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GEOTECHNICS

Introduction

Due to the high population density, there is a general shortage ofusable land for economic and industrial development in Singapore.The total land area of Singapore is about 660 km2 of which about35% of the total land surface area is below an elevation of 5 mabove M.S.L., and most of the low-lying land is covered by softsoils. The Urban Redevelopment Authority projects a land shortageof 40 km2 when Singapore’s population swells to 5.5 million, ifdevelopment continues at today’s pace.

To satisfy the need for new lands, the Government had embarkedon a land reclamation program starting in the early 1960s. Theland reclamation program was carried out on both the main andoffshore islands. Some of the ongoing land reclamation projectsare at Changi, Tuas, Jurong Island, Pulau Tekong and the SouthernIslands.

Soil improvement is necessary to increase the density of sand fillcommonly utilised for land reclamation. Hydraulically filled sandused for land reclamation is normally in loose to medium conditionif it is not compacted. Therefore, the sand fill needs to be densifiedin order to achieve suitable shear strength and compressibility tosupport future structures. Among soil improvement methods,dynamic compaction is often used due to its efficiency andeconomical considerations.

Dynamic compaction results in impact stress acting on the groundsurface, and in turn, causing densification of the ground. Theobjective of this research is to investigate the effects of input energyand initial density of dry sand on impact stress due to dynamiccompaction. The scope of the experiment covers only onedimensional sand column.

Experiments and results

Dry Ottawa sand in loose and dense conditions was used in theexperiment, as a continuation of previous research by Low [1].Raining and dry pluviation methods were used to prepare soilspecimens in dense and loose conditions. Nine sets of tests wereconducted for each condition, i.e., L1 ~ L9 and H1 ~ H9. Detailsof the experimental results can be found in Bay and Ng [2].

Figure 1 shows a set up of the equipment system. A free fallingpounder was dropped 15 times onto the sand surface, anddeceleration of the pounder during impact was measured by anoscilloscope through a signal conditioner.

Figure 2 shows the typical result of impact stress versus time duringimpact for loose sand condition. Impact stress can be defined asthe stress acting on the surface of the sand column due to the impactof a free falling weight. As the deceleration is monitored duringthe test, the impact stress can be calculated as mass of the pounder

Impact Stress on Dry Sand due toDynamic Compaction

Budi Wibawa (cwibawa@ntu.edu.sg)Bay Hong Seng (S7812801A@ntu.edu.sg)

Ng Yan Kit (S7802698G@ntu.edu.sg)

multiplied by deceleration per unit area. Figure 2 indicates that theimpact stress of the first drop has a relatively small amplitude withlonger impact duration, whereas the impact stress after the fifthdrop shows a quite high amplitude with relatively shorter impactduration.

The difference of the stress amplitudes is due to a higher sanddensity which resulted after the first drop. The loose sand becomesdenser because there is a hardening effect after dropping the pounderrepeatedly. During the first drop, the damping effect is probablythe largest since the density of the sand is in the loosest state. Thus,most of the impact is cushioned by the sand mass. However, as thesand density increases, the impact stress increases as well.

Figure 3 shows the typical result of impact stress versus time duringimpact for dense sand. The impact stress of the first drop has arelatively high amplitude whereas the stress after the fifth dropshows a smaller amplitude than that of the first drop. This is actuallydue to the fact that initial density of the sand is considered to bevery dense even before dynamic compaction. Thus the first dropactually breaks up the sand structure more than compacting it.However, subsequent drops slowly compact the sand.

The impact duration decreases insignificantly after the firstdrop. The rising limb and falling limb for all the curves arefairly symmetrical but the slope of the first drop is steeperthan the others. This shows that the initial soil structure of the sand

Figure 1. Impact testing set-up

Figure 2. Impact stress on loose sand for various drops

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Figure 3. Impact stress on dense sand for various drops

column is more rigid before the first drop. This indicates that thefirst drop of pounder must have broken down the soil structurenear the surface resulting in a higher impact stress than the rest.

Discussion

Figure 4 shows a relationship between the amplitude of the impactstress and input energy for loose and dense sand. The first findingis that the amplitude of the impact stress increases with densitybecause the loose sand probably absorbs more input energy. Thismeans loss of impact energy for loose sand is higher, and so theamplitude of the impact stress on loose sand is lower than that ondense sand.

Another finding is that the amplitude of the impact stress alsoincreases with the input energy. Higher input energy causes largerimpact on the sand column, especially the surface, resulting in thehigher impact stress.

Figure 4. Effect of input energy and initial densityon impact stress of the first drop

Conclusions

Based on the experimental results and the discussion above, withinthe range of the experiments, it can be concluded that:a. The amplitude of impact stress increases with the density of

sand.b. The amplitude of impact stress also increases linearly with

the input energy of the free falling pounder.

References

[1] Low, P. C., 1995. Dynamic Compaction of Sand Column, M.EngThesis, Nanyang Technological University, Singapore.

[2] Bay, H. S. and Ng, Y. K., 2003. Impact Stress due to DynamicCompaction on Cohesionless Soil, Final Year Project Report,Nanyang Technological University, Singapore.

Instability of Sand underPlane-Strain Conditions

J. Chu (cjchu@ntu.edu.sg)D. Wanatowski (darek@pmail.ntu.edu.sg)

Introduction

Singapore is a country with very limited land resources.Offshore land reclamation has been carried out using mainlyhydraulically deposited granular till in the past to cater forfurther economic expansion. A study of the engineeringproperties of the granular fill, in particular its instabilitybehaviour, has been conducted.

Experimental studies on sand are usually carried out underaxisymmetric stress conditions using a triaxial cell. However,for most practical problems, soil is subjected to a plane-strainor three-dimensional stress condition. Therefore, studies onbehaviour of sand should be conducted under plane-strain orother general stress conditions. Furthermore, the effect of shearband formation on the behaviour of sand can only be studiedunder plane-strain or three-dimensional conditions.

Plane-strain apparatus

A plane-strain apparatus has been developed at NTU forconducting more advanced soil testing. The design of the plane-strain cell and the testing arrangement are shown in Figure 1.In this apparatus, a 120 mm in height and 60 x 60 mm in crosssection prismatic specimen is tested. Both the vertical andhorizontal loading platens are enlarged and lubricated to reducethe boundary constraints and to delay the occurrence of non-homogeneous deformations. Local stress and strainmeasurements are made. A reconstituted sand specimen isshown in Figure 2.

