lrfd calibration of axially- loaded concrete piles driven ... sean.pdf · lrfd calibration of...

1

LRFD Calibration of Axially-Loaded Concrete Piles Driven into Louisiana

SoilsLouisiana Transportation Conference

February 10, 2009

Sungmin “Sean” Yoon, Ph. D., P.E. (Presenter)Murad Abu-Farsakh , Ph. D., P.E.

Ching Tsai, Ph.D., P.E.Zhongjie Zhang, Ph.D., P.E.

Louisiana DOTD and LTRC

2

Outline

Problem statement Different design methods Statistical concept Methods used in LADOTD for driven piles LRFD calibration Conclusion

3

Problem Statement and Research Objectives

Working Stress Design (WSD) versus LRFD

Bridge super structures vs. Foundation

Federal Highway Administration and ASSHTO set a transition date of October 1, 2007

Resistance Factor (Φ) reflecting Louisiana soil and DOTD design process

4

Stress Design Methodologies vs. LRFD

Working Stress Design (WSD) –also called Allowable Stress Design (ASD), since early 1800s.

where, Q=design load; Qall= allowable design load; and Rn= ultimate resistance of the structure

nall

RQ QFS

≤ = =

5


Limit State Design (LSD), 1950s

Ultimate Limit Stress (ULS)

Service Limit Stress (SLS)

Factored resistance ≥ Factored load effects

Deformation ≤ Tolerable deformation to remain serviceable

6


Load and Resistance Factor Design (LRFD)

where, Φ=resistance factor, Rn=ultimate resistance; γD=load factor for dead load; γL=load factor for live load; γi=corresponding load factor, and Qi=summation of load

n D D L L i iR r Q r Q rQφ ≥ + = ∑

7

Reliability Based FS

8

Working Stress Design (WSD) vs. LRFD

9

Limit State Function

Limit State Function can be defined as g = R – Q

10

Reliability Index, β

βσg β: reliability index

0 gQR =− lnln g

Pf = shaded area

f(g) = probability density of g2 2

R Q

g R Q

g µ µβ

σ σ σ

−= =

+

11

Relationship between β and Pf

Pf β10-1 1.2810-2 2.3310-3 3.0910-4 3.7110-5 4.2610-6 4.7510-7 5.1910-8 5.6210-9 5.99

12


β2β1

β Distance Overlapped area

Probability of failure

Design �φ

Pile Size

�β1 Short�β2 Large

13


β2β1



Design �φ

Pile Size

�β1 Short Large�β2 Large Small

14


β2β1



Design �φ

Pile Size

�β1 Short Large High�β2 Large Small Low

15


β2β1



Design �φ

Pile Size

�β1 Short Large High Large�β2 Large Small Low Small

16


β2β1



Design �φ

Pile Size

�β1 Short Large High Large Small�β2 Large Small Low Small Big

17

How to Treat Uncertainty

1 2

Graph Variability Overlapped area


Calculated φ

Pile Size

12

18


1 2



Calculated φ

Pile Size

1 Low2 High

19


1 2



Calculated φ

Pile Size

1 Low Small2 High Large

20


1 2



Calculated φ

Pile Size

1 Low Small Low2 High Large High

21


1 2



Calculated φ

Pile Size

1 Low Small Low Large2 High Large High Small

22


1 2



Calculated φ

Pile Size

1 Low Small Low Large Small2 High Large High Small Big

23

Benefits of LRFD

Improved reliability

More rational and rigorous treatment of uncertainties in design

Improved design and construction process (sub and super structures)

24

First Order Second Moment (FOSM)

Load and Resistance Factor Design (LRFD)

(1)

where, Φ=resistance factor, Rn=ultimate resistance; γD=load factor for dead load; γL=load factor for live load; γi=corresponding load factor, and Qi=summation of load

n D D L L i iR r Q r Q rQφ ≥ + = ∑

25

First Order Second Moment (FOSM)

(2)

Combining eq (1) and (2) using Rn

λQD, λQL = dead and live load bias factors

λR = resistance bias factors = Rm/Rp

AASHTO LRFD specification (1994)

