Abela 2011 Engineering-Structures

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Engineering Structures 33 (2011) 25632572

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Engineering Structures

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Blinding struts Part 1: Buckling response

J.M. Abela, R.L. Vollum, B.A. Izzuddin, D.M. PottsDepartment of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, United Kingdom

a r t i c l e i n f o

Article history:

Received 27 December 2010

Received in revised form

27 April 2011Accepted 2 May 2011

Available online 11 June 2011

Keywords:

Upheaval buckling

Geometric imperfections

Concrete

Cut-and-cover excavations

Nonlinear finite element analysis

Laboratory testing

a b s t r a c t

The term blinding is used to describe the thin layer of unreinforced over-site concrete which is used toprotect thebase of excavations fromconstructiontraffic andto provide a cleansurface for the constructionof the base slab. Blinding is not generally seen or exploited as a structural element even though it clearlyprovides some temporary lateral support to the retaining walls of cut-and-cover excavations. This papershows that enhanced blinding can be used to prop retaining walls in cut-and-cover excavations duringconstructionpriorto thecompletion of thebase slab. An experimentalprogram is conducted on 1/4 scalespecimens, which demonstrates that the failure load of blinding struts is governed by upheaval buckling,and which is employed for the validation of nonlinear finite element models. The main parametersgoverning the buckling load are shown to include: i) the amplitude of the geometrical imperfection, ii)the thickness of blinding, and iii) the eccentricity of the applied load with respect to the centroid of thestrut.

2011 Elsevier Ltd. All rights reserved.

1. Introduction

This work was motivated by Powderhams [1] innovative useof blinding struts on major infrastructure projects such as theChannel Tunnel, Limehouse Link and the Heathrow Cofferdam.The thickness of blinding used in these projects ranged from 100to 500 mm which is considerably thicker than the 5075 mmtraditionally used for over-site concrete. Blinding struts weretypically constructed in the following sequence on these projects:

1. The retaining walls are constructed from ground level usingsecant piles or other forms (e.g. diaphragm or sheet pile walls).

2. The soil is excavated from between the retaining walls in theraked fashion idealised inFig. 1for a cantilever retaining wall.In deeper excavations, the retaining wall may also need to bepropped with theroof slab andintermediate props as necessary.

3. The base of the excavation is carefully levelled before the

blinding is cast to minimise lateral imperfections due to lackof formation flatness.4. The blinding is cast and levelled to its specified thickness. In

practice, the thickness of blinding varies due to constructionaltolerances which induce geometrical imperfections into thestrut. These variations in slab thickness need to be carefullycontrolled within prescribed limits to ensure the strut hasadequate strength. Blinding is cast sequentially in strips as theexcavation moves forward with the width of each strip beingdependent on the stability of the unpropped excavation (Fig. 1).

Corresponding author. Tel.: +44 0 20 75945992.

E-mail address:[email protected](R.L. Vollum).

5. Since theaxialload is principally introduced into blinding strutswhen the ground is excavated ahead of the most recently cast

section of blinding [2], the concrete needs to gain sufficientstrength before the next stage of excavation can be takenforward. The concrete is typically designed to reach its requiredstrength within 1824 h from casting to maximise the benefitof using blinding struts.

6. Blinding is used to prop the retaining wall until the base slab iscast. During this time the concrete gains strength with time andcreeps under sustained load. Geometric imperfections can alsoincrease due to ground heave below the blinding. This heavearises due to (i) subsequent excavation after the blinding hasbeen cast and (ii) swelling of the soil below the blinding as aresult of the time dependent dissipation of excess pore waterpressures created as a result of the excavation process.

