Load and Resistance Factor

Design (LRFD)- Deep Foundations

1

Design (LRFD)- Deep FoundationsDonald C. Wotring, Ph.D., P.E.

February 2009

Presentation

• This presentation is intended as a detailed internal short-course with design examples. It will also be used as a brown-bag lunch

2

will also be used as a brown-bag lunch presentation, but with less detail covered.

Presentation Goals

1. Basic Differences between ASD and LRFD

3

2. Fundamentals of LRFD

3. Application of LRFD to Deep Foundations

Load < Resistance

4

Load = Resistance ?????

5

Load > Resistance

6

Examples of Uncertainty

• Material dimensions and location

• Material strength

• Failure mode and prediction method

7

• Failure mode and prediction method

• Long-term material performance

• Material weights

• Prediction of potential transient loads

• Load analysis and distribution methods

• General uncertainty with structure function

Allowable Stress Design

( ) FSRLLDL n /≤Σ+Σ

8

ADVANTAGES

Simplistic

Accustomed to use

DISADVANTAGES

Inadequate account of variability

Stress not a good measure of resistance

Factor of Safety is subjective

No risk assessment

Definition - Limit State

• A Limit State is a condition beyond which a structural component ceases to satisfy the provisions for which it is

9

to satisfy the provisions for which it is designed.

Definition - Resistance

•Resistance is a quantifiable value that defines the point beyond which the particular limit state under

10

the particular limit state under investigation, for a particular component, will be exceeded.

Resistance Can Be Defined in Terms of

• Load/Force

• Stress (normal, shear, torsional)

• Number of cycles

11

• Number of cycles

• Temperature

• Strain

• etc.

AASHTO LRFD Bridge Design

Specifications

• 4th Edition, 2007

• 2008 Interim Revisions

12

• 2008 Interim Revisions

Load and Resistance Factor Design

rniii RRQ =≤Σ φγη

13

ADVANTAGES

Load factor applied to each load combination

Types of loads have different levels of uncertainty

Accounts for variability

Uniform levels of safety

Risk assessment

DISADVANTAGES

More complex than ASD

Old habits

Requires availability of statistical data

Resistance factors vary

LRFD Equationrniii RRQ =≤Σ φγη

ηi Load modifier: factor relating to ductility, redundancy, and operational importance

14

γi Load factor: statistically based multiplier applied to force effects

Qi Force effect

φ Resistance factor: statistically based multiplier applied to nominal resistance

Rn Nominal resistance

Rr Factored Resistance

Limit States

• Strength – strength and stability sufficient to resist the specified statistically significant load combination during design life

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I – Normal vehicular use without windII – Owner-specified design vehicle without windIII – Bridge exposed to wind velocity exceeding 55

mph (WS)IV – Very high dead load to live load ratio (when

DL/LL > 7, construction)V – Normal vehicular use with 55 mph wind (WL)

16

Limit States

• Service – Restrictions on stress, deformation, and crack width under regular service conditions

I – Normal operational use with 55 mph wind.

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I – Normal operational use with 55 mph wind. Also related to deflection control in tunnels, slopes, etc.

II – Yielding of steel structures and slip of slip-critical connections due to vehicular live load

III – Longitudinal analysis relating to tension in prestressed concrete

IV – Relating to crack control from tension in concrete columns

18

Limit States

• Extreme – Structural survival during a major event (earthquake, flood, vessel impact, ice, etc.)

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I – Earthquake

II – Other events

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Limit States

• Fatigue – Limit crack growth under repetitive loads to prevent fracture during design life

21

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Load Modifier

When maximum value of γi is appropriate95.0≥= IRDi ηηηη

rniii RRQ =≤Σ φγη

23

0.11 ≤=

IRDi ηηη

η When minimum value of γi is appropriate

ηD Ductility load modifier

ηR Redundancy load modifier

ηD Operational importance load modifier

Load Modifier - Ductility

Strength Limit StateηD > 1.05 Non-ductile components and connections

24

= 1.00 Conventional designs according to AASHTO specs

< 0.95 Ductility enhancing measures specified beyond AASHTO specs

All other Limit StatesηD = 1.00

Load Modifier - Redundancy

Strength Limit StateηR > 1.05 Non-redundant members

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= 1.00 Conventional redundancy

< 0.95 Exceptional redundancy

All other Limit StatesηR = 1.00

Load Modifier – Operational

Importance

Strength Limit StateηI > 1.05 Important bridges

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= 1.00 Typical bridges

< 0.95 Relatively less important bridges

All other Limit StatesηI = 1.00

Loads rniii RRQ =≤Σ φγη

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Load Combinations and Load Factors

