Samuel G. PaikowskyGeosciences Testing & Research, Inc. (GTR)North Chelmsford, Massachusetts USAGeotechnical Engineering Research LaboratoryDept. of Civil and Environmental EngineeringUniversity of Massachusetts Lowell, USASafety Concepts and Calibration of Partial Factorsin European and North American Codes of PracticeNovember 30, 2011LRFD Calibration and Implementation of Strength and Serviceability Limit StatesReview of Research and Lessons LearnedWorkshop30/11 01/12/2011Delft University of Technology, Delft, The NetherlandsTable of Contents 1 DESIGN PRACTICE Codes in the USA Limit State Design 2 DESIGN METHODOLOGIES Review Working Stress Design Uncertainties Structural and Geotechnical Designs 3 LOAD AND RESISTANCE FACTOR DESIGN (LRFD) Principles Target Reliability Probability of Failure LRFD For Deep Foundations 4 LRFD Deep Foundation Design Report - NCHRP 507 Dynamic Analyses of Piles Framework Databases Static Analysis of Driven Piles Dynamic Analysis of Driven Piles Static Analysis of Drilled FoundationsTable of Contents 5 LRFD Shallow Foundations Design Report- NCHRP 651 Databases Uncertainty of Vertical Centric Loading Source of Uncertainty Investigation of N Development of Resistance Factors Eccentric and/or inclined Loading Resistance Factors for Controlled and Naturally Deposited Soils Shallow Foundations on Rock 6 LRFD Serviceability Limit State Design ReportNCHRP 12-66 7 Example Case History1DESIGN PRACTICE1DESIGN PRACTICECodes Code Any systematic collection of regulations and rules of procedure or conduct. Importance Standardization Recognition of methods and procedures 1DESIGN PRACTICECodes in the USA Every state in the USA has a building code which is part of the states laws.In addition, the Department of Transportation (a.k.a. Highway Department) of the state has its own specifications. A united code (IBC International Building Code) was developed in 2000 by uniting several previous codes (UBC Uniform Building Code and SBC Standard Building Code).Forty-four states (88%) adopted the IBC as their building code.1DESIGN PRACTICECodes in the USA The construction of most bridges (all highway bridges) is funded primarily by the Federal Government via FHWA.These structures are obliged to be designed by the AASHTO specifications - (American Association of State Highway Transportation Officials). The AASHTO specifications are traditionally observed on all federally aided projects and generally viewed as a national code of US Highway practice, hence influencing the construction of all the foundations of highway bridges throughout the USA1DESIGN PRACTICECodes in the USA The AASHTO Specifications, as well as most advanced codes worldwide, moved to RBD Reliability Based Design.The LRFD Load and Resistance Factor Design format of RBD is used by the AASHTO specifications since 1994. The major developments relevant to foundation design will be presented some had been implemented.1DESIGN PRACTICELimit State Design (LSD)A design of a structure needs to ensure that while being economically viable it will suit the intended purpose during its working life.LS Limit State Condition beyond which the structure or a component fail to fulfill in some way the intended purpose for which it was designed.ULS Ultimate Limit State deals with strength (maximum loading capacity) of the structure / element. (aka Strength Limit State)SLS Serviceability Limit State deals with the functionality and service requirements of a structure to ensure adequate performance under expected conditions.e.g. - Relevance to Foundations:By and large axial loading of piles is controlled by ULS and lateral loading by SLS.was initiated in the 1950s for a more economical design.Satisfying Limit States:Ultimate Limit State (ULS)Factored resistance Factored load effectsServiceability Limit State (SLS)Factored Deformation Tolerable deformation to remain serviceable1DESIGN PRACTICELimit State Requirements2DESIGN METHODOLOGIES2DESIGN METHODOLOGIESReview Working Stress DesignSTATE OF STRESS DESIGNWorking stress design (WSD) also called the Allowable Stress Design(ASD) method, has been used in Civil Engineering since the early1800s.Q Qall= Rn/ FS= Qult/ FSQ = Design load (F)Qall= Allowable load (F)Rn= Qult= Nominal Resistance = Ultimate geotechnical foundation force resistanceFS = Factor of safetyThe factor of safety is commonly defined as the ratio of the resistance ofthe structure (Rn) to the load effects (Q) acting on the structure.2DESIGN METHODOLOGIESReview - Working Stress DesignADVANTAGES Simple Vast Experience Serves as a ReferenceLIMITATIONS Lumps all uncertainty into a factor of safety Does not provide a direct evaluation of whether a method is conservative or un-conservativeFactor Of Safety On Ultimate Axial Geotechnical Capacity Based On Specified Construction Control (AASHTO 1997 Standard Specifications) X - Construction ControlIncreasing Construction ControlSpecified on PlansSubsurface Exploration X X X X XStatic Calculation X X X X XDynamic Formula XWave Equation X X X XCAPWAP Analysis X XStatic Load Test XXFactor of Safety (FS) 3.50 2.75 2.25 2.00* 1.90* Any combination that includes a static load testDesign Capacities Specified on Plans so FS can be Adjusted if Construction Control is Altered2DESIGN METHODOLOGIESReview - Working Stress DesignComments1. On the face of it logical and progressive but on what basis are the specifications founded? Is the control method F.S. suitable for the design method? 