Analysis Of Pile Foundation Subjected To Lateral And .

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International Journal of Engineering Trends and Technology (IJETT) – Volume-46 Number-2 -April 2017Analysis of Pile Foundation Subjected toLateral and Vertical LoadsThadapaneni Kanakeswararao1, B.Ganesh21,2Department of soil mechanics and foundation engg, Lenora college of Engineering and technology,Rampachodavaram,Thurpu Godavri, Andhra Pradesh, IndiaAbstract - Pile foundations are common foundationsfor bridge abutment, piers and buildings resting onsoft soil strata. The pile is subjected to both verticaland horizontal forces. The objective of the currentstudy is Lateral& Vertical loaded analysis of pile byusing various methods.Vertical load analysis of pile is done by P-Y curvesand Vesic’s methods in cohesive& cohesion lesssoils with different soil parameters.The piles are modelled as linear elements. The effectof soil structure interaction is taken into account byassuming it as vertical and horizontal soil spring(winkler soil spring). Lateral subgrade modulus andvertical subgrade modulus of soil (KH and Kv) iscalculated as per is code 2911.The lateral load analysis is carried out in FEM(Finite Element Method) Staad pro soft ware, L Pilesoftware & by empirical equations (Brom’s methodand Vesic’s method). The above problem solved asper the Brom's method mentioned in IS 2911 andcomparative results are also presented.Keywords — Laterally and Vertically Loaded PileFoundation, P-Y curves, Softwares: staad pro, ENSoft L-pile, empirical equations (Brom’s method andVesic’s method), IS 2911 Part I SECTION I,SECTION II.I.INTRODUCTIONWhen a soil of low bearing capacity extends to aconsiderable depth, piles are generally used totransmit vertical and lateral loads to the surroundingsoil media. Piles that are used under tall chimneys,television towers, high rise buildings, high retainingwalls, offshore structures, etc. are normallysubjected to high lateral loads. These piles or pilegroups should resist not only vertical movements butalso lateral movements. The requirements for asatisfactory foundation are,1. The vertical settlement or the horizontalmovement should not exceed an acceptableMaximum value,2. There must not be failure by yield of thesurrounding soil or the pile material. Vertical pilesare used in foundations to take normally verticalloads and small lateral loads. In the case offoundations of bridges, transmission towers,offshore structures and for other type of hugestructures, piles are also subjected to lateral loads.Extensive theoretical and experimental investigationISSN: 2231-5381has been conducted on single vertical piles subjectedto lateral loads by many investigators. Generalizedsolutions for laterally loaded vertical piles are givenby Matlock and Reese (1960). The effect of verticalloads in addition to lateral loads has been evaluatedby Davisson (1960) in terms of non-dimensionalparameters. Brom’s (1964a, 1964b) and Poulos andDavis (1980) have given different approaches forsolving laterally loaded pile problems. Brom'smethod is ingenious and is based primarily on theuse of limiting values of soil resistance. The methodof Poulos and Davis is based on the theory ofelasticity. The finite difference method of solvingthe differential equation for a laterally loaded pile isvery much in use where computer facilities areavailable. Matlock (1970) have developed theconcept of (p-y) curves for solving laterally loadedpile problems.Many numerical techniques such as FiniteDifference Method, Variational Method BoundaryElement Method Finite Element Method are beingused for the engineering analysis of Piles. FiniteElement Method itself as a powerful numericaltechnique, especially for Geotechnical Engineeringproblems complicated geometrical behaviour andboundary conditions. Using Finite element theseproblems can be solved easily.II.GENERALSOLUTIONSFORVERTICAL PILES1) Differential Equations of ElasticCurves for Vertical Piles SubjectedTo Lateral LoadsThe standard differential equations for slope, moment,shear and soil reaction for a beam on an elastic foundationare equally applicable to laterally loaded piles.The relationships between y, slope, moment, shearand soil reaction at any point on the Pile ishttp://www.ijettjournal.orgPage 113

