recent advances in soft ground improvement - from bumpy
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University of Wollongong University of Wollongong
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Faculty of Engineering and Information Sciences - Papers: Part A
Faculty of Engineering and Information Sciences
1-1-2014
Recent advances in soft ground improvement - from bumpy rides to rapid Recent advances in soft ground improvement - from bumpy rides to rapid
transit transit
B Indraratna University of Wollongong, [email protected]
A S. Balasubramaniam Griffith University
C Rujikiatkamjorn University of Wollongong, [email protected]
R Zhong University of Wollongong, [email protected]
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Recommended Citation Recommended Citation Indraratna, B; Balasubramaniam, A S.; Rujikiatkamjorn, C; and Zhong, R, "Recent advances in soft ground improvement - from bumpy rides to rapid transit" (2014). Faculty of Engineering and Information Sciences - Papers: Part A. 3766. https://ro.uow.edu.au/eispapers/3766
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Recent advances in soft ground improvement - from bumpy rides to rapid transit Recent advances in soft ground improvement - from bumpy rides to rapid transit
Abstract Abstract Much of the world's essential infrastructure is built along congested coastal belts that are composed of highly compressible and weak soils up to significant depths. Soft alluvial and marine clay deposits have very low bearing capacity and excessive settlement characteristics, with obvious design and maintenance implications on tall structures and large commercial buildings, as well as port and transport infrastructure. Stabilising these soft soils before commencing construction is essential for both long term and short term stability. Pre-construction consolidation of soft soils through the application of a surcharge load alone often takes too long, apart from which, the load required to achieve more than 90% consolidation of these mostly low lying, permeable, and very thick clay deposits can be excessively high over a prolonged period. A system of vertical drains combined with vacuum pressure and surcharge preloading has become an attractive ground improvement alternative in terms of both cost and effectiveness. This technique accelerates consolidation by promoting rapid radial flow which decreases the excess pore pressure while increasing the effective stress. Over the past 15 years, the authors have developed numerous experimental, analytical, and numerical approaches that simulate the mechanics of prefabricated vertical drains (PVDs) and vacuum preloading, including two-dimensional and three-dimensional analyses, and more comprehensive design methods. These recent techniques have been applied to various real life projects in Australia and Southeast Asia. Some of the new design concepts include the role of overlapping smear zones due to PVD-mandrel penetration, pore pressure prediction based on the elliptical cavity expansion theory, and the rise and fall of pore pressure via prefabricated vertical drain (PVD) under cyclic loads with a new constitutive model for soft soils under cyclic loads. These recent advances enable greater accuracy in the prediction of excess pore water pressure, and lateral and vertical displacement of the stabilised ground. As a rigid inclusion, the stone column can provide reinforcement to the soft soils apart from shortening the drainage path for the dissipation of excess pore water pressure. Factors such as arching, clogging and smear effects were included in a numerical solution developed recently by the authors and the simulation results showed a good agreement with field test results. This lecture note presents an overview of the theoretical and practical developments and salient findings of soft ground improvement via PVD, vacuum preloading, as well as stone columns, with applications to selected case studies in Australia, Thailand, and China.
Disciplines Disciplines Engineering | Science and Technology Studies
Publication Details Publication Details Indraratna, B., Balasubramaniam, A. S., Rujikiatkamjorn, C. & Zhong, R. (2014). Recent advances in soft ground improvement - from bumpy rides to rapid transit. In P. P. Rahardjo & I. Bin Haji Bakar (Eds.), Southeast Asia conference on Soft Soils Engineering and Ground Improvement: Soft Soils 2014 (pp. A1-1-A1-35). Malaysia: Universitas Katolik Parahyangan, Indonesia and Universiti Tun Hussein Onn, Malaysia.
This conference paper is available at Research Online: https://ro.uow.edu.au/eispapers/3766
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Proceedings of Soft Soils 2014, October 20-23rd 2014
RECENT ADVANCES IN SOFT GROUND IMPROVEMENT - FROM BUMPYRIDES TO RAPID TRANSIT
B. Indraratna 1, A. S. Balasubramaniam 2, C. Rujikiatkamjorn 3 and R. Zhong 4
ABSTRACT: Much of the world’s essential infrastructure is built along congested coastalbelts that are composed of highly compressible and weak soils up to significant depths. Softalluvial and marine clay deposits have very low bearing capacity and excessive settlementcharacteristics, with obvious design and maintenance implications on tall structures andlarge commercial buildings, as well as port and transport infrastructure. Stabilising thesesoft soils before commencing construction is essential for both long term and short termstability. Pre-construction consolidation of soft soils through the application of a surchargeload alone often takes too long, apart from which, the load required to achieve more than
90% consolidation of these mostly low lying, permeable, and very thick clay deposits can be excessively highover a prolonged period. A system of vertical drains combined with vacuum pressure and surcharge preloadinghas become an attractive ground improvement alternative in terms of both cost and effectiveness. This techniqueaccelerates consolidation by promoting rapid radial flow which decreases the excess pore pressure whileincreasing the effective stress.Over the past 15 years, the authors have developed numerous experimental, analytical, and numerical
approaches that simulate the mechanics of prefabricated vertical drains (PVDs) and vacuum preloading,including two-dimensional and three-dimensional analyses, and more comprehensive design methods. Theserecent techniques have been applied to various real life projects in Australia and Southeast Asia. Some of thenew design concepts include the role of overlapping smear zones due to PVD-mandrel penetration, pore pressureprediction based on the elliptical cavity expansion theory, and the rise and fall of pore pressure via prefabricatedvertical drain (PVD) under cyclic loads with a new constitutive model for soft soils under cyclic loads. Theserecent advances enable greater accuracy in the prediction of excess pore water pressure, and lateral and verticaldisplacement of the stabilised ground.As a rigid inclusion, the stone column can provide reinforcement to the soft soils apart from shortening the
drainage path for the dissipation of excess pore water pressure. Factors such as arching, clogging and smeareffects were included in a numerical solution developed recently by the authors and the simulation resultsshowed a good agreement with field test results.This lecture note presents an overview of the theoretical and practical developments and salient findings of softground improvement via PVD, vacuum preloading, as well as stone columns, with applications to selected casestudies in Australia, Thailand, and China.
Keywords: surcharge preloading, vacuum preloading, PVD, cyclic load, constitutive model, stone column
1 Professor of Civil Engineering, Director, Centre for Geomechanics and Railway Engineering, School of Civil, Mining andEnvironmental Engineering, University of Wollongong, Wollongong City, NSW 2522, AUSTRALIA
2 Emeritus Professor, School of Civil Engineering, Griffith University, Gold Coast, QLD 4222, AUSTRALIA3 Associate Professor, Centre for Geomechanics and Railway Engineering, School of Civil, Mining and EnvironmentalEngineering, University of Wollongong, Wollongong City, NSW 2522, AUSTRALIA
4 Research Associate, Centre for Geomechanics and Railway Engineering, University of Wollongong, Wollongong City,NSW 2522, AUSTRALIA
INTRODUCTION
The booming population and associateddevelopment in coastal and metropolitan areas havenecessitated the use of previously undeveloped low
lying areas for construction purposes (Indraratna etal., 1992; Indraratna, 2010). Most of the Australiancoastal belt contains very soft clays up to significantdepths, especially in Northern Queensland and New
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South Wales. The low bearing capacity and highcompressibility of these deposits affects the longterm stability of buildings, roads, rail tracks, andother forms of major infrastructure (Johnson 1970).Therefore, it is imperative to stabilise these soilsbefore commencing construction to preventunacceptable differential settlement. However,attempts to improve deep bearing strata may notcommensurate with the overall cost of theinfrastructure (Bo et al. 2003). In the past, varioustypes of vertical drains such as sand drains, sandcompaction piles, PVDs (geo-synthetic), stonecolumns, and gravel piles have commonly been used.Certain types of granular piles and deep stonecolumns may indeed significantly enhance theintensity of the soil. However, because of theminimum risk of damage to utilities from lateralground movement and a significant reduction in theprice of flexible PVDs over the years, they haveoften been used to more conventional the originalcompacted sand drains, gravel piles stone columnsetc. Their installation can significantly reduce thepreloading period by decreasing the length of thedrainage path, sometimes by a factor of 10 or more.More significantly, PVDs can be installed quickerwith minimum environmental implications andquarrying requirements.Preloading (surcharge embankment) is one of the
most successful techniques for improving the shearstrength of low-lying areas because it loads theground surface to induce a greater part of the ultimatesettlement that it is expected to bear afterconstruction (Richart 1957; Indraratna and Redana2000; Indraratna et al. 2005a). In order to control thedevelopment of excess pore pressure, a surchargeembankment is usually raised as a multi-stageexercise, with rest periods between the loading stages(Jamiolkowski et al. 1983). Since most compressiblelow-lying soils have very low permeability and areoften thick, a lengthy time period is usually needed toachieve the desired primary degree of consolidation(>95%). In these instances, the height of thesurcharge can be excessive from an economicperspective and stability consolidation (Indraratna etal. 1994). One drawback of this surcharge techniqueis that the preload should be applied for a sufficientlylong period, which may at times become impracticaldue to stringent construction schedules and deadlines.When PVDs combined with surcharge preloading isapplied, vertical drains provide a much shorterdrainage path in a radial direction which reduces therequired preload period significantly. PVDs are costeffective and can be readily installed in moderate tohighly compressible soils (up to 40m deep) that are
normally consolidated or lightly over-consolidated.PVDs do not offer particular advantages if installedin heavily over-consolidated clays.Apart from the method of drainage and PVDs
combined with surcharge preloading, vacuumpressure has been used to enhance the efficiency ofPVD when a desired degree of consolidation isrequired over a relatively short time period. Negativepore pressures (suction) distributed along the drainsand on the surface of the ground accelerateconsolidation, reduce lateral displacement, andincrease the effective stress. This allows the height ofthe surcharge embankment to be reduced to preventany instability and lateral movement in the soil.Today, PVDs combined with vacuum preloading arebeing used more and more in practical groundimprovement all over the world.Aside from PVDs, stone columns can be adopted
to improve the soft soils in two aspects. Firstly, theradial drainage paths are created due to the porosityof the stone aggregates, which speed up the time-dependent consolidation. In addition to smear zoneinduced by installation, another factor which couldadversely affect the performance is the cloggingcaused by the soil particles moving into the pores ofstones. Secondly, the arching effect can occur due tothe greater column stiffness compared to thesurrounding soils. To ensure the high accuracy of thepredictions of stone column behaviour, it is ofsignificance to develop a solution which considersthose factors.This lecture includes selected salient aspects of
more than 20 years of active research conducted atthe University of Wollongong in the area of soft soilstabilisation using PVDs, vacuum preloading as wellas stone columns, undoubtedly a vital Australiancontribution to the field of soft soil improvementworldwide, plus offering a significant component ofhigher education training through almost a dozendoctoral studies to date, promoting the advancementof current industry practices in infrastructuredevelopment in coastal and low lying areas.
PRINCIPLES OF VACUUM CONSOLIDATIONVIA PVDS
The vacuum preloading method for vertical drainswas arguably first introduced in Sweden by Kjellman(1942). Since then, it has been used extensively toaccelerate the consolidation of soft groundworldwide, for instance at the PhiladelphiaInternational Airport, USA; Tianjin port, China;North South Expressway, Malaysia; Reclamationworld in Singapore and Hong Kong, China;Suvarnabhumi Second Bangkok International
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Airport, Thailand; Balina Bypass New South Walesand the Port of Brisbane, Queensland in Australia,among many other projects (Holtan 1965; Choa1990; Jacob et al. 1994; Bergado et al. 2002; Chu etal. 2000; Yan and Chu 2003). When a high surchargeload is needed to achieve the desired undrained shearstrength, and this cost becomes substantial due to anexcessively high embankment and a long preloadingperiod in order to achieve 95% or moreconsolidation, the optimum solution is to adapt to acombined vacuum and fill surcharge approach. Invery soft clays where a high surcharge embankmentcannot be constructed without affecting stability(large lateral movement) or having to work within atight construction schedule, the application ofvacuum pressure is quite often the most appropriatechoice.This PVD coupled system is designed to
distribute the vacuum (suction) pressure to deeplayers of the subsoil to increase the consolidation rateof reclaimed land and deep estuarine plains (e.g.Indraratna et al. 2005b; Chu et al. 2000). Themechanism for vacuum preloading can be explainedby the spring analogy (Figure 1) described by Chuand Yan (2005), where the effective stress increasesdirectly due to the suction (negative) pressure, whilethe total stress remains the same. This is in thecontext of conventional case surcharge preloading.