2. Rewards the use of quality control through dynamic measurements during driving and/or static load-testing.3. Very Generic Does not provide any details regarding the methods. e.g.: What kind of subsurface investigation? What kind of static analysis? Dynamic Measurements - When? (EOD, Restrike ?) On what kind of piles? Driving conditions? What about field interpretation? Can be examined and/or explained only against actual data.2DESIGN METHODOLOGIESReview - Working Stress DesignSIMPLE EXAMPLECapacityEvaluationMethodF.S.Load per Pile (tons)# of PilesSavingsStatic Analysis3.50 28.6 7.0 -WEAP2.75 36.4 5.5 - 21%CAPWAP2.25 44.4 4.5 - 36%Static L.T.2.00 50.0 4.0 - 43%Assume a load of 200 tons and Pile Capacity Qult= 100 tons(accurately predicted by all methods, i.e.bias = 1.0)2DESIGN METHODOLOGIESReview - Working Stress DesignEvaluation of Parameters Static Analysis of Driven Piles In ClayNo. of cases and Mean of Prediction (msd. Over calculated using data 2 SD)Actual Mean FS for driven piles in clay Methods = 0.82 x 3.5 = 2.87 Method = 0.72 x 3.5 = 2.52(1/0.8 = 1.25)For Comparison FS for the Dynamic MethodsCAPWAP - BOR 162 Mean = 1.16Actual FSBOR= 1.16 x 2.25 = 2.612DESIGN METHODOLOGIESReview - Working Stress DesignRevisit Simple WSD ExampleAssume a load of 200 tons and Pile Capacity Qult= 100 tons (Specifying now a concrete pile in clay and using the bias known for the methods)CapacityEvaluationMethodF.S.(Load)Load per Pile - ton(w/o bias)# of Piles(w/o bias)Savings(w/o bias)Static Analysis API Clay3.50on 123t35.3(28.6)5.7 (7)-WEAP EOD2.75on 60t22.0(36.4)9.1 (5.5)+60%(-21%)CAPWAP BOR2.25on 86t38.4(44.4)5.2 (4.5)-9%(-36%)Static L.T.2.00on100t50.0 4.0 -30%(-43%)(values in original example ignoring the bias)2DESIGN METHODOLOGIESReview - Working Stress DesignINTERMEDIATED CONCLUSION1. The examination of factors of safety on the basis of their absolute values is misleading and do not represent the economical value of a specific method.2. The same holds for any other design method e.gresistance factors for LRFD as will be shown.3. Only the use of an actual database provides the bias of a design method and hence allows for a rational development of safety margins regardless of the design methodology.2DESIGN METHODOLOGIESReview - Working Stress DesignUncertainties - Structural DesignSimplified Example of Beam Design and Sources of UncertaintySources of Uncertainty1. Loading2. Dimensions3. Material Properties(Assuming homogenous cross-section, horizontal symmetry line and beam height, h.)Most Noticeable: 1. No uncertainty in the model under given loading conditions the uncertainty in the material properties (i.e. yield) dictates the uncertainty in strength or uncertainty in Modulus E will dictate the uncertainty in the deflection2. Largest uncertainty in the loading, source, magnitude, distribution(in case of bridges)qA Bshearmomentdeflectionloadingl ll lyhlE EIqly2max4max2453845 = =2qlB A = =82maxqlM =Uncertainties - Geotechnical DesignComponents of Foundations Design and Sources of UncertaintySoil sampling and testing for engineering material parametersUncertainty due to site, material and testing variability and estimation of parametersUncertainty in the assumptions made in the model development leaves unknown analysis versus actual performanceFOUNDATION DESIGNUncertainty in loads created by and applied to the bridge, e.g.Dead Load e.g. weight of the bridgeLive Load e.g. traffic and its effects (e.g. breaking)Wind & wind on trafficExtreme Events e.g. earthquake, ship collisionCode of practiceTraditional design although developed over many years and used as a benchmark has undocumented unknown uncertaintyAnalysis ModelAssumed Failure Pattern under FoundationsLoadingMethod of ApproachLOAD Use the load uncertainty from the structures (until better research is done)RESISTANCE Establish the uncertainty of the complete foundation capacity analysis by comparing a design procedure to measured failure.2DESIGN METHODOLOGIESUncertainties - Geotechnical Design Defining uncertainty in the soil properties alone is therefore not sufficient in most cases to determine the uncertainty of the designed element/structure. The relationship between loads and displacements requires a separate model having its own uncertainty.Significant uncertainties exist in: (1) The process of defining geomaterial properties. (2) The calculation model.3LOAD AND RESISTANCE FACTOR DESIGN (LRFD)3LRFD DESIGNLRFD for FoundationsPrinciplesThe design of a foundation depends upon predicted loads andthe capacity to resist them. Both loads and resistance(capacity) have various sources and levels of uncertainty thathistorically have been compensated for by experience andsubjective judgment.These uncertainties can be quantified using probability-baseddesign, or safety check expressions, aimed at achievingdesigns with consistent levels of reliability. The intent of theLoad and Resistance Factor Design (LRFD) method is toseparate uncertainties in loading from uncertainties inresistance and to assure a prescribed margin of safety .3LRFD DESIGN Probability Density Functions for Load and ResistanceR, QfR(R), fQ(Q)Load Ef f ect (Q)Resistance (R) __Q __RRnQn__FS = R/Q.An illustration of probability density functions for load effect and resistanceQ, R Mean Load/ResistanceQn, Rn NominalLoad/Resistanceconsistent levels of reliabilityAn Illustration of a Combined Probability Density Function (g(R,Q)) Representing the Margin of Safety and the Reliability Index, ( g = Standard Deviation of g).Relationship Between Reliability Index and Target ReliabilityReliability Index Probability of Failurepf1.0 0.1591.2 0.1151.4 0.08081.6 0.05481.8 0.03592.0 0.02282.2 0.01392.4 0.008202.6 0.004662.8 0.002563.0 0.001353.2 6.87 E-43.4 3.37 E-43.6 1.59 E-43.8 7.23 