1. 1
Load and Resistance Factor
Design (LRFD)- Deep Foundations
Donald C. Wotring, Ph.D., P.E.
February 2009

2. 2
Presentation
• This presentation is intended as a detailed
internal short-course with design examples. It
will also be used as a brown-bag lunch
presentation, but with less detail covered.

3. 3
Presentation Goals
1. Basic Differences between ASD and LRFD
2. Fundamentals of LRFD
3. Application of LRFD to Deep Foundations

4. 4
Load < Resistance

5. 5
Load = Resistance ?????

6. 6
Load > Resistance

7. 7
Examples of Uncertainty
• Material dimensions and location
• Material strength
• 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

8. 8
Allowable Stress Design
(ΣDL + ΣLL ) ≤ Rn / FS
ADVANTAGES DISADVANTAGES
Simplistic Inadequate account of variability
Accustomed to use Stress not a good measure of
resistance
Factor of Safety is subjective
No risk assessment

9. 9
Definition - Limit State
• A Limit State is a condition beyond
which a structural component ceases
to satisfy the provisions for which it is
designed.

10. 10
Definition - Resistance
• Resistance is a quantifiable value
that defines the point beyond which
the particular limit state under
investigation, for a particular
component, will be exceeded.

11. 11
Resistance Can Be Defined in Terms of
• Load/Force
• Stress (normal, shear, torsional)
• Number of cycles
• Temperature
• Strain
• etc.

12. 12
AASHTO LRFD Bridge Design
Specifications
• 4th Edition, 2007
• 2008 Interim Revisions

13. 13
Load and Resistance Factor Design
Σηiγ i Qi ≤ φRn = Rr
ADVANTAGES DISADVANTAGES
Load factor applied to each load More complex than ASD
combination Old habits
Types of loads have different levels of Requires availability of statistical data
uncertainty
Resistance factors vary
Accounts for variability
Uniform levels of safety
Risk assessment

14. 14
LRFD Equation
Σηiγ i Qi ≤ φRn = Rr
ηi Load modifier: factor relating to ductility, redundancy, and
operational importance
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

15. 15
Limit States
• Strength – strength and stability sufficient to resist
the specified statistically significant load
combination during design life
I – Normal vehicular use without wind
II – Owner-specified design vehicle without wind
III – 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. 16

17. 17
Limit States
• Service – Restrictions on stress, deformation, and
crack width under regular service conditions
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. 18

19. 19
Limit States
• Extreme – Structural survival during a major
event (earthquake, flood, vessel impact, ice, etc.)
I – Earthquake
II – Other events

20. 20

21. 21
Limit States
• Fatigue – Limit crack growth under repetitive
loads to prevent fracture during design life

22. 22

23. 23
Load Modifier Σηiγ i Qi ≤ φRn = Rr
ηi = η Dη Rη I ≥ 0.95 When maximum value of γi is appropriate
1
ηi = ≤ 1.0 When minimum value of γi is appropriate
η Dη Rη I
ηD Ductility load modifier
ηR Redundancy load modifier
ηD Operational importance load modifier

24. 24
Load Modifier - Ductility
Strength Limit State
ηD > 1.05 Non-ductile components and connections
= 1.00 Conventional designs according to AASHTO specs
< 0.95 Ductility enhancing measures specified beyond AASHTO
specs
All other Limit States
ηD = 1.00

25. 25
Load Modifier - Redundancy
Strength Limit State
ηR > 1.05 Non-redundant members
= 1.00 Conventional redundancy
< 0.95 Exceptional redundancy
All other Limit States
ηR = 1.00

26. 26
Load Modifier – Operational
Importance
Strength Limit State
ηI > 1.05 Important bridges
= 1.00 Typical bridges
< 0.95 Relatively less important bridges
All other Limit States
ηI = 1.00

27. 27
Loads Σηiγ i Qi ≤ φRn = Rr

28. 28
Load Combinations and Load Factors

29. 29
Load Factors for Permanent Loads
Destabilizing Stabilizing

30. 30
Loading Summary
Σηiγ i Qi ≤ φRn = Rr
Load modifier – Usually = 1.0
Load factor Develop a governing load
combination for each of:
Load - Strength
- Service
- Extreme
- Fatigue

31. 31
Probability Review Normal Distribution

32. 32
Probability of Failure Reliability Index, β
No. of standard deviations
that the mean value is
above 0

33. 33
Probability of Failure – Reliability
Index
Structure Pile Redundancy
β Pf
2.33 1.0%
3.00 0.13%

34. 34
Resistance Factor
1 + COV Q
2
λR (Σγ i Qi )
1 + COV R
2
φ=
{ [(
Q exp βT ln 1 + COVR 1 + COVQ
2
)( 2
)]}
Dead Load Factors
γD = 1.25
λQD = 1.05
COVQD = 0.1
QD
Live Load Factors γD +γL
γL = 1.75 QL 1.4167
λQL = 1.15
FS = ≅
 QD  φ
COVQL = 0.2 φ
 + 1

