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University of Wollongong

Research Online

Faculty of Engineering - Papers Faculty of Engineering

2003

Modelling of prefabricated vertical drains in softclay and evaluation of their effectiveness in practice

B. IndraratnaUniversity of Wollongong  , indra@uow.edu.au

C. BamunawitaCoffey Geosciences, Australia

I. RedanaUniversity of Wollongong 

G. McIntosh Douglaspartners, Australia

Research Online is the open access institutional repository for the

University of Wollongong. For further information contact Manager

Repository Services: morgan@uow.edu.au.

Publication DetailsThis article was originally published as Indraratna, B, Bamunawita, C, Redana, I and McIntosh, G, Modeling of Geosynthetic VerticalDrains in Soft Clays, Journal of Ground Improvement, 7(3), 2003, 127-138.

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Modelling of prefabricated vertical drains in softclay and evaluation of their effectiveness in practiceÃ

B. INDRARATNA,Ã C. BAMUNAWITA,Ã I. W. REDANAy and G. McINTOSH{

ÃCivil Engineering Discipline, University of Wollongong, Australia; yDepartment of CivilEngineering, Udayana University, Bali, Indonesia; {Douglas Partners Pty Ltd, Unanderra, Australia

Prefabricated vertical band drains are rapidly increasing in

popularity as one of the most cost-effective soft clayimprovement techniques worldwide. Nevertheless, pro-blems caused during installation (such as the smear effect),drain clogging and well resistance of long drains contri-bute to retarded pore pressure dissipation, making thesedrains less effective in the field. This leads to reducedsettlement compared with that which would be expectedfrom ideal drains. This paper is an attempt to discuss,comprehensively, the modelling aspects of prefabricatedvertical drains and to interpret the actual field data meas-ured in a number of case studies that demonstrate theiradvantages and drawbacks. Both analytical and numericalmodelling details are elucidated, based on the authors’

experience and other research studies. Where warranted,laboratory data from large-scale experimental facilities arehighlighted.

Les drains verticaux prefabriques deviennent de plus en

plus populaires car ils forment l’une des techniques desplus rentables d’amelioration de l’argile tendre. Nean-moins, les problemes causes pendant l’installation (commel’effet de remanence), l’occlusion des drains et la resistancedes puits dans le cas de drains longs, contribuent aretarder la dissipation de pression interstitielle, ce quirend ces drains moins efficaces sur le terrain. Ceci causeun tassement inferieur a celui qu’on attend normalementde drains parfaits. Cette etude essaie d’evaluer, de maniereglobale, les aspects de modelisation de drains verticauxprefabriques et d’interpreter les donnees reelles releveessur le terrain dans un certain nombre d’etudes de cas quimontrent leurs avantages et leurs inconvenients. Nous

expliquons les details de la modelisation analytique etnumerique en nous basant sur notre experience ainsi quesur d’autres recherches. Partout ou cela est necessaire, nousdonnons aussi les donnees relevees en laboratoire dansune installation experimentale grandeur nature.

Introduction

In South-East Asia during the past decade or two, the rapidincrease in population and associated development activitieshave resulted in the reclamation of coastal zones and theutilisation of other low-lying soft clay land for construction.

Industrial, commercial and residential construction sites areoften challenged by the low-lying marshy land, whichcomprises compressible clays and organic peat of varyingthickness. When such areas of excessive settlement areselected for development work, it is essential to use fill toraise the ground above the flood level. Damage to structurescan be caused by unacceptable differential settlement, whichmay occur because of the heterogeneity of the fill and thecompressibility of the underlying soft soils.

It has been common practice to overcome distress instructures, including road and rail embankments built onfilled land, by supporting them on special piled foundations.However, depending on the depth of the strong bearing

stratum, the cost of piling can become prohibitively high. Amore economically attractive alternative to the use of piledfoundations is improvement of the engineering properties of the underlying soft soils. Preloading with vertical drains is asuccessful ground improvement technique, which involvesthe loading of the ground surface to induce a greater part of 

the ultimate settlement of the underlying soft strata. In otherwords, a surcharge load equal to or greater than theexpected foundation loading is applied to accelerate con-solidation by rapid pore pressure dissipation via verticaldrains. Vertical drains are applicable for moderately tohighly compressible soils, which are usually normallyconsolidated or lightly overconsolidated, and for stabilisinga deep layer of soft clay having a low permeability.

In 1940, prefabricated band-shaped drains (PVDs) andKjellman cardboard wick drains were introduced in groundimprovement. Several other types of PVD have been devel-oped since then, such as Geodrain (Sweden), Alidrain(England), and Mebradrain (Netherlands). PVDs consist of aperforated plastic core functioning as a drain, and a

protective sleeve of fibrous material as a filter around thecore. The typical size of band drains is usually in the orderof 3·5 mm 3 100 mm.

