Calibration of Resistance Factors for Drilled Shafts for the 21 FHWA Design Method Murad Y. Abu-Farsakh, Ph.D., P.E. Qiming Chen, Ph.D., P.E. Md Nafiul Haque, MS Feb 2, 213 213 Louisiana Transportation Conference
Background ASD vs. LRFD ASD involves applying a FS to account for uncertainties in both the applied loads and soil resistances, LRFD separates uncertainties associated with estimated loads and resistances (load factors & resistance factors) Since the introduction of LRFD (AASHTO 1994): Bridge superstructures have been designed using LRFD, Bridge foundation were designed using ASD, This leads to inconsistent levels of reliability.
Background To maintain a consistent level of reliability, the FHWA & ASSHTO set up a mandate date (October 1, 27) after which all DOT bridge projects should be designed using LRFD method. To comply with this, several research efforts for LRFD calibration of 1999 FHWA drilled shafts method Paikowsky, 24, UF, FHWA, and O Neil 1996 Allen, 25, TRB Circular E-C79 Yang et al. 28, midwestern U.S., O-cell in weak rock Liang and Li 29, NCHRP 24-17 Abu-Farsakh et al. 21 (7-2GT, Report # 47)
Background In 21, a new design manual (Brown et al. 21) was published by the FHWA in which a new design methodology for drilled shafts was introduced, In addition, more than 1 new drilled shaft load tests were collected by Louisiana DOTD since the previous study. There is a need to calibrate the resistance factors (f) for the 21 FHWA design method that reflect Louisiana soil and LA DOTD design experience.
Objectives The main objective of this study was to calibrate resistance factors [side (f side ), tip (f tip ), and total (f total )] of axially loaded drilled shafts installed in Louisiana using the 21 FHWA drilled shafts design method based on local load test - soil profile database, and the LA DOTD design experience/practice. The resistance factors for the 1999 FHWA design method were also developed for comparison. The target reliability value (b T ) and the corresponding resistance factor were developed for both design methods.
ASD versus LRFD In Allowable Stress Design (ASD) Q Q D Q L Q all Rn FS where, Q = design load; Q all = allowable design load; R n = nominal (ultimate) resistance of the structure. In Load and Resistance Factor Design (LRFD) f R n g D Q D g L Q L g Q where, Φ = resistance factor, R n = nominal resistance; g D = load factor for dead load; g L = load factor for live load; Q D = dead load; and Q L = live load. i i
LRFD Concepts Limit state function: g (R, Q) = R Q b g g R 2 R Q 1 Q Pf Pr (g ) Probability density functions for load and resistance Probability of failure
LRFD Concepts The relationship between the probability of failure and the reliability index (b): Pf 1 ( b) The strength limit state I requires: γ f i Q ni R n The limit state LRFD design equation: g(r, Q) γ i Q ni f i R ni f i R ni P f b 1-1 1.28 1-2 2.33 1-3 3.9 1-4 3.71 1-5 4.26 1-6 4.75 1-7 5.19 1-8 5.62
Reliability Analysis Methods for Calibration First order second moment method (FOSM) (Closed form solution) Advanced First order second moment method (AFOSM) First order reliability methods (FORM) (Iterative procedure) Second order reliability methods (SORM) (Iterative procedure) Monte Carlo Simulation method (Iterative procedure)
Calibration Methodology Evaluate the measured (R m ) and predicted resistance (R p ) values for drilled shafts, Evaluate the bias factor (l R =R m / R p ) and COV R, Determine distribution function (Normal, lognormal) Formulate the limit state functions (g = R - Q) Develop the reliability analysis procedure and calculate reliability index (b) Select the target reliability index (b T ) Determine the resistance factor (f) for drilled shaft design method corresponding to b T.
