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Murad Y. Abu-Farsakh, Ph.D., P.E.
Qiming Chen, Ph.D., P.E.
Md Nafiul Haque, MS
2013 Louisiana Transportation Conference Feb 20, 2013
Calibration of Resistance Factors for
Drilled Shafts for the 2010 FHWA
Design Method
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, 2007) 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, 2004, UF, FHWA, and O’Neil 1996
• Allen, 2005, TRB Circular E-C079
• Yang et al. 2008, midwestern U.S., O-cell in weak rock
• Liang and Li 2009, NCHRP 24-17
• Abu-Farsakh et al. 2010 (07-2GT, Report # 470)
Background
In 2010, a new design manual (Brown et al. 2010) was
published by the FHWA in which a new design
methodology for drilled shafts was introduced,
In addition, more than 10 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 2010 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 (fside), tip (ftip), and total (ftotal)]
of axially loaded drilled shafts installed in Louisiana
using the 2010 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 (bT) and the corresponding
resistance factor were developed for both design
methods.
ASD versus LRFD
In Allowable Stress Design (ASD)
where, Q = design load; Qall= allowable design load; Rn=
nominal (ultimate) resistance of the structure.
In Load and Resistance Factor Design (LRFD)
where, Φ = resistance factor, Rn= nominal resistance; gD = load
factor for dead load; gL= load factor for live load; QD = dead
load; and QL = live load.
FS
RQQQQ n
allLD
iiLLDDn QQQR gggf
LRFD Concepts
Limit state function: g (R, Q) = R – Q
Probability density functions
for load and resistance Probability of failure
1
Q
2
R
QR
g
g
b
)0g( PrPf
LRFD Concepts
The relationship between the
probability of failure and the reliability
index (b):
The strength limit state I requires:
The limit state LRFD design equation:
f niinii RQγQ)g(R,
nii Rff nnii RQγ
)(1Pf b
Pf b
10-1 1.28
10-2 2.33
10-3 3.09
10-4 3.71
10-5 4.26
10-6 4.75
10-7 5.19
10-8 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 (Rm) and predicted resistance
(Rp) values for drilled shafts,
Evaluate the bias factor (lR =Rm/ Rp) and COVR,
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 (bT)
Determine the resistance factor (f) for drilled shaft
design method corresponding to bT.
Drilled Shaft Load Test Database
Approximate locations of the
investigated drilled shafts
19 cases from LA; 15 cases from MS
15 19
Summary of Drilled Shaft Tests
• B = 2 ft to 6 ft; L = 35.1 ft m to 138.1 ft
I.D. Dia
(feet)
Length
(feet) Soil Type
Load Test
Type
Predicted (2010
FHWA design
method (tons)
Predicted (1999
FHWA design
method) (tons)
Measured
(tons)
DS-01 2.5 53.1 Silty Clay, Sand Base Top Down 584 485 1007
DS-02 2.5 35.1 Clay and Sand with Sand Base Top Down 455 382 784
DS-03 3 54.1 Clayey Silt, Sand Base O-cell 326 247 344
DS-04 5.5 76.1 Silty Sand with Sand Base O-cell 2102 1571 1560
DS-05 6 86.9 Stiff Clay with Clay Base O-cell 1225 1045 1750
DS-06 2.5 77.4 Sand Clay with Sand Base O-cell 839 521 888
DS-07 2.5 65 Fully Sand with Clay Base O-cell 588 390 670
DS-08 2.5 49.9 Silt,Clay with Clay Base O-cell 377 325 285
DS-09 5.5 40.7 Clay,Silt with Clay Base O-cell 566 455 531
DS-10 3 44.9 Clay, Silty Clay with Clay
Base Top Down 327 270 405
DS-11 3 62 Clay with Sand Base Top Down 488 418 428
DS-12 4.5 49.9 Fully SAND O-cell 1066 881 1230
DS-13 4 73.1 Sand with Clay, Sand base O-cell 1032 900 1020
DS-14 4 123 CLAY/SAND-Sand Base O-cell 1428 920 1515
DS-15 4 138.1 SAND O-cell 1631 1047 1413
DS-16 4 119.1 CLAY, SAND with SAND
Base O-cell 2079 1610 1277
DS-17 5.5 94.1 SAND/CLAY with SAND Base O-cell 1978 1630 2145
Summary of Drilled Shaft Tests
I.D. Dia
(feet)
Length
(feet) Soil Type
Load
Test
Type
Predicted (2010
FHWA design
method (tons)