(a) 0
0( )u qp q q u u q u�
� � � � � � � � � � �
�p
pa
u0time
��u
pa
time
��
pa��
Sealed
��u�
q
�p
q
q
�p
(b) 0
0( )u qp q u u u�
� � � � � � �
Figure 1. Spring analogy of vacuum consolidationprocess: (a) under fill surcharge; (b) under vacuum
load (adopted from Chu and Yan 2005)
The general characteristics of vacuum preloadingcompared to conventional preloading are as follows(Qian et al. 1992; Indraratna and Chu 2005):
� The effective stress related to suction pressureincreases isotropically, whereby the correspondinglateral movement is compressive. Consequently, therisk of shear failure can be minimised even at ahigher rate of embankment construction, althoughany ‘inward’ movement towards the embankment toeshould be carefully monitored to avoid excessivelyhigh tensile stresses.
� The vacuum head can propagate to a greaterdepth of subsoil via the PVD system and the suctioncan propagate beyond the tips of the drain and theboundary of the PVD.
� Assuming on air leaks and depending on theefficiency of the vacuum system used in the field, thevolume of surcharge fill can be decreased to achievethe same degree of consolidation.
� Since the height of the surcharge can bereduced, the maximum excess pore pressuregenerated by vacuum preloading is less than theconventional surcharge method (Figure 2).
�With the applied vacuum pressure, theinevitable unsaturated condition at the soil-draininterface may be partially compensated for.
�With field vacuum consolidation, the confiningstress applied to a soil element may consist of twoparts: (a) vacuum pressure and (b) lateral earthpressure (Chai 2005). Chai et al. (2008)demonstrated the possibility of improving clayeydeposits by combining the cap-drain with a vacuumand the surface or subsurface soil as a sealing layer,in lieu of an air tight sheet on the ground surface.However, the efficiency of the method depends onpreventing the surface sand from being affected bythe pressure from pervious layers of sand anddiscontinuities in the ground.It is essential with vacuum assisted preloading
that some horizontal drains be placed in transverseand longitudinal directions after installing the sandblanket, in order to uniformly distribute the surfacesuction. All vertical and lateral drains can then beconnected to the edge of a peripheral Bentonite slurrytrench, which is normally sealed by an imperviousmembrane system (Figure 3a). The trenches can thenbe filled with water or Bentonite slurry to improvethe intact sealing of the membrane around theboundary of the treated zone. The vacuum pumps arethen connected to the prefabricated discharge systemextending from the trenches. The suction headgenerated by the vacuum pump helps dissipate theexcess pore water pressure via the PVDs.
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Time
-150
-75
0
75
150Stress/
Pressure(kPa)
Time
-150
-75
0
75
150
Stress/
Pressure(kPa)
�p (preloadingpressure)
�p (preloadingpressure)
p0 (Vacuumpressure)
Time
-150
-75
0
75
150
Excesspore
pressure(kPa)
Time
-150
-75
0
75
150
Excesspore
pressure(kPa)
Time
-150
-75
0
75
150
Verticaleffective
stress(kPa)
Time
-150
-75
0
75
150
Verticaleffective
stress(kPa)
Maximum excesspore pressure
Maximum excesspore pressure
(a) (b)
Figure 2. Consolidation process:(a) conventional loading(b) idealised vacuum preloading(inspired by Indraratna et al. 2005c)
When a reclaimed area has to be sub-divided intoa number of sections to facilitate installation of themembrane (e.g. Port of Brisbane, as shown in Figure),vacuum preloading can only be effectively carriedout in one section at a time. Vacuum preloading canbecome cumbersome over a very large area becausethe suction head may not be sustained due to thepressure of sand layers, or because it is too close to amarine boundary, in which case a cut off wall willoften be used. An alternative method is to apply thevacuum directly to the individual PVD with flexibletubes without using a membrane. Here, each PVD isconnected directly to the collector drain (Figure 3b).Unlike the membrane system where an air leak canaffect the entire PVD system, in this membrane-lesssystem, each drain acts independently. However,installing an extensive tubing system for a largenumber of PVDs can increase the time and cost ofinstallation (Seah 2006).Apart from the obvious inherent characteristics of
these two vacuum systems, their effectivenessdepends entirely on the properties of the soil, thethickness of the clay, the drain spacing, the type andgeometry of PVDs, and the mechanical design andcapacity of the vacuum pump. The selection and useof these systems are often based on empiricalassessments that are invariably influenced by variousaspects of the tender and/or the experience of thecontractors, rather than detailed numerical studies. Inthis section, the analytical solutions to vertical drainsincorporating the vacuum preloading of both systems(membrane and membrane-less) under time-dependent surcharge loading will be described.
The analytical modelling principles for bothsystems of the applied vacuum are shown in Figure.The smear zone and well resistance are alsoconsidered in both models. The general solutions forexcess pore water pressure, settlement, and degree ofconsolidation were derived through the Laplacetransform technique. In addition, a time dependentsurcharge preloading can be considered in lieu of aninstantaneously applied constant load that can neithersimulate the construction history of the embankmentnor the variation of the applied vacuum pressure. Theresults elicited the need for correctly determining thepermeability of the sand blanket in the membranesystem, and the role of any variation in vacuum in themembrane-less system. The permeability of the sandblanket can significantly affect overall consolidationin the membrane system.
(a)
(b)
(c)
Figure 3. Vacuum-assisted preloading system:(a) membrane system; (b) membrane-less system;
and (c) vacuum at Port of Brisbane(Indraratna et al. 2005c)
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With the Second Bangkok International Airport,various ground improvement schemes via PVDs withvacuum preloading and conventional surchargepreloading were studied by Indraratna and Redana(2000) and Indraratna et al. (2004). Consolidationwith only surcharge preloading would take muchlonger than using vacuum preloading (Figure 5). Thecorresponding settlements, excess pore waterpressure, and lateral displacement, are presented inFigure 5 and Figure 6, respectively. As expected, theuse of a vacuum pressure increased the rate of excesspore pressure dissipation. This is a direct result of anincreased pore pressure gradient towards the drainsdue to negative pressure (suction) along the length ofthe drain. The use of sufficient vacuum pressure withproperly sealed surface membranes accelerates thepreconstruction settlement faster and better than theconventional surcharge preloading method. Moreover,a combination of embankment load with vacuumpressure can reduce the outward lateral displacement(Chai et al. 2005; Indraratna and Redana 2000).
/ 0u z� � �
u p�
(a)
/ 0u z� � �
/ 0u z� � �
(b)
Figure 4. Analysis schemes of unit cell with verticaldrain: (a) membrane system; and(b) membrane-less system
(Geng et al. 2012, with permission from ASCE)
0
40
80
-60
-40
-20
0
120
60
0
0 100 200 300 400-60
-30
0
30
(d)
(c)
(b)
SurchargeLoads(kPa)
(a)
Vacuum Pressure
VacuumPressure(kPa)
Settlement(cm)
Pressure(kPa)
TS1TV1
Embankment TS1(surcharge loading only)Embankment TV1(surcharge loadingwith vacuum pressure)
TS1TV1
ExcessPoreWater
Time (days)
Figure 5. Second Bangkok International Airport(without vacuum pressure):
(a) Construction loading history;(b) Vacuum pressure history;
(c) Surface settlement at the centreline ofembankment;
(d) Variation of excess pore-water pressure at 8mdepth below ground level at the centreline for
embankments (for surcharge only) and at 3m depthbelow ground level, 0.5 m away from the centrelinefor embankments (with surcharge and vacuum
preloading together) (Indraratna et al. 2000, 2004)
0 20 40 60 80 100 120 140 160 180 20020
15
10
5
0
Depth(m)
Lateral displacement (mm)
TS1 365daysTv1 After 150 days
Figure 6. Lateral-displacement profiles 20m from thecentreline of embankments(Indraratna et al. 2000, 2004)
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VACUUM CONSOLIDATION THEORY
Mohamedelhassan and Shang (2002) developed acombined vacuum and surcharge load system andadopted the one-dimensional Terzaghi’sconsolidation theory (Figure 7). The mechanism forthe combined vacuum and surcharge loading (Figure7a) may be determined by the law of superposition(Figure 7b and Figure 7c). The average of degree ofconsolidation for combined vacuum and surchargepreloading can then be expressed by:
2
0
21 exp vcM Tvc
m
UM
�
�
� � (1)
2/vc vcT c t H� (2)
where vcT is a time factor for combined vacuumand surcharge preloading, and vcc is the coefficient ofconsolidation for combined vacuum and surchargepreloading.Indraratna et al. (2004) showed that when a
vacuum is applied in the field through PVDs, thesuction head along the length of the drain maydecrease with depth, thereby reducing its efficiency.Laboratory measurements taken at a few points alongPVDs installed in a large-scale consolidometer at theUniversity of Wollongong clearly indicated that thevacuum propagates immediately, but a gradualreduction in suction may occur along the length ofthe drain. The rate at which the suction develops in aPVD depends mainly on the length and type of PVD(core and filter properties). However, some fieldstudies suggest that the suction may develop rapidlyeven if the PVDs are up to 30 m long (Bo et al. 2003;Indraratna et al. 2005a).
Indraratna et al. (2004, 2005a) proposed amodified radial consolidation theory inspired bylaboratory observations to include differentdistribution patterns of vacuum pressure (Figure 8).These results indicated that the efficiency of the PVDdepended on the magnitude and distribution of thevacuum. In order to quantify the loss of vacuum, atrapezoidal distribution of vacuum pressure along thelength of the PVD was assumed.Based on these assumptions, the average excess
pore pressure ratio )/( 0upRu �� of a soil cylinderfor radial drainage that incorporates vacuumpreloading can be given by:
� � � �2
18exp2
11 1
0
010 kupTk
upR h
ou
��
�
����
��
��
��� �
���
(3)
and
���
��� �
���� �
����
��
��
���� 2)/)(/(
1/1)2(75.0)ln(ln
snkkkk
qk
zlzskk
sn
sh
sh
w
h
s
h ��
(4)where p0 = the vacuum applied at the top of the
drain, k1 = ratio between the vacuum at the top andbottom of the drain, 0u = the initial excess porewater pressure, kh = the horizontal permeabilitycoefficient of soil in the undisturbed zone, ks = thehorizontal permeability coefficient of soil in thesmear zone, Th = the time factor, n = the ratio de/dw(de is the diameter of the equivalent soil cylinder =2re and dw is the diameter of the drain = 2rw), s =ratio ds/dw (ds is the diameter of the smear zone = 2rs),z = depth, l = the equivalent length of drain, qw = thewell discharge capacity.