Powderhams[1] use of blinding struts allowed much of theintermediate steel strutting, which would otherwise have beenrequired, to be eliminated with considerable time savings. This inturn created a safer working environment which enabled theseprojects to be completed several months before scheduled withconsiderable savings in cost and materials. Despite their evidentadvantages, however, blinding struts have not been widely usedin practice. This is no doubt partly due to a lack of awareness oftheir potential strength which is not recognised by code-basedmethods for designing struts. In addition, Powderham [2] hasfound some clients unwilling to sanction the use of blinding strutssince their behaviour is considered uncertain and not definitivelyestablished. This paper demonstrates through tests on 1/4 scalemodels and accompanying nonlinear finite element analysis that

0141-0296/$ see front matter 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.engstruct.2011.05.002
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2564 J.M. Abela et al. / Engineering Structures 33 (2011) 25632572

Fig. 1. Schematic diagram of excavation process for cantilever retaining wall.

blinding struts can provide considerable compressive resistance.The tests are carried out to determine the potential failure modes

of blinding struts, which have not been tested to failure previously.

2. Research scope

The behaviour of blinding struts is complex and dependenton parameters which are difficult to quantify such as the endrestraint provided by the retaining walls, lack of initial groundflatness and subsequent concrete creep and ground heave. Thispaper focuses on the behaviourof blinding strutsunder short-termloading. The effects of time dependent ground heave and concretecreep are considered elsewhere [3]. The paper describes a seriesof 1/4 scale tests and associated nonlinear finite element analyses(NLFEA) that were carried out to investigate the influences of slabthickness, lateral imperfections and end restraint on the short-

term failure load of blinding struts. The strength and failure modeof blinding struts is shown to depend on the amplitude and profileof the ground imperfection, the eccentricity of the applied axialload with respect to the centroid of the strut and the verticalrestraint provided by the retaining wall. The paper shows that theperformance of the tested struts can be accurately predicted withNLFEA, which can thus be used in support of the design of blindingstruts. In this respect, NLFEA can either be employed directlyfor specified geometrical imperfections and end conditions orindirectly for the calibration of simplified design-oriented modelsas developed in the companion paper [4].

3. Basic mechanics of blinding struts

Blinding struts can potentially fail due to localised concretecrushing or buckling. Fig. 2 illustrates that blinding struts areconstrained to buckle upwards against their self-weight, andthat the buckle wavelength is not clearly defined. The behaviourillustrated in Fig. 2 is an example of upheaval buckling whichhas been widely researched in the context of thermally inducedbuckling of railway tracks [5,6], concrete pavements[7,8] and deepsea pipelines[911]. Upheaval buckling is most simply explainedwith reference to Crolls clamped column analogy [6,7,10,11],which is particularly relevant to the design of blinding struts sinceit makes allowance for the effects of geometric imperfections.According to this approach, the propagation load Pp for a buckleof amplitudew , relative to its lift-off points, and length Lp in aninfinitely long pipeline can be approximated as

Pp = Pc

1 w

(1)

Fig. 2. Upheaval buckling of blinding strut.

Fig. 3. Buckled shapes for blinding struts with (a) load applied below centroid and

(b) load applied above centroid with left hand end free to lift.

where Pcis the Euler buckling load for a clamped column of length

Lp, elastic modulus Eand second moment of areaI,

Pc= 42EI

L2p

and = wgwL is the difference between the geometric (wg) andgravity loading (wL) imperfections, with the loading imperfectiondefined as

wL =qL4p

384EI(2)

whereqis the self-weight of the strut per unit length.Eq. (1) implies that an initially perfectly straight strut with

wg = 0 will never buckle since w= 0 prior to uplift. This

raises the question of why struts buckle upwards in the first place.The answer lies in the observation that real struts are unlikely tobe perfectly straight. Furthermore, even perfectly straight strutsbuckle if the axial load is applied below the centreline of thestrut as shown in Fig. 3(a) or above the centreline as shown inFig. 3(b). The initial uplift axial load of the imperfect struts shownin Fig. 2 depends on the length and amplitude of the groundimperfection. After initial uplift, the amplitude and wavelengthof the buckle depends upon the magnitude of the axial load.The buckle propagates outwards from the lift-off points with

increasing amplitude as the axial load is increased, until the criticalbuckle length is reached and failure occurs.