International Journal of Engineering Trends and Technology (IJETT) – Volume-46 Number-2 -April 2017Z x/ Teqn (3.14)III.where El is the flexural rigidity of the pile material.The soil reaction p at any point at a distance x alongthe axis of the pile may be expressed asp -Esyeqn 3.5where “y” is the deflection at point x, and Es is thesoil modulus. Eqs (3.4) and (3.5) when combinedgiveswhich is called the differential equation for the elasticcurve with zero axial load.2) Non-DimensionalSolutionsforVertical Piles Subjected To LateralLoadsMatlock and Reese (1960) have given equations forthe determination of y, S, M, V, and p at any point xalong the pile based on dimensional analysis. Theequations areVERTICAL LOAD ANALYSIS OFPILES1) Vertical Load Analysis Of Piles By P-YCurvesLoad Transfer MechanismWhen the ultimate load applied on the top of the pileis Qu, a part of the load is transmitted to the soilalong the length of the pile and the balance istransmitted to the pile base. The load transmitted tothe soil along the length of the pile is called theultimate friction load or skin load Qf and thattransmitted to the base is called the base or pointload Qb. The total ultimate load Qu is expressed asthe sum of these two, that is,Ultimate Load Bearing CapacityQu Qb Qf qbAb fsAS-- (1)Where Qu ultimate load applied on the top of thepileqb ultimate unit bearing capacity of the pile at thebaseAb bearing area of the base of the pileAs total surface area of pile embedded belowground surfacefs - unit skin friction (ultimate)Allowable Load Bearing CapacityA safety factor of 2.5 is normally used.Therefore we may writeQa Qb Q f2.5--- (2)In case where the values of Qb and Q. can beobtained independently, the allowable load can bewritten asQa where T isexpressed astheISSN: 2231-5381relativestiffnessfactorQb Q f 3 1.5---- (3)2) General Theory For Ultimate BearingCapacity According To Vesic (1967)According to Vesic (1967)The total failure load Qu may be written as followsQu Qu Wp Qb Q f WpEq (4)Where Qu load at failure applied to the pileQb base resistanceQf shaft resistanceWp weight of the pile.http://www.ijettjournal.orgPage 114

International Journal of Engineering Trends and Technology (IJETT) – Volume-46 Number-2 -April 2017Ks average lateral earth pressure coefficientγ angle of wall friction.Cohesive SoilsFor cohesive soils such as saturated clays (normallyconsolidated), we have for / 0, N - 1 and N 0.The ultimate base load from Eq. (5) isThe general equation for the base resistance may bewritten asEq (5)where d width or diameter of the shaft at baselevelq' 0 effective overburden pressure at the base levelof the pileAb base area of pilec cohesion of soilγ effective unit weight of soilNc, Nq, Nγ bearing capacity factors which take intoaccount the shape factorCohesion less SoilsFor cohesion less soils, c 0 and the term 1I2ydNybecomes insignificant in comparison with the termqoNq for deep foundations. Therefore Eq. (5) reducestoQb q NqAb qbAbEq (6)Eq. (15.4) may now be written asQb Qu Wp q NqAb Wp QfEq (7)The net ultimate load in excess of the overburdenpressure load qoAb isEq (8)If we assume, for all practical purposes, Wp andq'oAb are roughly equal for straight side ormoderately tapered piles. Eq. (8) reduces toWhere As surface area of the embedded length ofthe pileq'o average effective overburden pressure over theembedded depth of the pileISSN: 2231-5381α adhesion factorcu average undrained shear strength of clay alongthe shaftcb undrained shear strength of clay at the baselevelNC bearing capacity factorVertical Load Bearing Capacity Of PileCalculations:From analysis of structure, it is found that maximumaxial load in working condition is 2932kN. Pilecapacity is checked for above value of axial loadrequired to be transmitted. Bearing capacity of pilesis calculated as per procedure given in Appendix BIS: 2911-1979 part 1/section- IIUltimate Skin ResistanceQs (α*C K*Pdi*tanδ)*AsiUltimate End Bearing CapacityQb (Cp*Nc Pd*Nq 0.5*γ*B*Nγ)*ApUltimate Bearing Capacity of SoilQu Qs Qb-WWhere,α reduction factor,C average cohesion throughout layer,K coefficient of earth pressure,Pdi effective over burden pressure for ith layer,δ angle of wall friction between soil and pile,Asi surface area of pile for ith layer,Cp cohesion at the base of pile,B diameter of pile,Ap area of pile tip,W weight of pile,γ effective unit weight of soil,Nc, Nq, Nγ bearing capacity factors as per IS:2911-1979 part 1/sec 2http://www.ijettjournal.orgPage 115