Predicted (1999
FHWA design
method) (tons)
Measured
(tons)
DS-18 4 96.1 SAND with Sand Base O-cell 1459 860 1082
DS-19 4 82 SAND/GRAVEL/Sand Base O-cell 1467 1210 1258
DS-20 4 97.1 Sand with Clay Interlayer
and Sand base O-cell 936 614 1109
DS-21 4 82 SAND with SAND Base O-cell 1159 840 875
DS-22 4 89 Clay O-cell 2558 2100 2203
DS-23 6 47.9 SAND O-cell 1585 1280 1302
DS-24 4.5 64 SAND/CLAY, Clay Base O-cell 1013 715 498
DS-25 4 64 Sand with Clay Base O-cell 600 496 445
DS-26 2 40 CLAY with Clay Base O-cell 315 262 215
DS-27 4 67.5 Fully Clay, Clay Base O-cell 425 360 549
DS-28 2.5 81.5 Fully Clay, Clay Base O-cell 455 384 570
DS-29 4 77.5 Fully Clay, Clay Base O-cell 751 639 802
DS-30 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 1507 1347 887$
DS-34 5.5 51.12 Clay, Sand with Sand Base O-cell 1149 902 1178
• B = 2 ft to 6 ft; L = 35.1 ft m to 138.1 ft
Geotechnical Conditions
180
160
140
120
100
80
60
40
20
00 15 30 45 60
mc, LL, PL
0 50 100 150
SPT (N)
180
160
140
120
100
80
60
40
20
020 40 60 80
c (kPa)Soil Description
180
160
140
120
100
80
60
40
20
0
De
pth
(ft)
Loose tan siltLoose clayey silt
Firm to stiff silty
clay with silt
Loose sandy
silt with clay
Very dense silty
fine sand
Dense to very dense
fine sand
Very dense gray and
green silty fine sand
SPT
c
mc
LL
PL
Typical summary of geotechnical data for a tested shaft
Measured Resistance from O-Cell Test
Settlement curves by O-cell SHAFT END BEARING
SHAFT
SIDE
SHEAR
SHAFT
SIDE
SHEAR
O-cell
Measured Resistance from O-Cell Test
Equivalent top-down settlement
curve SHAFT END BEARING
SHAFT
SIDE
SHEAR
SHAFT
SIDE
SHEAR
O-cell
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
0 1 2 3 4 5 6
Load (MN)
-60
-40
-20
0
20
40
60
80
Upw
ard
To
po
fB
ott
om
O-c
ell
Mo
vem
ent
(mm
)
Dow
nw
ard
Bott
om
of
Bo
ttom
O-c
ell
Mo
vem
en
t(m
m)
0 2 4 6 8 10
Load (MN)
50
40
30
20
10
0
Se
ttle
me
nt
(mm
)
Rm-tip
Rm-side
Rm 5% B 5% B
5% B
О О
О
Measured Resistance from O-Cell Test
FHWA Design Method for Drilled Shafts
1999 FHWA Design Method for Drilled Shafts (O’Neil and Reese)
The nominal ultimate axial resistance (Rp-u) of a drilled shaft:
Rp-u = Rp-b + Rp-s = qb.Ab + ∑ fsi.Asi
Soil Condition Resistance Component Equations
Cohesive Soil
Skin Friction
End Bearing
Cohesionless
Soil
Skin Friction
End Bearing
dAf R , Sαf L
0 szs-puzzsz
ub
srrc
ubcb
3S
EI , 1) I (ln 1.33N
SNq
1.20.25
15Nfor )z 0.135/15)(1.5(Nβ
15Nfor z 0.1351.5β
dAσ'βR , tsf 2.1σ'βf
60
0.5
60
60
0.5
L
0
zs-pzSZ
b
fs
qb
Rp-u
tsf 300.6Nq SPTb
FHWA Design Method for Drilled Shafts
2010 FHWA Design Method for Drilled Shafts (Brown et al.)
The nominal ultimate axial resistance (Rp-u) of a drilled shaft:
Rp-u = Rp-b + Rp-s = qb.Ab + ∑ fsi.Asi
Soil Condition Resistance Component Equations
Cohesive Soil
Skin Friction
End Bearing
Cohesionless
Soil
Skin Friction
End Bearing
dAf R , Sαf L
0 szs-puzzsz
ub
srrc
ubcb
3S
EI , 1) I (ln 1.33N
SNq
fs
qb
Rp-u
tsf 300.6Nq SPTb
m
60
zp
L
0
zs-pzSZ
N0.47/
an)tan/)(sin-(1β
dAσ'βR , tsf) (2.1 kPa200σ'βf
a
'
p
p
p
K
fff
Predicted Resistance (1999 FHWA Method)
a) Side load transfer for cohesive soil b) End load transfer for cohesive soil
The total developed load (RT) at a specific settlement:
RT = Rp-b (developed) + Rp-s (developed)
Predicted Resistance (FHWA 2010 Method)
The total developed load (RT) at a specific settlement:
RT = Rp-sN + h Rp-bN
Normalized load transfer representing the average trend value for drilled shaft
0
50
100
150
200
0 2 4 6 8 10 12
Axia
l C
om
pre
ssio
n F
orc
eF
ailu
re T
hre
shhold
displacement dia. of shaft
Cohesionless
Cohesive
,%
,%
Failure Threshhold
Predicted Resistance (FHWA Methods)
Example of load-settlement analysis and measured value
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0 200 400 600 800 1000
Dis
pla
cem
ent (i
n.)
