THE STRUCTURAL DESIGN OF PILE FOUNDATIONS BASED ON LRFD .

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THE STRUCTURAL DESIGN OF PILE FOUNDATIONS BASED ON LRFDFOR JAPANESE HIGHWAYSHideaki Nishida1,Toshiaki Nanazawa2, Masahiro Shirato3 ,Tetsuya Kohno4, and Mitsuaki Kitaura 5AbstractOne of the motivations for applying reliability-based design to geotechnicalengineering is to confirm that more reasonable and cost-effective design results will beobtained when owners and designers invest in more detailed geotechnical investigations.In this paper, we propose load and resistance factor design for the structural design of pilesin pile foundations for Level 1 earthquake situation. The proposed load factors in the studyare a function of the chosen soil investigation/testing and piling method, which is appliedto the bending moment in piles. Therefore, better choices of soil investigation/testing andhigh quality piling method will result in more reasonable design results.IntroductionReliability-based design approaches, such as load and resistance factor design(LRFD) and partial factor design have been widely accepted in structural design. Thesedesign methods are also applied to several foundation design codes. One of the motivationsfor applying reliability-based design in geotechnical engineering is to confirm that moredetailed geotechnical investigations will result in more reasonable and cost-effectivedesign. For example, the standard penetration test (SPT) is conducted for every project andalmost all design parameters can be derived using empirical transformation equationsbased on SPT-N values, though other soil investigations are carried out less frequently.However, the uncertainty in the Young’s modulus of soil depends on the adoptedgeotechnical measurement, testing method and soil types.As shown in Fig. 1, the peak bending moments at the pile top and undergroundgovern the structural design of piles. For example, when the surrounding soil is relativelysoft or when the number of pile rows is relatively large, a sway deformation mode prevailsand the pile-top bending moment should be the (absolute) maximum bending moment. Onthe other hand, when the surrounding soil is relatively hard or when the number of pile1Senior Researcher, CAESAR PWRIChief Researcher, CAESAR, PWRI3Senior Researcher, NILIM4Researcher, CAESAR, PWRI5Former Exchange Researcher, CAESAR, PWRI2

rows is relatively small, a rotation or inclination deformation mode prevails, and theunderground peak bending moment should be the maximum bending moment. Thisindicates that the variation in stiffness of surrounding soil or axial resistance of piles is amajor source of uncertainty in the calculated bending moment in piles.However, load and resistance factors for the structural design of foundationstructural members are usually the same as those used in typical structural design and theyhave no relationship with geotechnical aspects.This study proposes a structural LRFD concept for piles of foundation consideringthe difference in reliability of geotechnical testing/investigation methods and pilingmethods so that design codes can support the effort to achieve more reasonable soilinvestigations and piling methods.MomentHorizontalLoadCase AHorizontal MomentLoadPile topCase BFigure 1 Bending moment distribution in a pileVariation in the Coefficient of Horizontal Subgrade ReactionA horizontal load test database of piles is available in PWRI with boring log data.The observed coefficient of subgrade reaction at a displacement level of 1% of the pilediameter can be estimated using the beam-on-Winkler foundation theory, assuming auniform coefficient of horizontal subgrade reaction, where 1% of the pile diameter isdefined as the reference displacement level to estimate the coefficient of subgrade reactionin the Japanese Specifications for Highway Bridges. The average coefficient of horizontalsubgrade reaction for the subsoil layers can also be calculated using typical empiricalequations shown in the Japanese Highway Bridges Design Specifications. The coefficientof horizontal subgrade reaction is a function of Young’s modulus of soil. Whereas theJapanese Highway Bridges Design Specifications shows that the Young’s modulus of soil,E, is based on the secant modulus of an unloading-reloading cycle obtained by a plateloading test, an alternative empirical equation to derive the Young’s modulus of soil froman SPT-N value is also provided as E 2,800N (kN/m2), because soil testing other thanSPT is not often conducted. Accordingly, the model error in estimating the coefficient of