Croll [11] used Eq. (1) to derive simplified expressions forthe critical buckling load of an infinitely long elastic strut thatis draped over a sinusoidal imperfection with amplitude wg andlengthLg. Croll[11]showed that the buckle propagation load Ppcorresponding to a specific buckle amplitude w is determinedfrom Eq. (1) by a propagating buckle length Lpwhich minimises Pp .He went on to show that the least critical buckling load Pb occursfor a so-calledempatheticimperfection with amplitude equal andopposite to the downward deformation of a clamped beam ofthe same length subject to self-weight (i.e. ifwg = wL whenwL is calculated according to Eq. (2) with Lp = Lg). Croll [11]showed that the critical buckling load is less for a strut that is

cast onto an imperfection (i.e. unstressed when initially drapedover the imperfection) than for an otherwise identical strut that


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J.M. Abela et al. / Engineering Structures 33 (2011) 25632572 2565

Fig. 4. Model of strut in ADAPTIC.

Fig. 5. Nonlinear concrete modelcon1 used in ADAPTIC.

is unstressed when straight. The least critical buckling loadPbof a

strut that is cast on an empathetic imperfection is given by

Pb =42EI

L2po(3)

Lpo =4

384EIwg

q. (4)

The key differences between upheaval buckling in blindingstruts and railway tracks or deep sea pipelines are as follows: (i)the axial load is transferred into blinding struts from the retainingwalls rather than from restrained thermal expansion, (ii) thebuckle length is limited by the excavation width, and (iii) concreteis much weaker in tension than compression. Furthermore,concrete gains strength rapidly after casting and creeps withtime under sustained load. Consequently, Crolls analysis is oflimited applicability to the design of blinding struts where (i) endconditions are important and (ii) short imperfections with Lg


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Fig. 6. The experimental setup: (a) plan view of rig; (b) Section A left hand side, and Section B right hand side, (c) view of internal reaction frame and supports used to

adjust strut profile and (d) blinding strut in test rig.

to the test bed as shown in Fig. 6(b) for vertical support. Thetransverse members were positioned on plan at each of the sixpairs of vertical supports shown inFig. 6(c) which were secured

to the ground by means of 50 50 5 mm SHS rails boltedto the laboratory strong floor. The test bed was deformed intothe specified initial imperfection by means of pushing and pullingon the transverse members at the four intermediate supports. Asheet of plywood was fixed to the top surface of the channelsto eliminate the minor distortions introduced into the profile bywelding. The test bed profile was fine tuned to within 0.5 mmof the specified profile by sanding the layer of plywood fixedto the channels. The profile of the test bed was measuredwith a combination of precise levelling and measurements fromdisplacement transducers (LVDTs and potentiometers) for directinput into the numerical models. Nonlinear finite element analyseswith ADAPTIC[12,14] showed that the test bed was sufficientlyrigid to provide a rigid foundation to the strut being tested.

The concrete was cast onto a polythene layer to minimise theeffects of friction with the test bed. Externally mounted shakervibrators were used to compact the concrete since the specimenswere too thin for poker vibrators to be used. The top surface ofthe slab was trowelled to a smooth surface and covered withpolythene for curing. The surface profile of the as-cast surface wasdetermined with precise levelling.

5.2. Concrete material properties

The concrete mix was designed to have a target compressivestrength of 30 MPa at 14 days.Table 1gives the concrete materialproperties which were used in the NLFEA for each slab. Theconcrete strengths were determined at the time of testing the

slabs from control specimens cured alongside the slabs.The tensilestrengths were derived from split cylinder tests. The concrete

elastic moduli inTable 1were derived from strain measurementsin a) control cylinders cast from the concrete used in each slab orb) from in situ strain measurements in the slab.

5.3. Loading procedure and instrumentation

The strut was loaded uniformly in compression at each endthrough a roller bearing which was in turn attached to a sphericalseating as shown in Fig. 6(d). The axial load was measured witha load cell that was placed between the ram of the actuator andthe spherical seating. The axial and transverse displacements ofthe blinding strut were measured relative to the laboratory floorduring loading with transducers typically positioned at the ends,quarter span positions and mid-span of the blinding strut (seeFig. 6(d)). Transducers were also positioned one eighth of the slabspan from each end of the strut in Tests OQ, which were cast ontothe ICFEP profile[16]. All the transducers were positioned in pairson opposite sides of the strut.