Load (tons)
Measured Resistance
Calculated Resistance using 2010 FHWA Method
Calculated Resistance using 1999 FHWA Method
Rp RmRp
Predicted Resistance (FHWA Method)
Determine load settlement curves
Determine predicted side, tip, and total resistance
0 1 2 3 4Load (MN)
100
80
60
40
20
0
Se
ttle
me
nt(m
m)
----Predicted Resistance----Measured Resistance
5% of the shaft diameter
Shaft diameter = 1.52 m
Rp Rm
0 2 4 6Load (MN)
-200
-100
0
100
200
Se
ttle
me
nt
(mm
)
Interpreted side resistance (Rp_side)
Interpreted tip resistance (Rp_tip)
5%B
5%B
Shaft diameter = 1.52m
Measured vs. predicted resistance of drilled shafts
1999 FHWA Design Method
Results – Predicted versus Measured
1999 FHWA Design MethodRfit = 1.10Rm
0
500
1000
1500
2000
0 500 1000 1500 2000
Pre
dic
ted
Dri
lled
Sh
aft
Sid
e R
esis
tan
ce,
Rp
(to
ns)
Measured Drilled Shaft Side Resistance, Rm (tons)
Louisiana
Mississippi
1999 FHWA Design MethodRfit = 0.47Rm
0
300
600
900
1200
1500
0 300 600 900 1200 1500
Pre
dic
ted
Dri
lled
Sh
aft
Tip
Res
ista
nce
,
Rp
(to
ns)
Measured Drilled Shaft Tip Resistance, Rm (tons)
Louisiana
Mississippi
1999 FHWA design methodRfit = 0.79Rm
0
500
1000
1500
2000
2500
3000
0 500 1000 1500 2000 2500 3000
Pre
dic
ted
Dri
lled
Sh
aft
Res
ista
nce
, R
p
(ton
s)
Measured Drilled Shaft Resistance, Rm (tons)
Louisiana
Mississippi
2010 FHWA Design MethodRfit = 0.47Rm
0
300
600
900
1200
1500
0 300 600 900 1200 1500
Pre
dic
ted
Dri
lled
Sh
aft
Tip
Res
ista
nce
,
Rp
(to
ns)
Measured Drilled Shaft Tip Resistance, Rm (tons)
Louisiana
Mississippi
Measured vs. predicted resistance of drilled shafts
2010 FHWA Design Method
Results – Predicted versus Measured
2010 FHWA Design MethodRfit = 1.54Rm
0
500
1000
1500
2000
0 500 1000 1500 2000
Pre
dic
ted
Dri
lled
Sh
aft
Sid
e R
esis
tan
ce,
Rp
(to
ns)
Measured Drilled Shaft Side Resistance, Rm (tons)
Louisiana
Mississippi
2010 FHWA design methodRfit = 1.02Rm
0
500
1000
1500
2000
2500
3000
0 500 1000 1500 2000 2500 3000
Pre
dic
ted
Dri
lled
Sh
aft
Res
ista
nce
, R
p
(to
ns)
Measured Drilled Shaft Resistance, Rm (tons)
Louisiana
Mississippi
Results: Statistic Analyses
Arithmetic calculations
Best fit calculations
lR = Rm/Rp Rp/Rm
Mean σ COV Mean Rfit/Rm
0.99 0.30 0.30 1.10 1.02
Arithmetic calculations
Best fit calculations
lR = Rm/Rp Rp/Rm
Mean σ COV Mean Rfit/Rm
1.27 0.38 0.30 0.87 0.79
Statistical analysis of the 2010 FHWA drilled shaft design method
Statistical analysis of the 1999 FHWA drilled shaft design method
Histograms of bias, l, for different resistance
components – 1999 FHWA Method
0
10
20
30
40
50
60
0 1 2 3
Pro
bab
ilit
y (
%)
Rm/Rp
Log-Normal Distribution
Normal Distribution
Side Resistance (1999 FHWA design method)
0
10
20
30
0 1 2 3 4 5P
rob
ab
ilit
y (
%)
Rm/Rp
Log-Normal Distribution
Normal Distribution
Tip Resistance (1999 FHWA design method)
0
10
20
30
40
50
0 1 2 3 4
Pro
bab
ilit
y (
%)
Rm/Rp
Log-Normal Distribution
Normal Distribution
Total Resistance (1999 FHWA design method)
Histograms of bias, l, for different resistance
components – 2010 FHWA Method
0
10
20
30
40
50
60
0 1 2 3
Pro
bab
ilit
y (
%)
Rm/Rp
Log-Normal Distribution
Normal Distribution
Side Resistance(2010 FHWA design method)
0
10
20
30
0 1 2 3 4 5P
rob
ab
ilit
y (
%)
Rm/Rp
Log-Normal Distribution
Normal Distribution
Tip Resistance (2010 FHWA design method)
0
10
20
30
40
50
0 1 2 3 4
Pro
bab
ilit
y (
%)
Rm/Rp
Log-Normal Distribution
Normal Distribution
Total Resistance (2010 FHWA design method)
Cumulative Density Function (CDF) of Bias Values (l)
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
0 0.5 1 1.5 2 2.5
Sta
nd
ard
Norm
al V
ari
ab
le, Z
Bias (lR)
Measured Bias Value
Predicted Normal Dist.
