chek lap kok airport

Consolidation modelling of soils under the testembankment at Chek Lap Kok InternationalAirport in Hong Kong using a simplified finiteelement method

Guofu Zhu, Jian-Hua Yin, and James Graham

Abstract: This paper models consolidation of the foundation soils under a test embankment at the new Chek Lap KokInternational Airport in Hong Kong. The modelling used a simplified finite element method and material parametersderived from results in the original site investigation report. Various features that need to be considered in applying thesimplified method are illustrated through this case study. Good predictions of settlement results are obtained. Relativelylarge discrepancies in pore-water pressure predictions suggest that the nonlinear nature of hydraulic conductivity needsto be taken into account when large compressions are likely to occur. Geological conditions are shown to be a key fac-tor in successful modelling of consolidation behaviour.

Key words: consolidation, pore-water pressure, case modelling, finite element method, vertical drains, settlement.

Résumé: Cet article modélise la consolidation des sols de fondation sous un remblai d’essai au nouvel aéroport inter-national Chek Lap Kok de Hong Kong. La modélisation a utilisé une méthode simplifiée d’éléments finis et des para-mètres du matériau dérivés des résultats du rapport de l’investigation originale du site. Diverses caractéristiques quidoivent être considérées dans l’application de la méthode simplifiée sont illustrées dans cette étude de cas. De bonnesprédictions des résultats de tassement ont été obtenues. Des divergences relativement importantes dans les prédictionsdes pressions interstitielles portent à penser que la nature non linéaire de la conductivité hydraulique doit être prise encompte lorsque des compressions importantes peuvent vraisemblablement se produire. On montre que les conditionsgéologiques sont un facteur clé pour modéliser avec succès le comportement en consolidation.

Mots clés: consolidation, pression interstitielle, modélisation de cas, méthode d’éléments finis, drains verticaux, tasse-ment.

[Traduit par la Rédaction] Zhu et al. 363

Introduction

Vertical drains are often installed in soft-soil engineeringprojects where subsoils consist of fine-grained soils with lowhydraulic conductivity. The intention of the drains is toshorten the drainage path and hence speed up the consolida-tion process.

Following derivation of the differential equation byRendulic (1935) for one-dimensional (1D) radial dissipationof excess pore-water pressure, Carrillo (1942) showed thattwo-dimensional (2D) flow problems can be uncoupled. As aresult, solutions to vertical and radial consolidation problemscan be combined to give solutions to the entire 2D problem.

Probably the best known study of this topic was by Barron(1948). He assumed two types of vertical strains that mightoccur in a uniform clay layer: (i) “free vertical strain” result-ing from a uniform distribution of surface load, and(ii ) “equal vertical strain” resulting from imposing the samevertical deformation on the entire surface of the clay. Later,Horne (1964) presented a formal solution to the layered con-solidation problem with vertical drains. Yoshikuni andNakanodo (1974) gave a rigorous solution taking well resis-tance into consideration. Olson (1977) obtained an approxi-mate solution for the case of vertical drainage under ramploading using the equal strain assumption. Zhu and Yin(2001) used the free-strain assumption to develop a mathe-matical solution for consolidation analysis of soil with verti-cal and horizontal drainage subject to ramped loading.

Simplified solutions were also obtained by other research-ers, for example Hansbo (1981), Zeng and Xie (1989), andXie et al. (1994). These closed-form solutions cannot conve-niently be extended to account for layered systems, time-dependent loading, well resistance, variable coefficients ofconsolidation, and inelastic stress–strain behaviour.

To overcome these difficulties, some researchers (Hart etal. 1958; Olson et al. 1974; Atkinson and Elered 1981;Onoue 1988; Lo 1991) resorted to numerical solutions using

Can. Geotech. J.38: 349–363 (2001) © 2001 NRC Canada

349

DOI: 10.1139/cgj-38-2-349

Received January 18, 2000. Accepted October 13, 2000.Published on the NRC Research Press Web site onApril 9, 2001.

G. Zhu and J.-H. Yin. Department of Civil and StructuralEngineering, Hong Kong Polytechnic University, Hung Hom,Kowloon, Hong Kong, China.J. Graham.1 Department of Civil and GeologicalEngineering, The University of Manitoba, Winnipeg, MBR3T 5V6, Canada.

1Corresponding author (e-mail: [email protected]).

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finite differences. The finite element method has also beenused to investigate the consolidation behaviour of soils withvertical drains. Runesson et al. (1985) studied the efficiencyof partially penetrating vertical drains based on an assump-tion of linear free strains. Bergado (1993) analyzed the ef-fects of smear zone for Bangkok clay using a linear model.General two- and three-dimensional (2D and 3D) procedures(Siriwardane and Desai 1981; Selvadurai 1996; Lewis andSchrefler 1998; Cheng et al. 1998) are well developed, andvarious methods of matching the effect of drains underaxisymmetric and plane strain conditions are also available(Hird et al. 1995; Indraratna and Redana 1997). Some spe-cial problems have also been investigated, for example, thesensitivity of consolidation behaviour to mesh discretizationand the resulting damage of the poroelastic medium(Mahyari and Selvadurai 1998).