 QL 

35. 35

36. 36

37. 37
Does a low resistance value =
Inefficient Design method?
COV = 0.4
λ= 1.0
φ= 0.44
φ/λ = 0.44
COV = 0.4
λ= 1.5
φ= 0.67
φ/λ = 0.44
COV = 0.58
λ= 1.5
φ= 0.44
φ/λ = 0.29 Overpredictive Underpredictive (built in FS)

38. 38
Efficiency of the Method
φ/λ
λ
FS(λ)

39. 39
Summary - Where do we stand?
Σηiγ i Qi ≤ φRn = Rr
Resistance factor based on probability of failure for different methods
of estimating the resistance.

40. 40
Limit States as Applied to Deep
Foundations
• AASHTO, Section 10.5
• Service Limits
• Strength Limits
• Extreme Limits

41. 41
Service Limit States φ = 1.0
• Settlements – limitation to be compared with
costs of designing structure to tolerate more
movement or maintenance (jacking and shimming
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

42. 42
Extreme Limit States
• Scour – Check flood (Section 2.6.4)
• Earthquake
• Liquefaction
• Ice
• Vehicle or Vessel Impact
φ = 1.0 general
φ = 0.8 uplift

43. 43
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
• 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.

44. 44
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 (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.

45. 45
Driven Piles

46. 46
Driven Piles

47. 47

48. 48
What is a difficulty (driven piles)?

49. 49
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
driving criteria.
φdyn Rndr = φstat Rnstat

50. 50
MDOT Bridge Design Manual (7.03.09)
Nominal Driving Resistance Values, Rndr
Steel H-Piles Cast-in-place Concrete Piles
Pile Type Rndr (k) Pile Type Rndr (k)
HP10x42 300 12” O.D., 0.25” 350
HP10x57 450 14” O.D., 0.312” 400
HP12x53 400 14” O.D., 0.438” 500
HP12x74 600
HP12x84 650 Timber Piles
HP14x73 600 Pile Type Rndr (k)
HP14x89 700 Timber 150
HP14x102 800
HP14x117 900

51. 51
Structural Compressive Resistance -
Steel
Pn = 0.66λ Fy A λ < 2.25
If fully embedded,
0.88 Fy A λ=0
Pn = λ > 2.25
λ
2
 kL  Fy
λ =  Euler Equation
 rπ  E

52. 52
Structural Pile Resistance Values
Resistance during pile driving φ = 1.0
Axial resistance for compression subject Combined axial and flexural
to damage where pile type is required resistance for undamaged pile
H-piles φ = 0.5 Axial H-piles φ = 0.6
Pipe piles φ = 0.6 Axial pipe piles φ = 0.7
Axial resistance for compression not Axial pipe piles φ = 1.0
subject to damage
H-piles φ = 0.6
Pipe piles φ = 0.7

53. 53
Drilled Shafts

54. 54
Micropiles

55. 55
Summary
• LRFD – statistically based method to account for
the probability of failure
▫ Compared with ASD
▫ Limit states and resistance
▫ Load factors and combinations
▫ Resistance factors

56. 56
Example 1 - Estimate Pile Length
• Pier Factored Load = γQ = 1.25(3640) = 4550 kips
Fill γ= 130 pcf 10’
Clay γ= 125 pcf • Assume PDA w/ CAPWAP φdyn = 0.65
su = 2.5 ksf
120’ •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

57. 57
Pile Caps
12-inch Pipe Piles 14-inch Pipe Piles
49”
112”
42” 138”
49”
42” 259”
180”

58. 58
Example 1 - Estimate Pile Length
Assume PDA w/ CAPWAP φdyn = 0.65
Fill γ= 130 pcf 10’
Assume λ-method φstat = 0.40
Clay γ= 125 pcf
φdyn
su = 2.5 ksf
120’ Rnstat = Rndr = 1.625Rndr
φstat
Pile Type Rndr (k) Rstat (k)
12” O.D., 0.25” 350 570
14” O.D., 0.312” 400 650

59. 59
Depth Summary
Qs = Rnstat (kips)
0 200 400 600 800 1000
40
50
12 OD
60
14 OD
70
Depth (ft)
80
90
100
110
120
130
140

60. 60
Settlement • Unfactored Pier Load 3640 kips
• Service Factored Load = γQ = 1.0(3640) = 3640 kips
Stress at top of Piles
σ = 3640k / 172.5 ft 2 = 21.1ksf
2D/3 = 73’
I Stress at 2D/3
A 17’ 0.96 σ = 3640k / 2422.5 ft 2 = 1.5ksf
B 20’ 0.66
C 20’ 0.36
Clay Assumptions
OCR = 1.2 Cc = 0.2 Cr/Cc = 0.1
eo = 0.5 Cr = 0.02

