1. Seismic LRFD for Pile Foundation Design
Steve Kramer
Juan Carlos Valdez
University of Washington
Benjamin Blanchette
Hart-Crowser
Jack Baker
Stanford University

2. Acknowledgments California Department of Transportation – Tom Shantz
Washington State Department of Transportation – Tony Allen

3. Goal of Project
Develop framework for evaluation of load and resistance factors for pile foundation design using PEER PBEE concepts
Framework is to allow design for pile cap movement (vertical, horizontal, rocking) based on design return period for limit state exceedance in any seismic environment
Put framework in format where DOT foundation engineers can investigate effects of various assumptions regarding uncertainties on load and resistance factors
Framework will be used in AASHTO code development process to illustrate benefits of PBEE approach to load and resistance factor development

4. Current LRFD Procedure (simplified)
Develop design spectrum
Perform structural analyses
Check that capacity > demand for structure
Design foundations
Apply forces from structural analysis to foundation
Check foundation capacity
Maximum force(s) < available resistance(s)
Maximum displacement(s) < allowable displacement(s)
– for selected return period

5. Performance-based framework
Capacity and demand factors can be obtained from Cornell idealization
assumptions
Process requires hazard curve and ability to predict response given
ground motion level, i.e.
EDP | IM
where EDP = pile cap displacement / rotation
IM = Sa(To), etc.

6. Complicating Factors All bridges are different Pile foundations have –
Different static loads
Vertical
Horizontal (2)
Moment (2)
Different dynamic loads
Pile foundations can have –
Different group configurations
Different pile lengths
Different pile cap dimensions

7. Complicating Factors All sites are different
Conditions favoring end-bearing piles
Conditions favoring friction piles
Geometric and material variability / uncertainty
Checking procedures needed
Must be simple, straightforward
Force-based – check force demands against capacities
Displacement-based – check displ. demands against allowable displacements
To advance practice, procedures must be displacement-based
Design should imply certain reliability w/r/t exceedance of displ level

8. Permutations Ground motion hazards Ground motions Bridge
Multiple ground motion levels
Ground motions
Multiple time histories
Bridge
configurations
Multiple bridge configurations dx dy dz qx qy
Pile group configurations
Multiple response measures (EDPs)
Dynamic response
Multiple pile group configurations
Static loading conditions
Multiple static load states – 5 loads for each
Multiple dynamic load cases – 5 loads for each
Dynamic loading conditions

9. Permutations Ground motion hazards Ground motions
Multiple ground motion levels
Ground motions
Multiple time histories
For 5 hazard levels, 5 bridge configurations, 5 pile groups, 4 initial load levels, 3 hazard levels, and 100 simulations with 40 input motions, we need 30,000,000 EDP calculations.
Bridge
configurations
Multiple bridge configurations dx dy dz qx qy
Pile group configurations
Multiple response measures (EDPs)
Dynamic response
Multiple pile group configurations
Static loading conditions
Multiple static load states – 5 loads for each
Multiple dynamic load cases – 5 loads for each
Dynamic loading conditions

10. Permutations
For 5 pile groups, 4 initial load levels, and 100 simulations with 40 input motions, we need a little more than 400,000 EDP calculations. dx dy dz qx qy
Pile group configurations
Multiple response measures (EDPs)
Dynamic response
Multiple pile group configurations
Static loading conditions
Multiple static load states – 5 loads for each
Multiple dynamic load cases – 5 loads for each
Dynamic loading conditions

11. Response model – includes soil, foundations, and bridge
Performance-Based Framework
How do we take advantage of a performance-based framework in development of load and resistance factors?
We need to be able to predict a hazard curve for the EDPs of interest, which will consist of pile cap displacements/rotations
Normally, we predict EDPs from ground motion intensity measures
Response model – includes soil, foundations, and bridge

12. Performance-Based Framework
How do we take advantage of a performance-based framework in development of load and resistance factors?
We need to be able to predict a hazard curve for the EDPs of interest, which will consist of pile cap displacements/rotations
We can subdivide response model into two components
Pile cap response model – includes soil and foundation
Pile cap loading model – consists of bridge model