5.4. Test results and analysis

A total of seven struts (F, M, O, P, Q, D and E) were testedto failure under short-term loading. The geometric and materialproperties of the struts are summarised in Table 1 along withthe measured and predicted failure loads. Struts OQ were castonto the ICFEP profile which is defined in Table 2.The predictedresponse was calculated with ADAPTIC [12] using the nonlinearmaterial model shown in Fig. 5 with the appropriate materialproperties for each strut fromTable 1.

The tests showed that the failure load was significantly

influenced by the eccentricity of the applied axial load, if the endsof the slabs lifted. This observation was confirmed by numerical


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Table 1

Details of tested struts.

Parameters Test D Test E Test F Test M Test O Test Pb Test Q

Profile shape Sinusoidal Sinusoidal Sinusoidal Sinusoidal ICFEP ICFEP ICFEPMaximum imperfection amplitude (mm) 8.8 8.8 6.3 6.3 6.3 6.3 6.3

Thickness (mm) 52.6 50.0 55.0 68.0 54.0 48.0 60.0

Concrete compressive strength (MPa) 28.2 28.0 19.7 33.8 30.7 28.1 28.5

Initial concrete tangent modulusE(GPa) 25.6 27.7 29.7 34.6 29.7 29.1 28.5

Concrete tensile strength (MPa) 2.3 2.1 1.7 2.2 2.1 2.1 2.2Eccentricitiesa

Loading End(mm) 4.1 2.3 5.3 4.0 5.1 11.5 1.5

Reaction End(mm) 2.2 4.1 4.9 2.0 4.8 10.0 0.0

End Conditions

Loading End Pin Pin Pin Pin Pin Pin Fixed

Reaction End Lifted by 5 mm Lifted by 1.7 mm Pin Pin Pin Pin Fixed

Age at loading (days after casting) 18 16 14 14 14 14 15

Failure load (kN) 335 336 240 440 412 412 465

Predicted failure load (kN) 315 300 245 448 410 592c 477

Note:a The eccentricity is measured upwards from the centroid of the strut.b The ends of strut P were tapered as shown inFig. 14.The eccentricities are measured relative to the centroid of the unreduced cross-section depth of 48 mm in Test P.c Calculated neglecting the reduction in cross-section at the ends of the strut.

Table 2

Normalised ICFEP profile.

x/L 0 0.025 0.05 0.075 0.1 0.15 0.2

w(x)/wg 0 0.384 0.676 0.8 0.842 0.882 0.922

x/L 0.25 0.3 0.35 0.4 0.45 0.5

w(x)/wg 0.95 0.967 0.984 0.992 0.996 1

Notes:x/L = normalised distance along strut.

Fig. 7. Schematic diagram of loading arrangement at strut end with wedge.

analysis with ADAPTIC [12] which also showedthat thefailure loadreduced significantly if the load was applied below the centroidof the slab, but was insensitive to the eccentricity if the load wasapplied above the slab centroid and the ends were restrained fromlifting. The ends of the strut were prevented from lifting in TestsF, M, O, P and Q by inserting a timber wedge between the loadingplate and each end of the slab as shown inFig. 7,which inclinedtheline of thrust slightly downwards. The load was applied slightlyabove the centroid of the slab to avoid the possibility of thebuckling load being reduced due to the mode shown in Fig. 3(a).

5.4.1. Struts with sinusoidal imperfections and ends restrained from

lifting

Test F was designed to simulate a strut with an empatheticimperfection. The strut was cast over a sinusoidal imperfection oflength 5 m with amplitude 6.3 mm. The as-built slab thicknesswas 55 mm. The slab profile was notionally identical in Tests Fand M but the slab thickness was increased to 68 mm in Test M(see Table 1). Slab F failed at a load of 240 kN compared withSlab M which failed at 440 kN. Both struts failed explosively inupheaval buckling and fractured into several pieces as shown inFig. 8.It is worth noting that the localised discrete cracks whichcharacterise the failure mode formed post-buckling. Therefore, theuse of a smeared crack model is accurate up to the peak load

as evidenced by the good comparison between measured andpredicted displacements shown inFig. 10.Table 1shows that the

Fig. 8. Strut at end of test.