The vertical drains are generally installed using one of two different methods, either dynamic or static. In thedynamic method a steel mandrel is driven into the ground

Ground Improvement (2003) 7, No. 3, 127–137 127

1365-781X # 2003 Thomas Telford Ltd

(GI 1143) Paper received 5 March 2002; accepted 16 December 2002

à This paper was initially presented at the 4th International con-ference on Ground Improvement Techniques 2002, Kuala Lumpur.

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using either a vibrating hammer or a conventional drophammer. In the static method the mandrel is pushed into thesoil by means of a static force. Although the dynamicmethod is quicker, it causes more disturbance of thesurrounding soil during installation. It results in shear strainaccompanied by an increase in total stress and pore waterpressure, in addition to the displacement of the soil

surrounding the vertical drain.

Factors influencing PVD efficiency

2.1 Smear zone

The extent of the smear zone is a function of the size andshape of the mandrel. The installation of PVDs by a mandrelcauses significant remoulding of the su bsoil, especially inthe immediate vicinity of the mandrel. Barron (1948) andHansbo (1981) modelled the smear zone by dividing the soilcylinder dewatered by the central drain into two zones: thedisturbed or smear zone in the immediate vicinity of the

drain, and the undisturbed region outside the smear zone.Onoue et al. (1991) introduced a three-zone hypothesisdefined by:

(a) the plastic smear zone in the immediate vicinity of thedrain, where the soil is significantly remoulded duringthe process of installation of the drain

(b) the plastic zone where the permeability is moderatelyreduced

(c) the undisturbed zone where the soil is unaffected.

The size of the smear zone has been estimated by variousresearchers (Jamiolkowski and Lancellotta, 1981; Hansbo,1987), who proposed that the smear zone diameter is two to

three times the equivalent diameter of the mandrel (that is, acircle with equivalent cross-sectional area). Indraratna andRedana (1998) proposed that the estimated smear zone is threeto four times the cross-sectional area of the mandrel, based onlarge-scale consolidometer testing (Fig. 1). Within the smearzone, the ratio kh/kv can be approximated to unity (Hansbo,1981; Bergado et al., 1991; Indraratna and Redana, 1998).

Well resistance

The well resistance (resistance to flow of water) increaseswith increase in the length of the drain, and reduces theconsolidation rate. The well resistance retards pore pressuredissipation, and the associated settlement. The other mainfactors that increase well resistance are deterioration of thedrain filter (reduction of drain cross-section), silt intrusioninto the filter (reduction of pore space), and folding of thedrain due to lateral movement.

Analytical modelling of verticaldrains

Historical development

If the coefficient of consolidation in the horizontal direc-tion is much higher than that in the vertical direction, thensince vertical drains reduce the drainage path considerablyin the radial direction, the effectiveness of PVDs in accelerat-

ing the rate of consolidation is remarkably improved. Barron(1948) presented the most comprehensive solution to theproblem of radial consolidation by drain wells. He studiedthe two extreme cases of free strain and equal strain, andshowed that the average consolidation obtained in thesecases is nearly the same. Barron also considered the influ-ence of well resistance and smear on the consolidationprocess due to vertical well drains. Richart (1959) presenteda convenient design chart for the effect of smear, in whichthe influence of variable void ratio was also considered. Asimplified analysis for modelling smear and well resistancewas proposed by Hansbo (1979, 1981). Onoue et al. (1988)presented a more rigorous solution based on the free strainhypothesis. The Barron and Richart solutions for ideal drains(no smear, no well resistance) are given in standard soilmechanics text books under radial consolidation, with well-known curves of degree of consolidation (U v and U h) plottedagainst the corresponding time factors (T v and T h) forvarious ratios of drain spacing to drain radius (n).

Approximate equal strain solution

Hansbo (1981) proposed an approximate solution forvertical drains, based on the equal strain hypothesis, bytaking both smear and well resistance into consideration.The rate of flow of internal pore water in the radial directioncan be estimated by applying Darcy’s law (Fig. 2). The total

flow of water from the slice dz to the drain, dQ1, is equal tothe change of flow of water from the surrounding soil, dQ2,which is proportional to the change of volume of the soilmass. The average degree of consolidation, U , of the soilcylinder with a vertical drain is given by

U h ¼ 1 À exp À8T h ì

(1)

 ì ¼ lnn

s

þ

kh

k9h

ln (s) À 0:75þ ð z(2lÀ z)

kh

qw(2)

The effect of smear only (no well resistance) is given by

 ì ¼ln

n

s þ kh

k9h

ln(s)À

0:

75 (3)

