Analyses Of Lateral Loaded Piles With P-Y Curves .

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Analyses of Lateral Loaded Piles with P-Y Curves - Observations on theEffect of Pile Flexural Stiffness and Cyclic LoadingMiguel A. Pando, Ph.D., P. Eng.Associate Professor, UNC CharlotteNCDOT 7th Geo3 T2, Raleigh, NC, Thursday, April 04, 2013Session 3B - Geotechnical II (Room: Pinehurst) - Paper: 3B-1 A49

Outline Background Beam on Elastic Foundation (BEF) Subgrade Reaction Beam Theory (related to net soil reaction per unit length (P)and pile lateral deflection (Y) P-Y curves Elements of a P-Y curve (preferred terminology) Commonly used P-Y Curves (empirical basis) The analytical methodology Possible limitations/challenges Influence of pile cross section and EI? Effects of lateral load cycles? Summary and Conclusions


Beam on Elastic Foundation (BEF) After Winkler (1867) aka as Beam on WinklerFoundation (BWF)VERTICALHORIZONTALkh Modulus of Lateral (Horizontal) Subgrade Reaction [F/L3]Typically linear representation of soil reaction.

Vertical Modulus of Subgrade Reaction Modulus of subgrade reaction (k)Is it a soil property? NOFooting, rafts, pavement designZinfWestergaard’s work in 1920’sq k D (used by structural engineers)– q applied or contact pressure [F/L2]– D settlement of footing under q [L] k q/D slope (linear springconstant) modulus of subgradereaction [F/L3]q (F/L2)BEsq (F/L2)1ksecD (L)1k

Vertical Modulus of Subgrade Reaction(Continued) Elastic settlement of circular footing: 𝑞.𝐵.(1 𝜇2 )𝐼𝐸𝑠 m 0.5 (undrained) 0.3 (drained) Es Eu (undrained) vs E’ (drained) 𝑘𝑣 𝑞𝐸𝑠 𝐼.𝐵.(1 𝜇2 ) Not a fundamental soil property Not readily measured Depends on many factors such as size and shapeof footing, type of soil, relative stiffness of footingand soil, vary along footing, vary with time, etc.

Beam theory

Table 1 Relationships commonly used for elastic piles in flexionVariableFormulaUnitsDistance along the length of the pile(measured from pile head)x[L]Distance to neutral axis within pilecross sectionz[L]Deflectiony[L] Slope or rotation of pile sectionCurvatureBending momentShear forcedydxd2 y 2dxd2 yM E p Ip 2 E p Ip dxd3 yV E p Ip 3dx[Dimensionless][Radians/L][F x L][F]Axial loadQ[F]Soil reaction (or load intensity)d4 yp E p Ip 4dx[F/L]Notes: EpIp flexural stiffness of pile, where Ep elastic modulus of pile material, and Ip moment ofinertia of pile cross section with respect to the neutral axis

Relationships between variablesa) Pile loadingFb) Net soil reaction c) Pile deflectionypd) Slopee) Bending moment yMxp (soil resistance)dxpleftprightMpV dVVdxM dMxxxxx

The Genesis of the P-Y Curve:B(Reese and Van Impe, 2001)

P-y curve Method


p-y model used for analysis oflaterally loaded pilesx1Pilex2Nonlinearspringsxn-1Soil-pile reaction, p (F/L)LateralloadIncreasing depth, xPile deflection,y (L)p-y curvesxnx

Careful with confusingterminology: Horizontal modulus of subgrade reaction(kh): relates lateral pressure qh kh x y[units: F/L3] Subgrade reaction modulus (K): p K x y[units: F/L2] K kh x B Coefficient of subgrade reaction (nh): rate ofincrease of subgrade reaction modulus (K)with depth (z): K nh x z [units: F/L3]

Net soil reaction per unit length of pile (F/L)Soil reaction (p-y curve) and HorizontalModulus of Subgrade Reaction (kh)(kh B)1(kh sec B)1Type equationhere.qh kh . yUnits:qh [F/L2]y [L]kh [F/L3]qh p/Bp (kh x B) . yCareful units of kh same as kv (F/L3)but genesis is different

Epy-maxpy-max(p,y)pultEpyp Epy . yp-y modulus, Epy (F/L2)Soil reaction, p (F/L)Elements of a p-y curvePile deflection, y (L)Figure 3 Typical p-y curve and resulting p-y modulusEEpy-maxpy-maxPile deflection, y (L)

Elements of a p-y curve1. Initial slope Epy-max:– Considerable scatter of reported values.– Most Epy-max kh x B– Some P-Y curves have Epy-max – From ultimate load theories(e.g., Broms, E1964):Epy-maxE(p,y)pultEpyp Epy . yPile deflection, y (L)p-y modulus, Epy (F/L2)Soil reaction, p (F/L)2. Pult (asymptotic value):py-max Clays: 9SuB; Sands: 3Kps’vB or Kp2s’vB3. Transition curve(s) from origin toPult.Pile deflection, y (L)

Example p-y curves in Sands(Reese et al. 1974) Pult f( , stress level) Epy-max: related to soilstiffness, B, etc,p (F/L)CpultBAEpy-max[Note: b pile width]1b/603b/80Figure 5 Elements of a characteristic p-y curve for sand based ony (L)

P-Y Curves for Different Soil TypesreactionSoilSoilreactionStiff ClaySandSandSoil w/Soft ClayLateral deflection

Experimental P-Y Curves Lateral load tests on instrumented piles Vey few high quality tests are available Basis for P-Y Curves proposed in theliterature Typically from deflected shapemeasurements (e.g., inclinometers) Better if from Moment (or curvature)measurements using closely spaced pairs ofstrain gages (very few of these)