E-54.0 3.16 E-53LRFD DESIGN Target Reliability Probability of FailureReliability is expressed using the reliability index, , which is the number of standard deviations of the derived PDF ofthe limit state function g, (g = R Q)3LRFD DESIGNLRFD FOR DEEP FOUNDATIONSFor the strength limit state:Rr = Factored resistance (F or F/A); = Resistance factor (dimensionless); Rn = Nominal (Ultimate) resistance (F or F/A); = Factors to account for ductility ( D), redundancy ( R),and operational importance ( I) Structural (dimensionless) i= Load factor (dimensionless); Qi= Force effect, stress or stress resultant (F or F/A); =i i n rQ R R1994, 1st. AASHTO LRFD Bridge Design Specs for Foundations4LRFD Deep Foundations DesignAn extensive development of resistancefactors for the AASHTO specifications ofDeep Foundations was undertaken underNCHRP project 24-17 and presented inNCHRP Report 507. These factors weredeveloped based on large databasesexamining the deep foundations capacityprediction methods during design andconstruction.Google Search:NCHRP 507 will bring you to the pdf4LRFD Deep Foundations DesignResearch Project NCHRP 24-1730Massachusetts GroupSamuel G. Paikowsky, PIKirk StenersenKevin O'MalleyLes ChernauskasMaryland GroupGregory BaecherBilal AyyubDavid SchellingFlorida GroupMichael McVayChing KuoBjorn BirgissonThai NguyenConsultantsJames WithiamMichael O'Neill4LRFD Deep Foundations DesignResearch Team4LRFD Deep Foundations DESIGNFrameworkForThe Development Of The Resistance Factors In NCHRP 507R, QfR(R), fQ(Q)Load Ef f ect (Q)Resistance (R) __Q __R RnQn Distribution of Load - Type, Mean, SD Distribution of Resistance Type, Mean, SD Probability of FailureREQUIRED INFORMATIONPOSSIBLE SOURCES =i i n rQ R R Distribution of Load Measurements on andAnalyses of Structures e.g. Vehicles on a Bridge Distribution of Resistance Databases, Related Correlations - e.g. Soil Parameters, Judgment Probability of Failure Observations, Judgment, Probabilistic Theory4LRFD Deep Foundations DESIGNFrameworkForCalibration Required Information Sources of Information Load CombinationAASHTO Strength I DL & LL Load Factors D = 1.25 L = 1.75 Distribution of Load TypeLognormal Mean QD = 1.05 QL = 1.15 COVCOVQD = 0.1 COVQL = 0.2 Nature of ResistanceGeotechnical Axial resistance Distribution of ResistanceDatabase Analysis Probability of FailureReview Available Literature/Develop Required And Sources of Information4LRFD Deep Foundations DESIGNDatabasesMain Analyses: Driven Piles Static Analyses- 527 piles Drilled Shafts Static Analyses - 300 shafts Driven Piles Dynamic Analyses - 389 cases on 210 pilesPeripheral Analyses: Static Load Test Interpretation DP - 196 piles Static Load Test Interpretation DS - 44 shafts Influence of Loading Rate - 75 piles Dynamic Measurements both EOD - 456 cases on 228 piles & BOR(without Static Load Test) WEAP (GRL Database) - 99 piles Case Method (Florida Study): EOD - 40 pilesBOR - 37 piles4LRFD Deep Foundations DESIGNCalculated Resistance Factors34 Target Reliability (probability of exceedance = Probability of failure) Efficiency Factor Calibration Methods4LRFD Deep Foundations DESIGNRedundant vs. NonRedundant35RedundantNon - RedundantLogicallyNon - Redundant = 2.33Pf= 1.0% = 3.00 Pf= 0.1%NCHRP 507 Recommendations4LRFD Deep Foundations DESIGNDevelopment of Resistance Factors36The first version of the AASHTO specifications utilized First-Order,Second-Moment (FOSM) principles, assuming lognormal distributionfor the resistance and bias factors, closed form relations wereestablished (Barker et al., 1991).1. FOSM First Order Second Moment2. FORM First Order Reliability MethodFORM provides a means for calculating resistance and load factors and against a target reliability level using an iterative process.Allcurrent calibrations are using MC simulationsAlways practical to compare to FOSM (Mostly on the conservative side for foundations Strength LS by about 10%)NCHRP 507 Used two Calibration Methods:3. Comments4LRFD Deep Foundations DESIGNDesign Method Efficiency Resistance Factor Over Bias- / v0 0.5 1 1.5 2 2.5 3Bias ()0.00.51.01.52.02.5Resistance Factor ()0 0.2 0.4 0.6 0.8 1COVR00.20.40.60.8Efficiency (/)Efficiency-Resistance factor.grf FOSMQL = 1.15 QD = 1.05COVQL = 0.2 COVQD = 0.1QD/QL = 2.5 = 2.33D = 1.25 L = 1.75 FOSMQL = 1.15 QD = 1.05COVQL= 0.2COVQD =0.1QD/QL = 2.5 = 2.33D = 1.25,L = 1.75COV = 00.20.40.60.80.5COV = 1.00 Figure 15. Calculated resistance factors as a function of the bias and COV for the chosen load distributions and DD/LL ratio of 2.5 Figure 16. Illustration of the efficiency factor as a measure of the effectiveness of a design method when using resistance factors.374LRFD Deep Foundations DESIGNCalculated and Recommended Resistance Factors Static Analyses Driven Piles Dynamic Analyses Driven Piles Static Analyses drilled shafts4 LRFD Deep Foundations DESIGN DATABSE - Initial Relevant AnalysesI Interpretation of Static CapacityEstablisha Unique Failure Criterion as aReference Static Capacity for the Calibrations of the static and dynamic analyses. Analysis of 196 Driven Pile Load Tests to failure Approach using 5 interpretationmethodsII Influence of Load Test Procedure Examining two detailed case histories of the Newbury Test Site. Examining the UML/Ukraine Database of 75 cases comparing slow maintained and static-cyclic load test results.40Static Analyses of driven Piles Summary of Methods MethodSide resistanceTip resistance Parameters required Constraints -Tomlinson (Tomlinson, 1980/1995) Su; Db (bearing embedment) +Bearing layer must be stiff cohesive + Number of soil layers 2 -API (Reese et al., 1998) qs = Su Su in