The effect of well resistance (no smear) is given by

 ì % ln(n)À 0:75þ ð z(2lÀ z)kh

qw(4)

Settlement

transducer Load

Permeable

T1

T3

T5

T2

T4

T6

Specimen

Smear zone

Vertical drain

Pore water 

pressure

transducer 

ImpermeableD  450

23 cm

24 cm

24 cm

24 cm

k  k ′

d 

R

d s

Fig. 1. Schematic section of the large, radial consolidometer showing thecentral drain, and associated smear, settlement and pore water pressuretransducers (Indraratna and Redana, 1998)

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For ideal drains (that is, both smear and well resistance areignored), the last term in equation (3) also vanishes to give

 ì ¼ ln(n) À 0:75 (5)

Plane-strain consolidation model (Indraratnaand Redana, 1997)

Although each vertical drain is axisymmetric, most finite-element analyses on embankments are conducted on the

  basis of the plane-strain assumption for computationalefficiency. In order to employ a realistic two-dimensionalfinite-element analysis for vertical drains, the equivalence

  between the plane-strain and axisymmetric analyses needsto be established.

Equivalence between axisymmetric and plane-strain con-ditions can be achieved in three ways:

(a) geometric matching—the spacing of drains is matchedwhile the permeability is kept the same

(b) permeability matching—the permeability coefficient ismatched, while the drain spacing is kept the same

(c) a combination of the geometric and permeability andmatching approaches—the plane-strain permeability iscalculated for a convenient drain spacing.

Indraratna and Redana (1997) converted the vertical drainsystem into equivalent parallel drain elements by changingthe coefficient of permeability of the soil, and by assumingthe plane-strain cell to have a width of 2B (Fig. 3). The half-width of the drains, bw, and the half-width of the smearzone, bs, are taken to be the same as their axisymmetricradii, rw and rs respectively, to give

bw ¼ rw and bs ¼ rs (6)

The equivalent drain diameter, dw, or radius, rw, for banddrains were determined by Hansbo (1979) based on peri-

meter equivalence to give

dw ¼ 2(a þ b)

ð or rw ¼

(a þ b)

ð (7)

Considering the shape of  the drain and the effectivedrainage area, Rixner et al. (1986) presented the equivalent

drain diameter, d, as the average of drain thickness andwidth:

d ¼aþ b

2(8)

where a is the width of the PVD and b is its thickness.The average degree of consolidation in plane-strain condi-

tions can now be represented by

U hp ¼ 1Àu

u0¼ 1À exp

À8T hp

 ìp

!(9)

where u0 is the initial pore pressure, u is the pore pressure

at time t (average values), and T hp is the time factor in planestrain. If  khp and k9hp are the undisturbed horizontal andcorresponding smear zone permeabilities respectively, thevalue of  ìp can be given by

 ìp ¼ Æþ ( â)khp

k9hpþ (Ł)(2lz À z2)

" #(10)

In the above equation, the geometric terms Æ and â, and theflow parameter Ł, are given by

Æ ¼2

3À

2bs

B1À

bs

Bþ

b2s

3B2

(11a)

 â ¼

1

B2 (bs À bw)

2

þ

bs

3B3 (3b

2

w À b

2

s ) (11b)

Ł ¼2k2

hp

k9hpqz B1À

bw

B

(11c)

where qz is the equivalent plane-strain discharge capacity.For a given stress level and at each time step, the average

degree of consolidation for axisymmetric (U h) and equiva-lent plane-strain (U hp) conditions are made equal:

U h ¼ U hp (12)

Equations (9) and (12) can now be combined with Hansbo’soriginal theory (equation (1)) to determine the time factorratio, as follows:

T hp

T h¼

khp

kh

R2

B2¼

ìP

 ì(13)

For simplicity, accepting the magnitudes of  R and B to bethe same, the following relationship between khp and k9hp can

 be derived:

Drain

Smear zone

l 

z

dz

R

dQ1

dQ2

k w

k v

k h k ′h

r wr s

d 

d s

D

Fig. 2. Schematic of soil cylinder with vertical drain

l 

Drain

Smear 

zoner w

r s

R

bw

bs

B

l 

D 2B

(a) (b)

Fig. 3. Conversion of an axisymmetric unit cell into plane strain (Indraratnaand Redana, 1997)

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khp ¼

kh Æþ ( â)khp

k9hpþ (Ł)(2lzÀ z2)

" #

lnn

s

þ

kh

k9h

ln s À 0:75þ ð (2lzÀ z2)

kh

qw

" # (14)

If well resistance is ignored (that is, omit all terms contain-

ing l and z), the influence of smear effect can be modelled bythe ratio of the smear zone permeability to the undisturbedpermeability:

k9hp

khp¼

â

khp

khln

n

s

þ

kh

k9h

ln sÀ 0:75

" #À Æ

(15)