However, application of 2D and 3D finite element proce-dures for the design of vertical drains may not be practicalbecause of (i) difficulty in the determination of various modelparameters for 2D and 3D conditions, (ii ) the large amountof computation, and (iii ) the frequent occurrence of numeri-cal instability and convergence problems for nonlinear cases.

Recently, Zhu and Yin (2000a) used a general 1D soilmodel to develop a simplified finite element (FE) procedurefor 2D consolidation analysis of soils with vertical drains.Using a 1D soil model has the advantage that the soil param-eters needed for the analysis can be easily found using con-ventional oedometer tests. By comparing results from thesimplified method with those from a fully coupled 3D finiteelement analysis, the authors showed that the simplified FEprocedure is efficient and numerically stable.

This paper uses the simplified FE method of Zhu and Yin(2000a) to produce “true predictions” of the consolidation offoundation soils under a previously constructed test embank-ment at the new Chek Lap Kok International Airport inHong Kong. True prediction is here meant to be as muchlike class A prediction as possible, although this is in fact anafter-the-fact simulation. All the parameters adopted in themodelling were suggested in the original site investigationreport except for the coefficients of hydraulic conductivityfor the upper alluvial crust. These were estimated from theoriginal report.

Lessons from applying the new simplified method lead touseful conclusions that are described later in the paper. Thefollowing section presents a brief summary of the basicequations and provides an understanding of how the FE con-solidation model was used in this study. More details can befound in Zhu and Yin (2000a).

Basic equations

As in Barron (1948), the consolidation problem of soilswith vertical drains is simplified to an axisymmetric one, asshown in Fig. 1. The solution assumes (i) the soil is fullysaturated, (ii ) water and soil particles are incompressible,(iii ) Darcy’s law is valid, (iv) strains are small, and (v) allcompressive strains within the soil mass occur in the verticaldirection. Assumption (v) can be justified as follows. Inmost practical applications, vertical drains are installed in aregular pattern at close spacing in soils where the layers areapproximately horizontal and the surface area is extensive.

The thicknessD of the soil layer that contains the verticaldrains (lengthH) is normally much less than the dimensionsin plan. Average strains (and deformations) in soil with ver-tical drains occur almost exclusively in the vertical direc-tion. Engineers are normally concerned only with theaverage settlement (in plan) of soil layers with verticaldrains and give much less attention to differential settle-ments in the localized area surrounding a vertical drain. Thestress–strain behaviour of the soil can therefore be simpli-fied on average to be 1D. Numerical results from the simpli-fied method and from a fully coupled 3D finite elementanalysis demonstrate that the simplification is reasonable(Zhu and Yin 2000a).

The governing equations for finite element consolidationmodelling in this paper are given in the following sections.

The continuity equationThe continuity equation for axisymmetric consolidation

problems can be written

[1] ∇ = + + = =qqr

qr

qz t t

∂∂

∂∂

∂ε∂

∂ε∂

r r z v z

whereq = (qr , qz)T; qr andqz are the radial and vertical flow

rates, respectively;εv and εz are the volume and verticalstrains, respectively (positive for compression);r is the ra-dial coordinate;z is the vertical coordinate; andt is time.

The constitutive equationsZhu and Yin (1999) wrote the general 1D constitutive

model in the form

[2]∂ε∂

∂ σ∂

σ εz zz z

tf

tg= ′ + ′

( )( , )

whereσ z′ is the vertical effective stress.For the nonlinear elastic model used in part of this study,

[3]f

Vg

= ′

=

λ σln z

0

© 2001 NRC Canada

350 Can. Geotech. J. Vol. 38, 2001

Fig. 1. Geometry of the simplified model for consolidation ofsoils with vertical drains.D, depth of clay layer;H, depth ofdrain; r, radial coordinate;rd, equivalent radius of vertical drains;re, equivalent radius of influence of vertical drains;z, vertical co-ordinate.



whereλ/V is a constant in whichλ is the compression index(ln-scale) andV is the specific volume.

Most of the analysis described later used the 1D elasticviscoplastic (EVP) model suggested by Yin and Graham(1989, 1994):

[4]

fV

gVt

V

= ′

= −

′′

κ σ

ψ εψ

σσ

ln

exp

z

zz

00

λψ

whereκ/V is a constant related to elastic compression, whereκ is the recompression index (ln-scale);λ/V is a constant re-lated to a reference time line (approximately the normallyconsolidated compression line);σ 0′ is a constant in units ofstress locating the position of the reference time line; andψ/V and t0 (in units of time) are two constants related tocreep of the soil.