Figure 7. Schematic diagram of vacuum preloading system: (a) vacuum and surcharge combining load;(b) surcharge preloading; and (c) vacuum preloading (after Mohamedelhassan and Shang 2002)
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Figure 8. The distribution patterns of vacuumpressure in the vertical directions(after Indraratna et al. 2005a)
FACTORS INFLUENCING THEPERFORMANCE OF A VACUUM ORSURCHARGE PRELOADING WITHCONSOLIDATED PVDS
Smear zone
Installing vertical drains with a steel mandrelsignificantly remoulds the subsoil, especially in itsimmediate vicinity. This disturbed annulus in thesmear zone has a reduced lateral permeability andincreased compressibility. In varved clays, the finerand more impervious layers are dragged down andsmeared over the more pervious layers which inturn decrease the permeability of the soil near theperiphery of the drain. Barron (1948) suggested theconcept of reduced permeability by arbitrarilylowering the apparent value of the coefficient ofconsolidation. Hansbo (1979) included a furtherexplicit smear zone with a reduced permeabilitynear the drain, surrounded by an outer undisturbedzone.Based on constant but reduced permeability in
the smear zone, Jamiolkowski et al. (1983)proposed that the diameter of the smear zone (ds)and the cross section of the mandrel can be relatedby:
sd = (2.5 to 3) md (5)
In the above, dm is the diameter of the circlewith an area equal to the cross section of themandrel. Based on the results of Akagi (1979) andHansbo (1987), the smear zone is often evaluatedby the simple expression:
ms dd 2� (6)
Onoue et al. (1991) introduced a three zonehypothesis defined by (a) a plastic smear zone closeto the drain where the soil is highly remouldedduring installation, (b) a plastic zone where thepermeability is reduced moderately, and (c) anouter undisturbed zone where the soil is unaffectedby installation. For practical purposes a two-zoneapproach is generally sufficient.On the basis of their experimental work,
Indraratna and Redana (1998) proposed that theestimated smear zone is at least 3-4 times largerthan the cross section of the drain. This proposedrelationship was verified using a specially designedlarge scale consolidometer (the schematic section isshown in Figure 9). Figure 10 shows the variationof the ratio of horizontal to vertical permeability(kh/kv), and the water content along a radial distancefrom the central drain in the large scaleconsolidation apparatus (Indraratna and Redana1998; Sathananthan and Indraratna 2006a; Walkerand Indraratna 2006). The radius of the smear zoneis about 2.5 times the equivalent radius of themandrel. The lateral permeability (within the smearzone) is 61%~92% of the outer undisturbed zone,which is similar to Hansbo (1987) and Bergado etal. (1991) recommendations. Only recently,Sathananthan et al. (2008) used the cavityexpansion theory (CET), obeying the modifiedCam-clay model, to analyse the extent of the smearzone caused by mandrel driven vertical drains.Their predictions were verified by large scalelaboratory tests where the extent of the smear zonewas quantified based on (a) response of excess porepressure generated while driving the steel mandrel,(b) change in lateral permeability, and (c) obviousreduction in the water central towards the contentdrain.
Figure 9. Schematic section of the test equipmentshowing the central drain and associated smear
(Indraratna and Redana 1998, with permission fromASCE)
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0 1 2 3 4 5r/rm
64
65
66
67
68
69
70
Watercontent(%)
Applied pressure (kPa)2550100200
Drain
Smear zone
1.2
1.4
1.6
1.8
2.0
Permeabilityratio(kh/kv)
Drain
Figure 10. Smear zone determination using: (a)permeability ratio; and (b) water content(Sathananthan and Indraratna 2006a, with
permission from ASCE)
As inspired by field observations, a lowerboundary for drain spacing seems to exist, belowwhich there is no discernible increase in the rate ofconsolidation. Walker and Indraratna (2007)investigated the effect of overlapping smear zonesby incorporating a more realistic linear permeabilitydistribution. As shown in Figure 11, two smearzones will interact when the spacing parameter n isless than the parameter s of the smear zone. Withreference to the undisturbed soil properties, a newlymodified expression µX representing the effect ofinteracting smear zones can be defined. Figure 12shows the time required to reach 90% consolidation(t90) for various interacting smear zoneconfigurations. As Figure 12 suggests, a range ofdrain spacing values exist, across which the timerequired to reach a certain degree of consolidationdoes not change. These results are also inagreement with some observations reported by Saye(2001). This new analytical model for overlappingsmear zones provides the basis for selecting theminimum drain spacing, below which the rate ofconsolidation may decrease. It appears that thisradius of minimum influence is 0.6 times the valueof the radius of the linear smear zone assumed fornon-overlapping smear zones.
Figure 11. Schematic of overlapping smear zones(Walker and Indraratna 2007, with permission from
ASCE)
0.0 0.2 0.4 0.6 0.8 1.00
100
200
300
400
500
600
0.0 0.2 0.4 0.6 0.8 1.00
500
1000
1500
2000
2500
3000
3500
4000
0.0 0.2 0.4 0.6 0.8 1.00
200
400
600
800
1000
1200
1400
1600
c ht 90/r w
2
re/rs
kh/k0 = 5
4
3
21.5
1
c ht 90/r w
2
re/rs
kh/k0 = 5
4
3
2
1.51
c ht 90/r w
2
re/rs
kh/k0 = 543
21.51
Figure 12. Time required for 90% consolidation foroverlapping smear zones with linear variation ofpermeability: (a) 0/ 1v vm m � , / 10s wr r � ; (b)
0/ 1v vm m � , / 20s wr r � ; (c)0/ 0.25v vm m � ,
/ 10s wr r � (Walker and Indraratna 2007, withpermission from ASCE)
Effect of removing and re-applying a vacuum
A large scale consolidometer can be utilised toexamine the effect of vacuum preloading inconjunction with the surcharge load (Indraratna etal. 2004). A large scale consolidation test wasconducted by applying a vacuum pressure close tothe theoretical maximum of 100kPa to the PVD and
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the soil surface through the centre hole in the rigidpiston. A surcharge pressure was then applied intwo stages, 50kPa, and 100kPa. The vacuumpressure was released for a short time in two stagesover a 28 day period, to investigate the effect ofunloading and reloading (Figure 13a).The laboratory results indicated that the suction
head decreased with the depth of the drain becausea maximum suction of 100kPa could not bemaintained along the entire length of the drain. Thesettlement associated with a combined vacuum andsurcharge load is shown in Fig. 13b, which clearlyreflects the effect of removing and re-applying thevacuum by the corresponding gradient settlementplot. The above experimental procedure alsoshowed that it is very difficult to sustain a vacuumpressure greater than 90 kPa (the theoreticalmaximum is 100 kPa).
-100
-80
-60
-40
-20
0
20
0 5 10 15 20 25 30-80
-60
-40
-20
0
vacuumreloadingvacuum
removal
vacuumreloading
vacuumremoval
(b)
Suction(kPa) (a)
stage 2surcharge load) 100kPa
vacuumreloading
vacuumremovalvacuum
reloading
Settlement(m)
Time (Days)
stage 1surcharge load50kPa
vacuumremoval
surcharge load doubled
Figure 13. a) Suction in the drain (240mm frombottom); b) surface settlement surface settlementassociated with simulated vacuum loading and
removal (Indraratna et al. 2004)
Soil disturbance during mandrel installation andremoval
When a mandrel is removed quickly, the soilnear the drain can become unsaturated, i.e. an airgap. Indraratna et al. (2004) attempted to describethe apparent retardation of excess pore pressuredissipation using a series of models in large scalelaboratory tests, whilst considering the effects ofunsaturation at the drain-soil interface. Theconsolidation of soft clay in the large scaleconsolidometer under a combined vacuum andsurcharge preloading was analysed using the FEMprogramme ABAQUS employing the modifiedCam-clay theory (Roscoe and Burland 1968).Figure 14 illustrates the plane strain finite elementmesh using 8-noded linear strain quadrilateralelements (CPE8RP) with 8 displacement nodes and
4 pore pressure nodes. The associate shapefunctions for displacements and pore pressure arequadratic and linear respectively.
0.225m
0.95m
drainboundary
Uns aturated elements
Open
Figure 14. FEM discretisation for plane strainanalysis in large-scale consolidometer (Indraratna
et al. 2004)
The soil moisture characteristic curve (SMCC),including the effect of drain unsaturation could becaptured by a thin layer of elements governed byelastic properties. The permeability coefficientsconverted to the 2D plane strain condition werebased on the technique introduced by Indraratnaand Redana (2000). Three distinct models wereanalysed, as summarised below:Model 1 – fully saturated soil with a linear
vacuum pressure distributed along the drain,(suction could be reduced to zero at the pressurebottom of drain).Model 2 – The soil was fully saturated initially.
When a linearly varying vacuum was applied alayer of unsaturated elements was created at thePVD boundary. For convenience, the thinunsaturated layer was modelled elastically (E =1000 kPa, � = 0.25).Model 3 – Conditions were similar to Model 2,
but included a time-dependent variation in thevacuum pressure (i.e. vacuum removal andreloading) to represent typical field conditionsFigure 15 shows the surface settlement
predicted by the models described above. Thesepredictions confirmed that the assumption of anunsaturated layer of soil at the drain-soil boundarywith a time dependent variation in vacuum pressure(Model 3) was justified. Not surprisingly, the
A1-10
condition of full saturation Model 1 over-predictedthe settlement.The predicted and measured values of excess
pore water pressure (mid layer) are presented in Fig.16. Clearly, the Models 2 and 3 are in acceptableagreement with the laboratory observations. Asexpected, Model 1 (fully saturated) gives the lowestpore pressure suggesting that the unsaturated soil-drain boundary certainly retards the dissipation ofexcess pore water pressure. In view of bothsettlement and excess pore water pressure, Model 3provides the most accurate prediction compared tothe laboratory data. Applying a vacuum headaccelerates consolidation by increasing the lateralhydraulic gradient. Never the less, any soilunsaturation at the PVD boundary caused bymandrel driving would retard the excess porepressure dissipation during the early stages ofconsolidation. To simulate how a mandrel disturbsthe soil near the drain, Ghandeharioon et al. (2010)postulated that installing PVDs with a rectangular(conventional) steel mandrel would cause anelliptical cavity expansion with a concentricprogression in the horizontal plane (Figure 17).The elliptical cavity expansion theory (CET)
was formulated using modified Cam-clayparameters to address the undrained analysis ofPVDs installed in soft clay deposits.Mathematically, this process based on polarcoordinates accounts for the rate of mandrelpenetration and the time factor for predicting theinternal pressure in the cavity, and thecorresponding stresses and excess pore waterpressure in the soil while driving the mandrel. Thetrend of excess pore pressure was verified by thelaboratory results obtained from a fullyinstrumented large scale consolidometer (Figure18).
Figure 15. Predicted and measured settlement at thetop of the consolidometer cell (Indraratna et al.
2004)
Figure 16. Predicted and measured pore-waterpressure at transducer T2 (Indraratna et al. 2004)
a P
0
0 i 00
0
a1b0
b1
�
� �
�
x
r
y
�a P
0
0 i 00
0
a1b0
b1
�
� �
�
x
r
y
�
Figure 17. Expansion of an elliptical cavity in aninfinite soft saturated cohesive soil, shown in polarcoordinates (Ghandeharioon et al. 2010, with
permission from ASCE)
p��0p�fp�
fq
q
M��
fyp�
A
BC
DF
(a)
p��0p�fp�
fq
q
M��
fyp�
A
BC
DF
(a)
q
fq
q A
BC
D F
0
. ..
.maxu�
u�
F
. .BC
D
(b)
q
fq
q A
BC
D F
0
. ..
.maxu�
u�
F
. .BC
D
(b)
Figure 18. An undrained tri-axial compression teston normally consolidated soil (a) effective stresspath; and (b) deviator stress/excess pore pressureversus shear strain (Ghandeharioon et al. 2010, with
permission from ASCE)
A1-11
0.01% - 0.05%
0.10% - 0.17%
0.86% - 1.05%
r
pq
I
� ��mrr /
Cavity FailedZone
SmearZone
MarginallyDisturbedZone
Undisturbed Zone
Plastic
Zone
ElasticZone
0.01% - 0.05%
0.10% - 0.17%
0.86% - 1.05%
r
pq
I
� ��mrr /
Cavity FailedZone
SmearZone
MarginallyDisturbedZone
Undisturbed Zone
Plastic
Zone
ElasticZone
Figure 19. The distribution pattern for the ratio ofthe plastic shear strain to the rigidity index inrelation to the radial distance normalized by theequivalent elliptical radius of the mandrel
characterizing the disturbed soil surrounding a PVD(Ghandeharioon et al. 2010, with permission from
ASCE)
An elliptical smear zone based on the CET wasintroduced while the disturbed soil surrounding themandrel was characterised by plastic shear strainnormalised by the rigidity index. As shown in Fig.19, the analysis of three different cases mentioned
above revealed that this term3
pq fqG
was 0.86%-
1.05% of the boundary of the failed soil. ( pq was
the plastic shear strain,0 2
pf
nq Mp
!� �
�� � � �
, M is the
slope of critical state line in the 'p and q plane;
0p� is the Initial effective mean stress, pn is the
isotropic over-consolidation ratio, ! is the plasticvolumetric strain ratio, G is the shear modulus).The smear zone propagates outward where thenormalised plastic shear strain within the smearzone was from 0.10%-0.17%, and at the boundaryof the marginally disturbed zone, the magnitude of
3
pq fqG
was about 0.01%-0.05% (Figure 19). The
region where pq was greater than zero constituted
the plastic zone, while the outer elastic zone (zeroplastic shear strain) was not affected by any changein the excess pore water pressure before or afterdriving the mandrel. The dimensionless ratio of
plastic shear strain to the rigidity index was usefulfor estimating the extent of the smear zone, because,it facilitated the use of basic soil parameters inpurchase simulation without sophisticated largescale testing. The results also confirmed that theradius of the smear zone was at least 3 times theequivalent radius of the mandrel, a value close tothe extent of smear zones suggested by previousstudies. (Bergado et al. 1991; Indraratna andRedana 1997).The effect of vacuum consolidation on the
lateral yield of soft clays.