61. 61
Settlement
Point σ’vo I ∆σ σ’vf σ’p Ho/1+eo Sp
(ksf) (ksf) (ksf) (ksf) (in) (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
C 8.2 0.36 0.54 8.74 9.84 160 0.09
Σ 0.96
If σ’vf < σ’p If σ’vf > σ’p
Ho  σ 'vf  Ho  C   σ ' p   σ 'vf 
Sp = Cr log
σ '  Sp =  
 C   σ '  + log σ '
Cc   log
r
1 + eo   
 vo  1 + eo  c   vo 
  p 

62. 62
Example 2
Strength V Limit – Rigid Cap Model
Applied Factored Loads
Fx = 38.4 kips
Fy = 109.1 kips
Fz = 3,594.0 kips
Mx = 3,196.5 k-ft
My = -8,331.9 k-ft Loose Sand

63. 63
Calculate Pile Axial Loads
Fz M x yi M y xi 3594 3196.5(1.5) − 8331.9(−5)
Pi = + n + n P = + + = 243
n 14
∑ yi2 ∑ xi2
20 225 1000
i =1 i =1
Fz = 3,594.0 kips
Mx = 3,196.5 k-ft
My = -8,331.9 k-ft
n = 20 piles
xi = -60 in (-5 ft)
yi = 18in (1.5 ft)
36 in
Σxi2 = 1,000 ft2
Σyi2 = 225 ft2
60 in
s2
( )
∑ x (row) = 12 n n 2 − 1
2
i

64. 64
Lateral Loading – LPILE
Pile CTC P-Multiplier, Pm
Spacing Row 1 Row 2 Rows 3
(loading and
direction) higher
3B 0.7 0.5 0.35
5B 1.0 0.85 0.7

65. 65
Lateral Loading – LPILE
Row Pm Hy (k) Mm
(k-in)
1 0.35 4.5 -340
2 0.35 4.5 -340
3 0.5 5.9 -390
4 0.7 7.2 -450
Σ 110.5

66. 66
Lateral Loading – LPILE
Row Pm Hz (k) Mm
(k-in)
1 0.7 1.8 -75
2 0.7 1.8 -75
3 0.7 1.8 -75
4 0.85 2.0 -80
5 1.0 2.2 -90
Σ 38.4

67. 67
Pile Loading Summary
Maximum Shear (Row 4 piles) 7.2 kips
Maximum axial load in any pile (Pile 20) 327 kips
Maximum combined loading (Pile 20)
Pu 327 kips
Mux -37.5 k-ft
Muy -7.5 k-ft
Alternative to rigid cap
model, use FBPier

68. 68
Drivability Evaluation (GRL Weap)
Require a PDA/CAPWAP
Field Evaluation
φdyn = 0.65
Nominal must be >
327/0.65=503 kips
Nominal Driving Resistance
• HP12x53
• Delmag D 12-32
•Rndr = 550 kips at 120bpf
• 10 bpi = 5 b/0.5inch
Factored Driving Resistance
Rrdr = φdynRndr = 0.65(550) = 358 kips

69. 69
Drivability
Check Driving Stresses
Steel Piles in Compression
or Tension
σ DR = 0.9ϕ DA Fy
ϕ DA = 1.0
σ DR = 0.9(1.0)50 = 45ksi > 37.5

70. 70
Geotechnical Resistance - Static
Estimate the Depth of Penetration φdyn Rn = 358kips = φstat Rnstat
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).

71. 71
Structural Resistance - Compression
Nominal Compressive Resistance (Section 6.9.4.1)
Pn = 0.66λ Fy A Compression only, damage likely
φ = 0.5
λ =0 Fully embedded
Compression only, damage unlikely
Pn = Fy A = 50(15.5) = 775kips φ = 0.6
Combined
Factored Compressive Resistance φ = 0.7
Pr = φPn = 0.5(775) = 387.5kips
Good for lower portion of pile where damage is more likely
Pr = φPn = 0.7(775) = 542.5kips combined

72. 72
Structural Resistance - Shear
Nominal Shear Resistance (Section 6.10.9.2) Vn = 0.58CFy Dt w
HP12x53 Check shear buckling ratio
D = 11.78 in D Ek 5(29,000)
tw = 0.435 in = 27.1 < 60.3 1.12 = 1.12 = 60.3
tw Fy 50
C = 1.0
Vn = 0.58(1.0)50(11.78)0.435 = 148.6kips
Factored Shear Resistance
Vr = φVn = 1.0(148.6) = 148.6kips