Predicted Log-Normal Dist.Predicted Log-Normal Dist. (best fit to tail)
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
0 0.5 1 1.5 2S
tan
dard
Norm
al V
ari
ab
le, Z
Bias (lR)
Measured Bias Value
Predicted Normal Dist.
Predicted Log-Normal Dist.Predicted Log-Normal Dist. (best fit to tail)
2010 FHWA Design Method 1999 FHWA Design Method
Summary of Bias (l Rm/Rp) for Drilled Shafts
2010 FHWA Method
Statistics Tip Side Total
Max. 5.12 1.17 1.43
Min. 0.47 0.28 0.49
Mean (l) 2.16 0.65 0.94
COV 0.53 0.36 0.26
1999 FHWA Method
Statistics Tip Side Total
Max. 5.39 1.47 1.81
Min. 0.43 0.44 0.60
Mean (l) 2.26 0.91 1.22
COV 0.55 0.34 0.28
Contribution of Side and Tip Resistance
0
20
40
60
80
100
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33
Pre
dic
ted
res
ista
nce
con
trib
uti
on
(%)
Shaft Number
Tip Resistance (average: 29%)
Side Resistance (average: 71%)
1999 FHWA Method
0
20
40
60
80
100
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33
Pre
dic
ted
res
ista
nce
co
ntr
ibu
tio
n
(%)
Shaft Number
Tip Resistance (average: 23%)
Side Resistance (average: 77%)
2010 FHWA Method
0
20
40
60
80
100
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33
Mea
sure
d r
esis
tan
ce c
on
trib
uti
on
(%)
Shaft Number
Tip Resistance (average: 48%)
Side Resistance (average: 52%) O-Cell
Measurements
LRFD Calibration Methods
Monte Carlo Simulation method (MCS method)
Target reliability index: 3.0
Dead load/Live load ratio: 3.0
Load statistics and factors (AASHTO):
Monte Carlo Simulation
Random variables:
lR, lL, and lD
Number of simulation: 50000
lglgl
f
gg
LL
DLDLDLLLLLR
LL
DLDLLL
LLQ
Q-
Q
Q
Qg
Resistance factors
2010 FHWA Method 1999 FHWA Method
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 1.5 2 2.5 3 3.5
Res
ista
nce
Fact
or,
f
βT
From measured bias data
From "best fit to tail"
0.48
0.41
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1 1.5 2 2.5 3 3.5
Res
ista
nce
Fact
or,
f
βT
From measured bias data
From "best fit to tail"
0.60
0.50
LRFD Calibration Methods
Resistance Factors Tip Side Total
ftip ftip/λ fside fside/λ ftotal ftotal/λ
2010 FHWA design method 0.53 0.25 0.26 0.40 0.50 0.53
1999 design method 0.52 0.23 0.39 0.43 0.61 0.50
LRFD Calibration Methods
bT = 3.0 Resistance Factor, f Efficiency Factor, f/λ
Current study (2010
FHWA design method)
0.48 in mixed soils
0.41 in mixed soils (best fit to tail)
0.48 in mixed soils
0.41 in mixed soils (best fit to tail)
Current study (1999
FHWA design method)
0.60 in mixed soils
0.50 in mixed soils (best fit to tail)
0.47 in mixed soils
0.38 in mixed soils (best fit to tail)
Liang and Li (2009)
0.45 in clay
0.50 in sand
0.35 in mixed soils
Paikowsky (2004) and
AASHTO (2007)
0.45 in cohesive soils
0.55 in cohesionless soils
Summary and Conclusions
Statistical analyses showed that:
The 2010 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 2010 FHWA method:
ftotal = 0.48, fside = 0.26, and ftip = 0.53.
• The resistance factors for 1999 FHWA method:
ftotal = 0.60, fside = 0.39, and ftip = 0.52.
Acknowledgement
Louisiana Transportation Research Center, LTRC
Louisiana Department of Transportation and
Development, LA DOTD.
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