13. Engineering Demand Parameter, EDP
Performance-Based Framework
How do we take advantage of a performance-based framework in development of load and resistance factors?
We need to be able to predict a hazard curve for the EDPs of interest, which will consist of pile cap displacements/rotations
We can subdivide response model into two components
Pile
cap response model
Pile cap load model
Engineering Demand Parameter, EDP
Load Measure, LM
Intensity Measure, IM

14. Engineering Demand Parameter, EDP
Performance-Based Framework
How do we take advantage of a performance-based framework in development of load and resistance factors?
We need to be able to predict a hazard curve for the EDPs of interest, which will consist of pile cap displacements/rotations
We can subdivide response model into two components
Pile
cap response model
Pile cap load model
Engineering Demand Parameter, EDP
Load Measure, LM
Intensity Measure, IM
From structural analysis – assume computed loads are median loads, assume sln LM|IM

15. Engineering Demand Parameter, EDP
Performance-Based Framework
How do we take advantage of a performance-based framework in development of load and resistance factors?
We need to be able to predict a hazard curve for the EDPs of interest, which will consist of pile cap displacements/rotations
We can subdivide response model into two components
Pile
cap response model
Pile cap load model
Engineering Demand Parameter, EDP
Load Measure, LM
Intensity Measure, IM
From pile group response analyses – OpenSees models of pile groups under multiple initial load states subjected to multiple motions

16. Computing Load Measure, LM | IM
How do we evaluate pile group response to dynamic loading?
Compute representative structural response to input motion – LM|IM
Choose structural configuration and build model – SAP / OpenSees
Compute foundation stiffnesses – from OpenSees results
Compute foundation damping – DYNA4
Apply input motions at ends of springs
Compute pile cap deflections
Check foundation stiffness and iterate until compatible with displacements
Compute vertical load, horizontal loads (2), and overturning moments (2) at top of pile cap

17. Computing Load Measure, LM | IM
How do we evaluate pile group response to dynamic loading?
Compute representative structural response to input motion – LM|IM
Choose structural configuration and build model – SAP
Compute foundation stiffnesses – from OpenSees results
Compute foundation damping – use DYNA4
Apply input motions at ends of springs
Compute pile cap deflections
Check foundation stiffness and iterate until compatible with displacements
Compute vertical load, horizontal loads (2), and overturning moments (2) at top of pile cap
LM|IM

18. Input to OpenSees Model
Loading Histories
ATC-49 Bridge 4
W= 725 k, H = 20 ft
To = 0.5 sec
P/f’cAg = 0.10
3 x 3 group of 24” piles in clay
SAP model – fiber model for column allows yielding

19. Input to OpenSees Model
Ground motions
Suite of 45 three-component NGA ground motions identified
Representative of softer Class C to stiffer Class D ( m/sec)
Binned over three magnitude ranges, three distance ranges
Epsilon for Sa(0.5) and Sa(1.0) near zero FN

20. Input to OpenSees Model
Ground motions
Suite of 45 three-component NGA ground motions identified
Representative of softer Class C to stiffer Class D ( m/sec)
Binned over three magnitude ranges, three distance ranges
Epsilon for Sa(0.5) and Sa(1.0) near zero FP

21. Input to OpenSees Model
Ground motions
Suite of 45 three-component NGA ground motions identified
Representative of softer Class C to stiffer Class D ( m/sec)
Binned over three magnitude ranges, three distance ranges
Epsilon for Sa(0.5) and Sa(1.0) near zero UP

22. Computing Pile Group Response, EDP | LM
How do we evaluate pile group response to dynamic loading?
Compute pile group response to loading histories – EDP|LM
OpenSees pile model
Matlab script developed to automate OpenSees model development
N x M pile group at spacing Dx, Dy
Arbitrarily thick pile cap
Pile segment length definable
Piles can be linear or nonlinear (fiber)
p-y, t-z, Q-z behavior by Boulanger model