Darcy’s lawDarcy’s law for axisymmetric problems can be expressed

as

[5]q

qK

u

ru

z

K

k

kr

z

r

w

z

w

and =

= −

∂∂∂∂

γ

γ0

0

whereu is the excess pore-water pressure,K is the perme-ability constant,kr is the radial coefficient of permeability,kzis the coefficient of permeability in a vertical direction, andγw is the unit weight of water.

Vertical total stressFor simplicity, the vertical total stress is calculated by as-

suming that shearing stresses on every cylindrical surfaceare zero.

Equations [1], [2], and [5] are the governing equations forthe consolidation problem. Although the governing equa-tions are simplified greatly by assumingεz = εv, these equa-tions are still coupled in the solution. Several iterations arerequired to obtain the related solutions for vertical strainsand pore-water pressures (Zhu and Yin 2000a).

Project background

In the 1970s, it was proposed to build a replacement air-port for Hong Kong by levelling the islands of Chek LapKok and Lam Chau and reclaiming 600 ha of land from thesea. At the site, the seawater was up to 10 m deep and thetidal range was 2 m. Reclamation would involve placing ap-proximately 80 000 000 m3 of fill to a thickness of up to20 m.

Site investigations (RMP ENCON Ltd. 1982a; Koutsoftaset al. 1987) for the area revealed that the entire seabed iscovered by soft to very soft, dark grey, plastic, marine clay(upper marine clay) with pockets of shells. The thickness ofthe clay varies considerably over the site, from as little as1.0 m (or less) to over 15 m, but is generally in the range of6–8 m. Examination of “undisturbed” samples of the upper

marine clay showed no lamination or layering. The clay isunderlain at some locations by loose to medium-dense ma-rine sand up to 3 m thick. Underlying the upper marine clay(and the irregular sand) is an alluvial stratum (upper alluvialcrust) consisting of interbedded layers of mottled, oxidized,and discoloured very stiff clay and dense sand. The thick-ness of this deposit varies in an erratic manner over the sitebut rarely exceeds 7.5 m. The third stratum is a light grey todark grey medium stiff to stiff clay (lower marine clay)interbedded with medium-dense sand lenses and occasionallayers of very stiff mottled reddish and brown clay. Geo-logically, this is believed to have been deposited during aperiod of high sea levels. Underlying the lower marine clayis an alluvial deposit (lower alluvium) consisting primarilyof very dense, coarse to fine sands, grading into a layer ofgravel and cobbles. Occasional clay pockets are encounteredwithin this deposit and occasionally below the gravel. Thethickness of the lower alluvial deposit ranges from 0 to10 m. Below the lower alluvial deposit (or the lower marinedeposit where the lower alluvium is absent) is a layer ofcompletely decomposed granite. The compressibility of thislayer is very small. Experiments that examined the dissipa-tion of excess pore-water pressures demonstrate that it canbe viewed as a free-draining layer.

These soil conditions presented obvious geotechnical dif-ficulties for the development of the new airport. The optionof removing and replacing the soft marine clay would bevery expensive, involving excavation of approximately37 000 000 m3 of the material and transporting it for dis-posal about 20 km from the site. The alternative of leavingthe soft clay in place would result in settlements of up to4 m. The settlements could be expected to extend over manyyears because of the high compressibility and low perme-ability of the deposits. Settlement tolerance after completionof the airport was limited, because settlements would alsocause unacceptable differential settlements. Reclamation bysimply placing fill over the soft clay might result in the de-velopment of mud waves and lead to serious constructionproblems that could jeopardize the project.

To assess the feasibility of using vertical drains with fillplacement techniques that would reduce or prevent mud-wave formation, an instrumented test embankment (RMPENCON Ltd. 1982b; Cheung and Ko 1986; Koutsoftas et al.1987) was constructed between 1981 and 1983 on the westshore of Chek Lap Kok Island (Fig. 2). The main test areawas a 100 m × 100 m square in plan and was divided intofour quadrants. Alidrains were installed in the northwesternand northeastern quadrants at 1.5 and 3 m triangular spac-ing, respectively. The Alidrains were prefabricated band-shapedvertical drains with widthb = 100 mm and thicknesst =7 mm. The bottoms of the drains were positioned at –21 mPD (Hong Kong principal datum). Displacement sand drains500 mm in diameter were installed in the southwesternquadrant at 3 m triangular spacing. The southeastern quad-rant was used as a control area, with no additional drains.The fill and foundation soils were heavily instrumented(RMP ENCON Ltd. 1982b; Handfelt et al. 1987) to monitortheir performance during and after construction. The instru-mentation consisted of pneumatic and hydraulicpiezometers, settlement plates and pipes, subsurface settle-ment anchors, and other probes.

