore pressure variations (surchargeload and one-way drainage)

80

60

40

20

0

Vacuum

pressure:kP

a

101

100

101

102

103

Elapsed time: min

u1 (V-1)

u2 (V-1)

u1 (V-2)

u2 (V-2)

u0

u1

u2

Fig. 8. Measured vacuum pressure (vacuum pressure and one-way drainage)

80

60

40

20

0

Vacuum

pressure:kPa

101

100

101

102

103

Elapsed time: min

V-3 (C M)

V-4 (M C)

Vacuum pressure

between 2-layers ( )u1

Fig. 9. Measure vacuum pressure between two layers (two-layerwith two-way drainage, vacuum pressure)

640 CHAI, MATSUNAGA, SAKAI AND HAYASHI


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no lateral displacement vac value of less than about65 kPa. Therefore for an applied vacuum pressure of 80 kPa,it was highly possible that some kind of inward lateraldisplacement occurred. The direct evidence is the slightreduction of the vacuum pressure at the interface of the soillayers after t. 60 min (Fig. 9).

CONCLUSIONSLaboratory consolidation tests under oedometer conditions

were conducted with both vacuum pressures and surcharge

loads for a two-layer soil system. The effect of the order ofsoil layers on the characteristics of vacuum consolidationhas been investigated. Based on the results of the laboratorytests and theoretical interpretations, the following conclu-sions can be drawn.

(a) One-way drainage. For a two-layer soil system withone-way drainage tested with both surcharge load andvacuum pressure, the order of soil layers only influ-ences the rate of consolidation but not the finalsettlement. When a layer with a relative lower valueof hydraulic conductivity (k) is located at the drainageboundary, the consolidation rate is slower.

(b) Two-way drainage. It is well known that for two-way

drainage with a surcharge load, the order of soil layershas no influence on both the rate of consolidation andthe final settlement. However, for two-way drainagewith a vacuum pressure (vacuum pressure applied atone face only), the order of the soil layers not onlyinfluences the rate but also the magnitude of theconsolidation settlement. This is because for two-waydrainage with a vacuum pressure, the final state is asteady water flow towards the boundary where thevacuum pressure is applied. To satisfy the flowcontinuity condition, the vacuum pressure distributionin the soil layers is not only a function of relativevalues of the hydraulic conductivity, but also a functionof the order of the soil layers.

ACKNOWLEDGEMENTSThis research has been partially founded by the pro-

gramme of Grants-in-Aid for Scientific Research, JapanSociety for Promotion of Science (JSPS) under grant No.18560488. Sincere thanks are extended to Professor J. P.Carter at the University of Newcastle, Australia, for hisvaluable comments/suggestions during the preparation of thistechnical note.

REFERENCESBergado, D. T., Chai, J.-C., Miura, N. & Balasubramaniam, A. S.

(1998). PVD improvement of soft Bangkok clay with combinedvacuum and reduced sand embankment preloading. Geotech.

Engng 29, No. 1, 95121.Chai, J.-C., Hayashi, S. & Carter, P. J. (2005a). Characteristics of

vacuum consolidation. Proc. 16th ICSMGE, Osaka 3, 11671170.

Chai, J.-C, Carter, J. P. & Hayashi, S. (2005b). Ground deformationinduced by vacuum consolidation. J. Geotech. Geoenviron.

Engng, ASCE 31, No. 12, 15521561.Pyrah, I. C. (1996). One-dimensional consolidation of layered soils.

Geotechnique 46, No. 3, 555560.Tang, M. & Shang, J. Q. (2000). Vacuum preloading consolidation

of Yaogiang Airport runway. Geotechique 50, No. 6, 613623.Taylor, D. W. (1948). Fundamentals of soil mechanics. New York:

John Wiley.Tran, T. A., Mitachi, T. & Yamazoe, N. (2004). 2D finite element

analysis of soft ground improvement by vacuum-embankmentpreloading, Proc. 44th Annual Conference of Japanese Geo-technical Society, Hokkaido Branch, 127132.

00

02

04

06

08

10

Compression:mm

01 1 10 100 1000

Elapsed time: min

(a)

Compression of

clay samples

Vacuum pressure

2-layer, 2-way drainage

C M

M C

00

02

04

06

08

10

Compression

:mm

01 1 10 100 1000

Elapsed time: min

(b)

Compression of

mixed samples

Vacuum pressure

2-layer, 2-way drainage

C M

M C

Fig. 10. Comparison of the compressions of soil samples in atwo-layer soil system under vacuum pressure and two-waydrainage condition: (a) compressions of the clay samples;

(b) compressions of the mixed samples.

COMPARISON OF VACUUM CONSOLIDATION WITH SURCHARGE LOAD INDUCED CONSOLIDATION 641

Comparison of vacuum consolidation with surcharge load induced consolidation of a two-layer system

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