Fig.9. Comparisonof initial (sinusoidal), measuredand predicteddisplacedshapesof the blinding struts in Tests F and M immediately before failure.

measured andpredicted failure loads compared very well forstrutsF and M. Fig. 9 shows the initial imperfections of these strutsand compares the measured and predicted displaced shapes justbefore failure. The displacements were slightly underestimatedby the numerical model towards failure. This is likely to be dueto small inaccuracies in the modelling of the strut geometry,material properties and boundary conditions, none of which arefully known.

Fig. 10 compares the measured and predicted axial andtransverse load displacement responses of slabs F and M. Fig. 10(a)and(b) show that themeasuredand calculated axial andtransverse

displacements compare very favourably throughout the tests.The good correlation between the measured and calculated


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Fig. 10. Axial load versus (a) axial displacement and (b) transverse displacement

at centre of strut displacement in Tests F and M.

displacements shows that the response of the tested specimenscan be accurately predicted up to failure by NLFEA, provided thatthe specimen geometry and material properties are accuratelymodelled. The post-buckling path could not be traced in the testsdue to the snap-back axial response characteristic, which meansthat the static post-buckling response could not be experimentallyobtained even with displacement actuator control. This samecharacteristic is also responsible for the explosive bucklingbehaviour observed in the tests.

5.4.2. Struts with heave profile and ends restrained from lifting

Struts O and Q were tested to investigate the effect of changingthe slab profile from sinusoidal to the heave profile calculatedin the 3D geotechnical analysis using ICFEP [16]. The tests weredesigned to investigate the effect of varying the slab thickness andthe eccentricity of the applied axial load with respect to the strutcentroid. Both struts had the same geometrical imperfection butstrut O was 54mm thick comparedwith strut Q which was 60mmthick. Furthermore, the ends of strut O were pinned whereas theends of strut Q were prevented from lifting by G clamps whichalso provided rotational restraint. Details of the tested specimensare given in Table 1, while the ICFEP profile is defined non-dimensionally inTable 2.Strut O failed at 412 kN and strut Q at

465 kN which compare favourably with the predicted failure loadsof 410 kN and 477 kN respectively. Fig. 11shows the displaced

Fig. 11. Comparison of initial (ICFEP), measured and predicted displaced shapes of

the blinding struts in Tests O and Q immediately before failure.

Fig. 12. Axial load versus (a) transverse displacement at one eighth of the strut

length from each end and (b) axial displacement in Test O.

shape of the strut after casting and immediately before failure.Figs. 12and 13 show the axial displacements and the transversedisplacements measured at the eighth points from each end ofthe strut in Tests O and Q. The figures show that the measuredand predicted buckling loads agree well, but the numerical modeltendsto overestimate transversedisplacements. Again, the reasonsfor this are likely to be due to small inaccuracies in modellingthe specimen geometry, imperfections, material properties andboundary conditions, all of which are incompletely defined.

5.4.3. Effect of end reduction

There is a risk that the cross-sectional area of the strut isreduced adjacent to the retaining wall as a result of the groundformation not being properly trimmed. Test P (seeTable 1) wasdesigned to investigate the effect of such a reduction in the strut

cross-sectional area on its failure load for the ICFEP imperfectionprofile used in Tests O and Q. The ends of the strut were tapered


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Fig. 13. Load versus (a) transverse displacement at one eighth of the strut length

from each end and (b) axial displacement in Test Q.

Fig. 14. Schematic diagram of strut end showing wedges and end thickness

reduction.

by casting the strut onto a wedge at each end as shown inFig. 14.NLFEA suggested that the insertion of the wedges could increasethe buckling capacityto asmuchas 592 kN, due tothe upwardshiftin the centroid of the applied load, if buckling was not preceded byconcrete crushing at the ends of the strut. In reality, the strut failedat412kN due toconcretecrushingat one end ofthe strut.It followsthat care should be taken in the construction of blinding struts toensure the cross-section is not reduced sufficiently adjacent to theretaining walls to cause bearing failure.

Fig. 15shows the initial imperfection in strut P and comparesthe measured and predicted transverse displacements immedi-ately before failure. The displacements in the tested slab were verysmall dueto thepremature endbearing failure. Fig. 16(a) comparesthe measured and predicted lateral displacements at the quarter

and eighth points of the strut. The axial displacements are com-pared inFig. 16(b).