23. OpenSees Model Results
Computed response
Initial vertical force, Q = 0.6Qult
Vertical displacement
~ 5 mm
Horizontal displacement
Rocking rotation

24. OpenSees Model Results
Computed response
Multiple motions – how should response be characterized?
Multiple measures of force and displacement are involved
Pre-earthquake static demand + peak dynamic demand
Pre-earthquake static demand

25. OpenSees Model Results
Computed response
Multiple motions – how should response be characterized?
Multiple measures of force and displacement are involved
Dynamic loading

26. OpenSees Model Results
Computed response
Multiple motions – how should response be characterized?
Multiple measures of force and displacement are involved
Dynamic loading

27. OpenSees Model Results
Computed response
Multiple motions – how should response be characterized?
Depends on how design is to be checked
If force-based, we need to predict udp (or udm) as function of Fps/Fult
If displacement-based, need to predict udp (or udm) as function of ups

28. OpenSees Model Results
Force-based approach
Check based on relationship between peak force, Qps, and capacity, Qult
Curve is qualitatively similar to Makdisi-Seed curve

29. OpenSees Model Results
Force-based approach
Check based on relationship between peak force, Qps, and capacity, Qult
Vertical displacement

30. OpenSees Model Results
Force-based approach
Check based on relationship between peak force, Qps, and capacity, Qult
Horizontal displacement

31. OpenSees Model Results
Force-based approach
Check based on relationship between peak force, Qps, and capacity, Qult
Rocking rotation

32. OpenSees Model Results
Displacement-based approach
Check based on relationship between permanent displacement, wdp, and pseudo-static displacement, wps
Requires user to estimate pseudo-static displacements

33. OpenSees Model Results
Force-based approach
Check based on relationship between peak force, Qps, and capacity, Qult
Vertical displacement

34. OpenSees Model Results
Force-based approach
Check based on relationship between peak force, Qps, and capacity, Qult
Horizontal displacement

35. OpenSees Model Results
Force-based approach
Check based on relationship between peak force, Qps, and capacity, Qult
Rocking rotation

36. Framework Development
Model development
Need to be able to predict dynamic displacements/rotations given
Initial static loading
Dynamic loading
Letting the loading be represented by pseudo-static load ratios
or, using pseudo-static displacements

37. Framework Development
Develop probabilistic IM – LM – EDP relationship
Actual pile displacement
Computed pile displacement
Computed pile displacement
Pile properties
Soil properties ,
Pile-soil int. properties ,
Load measure , D L EI My
Qult
Strength-based
Pile driving formula-based
Wave equation-based
Pile load test-based

38. Framework Development
Develop probabilistic IM – LM – EDP relationship. First – EDP |LM
Actual pile displacement
Computed pile displacement
Computed pile displacement
Pile properties
Soil properties
Pile-soil int. properties
Load measure , , ,
FOSM-based collapse
Computed pile displacement
Load measure
Actual pile displacement
Load measure

39. Structural properties
Framework Development
Framework development
Develop probabilistic IM – LM – EDP relationship. Next – LM|IM
Actual load measure
Computed load measure
Computed load measure
Structural properties
Foundation stiffness ,
Foundation damping ,
Intensity measure ,
FOSM-based collapse
Computed load measure
Intensity measure
Actual load measure
Intensity measure

40. Load and resistance factors
Framework Development
Framework development
Develop probabilistic IM – LM – EDP relationship
Pile displacement
Load measure
Load measure
Intensity measure
EDP IM
Pile displacement
Intensity measure
Capacities
Load and resistance factors

41. Summary
Performance-based design concepts can be implemented in LRFD format
Form is familiar to practicing engineers
Additional analyses should not be required
For pile foundations, development process is complicated by
Wide range of bridge types, geometries, properties, …
Wide range of pile foundation types, geometries, properties, …
Wide range of initial, static loading conditions
Wide range of dynamic responses
Number of uncertain variables
Introduction of intermediate variable, LM, can allow efficiency in number of cases requiring analysis
Results will provide useful tool for exploring consequences of various implementation decisions on load and resistance factors

42. Thank you
You’re welcome