For ideal drains, if both smear and well resistance effects areignored, then equation (14) simplifies to the followingexpression, as proposed earlier by Hird et al. (1992):

khp

kh¼

0:67

[ln(n)À 0:75](16)

The well resistance can be derived independently to o btainan equivalent plane-strain discharge capacity of drains (Hirdet al., 1992), as given by

qz ¼2

ð Bqw (17)

The above governing equations can be used in conjunctionwith finite-element analysis to execute numerical predictionsof vertical drain behaviour, for both single-drain and multi-drain conditions. For analysis of embankments with manyPVDs, the above two-dimensional equivalent plane-strainsolution works well for estimating settlement, pore pressuresand lateral deformations.

Basic features of PVD modelling

Equivalent drain diameter for band-shapeddrain

The conventional theory of consolidation assumes verticaldrains that are circular in cross-section. Hence a band-shaped drain should be transformed to an equivalent circle,such that the equivalent circular drain has the same theor-etical radial drainage capacity as the band-shaped drain.Based on the initial analysis of  Kjellman (1948), Hansbo(1981) proposed the appropriate equivalent diameter, dw, fora prefabricated band-shaped drain (equation (7)), followed

  by another study (Rixner et al., 1986) that suggested asimpler value for dw (equation (8)), as discussed earlier.Pradhan et al. (1993) suggested that the equivalent diameterof band-shaped drains should be estimated by consideringthe flow net around the soil cylinder of diameter de (Fig. 4).The mean square distance of the flow net is calculated as

s2 ¼1

4d2

e þ1

12a2 À

2a

ð 2de (18)

On the basis of the above, the equivalent drain diameter isgiven by

dw ¼ de À 2 ffiffiffiffiffiffiffiffi

(s2)p 

þ b (19)

Discharge capacityThe discharge capacity of PVDs affects pore pressure

dissipation, and it is necessary to analyse the well resistancefactor. The discharge capacity, qw, of prefabricated verticaldrains could vary from 100 to 800 m3/year based on filterpermeability, core volume or cross-section area, lateral

confining pressure, and drain stiffness controlling its defor-mation characteristics, among other factors (Holtz et al.,

1991). For long vertical drains that demonstrate high wellresistance, the actual reduction of the discharge capacity can be attributed to:

(a) reduced flow in drain core due to increased lateral earthpressure

(b) folding and crimping of the drain due to excessivesettlement

(c) infiltration of fine silt or clay particles through the filter(siltation).

Further details are given by Holtz et al. (1991).As long as the initial discharge capacity of the PVD

exceeds 100–150 m3/year, some reduction in dischargecapacity due to installation should not seriously influence

the consolidation rates (Holtz et al., 1988). For syntheticdrains affected by folding, compression and high lateralpressure, qw values may be reduced to 25–100 m3/year(Holtz et al., 1991). Based on the authors’ experience, qw

values of 40–60 m3/year are suitable for modelling mostfield drains affected by well resistance, and clogged PVDsare characterised by qw approaching zero (Redana, 1999).

Influence zone of drains

The influence zone, D, is a function of the drain spacing,S, as given by

D ¼ 1:13S (20)

for drains installed in a square pattern, and

D ¼ 1:05S (21)

for drains installed in a triangular pattern. A square patternof drains may be easier to install in the field, but a triangularlayout provides more uniform consolidation between drainsthan a square pattern.

Effect of drain unsaturation

As a result of the installation process, air can be trappedin the annular space between the drain and the soil. Unlessthe soil is highly plastic, with a very high water content(dredged mud, for example), there is a possibility of having

an annular space partially filled with trapped air (an airgap) upon withdrawal of the mandrel. This results in asituation where the inflow of water into the drain becomesretarded. In the numerical analysis, it can be assumed thatthe PVD and the air gap together constitute an unsaturatedvertical interface, having a thickness equal to that of the

d w  2(a  b)/π (Hansbo, 1981)

d w  2(a  b)/2 (Rixner et al ., 1986)

Equivalent diameter:

b

 Assumed water flownet:

(Pradhan et al ., 1993)

d e

a

band drain

Fig. 4. Equivalent diameter of band-shaped vertical drain

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mandrel. Fig. 5 shows the variation of drain saturation withrespect to time (initial degree of saturation of 50% for a 1 mlength), and Fig. 6 shows the effect on consolidation curves,for varying levels of saturation.

