Analysis of Piles Subject to Lateral Soil Movements

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of The Institution of Engineers, SingaporeNo.2 1996

Y. K. Chowr MIES and

and deep ercavation forconstruction result in lateral soil movernentsadditional bending moments, shearand deflections in adjacent pile foundations. Athis problem is d.escribed in thisThe accuracy of this apprcqch is uerified bywith reported case histories, A case studypractical problem of local interest is reported tosome of the important considerations in

many situations where pile foundationsloading arising from lateral soilsituations include (a) pileof bridge abutments where the approachlateral movement ofthe subsoil,(b) pile foundations of existing buildings locatedexcavation for the construction ofThe latter is of particular releyance to thesituation where the incorporation of deepbuildings is a common feature tothe use of available land, Excessive lateralmovements arising from deep excavations inbuilt-up areas may cause damage to the pileof adjacent existing buildings. In suchthe lateral soil movements arisingto be properly contained toany detrimental effects they may have onpile foundations of adjacents buildings. Hence, itthat reliable methods of analysis areto assess the additional bending moments,and pile deflections due to these lateral

of analysis can be broadlymethods and theoreticalcommonly used empirical methods wereby Tschebotarioff, (1973), and De Beer and(1972). These methods were, however,estimating the bending moments ofpiles arising from lateral soil movementsloading and are not suitableproblem (b) discussedabove.(1973) developed a theoretical method ofproblem by idealising the pile as a

K. Y. Yonf MrEs

series of beam elements and the soil represented byan elastic continuum using Mindlin's solution (1937).Mindlin's solution is strictly valid for a homogeneoussoil medium. Thus, nonhomogenous soil is treated inan approximate manner. The problem is solved usingthe frnite difference rnethod.In this paper, the behaviour of piles subject to lateralsoil movements is analysed using the finite elementmethod in which the soil is idealised using themodulus of subgrade reaction. Using this idealisation,the formulation of the problem is considerably simplerthan the method of Poulos, (1973) andnonhomogeneous soil can be easily treated. Theaccuracy of this approach is assessedby analysingsome well-documented case histories, A case study ofa problem of local interest is reported to illustratethe practical application of this method.

METHOD OF ANALYSISThe behaviour of a pile subjected to lateral soilmovements can be analysed by assuming the soil tobe modelled by the modulus of subgrade reaction.The soil pressure (p) acting on the pile is given by

p - no(t - to) (1 )where kn = modulus of subgrade reaction of the soil,y = pile lateral deflection, and yn = lateral soilmovement due to embankment or eicavation.The governing differential equation for the pile-soilsystem subjected to lateral soil movements is givenby

-.qV.lotoa t hhd\y yo)=o (2)azwhere Eo = Young's modulus of the pile material,Ip = second moment area of pile section, z = depth insbil, and d = pile diameter. Alternatively, Eqn. (2)can be written as

^. cIy .. lEeIp-

- K h\y - yo) = 0 13)clzwhere Kn = kld is the soil stiffness per unit length ofthe pile. A schematic representation of the problemis shown in Fis 1.

ANALYSIS OF PILES SUBJECT TOLATERAL SOIL MOVEMENTS

Assoc. Professor, Department of Civil Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260.Assoc.Professorand Head, Department ofCivil Engineering, National University ofSingapore, 1OKent Ridge Crescent,Singapore119260.


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(a) Idealidation f (b) Lateral soil movemettsduepile and soil to embankmenrexcavationFig I Schematic representation of problem of pilesubject to lateral soil movements.

The solution to the above governing differentialequation can be obtained using the frnite elementapproach in which the pile is represented by beamelements. The continuous variable, y, in Eqn. (3) isapproxinated in terms of discrete nodal values asfollows:y=Nfl t+Nz0t+NsY2+N4e2 (4)

where y, and 0, are the lateral deflection and rotationat node 1, y2 and 0, are the lateral deflection androtation at node 2, and the shape functions are givenby

(7), (8 ).) 1

where L = element length. Eqn. (4) can be written inmatrix form asv ={N}r {r} (e)

where {N} = vector of shape functions, and {y} = vectorof pile deformations.Applying the Galerkin's method to the governingdifferential equation in Eqn. (3) yields the followingelment matrix equation

1L[xol{r} [x" {r} ) "xo{N}voQ)dz '{o} (10)where [\J = pile elernent matrix, [K"] = soil elementmatrix, {y} = vector of pile deformations, and yo(z) =lateral soil movements due to embankment/excavation. The form of the element matrices for thepile and the soil is as follows:

Dqn. (10) can be rewritten in the following forrn:(13)