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Zhu et al. 351



The test fill provided nearly 1D loading conditions. Thispermits the formulations presented by Zhu and Yin (2000a)to be used for this application. The following sections analyzethe consolidation behaviour of foundation soils in the north-western quadrant of the test fill. The analysis uses soil pa-rametersthat were selected from data provided by the originalprogram of site investigation and laboratory testing. Resultsof the analysis are then compared with measured values.

Index and consolidation test results

RMP ENCON Ltd. (1982a) and Koutsoftas et al. (1987)reported an extensive program to determine physical and en-gineering properties of the major strata within the limits ofthe site. The laboratory program included oedometer tests,K0-consolidated undrained triaxial compression tests,K0-consolidated undrained direct simple shear tests, unconsoli-dated undrained triaxial compression tests, isotropically con-solidated undrained triaxial compression tests, and indextests. Only the oedometer and index test results are used inthe following analysis of consolidation and settlement.

The oedometer tests were performed using conventionalincremental loading procedures. Generally, small load incre-ments were used in the recompression region and until thesoil had been stressed above its maximum past (precon-solidation) pressure. Most of the tests included unload–re-load cycles in the “normal” (first-time) compression range.A load increment ratio of 1.0 was generally used, with eachincrement being applied for approximately the time requiredto achieve 90% consolidation plus 1 h. For some tests, theloads were left on for 24 h to obtain sufficient data to definethe coefficient of secondary compression more clearly.

A number of special consolidation tests were also per-formed to evaluate the effects of surcharge on the coefficientof secondary compression in the upper and lower marineclays (RMP ENCON Ltd. 1982a; Koutsoftas et al. 1987).These special tests required four identical test specimens tobe prepared from the same sample tube. The four specimens

were loaded using conventional incremental loading proce-dures to the same value of maximum vertical stress, selectedto be well into the normally consolidated region. At the endof primary consolidation under the final load increment,three of the four specimens were unloaded to simulate theeffect of removing various amounts of surcharge. The fourthspecimen served as the control test and was allowed to con-solidate further at the applied stress level. The test speci-mens were monitored for a period of 3 days to collectsecondary compression data. The results allowed evaluationof the effects of surcharge on material behaviour.

The following section reproduces test results of the seabedstrata identified by the site investigation (RMP ENCON Ltd.1982a; Koutsoftas et al. 1987). Figure 3 defines the variouscompressibility parameters obtained from the consolidationtests, and Fig. 4 plots results of Atterberg limit tests on aCasagrande plasticity chart. Essentially all the data fall intogroups parallel to and slightly above the A line of the plas-ticity chart. This is typical of inorganic marine clays.

Figures 5–7 show index data and maximum past pressuresversus depth below the mudline for the three cohesive strataat the site. Natural moisture contents for the upper marineclay (Fig. 5) are typically at or above the liquid limit, indi-cating a very soft and (or) sensitive material. Theoverconsolidation ratios of the upper marine clay are in therange 1.5–2.0. The very stiff upper alluvial crust is over-consolidated (Fig. 6), with maximum past pressures rangingfrom 200 to 600 kPa, and usually above 300 kPa. Maximumpast pressures for the lower marine clay (Fig. 7) typicallyrange from 200 to 400 kPa.

Figure 8 summarizes compression indices (abbreviated toCI) versus natural water contentwn. There is a general trendin Fig. 8 for the value of CI to increase to aboutwn = 70%with increasing water content for all soil types. The soft up-per marine clay has the highest values of CI, ranging from0.3 to 0.5. Figure 9 presents the recompression index (RI)versus the compression index for the upper and lower marineclays. The recompression indices for the upper marine clayare on average 0.07 times the compression indices, and for

© 2001 NRC Canada


Fig. 3. Definition of compressibility parameters.Fig. 2. Plan of the test embankment at the new Chek Lap KokInternational Airport.



the lower marine clay the recompression indices are on aver-age 0.14 times the compression indices. Coefficients of sec-ondary consolidationCαe are plotted in Fig. 10. The valuesof Cαe increase with increasing natural water content.

Construction of the main test area

To construct the main test embankment, a 2 mthick layerof hydraulic sand fill was first pumped over the main testarea. Second, the centre of the embankment was filled to ele-vations above sea level. Third, the vertical drains and instru-mentation were installed from the newly formed ground.Fourth, the central portion was raised to elevation 6.4 m PDduring the period 13 June to 2 July 1982. This completed theinitial construction of the test fill. After approximately8 months of settlement, the northwestern quadrant was fi-nally raised to 10.8 m PD from 28 December 1982 to 21January 1983 in the second stage of testing (RMP ENCONLtd. 1982b; Cheung and Ko 1986; Koutsoftas et al. 1987).The 10.8 m PD elevation approximated the highest antici-pated loading from the reclamation.