Drilled Shaft Load Test Database 19 cases from LA; 15 cases from MS 19 15 Approximate locations of the investigated drilled shafts
Summary of Drilled Shaft Tests I.D. Dia (feet) Length (feet) Soil Type Load Test Type Predicted (21 FHWA design method (tons) Predicted (1999 FHWA design method) (tons) Measured (tons) DS-1 2.5 53.1 Silty Clay, Sand Base Top Down 584 485 17 DS-2 2.5 35.1 Clay and Sand with Sand Base Top Down 455 382 784 DS-3 3 54.1 Clayey Silt, Sand Base O-cell 326 247 344 DS-4 5.5 76.1 Silty Sand with Sand Base O-cell 212 1571 156 DS-5 6 86.9 Stiff Clay with Clay Base O-cell 1225 145 175 DS-6 2.5 77.4 Sand Clay with Sand Base O-cell 839 521 888 DS-7 2.5 65 Fully Sand with Clay Base O-cell 588 39 67 DS-8 2.5 49.9 Silt,Clay with Clay Base O-cell 377 325 285 DS-9 5.5 4.7 Clay,Silt with Clay Base O-cell 566 455 531 DS-1 3 44.9 Clay, Silty Clay with Clay Base Top Down 327 27 45 DS-11 3 62 Clay with Sand Base Top Down 488 418 428 DS-12 4.5 49.9 Fully SAND O-cell 166 881 123 DS-13 4 73.1 Sand with Clay, Sand base O-cell 132 9 12 DS-14 4 123 CLAY/SAND-Sand Base O-cell 1428 92 1515 DS-15 4 138.1 SAND O-cell 1631 147 1413 DS-16 4 119.1 CLAY, SAND with SAND Base O-cell 279 161 1277 DS-17 5.5 94.1 SAND/CLAY with SAND Base O-cell 1978 163 2145 B = 2 ft to 6 ft; L = 35.1 ft m to 138.1 ft
I.D. Summary of Drilled Shaft Tests Dia (feet) Length (feet) Soil Type Load Test Type Predicted (21 FHWA design method (tons) Predicted (1999 FHWA design method) (tons) Measured (tons) DS-18 4 96.1 SAND with Sand Base O-cell 1459 86 182 DS-19 4 82 SAND/GRAVEL/Sand Base O-cell 1467 121 1258 DS-2 4 97.1 Sand with Clay Interlayer and Sand base O-cell 936 614 119 DS-21 4 82 SAND with SAND Base O-cell 1159 84 875 DS-22 4 89 Clay O-cell 2558 21 223 DS-23 6 47.9 SAND O-cell 1585 128 132 DS-24 4.5 64 SAND/CLAY, Clay Base O-cell 113 715 498 DS-25 4 64 Sand with Clay Base O-cell 6 496 445 DS-26 2 4 CLAY with Clay Base O-cell 315 262 215 DS-27 4 67.5 Fully Clay, Clay Base O-cell 425 36 549 DS-28 2.5 81.5 Fully Clay, Clay Base O-cell 455 384 57 DS-29 4 77.5 Fully Clay, Clay Base O-cell 751 639 82 DS-3 6 43 Clay, Sand with Sand Base O-cell 2431 1914 2766 DS-31 5.5 47.5 Fully Sand wth Sand Base O-cell 1874 1537 2343 DS-32 5.5 48 Sand, Clay with Sand Base O-cell 1324 1139 682 DS-33 5.5 53.85 Clay, Sand with Sand Base O-cell 157 1347 887$ DS-34 5.5 51.12 Clay, Sand with Sand Base O-cell 1149 92 1178 B = 2 ft to 6 ft; L = 35.1 ft m to 138.1 ft
Geotechnical Conditions Soil Description Loose tan silt Loose clayey silt mc, LL, PL 15 3 45 6 c (kpa) 2 4 6 8 2 Firm to stiff silty clay with silt 2 2 4 4 4 6 Loose sandy silt with clay 6 6 Depth (ft) 8 1 Very dense silty fine sand Dense to very dense fine sand 8 1 mc LL PL 8 1 SPT c 12 12 12 14 Very dense gray and green silty fine sand 14 14 16 16 16 18 18 18 5 1 15 SPT (N) Typical summary of geotechnical data for a tested shaft
Measured Resistance from O-Cell Test SHAFT SIDE SHEAR SHAFT SIDE SHEAR O-cell SHAFT END BEARING Settlement curves by O-cell
Measured Resistance from O-Cell Test SHAFT SIDE SHEAR SHAFT SIDE SHEAR O-cell SHAFT END BEARING Equivalent top-down settlement curve
Measured Resistance from O-Cell Test 8 Load (MN) 2 4 6 8 1 Upward Top of Bottom O-cell Movement (mm) 6 4 2 5% B R m-side О 1 Downward Bottom of Bottom O-cell Movement (mm) -2-4 -6 5% B R m-tip О Settlement (mm) 2 3 4 5% B О R m 1 2 3 4 5 6 Load (MN) a) Settlement curves by O-cell b) equivalent top-down settlement curve Determine side, tip, and total resistance at 5%B from O-cell tests 5
FHWA Design Method for Drilled Shafts 1999 FHWA Design Method for Drilled Shafts (O Neil and Reese) The nominal ultimate axial resistance (R p-u ) of a drilled shaft: R p-u R p-u = R p-b + R p-s = q b.a b + f si.a si Soil Condition Resistance Component Equations Cohesive Soil Cohesionless Soil Skin Friction End Bearing Skin Friction f SZ f q N sz b c β (N α S z N c uz S, ub R 1.33 (ln I.25 b 1.2 p-s βσ' 2.1 tsf, β 1.5.135 6 z z r.5 L 1) R /15)(1.5.135 p-s z f sz, for N.5 da 6 ) I L r E 3S βσ' z 15 da for N s ub 6 15 f s q b End Bearing q.6n b SPT 3 tsf