28

Load Factors for Permanent Loads

29

Destabilizing Stabilizing

Loading Summary

rniii RRQ =≤Σ φγη

30

Load modifier – Usually = 1.0

Load factor

Load

Develop a governing load combination for each of:- Strength- Service- Extreme- Fatigue

Probability ReviewNormal Distribution

31

Probability of Failure Reliability Index, ββββNo. of standard deviations that the mean value is above 0

32

Probability of Failure – Reliability

Index

Structure Pile Redundancy

33

ββββ Pf

2.33 1.0%

3.00 0.13%

Resistance Factor

( )

( )( )[ ]{ }22

2

2

11lnexp

1

1

QRT

R

Q

iiR

COVCOVQ

COV

COVQ

++++Σ

=β

γλφ

34

Dead Load FactorsγD = 1.25λQD = 1.05COVQD = 0.1

Live Load FactorsγL = 1.75λQL = 1.15COVQL = 0.2

φφ

γγ4167.1

1

≅

+

+=

L

D

LL

DD

Q

Q

Q

Q

FS

35

36

Does a low resistance value =

Inefficient Design method?

COV = 0.4λ= 1.0φ= 0.44φ/λ = 0.44

37

Underpredictive (built in FS)Overpredictive

φ/λ = 0.44

COV = 0.4λ= 1.5φ= 0.67φ/λ = 0.44

COV = 0.58λ= 1.5φ= 0.44φ/λ = 0.29

Efficiency of the Method

38

φ/λφ/λφ/λφ/λ

FS(λλλλ)

Summary - Where do we stand?

rniii RRQ =≤Σ φγη

39

Resistance factor based on probability of failure for different methods of estimating the resistance.

Limit States as Applied to Deep

Foundations

• AASHTO, Section 10.5

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• Service Limits

• Strength Limits

• Extreme Limits

Service Limit States

• Settlements – limitation to be compared with costs of designing structure to tolerate more movement or maintenance (jacking and shimming bearings)

φ = 1.0

41

bearings)• Horizontal movements – top of foundation and

abutment movements based on tolerance of structure (bridge seat, bearing width, structure type, etc.)

• Overall stability – global slope stability of earth slopes

• Scour at design flood – Section 2.6.4

Extreme Limit States

• Scour – Check flood (Section 2.6.4)

• Earthquake

• Liquefaction

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• Liquefaction

• Ice

• Vehicle or Vessel Impact

φ = 1.0 generalφ = 0.8 uplift

Strength Limit States – Driven Piles,

Drilled Shaft, and Micropile• Axial compression resistance for single pile and pile group

• Uplift resistance of single pile and pile group

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• Uplift resistance of single pile and pile group

• Pile punching failure into weaker underlying stratum

• Single pile and pile group lateral resistance

• Constructability, including pile drivability

As part of strength limit state, the effects of downdrag, soil setup/relaxation, and buoyancy should be evaluated.

Strength Limit Resistance Factors

• Presented as a function of soil type (sand, clay). Sand = drained shear strength and Clay = undrained shear strength!!!!!

• β = 3.5 (P of 1 in 5,000)

44

• β = 3.5 (Pf of 1 in 5,000)

• Wave equations are for EOD only, if used for BOR, the resistance values need to be lowered. “In general, dynamic testing (signal matching) should be conducted to verify the nominal pile resistance at BOR in lieu of driving formulas.”

• Don’t reduce skin friction for uplift calcs. The resistance factor accounts for this.

• A load factor of 1.0 should be used for pile drivability analysis.

• The ENR news formula has had the FS=6 removed.

Driven Piles

45

Driven Piles

46

47

What is a difficulty (driven piles)?

48

Pile Length Estimate for Contract

Documents• Static analysis is only usually used to establish

the pile length estimate for contract documents. Field testing (e.g., PDA w/ CAPWAP) is used for

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Field testing (e.g., PDA w/ CAPWAP) is used for driving criteria.

nstatstatndrdyn RR φφ =

MDOT Bridge Design Manual (7.03.09)

Pile Type Rndr (k)

12” O.D., 0.25” 350

Cast-in-place Concrete Piles

Pile Type Rndr (k)

HP10x42 300

Steel H-Piles

Nominal Driving Resistance Values, Rndr

50

12” O.D., 0.25” 350

14” O.D., 0.312” 400

14” O.D., 0.438” 500

Pile Type Rndr (k)