Additional InstrumentationFront RowDeflection, mm0.020.040.001Depth From Top of Pile, m2345678910Average Load per Pile35.6 kN48.9 kN66.7 kN84.5 kN97.9 kN60.0

P-Y Curves from Experiments

P-Y Curves from Experiments𝑅𝑒𝑐𝑎𝑙𝑙 𝑓𝑟𝑜𝑚 𝑏𝑒𝑎𝑚 𝑡ℎ𝑒𝑜𝑟𝑦:𝑑2𝑀𝑝 𝑑𝑥 2

Commonly used p-y curves fordifferent soilsSoil Type and ConditionReferenceSoft clay below the water tableMatlock (1970)Stiff clay below the water tableReese, Cox, and Koop (1975)Stiff clay above the water tableWelch and Reese (1972),Reese and Welch (1972)SandsReese, Cox, and Koop (1974)SandsAPI RP2A (1991)Soils with cohesion and frictionEvans and Duncan (1982)Weak rockReese (1997)Strong rockNyman (1982)(adapted from Reese and Isenhower, 1997)


Software for p-y based analysis: Solve beam equation with finite differenceor finite elements COM624 LPILE FB-Pier (FB-Multipier) Matlab or Mathcad spreadsheets

Other Methodologies Strain Wedge Model FEM Characteristic Load Method (LPILE based)


Potential Limitations P-Y Curves The soil is idealized as a series ofindependent nonlinear springsrepresented by p-y curves. Therefore, thecontinuous nature of the soil is notexplicitly modeled.

Potential Limitations P-Y Curves The results are very sensitive to the p-ycurves used. The selection of adequatep-y curves is the most crucial problemwhen using this methodology toanalyze laterally loaded piles (Reeseand Van Impe 2001). P-Y curves in literature are empirical innature. Need to carefully reviewapplicability of the selected curves.

On selection of appropriate p-ymodulus and p-y curves Important and difficult task. Selection of values of initial p-y modulus, Epy-max,although related to the soil modulus, is alsorelated to the interaction between the pile and thesoil. Reese and Van Impe (2001) point out that p-ycurves and modulus are influenced by several pilerelated factors, such as: Pile type and flexural stiffness,Type of loading (monotonic or cyclic),Pile geometry,Pile cap conditions, andPile installation conditions.

Potential Limitations (Continued)Cross section of pile Most P-Y curves only depend on pile width(B). Shape or Depth is not explicitlyincluded in P-Y curves currently in theliterature.p1Bp2Bp3Bp2 p 1 p3

Potential Limitations (Continued)Flexural Stiffness (EI) of pileSoil reaction P-Y curves don’t directly incorporatedeffects of EI of pile (Only in pile model).Ashour and Norris (2000)Lateral deflection

400Soil-Pile Reaction, p, kN / mBased on the StrainWedge Model AnalysisThe traditional p-y curve (in LPILE) doesnot account for the pile/shaft EI variationEIStif f PileFlexible Pile 0.1 EI300Dense Sand200100Loose Sandp-y Curve at a Depth of 1.22 m004080Pile Deflection, y, mm120Ef f ect of Pile Bending Stif f ness on the p-y Curve in Sand

EI EffectsSoil Reaction, p (kN/m)DepthLateral Deflectionp 170 kN/mp 120 kN/mLateral Deflection, y (m)

Route 351 Bridge Case History

Route 351 Bridge Case History

Route 351 Bridge Case History

Route 351 Bridge Case History

Lateral Cyclic loading on Piles Limited experimental data. API P-Y curves for sands suggestincorporating 10% degradation of p-ycurve for offshore piles. A few experimental studies developedcyclic P-Y curves

Effect of Cyclic LoadingSingle Pile Test160140Load (kN)1201008060401st Cycle Peaks15th Cycle Peaks2000204060Deflection (mm)80100

Cyclic P-Y Curves by Little and Briaud (1988): Most experiments up to 20 lateral loadcycles. 𝑦𝑁 𝑦1 . 𝑁𝑎

Cyclic P-Y Curves by Long and Vanneste (1994): 34 experiments (some up to 500 lateralload cycles). Modified Pn and Yn as follows: 𝑃𝑁 𝑃1 . 𝑁 0.4𝑡 𝑦𝑁 𝑦1 . 𝑁0.6𝑡

Possible limitation with cyclicloading Little experience and scarce availability ofexperimental data. Available experiments very few loadcycles. Wind action on highway signs, soundbarrier foundations; Or loading on bridgepiles (thermal, current, wave, etc) caninvolve N 104 load cycles during piledesign life.

Experiments on Model Pile byPeng et al (2006) (N 104 cycles)(Experiment)

Summary & Conclusions The P-Y Curve based methodology for analysis oflaterally loaded piles is easy and reliable Empirical in nature, but backed by decades ofexperience. However, several items may still need additionalresearch to overcome some identified possiblelimitations. (i.e., still room for improvement). Also practitioners should be aware of alternativeemerging methodologies such as the SWM (Needto incorporate into design tool box) (Several DoT’salready using).

THANK YOU!Contact information:Dr. Miguel A. PandoAssociate ProfessorCEE Dept, UNC

inertia of pile cross section with respect to the neutral axis. Relationships between variables lem p M dM V dV V M dx x x x x x F y p y I M x dx p right p (soil resistance) p left a) Pile loading b) Net soil reactionc) Pile deflection d) Slope e) Bending moment. The Genesis of the P-Y Curve: (Reese and Van Impe, 2001) B . P-y curve Method . P-Y CURVES . p-y model used for analysis of .

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