Results

Some typical testing results obtained from plane-strain testson sand are shown in Figure 3. In all the tests, the specimens

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Figure 3. Typical plane-strain testing results:(a) effective stress paths; (b) stress-strain curves

(b)

Figure 2. A specimen used in the plane-strain apparatus

were first K0 consolidated to the same initial stress conditions

and then sheared along different stress or strain paths.

The results of a drained, undrained, and a strain path testunder dε

v/dε

1 = –0.5 are presented in Figures 3(a) and 3(b).

The influence of stress or strain paths on the stress-strainbehaviour of sand is clearly shown in Figure 3(b).

Shear bands were observed during plane-strain tests. Thetypical mode of the shear bands observed at the end of aplane-strain test is shown in Figure 4.

Another plane-strain test showing the instability behaviour ofsand is presented in Figure 5. In Figure 5b, the axial strainshoots up at point A indicating that the specimen had becomeunstable at point A. It can be seen from Figure 5a that thestress state at point A is below the failure line. Therefore, itis a type of prefailure instability.

Conclusions

A plane-strain apparatus has been developed at NTU to enablethe stress-strain behaviour of soil to be studied under more

(a)

Figure 1. The arrangement for plane-strain test

Figure 4. Typical mode of shear bands observedin plane-strain tests

(a)

(b)Figure 5. Instability behaviour observed under a plane-strain

condition: (a) effective stress path followed;(b) development of axial strain with time.

generalised stress conditions. Some typical results obtainedfrom tests on a granular fill are presented. The results showthat stress or strain paths affect the stress-strain behaviour ofsand considerably. Instability in the form of a sudden increasein strain rates can occur at a stress state below failure.

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Introduction

Geotechnical engineers have long been using the lumpedfactor of safety approach in the design of foundations andretaining walls. A more recent alternative is the limit stateapproach using specified partial factors, for example assuggested in Eurocode 7. Yet another approach is perhapsmore flexible and rational: design based on a target reliabilityindex which reflects the uncertainty of the parameters andtheir correlation structure. Among the various versions ofreliability indices, the Hasofer-Lind index and FORM (firstorder reliability method) are more consistent. This short articleillustrates reliability-based design for a shallow foundationand an anchored sheet-pile wall based on the Hasofer-Lindindex. An efficient computational approach that achieves thesame result as the Hasofer-Lind method and FORM isdescribed in Low & Tang (2004) and Low (2003), togetherwith an intuitive expanding dispersion ellipsoid perspective.Hence the computational procedures will not be elaboratedhere. Instead, the differences between a reliability-baseddesign and one based on specified partial factors are brieflydiscussed.

An example of reliability-basedshallow foundation design

Tomlinson (1995)’s Example 2.2 determines the factor ofsafety against bearing capacity failure of a retaining wall(Figure 1) that carries a horizontal load (Q

h) of 300 kN/m

run at a point 2.5 m above the base and a centrally appliedvertical load (Q

v) of 1100 kN/m run. The base (5 m × 25 m)

of the retaining wall is founded at a depth of 1.8 m in a siltysand with friction angle φ = 25°, cohesion c = 15 kN/m2, andunit weight γ = 21 kN/m3.

To illustrate reliability-based design, Tomlinson’sdeterministic example will be treated probabilistically here.The width B of the foundation is to be determined based ona reliability index β = 3.0 against bearing capacity failure.The parameters c, φ, Q

h, and Q

v are assumed to be lognormal

random variables with mean values equal to the values inTomlinson’s deterministic example, and with coefficient ofvariation equal to 0.20, 0.1, 0.15, 0.10, respectively. Themean and standard deviation of these four variables are shownin Figure 1. The random variables are partially correlated,with correlation matrix as shown in the figure. Thus cohesionc and friction angle φ are (consistent with observations)negatively correlated, with a correlation coefficient equal to-0.5, and Q

h and Q

v positively correlated with correlation

coefficient equal to 0.5. The foundation width required toachieve a reliability index β of 3.0 is B = 4.51 m. Thefollowing may be noted:- The x* column denotes the point where the 4-

Reliability-Based Design Illustratedfor a Footing and an Anchored Wall

B K Low (cbklow@ntu.edu.sg)

dimensional equivalent dispersion ellipsoid touches thelimit state surface. It is the most probable failurecombination of the parameters. More details are in Low& Tang (2004).

- For each parameter, the ratio of the x* value to theoriginal mean value is similar in nature to the partialfactors in the limit state design. However, in a reliability-based design one does not specify the partial factors.The design point values (x*) are determinedautomatically and reflect sensitivities, standarddeviations, correlation structure, and assumed probabilitydistributions in a way that prescribed partial factorscannot reflect.

- Comparing the x*/mean ratios (or the values under thenx column), it is evident that bearing capacity is moresensitive to Q

h than to Q

v, for the case in hand.

- The x* value for c is slightly higher than the originalmean value of c, due to the negative correlation betweenc and φ. In this case, the response is far more sensitiveto φ than to c.

An example of reliability-basedanchored wall design

Craig (1997, Example 6.9) illustrates the deterministic designof an anchored sheet pile wall using the free earth supportmethod. Relevant soil properties were the effective angle offriction φ′ and the interface friction angle δ between the soiland the wall. The cohesion of the soil was assumed to bezero. The required depth of embedment d and the tie force(per m wall length) T were determined, assuming a factor ofsafety of 2.0 with respect to gross passive resistance, i.e., thehorizontal component (K

ph) of the passive earth pressure

coefficient was divided by 2. Alternative calculations werealso shown for an assumed factor of safety of 1.2 with respectto shear strength, i.e., the mobilized angle of friction wastan-1(tanφ′ / 1.2). This resulted in computed values of d andT which were about 16% lower and higher, respectively,than those based on factored K

ph.