(a)
0 10 20 30 401.2
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
Embankment toe
Normalizedverticaldisplacement
Distance from the embankment certreline (m)
00.250.51
preloading ratio(preloading pressure/varcuum pressure)
Centreline of embankment
(b)
Figure 20. (a) Lateral displacements; and(b) surface settlement profiles (Indraratna et al.
2008, with permission from ASCE)
In order to investigate the effect of a combinedvacuum and surcharge load on lateral displacement,a simplified plane strain (2-D) finite elementanalysis could be used (Indraratna et al. 2008). Theoutward lateral compressive strain due to surchargecan be reduced by applying suction (vacuumpreloading). The optimisation of vacuum andsurcharge preloading pressure to obtain a givensettlement must be considered in any numericalmodel to minimise lateral displacement at theembankment toe (Figure 20a), while identifying
A1-12
any tension zones where the vacuum pressure maybe excessive.As expected, the vacuum pressure alone can
create inward lateral movement, whereaspreloading without any vacuum may contribute toan unacceptable outward lateral movement. Theparticular situations for most clays is generally acombination of 40% surcharge preloading stresswith a 60% vacuum, which seems to maintain alateral displacement close to zero. Figure 20bpresents the various profiles of surface settlementwith an increasing surcharge loading. A vacuumalone may generate settlement up to 10m awayfrom PVD treated boundary while the applicationof VP can minimise the value of soil heave beyondthe embankment toe.
Partially penetrating drains
In some situations, the soft clay is too deep forPVDs to fully penetrate, or the verticallypropagated load will not be high enough to justifythe full penetration of PVD into the entire claylayer. Therefore, consolidating the clay withpartially penetrating vertical drains will be adequate.Indraratna et al. (2008) have numerically analysedthe effects of partially penetrating vertical drainsand vacuum pressure on the correspondingsettlement and lateral displacement.Figure 21 illustrates the effect of partially
installed vertical drains (i.e. different l1/H ratios) onthe overall degree of consolidation (Figure 21a) andlateral displacement (Figure 21b). The degree ofconsolidation was calculated on settlement at thecentre line and lateral displacement at theembankment toe. The drain may be reduced inlength by up to 90% of the entire thickness of claywithout significantly affecting the degree ofconsolidation. The lateral displacements are ratherinsensitive to the PVD level, as shown in Figure21b. As shown in Figure 22a, vertical drains areassumed to be installed to a depth l2, while thedrains in between these are installed to the entiredepth of clay (H). It can be seen that l2 can bereduced by up to 0.6H without any significantincrease in the time for 90% primary consolidationto occur. In Figure 22a, the primary PVD can beshortened by up to 80-90% of the thickness of thesoil without seriously affecting the time for a givendegree of consolidation, whereas alternating shorterdrains can be reduced in length by up to 40% of theentire clay thickness.
0.1 1 10 100 1000 10000 100000Time (days)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
DegreeofConsolidation
l1/H=1
l1/H=0.9
l1/H=0.8
l1/H=0.7
l1/H=0.5
No PVD
(a)
0.1 1 10 100 1000 10000 100000Time (days)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
DegreeofConsolidation
l1/H=1
l1/H=0.9
l1/H=0.8
l1/H=0.7
l1/H=0.5
No PVD
(b)
Figure 21. Effects on partially penetrating drains(equal length) on: (a) degrees of consolidation; and(b) lateral displacement (Indraratna et al. 2008, with
permission from ASCE)
l2H
(a)
0.1 1 10 100 1000 10000Time (days)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
DegreeofConsolidation
l2/H=1
No PVD
l2/H varies from 1,0.9,0.8,..,0.5
(b)
Figure 22. (a) Vertical drains with alternatinglength; and (b) effects on the degree ofconsolidation (Indraratna et al. 2008, with
permission from ASCE)
A1-13
Non-Darcian flow
Hansbo (1997) stated that at small hydraulicgradients, conventional (linear) Darcy’s law may bereplaced by a non-Darcian flow condition definedby an exponential relationship. Based on non-Darcian flow, Hansbo (1997) modified the classicalaxi-symmetric solutions. The pore water flowvelocity v, caused by a hydraulic gradient i, mightdeviate from the original Darcy’s law v = k i, whereunder a certain gradient io below which no flowoccurs. Then the rate of flow is given by v = k (i -io), hence the following mathematical relations havebeen proposed:
1nv i for i i"� # (7)
� � 1ov k i i for i i� � $ (8)
where� �1 1
oi nin
��
and � �1 1 nn i k" � �� (9)
In order to study the effects of non-Darcian flow,Hansbo (1979, 1997) proposed an alternativeconsolidation equation. The time required to reach acertain average degree of consolidation includingsmear effect is given by:
� �
12
11 1
1
n
wn
o h
DDtu U %
&
�
�
� �� � � � �� � �� � � �
(10)
where the coefficient of consolidation & = h
w
M"
,
M=1/mv is the oedometer modulus, D is thediameter of the drain influence zone, ds is thediameter of smear zone, n=D/dw in which dw is thedrain diameter, uo is the initial average excess porewater pressure, and % is determined explicitly as ahigh non-linear function of n, D/ds and /h s" "(Hansbo 1997).When n'1 Eq. (10) gives the same result as the
average degree of consolidation represented as2/ ehh dtcT � , provided the well resistance is
neglected.Sathananthan et al. (2006b) developed a new
plane strain lateral consolidation equation whichcan be applied to the exponential and linearcorrelation between the hydraulic gradient and flowvelocity, while neglecting the well resistance ofvertical drains. A comparison was made betweenthe results obtained by a Darcian (linear) flowsolution and the new solution based on a non-Darcian (exponential) flow.The parameters described by Sathananthan and
Indraratna (2006b) under plane strain condition are:
� �
nn
wp
hphp
Bu
Bt
U��
(()
*
++,
- �
����
����
11
10
2211
%
& (11)
where subscript p stands for plane strain,wvhphp m "& � , B is the half width of plane strain
unit cell (m), 0u is the initial average excess porewater pressure (kN/m2) and
� �14 ��
n
np
p.
% (12a)
��
����(
)
*+,
- ��
����
��
���
�
����
��
Bb,nf
Bb,nf
Bb,nf s
ps
pw
p
n
sp
hpp
1
""
. (12b)
� � � � � �� � � �� �� �
� � � � � �� �
� �� �� � � �� �� �� � ...............yn!
n-n-n-n-yn!
n-n-n-
yn!n-n-y
n!n-y
n!n-y
......n!
nnn-n!nn-
n!n-
n!!y,nf p
���
����
()*
+,- �
���
�����
65
54
43
32
2
432
61513121
514121
4131
312
21
613121
5121
41
31
21
(12c)
It is noted that / /hp h hpk k & &� , because, the
coefficient of permeability is proportional to thecoefficient of consolidation for a particular soil ofgiven compressibility. Figure 23 shows thevariation in the equivalent parameters ( p% , p. ,
/ /hp h hpk k & &� and /hp spk k ) with spacing ratio
( / wB b ), smear ratio ( /s wb b ), and permeability
ratio ( /h sk k ) of the axi-symmetric cell for n = 1.5.Figure 24 shows a comparison between Darcianand non-Darcian analysis. The field data agree withthe non-Darcian analysis.The advantage of the above equivalent plane
strain procedure is that it not only matches theaverage degree of radial consolidation (axi-symmetric), but it also yields a more realisticdistribution of excess pore pressure in the lateraldirection compared to the Darcian condition. It wasverified that the conventional solution based onconventional Darcian flow (v = ki) was better whenit was replaced with an exponential equation( 1
1nv ni" �� ). It was also demonstrated that
for 1n' , the current non-Darcian solutionapproached the Darcian solution proposed earlierby Indraratna and Redana (1997), with a deviationof less than 0.01%. This analysis showed that theconsolidation process was clearly influenced by theexponent factor n. The graphical representations ofequivalent plane strain parameters as a function ofthe spacing ratio, smear ratio and the permeabilityratio of the axi-symmetric cell (e.g. Figure 23),would facilitate the practical use of this theory.
A1-14
10 100 1000 10000B/bw (=D/dw)
0
0.1
0.2
0.3
0.4
0.5Equivalentplnaestrain
%p
Perfect drainbs=2bwbs=3bwbs=4bw
"h/"s=2
"h/"s=3
"h/"s=4
2
Figure 23. Equivalent plane strain p% value as a
function of B/bw, bs/bw and h s" " of axi-symmetric unit cell for n = 1.5(Sathananthan et al. 2006b)
0 1 2 3 4Consolidation time (years)
100
75
50
25
0
Degreeofconsolidation(%)
non-Darcian equivalent plane strain (Authors)non-Darcian axisymmetry (Hansbo, 1997)
Darcian axisymmetry (Hansbo, 1981)Field Data
Figure 24. Variation of degree of consolidation atthe embankment centreline with time for the test
Area II at Ska-Edeby, Sweden field test(Sathananthan et al. 2006b)
Performance of PVD subjected to cyclic loading
Low lying areas with high volumes of plasticclays can sustain high excess pore water pressureduring static and repeated cyclic loading. Theeffectiveness of PVDs for dissipating cyclic porewater pressures has been discussed by Indraratna etal. (2009a).A large scale tri-axial test was used to examine
the effects of cyclic load on radial drainage andconsolidation by PVDs (Fig. 25a). This testchamber can accommodate specimens 300 mmdiameter and 600 mm high (Fig. 25b). The excesspore water pressure was monitored via miniaturepore pressure transducers. These instruments weresaturated under distilled water with vacuumpressure, and then fitted through the base of the cellto the desired locations on the samples.
1 (a) (b)
Figure 25. (a) Large-scale tri-axial rig; (b) soilspecimen (Indraratna et al. 2009a, with permission
from ASCE)
The test specimen of reconstituted estuarineclay was lightly compacted to a unit weight ofabout 17 to 17.5 kN/m3. Ideally, testing requires thesimulation of k0 conditions that may typically varyin many coastal regions of Australia from 0.6-0.7.Most soft clays will have natural water contents thatexceed 75% and a Plasticity Index > 35%. It is notuncommon to find that the undrained shearstrengths of the soft estuarine deposits are less than10 kPa. In Northern Queensland, some very softclays that have caused embankment problems havebeen characterised by cu values < 5 kPa.
0 40 80 120Time (mins)
Excessporepressure(kPa)
T4
T1
T3T2
End of cyclic loading
T1T2
T3
T4
5
10
15
Figure 26. Dissipation of excess pore pressure atvarious locations from the PVD (Indraratna et al.
2009a, with permission from ASCE)
The tests could be conducted at frequencies of5-10 Hz, typically simulating train speeds of say60-100 km/h with 25-30 tonnes/axle train loads.Figure 26 shows an example of the excess porepressure recorded. This indicates that the maximum
A1-15
excess pore water pressure closer to the PVD (T2)during cyclic load was significantly less than thatnear the cell boundary (T1), and the dissipation rateof excess pore pressure at T2 is faster than that ofT1.
0 1000 2000 3000 4000N (Cycles)
0
0.2
0.4
0.6
0.8
1
Excessporepressureratio,u*
CKoU, Without PVD
T6, with PVD
T3, with PVD
UU,Without PVD
Figure 27. Excess pore pressure generated with andwithout PVD under cyclic loading (Indraratna et al.