Salient aspects of numericalmodelling

Effect of horizontal to vertical permeabilityratio

The permeability characteristics of a number of intactclays have been reported by Tavenas et al. (1983). In thesetests the horizontal permeability was also determined usingsamples rotated horizontally (908) and of intermediateinclination (458). For some marine clays (Champlain seaformation, Canada), the anisotropy ratio (rk ¼ kh /kv) esti-mated using the modified oedometer test was found to vary

 between 0·91 and 1·42. According to the experimental results

plotted in Fig. 7 (Indraratna and Redana, 1995), the value of k9h/k9v in the smear zone varies between 0·9 and 1·3 (averageof 1·15). For the undisturbed soil (outside the smear zone), itis observed that the value of  kh /kv varies between 1·4 and1·9, with an average of 1·63. Shogaki et al. (1995) reportedthat the average values of  kh /kv were in the range 1·36–1·57 for undisturbed isotropic soil samples taken from

Hokkaido to the Chugoku region in Japan. Bergado et al.(1991) conducted a thorough laboratory study on the

development of the smear zone in soft Bangkok clay, andthey reported that the ratio of the horizontal permeabilitycoefficient of the undisturbed zone to that of the smear zonevaried between 1·5 and 2, with an average of 1·75. Moresignificantly, the ratio k9h/k9v was found to be almost unitywithin the smear zone, which is in agreement with resultsobserved by the authors for a number of soft soils in thesmear zone.

Soil model and types of element

The Cam-clay model has received wide acceptance, owing

to its simplicity and accuracy in modelling soft clay behav-iour. Utilising the critical-state concept based on the theoryof plasticity in soil mechanics (Schofield and Wroth, 1968),the modified Cam-clay model was introduced to address theproblems of the original Cam-clay model (Roscoe andBurland, 1968). The obvious difference between the modifiedCam-clay model and the original Cam-clay model is theshape of the yield locus: that of the modified model iselliptical.

The finite-element software codes CRISP, SAGE-CRISP,ABAQUS and FLAC include the modified Cam-clay model,and these programs have been successfully used in the pastfor soft clay embankment modelling. The basic element

types used in consolidation analysis are: the linear straintriangle (LST), consisting of six displacement nodes; three-noded linear strain bar (LSB) elements, with two-porepressure nodes at either end and a sole displacement nodein the middle; and the eight-noded LSQ elements, alsohaving a linear pore pressure variation (Fig. 8). More detailsare given by Britto and Gunn (1987).

0

20

40

60

80

100

   A  v  e  r  a  g  e   d  e  g  r  e  e  o   f  c  o  n  s  o   l   i   d  a   t   i  o  n ,

      U   h  p

100% saturation

90% saturation

80% saturation

75% saturation

Plane strain analysis

0.001 0.01 0.1 1 10

Time factor, T hp

Fig. 6. Variation of degree of consolidation due to drain unsaturation(Indraratna et al., 2001)

GL

Z 

0 2 4 6 8

z  0.975 mz  0.375 mz  0.075 m

z  0.775 mz  0.275 mz  0.025 m

z  0.575 mz  0.175 m

Time: h

100

80

60

40

20

0   D  e  g  r  e  e

  o   f  s  a   t  u  r  a   t   i  o  n  :   %

Fig. 5. Variation of drain saturation with time

Band Flodrain

Smear zone

Mean consolidation pressure:

260 kPa129.5 kPa

64.5 kPa32.5 kPa16.5 kPa

6.5 kPa

0 5 10 15 20

Radial distance, R: cm

2

1.5

1

0.5

0

      k   h

   /      k  v

Fig. 7. Ratio of  kh/kv along the radial distance from the central drain(Indraratna and Redana, 1998)

LST LSB LSQ

Pore pressure DOF Displacement DOF

Fig. 8. Types of element used in finite-element analysis: LST, linear straintriangle; LSB, linear strain bar; LSQ, (linear strain quadrilateral)

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Drain efficiency by pore pressure dissipation

In a comprehensive study, the performance of an embank-ment stabilised with vertical drains in Muar clay (Malaysia)was analysed using the modified Cam-clay model. Theeffectiveness of the prefabricated drains was evaluatedaccording to the rate of excess pore pressure dissipation atthe soil drain interface. Both single- and multi-drain (wholeembankment) analyses were carried out to predict thesettlement and lateral deformation beneath the embankment,employing a plane-strain finite-element approach. As ex-plained in detail by Indraratna et al. (1994), for multi-drainanalysis underneath the embankment the overprediction of settlement is more significant compared with the single-drain analysis. Therefore it was imperative to analyse moreaccurately the dissipation of the excess pore pressures at thedrain boundaries at a given time.

The average undissipated excess pore pressures could beestimated by finite-element back-analysis of the settlementdata at the centreline of the embankment. In Fig. 9, 100%represents zero dissipation when the drains are fully loaded.