73. 73
Structural Resistance – Flexural
Nominal Flexural Resistance (Section 6.12.2.2)
M n = Fy z zx 74.0 in3
zy 32.2 in3
M nx = 50(74) = 3700 k-in
M ny = 50(32.2) = 1610 k-in
Factored Flexural Resistance M r = φM n φ = 1.0
M rx = 1.0(3700) = 3700 k-in
M ry = 1.0(1610) = 1610 k-in

74. 74
Combined Loading
Nominal Combined Loading(Section 6. 9.2.2)
Pu Pu  M ux M uy 
< 0.2 + +  ≤ 1.0
Pr 2 Pr  M rx M ry 
 
Pu Pu 8  M ux M uy 
≥ 0.2 +  +  ≤ 1.0
Pr Pr 9  M rx M ry 
 

75. 75
Combined Loading
Pu 327 kips Pr 542.5 kips Pu/Pr 0.6 > 0.2
Mux -37.5 k-ft Mrx 308.3 k-ft Mrx 0.12
Muy -7.5 k-ft Mry 134.2 k-ft Mry 0.06
Pu 8  M ux M uy 
  = 0.6 + 8 (0.12 + 0.06) = 0.76 < 1.0
+ +
Pr 9  rx M ry 
M
 9

76. 76
Summary – Strength V Limit State
Structural Performance Ratios
Driven 327/358 = 0.91
Geotechnical N/A
Axial Compression only 327/387.5 = 0.84
Combined Axial and Flexural 0.76
Shear 7.2/148.6 = 0.05

77. 77
Example 3 - Drilled Shafts

78. 78
Example 3 - Drilled Shafts

79. 79
Example 3 - Drilled Shafts
Limestone Parameters
qu = 11,500 psi (79.3 Mpa)
RQD = 80%
~ 1 fracture per foot
Tight clean joints
Drilled Shaft
D = 3.3 m (10.8 ft)
L = 5 ft, 10 ft, and 15 ft
L Limestone
Reference
FHWA-IF-99-025

80. 80
Base Resistance for Compressive
Loading
Rock with 70 < RQD < 100 (FHWA, Eqn 11.6)
qmax ( MPa) = 4.83[qu ( MPa)]
0.51
qmax = 44.9 Mpa (469 tsf)
[ ]q
Jointed Rock (FHWA, Eqn, 11.7)
0.5
(
qmax = s + ms + s0.5
)
0.5
u
qmax = 49.5 Mpa (517 tsf)
Detroit Experience
qmax = qall (FS ) = 120(2.5) qmax = 28.7Mpa (300 tsf)

81. 81
Base Resistance
Say
s = 4(10)-2
m = 0.7

82. 82
Side Resistance for Compression
Loading
Smooth Rock (FHWA, Eqn 11.24)
0.5 0.5
 qu   f 'c 
f max = 0.65 pa   ≤ 0.65 pa   fmax = 1.02 Mpa (10.6 tsf)
 pa   pa 

83. 83
Nominal Resistance Values
Base Resistance
qmax = 300 tsf φ = 0.5
RBN = 27,605 tons
Shaft Resistance
fmax = 10.6 tsf φ = 0.55
RSN = 1,800 tons (L = 5 ft)
3,600 tons (L = 10 ft)
5,400 tons (L = 15 ft)

84. 84
Strain Incompatibility

85. 85
Strain Incompatibility
QT1 QT
QT1 = Total load on head at point where
δT1 socket side shear failure develops.
Some base resistance has
developed.
δT1+∆δ QT = Ultimate resistance of drilled
See Appendix C of FHWA-IF-99-025
plunging

86. 86
Drilled Shaft – Nominal Results
30000 1.0 1.0
0.9 0.9
Skin Resistance/Ultimate Skin Resistance
25000
End Bearing/Ultimate End Bearing
0.8 0.8
Nominal Resistance (tons)
0.7 0.7
20000
0.6 0.6
15000 0.5 0.5
5 ft
0.4 0.4
10000 10 ft
0.3 0.3
15 ft
0.2 0.2
5000
0.1 0.1
0 0.0 0.0
0 1 2 3 4 0 1 2 3 4 0 1 2 3 4
Settlement/Shaft Diameter (%) Settlement/Shaft Diameter (%) Settlement/Shaft Diameter (%)
For L = 10 ft
δ/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

87. 87
Drilled Shaft – Nominal and Factored
Values
For L = 10 ft
δ/D = 1%
Rn = 13,700 tons
Shaft Resistance
RSN(mob)/RSN = 0.7 RSN = 3,600 tons RSN(mob) = 2,520 tons
Base Resistance
RBN(mob)/RBN = 0.4 RBN = 27,605 tons RBN(mob) = 11,1180 tons
Factored Resistance
Rr = φRn = 0.5(11,180)+0.55(2,520) = 6,976 tons