Post on 23-Dec-2015
transcript
Seismic LRFD for Pile Foundation DesignSeismic LRFD for Pile Foundation Design
Steve KramerJuan Carlos Valdez
University of Washington
Benjamin BlanchetteHart-Crowser
Jack BakerStanford University
Acknowledgments
California Department of Transportation – Tom Shantz
Washington State Department of Transportation – Tony Allen
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
Current LRFD Procedure (simplified)
• Develop design spectrum
• Perform structural analyses
• Check that capacity > demand for structure
• Design foundationsApply forces from structural analysis to foundationCheck foundation capacity
Maximum force(s) < available resistance(s)Maximum displacement(s) < allowable displacement(s)
– for selected return period
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.
Complicating Factors
All bridges are different
Pile foundations have –
Different static loads
Vertical
Horizontal (2)
Moment (2)
Different dynamic loads
Vertical
Horizontal (2)
Moment (2)
Pile foundations can have –
Different group configurations
Different pile lengths
Different pile cap dimensions
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
Permutations
Bridgeconfigurations
Pile group configurations
Static loading conditions
Dynamic loading conditions
Ground motion hazards
Multiple ground motion levels
Multiple bridge configurations
Multiple pile group configurations
Multiple static load
states – 5 loads for each
Multiple dynamic load cases – 5 loads for each
Dynamic response
x y z yx
Multiple response measures (EDPs)
Ground motions
Multiple time histories
Permutations
Bridgeconfigurations
Pile group configurations
Static loading conditions
Dynamic loading conditions
Ground motion hazards
Multiple ground motion levels
Multiple bridge configurations
Multiple pile group configurations
Multiple static load
states – 5 loads for each
Multiple dynamic load cases – 5 loads for each
Dynamic response
x y z yx
Multiple response measures (EDPs)
Ground motions
Multiple time historiesFor 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.
Permutations
Pile group configurations
Static loading conditions
Dynamic loading conditions
Multiple pile group configurations
Multiple static load
states – 5 loads for each
Multiple dynamic load cases – 5 loads for each
Dynamic response
x y z yx
Multiple response measures (EDPs)
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.
IMEDP dIMEDPGedp |)(
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
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 loading model – consists of bridge model
IMEDP dIMLMGLMEDPGedp ||)(
Pile cap response model –
includes soil and
foundation
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
IMEDP dIMLMGLMEDPGedp ||)(
Intensity Measure, IM
Load Measure, LM
Engineering Demand Parameter, EDP
Pile cap load
model
Pilecap
response model
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
IMEDP dIMLMGLMEDPGedp ||)(
Intensity Measure, IM
Load Measure, LM
Engineering Demand Parameter, EDP
Pile cap load
model
Pilecap
response model
From structural analysis – assume computed loads are median loads, assume ln LM|IM
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
IMEDP dIMLMGLMEDPGedp ||)(
Intensity Measure, IM
Load Measure, LM
Engineering Demand Parameter, EDP
Pile cap load
model
Pilecap
response model
From pile group response analyses – OpenSees models of pile groups under multiple initial load states
subjected to multiple motions
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
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
Computing Load Measure, LM | IM
Input to OpenSees Model
Loading Histories
ATC-49 Bridge 4W= 725 k, H = 20 ftTo = 0.5 secP/f’cAg = 0.103 x 3 group of 24” piles in clay
SAP model – fiber model for column allows yielding
Input to OpenSees Model
Ground motions
Suite of 45 three-component NGA ground motions identified
Representative of softer Class C to stiffer Class D (270-560 m/sec)
Binned over three magnitude ranges, three distance ranges
Epsilon for Sa(0.5) and Sa(1.0) near zeroFN
Input to OpenSees Model
Ground motions
Suite of 45 three-component NGA ground motions identified
Representative of softer Class C to stiffer Class D (270-560 m/sec)
Binned over three magnitude ranges, three distance ranges
Epsilon for Sa(0.5) and Sa(1.0) near zeroFP
Input to OpenSees Model
Ground motions
Suite of 45 three-component NGA ground motions identified
Representative of softer Class C to stiffer Class D (270-560 m/sec)
Binned over three magnitude ranges, three distance ranges
Epsilon for Sa(0.5) and Sa(1.0) near zeroUP
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 x, y
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
Computed response
Initial vertical force, Q = 0.6Qult
OpenSees Model Results
~ 5 mm Vertical displacement
Horizontal displacement
Rocking rotation
Computed response
Multiple motions – how should response be characterized?
Multiple measures of force and displacement are involved
OpenSees Model Results
Pre-earthquake static demand
Pre-earthquake static demand + peak dynamic demand
OpenSees Model Results
Dynamic loading
Computed response
Multiple motions – how should response be characterized?
Multiple measures of force and displacement are involved
OpenSees Model Results
Dynamic loading
Computed response
Multiple motions – how should response be characterized?
Multiple measures of force and displacement are involved
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
OpenSees Model Results
Force-based approach
Check based on relationship between peak force, Qps, and capacity, Qult
OpenSees Model Results
Curve is qualitatively similar to Makdisi-Seed curve
Force-based approach
Check based on relationship between peak force, Qps, and capacity, Qult
OpenSees Model Results
Vertical displacement
Force-based approach
Check based on relationship between peak force, Qps, and capacity, Qult
OpenSees Model Results
Horizontal displacement
Force-based approach
Check based on relationship between peak force, Qps, and capacity, Qult
OpenSees Model Results
Rocking rotation
Displacement-based approach
Check based on relationship between permanent displacement, wdp, and pseudo-static displacement, wps
OpenSees Model Results
Requires user to estimate pseudo-static displacements
Force-based approach
Check based on relationship between peak force, Qps, and capacity, Qult
OpenSees Model Results
Vertical displacement
Force-based approach
Check based on relationship between peak force, Qps, and capacity, Qult
OpenSees Model Results
Horizontal displacement
Force-based approach
Check based on relationship between peak force, Qps, and capacity, Qult
OpenSees Model Results
Rocking rotation
Model development
Need to be able to predict dynamic displacements/rotations givenInitial static loadingDynamic loading
Framework Development
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or, using pseudo-static displacements
Framework development
Develop probabilistic IM – LM – EDP relationship
Framework Development
Actual pile displacement
Computed pile displacement
Computed pile displacement
Pile properties
Load measure
D
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Qult
Strength-basedPile driving formula-basedWave equation-basedPile load test-based
Soil properties,
Pile-soil int. properties, ,
Framework development
Develop probabilistic IM – LM – EDP relationship. First – EDP |LM
Framework Development
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
Framework development
Develop probabilistic IM – LM – EDP relationship. Next – LM|IM
Framework Development
Actual load measure
Computed load measure
Computed load measure
Structural properties
FOSM-based collapse
Computed load measure
Intensity measure
Foundation stiffness,
Foundation damping,
Intensity measure,
Actual load measure
Intensity measure
Framework development
Develop probabilistic IM – LM – EDP relationship
Framework Development
Load measure
Intensity measure
Pile displacement
Load measure
Pile displacement
Intensity measureEDP IM
Load and resistance factors
Capacities
Performance-based design concepts can be implemented in LRFD formatForm is familiar to practicing engineersAdditional analyses should not be required
For pile foundations, development process is complicated byWide range of bridge types, geometries, properties, …Wide range of pile foundation types, geometries, properties, …Wide range of initial, static loading conditionsWide range of dynamic responsesNumber 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
Summary
Thank you
You’re welcome