the subgrade reaction can be derived by comparing the observed and calculated values forthe case in which SPT-N values are used to estimate the Young’s modulus of soil.The ordinate indicates the ratio of the observed value to the calculated value of thecoefficient of horizontal subgrade reaction. The abscissa indicates the average SPT-Nvalue, Nave, for the subsoil layers over the characteristic pile length, , [(kB) / (4EpIp)]1/4(1)where k is the coefficient of subgrade reaction, B is the foundation width (i.e., pilediameter), and EpIp is the bending rigidity of the pile. The governing soil classification forthe subsoil layers within the characteristic pile length is indicated by different symbols. Forsubsoil layers having an SPT-N value smaller than 5, even the bias, k, ranges from 1 to 4.For subsoil layers having an SPT-N value not smaller than 5, the bias, k, is approximately1.0 and the coefficient of variation, COVk, is 0.60 for sandy soils and 0.70 for cohesivesoils.The model error in the estimation of the coefficient of subgrade reaction, k, iscomprised of the model error in the estimation of the Young’s modulus of soil, E, and thetransformation error from the Young’s modulus of soil, E, to the coefficient of subgradereaction, k. The bias k and the coefficient of variation COVk of the subgrade reaction, k,are given as follows: k E T(2)COVk2 COVE2 COVT2(3)where E and COVE are the bias and COV of the Young’s modulus of soil, E, and T andCOVT are the bias and COV of the transformation error from E to k. Accordingly, theuncertainty in k is a function of the uncertainty in E that depends on the choice of soilinvestigation and testing method as well as soil classification.The PWRI database indicates that the empirical equation of E 2800N (kN/m2) hasa bias, E, and coefficient of variation, COVE, of approximately 1.0 and 0.55 for sandysoils, where the data for cohesive soils is not available. Finally, based on Eq. (3), we canapproximate the COV of the transformation error from E to k, COVT as 0.25. This value isconsidered independent of the soil investigation method.Based on a study by Phoon and Kulhawy, the uncertainty in estimating the Young’smodulus of soil, E and COVE, is modeled as shown in Table 1 for several soilinvestigation and testing methods. Finally, using Eq. (3), the values of E and COVE shownin Table 1 and the transformation error from E to k, E 1.0 and COVE 0.25, theuncertainty in the coefficient of subgrade reaction can be set as listed in Table 2 as afunction of soil investigation methods and soil classification.

Table 1 Uncertainty in the Young’s modulus of soilSoil investigation / testingPressure meter test (PMT, Direct)Laboratory test (Lab, Direct)SPT-N (Transformation)Uncertainty in EPMT or ELabCOVE E1.00.301.00.301.00.55Table 2 Uncertainty in the coefficient of subgrade reactionSoil investigation /testingPile load testPressure meter test orlaboratory testOnly SPTPrevailing soil Uncertainty in kconditionBiasCOV 1.00.25 1.00.45SandyCohesiveNave 51.01.01.00.600.701.00Variation in the Axial Pile Spring ConstantIn the current Japanese design specification, axial pile spring constant whichinstalled at the pile top is modeled as function dependent on the rigidity of pile and pilelength. However, the estimation accuracy is low especially the case of short pile or highrigidity pile.In order to improve estimation accuracy of Kv, estimation equation is newlyproposed. Displacement at pile top depends on not only the rigidity of pile but also thedeformation of the tip of the pile. Therefore, displacement at the top of the pile can beexpressed by the sum of pile deformation and displacement at the tip of pile shown thisequation, and Kv is expressed as Eq(4).KV 14γyL 1 γy 22 EAπD p kv(4)Where, y:Estimated tip transmitting ratio which the pile is yield at the top of pile(0 gy 1) . It is assumed as y X 10d 10d: Estimated tip transmitting ratio which the displacement of the top ofpile is reached at 10% of pile diameter. It is assumed as 10d Rp / RNuRp:Ultimate bearing at the tip of pile estimated by using bearing

estimation equation( qd・A)RNu:Ultimate Bearing estimated by using bearing estimation equationX:Modification coefficient to estimate tip transmitting ratio which thepile is yield at the top of pile shown in Table 3ζ:Modification coefficient to estimate deformation of pile shown in Table 3 :Modification coefficient to estimate displacement of the tip of pile shown in Table 3Table 3 Modification coefficientsPilling MethodXDriven pile methodVibro-hammer methodCast-in-place RC pile MethodBored pile methodSteel pipe soil cement pile methodScrewed steel pile methodPre bored pile method0.890.980.620.760.720.780.69 0.630.300.310.400.20Cohesive0.420.47-This equation includes three modification coefficients, X, ζ and . Thesecoefficients were adjusted to estimate the Kv values obtained by vertical pile loading testresults. Fig.2 shows the comparison of estimated and measured Kv in case of cast-in-placeRC pile. It is found that the improved Kv estimates the measured one well in comparisonwith the conventional one.Table 4 shows the statistic of uncertainty of model error of the Kv. Thecharacteristic point is that the each bias of proposed Kv is approx.1.0. This means that theproposed Kv is estimated the average of Kv well.2MeasuredKv(GN/m)1.6j・m/NiG1.2・l・vKェ 0.8・タ・0.4000.40.81.21.62計算 Kv 値 (GN/m)Estimated Kv(GN/m)Figure 2 Estimated and Measured Kv relationships (Cast-in-place RC pile)