cohesive (AASHTO, 1996/2000) qs = OCR (US Army Corps of Engineers, 1992) qs = (+2Su) qp = 9 Su SuOnly for cohesive soils in cohesionless (Bowles, 1996) Dr Nordlund and Thurman (Hannigan et al., 1995) cos) sin('+=F sC K q qp = t Nq Meyerhof SPT (Meyer-hof, 1976/1981) qs = k N qp = 0.4D/BN N + For cohesionless soils + SPT data SPT 97(Lai and Gra-ham, 1995) qs = function(N)qp = fn(N)NSPTdata FHWA CPT (McVay and Townsend, 1989) qs = function(fs)qp = fn(qc)qc, fs CPT data 4 LRFD Deep Foundations DESIGN DATABSE - AnalysesSpecific Correlations were provided for soil parameters Interpretations41Histogram & Frequency Distributions for 52 Cases of All Pile Types (Concrete, Pipe, H) in Clay Using - API MethodThe performance of driven piles static analysis methods0 0.5 1 1.5 2 2.5 3Ratio of Static Load Test Results over the Pile CapacityPrediction using the -API method012345678910Number of Pile-Cases00.0250.050.0750.10.1250.150.175Relative Frequencylog-normaldistributionmlnx = -0.270lnx = 0.428normal distributionmx = 0.832x = 0.3494LRFD Deep Foundations DESIGN DATABSE - Analyses42Histogram & Frequency Distributions for 146 Cases of All Pile Types (Concrete, Pipe, H) in Mixed Soils Using -API/Nordlund/Thurman Design MethodsThe performance of driven piles static analysis methods0 0.5 1 1.5 2 2.5 3Ratio of Static Load Test Results over the Pile CapacityPrediction using the -API/Nordlund/Thurman design method0246810121416182022Number of Pile-Cases00.020.040.060.080.10.120.14Relative Frequencylog-normaldistributionmlnx = -0.293lnx = 0.494normal distributionmx = 0.835x = 0.3874LRFD Deep Foundations DESIGN DATABSE - Analyses43Histogram & Frequency Distributions for 80 Cases of Concrete Piles in Mixed Soils Using -API/Nordlund/Thurman Design MethodsThe performance of driven piles static analysis methods0 0.5 1 1.5 2 2.5 3Ratio of Static Load Test Results over the Pile CapacityPrediction using the -API/Nordlund/Thurman design method0123456789101112131415Number of Pile-Cases00.020.040.060.080.10.120.140.160.18Relative Frequencylog-normaldistributionmlnx = -0.260lnx = 0.502mx = 0.868x = 0.416normal distribution4LRFD Deep Foundations DESIGN DATABSE - Analyses Table 25. Recommended resistance factors for driven piles static analyses Notes: 3/19/027/11/02 7/15/02 Non-Redundant = Four or less piles under one pile cap ( = 3.0 pf = 0.1%) Redundant = Five piles or more under one pile cap ( = 2.33 pf = 1.0%) = bias = Mean KSX = measured/predicted / = efficiency factor, evaluating the relative economic performance of each method (the higher the better) / values relate to the exact calculated and and not to the assigned values in the table Pile Type Soil Type Design Method Resistance Factor /Redundant Non-redundant Redundant Non-redundant Concrete Pile MixedSPT97 mob0.700.500.400.29 Clay -API 0.500.40 0.67 0.55 -Method0.630.55 Sand -Method0.460.34 SPT97 mob0.420.31 Mixed FHWA CPT0.600.48 -Method/Thurman 0.400.30 0.510.39 Tomlinson/Nordlund/Thurman0.410.30 SandNordlund0.420.31 Clay-Tomlinson 0.350.25 0.410.30 Mixed-API/Nordlund/Thurman0.410.30 SandMeyerhof0.200.150.320.22 . Pipe Pile Sand SPT97 mob,0.550.45 0.380.28 Nordlund0.380.27 Mixed SPT 97 mob0.400.300.510.40 -API/Nordlund/Thurman 0.350.25 0.440.31 Sand-Method0.310.21 Clay-API 0.300.20 0.360.26 SandMeyerhof0.330.23 Mixed Tomlinson/Nordlund/Thurman 0.250.15 0.320.23 -Method/Thurman0.410.30 Clay -Tomlinson0.400.29 -Method0.360.25 H Piles Mixed SPT 97 mob 0.550.45 0.450.33 Sand SPT 97 mob0.460.35 Nordlund 0.450.35 0.490.37 Meyerhof0.510.39 Clay -API0.480.37 -Tomlinson 0.400.30 0.490.37 -Method0.500.39 Mixed -API/Nordlund/Thurman0.35 0.25 0.450.34 Tomlinson/Nordlund/Thurman 0.30 0.510.39 Sand-Method0.390.28 Mixed-Method/Thurman0.200.150.420.31 NCHRP 507 Recommended Resistance FactorsDriven Piles Static AnalysesHistogram & Frequency Distributions for all (377) CAPWAP pile-cases in PD/LT20000 0.5 1 1.5 2 2.5 3Ratio of Static Load Test Results over the PileCapacity Prediction using the CAPWAP method051015202530354045505560Number of Pile-Cases00.010.020.030.040.050.060.070.080.090.10.110.120.130.140.15Relative Frequencylog-normaldistributionmlnx = 0.233lnx = 0.387normal distributionmx = 1.368x = 0.620>5PERFORMANCE OF THE DYNAMIC METHODSHistogram & Frequency Distributions for all BOR (162) CAPWAP pile-cases in PD/LT20000 0.5 1 1.5 2 2.5 3Ratio of Static Load Test Results over the Pile CapacityPrediction using the CAPWAP method051015202530354045505560Number of Pile-Cases00.040.080.120.160.20.240.280.320.36Relative Frequencylog-normaldistributionmlnx = 0.100lnx = 0.295normal distributionmx = 1.158x = 0.393>5PERFORMANCE OF THE DYNAMIC METHODSHistogram & Frequency Distributions for all EOD (128) Energy Approach pile-cases in PD/LT20000 0.5 1 1.5 2 2.5 3Ratio of Static Load Test Results over the Pile CapacityPrediction using the Energy Approach method051015202530354045505560Number of Pile-Cases00.040.080.120.160.20.240.280.320.360.40.44Relative Frequencylog-normaldistributionmlnx = 0.011lnx = 0.366normal distributionmx = 1.084x = 0.4315PERFORMANCE OF THE DYNAMIC METHODS4LRFD DESIGNRecommended resistance factorsDriven Piles Dynamic Analyses Table 27.Recommended resistance factors for driven piles dynamic analyses Resistance factor, / MethodCase Redundant Non-Redundant Redundant Non-Redundant EOD0.650.450.400.28 EOD, AR 6m13 -- -- 5 1 19 1 18Total 415 48 0 12 74 549 254 295Note:Mixed are cases with alternating layers of sand or gravel and clay or siltOthers are cases with either unknown soil types or with other granular materials like loamy Scoria1m 3.3ftTotalPredominant Soil Type Country Foundation type59Large foundations are often not loaded to ULS failure (SLS controls)5LRFD Shallow Foundations DESIGNBias of Estimated BC - Vertical Centric Loading Granular Soil Controlled ConditionsFigure 62.