International Journal of Engineering Trends and Technology (IJETT) – Volume-46 Number-2 -April 2017Calculation Of Skin frictional resistance:Layer 1:Layer thickness 6.53 mγsub 7.75 kN/m3, C 150 kN/m2Angle of internal friction 0 degSPT ‘N’ value 38Level of water table ( ) 5.10 mLength of pile above bed level 11.245 mCritical depth 20 times dia.Factor of safety 2.5Surface area 20.518 m2Reduction factor 0.3Wall friction between soil and pile 0 degCo-efficient of earth pressure 2Avg. over burden pressure 50.6075 kN/m2Design over burden pressure 50.6075 kN/m2Skin frictional resistance, Qsf1 923 kNLayer 2:Layer thickness 9 mγ 7.75 kN/m3, C 80 kN/m2Angle of internal friction 0 degSPT ‘N’ value 26Surface area 28.274 m2Reduction factor 0.3Wall friction between soil and pile 0 degCo-efficient of earth pressure 1Avg. over burden pressure 69.75 kN/m2Design over burden pressure 120.3575 kN/m2ISSN: 2231-5381Skin frictional resistance, Qsf3 1131 kNLayer 3:Layer thickness 3 m, γ 0 kN/m2Angle of internal friction 35 degSPT ‘N’ value 50Surface area 9.425 m2Reduction factor 0.3Wall friction between soil and pile 35 degCo-efficient of earth pressure 2Avg. over burden pressure 23.25 kN/m2Design over burden pressure 155 kN/m2Skin frictional resistance, Qsf4 2045.8 kNTotal Skin Frictional Resistance, Qsf 4778.5 kNEnd Bearing Resistance:Layer 4:Angle of internal friction 35 degPile tip area 0.7853 m2Nq 50, Nγ 48Design over burden pressure 155 kN/m2End bearing resistance at pile tip, Qb 4241 kNWeight of Pile:Weight of pile above scour level Wp1 220.893 kNWeight of pile below scour level Wp2 301.548 kNTotal ultimate resistance of pileQsf Qb – Wp2 8717.452 kNAllowable load (8717.452 / F.S.) – Wp1 3266 kN.From above calculations,Required depth 26.03m below design seabed levelE.G.L. ( ) 1.15 m CDhttp://www.ijettjournal.orgPage 116