Timber 150

Timber Piles

HP10x42 300

HP10x57 450

HP12x53 400

HP12x74 600

HP12x84 650

HP14x73 600

HP14x89 700

HP14x102 800

HP14x117 900

Structural Compressive Resistance -

Steel

AFP ynλ66.0= λ < 2.25

AF88.0If fully embedded,

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λ > 2.25

λAF

P yn

88.0=

E

F

r

kL y2

=π

λ Euler Equation

If fully embedded, λ = 0

Structural Pile Resistance Values

Resistance during pile driving φ = 1.0

Axial resistance for compression subject Combined axial and flexural

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Axial resistance for compression subject to damage where pile type is required

H-piles φ = 0.5Pipe piles φ = 0.6

Axial resistance for compression not subject to damage

H-piles φ = 0.6Pipe piles φ = 0.7

Combined axial and flexural resistance for undamaged pile

Axial H-piles φ = 0.6Axial pipe piles φ = 0.7Axial pipe piles φ = 1.0

Drilled Shafts

53

Micropiles

54

Summary

• LRFD – statistically based method to account for the probability of failure

▫ Compared with ASD

55

▫ Compared with ASD

▫ Limit states and resistance

▫ Load factors and combinations

▫ Resistance factors

Example 1 - Estimate Pile Length

Fill

Clay

γ= 130 pcf

γ= 125 pcf

10’• Pier Factored Load = γQ = 1.25(3640) = 4550 kips

• Assume PDA w/ CAPWAP � φdyn = 0.65

56

Clay γ= 125 pcfsu = 2.5 ksf

120’

• Assume PDA w/ CAPWAP � φdyn = 0.65

•Driven: Rr = φdynRndr

Pile Type Rndr (k) Rr (k) #Piles

12” O.D., 0.25” 350 227.5 20

14” O.D., 0.312” 400 260 18

Pile Caps

12-inch Pipe Piles 14-inch Pipe Piles

57

42”

42”

180”

138”

49”

49”

259”

112”

Example 1 - Estimate Pile Length

Fill

Clay

γ= 130 pcf

γ= 125 pcf

10’Assume PDA w/ CAPWAP � φdyn = 0.65Assume λ-method � φstat = 0.40

φ

58

Clay γ= 125 pcfsu = 2.5 ksf

120’

Pile Type Rndr (k) Rstat (k)

12” O.D., 0.25” 350 570

14” O.D., 0.312” 400 650

ndrndrstat

dynnstat RRR 625.1==

φφ

Depth Summary

40

50

0 200 400 600 800 1000

Qs = Rnstat (kips)

12 OD

59

60

70

80

90

100

110

120

130

140

De

pth

(ft

)

12 OD

14 OD

Settlement

2D/3 = 73’

• Unfactored Pier Load 3640 kips• Service Factored Load = γQ = 1.0(3640) = 3640 kips

ksfftk 1.215.172/3640 2 ==σStress at top of Piles

60

2D/3 = 73’

I Stress at 2D/3

ksfftk 5.15.2422/3640 2 ==σ

0.36

0.66

0.96

Clay AssumptionsOCR = 1.2 Cc = 0.2 Cr/Cc = 0.1eo = 0.5 Cr = 0.02

17’

20’

20’

AB

C

Settlement

Point σσσσ’vo(ksf)

I ∆σ∆σ∆σ∆σ(ksf)

σσσσ’vf(ksf)

σσσσ’p(ksf)

Ho/1+eo(in)

Sp(in)

A 5.8 0.96 1.44 7.24 6.96 136 0.68

B 6.9 0.66 0.99 7.89 8.28 160 0.19

61

B 6.9 0.66 0.99 7.89 8.28 160 0.19

C 8.2 0.36 0.54 8.74 9.84 160 0.09

Σ 0.96

+=

vo

vfr

o

op C

e

HS

'

'log

1 σσ

If σσσσ’vf < σσσσ’p If σσσσ’vf > σσσσ’p

+

+=

p

vf

vo

p

c

rc

o

op C

CC

e

HS

'

'log

'

'log

1 σσ

σσ

Example 2

Strength V Limit – Rigid Cap ModelApplied Factored Loads

62

Applied Factored Loads

Fx = 38.4 kipsFy = 109.1 kipsFz = 3,594.0 kips

Mx = 3,196.5 k-ftMy = -8,331.9 k-ft Loose Sand

Calculate Pile Axial Loads

∑∑==

++= n

ii

iy

n

ii

ixzi

x

xM

y

yM

n

FP

1

2

1

2243

1000

)5(9.8331

225

)5.1(5.3196

20

359414 =−−++=P

63

36 in

60 in

== ii 11

Fz = 3,594.0 kipsMx = 3,196.5 k-ftMy = -8,331.9 k-ftn = 20 pilesxi = -60 in (-5 ft)yi = 18in (1.5 ft)Σxi