(a) Histogram and probability density functions of the bias and (b) relationship between measured and calculated bearing capacity for vertical centrically loaded shallow foundations on controlled soil conditions.0.2 0.6 1 1.4 1.8 2.2 2.6 3 3.4 3.8Bias, = qu,meas / qu,calc010203040Number of observations00.10.20.3FrequencyControlled soil conditionsn = 159mean = 1.64COV = 0.267lognormaldistributionnormaldistribution0.1 1 10 100Calcualted bearing capacity, qu,calc(Vesic, 1975 and modified AASHTO)(ksf)0.1110100Interpreted bearing capacity, qu,measusing Minimum Slope criterion (Vesic, 1963)(ksf)Controlled soil conditionsData (n = 159)Data best fit lineNo bias line605LRFD Shallow Foundations DESIGNSource of UncertaintyInvestigationof N Comparison of bearing capacity factor calculated based on test results; N = qu/ (0.5 B s ) from 125 tests carried out in controlled soil conditions (tests by Perau, 1995) and N proposed by Vesic (1973) in the range of soil friction angle of 42 and 46 42 43 44 45 46friction angle, f (deg)101001000qu / (0.5 B s)N from load tests; n = 125N (Vesic, 1973)N = exp(0.39f 11.546)(R2 = 0.666)615LRFD Shallow Foundations DESIGN42 43 44 45 46Friction Angle, f (deg)00.511.522.53N = [qu / (0.5 B s)] / NVesicload test data; n = 125 = exp(0.205f 8.655) (R2 = 0.351)Figure 93.The ratio ( N ) between the back-calculated B.C. factor N based on experimental data to that proposed by Vesi versus soil friction angle.625LRFD Shallow Foundations DESIGNSource of UncertaintyInvestigationof N Uncertainty in B.C. compared to the Uncertaintyof N Figure 94.The ratio between measured and calculated bearing capacity (bias ) compared to the bias in the B.C. factor N ( N ) versus the soils friction angle for footings under vertical-centric loadings.43 44 45 46Friction Angle, f (deg)00.511.522.53Bias Data BC bias (n = 131)Bearing Capacity (BC) bias, N bias, 635LRFD Shallow Foundations DESIGNFigure 103.Bearing resistance bias vs. average soil friction angle (taken f 0.5 ) including 95% confidence interval for all cases under vertical-centric loading.30 32 34 36 38 40 42 44 46Friction angle f (deg)0.00.51.01.52.02.53.03.5Bias (2)(90)(30)(14)(4)(2)(12)(4)(3)(2)(3)(4)(2)Mean bias, BC (n = 172)1 s.d.(x) no. of cases in each intervalBC = 0.308exp(0.0372f)(R2=0.200)95% confidence interval64Uncertainty in B.C.5LRFD Shallow Foundations DESIGNFigure 104.Recommended resistance factors for soil friction angles (taken f 0.5 ) between 30 and 46 , with comparisons to 95% confidence interval and resistance factors obtained for the cases in the database; the bubble size represents the number of data cases in each subset.30 32 34 36 38 40 42 44 46Friction angle f (deg)0.00.20.40.60.81.0Resistance factor, 0.00.51.01.52.02.53.0Bias (2)(90)(30)(14)(4)(2)(12)(4)(3)(2)(3)(4)(2)95% confidence interval for Resistance factor based on database(x) no. of cases in each intervalRecommended f for Controlled soil conditionsRecommended f for Natural soil conditionsn = 172655LRFD Shallow Foundations DESIGNUncertainty in B.C. and Resistance FactorsFinal Resistance Factors Controlled ConditionsTable 66Recommended resistance factors for shallow foundations on granular soils placed under controlled conditionsSoil frictionangle fLoading conditionsVertical-centric or-eccentricInclined-centricInclined-eccentricPositive Negative30 34 0.500.40 0.40 0.7035 36 0.6037 39 0.70 0.45 0.45 0.7540 44 0.75 0.500.50 0.80 45 0.80 0.55Notes:1) fdetermined by laboratory testing2) compacted controlled fill or improved ground are assumed to extend below the baseof the footing to a distance to at least two (2.0) times the width of the foundation (B).If the fill is less than 2B thick, but overlays a material equal or better in strength thanthe fill itself, then the recommendation stands. If not, then the strength of theweaker material within a distance of 2B below the footing; prevails.3) The resistance factors were evaluated for a target reliability T= 3.0.665LRFD Shallow Foundations DESIGNIntermediate Conclusions and Summary It was found that for the footings of larger sizes (B>3m (9.9ft)), the load tests were not carried out to the failure loadBiases for the tests in Natural Soil Condition and Controlled Soil Conditions were analyzed separatelyFor the footing sizes in similar ranges (0.1m < B 1.0m), the scatter of bias was larger for footings on/in natural soil conditionsThe majority of the relevant data refers to small size foundations (B 3.3ft (1.0m)) on controlled compacted material. Many of the highway shallow foundations on soils are built on compacted materials and hence, the statistical data of the uncertainty can be used for that purposeThere appears to be a trend of increase in bias with the footing size within the range of footing sizes available for testing (which seems to conform with the observation made by Vesic (1969))675LRFD Shallow Foundations DESIGNULS of Inclined LoadingFigure 64.Loading convention and load paths used during tests.3b1x2F3M1M2M1F2x3F2bD3x, g