2009a, with permission from ASCE)
0 1000 2000 3000 4000No. of Cycles
12
8
4
0
Verticalstrain,/a(%)
12
8
4
0
Axialstrain,/a(%)
10 100 1000 10000N (Cycles)
With PVD
CKoU,Without PVD
(a)
(b)
CKoU, Without PVD
UU, Without PVD
UU, Without PVD
With PVDFailure
Failure
Figure 28. Axial strains during cyclic loading withand without PVD versus number of loading cycles(N): (a) arithmetic; (b) semi logarithmic scales(Indraratna et al. 2009a, with permission from
ASCE)
Figure 27 shows the excess pore pressures andcorresponding excess pore water pressure ratio Ruversus the number of loading cycles N under thethree separate series of tests. Without PVD, theexcess pore pressure increased rapidly Ru 0 0.9, andundrained failure occurred very quickly. Thecorresponding axial strains are shown in Figure 28a.Without a PVD, large cyclic axial strains developedand failure occurred rapidly after about 200 cyclesin the cyclic CK0U test, and after about 100 cyclesin the cyclic UC (cyclic confined compression) test.
As seen from Fig. 28b, failure was detected whenloga N/ � curves began to concave rapidly
downwards. With a PVD, the axial strain graduallyincreased to a constant level and no failure wasevident even after 3,000 cycles, as shown in Figure28a and Figure 28b.The test results revealed that PVDs effectively
decreased the maximum excess pore pressure, evenunder cyclic loading, and they also decreased thebuild up of excess pore pressure and helped toaccelerate its dissipation during any rest periods. Inreality, dissipating pore water pressure during a restperiod stabilises the track for the next loading stage(i.e. subsequent passage of train). This cyclic-induced excess pore pressure tends to risesubstantially as the shear strain exceeds 1.5-2%.Soft clays provided with radial drainage via PVDcan be subjected to cyclic stress levels higher thanthe critical cyclic stress ratio without causingundrained failure.In practice, railway tracks and airport runways
are constantly subjected to relatively high cyclicloads that build up pore water pressures in theunderlying subsoil unless sufficient drainage isprovided. Laboratory experiments indicate thatcyclic pore pressures build up rapidly at highfrequencies and the rate of pore pressure dissipationis less than its rate of build up under cyclic loading.The Author worked as a consultant in themonitoring of the Sandgate rail track nearNewcastle where relatively short drains wereinstalled to stabilise the track that was constructedon at least 30m of soft estuarine clays in some areasof the track (Indraratna et al. 2010). As the verticalload from 25 tonne axle trains is mainly taken bythe shallow subgrade, relatively short PVD wereadequate to dissipate the cyclic excess pore waterpressure (Figure 29). Moreover, the short PVD alsocontributed to the control of laterals displacementson the shallow soft estuarine clay having effectivelyconsolidated the very soft clay beneath the trackwithin a period of a few months upon the initialpassage of trains. In this case, no external surchargefill was used as preloading and no vacuumapplication was required as only the shallow claylayer immediately beneath the ballast and sub-ballast warranted stabilisation. A FEM model basedon PLAXIS was used to simulate the trackbehaviour, and the Class A prediction of excesspore pressure, settlement and lateral movement wasin very good agreement with the field data (Figure30 and Figure 31). The field measurements wereonly made available to the Author one year after theFEM results had been submitted to the client.
A1-16
104 kPa @ 2.5m width (including impact factor of 1.3)
20m
65m
1m
9m
10m
Crust
Soft Soil 1
Soft Soil 2
Figure 29. Vertical cross section of rail track and foundation(Indraratna et al. 2010, with permission from ASCE)
0 100 200 300Time (days)
0.25
0.2
0.15
0.1
0.05
0
Settlement(m) Field Data
Prediction-Class A
Figure 30. Predicted and measured settlement at thecentre line of rail tracks (Indraratna et al. 2010,
with permission from ASCE)
0 10 20 30 40Lateral displacement (m)
-20
-16
-12
-8
-4
0
Depth(m)
Field DataPrediction-Class A(PVD Spacing @2m)
Crust
Soft Soil 1
Soft Soil 2
Figure 31. Measured and predicted lateraldisplacement profiles near the rail embankment toe
after 180 days (Indraratna et al. 2010, withpermission from ASCE)
Constitutive model of soft soils under cyclic loading
A constitutive model for soft soils under cyclicloading was presented by Ni et al. (2014).Compared to the static behaviour, the cyclic
behaviour of soft subgrade soils is more complex asthe excess pore pressure and strain continue to
develop with increasing number of cycles. Based onthe Modified Cam-clay theory (Roscoe and Burland1968), Carter et al. (1980, 1982) proposed a modelfor the cyclic behaviour of soft soils, in which onlyone additional parameter characterizing the cyclicbehaviour is added. In order to consider thedependence of the generation rate of excess porepressures on the number of cycles, a new cyclicmodel extending that of Carter et al. (1980, 1982)was presented by Ni et al. (2014). In this model,only two additional parameters are included in theparameters of Modified Cam Clay model.It is assumed that during elastic unloading, the
yield surface remains unchanged, but reduces thesize in an isotropic manner (Carter et al. 1980,1982) as follows,
''yc
' 'c y
dd ppp p
� 1� (13)
where, 'cp is a hardening parameter and '
yp is
defined as (Roscoe and Burland 1968):2
' 'y '
1qp pM p
� �� � � � �
(14)
In the above, M is the slope of the critical stateline in 'p - q space and 'p and q are the effectivemean stress and deviator stress, respectively.The parameter � 1 is assumed to be (Ni et al.,
2014):
1 2
1N
�2 2
1 ��
(15)
where, 12 and 22 are experimental constants, and Nis the number of cycles.The stress path for normally and isotropically
consolidated soils under cyclic loading is shown inFigure 32. When the stress path moves from point'A to point A during the first loading period, the
A1-17
soil behaves elastically. During the first unloadingperiod, while the stress path travels from point A toA*, the effective mean stress remains constant. Theyield stress for the second cycle (i.e. yield stressafter unloading) can be calculated through Eqn.(13). During the first part of the second cycle, the
stress path travels from point A* to point 'B and thesoil behaves elastically. Subsequently, the stresspath moves from point 'B to B and the soilbehaves plastically.
q
o'p
M
1
A
DCB
'B'C'D
'c0p
'y,4p'y,3p'y,2p'y,1p
'cu,1p'cu,2p'cu,3p
'cl,4p'cl,3p'cl,2p'cl,1p
'A*A*B*C*D 'A*A*B*C*D
Figure 32. The stress path for cyclic loading. (Ni et al. 2014, with permission from ASCE)
Figure 33. Predictions of excess pore pressures andaxial strains: (a) 0.1f � , (b) 5f � (Ni et al.
2014, with permission from ASCE)
Undrained cyclic triaxial loading tests wereconducted on reconstituted kaolinite specimens.The experimental results in terms of the axial strainand excess pore pressure are given in Figure 33. Itcan be observed that the excess pore pressure showsa sharp increase at the low cycle range andincreases only modestly towards the large numberof cycles. The excess pore pressures reached astable state for the specimens with CSR= 0.4 and0.6, but for the specimen with CSR= 0.8, a criticalvalue of normalized excess pore pressure is reachedafter only a few cycles. It is also observed that thefailure cannot be assessed only on the basis of thenormalized excess pore pressures. In fact, thefailure of the two samples U03 and U12 is indicatedby a sharp rise in axial strains at a critical numberof cycles. In contrast, for samples U01, U02, U10 andU11, the final axial strains are still very small in theend.The simulation results are also plotted together
with the experimental data in Figure 33. It can beobserved that the model proposed accuratelypredicts the experimental behaviour both in termsof excess pore pressures and axial strains.
NUMERICAL ANALYSIS
Two-dimensional plane strain conversion
For multi-drain simulation, plane strain finiteelement analysis can be readily adapted to mostfield situations (Indraratna and Redana 2000;
A1-18
Indraratna et al. 2005a). Nevertheless, realistic fieldpredictions require that the axi-symmetricproperties to be converted to an equivalent 2Dplane strain condition, especially the permeabilitycoefficients and drain geometry. Plane strainanalysis can also accommodate vacuum preloadingin conjunction with vertical drains (e.g. Gabr and
Szabo 1997). Indraratna et al. (2005b) proposed anequivalent plane strain approach to simulatevacuum pressure for a vertical drain system withmodification to the original theory introduced byIndraratna and Redana (1997), as shown in Figure34.
2l
z
r
R B
DrainSmear zone
(a) Axi-symmetric (b) Plane strain
Figure 34. Conversion of an axi-symmetric unit cell into plane strain condition(Indraratna et al. 2005b, with permission from ASCE)
Equivalent plane strain conditions can befulfilled in three ways:(1) Geometric approach where the PVD spacing
varies, but the soil permeability remains constant;(2) Permeability approach where the equivalent
permeability coefficient is determined while thedrain spacing remains unchanged;(3) Combined permeability and geometric
approach where plane strain permeability iscalculated based on a convenient space between thedrains.Indraratna et al. (2005b) proposed an average
degree of consolidation for plane strain byassuming that the plane strain cell (width of 2B),the half width of the drain bw and the half width ofthe smear zone bs may be kept the same as their axi-symmetric radii rw and rs, respectively. This impliesthat w wb r� and s sb r� (Figure 34). To excesspore pressure can be determined form:
� � � �2
18exp
21
1 1
0
010
0
ku
pTku
p
uu p
p
hp
o
p ��
�
����
��
�
����
� ���
�(16a)
and
� �(()
*
++,
-
���
hp
hpp k
k.%� (16b)
where 0u = the initial excess pore pressure, u =the pore pressure at time t (average values) andhpT = the time factor in plane strain, and hpk and hpk �are the equivalent undisturbed horizontal and
corresponding smear zone permeability,respectively. The geometric parameters % and .are given by:
�
����
�����
2
2
31
232
Bb
Bb
Bb sss% (17a)
� � � �223
22 3
31
sws
ws bbBb
bbB
����. (17b)
At a given level of effective stress, and at eachtime step, the average degree of consolidation forthe axi-symmetric ( pU ) and equivalent plane strain( plpU , ) conditions are made equal.
By making the magnitudes of R and B thesame, Indraratna et al. (2005a) presented arelationship between hpk and hpk� . The smeareffect can be captured by the ratio between thesmear zone permeability and the undisturbedpermeability, hence:
� � %
.
�(()
*
++,
-�
�
����
��
� ��
���
��
75.0lnln skk
sn
kkk
k
h
h
h
hphp
hp (18)
Ignoring the effects of smear and well resistancein the above expression would lead to the simplifiedsolution proposed earlier by Hird et al. (1992):
� �3 475.0ln67.0�
�n
k
h
hp
k (19)
A1-19
Indraratna et al. (2005b) compared two differentdistributions of vacuum along a single drain for theequivalent plane strain (2D) and axi-symmetricconditions (3D). Varying the vacuum pressure inPVDs installed in soft clay would be more realisticfor long drains, but a constant vacuum with depth isjustified for relatively short drains.
CASE HISTORIES
Port of Brisbane
The Port of Brisbane is located at the mouth ofthe Brisbane River at Fisherman Islands. Anexpansion of the Port includes a 235ha area to beprogressively reclaimed and developed over thenext 20 years using dredged materials from theBrisbane River and Moreton Bay shipping channels.The site contains compressible clays of over 30 min thickness. At least 7 m of dredged mud capped
with 2 m of sand was used to reclaim the sub-tidalarea. Generally, the complete consolidation of thesoft deep clay deposits may well take in excess of50 years, if surcharging was the only treatment,with associated settlements of probably 2.5-4 mlikely. To reduce the consolidation period, themethod of PVDS and surcharge or PVD combinedwith vacuum pressure (at sites where stability is ofa concern) was chosen to be trialled (Indraratna etal., 2011). Three contractors undertook the trialworks being Austress Menard, Van Oord andCofra/Boskalis. All three trialled prefabricateddrains and surcharge with Austress Menard andCofra/Boskalis also trialling their respectiveproprietary membrane and membrane-less vacuumsystems. Figure 35 shows the final layout of atypical trial area with the PVD design results foreach area.