At the end of the first stage of consolidation (that is, 2·5 m of fill after 105 days), the undissipated pore pressure hasdecreased from 100% to 16%. For the second stage of loading, the corresponding magnitude decreases from 100%to 18% after a period of 284 days, during which the heightof the embankment has already attained the maximum of 4·74 m. It is clear that perfect drain conditions are ap-proached only after a period of 400 days. An improvedprediction of settlement and lateral deformation could bemade when non-zero excess pore pressures at the draininterface were input into the finite-element model (FEM),simulating partially clogged conditions. The retarded excesspore pressure dissipation also represents the smear effectthat contributes to decreased drain efficiency.

Matching permeability and geometry

Hird et al. (1992, 1995) presented a modelling technique inwhich the concept of permeability and geometry matchingwas applied to several embankments stabilised with verticaldrains in Porto Tolle (Italy), Harlow (UK) and Lok Ma Chau(Hong Kong). The requirement for combination of per-meability and geometry matching is given by the followingequation (parameters defined earlier in Fig. 3):

khp

kh¼

2B2

3R2 lnR

rs

þ

kh

k9hln

rs

rw

À 0:75

" # (22)

The effect of well resistance is independently matched by

qz

qw

¼2B

ð R2

(23)

An acceptable prediction of settlements was obtained (Fig.10), although the pore water pressure dissipation was moredifficult to predict (Fig. 11). At Lok Ma Chau (Hong Kong),the settlements were significantly overpredicted, because theeffect of smear was not considered, although the plane-strainmodel (Hird et al., 1992) allows the smear effect to beincorporated.

At Porto Tolle embankment, prefabricated vertical geo-drains were installed on a 3·8 m triangular grid to a depth of 21·5 m below ground level. The embankment, which wasconstructed over a period of 4 months, had a height of 5·5 m,a crest width of 30 m, a length of over 300 m, and a side

slope of about 1 in 3. The behaviour of soft clay wasmodelled using the modified Cam-clay theory. The results of single-drain analysis at the embankment centreline wereconsidered. Typical results of the finite-element analysis arecompared with observed data in Figs 10 and 11.

Modelling of discharge capacity

Chai et al. (1995) extended the method proposed by Hirdet al. (1992) to include the effect of well resistance and

1st stageloading

2nd stageloading

0 100 200 300 400 500

Time: days

100

80

60

40

20

0

   E  x  c  e  s  s  p  o  r  e  p  r  e  s  s  u  r  e  :   %

Fig. 9. Percentage of undissipated excess pore pressures measured atdrain–soil interfaces due to smear effect and well resistance (Indraratna et 

al., 1994)

Observed

Computed

0 100 200 300 400

Time: days

70

60

50

40

30

20

10

0

   E  x  c  e  s  s  p  o  r  e  p  r  e  s  s  u  r  e  :   k   P  a

Fig. 11. Comparison of excess pore pressure midway between the drainsat mid-depth, for Porto Tolle embankment (Hird et al., 1995)

 Axisymmetric

Plane strain

Observed

0 10 20 30 40

Time: days

0

200

400

600

800

1000

   A  v  e  r  a  g  e  s  e   t   t   l  e  m  e  n   t  :  m  m

Fig. 10. Comparison of average surface settlement for Porto Tolle

embankment (Hird et al., 1995) at embankment centreline

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water pressure increase is well predicted during stage 1 andstage 2 loading. Nevertheless, after stage 3 loading, thepredicted pore pressure values are significantly smaller thanthe field data. The ‘perfect drain’ predictions, as expected,underestimate the measurements. Inclusion of the effects of 

 both smear and well resistance in the FEM analysis gives a  better prediction of pore water pressure dissipation for all

stages of loading.The prediction of settlement along the ground surface

from the centreline of a typical embankment in Muar clay(after 400 days) is shown in Fig. 18. At the embankmentcentreline, the limited available data agree well with thesettlement profile. Also, using the current plane-strain

model, heave could be predicted beyond the toe of theembankment: that is, at about 42 m away from the centre-line. Note that the prediction of heave is usually difficultunless the numerical model is functioning correctly.