In this section, the anchored sheet pile wall will be designedbased on reliability analysis (Figure 2). The deterministicvalues used in Craig (1997) are taken to be the mean valuesin the reliability analysis. Instead of factors of safety, standarddeviations and correlations are used in the reliability analysis.The analytical formulations based on force and momentequilibrium in the deterministic analysis are also required ina reliability analysis, but are expressed as limit state functionsor performance functions. For the case in hand, the standarddeviations (StDev) are 10% of the corresponding mean valuesfor random variables σ

s, φ′ and δ, and 5% for random

variables γ and γsat

. These random variables are assumed tobe normally and lognormally distributed, as shown in

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Figure 2. Some correlations among parameters are assumed,as shown in the correlation matrix (crmatrix). It is judgedlogical that the unit weights γ and γ

sat should be positively

correlated, and that each is also positively correlated to theangle of friction φ′.

Given the uncertainties and correlation structure in Figure 2,it is desired to find the required embedment depth d so as toachieve a reliability index of 3.0 with respect to rotationfailure about the anchor level “A”. The solution is as shownin Figure 2, that is, a design embedment depth d of 4.15 mwould give a reliability index β of 3.0. Note that in this casethe performance function (=sum(Moments)) is a nonlinearand lengthy function of the five random variables under thecolumn labeled “x*”. It is interesting to note that at the pointwhere the five-dimensional equivalent normal dispersionellipsoid touches the limit state surface, both unit weights γand γ

sat (15.98 and 18.15 kN/m3) are lower than the

corresponding mean values (17 and 20 kN/m3), contrary tothe expectation that higher unit weights will cause higheractive pressure and hence greater instability. This apparentparadox is resolved if one notes that smaller γ

sat will reduce

passive resistance, smaller φ′ will cause greater activepressure and smaller passive pressure, and that γ, γ

sat, and φ′

are positively correlated.

Figure 1. Determining foundation width B,for a reliability index β of 3.0

Figure 2. Reliability-based design of embedment depth d

One may note that the ratio x*/mean for γ is different fromthat for γ

sat, reflecting their different sensitivities. Likewise,

the ratio x*/mean for the φ′ in Figure 2 is different from thatfor the φ′ in Figure 1, again reflecting the different sensitivitylevels of the same parameter φ′ in different settings (shallowfoundation versus anchored wall). In a reliability-based design(such as the two illustrative examples provided in this article)one does not prescribe the ratios x*/mean–such ratios, orratios of x*/(characteristic values), are prescribed in limitstate design–but leave it to the expanding equivalentdispersion ellipsoid to seek the most probable failure pointon the limit state surface, a process which automaticallyreflects the sensitivities of the parameters. Besides, one canassociate a probability of failure for each target reliabilityindex value, regardless of the problem setting.

References

[1] Craig, R.F., 1997. Soil Mechanics, 6th ed., Chapman & Hall.

[2] Low, B.K. and Tang, W.H., 2004. Reliability analysis usingobject-oriented constrained optimization. Structural Safety,Elsevier Science Ltd., 26(1): 69-89.

[3] Low, B.K., 2003. Practical probabilistic slope stability analysis.Proceedings, Soil and Rock America, M.I.T., Cambridge,Massachusetts, June 2003, Verlag Glückauf GmbH Essen, Vol.2, 2777-2784.

[4] Tomlinson, M.J., 1995. Foundation Design and Construction,6th ed., Longman Scientific.

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Introduction

The construction of deep excavations systems for basementconstruction and cut-and-cover tunnels inevitably leads toground movements in the vicinity of the excavation. Since manyof these excavations are carried out close to existing buildings,there is a concern that lateral ground movements resulting fromthe soil excavation may adversely affect the nearby pilefoundation systems supporting these buildings. The lateral loadsimposed by these soil movements induce bending moments anddeflections in the pile, which may lead to structural distress andfailure.

This paper presents the results of an actual full-scaleinstrumented study that was carried out to examine the behaviourof an existing pile due to nearby deep excavation activities. Theconstruction of a cut-and-cover tunnel as part of the new North-East Line (Mass Rapid Transit system) presented a uniqueopportunity to carry out a full-scale study.

Project details

This section of the cut-and-cover tunnel is 127.5 m long and20.0 m wide, with an excavation depth of 16.0 m. The excavationwas supported by 31 m long and 0.8 m thick diaphragm wallswith 6 levels of struts. Part of the requirement by the UrbanRedevelopment Authority was for the construction of a row of1 m diameter and 46 m long bored piles (Grade 40 concretewith 1.6% reinforcement) about 3 m behind a section of thiscut-and-cover tunnel for future development works. The planlayout of the piles is shown in Figure 1. In order to monitor thepile behaviour during excavation, an in-pile inclinometer wasinstalled in one pile (Pile 17A). In addition, an in-soilinclinometer was installed about 6 m away as shown in Figure1. This enabled the soil and pile lateral deformations to beprogressively monitored during the excavation process.

Ground conditions

The soil at this section of cut-and-cover tunnel is highly variablewith a number of buried valleys infilled with marine clay andfluvial sand. Near the pile, the soil profile consisted of a 8 mthick sand fill over a 10 m thick soft marine clay underlain bythe geological formation known as Old Alluvium (OA) as shownin Figure 2.

Observed behaviour

The piles were installed after the construction of the diaphragm

Pile Behaviour fromExcavation-Induced Soil Movements

Goh Teck Chee Anthony (ctcgoh@ntu.edu.sg)Wong Kai Sin (ckswong@ntu.edu.sg)

Teh Cee Ing (cciteh@ntu.edu.sg)

wall. Excavation activities in the vicinity of these piles onlycommenced about a month after the installation of theinclinometers. The inclinometer readings were taken at twostages of excavation: Stage A - when the excavation had reachedthe 3rd strut level at a depth of 6.5 m below the ground surface(approximately 3 months after the commencement of excavationactivities) and Stage B - when the excavation had reached theformation level at a depth of 16 m (approximately 5 monthsafter the commencement of excavation activities).

The pile movement increased with increasing depth ofexcavation. The maximum lateral pile deflections were 15 mmand 28 mm at Stage A and Stage B, respectively, and occurredin the soft marine clay. The pile movements were minimalapproximately 30 m below the ground surface. For brevity, onlythe measured pile movement for Stage B is shown in Figure 2.The shape of the curve is similar to the shape observed in manymulti-strutted diaphragm walls.

