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Current U.S. Practice forLRFD Design of Drilled ShaftsDan Brown, P.E.Dan Brown and Associates
Major Factors Favoring Selection/Use ofDrilled Shafts Magnitude of loads Presence of strong bearing stratum at suitabledepth Urban / Environmental (e.g., avoidance of piledriving noise & vibration) Elimination of footing (e.g., top downconstruction, cofferdams, congested area) Seismic or other high lateral demands
Trends Larger diameters and depths: up to 13ft(4m) dia and 260ft (80m) deep Greater demands for flexure, includingconsiderations of seismic or other extremeevent loads Greater acceptance of slurry or wet-holetechniques More congested sites, challengingapplications Increased use of load testing and integritytesting Applications other than foundations; e.g.,secant or tangent walls, cutoff walls
Axial Resistance – AASHTO (LRFD) Computed static side & base resistance fromFHWA & State DOT guidelines Strength limit state, serviceability limit state Resistance factor increase for site-specificload testing (0.7 max for strength limit) 20% reduction in axial resistance formonoshaft foundation on single column pier Resistance factor of 1.0 for extreme eventloading or conditions (seismic, collision, ice,extreme scour)vesselPSMean WaterLevel
Concept of Limit StateA condition for which some component of the structuredoes not fulfill its design functionCan be defined in terms of: strength: for example, bearing capacity failure,structural yield in flexure serviceability: e.g., excessive settlement or in terms of strength or serviceability but for anextreme event, e.g., earthquake
LRFD Design Equation i i Qi i Riηi iQi iRi load modifier for load component i load factor for force component i nominal value of force component i resistance factor for resistance component i nominal value of resistance component i
Notations(phi) is used for the LRFD resistance factor;not to be confused with f (phi) used for the soilfriction angle (gamma) is used for both soil unit weight andLRFD load factor Load factors are subscripted to differentiate loadsource, e.g., p permanent load, L live load
LRFD: The Basic IdeaForceFrequency ofOccurrenceResistanceMagnitude of Force Effect or Resistance
LRFD: The Basic Idea (Cont’d)Nominal (unfactored)force effects (loads)Factoredforce effectsQN QN Factoredresistances RN Nominal (unfactored)resistancesRN RN Q RNQNLoadX factors, ResistanceXfactors,
Resistance Factor: What Does it Mean? Resistance Factor: a multiplier used to reduce thenominal (calculated) resistance to achieve a design thatis safe Safe: the probability that force effects will exceedresistance is sufficiently low Sufficiently low: 1 : 1,000 typical varies with limit state,consequences of failure, other factors
TerminologyAcceptable terms Nominal Resistance Nominal base resistance Factored resistance Displacement at service limit Factored force effects Extreme event conditionsAvoid these! Allowable load Capacity Design loads Ultimate capacity
AASHTO Limit States for Bridge DesignLimit State TypeStrengthAASHTO LIMIT STATES FOR BRIDGE DESIGNCaseLoad CombinationINormal vehicular use of the bridge without windIIUse of the bridge by Owner-specified special vehicles, evaluation permitvehicles, or both, without windIIIBridge exposed to wind velocity exceeding 55 mphIVVery high dead load to live load force effect ratiosVNormal vehicular use of the bridge with wind of 55 mphILoad combination including earthquakeExtreme EventIIIIIServiceIIIIVFatigueIce load, collision by vessels and vehicles, and certain hydraulic events with areduced live load other than that which is part of the vehicular collision load, CTNormal operational use of the bridge with a 55 mph wind and all loads taken attheir nominal valuesIntended to control yielding of steel structures and slip of slip-criticalconnections due to vehicular live loadLongitudinal analysis relating to tension in prestressed concrete superstructureswith the objective of crack control and to principal tension in the webs ofsegmental concrete girdersTension in prestressed concrete columns with the objective of crack controlRepetitive gravitational vehicular live load and dynamic responses under theeffects of a single design truck
AASHTO Load Combinationsand Load Factors(AFTER AASHTO 2007, TABLE 3.4.1-1)LoadCombinationLimit StateStrength IStrength IIStrength IIIStrength IVStrength VExtreme Event IExtreme Event IIService IService IIService IIIService IVFatiguePLLLWAWSUse one of these at a timePL p p CS0.50/1.200.50/1.200.50/1.20 p p p p1.001.001.001.001.35 201.00/1.20--0.75permanent loadlive loadwater load and stream pressurewind load on structureWLFRTGSETCSTG TG TG TG-SE SE SE SE- TG- SE- TG- SE- TG- SE1.00EQ-IC-CT-CV-1.00-1.001.001.00----wind on live loadEQearthquakefrictionICice loadtemperature gradientCTvehicular collision forcesettlementCVvessel collision forceuniform temperature, creep, and shrinkage