λQD=1.08, λQL=1.15, rD=1.25, rL=1.75, COVQD=0.13, COVQL=0.18

( )( )[ ]2LL

2DL

2R

2R

2LL

2DL

2R

LLLL

DLDL

LL

DL

R

COVCOV1COV1ln

COV1COVCOVCOV1

λQQλ

1QQ

FSλln

β+++

++++

+

+

=

( )( )[ ]( )2QL

2QD

2RTQL

L

DQD

2R

2QL

2QD

LL

DDR

COV+COV+1COV+1lnβexpλ+QQλ

COV+1COV+COV+1

γ+QQγλ

=

φ

26

Statistical Methods for LRFD Calibration

First Order Second Moment (FOSM) method: Linearization of limit state function by expanding Taylor series

expansion First Order Reliability Method (FORM):

Transformation of variables into the standardized and uncorrelated normal variables using the Hosofer-Lind Transformation

Monte Carlo Simulation Method: Extrapolate CDF for each random variable using random number

generator

27

Pile Load Test Database(Ultimate Capacity for Driven Piles)

Square PPC Pile Size (mm)

Pile Type Predominant Soil Type

Friction End-Bearing

Cohesi-ve

Cohesi-onless

Limit of Informa

-tion

360 18 0 16 2 0

410 5 0 3 0 2

610 9 0 6 3 0

760 10 0 5 5 0

Total 42 0 30 10 2

28

Methods used in LADOTD(Ultimate Capacity for Driven Piles)

Static method α - method - for cohesive soil (Tomlison 1979) Nordlund method – for sand inter-layers

CPT method Schmertmann, LCPC, De Ruiter and Beringen

Dynamic Measurement CAPWAP

Measured Ultimate Pile Capacity Butler-Hoy Method Davisson Method

29

Davisson (Interpretation of Pile Load Tests)Static Load Test Results

0.00

0.50

1.00

1.50

2.00

2.50

0 50 100

Load (Tons)Se

ttlem

ent (

in)

Qult

L/AE1

0.15+D/120

30

Pile Capacity from Soil Borings (Static Method)

Shaft Friction CapacityCohesive soils – clays (α-method, Tomlinson)

where f = clay adhesion = α Su

Non-cohesive soils – sands and silts (Nordlund method)

End Bearing CapacityCohesive soils – clays (α-method, Tomlinson)

where Ab= cross sectional area, Nc = 9

Non-cohesive soils – sands and silts (Nordlund method)

∫=L

d dzCf0

s Q

∫ δ= δ

L

0dDfs dzC).sin(PC KQ

qbb N..q.AQ ′α=

cub NSA ..Qb =

31

Ultimate Pile Capacity

End-bearing Capacity, Qtip= qt . At

Shaft friction Capacity, Qshaft = Σfi . Asi

Qult = Qtip + Qshaft

f

qt

32

Cone Penetration Test (CPT/PCPT)

qc

fs

U3

U2U1

Penetration Rate = 2 cm/sBase area = 10 cm2

Sleeve area = 150 cm2

Cone angle = 60o

33

Cone Penetrometer Versus Pile

qc

f s

f

qt

Qult

Due to similarity between the cone and pile, the cone can be considered as a simple mini pile.

fs can be correlated to f, qc can be correlated to qt.

34

Typical PCPT Test Results

qc

fs

U3

U2U1

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Dept

h (m

)

0 2 4 6 8 10Tip Resistance (MPa)

0123456789

10111213141516

0.00 0.05 0.10 0.15Sleeve Friction (MPa)

0123456789

10111213141516

0 2 4 6 8Rf (%)

0123456789

10111213141516

0.0 0.1 0.2 0.3 0.4 0.5Pore Pressure (MPa)

Tip

Base

u1

u2

%100qfR

c

sf =

35

Schmertmann method (CPT)

where,qt: unit bearing capacity of

pilef: unit skin frictionαc: reduction factor (0.2 ~

1.25 for clayey soil)fs: sleeve friction

e

D

a

bb

Envelope of minimum qc values yD

?