The measured in-soil inclinometer readings are also shown inFigure 2. The maximum lateral soil deflections were 24 mmand 39 mm at Stage A and Stage B, respectively, and occurredin the soft marine clay. Generally, in the top 17 m, the soilmovements were larger than the pile movements.

Numerical analysis

A simplified numerical procedure based on the finite elementmethod (Teh 1995) was used to back-analyse the pile response.The analysis required input on the pile radius, the pile flexuralrigidity E

pI

p, the distribution of the initial shear modulus G

i, the

Poisson’s ratio, the limiting lateral soil pressure py with depth,

and the free-field lateral soil movements (Goh et al. 1997). Themeasured soil movements were used as input for the free-fieldlateral soil movement.

The measured and predicted pile deflection profiles are shownin Figure 2. The measured and predicted pile bending momentprofiles for Stage B are shown in Figure 3. The measured pilebending moments were obtained by differentiating the pile

Figure 1. Plan layout of the piles and inclinometersPLAN VIEW (Not to scale)

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deflection profile twice. The shape of the measured and predicteddeflection profiles are in good agreement. The predicted piledeflections overestimate the pile deflection in the top 12 m. Theshape and magnitude of the predicted and measured pile bendingmoments are in reasonable agreement. There is also reasonableagreement between the measured and predicted results withrespect to the location of the maximum deflection and maximumbending moment.

Summary

This paper presents an actual full-scale instrumented studycarried out to examine the behaviour of an existing pile due tonearby excavation activities resulting from the construction ofa cut-and-cover tunnel. The pile was located 3 m behind a 0.8m thick diaphragm wall. Excavation to the formation level thatwas 16 m below the ground surface resulted in a maximumlateral pile movement of 28 mm. A simplified numericalprocedure based on the finite element method was used to back-analyse the pile response. Generally the computed predictions

were in reasonable agreement with the measured results.

Acknowledgements

The authors would like to thank the following Land TransportAuthority engineers, Wen Dazhi, Simon Young, Nick Shirlaw,and James Kimmance for their invaluable assistance inoverseeing the instrumentation for this project.

References

[1] Goh, A. T. C., Teh, C. I., and Wong, K. S. (1997). Analysis ofpiles subjected to embankment induced lateral soil movements.Journal of Geotechnical and Geoenvironmental Engineering,ASCE, 123(9), 792-801.

[2] Teh, C. I. (1995). BCPILE - A computer program for the analysisof lateral pile behaviour. Geotechnical Research Report No. GT/95/05, School of Civil and Structural Engineering, NanyangTechnological University, Singapore.

Figure 2. Measured and predicted pile movements Figure 3. Measured and predicted pile bending moments

Interaction between Existing andNew Adjacent Bored Tunnels

Ashraf Mohamed Hefny (camhefny@ntu.edu.sg)Chua Heng Choon (cchuahc@ntu.edu.sg)

Introduction

In urban areas and countries of limited ground surface areasuch as Singapore, it is necessary to make rational and efficientuse of underground space. In such cases, new tunnels mighthave to be constructed in close proximity to pre-existingtunnels. The interaction between the existing and the newlyconstructed adjacent tunnels must be evaluated to ensure thatexcessive stresses will not be developed in the lining of theexisting tunnels.

A numerical study to investigate the effect of construction ofnew bored tunnels on the stresses induced in the lining of anexisting parallel tunnel is carried out. In this paper, the studyperformed and some of the results obtained are summarised.

Methodology

The two-dimensional finite element program PLAXIS wasadopted in this study. Full-face excavation of an existing and

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a new adjacent tunnel with lining supporting the tunnelsimmediately after the excavation were modelled. Typical liningparameters of North-East Line MRT Tunnel in Singapore wereadopted. Table 1 summarises the properties of tunnel lining.The analysis was performed on tunnels of 6.0m in diameter(D) with a cover-to-diameter ratio of 3.5 for the existing tunnel.The main analysis was performed on a soil with propertiessimilar to those of the marine clay at the new Dhoby GhautStation for MRT North-East Line, as given in Table 2.

Influence of tunnel angular relative position

This study was performed to investigate the effect of theangular position of a new tunnel relative to a parallel existingtunnel. The relative position was measured by the angle “_”between the centre-to-centre line and the crown-invert line ofthe existing tunnel. An angle of 0o represents a new tunnelvertically above the crown of an existing tunnel, while anangle of 90o represents a new tunnel excavated at the samedepth as the existing tunnel. In this study, the distance betweentunnels was kept constant at three times the tunnel radius(centre-to-centre). Besides, all the soil and lining propertiesremained unchanged throughout the analysis.

Results of two cases of Volume Loss (VL of 0% and VL of2%) are presented in this section due to the fact that theresults generated are sensitive to Volume Loss. The VolumeLoss of 0% represents an ideal excavation case while theVolume Loss of 2% represents an upper bound for 93% of theVolume Loss values measured during the construction of North-East Line of Singapore MRT (Shirlaw et. al., 2001).

Case 1: No Volume Loss (VL of 0%)Figure 1 shows that when the new tunnel is driven above theexisting tunnel, the existing tunnel experiences a decrease inthe maximum axial force. This can be attributed to the decreasein vertical pressure acting onto the existing tunnel due to theremoval of a mass of soil above the tunnel. It can be seenfrom Figure 1 that the excavation of the new tunnel beside orbelow the existing tunnel has negligible effect on the maximumaxial force induced in the lining.