Table 1. Typical Soil Properties (Indraratna, 2010)
Figure 35. S3A Trial Area – Layout and detail design specifications(Indraratna et al., 2011, with permission from ASCE)
To compare two locations with a differentloading history, the lateral displacement normalisedby the applied effective stress at two inclinometerpositions (MS24 and MS34) are plotted in Fig. 36.It was clear that the lateral displacements werelargest in the upper Holocene shallow clay depths
and were insignificant below 10m. From thislimited inclinometer data, the membrane-lessBeauDrain system (MS34) had controlled thelateral displacement more effectively than thesurcharge only section (MS24). Settlement andexcess pore water pressure predictions and field
Soillayer
Soil type �t(kN/m3)
Cc/(1+e0) Cv(m2/yr) Ch(m2/yr) kh/ks s=ds/dw C/(1+e0)
1 Dredged Mud 14 0.3 1 1 1 1 0.0052 Upper Holocene Sand 19 0.01 5 5 1 1 0.0013 Upper Holocene Clay 16 0.18 1 2 2 3 0.0084 Lower Holocene Clay 16 0.235 0.8 1.9 2 3 0.0076
A1-20
data for a typical settlement plate (TSP3) are shownin Figure 37. The predicated settlement curveagreed with the field data. The excess pore waterpressures were more difficult to predict thansettlement, but they did indicate a slower rate ofdissipation in the Holocene clays in every sectionmonitored, in spite of the PVDs. From theperspective of stability, the incremental rate ofchange of the lateral displacement/settlement ratio(µ) with time can be plotted as shown in Fig. 38.This rate of change of µ can be determined forrelatively small time increments where a small anddecreasing gradient can be considered to be stablewith respect to lateral movement, while acontinuously increasing gradient of µ reflectspotential lateral instability. In Figure 38, thegradient in the non-vacuum area WD3 increasedinitially, which could be attributed to the finalsurcharge loading placed quickly, while the claywas still at early stages of consolidation. However,as the PVDs become fully active and settlementincreased at a healthy rate, the gradient of µdecreased, as expected. In general, Figure 38illustrates that the vacuum pressure provides arelatively unchanging gradient of µ with time.Figure 39 provides approximately linear
relationships between the long term residualsettlement (RS) and the clay thickness of clay foran over-consolidation ratio (OCR) from 1.1 to 1.4,and for a degree of consolidation (DOC) thatexceeding 80%. The reduced settlement (RS) wasdetermined based on the theory secondaryconsolidation employing the secondarycompression index C% (Table 1). More detail onthe computation of RS are given by Mesri andCastro (1987), Bjerrum (1972) and Yin and Clark(1994). As expected, when the OCR increased, theRS decreased substantially. In general, as thethickness of Holocene clay increased, the RS alsoincreased. The corresponding regression lines andbest–fit equations are also shown in Figure 39. Inparticular, the vacuum consolidation locations(VC1-2, VC2-2 and VC2-3) show a considerablyreduced RS at an OCR approaching 1.4, which iswell below the permissible limit of 250mm. At anOCR of approximately 1.3, the residual settlementassociated with membrane-less BeauDrainconsolidation (TA8) and membrane type (VC1-5)were also small.
-30
-25
-20
-15
-10
-5
00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Lateral displacment/total chance in effective stress(mm/kPa)
Depth(m)
MS 24 (with surcharge)
MS 34 (with vaccum)
Section /plate no.
Lateral Displacement/Change in Effective Stress with depth (mm/kPa)
Lateral Displacement/Change inEffective Stress with depth (mm/kPa)
Depth
Figure 36. Comparison of lateral displacements invacuum and non-vacuum areas (Indraratna, 2010)
Settlement
(m) Degreeof
Consolidation
(%)
Excesspore
pressure(kPa)
Figure 37. (a) Settlement; and (b) excess pore waterpressure predictions and field data for a typicalsettlement plate location. (Indraratna, 2010)
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
0 50 100 150 200 250 300 350time, t (days)
Averagerateofchangeof
�(day-1)
VC1/MS28(Menard)
WD3/MS27(Menard)
� � ratio of maximum lateral displacement / Settlement at that depth
Area S3A
Effect ofVacuum
Averagerateofchangeof�(day-1)
Figure 38. Rate of change of lateral displacement/settlement ratio with time. (Indraratna, 2010)
A1-21
RS = 14.3hc + 34R2 = 0.96
RS= 10.8hc - 4R2 = 0.9
RS = 8.1hc - 14R2 = 0.99
RS = 3.8hc - 27R2 = 0.91
0
50
100
150
200
250
300
0 5 10 15 20 25 30
Clay thickness,hc (m)
ResidualSettlement(mm)
OCR = 1.1
OCR = 1.2
OCR = 1.3
OCR = 1.4
VC1-5
VC 2-3VC 2-2
VC 1-2
TA 8
Figure 39. Effect of OCR and clay thickness on residual settlement. (Indraratna, 2010)
Ballina Bypass
The Pacific Highway linking Sydney andBrisbane is constructed to reduce the high trafficcongestion in Ballina. This bypass route has tocross a floodplain consisting of highly compressibleand saturated marine clays up to 40 m thick. Asystem of vacuum assisted surcharge load inconjunction with PVDs was selected to shorten theconsolidation time and stabilise the deeper claylayers. To investigate the effectiveness of thisapproach, a trial embankment was built north ofBallina, 34mm diameter circular PVD at 1.0mspacing were installed in a square pattern. Thevacuum system consisted of PVDs with an air andwater tight membrane, horizontal transmissionpipes, and a heavy duty vacuum pump.Transmission pipes were laid horizontally beneaththe membrane to provide uniform distribution ofsuction. The boundaries of the membrane were
embedded in a peripheral trench filled with soil-bentonite to ensure absolute air tightness. Figure 40presents the instrument locations, including surfacesettlement plates, inclinometers and piezometers.The piezometers were placed 1m, 4.5m, and 8mbelow the ground level, and eight inclinometerswere installed at the edges of each embankment.The embankment area was then divided intoSection A (no vacuum pressure), and Section B,subject to vacuum pressure and surcharge fill. Asthe layers of soft clay fluctuated between 7m to 25m (Table 2), the embankment varied from 4.3m to9.0m high, to limit the post-construction settlement.A vacuum pressure of 70 kPa was applied at thedrain interface and removed after 400 days. Thegeotechnical parameter of the three subsoil layersobtained from standard odometer tests are given inTable 3.
Figure 40. Instrumentation layout for the test embankments at Ballina Bypass (Indraratna et al. 2009b)
A1-22
Table 2. Bottom level of soft clay layer at each settlement plate (Indraratna et al. 2009b)
Settlement plate SP1,SP2 SP3,SP4 SP5,SP6 SP7, SP8 SP9, SP10 SP11, SP12
Bottom level of soft clay layer (m-RL) 2.7-6.7 6.7-9.7 9.7-11.7 11.7-14.7 14.7-17.7 20.7-24.7
Table 3. Soil parameters at SP12 (Indraratna et al. 2009b)
8 12 16Density (kN/m3)
20
10
0
Dry densityWet density
40 80 120Moisture content (%)
In-situLiquid limitPlastic limit
0.32 0.36 0.4Cc/(1+e0)
0.04 0.08 0.12
Cr/(1+e0)
40 60 80
pc'
0 10 20 30 40 50
Undrained shearstrength (kPa)
Soft SiltyClay
MediumSiltyClay
Density(kN/m3)
Moisture content(%) Cc/(1+e0) Cr/(1+e0) pc’
Untrained shearstrength (kN/m3)
Soft Silty Clay
Medium Silty Caly
Figure 41. General soil profile and properties at Ballina Bypass (Indraratna et al. 2009b)
The soil profile with its relevant properties isshown in Figure 41. A soft silty layer of clayapproximately 10m thick was underlain bymoderately stiff and silty layer clay located 10-30mdeep, which was in turn underlain by firm clay. Thegroundwater was almost at the ground surface. Thewater content of the soft and medium silty clayvaried from 80 to 120%, which was generally at orexceeded the liquid limit, ensuring that the soilswere fully saturated. The field vane shear testsindicated that the shear strength was from 5-40 kPa.The compression index (
0/ (1 )cC e� ) determined bystandard oedometer testing was between 0.30-0.50.Settlement and associated pore pressure
recorded by the settlement plates and piezometersare shown in Figure 42, with the embankmentconstruction schedule. The actual suction variedfrom -70 kPa to -80 kPa, and no air leaks wereencountered. Suction was measured by miniaturepiezometers embedded inside the drains. 0 200 400 600 800
Time (days)
-100
0
100
Porepressure(kPa)
P3A (-11.8m)P3B (-8.3m)P3C (-4.8m)P1B (-3.3m)Vacuum Guage
4
2
0
Settlement(m)
SP1SP3SP5SP7SP9SP11
2
4
6
8
EmbankmentH
eight(m)
Vacuum removalVacuum application
Figure 42. Embankment stage construction withassociated settlements and excess pore pressures
(Indraratna et al. 2009b)
Depth (m) Soil Type & "�
(kN/m3) e0kh,ax
(10-10 m/s) OCR
0.0-0.5 Clayey silt 0.57 0.06 14.5 2.9 10 20.5-15.0 Silty Clay 0.57 0.06 14.5 2.9 10 1.715.0-24.0 Stiffer Silty Clay 0.48 0.048 15.0 2.6 3.3 1.1
A1-23
Lateral displacement at the border of theembankments needed to be examined carefully,particularly the vacuum area where the surchargeloading was raised faster than that at the non-vacuum area. The soil properties and lateraldisplacement plots before and after vacuum areshown in Figure 43. Inclinometer I1 was installed atthe border of the vacuum area, whereasinclinometers I2-I4 were located at the edge of thevacuum area. Here the lateral displacementsubjected to vacuum was smaller even though theembankments were higher. In Figure 43b the plot oflateral displacement normalised to embankmentheight showed that the vacuum pressureundoubtedly reduced lateral displacement.
40 60 80 100 120Water Content
(%)
25
20
15
10
5
0
Depth(m)
0.8 1.2 1.6Cc
2 3 4 5e0
After VaccumApplicationBefore VaccumApplication
(a)
0 200 400Lateral displacement (mm)
-20
-10
0
Depth(m)
I1I2I3I4
0 0.04 0.08 0.12
Lateral displacementnormalised by
embankment Height
I1I2I3I4
(a) (b)
(b)
Figure 43. (a) Soil properties before and aftervacuum application; and (b) Measured lateral
displacement and lateral displacement normalisedwith embankment height (Indraratna et al. 2009b)
2D and 3D single drain analyses were used tocompute the settlement at location SP-12. Typical2D finite element mesh is shown in Figure 44a. The
construction history and measured settlement at thesettlement plate SP-12 are shown in Fig. 44b. Herethe clay was assumed to 24m thick, based on theCPT data. The analytical pattern was similar toIndraratna et al. (2005a). The predictions from 2Dand 3D analyses agreed with the measured data,where the rate of settlement increased significantlyafter a vacuum was applied (Figure 44c).
y
z
0
(a)
0 100 200 300 400Time (days)
5
4
3
2
1
0
Settlement(m)
Field3D2D
0
2
4
6
8
10
FillHeight(m)
PVDs installation
Vacuum application(-70 kPa)
(b)
(c)
(b)
Figure 44. (a) 2D Finite element mesh; (b) loadinghistory; and (c) consolidation settlements forsettlement plate SP-12 (Indraratna et al. 2009b)
Second airport Bangkok international airport
The location of the Second BangkokInternational Airport is about 30 km east ofBangkok. The subsoil consists of a relativelyuniform, top weathered crust with thickness ofapproximately 1.5 m. At a depth of 20-24 m belowthe ground surface, a stiff clay layer underlies thesoft clay. Due to the frequent flood recurrenceduring the wet seasons, the soil generally has veryhigh moisture content. The sub-soil profile andpattern of the vertical drain adopted are shown inFigure 45. Table 4 gives the geometric drainparameters whereas the plane strain permeabilitycoefficients for Bangkok clay are shown in Table 5.