Fig. 15. Comparison of initial (ICFEP profile), measured and predicted transverse

displaced shapes in Test P immediately before failure.

5.4.4. Ends allowed to lift: buckling in a combined cantilever mode

Struts D and E were cast over sinusoidal imperfections withlength 5 m and amplitude 8.8 mm as described in Table 1. Thestrut thicknesses were 52.6 mm and 50 mm respectively. Thesestruts failed at loads of 335 kN and 336 kN respectively whichwere significantly greater than thefailure load of 202kN calculated

assuming that the ends of the struts were restrained from lifting.The difference between the measured and predicted loads waseventually explained by the observation that the ends of theblinding strut lifted during the test as the axial load was increased.This caused the struts to buckle in the combined modes shownin Fig. 17, which increased the buckling load above that of acomparable strut in which the ends are prevented from lifting.Strut D failed in a cantilever mode and strut E buckled in thespan. Additional numerical analysis, in which the ends of the strutwere not restrained from lifting, demonstrated the existence of acombined buckling mode with similar transverse displacementsand failure loads to those measured in the tests (see Fig. 17).The measured and predicted axial and transverse displacementsare shown in Fig. 18 for Tests D and E. Table 1 shows that the

measured and predicted failure loads of struts D and E comparevery favourably when the ends of the struts are allowed to lift inthe analyses as in the tests.

Notwithstanding this finding, the ends of blinding struts areconsidered unlikely to lift in reality due to the inward deflectionof the retaining walls which restrains the slab from movingupwards. Therefore, practical blinding struts are unlikely to bucklein combined modes like those shown inFig. 17.

5.5. Overview of test results

The tests showed that the response of blinding struts underaxial load can be accurately predicted with NLFEA (seeTable 1)when the slab profile, end conditions, ground profile and material

properties are accurately known, which is unlikely to be the casein reality. The ground profile is particularly difficult to define sinceit depends on both the lack of initial ground flatness and thesubsequent ground heave. Therefore, conservative assumptionsneed to be made in practice with regard to end restraints, lackof ground flatness and subsequent ground heave. These issuesare addressed further in the development of the design-orientedmodel presented in the companion paper [4].

6. Parametric studies

A series of parametric studies are carried out here using thevalidated NLFEA models to determine the effect of varying thegeometry, loading eccentricity and rotational end restraint of a full

scale 20 m long blinding strut.The nonlinearconcrete stressstrainrelationship shown in Fig. 5 was used in all the analyses with


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Fig. 16. Load versus displacement at (a) one quarter span from each end of strut,

(b) one eighth span from each end of strut and (c) axial displacement for Test P.

fc = 30 MPa. The initial concrete tangent modulus E (seeFig. 5)was taken as 32 GPa and the concrete tensile strength wastaken as 3.0 MPa. The excavation width of 20 m is chosen to berepresentative of a typical cut-and-cover excavation. The groundprofile is assumed to be (i) sinusoidal, (ii) parabolic and (iii) theheave profile determined from the incremental 3D geotechnicalanalysis using ICFEP[16]. The imperfection length was assumed toequal the excavation width of 20 m in all cases.

The parametric studies show that the buckling mode varies

with the shape of the geometric imperfection and the loadingeccentricity, as shown inFig. 19.The initial lift-off point is at the

Fig. 17. Comparison of measured and predicted displaced shapes in Tests D and Eimmediately before failure.

Fig. 18. Load versus (a) transverse displacement at the centre of the strut and (b)

axial displacement for Tests D and E.

centre of the imperfection for concentrically loaded struts cast on

sinusoidal and parabolic profiles, but near the ends for struts caston the heave profile obtained with ICFEP[3,16].