It can be seen from Figure 2 that the influence of angularrelative position of the new tunnel on the bending momentinduced in the existing tunnel is significant compared to theaxial force. Figure 2 also shows that for the case of no VolumeLoss, there is a decrease in the maximum bending momentinduced in the existing tunnel after interaction with the newtunnel, when the new tunnel is excavated above the existingtunnel with relative position from 0o to about 45o. This can beattributed to the decrease in vertical earth pressure acting on

Table 1. Properties of elastic tunnel lining (afterSebastian and Nadarajah, 2000)

Parameter Symbol Value Unit

Thickness t 0.275 mWeight w 6.6 kN/m/mYoung’s modulus E

l32000 MN/m2

Poisson’s ratio νl

0.2 -

Table 2. Properties of soft marine clay(after Orihara et. al., 2001)

Parameter Symbol Value Unit

Unit weight γ 16 kN/m3

Coefficient of earthpressure at rest K

o0.625 -

Young’s modulus Es

6 MN/m2

Poisson’s ratio νs

0.495 -Shear strength C

u20 kN/m2

Friction angle ϕ 22 O

Ground water table G.W.L -2 m

the existing tunnel after the new tunnel is excavated. Besides,it should also be noted that the bending moment substantiallyincreases in the existing tunnel when the new tunnel isexcavated below the existing tunnel. This can be attributed tothe fact that the excavation of the new tunnel below the existingtunnel reduces the ground stiffness in the vertical directionthat leads to more vertical deformation to the lining andtherefore the bending moment increases. In this case, themaximum change in bending moment in the existing tunnelwas about 30% of that before interaction with the new tunnel.

Case 2: Volume Loss (VL of 2%)It can be seen from Figure 2 that for the case of Volume Lossof 2%, the position of the new tunnel relative to the existingtunnel has significant influence on the maximum bendingmoment. The maximum bending moment induced in theexisting tunnel after interaction with the new tunnel increaseswhen the new tunnel is excavated at the relative position ofabout 45o to 135o, i.e. when the new bored tunnel is excavated

Figure 1. Variation of maximum axial forcewith relative position of new bored tunnel

Figure 2. Variation of maximum bending momentwith relative position of new bored tunnel

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at a position relatively near the springline of the existingadjacent tunnel. The increase in bending moment is about50% of the values before excavation of the new tunnel. Theincrease in bending moment can be attributed to the decreasein horizontal earth resistance after excavating the new tunnelclose to the springline of the existing tunnel. The decrease inthe horizontal earth resistance increases the deformation ofthe tunnel and hence the bending moment increases.

Influence of distance between tunnels

In this study, the new and existing tunnels are considered onthe same elevation (θ=90o). The distance between the twohorizontally parallel tunnels was varied between 2.5 to 10times of tunnel radius (R), centre-to-centre. All the soil andlining properties were kept constant during the study as givenin Table 1 and Table 2. Results of two cases of Volume Loss(0% and 2%) are presented in Figure 3.

Figure 3 shows that for Volume Loss of 2%, the proximity ofthe new tunnel to the existing tunnel has significant effect onthe bending moment induced in the existing tunnel comparedto the case of no Volume Loss. For the case of 2% VolumeLoss, as the distance between the two tunnels decreases, theincrease in the maximum bending moment induced is larger.The critical distance between two tunnels below which thebending moment increases substantially is about five timestunnel radius (centre-to-centre). An increase in maximumbending moment of about 30% occurs when the new tunnelis excavated at a distance of three times the tunnel radius(centre-to-centre).

Influence of volume loss

The study of Volume Loss was conducted with the new boredtunnel positioned beside and at the same elevation as theexisting tunnel at a distance of three times tunnel radius (centre-to-centre). A Volume Loss ranging from 0% to 8% was adoptedin both tunnels. The same workmanship quality was assumedfor both tunnels. All the soil and lining properties were keptconstant as those given in Table 1 and Table 2.

The Volume Loss has a significant effect on the bendingmoment induced in the existing tunnel. For Volume Loss ofabout 0.5%, no change in the value of maximum bending

Figure 3. Variation of maximum bending momentwith distance of new bored tunnel

moment occurs. For Volume Loss less than 0.5%, there is aslight decrease in the maximum bending moment afterinteraction. However, for Volume Loss greater than 0.5%, themaximum bending moment induced in the existing tunnelafter interaction increases with Volume Loss. For typicalVolume Loss of 2%, the increase in maximum bending momentin the existing tunnel after interaction is about 30%. Thisshows the importance of controlling Volume Loss in the newtunnel in order not to induce larger bending moment in theexisting tunnel.

Influence of lining thickness

In this study, three values of lining thickness were adopted forthe existing tunnel, i.e. 50mm in thickness (represents veryflexible lining), 275mm (represents relatively stiff lining), and800mm (represents very stiff lining). For each value of liningthickness of the existing tunnel, the lining thickness of thenew tunnel was varied from 50mm to 800mm and the effecton the bending moment induced in the existing tunnel wasstudied. A value of Volume Loss of 2% was simulated in boththe existing and new bored tunnels.

The results obtained are shown in Figure 4 and they arepresented as a relationship between the flexibility ratio andthe dimensionless moment coefficient. The dimensionlessmoment coefficient and flexibility ratio are defined in Equations1 and 2, respectively (Peck, 1972).

(1)

(2)

where M is the maximum bending moment induced in thelining and I

l is the moment of inertia of the lining per unit

length.

It can be seen from Figure 4 that, in general, the momentcoefficient decreases as the flexibility ratio increases. Thechange in moment coefficient is large for small values offlexibility ratio and becomes insignificant once the flexibilityratio is greater than 10. This implies that the lining withflexibility ratio larger than 10 behaves as a flexible lining.

Conclusions

A numerical study on the interaction between a new and anexisting parallel tunnel is performed. The influence of tunnelrelative position, distance between tunnels, Volume Loss andlining thickness have been studied in details. From the studyperformed, the following conclusions can be made:(a) The tunnel relative position, distance between tunnels,

Volume Loss and lining thickness have a significant effecton the bending moment induced in the lining of theexisting tunnel after interaction.

(b) The excavation of the new tunnel above the existing tunnel

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Figure 4. Variation of moment coefficient with flexibility ratio

is favourable. The maximum bending moment inducedin the lining of the existing tunnel decreases when thenew tunnel is excavated above the existing tunnel.

(c) For small percentage of Volume Loss of less than about0.5%, the excavation of the new tunnel below the existingtunnel leads to an increase in the bending moment in thelining of the existing tunnel.

(d) The excavation of the new tunnel beside and at the samedepth as the existing tunnel may lead to significant increasein the bending moment of the existing tunnel.

(e) The decrease of springline pillar distance between tunnelsmay lead to substantial increase in the bending momentinduced in the existing tunnel.

(f) The critical distance of the springline pillar distancebetween the two tunnels below which the bending momentincreases substantially is about three times of tunnel radius(3R).