The vector on the right hand side of Eqn. (13)represents the induced lateral forces acting on thepile resulting from lateral soil movements due to theernbankment or excavation. The assembly of th eelement matrices of the pile elements and the soil isdone in the usual manner to give the global stiffnessmatrix equations for the pile-soil systen.For a given set of lateral soil movements, thedeformations ofthe pile foundation can be determinedby solving the global stiffness matrix, and the bendingmoments and shear forces in the pile obtained fromthe resulting pile deforrnations. The soil pressureaacting on the pile, if required, can be determinedusing Eqn. (1).The nonlinear behaviour of the soil can beincorporated by limiting the soil pressure that canact on the pile using an iterative technique adescribed by Chow, (1988) for axially and laterally5,zloaded piles.The analysis of this problem requires a knowledge ofthe pile bending s6iffness (ErIr), the distributions ofthe lateral soil stiffnesses (K1) and limiting lateralsoil pressures acting on the pile with depth, and thehorizontal soil movernents. In the analysis, the pileelement length is typically taken to be about I m formost problems, except in the case of short piles whereshorter element length may be necessary.

SOIL PARAMETERSThe main soil parameters required for this analysisare:

Kn the lateral soil stiffness, andp, the liniting soil pressure.

Lateral Soil Stiffiress --'The lateral soil stiffness can be related to the Young'smodulus of the soil (E.) as follows:

' 'L{ [ I (e] - lK" l l t l= )oKa.lNlvs(zlz

u,=(f -su'*z"s) fx,=(r'"-z* J)fr 'ws=(e* 2"3)ffu,=(" ' -#) f

(5)(6 )

For clays, the Young's modulus is usqglly correlatedto the undrained sh-ear trength "" r"'%iTo*"t

(14)

E" = Atc" (15)where p, typically lies between 150 and 300 (Poulosand Davis, 1980).For sands, the Young's modulus can be correlated tothe SPT blow count (N) as follows:

Es = p2 N (MN /m2) (16)where p, typically lies in the range of 1 to 1.5.

K^ = Es ( tr-o ( ,nt" )

l*. t="r-,l t4l t4l ' , ,' ' ' t9 . . ldz') ldz ' l (11)(72)l""l=l'",t"1u}" dz


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Limiting Soil PressureFoi piles in clays, the limiting soil pressure p isrelated to the undrained shearstrength c, as follows:

N.A.L. Dnsity

1.900.99 85

1.80l a5

1550

1.50

1.90 40

where the factor N- can be assurned to vary linearlyfron 3 at the grouritl surface to a limiting value of 9at a depth of about 3.5 diameters (Broms, 1964a).For piles in sands, the limiting soil pressure p" ca nbe determined as follows (Broms, 1964b):

Pr=3Krou (18)where Ko = Rankine passive earth pressurecoefficient, and o', = effective overburden pressure.PILES AD'IACENT TO EMBANKMENTSThere are only a limited number of well-documentedcase histories of measured behaviour of piles subjectto lateral soil movements due to embankmentconstruction. Two such cases are considered in thispaper.Heynan (1966)In the western city extension of Ansterdam, a sandembankment 1 km long and 4 m high had to beconstructed along a group of houses built on pilefoundations. Since the subsoil was weak, there wereconcern that the lateral pressure exerted on the piledue to the construction of the embankment mayendanger the stability of the pile foundations of theadjacent buildings. As part of the precautions toprevent damage to the existing building foundations,a field test was carried out to evaluate the influenceof the lateral subsoil movements on the pilefoundations.The test pile was an instrumented steel box pile 300mm by 300 mm with thickness of 6 mm and 12.5 rnlong. The pile was instrumented with electrical straingauges at distances between 2.2 m and 6.7 rn fromthe pile top. The boundary condition at the pile headwas such that it cannot move laterally but allowed torotate. The bending stiffness of the pile (EoIo) was21,31?kN-m2. The soil profile at the test site is ho*ttin Fig 2. The reference level indicated in the frgure isthe normal Amsterdam level (N.A.L.). The conepenel,ration est data is shown in Fig 3. Fg1the sand,lavers. the eouivalent Sp'r ltoicoui-t-TNf-rrae-


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Shear force (kN)

rotation movement---;;-t;a-

Late.al soil movement (mm)o204060

E

Fig 8 Influenbe of pile head boundary conditions onshear forces.

Pile deflection (nn)10 20 30 40

i]>."rolain Menl

__- fre lixed-- fixed free- ftd fired..- free free

Fig I Influence of pile head boundary conditions onpile deflections.

pile. Constraining the pile head against movementand rotation, large moment and shear wereexperienced at the pile head. These rnoment and shearreduced significantly when the pile head was allowedto move and rotate, but large deflection wasexperienced by the pile. Hence, it is very importantthat the pile is analysed using the appropriateboundary conditions and designed accordingly.