Table 4 Uncertainty of model error of axial pile spring Constant KvConventionalProposedPiling MethodDriven pile methodVibro-hammer methodCast-in-place RC pile MethodBored pile methodSteel pipe soil cement pile methodScrewed steel pile methodPre bored pile ata2943333122013Design EquationIn allowable stress design, both the tensile stress in reinforcement and the compressivestress in concrete are checked. Accordingly, the present study proposes the followingLRFD equations for the pile bending moment: Mcal Y MY Mcal U MU(5)(6)where is the load factor or modifier that considers the uncertainty in the calculatedpile bending moment in the pile, Y and U are the resistance factors for yield andmaximum bending moment strengths, respectively, Mcal is the calculated pile bendingmoment in the pile, and MY and MU are the yield and maximum bending moment strengthsof the pile, respectively. The yield bending moment strength, MY, agrees with the bendingmoment at which a reinforcement bar becomes plastic and the maximum bending momentstrength, MU, agrees with the bending moment at which the bending strain in concretereaches the compressive collapse strain. Based on above considerations, it is expected thatthe load factor, , that is applied to the calculated bending moment in piles becomes afunction of the soil investigation/testing method and soil classification, because thedistribution of the pile bending moment in the depth direction varies with the uncertaintyin the coefficient of subgrade reaction, as stated above.Code Calibration1) Prototype foundationsA code calibration will be conducted for two prototype highway bridge foundationof piers for each piling methods using FOSM. The prototype highway bridge substructuresare designed by Japanese Highway Bridges Design Specifications and are checked forallowable stresses for concrete and reinforcement with factors of safety. In this study, wedeal with seismic design of pile foundations for the Level 1 (or frequent scale) Earthquake

Design situation. The combination of all dead loads and seismic inertial force from thesuperstructure is considered, and these loads are also considered as given conditions withno uncertainty. The design calculation is conducted using a typicalbeam-on-Winkler-foundation model. A schematic diagram is shown in Fig. 3. The axialresistance of a pile subjected to vertical loads is expressed using a spring arranged at thepile top.VMHKVMkHEIFigure 3 Design calculation modelIn this paper, we basically introduce the cast-in-place RC piles (Drilled shaft) cases.The prototype highway bridge substructures are shown in Fig. 4. Because of simplicity, inconsideration of the variation in the Young’s modulus of soil, a uniform subsoil layeroverlaying the bearing layer is assumed for both cases. The Case A foundation is designedso that the maximum bending moment in the piles will appear at the top of pile. The CaseB foundation is designed so that the maximum pile bending moment will appear deepunderground.Case A (EPMT 1,400 kN/m2, KV, 580,000 kN/m, Pile diameter, B, 1,100 mm)Case B (EPMT 8,400 kN/m2, KV, 687,000 kN/m, Pile diameter, B, 1,350 mm)Figure 4 Prototype highway bridge substructures (cast-in-place RC piles)

2) Monte Carlo simulation for estimating the uncertainty in the calculated pile bendingmomentThe Monte Carlo simulation is conducted to estimate the variation in the calculatedpile bending moment. The model uncertainties considered in the Monte Carlo simulationare listed in Tables 2, 4, and 5. All of the parameters are assumed to follow a lognormaldistribution. The model uncertainty in the bending rigidity of the pile is estimatedseparately using a Monte Carlo simulation for the designed cross-sections considering themodel uncertainty in the material property such as the Young’s modulus of reinforcementand the unconfined strength of concrete that is cast underwater.Monte Carlo simulation was conducted for different prototype design cases anddifferent soil investigation or testing cases or piling methods. The calculation error isestimated by dividing the (absolute) maximum bending moment calculated in the MonteCarlo simulation by the (absolute) maximum bending moment obtained in the prototypedesign calculation.Table 5 Model uncertainty in the material property of drilled shaftsItemsConcrete strength, fckYoung’s modulus ofconcreteYield strength ofreinforcement (SD345)Young’s modulus ofreinforcementNominal valueBiasCOV224 N/mm1.400.18Given as a function of fck in the JapaneseSpecifications for Highway Bridges andmodeled to be deterministic in this study345 N/mm21.140.042.00 105 N/mm2(constant)(constant)3) Monte Carlo simulation for estimating the uncertainty in the bending strength of the pileA separate Monte Carlo simulation is conducted for the bending strength of a pilefor the cross section of prototype structures. The material uncertainties in concrete andreinforcement are as listed in Table 5. The bending strength of a pile changes with the axialforce on the pile with increasing seismic force. In other words, the increment in the axialforce during an earthquake has an uncertainty because of the model error of the typicaldesign calculation model, such as the coefficient of horizontal subgrade reaction and theaxial spring of the pile. The variation in the axial force of the tensile pile can be estimatedfrom the numerical results obtained in the previous Monte Carlo simulation for theuncertainty in the calculated bending moment, in which the structural design of the pile isgoverned by the design of the tensile piles. As a result, the uncertainty in the increment ofthe axial force during an earthquake is estimated to have a bias of 1.0 and a COV of 0.10.The uncertainty in the yield bending moment strength, MY, and the ultimatebending moment strength, MU, considered in this study is used based on the Monte Carlo