(g) The bending moment induced in the lining of the existingtunnel increases with Volume Loss for cases of VolumeLoss greater than 0.5%.

The results obtained from this study are believed to be usefulfor interpretation of field measurements and designconsiderations of closely spaced bored tunnels.

References

[1] Orihara, K. and Chan, M.L., Chabayashi, K. and Okamoto, S.,Teo, P.T.P and Tan, C.G., 2001. Excavation of New Dhoby GhautStation for MRT North East Line. Proceedings of UndergroundSingapore 2001, Singapore, 29-30 November.

[2] Peck, R.B., Hendron, A.J. and Mohraz, B., 1972. State of the artof soft ground tunnelling. 1st North A M. Rapid Excavation andTunnelling Conference, Chapter 19.

[3] Sebastian, P. and Nadarajah, P., 2000. Construction of NorthEast Line tunnels at Singapore River Crossing. Tunnelling insoft ground. Proceedings of the international conference ontunnels and underground structures, Singapore, pp.191-198.

[4] Shirlaw, J.N., Ong, J.C.W., Rosser, H.B., Osborne, N.H., Tan,C.G. and Heslop, P.J.E., 2001. Immediate Settlements Due ToTunnelling For The North East Line. Proceedings ofUnderground Singapore 2001, Singapore, 29-30 November.

Cyclic Triaxial Testing of Residual SoilsE.C. Leong (cecleong@ntu.edu.sg)

H. Rahardjo (chrahardjo@ntu.edu.sg)J. Cahyadi (cjcahyadi@ntu.edu.sg)

Introduction

The stress-strain behaviour of soil is highly non-linear.Depending on the geotechnical problem, the operative stiffnessis different depending on the strain level. To date, a number oflaboratory tests are available for measuring the stiffness of soilat different strain ranges. Usually the strain range of any singletest apparatus does not extend from the very small strain to thevery large strain. Two or more test methods are normallycombined to provide soil stiffnesses over the entire strain range.Values for the shear moduli of saturated sands and clays overa wide strain range are plentiful in the literature. However,values for shear moduli of residual soils which are a dominantfeature of Singapore geology are scarce. An importantcharacteristic of these residual soils is that they are mostlyunsaturated.

The triaxial test is one of the most versatile tests forcharacterising soil behaviour. With a servo-controlled loadingsystem, a triaxial apparatus can be made to perform cyclictriaxial tests at strain levels ranging from 0.001% to 1%. Formeasuring soil stiffness at strain levels less than 0.001%, apulse transmission test can be easily incorporated into the triaxialapparatus. A cyclic triaxial apparatus with bender element testincorporated was developed at NTU. This article serves tohighlight the features of the cyclic triaxial apparatus and presentstypical test results obtained from compacted residual soils.

Description of NTU cyclic triaxial apparatus

Commercial laboratory apparatuses capable of performingdynamic soil tests are usually expensive where cost increaseswith the number of included instrumentations. Integration of

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Figure 1. Schematic drawing of NTU cyclic triaxial apparatus with bender element test incorporated.

cyclic triaxial test and bender element test in one set-up isanother issue that has to be addressed. A well equipped cyclictriaxial apparatus with bender element test capability wasdeveloped at NTU at a modest cost. A schematic diagram ofthis cyclic triaxial apparatus with bender element test capabilityis shown in Figure 1.

The triaxial cell was custom built to have internal tie rods andan external cell for ease of setting up the test specimen andon-specimen instrumentation. Eight ports were provided onthe base of the triaxial cell to provide passage for the signalcables of the instrumentation on the test specimen. Theinstrumentations included a pair of local displacementtransducer (LDT) for measurement of local axial strains, a pairof proximity transducer for measurement of radial strains, apore-water pressure transducer for measurement of pore-waterpressure of the soil specimen, an internal submersible loadcell to measure deviatoric stress on the test specimen as wellas to provide feedback during load-control test and an externallinear variable differential transducer (LVDT) for measurementof axial strain as well as providing feedback duringdisplacement-control test. The local displacement transducerswere fabricated in-house following Goto et al. (1991).

For incorporation of bender element test, the top and bottomplatens were specially designed to enable the installation ofthe bender elements as shown in Figure 2. The bender elementtransmitter and receiver were fabricated in-house from PZT5Apiezoceramic strips. The bender element test instrumentationincluded a function generator and a voltage amplifier to providethe excitation signal to the transmitter bender element and adigital oscilloscope to record the transmitter and receiver benderelement signals.

Figure 3 shows the instrumentation on a soil specimen set upin the cyclic triaxial apparatus. All the instruments wereconnected to the control and data acquisition system. Cyclicloading was provided by a pneumatic servo actuator that has

Figure 2. Top and bottom platens with bender elements.

Figure 3. Instrumentation on soil specimen.

a maximum stroke of 30 mm and a maximum capacity of 14kN with a closed loop control. The pneumatic actuator iscapable of providing a load or displacement-control cyclicloading up to a maximum frequency of 2 Hz. The dataacquisition system had eight 12-bits input channels and thesewere connected to the submersible load cell, pore-waterpressure transducer, pneumatic actuator displacement sensor,LVDT, local displacement transducers and proximitytransducers.

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to a very large strain (1%). Soil stiffness is affected by anumber of factors: shear strain amplitude, void ratio, confiningpressure, number of loading cycles, frequency, plasticity index,overconsolidation ratio, degree of saturation and stress history.The effects of strain levels and the number of loading cycleswere illustrated and discussed in this article. The stiffness ofcompacted residual soils was shown to decrease with increasingstrain levels. At a low strain level, the stiffness of the compactedresidual soil does not degrade with the number of loadingcycles. However at a high strain level, the stiffness of thecompacted residual soil degrades as the number of loadingcycle increases.

Acknowledgements

The work described in this article is part of research projectPTRC-CSE/LEO/99.02 funded by Defence Science andTechnology Agency, Singapore.

References

[1] ASTM (1997). D3999-91 – Standard test methods for thedetermination of the modulus and damping properties of soilsusing cyclic triaxial apparatus. Annual Book of ASTMStandards, Vol. 04.08.