'x'

8D

Cone resistance qc

Dept

h

qc1 + qc2

2

c

qc1

qc2

qt =

36

LCPC method (CPT)

Pile

a=1.5 D

0.7qcaqca 1.3qca

qc

Dept

ha

a

qeq

Dqt = kb qeq (tip)

kb = 0.6 clay-silt0.375 sand-gravel

maxs

eq k(side)/q

ff <=

ks = 30 to 150

37

De Ruiter and Beringen (CPT) In clay

Su(tip) = qc(tip) / Nk Nk = 15 to 20 qt = Nc.Su(tip) Nc = 9 f = β.Su(side) β = 1 for NC clay

= 0.5 for OC clay In sand

qt similar to Schmertmann method

=

TSF21tension400side

ncompressio300sideiction)(sleeve fr

. )( /)(q

)( /)(q f

minfc

c

s

38

Implementation into a Computer Program

Louisiana Pile Design by Cone Penetration Test

http://www.ltrc.lsu.edu/

39

Predicted vs. Measured Ultimate Pile Resistances

(a) Static analysis method (b) Schmertmann method

0 100 200 300 400 500 600 700 800

Measured pile capacity, Rm (tons)

0

100

200

300

400

500

600

700

800

Pre

dict

ed p

ile c

apac

ity, R

P (t

ons)

RFit = 0.96 * Rm

R2 = 0.87

0 100 200 300 400 500 600 700 800


0

100

200

300

400

500

600

700

800

Pre

dict

ed p

ile c

apac

ity, R

P (t

ons)

RFit = 1.12 * Rm

R2 = 0.86

40


(c) LCPC method (d) De Ruiter& Beringen method

0 100 200 300 400 500 600 700 800


0

100

200

300

400

500

600

700

800

Pre

dict

ed p

ile c

apac

ity, R

P (t

ons)

RFit = 1.07 * Rm

R2 = 0.81

0 100 200 300 400 500 600 700 800


0

100

200

300

400

500

600

700

800

Pre

dict

ed p

ile c

apac

ity, R

P (t

ons)

RFit = 0.91 * Rm

R2 = 0.88

41


(e) CAPWAP-EOD (f) CAPWAP-14 days BOR

0 100 200 300 400 500 600 700 800


0

100

200

300

400

500

600

700

800

Pre

dict

ed p

ile c

apac

ity, R

P (t

ons)

RFit = 0.32 * Rm

R2 = 0.69

0 100 200 300 400 500 600 700 800


0

100

200

300

400

500

600

700

800

Pre

dict

ed p

ile c

apac

ity, R

P (t

ons)

RFit = 0.92 * Rm

R2 = 0.91

42

Evaluation of Different Prediction Methods

Pile Resistance Prediction Method

No. of cases

Arithmetic calculations Best fit calculationsRm/Rp Rp/Rm

Mean σ COV Mean Rfit/Rm R2

Static method 33 0.97 0.24 0.25 1.11 0.96 0.87

Schmertmann method 29 0.93 0.28 0.30 1.17 1.12 0.86

LCPC method 29 1.07 0.32 0.30 1.04 1.07 0.81

De Ruiter& Beringen method 29 1.22 0.33 0.27 0.89 0.91 0.88

CAPWAP-EOD 12 3.65 1.74 0.48 0.35 0.32 0.69

CAPWAP-14 days BOR 8 1.32 0.51 0.39 0.83 0.92 0.91

43

Distribution of Bias (Static Analysis)

0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0

Rm / RP

0

5

10

15

20

25

30

Pro

babi

lity

(%) Log-Normal Distribution

Normal Distribution

Static MethodStatic Method

-3

-2

-1

0

1

2

3

0 0.5 1 1.5 2

Bias, X

Stan

dard

Nor

mal

Var

iabl

e, z

measuredbias value

predictednormaldist.

predictedlognormaldist. fromnormalstat.