f(a) Loading conventionF1F3F1F31,const.increasing = const.F1M2arctan e = const(b) Radial load path (c) Step-like load pathF685LRFD Shallow Foundations DESIGNFigure 66.(a) Histogram and probability density functions of the bias and (b) relationship between measured and calculated bearing capacity for all cases of vertical eccentrically loaded shallow foundations.0.4 1.2 2 2.8 3.6Bias, = qu,meas / qu,calc024681012Number of observations00.050.10.150.20.25FrequencyVertical-eccentric loadingn = 43mean = 1.83COV = 0.351lognormaldistributionnormaldistribution0.1 1 10 100Calcualted bearing capacity, qu,calc(Vesic, 1975 and modified AASHTO)(ksf)0.11101001000Interpreted bearing capacity, qu,measusing Minimum Slope criterion (Vesic, 1963)(ksf)Vertical-eccentric loadingData (n = 43)Data best fit lineNo bias lineBias of BC for Vertical-Eccentric Loading (using B )695LRFD Shallow Foundations DESIGNFigure 67.(a) Histogram and probability density functions of the bias and (b) relationship between measured and calculated bearing capacity for all cases of inclined centric loaded shallow foundations.0.2 0.6 1 1.4 1.8 2.2 2.6Bias, = qu,meas / qu,calc04812Number of observations00.10.20.3FrequencyInclined-centric loadingn = 39mean = 1.43COV = 0.295lognormaldistributionnormaldistribution0.1 1 10 100Calcualted bearing capacity, qu,calc(Vesic, 1975 and modified AASHTO)(ksf)0.1110100Interpreted bearing capacity, qu,measusing Minimum Slope criterion (Vesic, 1963)(ksf)Inclined-centric loadingData (n = 39)Data best fit lineNo bias lineBias of BC for Inclined-Centric Loading705LRFD Shallow Foundations DESIGNLoading Directions for Inclined-Eccentric LoadingsFigure 69.Loading directions for the case of inclined-eccentric loadings:(a) along footing width and (b) along footing lengthe3F1b3F3M2F1F3++e3F1b3F3M2F1F3+Moment acting in the same direction as the lateral loading positive eccentricityMoment acting in direction opposite to the lateral loading negative eccentricityb3b3(a) along footing widthe2F1b2F2M3F1b2F2+-e2F1b2F2M3F1b2F2++Moment acting in the same direction as the lateral loading positiveeccentricityMoment acting in direction opposite to the lateral loading negative eccentricity(b) along footing length715LRFD Shallow Foundations DESIGNFigure 68.(a) Histogram and probability density functions of the bias and (b) relationship between measured and calculated bearing capacity for all cases of inclined eccentrically loaded shallow foundations.1.2 1.8 2.4 3 3.6 4.2 4.8 5.4 6 6.6 7.2Bias, = qu,meas / qu,calc0123456789Number of observations00.050.10.150.20.250.3FrequencyInclined-eccentric loadingn = 29mean = 2.43COV = 0.508lognormaldistributionnormaldistribution0.1 1 10 100Calcualted bearing capacity, qu,calc(Vesic, 1975 and modified AASHTO)(ksf)0.1110100Interpreted bearing capacity, qu,measusing Minimum Slope criterion (Vesic, 1963)(ksf)Inclined-eccentric loadingData (n = 29)Data best fit lineNo bias lineBias of BC for Inclined-Eccentric Loading725LRFD Shallow Foundations DESIGNFigure 71.(a) Histogram and probability density functions of the bias and (b) relationship between measured and calculated bearing capacity for all cases of inclined eccentrically loaded shallow foundations under negative eccentricity.1.2 1.8 2.4 3 3.6 4.2 4.8 5.4 6 6.6 7.2Bias, = qu,meas / qu,calc0123Number of observations00.10.20.30.40.5FrequencyInclined-eccentric loadingNegative eccentricityn = 7mean = 3.43COV = 0.523normaldistributionlognormaldistribution0.1 1 10Calcualted bearing capacity, qu,calc(Vesic, 1975 and modified AASHTO)(ksf)0.1110Interpreted bearing capacity, qu,measusing Minimum Slope criterion (Vesic, 1963)(ksf)Inclined-eccentric loadingNegative eccentricityData (n = 7)Data best fit lineNo bias lineBias of BC Cases with Inclined-Eccentric Loading735LRFD Shallow Foundations DESIGNFinal Resistance Factors Controlled ConditionsTable 66Recommended resistance factors for shallow foundations on granular soils placed under controlled conditionsSoil frictionangle fLoading conditionsVertical-centric or-eccentricInclined-centricInclined-eccentricPositive Negative30 30 30 30 34 34 34 34 0.500.40 0.40 0.7035 35 35 35 36 36 36 36 0.6037 37 37 37 39 39 39 39 0.70 0.45 0.45 0.7540 40 40 40 44 44 44 44 0.75 0.500.50 0.80 45 45 45 45 0.80 0.55Notes:1) fdetermined by laboratory testing2) compacted controlled fill or improved ground are assumed to extend below the baseof the footing to a distance to at least two (2.0) times the width of the foundation (B).If the fill is less than 2B thick, but overlays a material equal or better in strength thanthe fill itself, then the recommendation stands. If not, then the strength of theweaker material within a distance of 2B below the footing; prevails.3) The resistance factors were evaluated for a target reliability T= 3.0.745LRFD Shallow Foundations DESIGNFinal Resistance Factors Natural ConditionsTable 67Recommended resistance factors for shallow foundations on natural deposited granular soil conditionsNotes:1) fdetermined from Standard Penetration Test results2) granular material is assumed to extend below the base of the footing at least two (2.0) times the width of the foundation.3) The resistance factors were evaluated for a target reliability T= 3.0Soil frictionangle fLoading conditionsVertical-centric or-eccentricInclined-centricInclined-eccentricPositive Negative30 30 30 30 34 34 34 34 0.400.400.350.6535 35 35 35 36 36 36 36 0.450.7037 37 37 37 39 39 39 39 0.500.4040 40 40 40 44 44 44 44 0.55 0.450.75 45 45 45 45 0.65 0.50 0.45755LRFD Shallow Foundations DESIGNDATABASE UML/GTR RockFound 07Comprised of 122 foundation case histories of load tests in/on rock and IGMs.The database has 61 footings cases (28 cases D>0, 33 cases D=0) and 61 rock socket cases for which the base behavior (load and displacement) under loading was monitored.89 of the 122 cases were used for the uncertainty determination of the settlement of foundations on rock.765LRFD Shallow Foundations DESIGNFigure 78.Relationship between Goodmans (1989) calculated bearing capacity (qult) and the interpreted bearing