[2] Goto, S., Tatsuoka, F., and Shibuya, S. (1991). A simple gaugefor local strain measurements in the laboratory. Soils andFoundations, 31(1): 169-180.

Axial strain = ±0.013% Axial strain = ±0.75%

(a) Axial displacement versus time

(b) Axial load versus timeFigure 4. Axial displacement and axial load versus time for

displacement-control tests at two axial strain levels.

Test results

Procedures for determining modulus and damping propertiesof soils using a cyclic triaxial apparatus are given in ASTMD3999-91. A soil specimen can be tested under load ordisplacement control cyclic loading. Figure 4 shows the loadresponse of a compacted soil specimen subjected to two axialstrain levels at a sinusoidal loading frequency of 1 Hz. Theshear moduli at 1, 5, 10, 20 and 40 loading cycles werecomputed and are presented in Figure 5. Figure 5 shows thatthe shear modulus at a low strain level is much higher thanthat at a high strain level. Furthermore, the shear modulus ata low strain level does not deteriorate with the number ofloading cycles. However, the shear modulus at a high strainlevel deteriorates with the number of loading cycles.

The bender element can be excited to produce either acompression wave (P wave) or a shear wave (S wave) to givethe compression wave velocity or shear wave velocity,respectively. A typical set of S wave data for a compactedresidual soil specimen from a bender element test is shown inFigure 6. The time lapse, t, between the transmitter and thereceiver signals gives the travel time of the wave between thetips of the bender elements. Therefore the wave velocity iscomputed as,

(1)

where Vp and V

s are the P-wave velocity and S-wave velocity,

respectively, and Ltt is the distance between the tips of the

elements. The corresponding Young’s modulus, E, or shearmodulus, G, can then be estimated from the respective wavevelocity and the density of the soil. The strain levels associatedwith the stiffness moduli determined from the bender elementtest are of the order of 0.00001%.

Discussion and conclusion

The stress-strain behaviour of soil is highly non-linear and itis important to determine the appropriate stiffness for aparticular geotechnical problem. The cyclic triaxial apparatuswith bender element test incorporated can be used to determinethe stiffness of the soil from a very small strain (0.00001%)

Figure 6. Typical transmitter and receiver bender elements’signals for shear wave.

Figure 5. Shear modulus versus number of loading cycleat two strain levels.

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Capillary Barrier for Slope StabilisationHarianto Rahardjo (chrahardjo@ntu.edu.sg)

Leong Eng Choon (cecleong@ntu.edu.sg)Denny Tami (dennytami@pmail.ntu.edu.sg)

Motivation and objectives of study

Rainfall-induced landslide is one of the most destructivenatural disasters that occurs frequently in natural orengineered residual soil slopes. Previous research indicatesthat rainfall infiltration has been found to significantly affectthe pore-water pressures and the shear strengths of residualsoils. Residual soil slopes are naturally in an unsaturatedcondition and the ground water elevation is relatively deep.The infiltration of rainwater into the slopes can cause anincrease in pore-water pressure. An increase in pore-waterpressure decreases the shear strength of the soil making theslope more susceptible to failure.

One possible preventive method for rainfall-inducedlandslides is the utilisation of capillary barrier; a fine-grained soil layer placed over a coarse-grained soil layer.The construction of a capillary barrier as a slope cover cansignificantly reduce the infiltration of rainwater into theslope and keep the slope in a safe condition. In addition,the application of capillary barrier for slope stabilisation isan environmentally friendly measure. Using this method, itis possible to use local soils for the capillary barrier andvegetation can grow on the slope surface.

Although capillary barrier has been studied and widely usedin geo-environmental engineering as a soil cover in landfillto reduce water infiltration into protected waste materials,its application for slope stabilisation has never beeninvestigated and requires further research. As a landfillcover, capillary barriers have been constructed underrelatively flat slope conditions in arid to semiarid climates.However, for slope stabilization purposes, the geometry ofa capillary barrier will have to follow the surface of theprotected slope and the slope can be rather steep. In additionthe capillary barrier for slope stabilisation will be underthe influence of tropical climatic conditions with highrainfall intensities. The application of capillary barriers forslope stabilisation against rainfall-induced landslides hasnever been fully investigated and hence becomes the focusof the research.

Introduction to capillary barriers

A capillary barrier is a cover system commonly consistingof a relatively fine soil layer placed over a relatively coarsesoil layer. Capillary barriers are generally unsaturated andfunction in response to changes in negative pore-waterpressures. The basic requirement for a cover system to bedefined as capillary barrier is that it has unsaturated fine-grained layer overlying unsaturated coarse-grained layer,with a proper contrast in their hydraulic properties (i.e.,

soil-water characteristic curves and permeability functions).The contrast in the hydraulic properties of the fine-grainedand coarse-grained soil layers forms the hydraulicimpedance, which limits the downward water movement.Infiltrating water is held in the overlying fine-grained layerand prevented from moving into the underlying coarse-grained layer.

Figure 1 shows the coefficient of permeability versus matricsuction relationships for typical fine-grained and coarse-grained soils. As shown in the figure, the coefficient ofpermeability of the coarse-grained soil is significantly lowerthan that of the fine-grained soil for almost all values ofmatric suction. Matric suction in soil is related to itsvolumetric water content. This relationship is known assoil-water characteristic curve (Figure 2). As matric suctionincreases, volumetric water content and the coefficient ofpermeability decrease. However, the rate of decrease of thecoefficient of permeability of the coarse-grained soil is muchfaster than that of the fine-grained soil.

At relatively dry conditions or high matric suctions, the

Figure 1. Coefficient of permeability - matric suctionrelationships of capillary barrier materials

Figure 2. Soil-water characteristic curvesof capillary barrier materials

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fine-grained soil has a finite coefficient of permeability,while the coarse-grained layer has an extremely lowcoefficient of permeability (Figure 1). When the volumetricwater content increases (i.e., due to water infiltration fromthe surface), the coefficient of permeability of the fine-grained layer increases gradually, while that of the coarse-grained layer remains extremely low. As the infiltratingwater accumulates and reaches the fine-coarse interface,the matric suction of the coarse-grained layer begins todecrease significantly. Once the matric suction of the coarse-grained layer reaches its water-entry value, ψ

w, the

coefficient of permeability of the coarse-grained layerincreases rapidly and may exceed the coefficient ofpermeability of the fine-grained layer. As a result, theinfiltrating water begins to penetrate into the coarse-grainedlayer (known as breakthrough or percolation). In this case,the capillary barrier is no longer effective as a barrier forthe downward water movement.