International Journal of Engineering Trends and Technology (IJETT) – Volume-46 Number-2 -April 2017IV.LATERALLY LOADED ANALYSISOF PILE1) Laterally Loaded Analysis By UsingSubgrade Reaction Using Vesics Method:A pile may be subjected to transverse force from anumber of causes, such as wind, earthquake, watercurrent, water waves, earth pressure, effect ofmoving vehicles or ships, plant and equipment, etc.The lateral load carrying capacity of a single piledepends not only on the horizontal subgrademodulus of the surrounding soil but also on thestructural strength of the pile shaft against bendingconsequent upon application of a lateral load. Whileconsidering lateral load on piles, effect of othercoexistent loads including the axial load on the pileshould be taken into consideration for checking thestructural capacity of the shaft. There are variousmethods available for analysis of laterally loadedpiles such as Equivalent Fixity Depth Approach Asper IS: 2911-1979, Subgrade Modulus Approach(FEM or Matrix method), Closed Form Solution,Non dimensional Method, p-y Curve Method,Brom’s Method, Vesic’s Method etc.A horizontal load on a vertical pile is transmitted tothe subsoil primarily by horizontal subgrade reactiongenerated in the upper part of the shaft. A single pileis normally designed to carry load along its axis.Transverse load bearing capacity of a single piledepends on the soil reaction developed and thestructural capacity of the shaft under bending.In case the horizontal loads are of higher magnitude,it is essential to investigate the phenomena usingprinciples of horizontal subsoil reaction adoptingappropriate values for horizontal modulus of the soil.In this study, piles are analyzed using modulus ofsubgrade reaction and lateral resistance offered bysoil is modeled by providing springs having stiffnessderived using modulus of subgrade reaction. Themodulus of subgrade reaction is seldom measured inlateral pile load test. Node values of “Ks” arerequired in FEM solution for lateral piles.However in absence of test results, this value may beapproximated as per procedure given below: As perVesic (1961), modulus of subgrade reaction can becomputed using stress-strain modulus Es based on as,Where Es, Ef modulus of soil and footingrespectively, in consistent units B, If footing widthand its moment of inertia based on cross section inconsistent unitsOne can obtain ks from ks’ as,Since the twelfth root of any value multiplied by0.65 will be close to 1, for practical purposes theVesic’s equation reduces to,ISSN: 2231-5381Now, we know that immediate (elastic) settlement,Where qo foundation pressureB width of foundationμ Poisson’s ratioIf influence factorBut we know ks ratio of soil pressure to deflectionBut since one does not often have values of Es, otherapproximations are useful and quite satisfactory ifthe computed deflection is reasonable. It has beenfound that bending moments and computed soilpressure are not very sensitive to what is used for‘Ks’ because the structural member stiffness isusually 10 or more as great as soil stiffness asdefined by ‘Ks’.Vesic has suggested the following for approximating‘Ks’ from the allowable bearing capacity qa basedon geotechnical data:Where, qa is in kPa. This equation is based onassumption that ultimate soil pressure occurs at asettlement of 0.0254 m. For other values of ΔH 6,12, 20 mm etc., the factor 40 can be adjusted to 160,83, 50 etc. 40 is reasonably conservative but smallerassumed displacement can always be used. The mostgeneral form for either horizontal or lateral modulusof subgrade reaction is,A s constant for either horizontal or verticalmembersBs coefficient based on depth variationZ depth of interest below groundn exponent to give ks the best fit.We know that ultimate bearing capacity is given by,Observing that,The C factor is 40 for SI units and 12 for FPS, usingthe same reasoning that qult occurs at a0.0254-m and 1-in. settlement but with no SF, sincethis equation directly gives qult .http://www.ijettjournal.orgPage 117

International Journal of Engineering Trends and Technology (IJETT) – Volume-46 Number-2 -April 2017Table-A may be used to estimate a value of ‘Ks’ todetermine the correct order of magnitude of thesubgrade modulus obtained using one of theapproximations given here. Obviously if a computedvalue is two or three times larger than the table rangeindicates, the computations should be rechecked fora possible gross error. Note, however, if you use areduced value of displacement (say, 6 mm or 12 mm)instead of 0.0254 m you may well exceed the tablerange other than this, if no computational error (or apoor assumption) is found then use judgment inwhat value to use.Range of modulus of subgrade reaction ks.SoilKs ( kN/m3)Loose sandMedium dense sand4800-60009600-80000Dense sand64000-128000medium32000-80000Slitymediumdense sandClayey soilqa 200 kPa24000-48000Clayeydense sand200kPa qa 800qa 800 kPa12000-2400024000-48000 48000following formula for finding spring constantsrepresenting soil in the model.Calculation of Soil Spring Constant:Input Data:Design scour level ( ) 1.15 mDepth of consideration 26.00 mDiameter of pile 1.00 mThe horizontal modulus of subgrade reactionExponent n 0.5Size factor Cm 1.555824Factor depending on displacement of pile C 40Soil data and calculation is as under:For layer 1,Thickness of layer 5mAngle of internal friction 0Cohesion of soil 150 kN/m2Submerged unit weight of soil 7.75 kN/m3Bearing capacity factor, Nc 5.14, Nq 1, Nγ 0As 1.555*40* (150*5.14 0.5*7.75*1*0) 47981.6 kN/m3Bs 1.555*40* (7.75*1) 482.32 kN/m3Ks 47981.6 (482.32* Z 0.5) kN/m3Similarly for other layers, Ks is found out and fromthat, value of spring constant is also found out forevery 1m interval as per equations given above.Values of spring constants throughout Similarly forother layers, ‘Ks’ is found out and from that, valueof spring constant is also found out for every 1minterval as per equations given above. Values ofspring constants throughout the entire depth arecalculated using spread sheet “Spring Constant”.Calculated values are shown below in Table-C andDISSN: 2231-5381http://www.ijettjournal.orgPage 118