2 = 1,000 ft2

Σyi2 = 225 ft2

( )112

)( 22

2 −=∑ nns

rowxi

Lateral Loading – LPILE

Pile CTC Spacing(loading

P-Multiplier, Pm

Row 1 Row 2 Rows 3

64

(loading direction)

Row 1 Row 2 Rows 3 and

higher

3B 0.7 0.5 0.35

5B 1.0 0.85 0.7

Lateral Loading – LPILERow Pm Hy (k) Mm

(k-in)

1 0.35 4.5 -340

2 0.35 4.5 -340

3 0.5 5.9 -390

65

3 0.5 5.9 -390

4 0.7 7.2 -450

ΣΣΣΣ 110.5

Lateral Loading – LPILERow Pm Hz (k) Mm

(k-in)

1 0.7 1.8 -75

2 0.7 1.8 -75

3 0.7 1.8 -75

66

3 0.7 1.8 -75

4 0.85 2.0 -80

5 1.0 2.2 -90

ΣΣΣΣ 38.4

Pile Loading Summary

Maximum Shear (Row 4 piles) 7.2 kips

Maximum axial load in any pile (Pile 20) 327 kips

67

Maximum combined loading (Pile 20)Pu 327 kipsMux -37.5 k-ftMuy -7.5 k-ft

Alternative to rigid cap model, use FBPier

Drivability Evaluation (GRL Weap)

Require a PDA/CAPWAP Field Evaluationφdyn = 0.65

68

Nominal Driving Resistance• HP12x53• Delmag D 12-32•Rndr = 550 kips at 120bpf• 10 bpi = 5 b/0.5inch

Nominal must be >327/0.65=503 kips

Rrdr = φdynRndr = 0.65(550) = 358 kips

Factored Driving Resistance

Drivability

Check Driving Stresses

Steel Piles in Compression

69

yDADR Fϕσ 9.0=

Steel Piles in Compression or Tension

0.1=DAϕ

5.374550)0.1(9.0 >== ksiDRσ

Geotechnical Resistance - Static

Estimate the Depth of Penetration nstatstatndyn RkipsR φφ == 358

70

Use SPT method φ = 0.3

Rnstat = 358/0.3 = 1193 kips !!!

Very long piles would be required if all loose sand!! For our geology, the piles would end bear on till or bedrock and develop full capacity within a few feet of penetration (usual for H-piles). End bearing on rock (φ = 0.45). Pile tips required and driving resistance and criteria will be based on dynamic testing in the field (PDA/CAPWAP).

Structural Resistance - Compression

AFP ynλ66.0=

Nominal Compressive Resistance (Section 6.9.4.1)

5.0=φCompression only, damage likely

71

AFP yn 66.0=

0=λ Fully embedded

kipsAFP yn 775)5.15(50 ===

Factored Compressive Resistance

kipsPP nr 5.542)775(7.0 === φ

Good for lower portion of pile where damage is more likely

5.0=φ

6.0=φCompression only, damage unlikely

7.0=φCombined

kipsPP nr 5.387)775(5.0 === φ

combined

Structural Resistance - Shear

wyn DtCFV 58.0=Nominal Shear Resistance (Section 6.10.9.2)

HP12x53D = 11.78 in <=D

Check shear buckling ratio

)000,29(5Ek

72

D = 11.78 intw = 0.435 in

Factored Shear Resistance

kipsVV nr 6.148)6.148(0.1 === φ

3.601.27 <=wt

D3.60

50

)000,29(512.112.1 ==

yF

Ek

C = 1.0

kipsVn 6.148435.0)78.11(50)0.1(58.0 ==

Structural Resistance – Flexural

Nominal Flexural Resistance (Section 6.12.2.2)

zFM yn = zx 74.0 in3

73

zFM yn = zx 74.0 inzy 32.2 in3

3700)74(50 ==nxM

1610)2.32(50 ==nyM k-in

k-in

Factored Flexural Resistancenr MM φ=

3700)3700(0.1 ==rxM

0.1=φ

1610)1610(0.1 ==ryM k-in

k-in

Combined Loading

Nominal Combined Loading(Section 6. 9.2.2)