simulation’s result shown in Table 6.Table 6 Uncertainty in MY and MU (Cast-in-place RC pile)Bias1.15COV0.104) Load and resistance factors obtained by FOSMFOSM is used to obtain the load and resistance factors. First, the reliability indexesof the prototype foundations are estimated. Table 7 shows the example of reliabilityindexes of Cast-in-place RC pile designed by current Japanese highway designspecification for L1 Earthquake. It is found that for positive side is more sensitive thanfor negative side by the difference of soil investigation methods. Additionally, beta valueevaluated by SPT test which N value is less than 5 is smaller than the other cases. Theseresults indicated that reliability of piles depend on the soil investigation methods,especially maximum bending moment appears at the head of pile.Target Reliability index T is set based on evaluated reliability indexes of thetypical types pile foundation designed by current design specification. Soil investigationmethod is assumed as SPT on sandy soil. Typical types pile foundations are assumed asfollowing 3 types of pile foundations; Cast-in-place RC pile, Steel pipe pile by driven pileconstruction method and by embedding method by an inner excavation construction.Accordingly, we finally use the target reliability indexes of T 1.8 and 3.1 for the yieldand ultimate bending moment strengths, MY and MU, respectively.Table 7 Reliability indexes of Cast-in-place RC pile designed by current designspecification for L1 EarthquakeSoil investigation / testingPile load testPressuremeter test orlaboratory testSandy soilOnlyCohesive soilSPTNave 5 (bias 1.0)Yield Bending momentMYPositiveNegative1.841.50Maximum bendingmoment MUPositive 072.852.592.590.861.502.272.59Basically, load factor and resistance factor are set separately. However, we found thatresistance factor was not sensitive, so resistance factor puts together in loading factor likeEq.(7) in this study. Moreover, new loading factor divides into two factors shown in Eq(8).

One is a loading factor considering the difference of pile types and piling methods. Theother is a loading factor considering the difference of soil investigation or load tests. Bythis modification, we are able to clarify a merit to introduce the LRFD more clearly. Thesefactors divided though trial and error method. ' / Md Ψ1・Ψ2・ M(7)(8)Where,Md :Design bending moment of pilesM :Calculated Bending moment of pile 1 :Load factor considering the difference of pile types and piling methods 2 : Load factor considering the difference of soil investigation / load testsFinally, the load factors are obtained as summarized in Table 9 and Table 10. As for theload factor considering the difference of pile type and piling methods 1, the load factorof cast-in-place RC pile tends to be larger than the others. It is assumed because the COVof Kv of this pile type is larger than the others. As for the load factor considering thedifference of soil investigation and load tests 2, it is found that it is to enable reasonabledesign by detailed soil investigation or load test.Table 9 Load factor considering the difference of pipe type and piling method Ψ1Pile type and Piling MethodCast-in Place RC PileSteel Pipe Pile(Drilled pile)Prestressed High strength ConcretePile(Drilled pile)Steel Pipe Pile (embedding method byan inner excavation construction)Prestressed High strength ConcretePile(embedding method by an innerexcavation construction)Steel Pipe Soil Cement Composite PileSteel Pipe Pile(Screwed Steel Pile Method)Preboring Pile Driving MethodYield BendingMoment MYPositive Negative1.802.051.401.50Maximum bendingmoment MUPositive 2.101.651.601.952.

in pile foundations for Level 1 earthquake situation. The proposed load factors in the study are a function of the chosen soil investigation/testing and piling method, which is applied to the bending moment in piles. Therefore, better choices of soil investigation/testing and high quality piling method will result in more reasonable design results. Introduction Reliability-based design .

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