Department of Computer Science

Tang-Tat Ng and Sadia Faiza

University of New Mexico

Department of Civil Engineering

Background

Drilled Shaft Load Test Database

Design Methods for Drilled Shafts

Statistical Analysis

LRFD Calibration

Numerical Simulation

Conclusions and Future works

Outline

2

Two design approaches for geotechnical structures: ◦ The Load Resistance Factor Design (LRFD) LRFD deals with the uncertainties associated with the design variables as

load and resistance ◦ Working Stress Design (WSD) factor of safety approach

October 1st , 2007 AASHTO LRFD Specifications become mandatory

Background

3

The resistance of a drilled shaft is the combination of side resistance and end bearing

Side Resistance and End Bearing of A Drilled Shaft

4

BNi

SNTN RRQi+= ∑

=

layersn

1

• Arizona (7) • Georgia (3) • Alabama (1) • Iowa (1)

Drilled Shaft Load Test Database

• Texas (1) • Florida (4) • New Jersey (1) • Japan (1)

• 95 cases have been collected • 24 cases have been finally selected based on the soil and shaft conditions

5 cases are from New Mexico Other cases are from:

5

The soil strengths of these cases are similar or greater than the soils in New Mexico

Drilled Shaft Load Test Database

Case Name Diameter (ft) Length (ft) Sand Layer Info. (ft)

NMDOT Big I, Albuquerque (L-1) 6 81 30 NMDOT Big I, Albuquerque (A-1) 4.5 52 Sand* NMDOT_south_test shaft_2 2.8 30 Sand* NMDOT Sunland park 4 74.6 73.9 NMDOT I-40 2.67 40 40 Soil & material Eng. Inc 3 60 Sand* John Pazzi 1.5 68 Sand* AASHTO (Tuscaloosa, Alabama) 4 33.2 Sand* AASHTO (Iowa) 4 59.8 9.2 – 48 AASHTO (Coosa, Georgia) 5.5 60 Sand* AASHTO (Juliette, Georgia) 2.6 47 Sand* I-10 (ADOT)-a 6 62 62

I-10 (ADOT)-b 6 53 48

6

Drilled Shaft Load Test Database

Case Name Dia (ft) Length (ft) Sand Layer Info. (ft)

San Carlos (ADOT) 6 90 68 Sky Harbor (ADOT) 6 48 48 SR-24 (ADOT)-a 6 77 55 SR-24 (ADOT)-b 6 24.3 8.3 Gila river (ADOT) 7 115 56 O'Neill & Reese, Texas 3 34 15.8 Yasufuku & Ochiai 3.94 134.5 134.5 Owens & Reese, Florida 4 46.8 33.2 Shaft 11 (FDOT) 5 90 37 Shaft 2 (FDOT) 6 90 41

Shaft7 (FDOT) 5 100 57

7

Measured and Predicted Resistances

Measured Resistance

The O-cell load-displacement curve

The strain gage data

Predicted Resistance

O’Neill & Reese Method

Unified Design Equation

NHI Design Method

8

Measured Resistance from O-Cell test

9

7.1 MN

12.5

Location: Blue Springs, Alabama. Length: 13.2 ft, Diameter: 54 in. Field side resistance: π*4.5*(294.6-292.7)*.03+ π*4.5*(292.7-279.5)*0.88= 164.13 k= 82 T.

Side Resistance Measurement from Strain Gauge Data

10

O’Neill & Reese Method (FHWA 1999)

11

fult ≤ 2.1 tsf zi = represented depth of the layer i in ft N60 = Standard penetration resistance βi = limited to a maximum value of 1.20 and a minimum value of 0.25

Side resistance:

Cohesionless Soil:

15);135.05.1(15

,15;135.05.1

605.060

605.0

'

<Ν−Ν

=

≥Ν−=

=

ii

ii

viiult

Z

Zf

β

β

σβ

12

Cohesionless Intermediate Geomaterials (IGM):

Side resistance:

Coefficient of horizontal soil stress:

Friction angle: 34.0

'601

sin'

60

'

])(3.203.12

)([tan

])(2.0)[sin1(

tan

'

a

vi

ii

vi

iaioi

ovult

P

layerN

layerNPK

Kf

i

σφ

σφ

ϕσ

ϕ

+=

−=

=

−

O’Neill & Reese Method (FHWA 1999)

NHI Design Method (FHWA 2010)

13

Side resistance:

Rankine passive earth pressure coefficient:

Preconsolidation stress:

Angle of internal friction: 601

'

60'

2

sin'

'

'