2.0<uP0.1≤

++ uyuxuMMP

74

2.0<r

u

P0.1

2≤

++

ry

uy

rx

ux

r

u

MM

M

P

P

2.0≥r

u

P

P0.1

9

8 ≤

++

ry

uy

rx

ux

r

u

M

M

M

M

P

P

Combined Loading

Pu 327 kipsMux -37.5 k-ftMuy -7.5 k-ft

Pr 542.5 kipsMrx 308.3 k-ftMry 134.2 k-ft

Pu/Pr 0.6 > 0.2Mrx 0.12Mry 0.06

75

( ) 0.176.006.012.09

86.0

9

8 <=++=

++

ry

uy

rx

ux

r

u

M

M

M

M

P

P

Summary – Strength V Limit State

Structural Performance Ratios

Driven 327/358 = 0.91

76

Driven 327/358 = 0.91Geotechnical N/AAxial Compression only 327/387.5 = 0.84Combined Axial and Flexural 0.76Shear 7.2/148.6 = 0.05

Example 3 - Drilled Shafts

77

Example 3 - Drilled Shafts

78

Example 3 - Drilled Shafts

79

Limestone Parametersqu = 11,500 psi (79.3 Mpa)RQD = 80%~ 1 fracture per foot

L

~ 1 fracture per footTight clean joints

Drilled ShaftD = 3.3 m (10.8 ft)L = 5 ft, 10 ft, and 15 ft

ReferenceFHWA-IF-99-025

Limestone

Base Resistance for Compressive

Loading

80

[ ] 51.0max )(83.4)( MPaqMPaq u=Rock with 70 < RQD < 100 (FHWA, Eqn 11.6)

qmax = 44.9 Mpa (469 tsf)[ ]max )(83.4)( MPaqMPaq u=

( )[ ] uqsmssq5.05.05.0

max ++=

( ) )5.2(120max == FSqq all

Jointed Rock (FHWA, Eqn, 11.7)

Detroit Experience

qmax = 44.9 Mpa (469 tsf)

qmax = 49.5 Mpa (517 tsf)

qmax = 28.7Mpa (300 tsf)

Base Resistance

81

Says = 4(10)-2

m = 0.7

Side Resistance for Compression

Loading

82

5.05.0' fq

Smooth Rock (FHWA, Eqn 11.24)

5.05.0

max

'65.065.0

≤

=

a

ca

a

ua p

fp

p

qpf fmax = 1.02 Mpa (10.6 tsf)

Nominal Resistance Values

83

Base Resistanceqmax = 300 tsf φ = 0.5RBN = 27,605 tonsRBN = 27,605 tons

Shaft Resistancefmax = 10.6 tsf φ = 0.55RSN = 1,800 tons (L = 5 ft)

3,600 tons (L = 10 ft)5,400 tons (L = 15 ft)

Strain Incompatibility

84

Strain Incompatibility

85

QT1 QT

δT1

QT1 = Total load on head at point where socket side shear failure develops. Some base resistance has developed.

δT1+∆δ

developed.

QT = Ultimate resistance of drilled

See Appendix C of FHWA-IF-99-025

plunging

Drilled Shaft – Nominal Results

20000

25000

30000

No

min

al

Re

sist

an

ce (

ton

s)

0.6

0.7

0.8

0.9

1.0

En

d B

ea

rin

g/

Ult

ima

te E

nd

Be

ari

ng

0.6

0.7

0.8

0.9

1.0

Sk

in R

esi

sta

nce

/U

ltim

ate

Sk

in R

esi

sta

nce

86

0

5000

10000

15000

0 1 2 3 4

No

min

al

Re

sist

an

ce (

ton

s)

Settlement/Shaft Diameter (%)

5 ft

10 ft

15 ft

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4

En

d B

ea

rin

g/

Ult

ima

te E

nd

Be

ari

ng

Settlement/Shaft Diameter (%)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4

Sk

in R

esi

sta

nce

/U

ltim

ate

Sk

in R

esi

sta

nce

Settlement/Shaft Diameter (%)

For L = 10 ftδ/D = 1% Rn = 13,700 tons RSN(mob)/RSN = 0.7 δ = 0.1*10.8*12 = 1.3 inch RBN(mob)/RBN = 0.4

Drilled Shaft – Nominal and Factored

Values

87

For L = 10 ftδ/D = 1%Rn = 13,700 tonsRn = 13,700 tons

Shaft ResistanceRSN(mob)/RSN = 0.7 RSN = 3,600 tons RSN(mob) = 2,520 tons

Base ResistanceRBN(mob)/RBN = 0.4 RBN = 27,605 tons RBN(mob) = 11,1180 tons

Factored ResistanceRr = φRn = 0.5(11,180)+0.55(2,520) = 6,976 tons