PILES ADJACENT TO DEEP EXCAVATIONSThe authors are not aware of any freld measurementson piles located adjacent to deep excavations forbasenent construction. Hence, a hypothetical casewas analysed to illustrate the application of thisapproach to this class of problem and to highlightsorne of the salient points which are of interest tothe design engineer.The pile foundations of a building adjacent to anexcavation were assumed to be 0.8 m diameterconcrete bored piles. The soil profrle at the site shownin Fig 10 consisted of a 5 m thick granular frlloverllng soft to firm marine clay; below the marineclay is the Old Alluvium formation conprising denseto very dense clayey sand. This type of soil profile isquite typical of some parts of Singapore. The boredpile was assumed to be 35 rn deep with a cut-offlevelof 3 m below the existing ground level. The depth ofthe excavation analvsed was about 12 m below the

Fig 10 Pile foundation adjacent to deep excavation.ground level. It was assumed that this excavationwill be supported by diaphragm wall with internalbracing.The influence of the lateral ground movements onthe bored piles due to excavation may be consideredby analysing the problem based on the groundmovement profrles at critical stages ofthe excavation.For excavation near to adjacent buildings it isnecessary to contain the lateral movements of thediaphragm wall to control the ground movements. Inthis study, the assumed lateral soil movement profileat the frnal stage of excavation at the location of thepiles nearest to the excavation is shown in Fig 10.The shape of the assumed profile is based onexperience ofexcavations of similar soils in Singaporeand a maximum magnitude of 50 mn was assumed.For the granular fill, the friction angle was assumedto be 30". The undrained shear strength of the softmarine clay and firm marine clay were estimated to _be 20 kN/m2 and 36 kN/m2, respectively, from theSPI blow count. The assumed angles of friction forthe dense and very dense clayey sand were 38o and40", respectively. The Young's modulus of thegranular hll and sand was taken to be E" = lrf (11MN/m") and the Young's modulus of clay E" = 200 cu.The soil stiffness Kr' = E". The Young's modulus ofconcrete was taken to be 26 x 106 kN/m2.The following three boundary conditions at the pilehead were considered:(a) Pile head not allowed to rotate (due to restraintimposed by the pile cap) but lateral movementallowed. This correspond to the fixed-free casediscussed earlier.(b) Pile head not allowed to rotate or move laterally.This corresponds to the fixed-fixed case.(c) Pile head not allowed to rotate (due to restraintimposed by the pile cap) but lateral movementpartially restrained due to the stiffness of the

;l5


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whole pile foundation system which was tied byground beams.The boundary condition (a) in which the pile headwas not al lowed to rotate but was free to move wil lsimulate the condition where the pile foundationsare not t ied together by ground beams. The bendingmoments, shear forces and pile deflections are shownin Figs 11, 12 and 13, respectively as the fixed-freecase. For this case, the computed lateral deflectionat the pile head is about 28 mm. Since the pilefoundations are located at varying distances from thediaphragm wall, the lateral soil movement Drofilesat the other pi les will be dif ferent, thus leading todifferential lateral movement of the foundations. Thiswill induce additional stresses on the structure whichwill need to be designed for.The second boundary condition (b) in which the pilehead was not al lowed to rotate or move lateral lv is

Bending rnoment (kNm)1500 1000 -500

5

l0

l5

=--\

rot.tion movement- fixed fixed_-_ fixed 2 dtage

\

)

likely to correspond to the situation where the pile ispart of a pile raft foundation for a larse strutture.Since the pile head was restrained, la"rgemomenand shear are experienced at the pile head which arc:r'shown in Figs 11 and 12, respectively.In a small development where the pile foundationsystem is tied by ground beans, the likely pile headcondition is that given by (c) in which the pile headis not allowed to rotate but is partially restrainedagainst lateral movement. In the present problern, itwas assumed that there is only another row of pilefoundations behind the front row which is nearesi tothe excavation and for the typical column spacing,the lateral soil movements were assumed to be halfof that shown in Fig 10. Hence, the partial restraintis due to the back row of piles being tied to the frontrow by ground beams. The simulation of thisboundary condition can be carried out in two stagesas follows.Stage 1: Analyse the pile subjected to lateral soilmovements half of those shown in Fie l0 withboundary condit ions at the pi le head iestrainer 'against rotation but free to nove laterally, \7Stage 2: Subject the pile to the remaining half of thelateral soil movements with boundarv conditions atthe pile head restrained against rotat ion but withlateral movement restrained by the pile at the back.This restraint can be simulated by a spring, thestiffness of which is the lateral stiffness of the pilehead. This st i f fness can be estimated by applying aload at the pi le head instead of the lateral soi lmovements. The estimated spring stiffness for thisproblem was 20,954 kN/m.Using the above procedure, the computed bendingmoments, shear forces and pile deflections from thecumulative effects of stages 1 and 2 in the simulationare shown in Figs 11, 12 and 13, respectively. Asexpected, these results fall in between the results forpile head boundary conditions (a) and (b). The partialrestraint at, the pi le head provides rel ief of th ebending moment and shear force, result ing in asignifrcant reduction of the magnitude of the bendingmoment and shear force at the pile head.