capacity (qL2).Goodman (1989) - B.C. of Foundations on Rock771 10 100 1000 10000 100000Goodman (1989) Bearing Capacity qult (ksf)110100100010000100000Interpreted Foundation Capacity qL2 (ksf)58 Footings cases61 Rock Socket casesqL2 = 2.16 (qult)0.868 (n = 119; R2 = 0.897)qL2 = qult5LRFD Shallow Foundations DESIGNGoodman (1989) - B.C. of Foundations on Rock780 0.6 1.2 1.8 2.4 3 3.6 4.2 4.8Bias, = qu,meas / qu,calc010203040Number of observations00.050.10.150.20.250.30.35Frequency119 Rock-sockets and Footing casesGoodman (1989)mean = 1.35COV = 0.535lognormaldistributionnormaldistribution0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2Bias, = qu,meas / qu,calc024681012Number of observations00.10.20.30.40.50.6Frequency20 Foundation cases on Fractured RocksGoodman (1989)mean = 1.24COV = 0.276lognormaldistributionnormaldistributionFigure 79.Distribution of the ratio of the interpreted bearing capacity (qL2) to the bearing capacity (qult) calculated using Goodmans (1989) method for the rock sockets and footings in database UML-GTR RockFound07.Figure 80.Distribution of the ratio of the interpreted bearing capacity (qL2) to the bearing capacity (qult) calculated using Goodmans (1989) method for foundations on fractured rock in database UML-GTR RockFound075LRFD Shallow Foundations DESIGN79Method ofAnalysisEquation Application Efficiency Factor / (%)Carter andKulhawy(1988)All 0.35 4.4RMR 85 0.50 17.165 RMR < 851.0026.544 RMR < 65 11.33 RMR < 44 4.2Goodman(1989)For fractured rocks:For non-fractured rocks:All 0.30 22.2Measured f0.35 24.8Measured s 0.40 28.0Measured s and f0.45 29.8( )ult uq q m s = +( )1ult uq q N= +( 1)111N Nult usq q NN B | | | | | = ` | |\ )\ Table 70Recommended resistance factors for foundations in/on rock based on T= 3.0 (pf= 0.135%)5LRFD Shallow Foundations DESIGNNCHRP 12-66 AASHTO LRFD Specifications for Serviceability in the Design of Bridge FoundationsFinal report in NCHRP never Published Can be obtained6LRFD Serviceability Limit StateRESEARCH TEAM6LRFD Serviceability Limit StateSamuel G. Paikowsky, Mary Canniff, GTR, Inc.Ayhan Garbuz, Yu Fu, Roiy Guy Geotechnical Eng. Research Lab., University of Massachusetts LowellZeidan Ashraf, Guy Levi, Wisam Mualem and Sam Frydman, Technion Israel Institute of Technology, Structural Engineering and Construction Management area of the Civil Engineering DepartmentJapan Team: Yusuke Honjo, Gifu University, IkumasaYoshida, Shuichi Suzuki, Hyoudou Junichi, TEPSCO, Tokyo, Masahiro Shirato, PWRI, JapanSusan Faraji, Faraji Consulting, Inc., Winchester, MAMain Challenges Establish serviceability criteria for bridges under normaloperation. Compilation of large high quality databases for axial andlateral single and group deep foundation displacements, aswell as shallow foundations and bridge substructures. Establish uncertainty of displacement prediction methods. Develop methodology for establishing LRFD parameters forserviceability.ObjectivesDevelop procedures for serviceability design of bridgefoundations, calibrate them and write specificationsPractically, develop new methodology to calibrateserviceability in LRFD and write new specifications.6LRFD Serviceability Limit StateDeveloped Serviceability Criteria CriteriaBridge TypeLimit StateLimitationsComments Angular distortion Simple Support /l < 1/200 l ll l 50ft subjected to limit vertical displacements exc. rigid frame structures Angular distortionContinuous/l < 1/250 l ll l 50ft steel exc. integral abutment bridges assuming pinned connection at the abutment SteelVA < 3in l ll l 50ft steel I/l ll l 20in3 Moulton, 1986, Table 7; Current study Table 4.14 Abutment differential vert. displacement for bridge lifetime ConcreteVA < 3in l ll l 100ft Moulton, 1986, p.58; Current study Table 4.14 SteelVP < 2in l ll l 50ft Moulton, 1986, Table 7; Current study Table 4.14 Pier differential vert. displacement for bridge lifetimeConcreteVP < 2in SteelVA < 2inl ll l 50ft Abutment differential vert. displacement following bridge completion ConcreteVA < 2in SteelVP < 1.25in Pier differential displacement following bridge completion ConcreteVP < 1.50in Horiz. displacementsAll Substructuresh < 1.5inControlling criteriaAASHTO Moulton 1986, h < 2.0in Horiz. displacements combined with vert. displacements All Substructuresh < 1.0inControlling criteriaAASHTO Moulton 1986, h < 1.5in 6LRFD Serviceability Limit StateDatabases and Their AnalysesPerformance of DP Compression, Tension, and Lateral / Pile Type/Soil TypePerformance of DFCompression, Tension, and Lateral / Construction Type/Soil TypePerformance of Pile GroupsVertical / Lateral / Soil TypePerformance of Shallow FoundationsPrototype / Full Scale / Soil TypePerformance of Full Scale StructuresPiers / Abutments6LRFD Serviceability Limit StateMethods of Analysis for Lateral Displacement of a Deep Foundation Equilibrium Method Broms (1964a, 1964b) p-y Curves Method (BEF, Winkler, 1887, McCllelandand Focht, 1958, Matlock, 1970, Reese 1977,1984, 1985). COM624P (Wang and Reese, 1993) LPILE 5.0 (Reese et al. 2004) Strain Wedge Method (Norris, 1986) SWM 6.0(Ashour and Norris, 2000) Normalized Relations Lateral Load vs. Normalized Disp.