The densityρt of the fill is very important for accuratelyassessing the incremental vertical stress. After careful exam-ination of the test data and other relevant material, Cheungand Ko (1986) suggested that the saturated unit weight ofthe hydraulic fill material and the bulk density of the decom-

posed granite placed above +2 m PD up to +10.8 m PDcould be chosen as 1.9 Mg/m3. Figure 11 shows a simplifiedversion of the incremental vertical loading (total stress at thetop of the soft marine clay) calculated using these values.The figure is for the loading of the northwestern quadrantand has been used for the consolidation analysis in the fol-lowing sections.

Soil profile and soil parameters

The general geology and sequences of stratification weredescribed in RMP ENCON Ltd. (1982a) and Koutsoftas elal. (1987). As indicated earlier (Figs. 5–7), the subsoils atthe site can generally be classified as consisting of four lay-ers, namely upper marine clay, upper alluvial crust, lowermarine clay, and lower alluvium (Fig. 12). A number of ris-ing- and falling-head permeability tests were performed inthe field during the original site investigation to measure hy-draulic conductivity coefficients in the upper and lower ma-rine clay.

For design of the reclamation works for the airport, RMPENCON Ltd. (1982a) suggested the soil parameters outlinedin the following paragraphs (see also Table 1). All the pa-rameters (kv, kr, λ/V, κ/V, ψ/V, unit weights, and maximumpast pressure) were suggested in the site investigation reportexcept the coefficients of hydraulic conductivity for the up-per alluvial crust. These have been estimated by the authorsfrom data given in the original site investigation report.

Upper marine clayFor the upper marine clay (with plasticity indexIp ranging

from 40 to 65%; Fig. 5), a density value of 1.45 Mg/m3 ap-pears suitable. The soil has low compressibility in theoverconsolidated range, but is highly compressible when themaximum past pressure (yield stress) is exceeded.Recompression indices (Fig. 3) range from 0.02 to 0.03. Inthe normal consolidation range, the soil is highly compress-ible, with CI ranging from 0.30 to 0.50. Representative val-ues of 0.025 for RI and 0.40 for CI are consideredappropriate for this soil for design purposes. The upper ma-rine clay exhibits very low secondary compression atstresses below the maximum past pressure. However, in thenormal consolidation range coefficients of secondary consol-idation are typically aboveCαe = 1.5% per logarithm cycleof time. A value of 1.75% per logarithm cycle of time hasbeen recommended for design. Coefficients of vertical hy-draulic conductivity calculated from the consolidation testsare in the range of 2 × 10–9 to 5 × 10–9 m/s, with a meanvalue of 2.2 × 10–9 m/s. The horizontal coefficients of hy-draulic conductivity from variable head field permeabilitytests range from 3 × 10–9 to 5 × 10–9 m/s. A value of 4 ×10–9 m/s appears to be a suitable average.

Upper alluvial crustThe upper alluvial crust is a medium-plasticity clay with

plasticity index in the range 20–35%. A bulk unit densityvalue of 1.95 Mg/m3 was recommended for design.Recompression indices RI range from 0.015 to 0.035. In thenormal consolidation region, the compressibility is compara-tively small, with CI ranging from 0.10 to 0.20. Representa-tive design values of RI = 0.025 and CI = 0.15 were

© 2001 NRC Canada

Zhu et al. 353

Fig. 4. Summary of Atterberg limits data for upper marine clay,upper alluvial crust, and lower marine clay.



selected. Coefficients of secondary compressionCαe in thenormal consolidation range are about 0.8%, and this valueappears to be a suitable average. No permeability data were

available for this stratum. The vertical coefficient of hydrau-lic conductivity was estimated as 6 × 10–9 m/s from thesite investigation report (RMP ENCON Ltd. 1982a), and

© 2001 NRC Canada


Fig. 6. Index results and maximum past pressure profile of upper alluvial crust and stiff lenses within lower marine clay.

Fig. 5. Index results and maximum past pressure profile of upper marine clay.wn, natural water content;wl, liquid limit; wp, plasticlimit.



this value was used in the analysis. We selected a value of12 × 10–9 m/s for the horizontal hydraulic conductivity.

Lower marine clayThe lower marine clay is of medium plasticity (25≤ Ip ≤

40%). A saturated unit density of 1.85 Mg/m3 was recom-

mended for design. In the recompression stress range, com-pressibility is low, with RI ranging from 0.02 to 0.05. In thenormally consolidated range, the soil is quite compressible,with CI ranging from 0.20 to 0.35. Representative values ofRI = 0.035 and CI = 0.25 were selected. Coefficients of sec-ondary compressionCαe in the normal consolidation range

© 2001 NRC Canada

Zhu et al. 355

Fig. 8. Compression index versus natural water content for upper marine clay, upper alluvial crust, and lower marine clay.