FHWA Design Method for Drilled Shafts 21 FHWA Design Method for Drilled Shafts (Brown et al.) The nominal ultimate axial resistance (R p-u ) of a drilled shaft: R p-u R p-u = R p-b + R p-s = q b.a b + f si.a si Soil Condition Resistance Component Equations Cohesive Soil Skin Friction End Bearing f q N sz b c α S z N c uz S, ub R 1.33 (ln I p-s r L f sz 1), da I r E 3S s ub f s Cohesionless Soil Skin Friction f SZ βσ' 2 kpa (2.1 tsf), z ' / p p.47 N z m 6 R p-s β (1- sinf )( / )tanf K p a L βσ' z anf p da q b End Bearing q b.6n SPT 3 tsf
Predicted Resistance (1999 FHWA Method) The total developed load (R T ) at a specific settlement: R T = R p-b (developed) + R p-s (developed) a) Side load transfer for cohesive soil b) End load transfer for cohesive soil
Axial Compression Force Failure Threshhold,% Predicted Resistance (FHWA 21 Method) The total developed load (R T ) at a specific settlement: R T = R p-sn + h R p-bn 2 Cohesionless Cohesive 15 Failure Threshhold 1 5 2 4 6 8 1 12 displacement,% dia. of shaft Normalized load transfer representing the average trend value for drilled shaft
Displacement (in.) Predicted Resistance (FHWA Methods). Load (tons) 2 4 6 8 1.5 1. 1.5 2. 2.5 Rp Rp Rm 3. 3.5 4. Measured Resistance Calculated Resistance using 21 FHWA Method Calculated Resistance using 1999 FHWA Method Example of load-settlement analysis and measured value
Predicted Resistance (FHWA Method) Determine load settlement curves Determine predicted side, tip, and total resistance 2 Load (MN) 1 2 3 4 Settlement (mm) 1-1 Interpreted side resistance (Rp_side) 5%B 2 4 6 Load (MN) 5%B Shaft diameter = 1.52m Interpreted tip resistance (R p_tip ) Settlement (mm) 2 4 6 8 ----Predicted Resistance ----Measured Resistance 5% of the shaft diameter Shaft diameter = 1.52 m R p R m -2 1
Predicted Drilled Shaft Side Resistance, Rp (tons) Predicted Drilled Shaft Resistance, Rp (tons) Predicted Drilled Shaft Tip Resistance, Rp (tons) Results Predicted versus Measured 2 3 15 15 1999 FHWA Design Method Rfit = 1.1Rm 25 2 1999 FHWA design method Rfit =.79Rm 12 9 1999 FHWA Design Method Rfit =.47Rm Louisiana Mississippi 1 5 15 6 1 Louisiana 5 Louisiana 3 Mississippi Mississippi 5 1 15 5 1 2 15 2 25 3 3 6 9 12 15 Measured Drilled Shaft Side Resistance, Measured Rm Drilled (tons) Shaft Resistance, Measured Rm (tons) Drilled Shaft Tip Resistance, Rm (tons) Measured vs. predicted resistance of drilled shafts 1999 FHWA Design Method
Predicted Drilled Shaft Side Resistance, Rp (tons) Predicted Drilled Shaft Tip Resistance, Rp (tons) Results Predicted versus Measured 2 15 1 5 Predicted Drilled Shaft Resistance, Rp (tons) 3 25 2 15 15 21 FHWA design method Rfit = 1.2Rm 12 21 FHWA Design Method Rfit = 1.54Rm 5 Louisiana Mississippi 9 6 3 21 FHWA Design Method Rfit =.47Rm Louisiana Mississippi Louisiana Mississippi 5 1 15 1 2 15 2 25 3 3 6 9 12 15 Measured Drilled Shaft Side Resistance, Measured Rm Drilled (tons) Shaft Resistance, Measured Rm (tons) Drilled Shaft Tip Resistance, Rm (tons) Measured vs. predicted resistance of drilled shafts 21 FHWA Design Method
Results: Statistic Analyses Statistical analysis of the 21 FHWA drilled shaft design method Arithmetic calculations l R = R m /R p R p /R m Best fit calculations Mean σ COV Mean R fit /R m.99.3.3 1.1 1.2 Statistical analysis of the 1999 FHWA drilled shaft design method Arithmetic calculations l R = R m /R p R p /R m Best fit calculations Mean σ COV Mean R fit /R m 1.27.38.3.87.79
Probability (%) Probability (%) Histograms of bias, l, for different resistance components 1999 FHWA Method Probability (%) 6 5 4 3 2 1 5 3 Side Resistance (1999 FHWA design method) Total Resistance (1999 FHWA design Tip method) Resistance (1999 FHWA design method) Log-Normal 4 Distribution Normal Distribution 3 2 1 Log-Normal Distribution Normal Distribution 2 1 Log-Normal Distribution Normal Distribution 1 2 13 2 3 1 4 2 3 4 5 Rm/Rp Rm/Rp Rm/Rp