International Journal of Engineering Trends and Technology (IJETT) – Volume-46 Number-2 -April 2017ISSN: 2231-5381http://www.ijettjournal.orgPage 119

International Journal of Engineering Trends and Technology (IJETT) – Volume-46 Number-2 -April 20172) Lateral Load Analysis Using BromsMethodAnalysis of piles using Broms methods by IS 2911Analysis of a single pile according to Broms isdescribed in Broms, 1964. This method exclusivelyassumes a pile in the homogeneous soil. Thus theanalysis method does not allow for layered subsoil.The lateral soil resistance for granular soils andnormally consolidated clays which have varying soilmodulus is modelled according to the equation:wherep lateral soil reaction per unit length of pile atdepth z below ground level;y lateral pile deflection; andϕh modulus of subgrade reaction for which therecommended values are given in IS 2911Modulus of Subgrade Reaction for GranularSoils, ϕh, in kN/m3Table D-Parameters for the M4kN/m21.44x10-42.18 108My1((kNm)231My2(kNm)304Table E-Parameters for the SandEffective unit Friction angle, φweight,γkN/m31032.3Strain at 50% ofthemaximumstress, ε500.012Step 1: Open STAAD Pro, create a model of thestructure, and assign properties to the model, asshown in Figure. Once the properties are assigned,select the pile.Step 2: Open the Staad pro. By clicking“SelectPiles”; the pile dimensions are shown in thetable. Then, by clicking “Strata, Vertical Axis, andLoading Directions”, select the directions associatedwith the deposit of the strata, global vertical axis inSTAAD Pro, and lateral loading in global coordinatesystem in STAAD ProThe lateral soil resistance for preloaded clays withconstant soil modulus is modelled according to theequation:3) Lateral Load Analysis Using Staad ProLaterally loaded single pipe pile in soft clay,representative of a test performed was analyzed inthe StaadPro Parameters of the pile and soft clay aretabulated in Tables D and E. The lateral load wasapplied to the pile head at a distance 0.0635 m (2.5in) above the ground line, and the water table waskept above the ground line.ISSN: 2231-5381http://www.ijettjournal.orgPage 120

International Journal of Engineering Trends and Technology (IJETT) – Volume-46 Number-2 -April 2017The Structure Model of Group of 9 piles afterbeing assigned with(a) Elastic Soil springs(b) Multi linear Soil Springs4) Lateral Load Analysis Using LpileSoftwareThe LPile software uses a finite difference scheme toanalyze individual laterally loaded piles. Todetermine pile displacements and stresses, the basicdifferential equation for a beam-column is solvedusing a finite difference approximation. Thedifferent subsoil layers and their properties weremodelled along with the physical and elasticpropertiesofthepile.(a)(b)Comparison of Lateral Displacement of the PileGroup(a)Interior Pile(b)Exterior Pile; at Ft 1500 kN (337 k

Weight of pile above scour level Wp1 220.893 kN Weight of pile below scour level Wp2 301.548 kN Tota l ultimate resistance of pile Qsf Qb – Wp2 8717.452 kN Allowable load (8717.452 / F.S.) – Wp1 3266 kN. From above calculations, Required depth 26.03m below design seabed level E.G.L. ( ) 1.15 m CD . International Journal of Engineering Trends and Technology (IJETT) – Volume .

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