Fig. 7. Index results and maximum past pressure profile of lower marine clay.



vary from about 1.7 to 3.0%, and 1.7% has been selected forthe analysis. Coefficients of vertical hydraulic conductivityfrom laboratory consolidation tests are typically 2 × 10–10 to3 × 10–10 m/s, with a mean value of 2.5 × 10–10 m/s. The insitu horizontal hydraulic conductivities from variable-headpermeability tests are 4 × 10–10 to 8 × 10–10 m/s. A value of6.2 × 10–10 m/s was selected as a suitable average.

Lower alluviumIn this is very dense layer, the bulk density was chosen as

2.01 Mg/m2. The preconsolidation (yield) pressure of thislayer was larger than the final stresses imposed by the fill.Therefore, a small recompression index of 0.01 was adopted

for the analysis. The vertical hydraulic conductivity waschosen as 1 × 10–8 m/s, and the horizontal hydraulic conduc-tivity was 2 × 10–8 m/s.

Location of instrumentationFigure 12 shows the elevations of pneumatic piezometers

(PP) and Sondex anchors in the northwestern quadrant.These instruments were placed at the centre of a triangulargrid (in plan) of the vertical drains (RMP ENCON Ltd.1982b; Handfelt et al. 1987). The construction drawingsgenerally gave only approximate locations for the Sondexrings.

© 2001 NRC Canada


Fig. 9. Recompression index versus compression index for upper and lower marine clay.

Fig. 10. Coefficient of secondary consolidation versus natural water content for upper marine clay, upper alluvial crust, and lower ma-rine clay (normal consolidation region).



Soil model and parametersAnalysis of the settlements used the 1D EVP soil model

in eq. [4] (Yin and Graham 1989, 1994) for the top threelayers. The simpler nonlinear elastic model in eq. [3] wasadopted for the lower alluvium. The parameters for thesemodels are the values originally suggested for the design ofthe reclamation site and outlined in preceding paragraphs.These are listed in Table 1. The parameterskr and kz in Ta-ble 1 are the horizontal and vertical hydraulic conductivities,respectively, and are taken as constants in the analysis. Theparameterρt is the bulk density. Although these values aretypical for the whole site, no borehole was located in the im-mediate location of the test embankment.

Initial and boundary conditionsAs boundary conditions, the top surface of the upper ma-

rine clay and the bottom surface of the lower alluvium weretreated as free drainage boundaries. The initial stresses andthe modelling of the maximum past pressures used in thecalculations are plotted in Fig. 13. Initial strains were calcu-lated using the methods suggested by Zhu and Yin (2000b).

Vertical drain characteristics and smearzone

As mentioned earlier, the Alidrains (widthb = 100 mmand thicknesst = 7 mm) were arranged in a triangular pat-

tern with drain spacing of 1.5 m and their tips at 21 m PD.The equivalent radius of vertical drains,rd, can be deter-mined in several ways (for example, Hansbo 1979; Atkinsonand Elered 1981; Long and Alvaro 1994). It seems that theformula rd = (b + t)/4 + t/10 suggested by Long and Alvaro(1994) agrees well with experimental values most closelyand has been adopted in this analysis. On this basis,rd is27.45 mm. For triangular installation patterns, the equivalentradiusre of influence of the vertical drain is 0.525 times thedrain spacing (Fig. 14). That is,re = 0.525 × drain spacing =0.7875 m (Barron 1948).

Installation of vertical drains creates a region of disturbedsoil, called the smear zone, with outer radiusrs around thedrain. Installation procedures that use a mandrel of radiusrmcause the most severe disturbance. Outward displacement ofthe soil distorts the adjacent ground. The zone of soil nearthe drain is remolded and dragged first downwards and thenupwards as the mandrel is pushed into and then pulled fromthe ground. In soft soils where the technique is most useful,the overall effect is to produce a disturbed soil zone of re-duced permeability, reduced preconsolidation pressure, andincreased compressibility (Johnson 1970). The analysis as-sumedrs to be five times the equivalent radius of the verticaldrain, that is, 137 mm.

A diamond-shaped mandrel with external dimensions of75 mm and 166 mm was used to install the Alidrains. Theequivalentradius of the mandrel isrm = 63 mm. These

© 2001 NRC Canada

Zhu et al. 357

Fig. 11. Simplified fill loading. Fig. 12. Soil profile and instrumentation setup.

Parameter Upper marine clay Upper alluvium Lower marine clay Lower alluvium

Soil model Yin and Graham(1994) 1D EVPmodel

Yin and Graham(1994) 1D EVPmodel

Yin and Graham(1994) 1D EVPmodel

Nonlinearelastic

Vertical coefficient of permeability,kz (m/s) 2.2×10–9 6.0×10–9 2.5×10–10 1.0×10–8

Radial coefficient of permeability,kr (m/s) 4.0×10–9 1.2×10–8 6.2×10–10 2.0×10–8

Elastic compression constant,κ /V 1.086×10–2 1.086×10–2 1.52×10–2 —Reference time line constant,λ /V 0.174 0.065 1.086×10–1 4.343×10–3

Creep constant,ψ/V 7.6×10–3 3.47×10–3 7.38×10–3 —Creep constant,t0 (days) 1 1 1 —Bulk density,ρ t (Mg/m3) 1.45 1.95 1.85 2.01

Table 1. Modelling parameters.



values of rs and rm correspond to a value ofrs/rm = 2.2,within the range proposed by Mesri and Lo (1991).