Observed and computed lateral deformation for theinclinometer 23 m away from the centreline of the Muar clayembankment are shown in Fig. 19. The lateral displacements

at 44 days after loading are well predicted, because theeffects of smear and well resistance are incorporated. The‘perfect drain’ condition, as expected, gives the least lateraldisplacement. The predicted lateral yield for the condition of ‘no drains’ is also plotted for comparison. It is verified thatthe presence of PVDs is capable of reducing the lateral

Weathered clay

0.07 0.34 2.8 1.2 0.25 16 30

Very soft clay

0.18 0.9 5.9 0.9 0.30 14 6.8

Soft clay

0.10 0.5 4 1.0 0.25 15 3

κ  λ ecs M  υ

γs

(kN/m3)

k v  109

(m/s)

Soft to medium clay

Stiff clay

End of PVD

Effective stress:VerticalHorizontal

Pore water pressure

P ′c

0 20 40 60 80 100 120 140

Stress: kPa

0

2

4

6

8

10

12

14

16

   D  e  p   t   h   b  e   l  o  w  g  r  o  u  n   d   l  e  v  e

   l  :  m

Fig. 14. Subsoil profile, Cam-clay parameters and stress condition used in numerical analysis, Second Bangkok International Airport, Thailand (Asian Instituteof Technology, 1995)

Piezometer 

Drain

Smear zone

0 0.75 1.5 3

k h/k v  1.8

Smear zone

k h/k v  1.0

Drain

4.2 m fill

   1   2  m

PVD; S  1.5 m

0 m 20 25 100 m

Inclinometer 

0 m

2 m

7 m

12 m

Fig. 15. Typical finite-element mesh of the embankment for plane-strain analysis (Indraratna and Redana, 2000)

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movement of soft clay significantly, as long as the spacing of the drains is appropriate and pore pressure dissipation isnot prevented by clogging or excessive smear.

Lateral displacement as a stability factor 

Vertical drains accelerate the settlement, but they decreasethe lateral displacement of soft clay foundations (Fig. 19).The effect of PVDs on lateral displacement is a function of drain spacing and the extent of smear. Indraratna et al.

(2001) have shown that the ratio of lateral deformation tomaximum settlement, Æ, and the ratio of lateral deformationto maximum fill height, â, can be considered as stabilityindicators for soft clays improved by vertical drains. Figs 20and 21 show a comparison between sand compaction piles(SCPs) and PVDs installed in Muar clay, Malaysia. Thevalues of indicators Æ and â for the PVDs are considerablyless than for the SCPs. This is because the SCPs wereinstalled at a much larger spacing of 2·2 m, whereas thePVDs were installed at a spacing of 1·3 m. Although SCPshave a much higher stiffness than PVDs, the spacing of 2·2 m is excessive for effectively curtailing the lateral

displacement. This demonstrates that the stiffness of verticaldrains is of secondary importance in comparison with theneed for appropriate spacing in controlling lateral deforma-tion.

Application of vacuum pressure

Kjellman (1952) proposed vacuum-assisted preloading toaccelerate the rate of consolidation. Since then, the use of vacuum preloading with PVDs has been discussed in anumber of studies (Holtz, 1975; Choa, 1989; Bergado et al.,1998). The application of vacuum pressure can compensatefor the effects of smear and well resistance, which are ofteninevitable in long PVDs.

Field measurements

Perfect drain (no smear)With smear Smear and well resistance

Finite-element analysis:

0 100 200 300 400 500

Time: days

0

50

100

150

200

   S  e   t   t   l  e  m  e  n   t  :  c  m

Fig. 16. Surface settlement at the centreline for embankment TS1, SecondBangkok International Airport (Indraratna and Redana, 2000)

0 100 200 300 400 500

Time: days

40

30

20

10

0

   E  x  c  e  s  s  p  o  r  e  p  r  e  s  s  u  r  e  :   k   P  a

Field measurements

Perfect drain (no smear)With smear Smear and well resistance

Finite-element analysis:

Fig. 17. Variation of excess pore water pressures at 2 m depth below

ground level at the centreline for embankment TS1 (Indraratna and Redana,2000)

Swelling

Measured settlements (400 days):

Predicted FEM (400 days):

No smear 

With smear 

0 20 40 60 80 100 120 140

Distance from centreline: m

20

0

20

40

60

80

100

120

140

160

   S  u  r   f  a  c  e  s  e   t   t   l  e  m  e  n   t  :  c  m

Fig. 18. Surface settlement profiles after 400 days, Muar clay, Malaysia (Indraratna and Redana, 2000)

No drains

(unstabilised foundation)

Field measurement:

44 days

Prediction FEM:Perfect drains (no smear)Smear only

Smear and well resistance

0 50 100 150 200

Lateral displacement: mm

0

5

10

15

20

25

   D  e  p   t   h  :

  m

Fig. 19. Lateral displacement profiles at 23 m away from centreline of Muarclay embankment after 44 days (Indraratna and Redana, 2000)

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Finite-element analysis was applied by Bergado et al.(1998) to analyse the performance of embankments stabilisedwith vertical drains, where combined preloading andvacuum pressure were utilised at the Second BangkokInternational Airport site. A simple approximate method formodelling the effect of PVDs as proposed by Chai andMiura (1997) was incorporated in this study. PVDs increasethe mass permeability in the vertical direction. Conse-

quently, it is possible to establish a value of the permeabilityof the natural subsoil and the radial permeability towardsthe PVDs. This equivalent vertical permeability (K ve) isderived based on the equal average degree of consolidation.