6.1. Influence of imperfection amplitude andshape, slab thickness and

loading eccentricity

Eq.(1)shows that the buckling load depends on the amplitudeof the geometric imperfection. This is illustrated in Fig. 20(a)which shows the effect of varying the amplitude and shape of theground profile for a 200 mm thick strut of length Lexc = 20 mcast onto an imperfection of length Lg = 20 m. The bucklingload decreased rapidly with increasing imperfection amplitudefor all the imperfection profiles considered. Fig. 20(b) shows theinfluenceof strut thicknesson thecriticalbucklingload forall three

imperfections shapes with wg =

100 mm, which is equivalentto 6.3 mm in the tested slabs, and Lg = 20 m. The results


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Fig. 19. Buckled shapes for (a) sinusoidal, (b) parabolic and (c) ICFEP ground

profiles considered.

Fig. 20. Influence on the buckling load of a 20 m long strut of (a) imperfectionamplitude for a 200 mm thick strut and (b) strut thickness for an imperfection

amplitude of 100 mm.

show that the buckling load increases as the thickness of the strutincreases due to the increase in self-weight and flexural rigidity.Furthermore, the relative magnitude of the failure load for eachground profile varies with slab thickness. It should be noted thatthe results for the sinusoidal profile are not affected by the endrestraint (pinned or fixed). Consequently, only one line appears inFig. 20for the sinusoidal profile.Fig. 20also shows that the failureload for the strut with a parabolic profile and pinned ends is veryclose to the least of the lift-off (PL) and the uniaxial crushing loadwherePLis given by

PL =qL2

8wg. (5)

The influence of varying the eccentricity of the axial load wasinvestigated for a 200 mm thick strut with wg = 100 mm and

Fig. 21. Effect of the eccentricity of the axial load within the cross-section depth.

Lg = 20 m. The results are presented for all three imperfection

profiles in Fig. 21 which shows that the ICFEP profile withpinned ends was particularly sensitive to variations in the loadingeccentricity with the failure load reducing significantly as thecentroid of the load moved towards the bottom of the slab. Thegeotechnical analysis [3] suggested that the load is likely to betransferred into the slab above the centroid of the slab due to theinward rotation of the retaining wall as it deflects.

Figs. 20 and 21 also show that the critical buckling load dependson the imperfection shape, and furthermore that the shape ofthe most critical profile varies with slab thickness and loadingeccentricity with the parabolic profile becoming more critical asthe strut thickness increases.

7. Conclusions

It has been found in practice that the use of blinding strutscan significantly reduce construction times in major infrastructureprojects.The test results andanalyses presentedin this paper showthat blinding struts can resist significant axial loads before failingin upheaval buckling. It is also shown that the structural responseof blinding struts can be accurately described with NLFEA if theground profile and section properties are known.

The test results show that the buckling load depends on factorsincluding the amplitude and shape of the ground imperfection,the slab thickness, the end restraints provided by the retainingwall, and the eccentricity of the applied axial load. The criticalbuckling load reduces significantly as (i) the amplitude of theground imperfection increases and (ii) the slab thickness reduces.

The tests show that the influence of the axial loading eccentricitydepends on whether or not the ends of the strut are allowedto lift. The tests combined with the numerical study indicatethat the buckling load is relatively insensitive to the eccentricityof the axial load for the sinusoidal and parabolic profiles if theload is applied above the centroid of the slab and the ends ofthe strut are prevented from lifting. This is not the case for thepredicted heave profiles, where the buckling load increases withincreasing eccentricity of the axial load above the strut centroid.More significantly, the critical buckling load reduces significantlyas the line of thrust moves progressively below the centroid ofthe slab. However, geotechnical analysis [3] indicates that theretaining wallrotates inwards as it deflects. Consequently, the axialload is likely to be applied above the centroid of the slab.

The companion paper builds on the experimental and numeri-cal findings of this paper, and proposes a simplified design method


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which can be used for assessing the axial load capacity of blindingstruts, accounting for upheaval buckling, imperfections, concretecracking and compressive material strength.

Acknowledgements

The authors would like to thank Alan Powderham for bringingblinding struts to their attention and for his continued supportthroughout the project. We also wish to acknowledge the financialsupport of the Engineering and Physical Sciences ResearchCouncil (EPSRC) under grant EP/D505488/1. Additionally, theauthors would like to thank the technical staff of the StructuresLaboratories at Imperial College London, particularly Mr. S. Algar,for their assistance with the experimental work.

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