Results of fully coupled finite element analysis by Zhuand Yin (2000a) show that vertical effective stresses withinfive times the equivalent radius of the vertical drain aremuch higher than in other parts of the domain. These higherstresses will reduce the permeability of the soil near verticaldrains regardless of the installation method. In addition, re-molding due to drain installation may reduce the permeabil-ity in the smear zone. However, the reduction and size of thesmear zone are still not exactly known. In the following

analysis, the horizontal and vertical hydraulic conductivitiesin the smear zone are assumed equal to the vertical hydrau-lic conductivity of undisturbed soil (Broms 1987). Since theequivalent cross section of the Alidrain is small and thedrain length is up to 17.1 m, the effect of internal resistanceto water flow in the drain needs to be considered. In theanalysis, the hydraulic conductivity coefficient of the verti-cal drain is assumed equal to 1.2 m/day (this is essentiallythe hydraulic conductivity of clean sand, and since it ismuch larger than the hydraulic conductivity of the variousclay layers, the solution is not sensitive to this assumption).

© 2001 NRC Canada


Fig. 13. In situ vertical effective stress and maximum past pressure.

Fig. 14. Geometry of the simplified model for consolidation of soils with a vertical drain.rs, outer radius of the smear zone.



The deformation behaviour of the Alidrain material allows itto adopt the recompression stress–strain relationships of thesurrounding soil.

Finite element analysis results anddiscussions

The computed settlements at the elevations of the Sondexsettlement gauge anchors are plotted in Fig. 15. Measuredvalues were reported earlier by Cheung and Ko (1986) andare also shown in the figure. In the early stages of loading,the measured values are larger than the computed results.This may have been caused by shear straining and lateralmovement of the soils from under the fill, particularly in thevery soft upper marine clay. After the final loading stage, thecomputed settlements are larger than the measured results.

Taking into consideration the effort here to produce true pre-dictions in the sense defined earlier, and the conservatism inthe design parameters, the results are quite good. A subse-quent laboratory program of oedometer tests (Cheung andKo 1986) on 17 undisturbed samples of the upper marineclay close to the location of the test embankment showed amaximum compression index of 0.333. This is smaller thanthe value of 0.40 suggested by RMP ENCON Ltd. (1982a)from the overall investigation and used in the analysis.Using a lower value of 0.32 instead of 0.40 for the uppermarine clay in the finite element analysis produced betteragreement (Fig. 16) between computed settlements and mea-sured results. The predicted settlements in the upper layerare still larger than the measured settlements.

Computed and measured pore-water pressures are shownin Fig. 17. The computed values were again obtained using

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Zhu et al. 359

Fig. 15. Comparison between measured settlement (points) and computed settlement (lines) using design values.



the soil parameters in Table 1 that came from the originaltesting for design of the reclamation works. Figure 17 showsthat, although the trends have been modelled well, the com-puted pore-water pressures (shown as lines) during the ini-tial loading stages are higher than measured results (shownas symbols). After the final loading stage, however, thecomputed pore-water pressures are lower than measured val-ues. In other words, the rates and durations of the pore-waterpressure dissipation and the settlements have not been wellmodelled. Using vertical total stress changes determinedfrom Boussinesq elastic stress distributions produces resultsthat are almost the same as those from the new modelling.The simulation is from the start of construction (contract day136), whereas field measurements only began after the ini-

tial loading stage (after contract day 201). Therefore, thereare no records available for the initial loading as simplifiedin the loading curve. When plotted in the figures, there areonly two large increases in measured pore-water pressure,whereas the predictions suggest there will be three in-creases.

One reason for the lack of agreement may be nonlinearchanges of hydraulic conductivity with increasing effectivestress and the resulting decreases in void ratio. Hydraulicconductivities are larger at the beginning of loading and be-come smaller as consolidation proceeds. The soils in thisstudy undergo relatively large deformations, and the effectsof nonlinear hydraulic conductivity may be significant. Al-though the program used for theanalysis can take some

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Fig. 16. Comparison between measured settlement (points) and computed settlement (lines) using test embankment site experiment data.