The approximate average degree of vertical consolidation,U v, is given by

U v ¼ 1À exp(À3:54)T v (25)

where T v is the dimensionless time factor.The equivalent vertical permeability, K ve, can be expressed

 by

K ve ¼ 1 þ2:26L2 K h

FD2e K v

!K v (26)

where

F ¼ lnDe

dw

þ

K hK sÀ 1

ln

ds

dw

À

3

4þð 2L2 K h

3qw(27)

In equation (26), De is the equivalent diameter of a unit PVD

influence zone, ds is the equivalent diameter of the disturbedzone, dw is the equivalent diameter of PVD, K h and K s arethe undisturbed and disturbed horizontal permeability of the surrounding soil respectively, L is the length for one-way drainage, and qw is the discharge capacity of PVD. Theeffects of smear and well resistance have been incorporatedin the derivation of the equivalent vertical permeability.

Two full-scale test embankments, TV1 and TV2, each witha base area of 40 m 3 40 m, were analysed by Bergado et al.(1998). The performance of embankment TV2 with vacuumpreloading, compared with the embankment at the same sitewithout vacuum preloading, showed an acceleration in therate of settlement of about 60%, and a reduction in theperiod of preloading by about 4 months.

Conclusion

The two-dimensional plane-strain theory for PVDs in-stalled in soft clay has been discussed, and a multi-drainanalysis has been conducted for several embankmentsstabilised with PVDs. The results show that the inclusion of 

 both smear and well resistance improves the accuracy of thepredicted settlements, pore pressures and lateral deforma-tions. For short drains, normally less than 20 m, theinclusion of well resistance alone does not affect thecomputed results significantly. The ‘perfect drain’ analysisoverpredicts the settlements and underpredicts the porepressures. Predictions of surface settlement are generallyfeasible, but accurate predictions of lateral displacement arenot an easy task by two-dimensional plane-strain analysis.

The prediction of lateral deformation is acceptable when both smear and well resistance are included in the analysis.It is also found that adoption of the appropriate value of discharge capacity of the PVD improves the accuracy of thepredicted lateral displacement. This is because the drainshaving a small discharge capacity tend to increase lateralmovement, as well as retarding the pore water pressuredissipation. The spacing of the drains is another factor thatsignificantly affects the lateral displacement.

The possible air gap between drain and soil caused duringmandrel withdrawal can affect the pore pressure dissipation,and hence the associated soil deformation. Based on pre-liminary studies, it has been verified that an unsaturated

interface can significantly reduce the rate of consolidation.The application of vacuum pressure is an effective way of accelerating the rate of consolidation, especially for longPVDs that are vulnerable to smear and well resistance. Theuse of a traditional earth fill preloading combined withvacuum pressure can shorten the duration of preloading,especially in soft clays with low shear strength. However, themodelling aspects of vacuum pressure and its effect on soilconsolidation via PVDs warrant further study and research.

Finally, it seems that the proper use of the two-dimen-sional plane-strain model in a multi-drain finite-elementanalysis is acceptable, based on computational efficiency in aPC environment. The behaviour of each PVD is axisym-metric (truly three-dimensional), but it is currently impossi-

  ble to model, in three dimensions, a large number of PVDsin a big embankment site without making simplifications. Inthis context, the equivalent plane-strain model with furtherrefinement will continue to offer a sufficiently accuratepredictive tool for design, performance verification and

 back-analysis.

PVD @ 1.3 m

SCP @ 2.2 m

0 0.1 0.2 0.3 0.4 0.5

Lateral deformation/maximum settlement, α

0

5

10

15

20

25

30

   D  e  p   t   h  :  m

Fig. 20. Normalised lateral deformation with respect to maximum settle-ment (Indraratna et al., 2001)

PVD @ 1.3 m

SCP @ 2.2 m

0 0.02 0.04 0.06 0.08 0.1

Lateral deformation/maximum fill height, β1

0

5

10

15

20

25

30

   D  e  p   t   h  :  m

Fig. 21. Normalised lateral deformation with respect to maximum fillheight (Indraratna et al., 2001)

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Acknowledgements

The authors gratefully acknowledge the continuing sup-port of Professor Balasubramaniam, formerly at AIT Bang-kok (currently at NTU, Singapore), in providing much-needed field data for various past and present studies. Theassistance of the Malaysian Highway Authority is also

appreciated. The various efforts of past research studentswho worked under Professor Indraratna in soft clay im-provement are gratefully appreciated.

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 Modelling prefabricated vertical drains in soft clay