)log(2.95.27

)(47.0

)2

45(tan

)(tan)sin1(

N

PN

K

f

am

p

op

v

pF

vFult

+=

=

+=

−=

=

φ

σ

φ

σσ

φφβ

σβ

φ

25

27

29

31

33

35

37

39

41

43

45

0 20 40 60 80 100

Angl

e of

inte

rnal

resi

stan

ce

Relative density of granular soil

GW GP

SW SP

SM ML

Unified Design Equation (Chu and Meyers 2002)

14

Friction Angles with consideration of soil classification. (after US Navy, 1971)

Side resistance:

Relative density:

Angle of internal friction:

R

a

vR

o

p

ou

vus

D

NP

D

zKK

K

f

15.030

)(4.20

)1

11(tan

41.0223.0'

'

+=

=

+

−+=

=

−

φ

σ

φβ

σβ

Measured vs. Predicted Resistance O’Neill & Reese Method

15

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000 3500

Pred

icte

d Si

de R

esis

tanc

e (t)

Field Side Resistance (t)

NM cases

Measured vs. Predicted Resistance Unified Design Equation

16

0

500

1000

1500

2000

2500

3000

3500

0 1000 2000 3000 4000

Pred

icte

d Si

de R

esis

tanc

e (t)

Field Side Resistance (t)

NM cases

Measured vs. Predicted Resistance NHI Design Method

17

0

500

1000

1500

2000

2500

3000

3500

0 1000 2000 3000 4000

Pred

icte

d Si

de R

esis

tanc

e (t)

Field Side Resistance (t)

NM cases

Statistics of the resistance bias (ratio of measured resistance and the predicted resistance) of the three design methods.

Statistic Analysis

18

DESIGN METHOD Mean (µ) Standard

Deviation (σ) COV

O’Neill & Reese 1.14 0.66 0.58 Unified 1.13 0.59 0.52

NHI 1.21 0.73 0.60

The Best-fit-to-tail Lognormal Distribution of Bias (O’Neill and Reese Method)

NHI method

Unified method O’Neill & Reese method

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0.00 1.00 2.00 3.00 4.00

Stan

dard

Nor

mal

Var

iabl

e

Bias

19

The Best-fit-to-tail Lognormal Distribution of Bias (the Unified Design Method)

20 -2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

Stan

dard

Nor

mal

Var

iabl

e

Bias

The Best-fit-to-tail Lognormal Distribution of Bias (the NHI Method)

21 -2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

0.00 1.00 2.00 3.00 4.00 5.00

Stan

dard

Nor

mal

Var

iabl

e

Bias

Characteristics of these Best-fit-to-tail Lognormal Distributions

Design Method Mean (µ) Standard

Deviation (σ) COV

O’Neill & Reese 0.95 0.39 0.41

Unified 1.2 0.68 0.57

NHI 0.88 0.31 0.35

22

Cumulative Distribution Functions of the Best Fitted Polynomial Curves

Unified Method NHI Method

O’Neill & Reese Method

23

Probability of failure and reliability index (Withiam et al. 1998) g (R, Q) = R – Q

LRFD Concepts

Probability density functions for load and resistance Probability of failure

24

Reliability Index (β) and Resistance Factor (φ)

Q and R are uncorrected normal distributions

Q and R are lognormal distributions (γ = load factor)

The limit state LRFD design equation jjii RQ ∑∑ ≤ φγ

[ ])cov1)(cov1(ln

)cov1()cov1(

lnln

22

2

2

RQ

R

Q

QR

RQ

+++

+++

=λφλγ

β

22QR

QR

σσµµ

β−

−=

25

Probability of Failure

The probability of failure is the number of the failed cases (g < 0) over the total number of the cases

26

Calibration of Resistance Factor

Bias COV Load Factor

Live load λ LL = 1.15 COV LL = 0.2 γ LL = 1.75

Dead load λ DL = 1.05 COV DL = 0.1 γ DL = 1.25

27

• LRFD calibration of drilled shafts is performed to obtain the resistance factor

• The probability of failure is approximately1 in 1000 • The DL/LL ratio of 3.0; Both live and dead loads are assumed to be

lognormal distributions (similar to Paikowsky 2004):

Calibrated Resistance Factors

Design Method Resistance Factor

O’Neill & Reese Method 0.32

Unified Method 0.26

NHI Method 0.37

Design Method Resistance Factor

O’Neill & Reese Method 0.45

Unified Method 0.49

NHI Method 0.47

28

Resistance bias: best-fit-to-tail Lognormal Distribution

Resistance bias: Polynomial Curve

Recommended and Calibrated Resistance Factors (for O’Neill and Reese Method)

29

Resistance Factor φ

Current Study 0.45

AASHTO (2007) 0.55 in cohesionless soils

Paikowsky (2004) 0.60 in IGM/weak rock

Since the CDF of the resistance bias is not lognormally distributed, fitted with polynomial curves is more appropriate

Based on current study, the resistance factors are similar for these three design equations (0.45 ~ 0.49)

The resistance factor for the Unified design equation (0.49) is slightly higher than that for the O’Neill and Reese Method (0.45).