Fig 13Deep excavation problem:influence of pile headboundary conditions onpile deflections.

Fig rr Deep excavationhead boundarymoments.problem: influence of pileconditions on bending

Fig 12 Deep excavation problem: inf luence of pilehead boundarycondit ionson shear forces.

roiaton hovement- frxed lixed--- lixed 2-.tage

Shear force (kN)

rotation movment- fixed fixed--- fixed 2-8tage


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It can be seen from the above analyses that theboundary condit ions at the pile head have asignifrcant influence on the behaviour of the pileswhich was also demonstrated in the earl ier example.Hence. t is imponant that the appropriate boundarycondit ions be identi f ied in the problem underconsiderationand where necessarya higher factor ofsafety applied to account for the uncertaintv of therestraint at the pile head.It is noted that above analyses considered only thesingle pile. The single pile analysis can be extendedto pile groups in the manner described by Chow(1987a,b; 1988) for laterally loaded pi le groups.However, the single pile analysis will likely to beconservative since the presence of group piles willreduce the lateral soil movements.

CONCLUSIONSLateral soil movements arising from the constructionof embankments or excavation for deep basementsinduce additional pile deflections, bending momentsand shear forces in a pile. This problem was analysedusing the frnite element approach described in thisp-aper in which the pile was represented by beamelements and the soil modelled using the modulus ofsubgrade reaction.Comparisons with available well-documented casehistories on piles located adjacent to embankmentssuggest that the method is capable of predicting thegeneral behaviour of the pile foundation sub;e"ct tolateral soil movements. Additional case studies showthat the boundary conditions at the pile head have asignificant influence on the bending moments andshear forces in the pile. A case study on piles adjacentto a deep excavation highlighted lo-" of th"important design considerations.The approach can be used to evaluate the effect oflateral soil movements on pile foundations byinstituting an instrumentation programme wherebyinclinometers can be used to measuie the lateral soiimovements. This will at least provide sorne means ofassessing the impact of such construction activitieson the pile foundations of nearby existing structures.REFERENCESBroms, B.B. (1964a). Lateral resistance of Diles incohesive soi ls. Journal of Soil Mech and FoundEng Div, ASCE, Vol 90, No SM2, 2Z-63.Broms, B.B. (1964b). Lateral resistance of piles incohesionlessoils.Journal ofSoil Mech and FoundEng Div, ASCE, Vol 90, No SM3, 128-1b6.Chow, Y.K. (1987a). Iterative analysis of pile-soil-pile interaction. Geotechnique, Vol AZ, N; B, 821-Chow, Y.K. (1987b). Three dimensional analvsis ofpi le groups.Journal of GeotechnicalEngineering,ASCE, Vol 113, No 6. 63?-651.

Chow. Y.K. (1gfr). Axial and lateral responseof pi legroups erdbedded in nonhomog"n"o.," "oi l".nternational Journal for Numerical an dAnalyt ical Methods in Geomechanics. Vol. 11.621-638.De Beer, E.E. and Walleys, M. G9Z2). Forces nducedin piles by unsymmetrical surcharges on the soilaround the piles. Proc. bth European Conferenceon Soil Mechanics and Foundation Engineering,Madrid, Vol. 7, 325-382.Heyman, L. (1965). Measurement of the influence oflateral earth pressure on pile foundation. proc6th International Conference on Soil Mechanicsand Foundation Engineering, Montreal, Vol. 2,257-260.Meigh, A.C. {1987). Cone penetrat ion test ing.Construction Industry Researchand InformationAssociation.Mindlin, R.D. (1936). Force at a point in the interiorof a semi-infrnite sol id. physics. yol 7, l9E-2O2.Poulos, H.C. (19?3, . Analysis of pi les in soi lundergoing lateral movement. Journal of SoilMechanics and Foundation Engineering, ASCE,

Vol 99, No SM5, 391-406.Poulos, H.G. and Davis, E.H. (1989). pi le foundationanalysis and design. John Wiley & Sons, NewYork.Tschebotarioff, G P (19?3). Foundation, retaining andearth structures. 2nd Edition.

Analysis of Piles Subject to Lateral Soil Movements

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