44

Distribution of Bias (Schmertmann Method)

0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0

Rm / RP

0

5

10

15

20

25

30

Pro

babi

lity

(%) Normal Distribution

Log-Normal Distribution

Schmertmann Method Schmertmann Method

-3

-2

-1

0

1

2

3

0 0.5 1 1.5 2

Bias, X

Stan

dard

Nor

mal

Var

iabl

e, z

measuredbias value



45

Distribution of Bias (LCPC method)

0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0

Rm / RP

0

5

10

15

20

25

30

Pro

babi

lity


Normal Distribution

LCPC Method LCPC Method

-3

-2

-1

0

1

2

3

0 0.5 1 1.5 2

Bias, X

Stan

dard

Nor

mal

Var

iabl

e, z

measuredbias value



46

Distribution of Bias (De Ruiter& Beringen Method)

0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0

RP / Rm

0

5

10

15

20

25

30

Pro

babi

lity


Normal Distribution

De Ruiter MethodDe Ruiter& Beringen Method

-3

-2

-1

0

1

2

3

0 0.5 1 1.5 2

Bias, X

Stan

dard

Nor

mal

Var

iabl

e, z

measuredbias value



47

CAPWAP - Dynamic Analyses

0.0 0.6 1.2 1.8 2.4 3.0 3.6 4.2 4.8 5.4 6.0 6.6 7.2 7.8 8.4

Rm / RP

0

5

10

15

20

25

30

Pro

babi

lity


Normal Distribution

CAPWAP (EOD) Method

0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0

Rm / RP

0

5

10

15

20

25

30

Pro

babi

lity

(%)

Log-Normal DistributionNormal Distribution

CAPWAP (BOR) Method

EOD 14 days BOR

48

Resistance Factors, φ (Static analysis)

0 0.5 1 1.5 2 2.5 3 3.5 4βT

0

0.5

1

1.5

φ (S

tatic

Ana

lysi

s)

49

Resistance Factors, φ (Direct CPT Methods)

0 0.5 1 1.5 2 2.5 3 3.5 4βT

0

0.5

1

1.5

φ (D

irect

CP

T M

etho

ds)

SchmertmannLCPCDeRuiter&Beringen

50

Resistance Factors, φ (CAPWAP-BOR)

0 0.5 1 1.5 2 2.5 3 3.5 4βT

0

0.5

1

1.5

φ (C

PT

CA

PW

AP

-BO

R A

naly

sis)

51

Resistance Factors, φ (βT=2.33) using FOSM

Design MethodResistance Factor, φ

Efficiency Factor (φ/λ)

Proposed for soft soil

AASHTO Proposed forsoft soil

Static Method α-Tomlinson method and Nordlund method 0.56 0.35 - 0.45 0.58

Direct CPTMethod

Schmertmann 0.48 0.5 0.52

LCPC/LCP 0.56 NA 0.52

De Ruiter and Beringen 0.68 NA 0.55

Dynamicmeasurement

CAPWAP (EOD) 1.31 NA 0.36

CAPWAP (14 days BOR) 0.58 0.65 0.44

52

Comparison of Resistance Factors, φ (βT=2.33) using FOSM, FORM and M-C

Design MethodResistance Factor, φ

FOSM FORM M-C

Static Method α-Tomlinson method and Nordlund method 0.56 0.63 0.63

Direct CPTMethod

Schmertmann 0.48 0.54 0.53

LCPC/LCP 0.56 0.63 0.62

De Ruiter and Beringen 0.68 0.77 0.75

Dynamicmeasurement

CAPWAP (EOD) 1.31 1.41 N/A

CAPWAP (14 days BOR) 0.58 0.63 0.63

53

Conclusions

Preliminary resistance factors (φ) for Louisiana soil were evaluated for different driven pile design methods

Statistical analyses comparing the predicted and measured pile resistances were conducted to evaluate the performance of the different pile design methods.

LRFD in deep foundation can improve its reliability due to more balanced design.

More statistical data is needed for more rational resistance factor.

54

Issues

Load sharing and overall redundancy Reduced φ to reflect increased β

Site variability Based on the filed and laboratory testing Resistance factor and number of static load test

needed

Scour

55

Acknowledgement

The project is financially supported by the Louisiana Transportation Research Center and Louisiana Department of Transportation and Development (LA DOTD).

LTRC Project No. 07-2GT.

56

THANK YOU!

Sungmin “Sean” YoonLADOTD

lrfd calibration of axially- loaded concrete piles driven ... sean.pdf · lrfd calibration of...

Documents