Histograms of bias, l, for different resistance components 21 FHWA Method Probability (%) 6 5 4 3 2 1 5 3 Total Resistance (21 FHWA design Tip method) Resistance (21 FHWA design method) Side Resistance (21 FHWA design method) Log-Normal Distribution 4 Log-Normal Distribution Normal Distribution Log-Normal Distribution Normal Distribution Normal Distribution 2 3 Probability (%) 2 1 Probability (%) 1 1 2 31 2 3 1 42 3 4 5 Rm/Rp Rm/Rp Rm/Rp
Cumulative Density Function (CDF) of Bias Values (l) 2.5 2.5 2. 2. Standard Normal Variable, Z 1.5 1..5. -.5-1. -1.5-2. -2.5.5 1 1.5 2 2.5 Bias (lr) Measured Bias Value Predicted Normal Dist. Predicted Log-Normal Dist. Predicted Log-Normal Dist. (best fit to tail) 1999 FHWA Design Method Standard Normal Variable, Z 1.5 1..5. -.5-1. -1.5-2. -2.5.5 1 1.5 2 Bias (lr) Measured Bias Value Predicted Normal Dist. Predicted Log-Normal Dist. Predicted Log-Normal Dist. (best fit to tail) 21 FHWA Design Method
Summary of Bias (l R m /R p ) for Drilled Shafts 21 FHWA Method Statistics Tip Side Total Max. 5.12 1.17 1.43 Min..47.28.49 Mean (l) 2.16.65.94 COV.53.36.26 1999 FHWA Method Statistics Tip Side Total Max. 5.39 1.47 1.81 Min..43.44.6 Mean (l) 2.26.91 1.22 COV.55.34.28
Contribution of Side and Tip Resistance Predicted resistance contribution (%) Measured resistance contribution (%) 1 8 6 4 2 1999 FHWA Method Side Resistance (average: 71%) Tip Resistance (average: 29%) 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 Shaft Number 1 8 O-Cell Measurements Predicted resistance contribution (%) 1 8 6 4 2 21 FHWA Method Side Resistance (average: 77%) Tip Resistance (average: 23%) 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 Shaft Number Side Resistance (average: 52%) 6 4 2 Tip Resistance (average: 48%) 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 Shaft Number
LRFD Calibration Methods Monte Carlo Simulation method (MCS method) Target reliability index: 3. Dead load/live load ratio: 3. Load statistics and factors (AASHTO):
Monte Carlo Simulation g Q LL g LL g DL f Q Q DL LL l R - g LL l LL g DL l DL Q Q DL LL Random variables: l R, l L, and l D Number of simulation: 5
Resistance Factor, f Resistance Factor, f Resistance factors 1. 1..9 From measured bias data From "best fit to tail".9 From measured bias data From "best fit to tail".8.8.7.6.5.48.7.6.6.4.41.5.5.3 1 1.5 2 2.5 3 3.5.4 1 1.5 2 2.5 3 3.5 β T β T 21 FHWA Method 1999 FHWA Method
LRFD Calibration Methods Resistance Factors Tip Side Total f tip f tip /λ f side f side /λ f total f total /λ 21 FHWA design method.53.25.26.4.5.53 1999 design method.52.23.39.43.61.5
LRFD Calibration Methods b T = 3. Resistance Factor, f Efficiency Factor, f/λ Current study (21 FHWA design method) Current study (1999 FHWA design method) Liang and Li (29) Paikowsky (24) and AASHTO (27).48 in mixed soils.41 in mixed soils (best fit to tail).6 in mixed soils.5 in mixed soils (best fit to tail).45 in clay.5 in sand.35 in mixed soils.45 in cohesive soils.55 in cohesionless soils.48 in mixed soils.41 in mixed soils (best fit to tail).47 in mixed soils.38 in mixed soils (best fit to tail)
Summary and Conclusions Statistical analyses showed that: The 21 FHWA design method overestimates the total drilled shaft resistance by an average of two percent, The 1999 FHWA design method underestimates the total drilled shaft resistance by an average of 21 percent. The prediction of tip resistance is much more conservative than that of side resistance. A large scatter in the prediction of side resistance was observed. The tip, side, and total resistance factors for drilled shafts were calibrated using MCS reliability-based method. The lognormal distribution of bias was assumed.
Summary and Conclusions Based on reliability-based analyses: The resistance factors for 21 FHWA method: f total =.48, f side =.26, and f tip =.53. The resistance factors for 1999 FHWA method: f total =.6, f side =.39, and f tip =.52.
Acknowledgement Louisiana Transportation Research Center, LTRC Louisiana Department of Transportation and Development, LA DOTD.
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