A1-24
Weathered clay
Very soft clay
Soft clay10
20
2
6
Depth
Soft to medium clay
Stiff clay
14
CL
Stiff clay
4.2 m20 m 3 m2.5 m
1 m
Prefabricated Vertical Drains(Square pattern)
Sand blanket
Figure 45. Cross section of an embankment with the subsoil profile, Second Bangkok International Airport,Thailand (Indraratna et al. 2000)
Table 4. Geometric parameters of the drains for embankments TS1, TS2 and TS3 at Second BangkokInternational Airport (Indraratna et al. 2000)
Embankment Spacing (m) B (m) bw (m) bs (m)TS1 1.5 0.75 0.03 0.27TS2 1.2 0.60 0.03 0.27TS3 1.0 0.50 0.03 0.27
Table 5. Undisturbed and smear zone hydraulic conductivities for Bangkok clay and Muar clay(Indraratna et al. 2000)
Embankment Depth (m)
kh (m/s) kv (m/s) khp (m/s)(no smear)
�khp (m/s)(with smear)
0-2 5.23 ×10-8 2.99 x10-8 1.47 ×10-8 1.18 ×10-9
TS1 2-7 1.2 ×10-8 6.83 ×10-9 3.36 ×10-9 2.7 ×10-10
(S=1.5 m) 7-12 5.25 ×10-9 3.0 ×10-9 1.48 ×10-9 1.19 ×10-10
0-2 5.23 ×10-8 2.99 ×10-8 1.62 ×10-8 2.04 ×10-9
TS2 2-7 1.2 ×10-8 6.83 ×10-9 3.63 ×10-9 4.67 ×10-10
(S=1.2 m) 7-12 5.25 ×10-9 3.0 ×10-9 1.63 ×10-9 2.05 ×10-10
0-2 5.23 ×10-8 2.99 ×10-8 1.78 ×10-8 2.91 ×10-9
TS3 2-7 1.2 ×10-8 6.83 ×10-9 4.05 ×10-9 6.65 ×10-10
(S=1 m) 7-12 5.25 ×10-9 3.0 ×10-9 1.78 ×10-9 2.92 ×10-10
A1-25
100 m
12m
4.2 m Fill
12 m
7 m
2 m0 m
0 1.5 3
Drain
Smear zone
Smear zone
Piezometer
0.75
0 m 20 25
Drain
PVD; S=1.5 m
k kh v/ .� 10
k kh v/ .�18
k kh v/ .� 10
Inclinometer
Figure 46. Finite element mesh of embankment for plane strain analysis at Second Bangkok International Airport(Indraratna et al. 2000)
The surcharge load of the embankment wasapplied in stages, whereby Stage 1 was equivalentto 18 kPa including a sand blanket and clay sand1.0 m high. The construction of Stage 2 (45 kPa),Stage 3 (54 kPa) and Stage 4 (75 kPa) followed andit resulted in an equivalent total fill height of 4.2 m.In order to maintain the stability requirements, aberm of 5 m width and 1.5 m height was addedafter the surcharge was increased from 45 to 54 kPa.The berm was further extended to 7 m wide whenthe surcharge load exceeded 54 kPa. The settlementand excess pore water pressure development in thesub-soil were measured for over 1 year, and thebehaviour of embankment was monitored bysettlement plates, slope inclinometers, andpiezometers such as closed hydraulic piezometersand open standpipes.The finite element mesh used in the
embankment is shown in Figure 46. The clayfoundation was discretised into linear strainquadrilateral (LSQ) elements. A finer mesh wasused for the PVD zone where each drain elementrepresents a PVD containing the smear zone oneither side of it (see insert, Figure 46). Theproperties of the soil inside and outside the smearzone were assumed to be similar to those used inthe single drain analysis. The instrumentation wasplaced in the mesh in such a way that so themeasuring points coincided with the mesh nodes.The piezometers were placed 0.75 m from thecentreline of the embankment between 2 drains, tomeasure the excess pore water pressure.
Ground settlement for the three embankments isshown in Figure 47, and the predictions were modefrom the centreline of each embankment up to 100m away. As shown, the predicted and measuredsettlement was very similar. Heave or swelling waspredicted to take place past the toe of theembankment, i.e. about 27 m away from thecentreline. Surface settlement was measured oneither side of the centreline and proved to beacceptable with the calculated settlement profiles.In Figure 48 the lateral deformation measured
by an inclinometer 7.5 m away from the centrelineof embankments TS1, TS2 and TS3 were plottedrespectively. The finite element predictions (smearand well resistance) were also plotted forcomparison purposes. Given the limitations of the2-D plane strain model, the predictions areacceptable. Undoubtedly, the inclusion of bothsmear and well resistance in the plane strain, FEMmodel helped to predict the lateral yield of the softclay foundation. In comparison with a no drainsituation, vertical drains definitely reduce lateraldisplacement, thereby directly contribution to thestability of the embankment.
Tianjin Port
Tianjin port is approximately 100km fromBeijing, China. The top 15m of soil at this site wassoft to very soft and needed to be improved using apreloading surcharge of more than 140kPa(Rujikiatkamjorn et al. 2008). To avoid any
A1-26
stability problems (high lateral yield) associatedwith a high surcharge embankment, a fill height of50 kPa plus a vacuum pressure of 80kPa wereapplied on top of the 20m thick soft soil layer inconstruction with PVDs installed at 1.2 m spacing.The conversion method proposed by Indraratna etal (2005b) was used for the 2D plane strain FEManalysis (Fig. 49), and the finite element program(ABAQUS) was used to simulate the 3D multi-drain analysis (Figure 50), employing the Biotcoupled consolidation theory.
-30 -20 -10 0 10 20 30
020406080100120140160180200
Distance from centerline of embankment
Settlement(cm)
a) TS1
90 days210 days365 days
Measurements Predictions
1.5 m Total fill height 4.2 m
-30 -20 -10 0 10 20 30
020406080100120140160180200
Distance from centerline of embankment
Settlement(cm)
b) TS2
90 days230 days410 days
Measurements Predictions
1.5 m Total fill height 4.2 m
-30 -20 -10 0 10 20 30
020406080100120140160180200
Distance from centerline of embankment
Settlement(cm)
c) TS3
90 days230 days410 days
Measurements Predictions
1.5 m Total fill height 4.2 m
Figure 47. Surface settlement profile forembankments: a) TS1; b) TS2; and c) TS3,Second Bangkok International Airport
(Indraratna et al. 2000)
0 50 100 150 200 250 300
0
5
10
15
20
Lateral displacement, mm
Depth,m
365 days
210 days
365 days210 days
Field Measurement:
Prediction FEM:
365 days210 days
TS1No drains (365 days)
0 50 100 150 200 250 300
0
5
10
15
20
Lateral displacement, mm
Depth,m
365 days
210 days
365 days210 days
Field Measurement:
Prediction FEM:
365 days210 days
TS2No drains (365 days)
0 50 100 150 200 250 300
0
5
10
15
20
Lateral displacement, mm
Depth,m
365 days
210 days
365 days210 days
Field Measurement:
Prediction FEM:
365 days210 days
TS3No drains (365 days)
Figure 48. : Lateral displacement profiles at 7.5 maway from centreline of embankments TS1, TS2and TS3, Second Bangkok International Airport
(Indraratna et al. 2000)
A1-27
X
Integration point
Displacement node
X X
X
14m 20m
y
z
0
x
z
20m
0
25m 20m
(a)
(b)Figure 49. 2D finite-element mesh: (a) x=0 plane; (b) y=0 plane(Rujikiatkamjorn et al. 2008, with permission from ASCE)
x
z
y
14m25m
20m
20m
20m
20m
0
x=0 plane
y=0 plane
(a)
25m 20m
14m
20m
x
y
Soil region improvedby PVDs
0
(b)
Figure 50. 3D finite-element mesh: (a) Isometric view; (b) top view(Rujikiatkamjorn et al. 2008, with permission from ASCE)
A1-28
In terms of settlement, excess pore pressure, andlateral displacement, the numerical results from theequivalent 2D and true 3D analyses were quitesimilar (Figure 51 and Figure 52). This proves that,the equivalent plane strain (i.e. 2D) analysis wassufficient from a computational point of view,especially for multi-drain analysis of large projectswhere a 3D model would be more time consuming.From a practical point of view, the height ofsurcharge fill can be reduced by applying a vacuumpreloading to achieve the same rate and degree ofconsolidation. Applying a surcharge pressure afterthe initial vacuum preloading could also reduceexcessive inward lateral movement near the toe ofthe embankment (Rujikiatkamjorn et al. 2008;Rujikiatkamjorn et al. 2007).
020406080100120140160180
-80
-60
-40
-20
0
0 20 40 60 80 100 120 140 160 180-80
-60
-40
-20
0
vacuum pressure under membrane
PeriodandPressure(kPa)
vacuum plus preloading
(a)
(d)
(c)
(b)
Time (days)
0.8
0.4
1.2
1.6
Settlement(m)
Field data (surface depth)2D FEM3D FEM
reduction(kPa)
Porepressure
Porepressure
reduction(kPa)
Application of surcharge load
Field data2D FEM3D FEM
Figure 51. (a) Loading history; (b) consolidationsettlements; (c) pore pressure variation at 0.25maway from embankment centreline (Section II):5.5m depth; (d) pore pressure variation at 0.25maway from embankment centreline (Section II):
11.0m depth (arrows indicate items when surchargeloads were applied) (Rujikiatkamjorn et al. 2008,
with permission from ASCE)
20
18
16
14
12
10
8
6
4
2
0-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2
outward
Depth(m)
Field2D FEM3D FEM
Lateral displacement (m)
inward
Figure 52. Lateral displacements at embankmenttoe (Section II at 180th day) (Rujikiatkamjorn et al.
2008, with permission from ASCE)
DESIGN CHARTS OF PVDS WITH VACUUMPRELODAING
Design steps
Rujikiatkamjorn and Indraratna (2008) proposeddesign charts eliminating cumbersome iterationprocedures using the equivalent drain diameter asan independent variable to obtain the relevant drainspacing. The design steps are summarised below:1. Use the available soil profiles, in-situ test
measurements and laboratory data to obtain therelevant soil properties, hence, determine theappropriate installation depth (l), and the desiredconsolidation time (t);
2. Assume the required degree of consolidationUt for surcharge fill alone;
3. For vacuum pressure application, specify themean suction, 0p , required total design stress �� ,
and the surcharge fill pressure, p� and thendetermine the required degree of consolidation from
� �� � tvact UppU */ 0, ���� �
4. Use cv, t and l, to determine u* using Figure53 or from,
� � �
����
� ��
��� �
��
�
�v
mTm
mu 2
2
122 2
12exp128* �
�(20)
5. Determine the available size of the PVD(circular or wick shape) and then compute theequivalent drain diameter (for wick drains), dw fromdw =2(a+b)/�;
6. Find hT � from:2
h h wT c t d� � (21)
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7. Calculate 81ln*
h
t
TUu
�
� ��� �
� � �
for surcharge fill
only (no vacuum), (22)
or ,18 / ln
*t vac
h
UT
u
�� ��� � � � �
for vacuum pressure
plus surcharge fill (23)
8. Establish the diameter and permeability of thesmear zone;
9. Determine 2 using Fig. 54 or from theequation:
� �1 lnh
s
k sk
2� �
� �� � �
(24)
10. Calculate n from exp( ln )n % .� � ;(25)
where, 5.05.1403714.010505.93938.0 22% �5��
�
(26a)
an 3 2 0.50.4203 1.456 10 0.5233. 2 2�� � 5 � ; (26b)
11. Calculate the influence zone (de = ndw);
12. Choose the drain pattern and determine thespacing of drain (d) from either d =de/1.05(triangular grid) or d =de/1.128 (square grid).