A cost saving is found when using these calibrated resistance factors (0.45 and 0.49) ◦ 19 out of 24 cases show that the design resistance using the Unified design

equation is greater than that of the O’Neill and Reese method When the recommended AASHTO value (0.55) is used, only 4 cases

shows that the Unified method is better (greater design resistance)

Conclusions (Resistance factor calibration)

30

DEM Simulations

31

Particles are randomly generated The system is compressed vertically with a

friction coefficient of 0.1 No lateral displacement is allowed The compression is stopped as the

intermediate system has a void ratio of 0.8, 0.75, 0.7, 0.65, and 0.6

The vertical stresses of these intermediate systems are less than 200 psf

Then, the friction coefficient is set to 0.5 and the system is compressed again with a vertical stress of 2000 psf, 4000 psf, and 8000 psf

DEM Results of Ko

32

Ko = 26.696e2 - 32.264e + 10.144

Results of (Ko)OC

33

OCR=4

OCR = 2

OCR = 1 Ko = 26.696e2 - 32.264e + 10.144

Results of (Ko)OC

34

)1()( oK

o

OCo

OCRK

K −=

Solid curves are estimated: Ko = 26.696e2 - 32.264e + 10.144

Side Resistance Simulations with DEM

35

Results of Side Resistance Simulations

36

OCR = 1

Hyperbolic Curve Fitting

37

bae −=

1βrdDc −

=1β

vr gf

NDσ ′+

= 12

'1

1

vgfNdcσ

β

+−

=

2000 psf

4000 psf

8000 psf

Predications Based on Design Equations

38

+

−−

+=z

KK

K

KKo

o

o

ooU 1

2

tanφβ

φβ tanoF K=

Ko = (1 – sin φ) = 26.696e2 - 32.264e + 10.144

Side Resistance of OC Samples

39

OCR = 4

OCR = 2

σv = 2000 psf

Effect of Vertical Stress (OC Samples)

40

σ = 2000 psf

σ = 4000 psf

OCR = 2

Comparisons between Design Equations and Numerical Results

41

Void Ratio

Unified design equation

O’Neill and Reese Method

φ = 30° 36° 42°

β is found to be a function of relative density, vertical stress, and OCR

For normally consolidated samples at a certain effective stress, a simple hyperbolic curve can describe the relationship between β and void ratio

The effect of OCR on β is rather complicated More data are needed to clarify the role of OCR

Conclusions (Numerical Result)

42

Differences between the numerical simulations and the predicated equations are observed.

For NC samples, the Unified design equation considers the effect of depth (vertical stress) while the NHI equation ignores this factor which is not quite right

In the NHI equation, the effect of OCR is attempted However, the numerical data show that the effect of OCR on β is different from that of the NHI equation (βOC always greater than β for any OCR)

Conclusions (Numerical Result)

43

The Unified design equation should incorporate the effect of OCR

The Unified design equation does consider the effect of vertical stress, however, the effect of vertical stress is more complicated than the term used in the equation (reciprocal of the square root of depth)

Conclusions (Numerical Result)

44

The resistance factors of the three design equations are similar

The resistance factor for the Unified design equation is slightly higher than the other two methods.

The DEM simulations presented here are very promising as they show the advantages and disadvantages of these design equations

The result indicates the possibility of the development of the modified Unified Design Equation as a cost saving design tool

Conclusions

45

Future Works Improve the database by collecting more local field

test data obtain a local regional resistance factor Generate more numerical samples understand the

mechanism of side resistance mobilization of a drilled shaft modify the Unified Design Equation

Develop a better Unified Design Equation obtain a higher design resistance reduce construction cost

(Save $$$)

New Mexico Department of Transportation (NMDOT) Federal Highway Administration Project Sponsor: Mr. Bob Meyers, NMDOT Project manager: Mr. Virgil Valdez, NMDOT Members of the Technical Panel Mr. Jim Wilson of ADOT

ACKNOWLEDGEMENT

47