Structural Analysis of Bridge Used to EstablishFoundation Force EffectsBridge subjected to load combination corresponding to oneBridge subjected to load combination correspondingthelimitin Table10-3toofoneof thelimit statesstates in Table10-2VRQRQMRMVReactions at column-shaftconnection obtained fromare taken as axial, shear, and momentforce effects applied to top of thestructural analysis model offoundationsuperstructure are takenas axial, shear, andmoment force effectsapplied to top of foundationReactions at fixed-end column supportsobtained from structural analysis modelof superstructure
Strength Limit States for Drilled Shafts Lateral geotechnical resistance of soil and rock stratum,for single shafts and shaft groups Geotechnical axial resistance (compression and uplift),for single shafts and shaft groups Structural resistance of shafts, including checks for axial,lateral, and flexural resistances Resistance when scour or other unusual conditions occur
Service Limit States for Drilled Shafts Settlement (vertical deformation) Horizontal movements at the top of the foundation Rotations at the top of the foundation Settlement and horizontal movements under scour at thedesign flood Settlement due to downdrag
Design for Lateral Loading Geotechnical Strength Limit State Pushover failure – minimum embedment Structural Strength Limit State Yield in flexure Serviceability Limit StateNominal ResistanceFactored Resistance Extreme Event Conditions Strength at max scour, seismicP (kips) Lateral DeformationsPermissibleMoment (ft-kips)7-17
Design for Axial Loading Geotechnical Strength Limit State Axial failure – plunging or 5% displacement Structural Strength Limit State Serviceability Limit State Settlement Extreme Event Conditions Strength at max scour, seismic
Interpretation of Axial Load Test DataTest Shaftsand23’38’rock50’Displacement (inches)0.0-0.5-1.0-1.5-2.0-2.50100020003000Load (kips)19-19
0.0Toe Displacement(inches)Segment Displacement(inches)Interpretation of Strain Gauge Data0-0.5-1-1.5-2051015Side Shear (ksf)20-0.5-1.0-1.5-2.00200400600800 1000 1200Load (kips)19-20
Resistance Factors for Drilled ShaftsLimit StateComponent of ResistanceStrength I throughStrength VGeotechnicalLateral ResistanceOverturning of individual elastic shaft;head free to rotateOverturning of single row, retaining wallor abutment; head free to rotatePushover of elastic shaft within multiplerow group, w/ moment connection to capSide resistance in compression/upliftStrength I throughStrength VBase resistance in compressionGeotechnical AxialResistanceGeomaterialp-y method pushover analysis;Ch. 120.67All geomaterialsp-y pushover analysis0.67All geomaterialsp-y pushover analysis0.80Cohesionless soil or IGMBeta method0.55 / 0.45Cohesive soilAlpha method0.45 / 0.35RockEq. 13-350.55 / 0.45Cohesive IGMModified alpha method0.60 / 0.50Cohesionless soil1. N-value0.50Cohesive soilBearing capacity eq.0.40Static compressive resistance from loadtestsStatic uplift resistance from load testsGroup uplift resistanceExtreme Eventand IITable 10-5Reference ManualEq. 13-22CGS (1985)0.550.50 0.7All geomaterials0.60Cohesive soil0.55Cohesive and cohesionless soil0.45Axial compression0.75Combined axial and flexure0.75 to 0.90Shear0.90All cases, all geomaterialsI1.2.All geomaterialsGroup block failureStructuralResistance of R/CService IResistanceFactor, All geomaterialsRock and Cohesive IGMStrength I throughStrength V;Equation, Method, or ChapterReferenceCh. 13, Appendix BAxial geotechnical uplift resistanceAll geomaterialsGeotechnical lateral resistanceAll geomaterialsAll other casesAll geomaterialsMethods cited above for StrengthLimit Statesp-y method pushover analysis; Ch.12Methods cited above for StrengthLimit States1.000.800.801.00
Resistance Factors: RedundancyResistance factor values in AASHTO and inthe Reference Manual are based on theassumption that drilled shafts are used ingroups of 2 to 4 shafts φ-values decreased by 20% for single shaftsupporting a bridge pier
Agency-Specific Resistance Factors For design equations not covered in AASHTO or in theReference Manual For specific geomaterials encountered locally orregionally For local construction practicesAgencies have the option, in fact are encouraged, toconduct in-house calibration studies to establishresistance factors for the cases aboveSection 10.1.1.2 of Reference ManualTransportation Research Circular No. E-C079
Summary LRFD base design approach is now well-established Basis for design includes rational approach for: Serviceability Strength Extreme event conditions We need to use consistent terminology to avoid confusion andmistakes!Thanks for Listening!
LRFD Design of Drilled Shafts Dan Brown, P.E. Dan Brown and Associates . Major Factors Favoring Selection/Use of Drilled Shafts . Bridge subjected to load combination corresponding to one of the limit states in Table 10 - 2 Reactions at column-shaft connection obtained from