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Zhu et al. 361

Fig. 17. Comparison between measured pore pressure (points) and computed pore pressure (lines) using design values.



account of nonlinear hydraulic conductivity, suitable infor-mation was not available from the laboratory program. Themeasured pore-water pressures at PP60 near the top of theupper marine clay during early loading dissipate moreslowly than the predicted values. This suggests that the up-per boundary (the mudline) may not be a free drainageboundary or that some destructuring was taking place. Com-puted pore-water pressures at PP43 agree well with mea-sured values. Relatively large differences were noted,however, between computed and measured pore-water pres-sures at PP42, PP41, PP40, PP35, and PP38.

The hydraulic conductivity at PP35 (located in the lowermarine clay) is examined in more detail in the followingparagraph. The measured pore-water pressure increasedfrom 15.0 kPa at contract day 213 to 63.4 kPa at contractday 232. This corresponds to a vertical total stress incrementof 99.8 kPa in the second loading step. The measured pore-water pressure increased again from 28.4 kPa at contract day411 to 107.14 kPa at contract day 437, corresponding to avertical total stress increment of 104.5 kPa in the third load-ing step. From the test arrangement, deformations can beconsidered as 1D. To estimate a lower limit of hydraulicconductivity of the lower marine clay using the measuredvalue at PP35, it is assumed that the vertical drain is com-pletely free draining. In the second loading step, 51.5% ofthe increased excess pore-water pressure dissipated; and inthe third loading step, 24.7% of the increased excess pore-water pressure dissipated. The analytical solution developedrecently by Zhu and Yin (2001) suggests that this corre-sponds to time factors ofT = 1.93 for the second loadingstep andT = 0.77 for the third loading step. The respectivecoefficients of radial consolidation are 0.0815 and0.0213 m/day for the two loading steps. Substituting therecompression index RI = 0.035 and the initial effectivestress (105.5 kPa), the radial coefficient of permeability willbe 1.33 × 10–9 (m/s) for the second loading step and 3.48 ×10–10 (m/s) for the third loading step. The coefficient of per-meability in the second loading step is much larger than thatused in the calculations. It can also be seen that the coeffi-cient of permeability in the third loading step is about 30%of the value in the second loading step.

Examination of the borehole log obtained during the 1984testing program described by Cheung and Ko (1986) in thenorthwestern quadrant of the test fill indicates a layer of me-dium-dense,dark grey, fine to medium sand from –21.4 to–21.8 m PD. These elevations place it in the range of thelower marine clay in the soil profile (Fig. 12) used for thecalculations. Also, a borehole log for the southwestern quad-rant exposes a medium-dense, greyish brown, fine to me-dium sand layer from –11.0 to –11.9 m PD. These elevationsare in the upper alluvium crust. It is likely therefore that thehydraulic conductivities and drainage boundaries at the sitemay be rather different from those determined from the orig-inal investigation and used in the modelling.

Although it appears that settlement magnitudes can bepredicted with some success, attempts to compare predictedand measured excess pore-water pressures under embank-ment projects have generally been less successful. Excesspore-water pressures vary rapidly in the horizontal directionaround sand drains and wicks and can produce changes inhydraulic conductivity. As a result, relatively small variation

in the positions of the wicks or piezometers can lead to largepotential errors (Olson 1998).

The compression of the lower three layers in Fig. 12 isrelatively small compared with that of the upper marine clay.Thus, the relatively large discrepancies in the modelling ofpore-water pressure in the lower three layers are of little im-portance for the prediction of total settlements of the re-claimed land.

Validation of the simplified finite element procedurethrough modelling of a case study has proved very helpful indeveloping confidence in the ability of the model. Case his-tory projects of this nature are invaluable in providing fac-tual results for developing models, validating theassumptions, and learning how to use them successfully inpractical applications.

Conclusions

This paper presents a simulation of settlements of a testembankment at the new Chek Lap Kok International Airportin Hong Kong. The modelling was done using the finite ele-ment method suggested in Zhu and Yin (2000a). The predic-tions were done using, for the most part, results from theoriginal laboratory testing and site investigation report. Goodresults were obtained for predictions of settlement magni-tudes. However, relatively large discrepancies were encoun-tered in modelling pore-water pressures. This has beenrelated to nonlinear characteristics of hydraulic conductivitythat should be taken into account when the soil experienceslarge compression. Localized coarser layers in the geologicalsequence are also key factors that influence the possibility ofsuccessful modelling of consolidation behaviour.

Acknowledgements

Financial support (Grant No. H-ZJ73) from the HongKong Polytechnic University, a research grant (Grant No.PolyU 63/96E) from the Research Grants Council of UGCof the Hong Kong SAR Government of China, and supportfrom the Natural Sciences and Engineering ResearchCouncil of Canada are gratefully acknowledged. We also ap-preciate permission from the Civil Engineering Office, CivilEngineering Service Department of the of Hong Kong SARGovernment, to use information about materials and perfor-mance at the test embankment site at the Chek Lap Kok In-ternational Airport. The authors acknowledge thoughtful andhelpful comments from the reviewers.

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