0.001 0.01 0.1 1 10Time factor (Tv=cvt/l2)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
u*
Figure 53. Relationship between Tv and u*(Rujikiatkamjorn and Indraratna, 2007)
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
s=d s/dw
Figure 54. Contours of 2 based on Eq. (22)(Rujikiatkamjorn and Indraratna, 2007)
Worked-out Example
The required soil parameters for the project areassumed to be: Ut = 90%, l = 24m, dw = 34 mm(circular drain: Mebra-MCD34), ch = 2.5 m2/year,cv = 1.0m2/year, kh/ks = 5, s = 3, Maximum DesignSurcharge, �� = 120 kPa, surcharge fillpressure, p� = 60 kPa, vacuum pressure, 0p = -
60kPa (suction). Well resistance is neglected.Calculate the drain spacing (d), for (a) t = 1.0 year;(b) t = 9 months; and (c) how the drain spacing canbe altered with an increased vacuum pressure up to90 kPa over 9 months.
Solution:Part (a) t = 1.0 year1. 002.02410.1 2 �5�vT ;
� �� � 9.09.0*6060/120, ���vactU2. Calculate *u using Equation (20) or from
Figure 53, hence, u*= 0.95
3. 2163034.0/0.15.2 22 �5��� whh dtcT
4. 7686
95.09.01ln
21638
*1
ln
8,
� ��
��� �5
��
�
����
� ��
��
uUT
vact
h
5. From Figure 54 or using Equation (24),39.4�2
6. Using Equations (26a and 26b), determine0.463% � and 0.649. � � .7. From Equation (25),
33)649.07686ln463.0exp()lnexp( ��5��� . %n8. Calculate de from, de = n dw = 33×0.034 =1.122m9. Drain spacing = 1.1 m for triangular
(1.122/1.05) or 1.0 m for square grid (1.122/1.128),respectively.
The above calculations confirm that the designspacing of 1m×1m used at Ballina Bypass can bejustified for similar soil properties.
Part (b) t = 0.75 years (9 months)1. 001.02475.00.1 2 �5�vT ;
� �� � 9.09.0*6060/120, ���vactU
2. Calculate *u using Equation (20) or fromFig. 53; hence, u*= 0.963. 1622034.0/75.05.2 22 �5��� whh dtcT4.
5737
96.09.01ln
16228
*1
ln
8,
� ��
��� �5
��
�
����
� ��
��
uUT
vact
h
5. Using Figure 54 or from Equation (28),39.4�2
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6. From Equations (26a and 26b), find0.463% � and 0.649. � � .7. From Equation (25),
29)649.05737ln463.0exp()lnexp( ��5��� . %n
8. Calculate de from de = n dw = 29×0.034 =0.986 m9. Drain spacing = 0.95m for triangular grid (i.e.
0.986/1.05) or 0.90m for square grid (i.e.0.986/1.128).
Part (c): Vacuum pressure increased up to 90kPa over 9 months. Revised Drain Spacing?1. 001.02475.01 2 �5�vT ;
� �� � 72.09.0*6090/120, ���vactU2. C Calculate *u using Equation (20) or Fig.
53, Hence, u*= 0.963. 1622034.0/75.05.2 22 �5��� whh dtcT4. 10531
96.072.01ln
16228
*1
ln
8,
� ��
��� �5
��
�
����
� ��
��
uUT
vact
h
5. Use Fig. 542 or Equation (28), 39.4�26. Using Equations (26a and 26b), find0.463% � and 0.649. � � .7. From Equation (25),
38)649.010531ln463.0exp()lnexp( ��5��� . %n8. Calculate de from de= n dw = 38×0.034 =1.29
m9. Drain spacing = 1.23m for triangular pattern
(i.e. 1.29/1.05) or 1.14m for square grid(i.e.1.29/1.128)
This demonstrates that increased vacuumpressure allows the drain spacing to be increased.This should also reduce the risk smear overlappingand reduced drain costs.
NUMERICAL SOLUTION OF STONECOLUMNS WITH CONSIDERATION OFARCHING, CLOGGING AND SMEAR EFFECTS
Indraratna et al. (2013) presented a numericalmodel based on finite difference technique toanalyse the response of stone column reinforcedsoft soil considering arching, clogging effects aswell as smear effects, adopting free strainhypothesis. In contrast with the conventionalvertical drains, the stone columns have areinforcement effect as well as allow radialdrainage at a much faster rate that enables the quickdissipation of excess pore water pressure caused bysurcharge loading.
Figure 55. (a) Typical stone column reinforced soft clay deposit supporting an embankment; (b) unit cellidealization; (c) cross section of the unit cell (Indraratna et al. 2013, with permission from ASCE)
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Upon installation, alike the vertical drains, thestone columns develop a smear zone in the interfacebetween the soil and the stones. In addition, aclogged zone can be formed by the movement ofsoil particles into the voids of the stone column.This is better illustrated in Figure 55 and the fourdistinct zones of the cross section are given inFigure 55 (c).Vertical stress distribution w(r) on the soil is
governed by (Low et al., 1994):
w(r) = w(re) + (N-r/rc)2F(N, ns) (27)
where N=re/rc, and ns is the stress concentrationfactor.The dissipation of the excess pore pressure is
governed by (Indraratna et al., 2013):2
2
1v h
w
k u ut r r r/
� �� � �
� � �� � � �� �(28)
where v/ is the volumetric strain in the elementand u is the excess pore water pressure.The clogging effect can have an adverse impact
on the performance of stone columns. The effectiveradius of the clogging zone can be written as(Indraratna et al., 2013):
c cr r%� � (29)
and the coefficient of horizontal permeability in itcan be expressed as (Indraratna et al., 2013):
cl k sk k%� (30)
An example case is calculated with theparameters as N=2, kh/ks=10, rs/rc=1.1, H/rc=20,ns=3, and 1k% %� � , and the results are comparedagainst the existing models of Han and Ye (2000,2002) and Wang (2009). The average degree ofconsolidation variation with the time factor isshown in Figure 57. It is observed that proposedmodel agree well with the existing models. Oh et al.(2007) have carried out some field tests in the softestuarine clay site in Queensland, Australia. Figure58 shows the ground settlement data together withthe predictions of the model of Indraratna et al.(2013). A reasonable agreement was reached,although the computed settlements were slightlyover-predicted.
Figure 56. Comparison of computed rates ofconsolidation using different methods (Indraratna et
al. 2013, with permission from ASCE)
Figure 57. Comparison of computed settlementwith field test results (Indraratna et al. 2013, with
permission from ASCE)
CONCLUSION
It is clear that the application of PVDscombined with vacuum and surcharge preloadinghas become common practice, and is nowconsidered to be one of the most effective groundimprovement techniques. Analytical and numericalmodelling of vacuum preloading is still adeveloping research area. There has always been adiscrepancy between the predictions and observedperformance of embankments stabilised withvertical drains and vacuum pressure. Thisdiscrepancy can be attributed to numerous factorssuch as the uncertainty of soil properties, the effectof smear, inaccurate assumptions of soil behaviourand vacuum pressure distribution, and an improperconversion of axi-symmetric condition to planestrain (2D) analysis of multiply drains.Vacuum assisted consolidation is an innovative
method which has recently, and successfully, beenused for large scale projects on very soft soils inreclamation areas. The extent of surcharge fill canbe decreased to achieve the same amount ofsettlement and the lateral yield of the soft soil can
A1-32
be controlled by PVDs used in conjunction withvacuum pressure. The effectiveness of this systemdepends on (a) the air tightness of the membrane,(b) the seal between the edges of the membrane andthe ground surface, and (c) the soil conditions andlocation of the ground water level. The exact role ofmembrane type and membrane-less systems forvacuum preloading requires detailed evaluation. Inthe absence of a comprehensive and quantitativeanalysis, the study of suitable methods to applyvacuum preloading becomes imperative,experimentally, numerically and in the field.To study the performance of vacuum assisted
consolidation, a process simulation test using alarge-scale consolidometer was conducted to obtainmore realistic parameters, including the correctsmear zone characteristics, the distribution ofvacuum along the length of the drain, as well as soiland drain properties. Conventional small equipment(e.g. Rowe cell) cannot capture these parameters.The equivalent radius of the smear zone is generally2-3 times larger than the equivalent radius of themandrel and the soil permeability in the smear zoneis lower than the undisturbed zone by a factor of1.5-2. The presence of even a thin unsaturated layerof soil at the boundary of the PVD would retard thepore pressure dissipation at the initial stage ofconsolidation.Analytical modelling of vertical drains that
include vacuum preloading under axi-symmetricand plane strain conditions that simulate theconsolidation of a unit cell surrounding a singlevertical drain has been developed. The effects ofvacuum propagation along the length of a drain andthe occurrence of non-Darcian flow conditions havebeen incorporated in the proposed solutions toobtain a more realistic prediction. The ellipticalcavity expansion theory provided further insight toevaluate the role that smear zone characteristicsplay on consolidation.In large construction sites where many PVDs
are installed, a 2D plane strain analysis is usuallysufficient. The proposed conversion from axi-symmetric to a plane strain condition agreed withthe data available from case histories, includingBallina Bypass and Port of Brisbane (Australia), theSecond Bangkok International Airport (Thailand)and Tianjin Port (China). These simplified planestrain methods can be readily incorporated innumerical (FEM) analysis. The conversionprocedure from 3D to 2D based on the correcttransformation of permeability and vacuumpressure, ensure that the time-settlement curves arethe same as the true 3D analysis. Field behaviour
and model predictions indicate that the efficiency ofvertical drains depends on the magnitude anddistribution of vacuum pressure as well as thedegree of drain saturation during installation, andthe extent of smear caused by the verticallypenetrating mandrel.From a practical point of view, the surcharge fill
can be reduced in height by using vacuumpreloading to achieve the same desired rate ofconsolidation. This system eliminates the need for ahigh embankment surcharge load, but air leaks mustbe prevented as much as possible. Suitable designcharts for vertical drains that consider both verticaland horizontal drainage have been developed. As aresult, the conventional and often cumbersome trialand error methods used to estimate the appropiateparameters and spacing of drains be avoided. Oncethe equivalent drain diameter and other relevantparameters are known, the diameter of the influencezone can be readily obtained without any furtheriterations or interpolations. These preliminarydesign charts have now been extended to representa larger array of soil properties and drain patterns,on the basis of the same governing equationspresented here.Apart from road embankments, PVDs will also
help stabilise rail tracks in coastal areas containinga high percentage of clayey subgrades. It has beenshown that short PVDs can be used under railtracks to improve stability by dissipating excesscyclic pore pressure and curtailing lateraldisplacement. Much of this research is still ongoingat the University of Wollongong, particularly inview of future high speed rail. Current laboratoryobservations prove without doubt that high speedtrains cannot operate efficiently on tracks built onsoft subgrade clays unless it is consolidated beforeconstruction, or alternative improvements such aschemical treatment or stone columns are considered.For stone column application, arching, clogging,
and smear effects can affect the performance of thestone column. A numerical solution based on FiniteDifference Method was developed with acomprehensive consideration of these effects. Theresults showed that this solution had a goodagreement with other existing models and field tests.In future, the laboratory studies on these factors areexpected to be conducted so that more models forthem could be developed for determining theparameters.
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ACKNOWLEDGEMENTS
A number of research projects on theapplication of vertical drains and vacuumpreloading have been supported in the past andpresent by the Australian Research Council (ARC).Keen collaborations with industry throughnumerous projects have facilitated the applicationof theory to practice. In this respect, I sincerelythank Queensland Department of Main Roads, Portof Brisbane Corporation, Roads and TrafficAuthority, Coffey Geotechnics, Polyfabrics,Geofabrics, ARUP, Douglas Partners, SydneyTrains, ARTC, Chemstab and Austress Menard. Atleast a dozen PhD students and half a dozenresearch fellows have contributed to the soft soilengineering research over the past 12-15 years.This invited Keynote lecture can be considered
as a significant extension of the 1st Author’s 2009EH Davis Memorial Lecture of AustralianGeomechanics Society. Much of the contents havealso been elaborated in past issues of the CanadianGeotechnical Journal, ASCE Journal ofGeotechnical & Geoenvironmental Engineering,Geotechnique, Int. J. of Geomechanics, and J. ofGround Improvement, among others. Salientcontents from these past articles have beenreproduced here with kind permission from theoriginal sources.
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