The infiltrating water held in the fine-grained layer can beremoved by evaporation, transpiration, internal drainage orpercolation into the underlying layers (breakthrough). Ifthe fine-coarse interface is inclined, the infiltrating watercan also drain laterally in the fine-grained layer underunsaturated conditions. A capillary barrier is effective ifthe combined effect of evaporation, transpiration and lateraldiversion exceeds the infiltration from the precipitation.Therefore, keeping the capillary barrier system sufficientlydry will prevent appreciable breakthrough to occur.

Research methodology

This research consists of both laboratory experiments andnumerical analyses. The performance of the capillary barrierin both one-dimension and two-dimensions was observedin the laboratory using physical models specially designedfor this study. An infiltration column (200mm diameter,2m high) and an infiltration box [2.45m (L) × 2.0m (H) ×0.4m (W)] were constructed. These facilities werecomplemented with current state-of-the-art sensing devicesand data acquisition systems, thereby allowing the behaviourof capillary barrier system in one-dimension and two-dimensions to be studied closely. Various soils were firstexamined as capillary barrier materials in the soil columnand subsequently, some soils were selected to constructsloping capillary barrier models to investigate themechanism and effectiveness of capillary barrier for slopestabilization purposes. Figure 3 shows the experimentalsetup constructed in NTU.

Each series of experiment was analysed numerically andthe results of these analyses were compared with theexperimental data to verify the numerical model adopted.Having verified the numerical model, a parametric studywas then conducted by considering other parameters andconditions that could not be incorporated in the experimentsusing the laboratory physical model.

Research findings

Figure 4 illustrates typical results from a series of tests inthe infiltration box, demonstrating the effectiveness of thecapillary barrier model. From the experimental studiescarried out, the major findings of the research can besummarized as follows: (1) Physical models of slopingcapillary barriers and soil column constructed can be usedto study the mechanism and effectiveness of capillarybarriers under high precipitation rates. The data obtainedfrom different instruments were found to be consistent andin adherence to unsaturated soil behaviour; (2) The capillarybarrier models behaved differently during the adsorptionand desorption processes and the magnitude of the pore-water pressure within the capillary barrier model during asteady-state infiltration was governed by the process thatwas experienced by the soils. This observation indicatesthat the hysteretic behaviour affected the steady-state pore-water pressures within the capillary barrier model.Experimental data also showed that the hysteretic behaviouraffected the water content less than the pore-water pressurewhere the magnitude of water content is the same regardlessof the process experienced by the soils; (3) The primarywetting and the primary drying curves of the soil-watercharacteristic curve were found to provide an envelope fora series of scanning curves obtained from the capillarybarrier model experiments. The scanning curves followedthe primary wetting curve during the adsorption processand then followed the primary drying curve during thedesorption process. During the transition period when thescanning curve moved from the primary drying curve tothe primary wetting curve (or vise versa), the scanningcurve developed had a relatively flat slope as compared tothe slope of the primary curve, and sometimes it was almosthorizontal; (4) The performance of the capillary barrierunder the influence of high precipitation rates is mainlycontrolled by its storage capacity. The results also indicatedthat the behaviour of capillary barrier before and after theoccurrence of breakthrough is slightly different.

Numerical analyses, employing both the drying and wettinghydraulic properties of the soils, were performed to studythe difference in pore-water pressures as observed in the

Figure 3. Experimental setup (1: rainfall simulator;2: tensiometer & pressure transducers;

3: TDR, time domain reflectometry; 4: data acquisition system;5: water balance measurement;

6: instrumented capillary barrier column;7: instrumented capillary barrier slope model)

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data obtained during the draining process. The appropriatehydraulic properties of the soils (i.e., drying or wetting)should be used in accordance with the process that thesoils actually experience (i.e., desorption process oradsorption process). The analyses also showed that the useof the soil-water characteristic curve and the permeabilityfunction does not depend on the flux-boundary condition(i.e., infiltration or evaporation) but depends on theantecedent condition experienced by the soils (i.e.,increasing or reducing of water content of the soils). Theappropriate use of soil-water characteristic curve andpermeability function in simulating the flow of water in anunsaturated soil is important in order to capture the correctsoil response.

The results of the parametric study indicated that themagnitude of breakthrough decreases when: (i) the thicknessof the fine-grained layer of the capillary barrier increases;(ii) the contrast in hydraulic properties of the fine-grainedand coarse-grained layer increases; (iii) the water-entryvalue of the coarse-grained layer decreases; (iv) theinclination angle of the capillary barrier increases; (v) theintensity, the total or the duration of the rainfall decreases.

Conclusions and recommendations

Using appropriately selected materials, capillary barrierswere found to be effective in minimising infiltration fromrainwater into unsaturated soil slopes under highprecipitation rates. Therefore, capillary barriers have highpotential for application in slope stabilisation measuresagainst rainfall-induced slope failure. The mechanism ofthe physical process associated with the storage of water,the transmission of water and the method for modelling atwo-layered soil system of capillary barriers were studiedin detail. Further studies, including the assessment of localsoils or synthetic materials as components of the capillarybarrier, mechanism of water release to the atmosphere(infiltration-evaporation) as well as issues related to theconstruction of capillary barrier (e.g. stability problem),however, are still required prior to the application of thisproposed method.

Acknowledgments

The work described is supported by research grant No.RG7/99 - NTU.

Figure 4. Experimental results (pressure head changes;volumetric water content changes; and water balance)

experiments. The comparison of numerical results andexperimental data suggested that the hysteretic behaviourof the soils needs to be accounted for in the modelling ofthe unsaturated flow systems in order to provide realisticresults. The pore-water pressure head from the results ofthe numerical analysis using the wetting soil-watercharacteristic curve and the wetting permeability functionmatched well with the experimental data during theprecipitation process. Similarly, the pore-water pressurehead from the result of the numerical analysis using thedrying soil-water characteristic curve and the dryingpermeability function matched well with the experimental

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