(current research)6LRFD Serviceability Limit StateLaterally Loaded Single Piles Summarized by Method of Analysis0 0.5 1 1.5 2 2.5 3Pile Top Deflection (inch)0.000.200.400.600.801.001.201.401.601.80, COV COVH-PilesPipe Piles (18")Pipe Piles (24")PPCAll Pipe PilesAll PilesDS in SoilCOM624P Analysis0 0.5 1 1.5 2 2.5 3Pile Top Deflection (inch)0.000.200.400.600.801.001.201.401.601.80, COV COVH-PilesPipe Piles (18")Pipe Piles (24")PPCAll Pipe PilesAll PilesSWM Analysis6LRFD Serviceability Limit StateLateral Displacement of Single Pilesvs. Resistance Factor 0 0.5 1 1.5 2 2.5 3Lateral Displacement (inch)00.20.40.60.81Resistance Factor (25)(23)(18)(12)(11)H-PilesBroms(no. of cases)Fit 1: BromsY = -0.130X + 0.705, R2 = 0.927Fit 2: LogY = -0.168ln(X) + 0.554, R2 = 0.9900 0.5 1 1.5 2 2.5 3Lateral Displacement (inch)00.20.40.60.81Resistance Factor (26)(24)(19)(12)(12)(25)(23)(18)(12)(11)H-PilesCOM624P(no. of cases)Broms(no. of cases)SWM(no. of cases)Normalized(no. of cases)6LRFD Serviceability Limit StateExample of Resistance factors for SLSRecommended Resistance Factors for SLS of Deep Foundations Pile TypeMethod Range of Settlement (inch) Resistance Factor H p-y curves COM624P / LPile 0.00 < 0.500.55 0.50 < 1.500.60 1.50 < 2.000.65 2.00 < 2.500.70 SWM 0.00 < 0.500.55 0.50 < 2.500.60 Normalized 0.00 < 1.500.60 1.50 < 2.500.65 6LRFD Serviceability Limit StateShallow Foundations Bias & COV vs. Settlement0.5 1.0 1.5 2.0 2.5 3.0Foundation Settlement (inch)0.00.51.01.52.02.53.0, COVAASHTOBias ()COV0.5 1.0 1.5 2.0 2.5 3.0Foundation Settlement (inch)0.00.51.01.52.02.53.0, COVD'AppoloniaBias ()COVBias ( ) Relates to the mean of the ratio of measured over calculated loads for a given displacement6LRFD Serviceability Limit State0 0.5 1 1.5 2 2.5 3Settlement (inch)00.20.40.60.81Resistance Factor (85)(51)(36)(18)(18)(17)(14)(13)(7)(6)AASHTO (No. of cases)Recommended Data Ranges0 0.5 1 1.5 2 2.5 3Settlement (inch)00.20.40.60.81Resistance Factor (74)(52)(40)(22)(22)(21)(19)(18)(14)(11)D'Appolonia (no. of cases)Recommended Y = 0.25*X-0.85, 0.7Shallow Foundations Settlement vs. Resistance Factor 6LRFD Serviceability Limit StateFor reliability index = 1.28 (pf= 10%), and load factors taken as unityBias of LL = 1.15, COVQL= 0.2Bias of DL = 1.05, COVQD= 0.1Method Range of Settlement (inch) Resistance Factor Efficiency Factor / 0.00 < 1.000.850.34 1.00 < 1.500.800.48AASHTO 1.50 < 3.000.600.48 Resistance Factors for Shallow Foundations SLS916LRFD Serviceability Limit StateCASE HISTORY LRFD BRIDGE DESIGNUSING AASHTO 2006 SPECIFICATIONSExisting and Replacement SakonnetRiver BridgesReplacement Bridge Foundation LayoutW. AbutH-PILESP1 P2 P3P4P5P6PIPE PILESH-PILESP8P7SPREAD FOOTINGE. Abut.P9Test SiteSOIL PROFILETest SiteHP 14x117El 4 to -109.6 ft,1 to 33 mHP 14x117 (112 ft/4m! "est Pile Vibrated to 92 ft (28m) Driven w/ ICE 1070 dieselhammer (3 bpi @ 22 kip-ft) (1 bl/10mm @ 30 kN-m) Restrikes @ 1, 7, & 14 daysCurrent Specifications Resistance Factors for Driven Piles (Static Analysis)Condition/Resistance Determination MethodResistanceFactorNominal Resistance of Single Pile in Axial CompressionStatic Analysis Methods, statSkin Friction and End Bearing Clay&Mixed Soils-method (Tomlinson, 1987; Skempton, 1951)-method (Esrig & Kirby, 1979; Skempton, 1951)-method (Vijayvergiya & Focht, 1972; Skempton, 1951)Skin Friction and End Bearing: SandNordlund/Thurman Method (Hannigan et al., 2005)SPT-method (Meyerhof)CPT-method (Schmertmann)End bearing in rock (Canadian Geotech. Society, 1985)0.350.25 0.40 0.45 0.300.500.45Block Failure, b1Clay 0.60Uplift Resistance of Single Piles, upNordlund Method-method-method-methodSPT-methodCPT-methodLoad test0.350.250.200.300.250.400.60Group Uplift Resistance, ugSand and clay 0.50Horizontal Geotechnical Resistance of Single Pile or Pile GroupAll soils and rock 1.0(AASHTO 2008Interim 2006,, Table 10.5.5.2.3-1) continued}Where is the end bearing?Where arethe pile/soil types?Where is method?H Pile # S$mmar% (14x177& penetration ' 112ft/4m!Analysis CombinationEstimatedCapacity (Rn)(kips)NCHRP 507ResistanceFactor for HPiles inSand()FactoredResistance(Rr)NCHRP 507ResistanceFactor for HPiles in MixedSoils ()FactoredResistance(Rr)AASHTO LRFDSpecifications2006ResistanceFactor ()FactoredResistance(Rr)-Method/Thurman (Steel Only) 1,1570.303470.20231Not Specified--Method/Thurman (Box Area) 1,339 402 268 -Nordlund/Thurman (Steel Only) 1,1370.455120.353980.45512Nordlund/Thurman (Box Area) 1,319 594 462 594FHWA Driven Ver. 1.2 (Steel Only) (2)1,1420.45514FHWA Driven Ver. 1.2 (Box Area) (2)1,329 598FHWA Driven Ver. 1.2 (Steel Only) (3)935 421FHWA Driven Ver. 1.2 (Box Area) (3)976 439Prediction for Static Pile Capacity Combinations (112ft /34m penetration)(1kip=4.45kN)Notes:1. Resistance Factors taken from NCHRP Report 507 Table 25 for a Redundant Structure.2. Calculated by inserting the friction angles and unit weights directly into DRIVEN.3. Calculated by inserting the uncorrected SPT N-values directly into DRIVEN. N-values were takenfrom boring HA-HP only. Friction angle was limited to 36 degrees.Recommended range for preliminary designFoundation Test ProgramHP 14x117 "est (rameHP 14x117 (112 ft 4m! Static )oad "estMax. Applied Load583kips2593kNMax. Settlement,Pile Top2.7in6.9cmFailure Load by Davisson Criterion378kips1681kNDavisson Settlement, Pile Top0.7in1.8cmPile TopPile Tip)" Recommended resistance factors (*+HRP ,-7! Static Load Test (in/out the AAST! Specs)Table 30. Recommended resistance factors for static load tests Resistance Factor - Site Variability No. of Load Tests Per Site Low Medium High 10.800.700.55 20.900.750.65 30.900.850.75 4 0.900.900.80 HP 14x117 (112 ft 4m! S$mmar% Res$ltsEstimation MethodNominal CapacityResistance FactorFactored ResistanceStatic Prediction Nordlund/Thurman1248 kips5551 kN0.45 (AASHTO)562 kips2500 kNStatic Prediction (GTR) Beta/Thurman1248 kips5551 kN0.20 (NCHRP 507)250 kips1112 kNStatic Load Test378 kips1681 kN(Davisson)0.55 (large variability)208 kips925 kN0.70 (med. Variability)265 kips1179 kNAASHTO Factored Design load 1.5 times Failure Load and 2.1 to 2.7 Factored LT