Seismic LRFD for Pile Foundation Design Steve Kramer Juan Carlos Valdez University of Washington

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

http://www.clasohm.com/photodb/photo?photo_id=3549&size=md

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




Ground motion hazards

Multiple ground motion levels

Multiple bridge configurations





Dynamic response

x y z yx


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








Dynamic response

x y z yx


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




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






Intensity Measure, IM

Load Measure, LM

Engineering Demand Parameter, EDP

Pile cap load

model

Pilecap

response model







Load Measure, LM


Pile cap load

model

Pilecap

response model

From structural analysis – assume computed loads are median loads, assume ln LM|IM







Load Measure, LM


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


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


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


Ground motions




Epsilon for Sa(0.5) and Sa(1.0) near zeroFP


Ground motions




Epsilon for Sa(0.5) and Sa(1.0) near zeroUP

Computing Pile Group Response, EDP | LM


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


Pre-earthquake static demand

Pre-earthquake static demand + peak dynamic demand


Dynamic loading

Computed response




Dynamic loading

Computed response



Computed response


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


Force-based approach

Check based on relationship between peak force, Qps, and capacity, Qult


Curve is qualitatively similar to Makdisi-Seed curve




Vertical displacement








Rocking rotation

Displacement-based approach

Check based on relationship between permanent displacement, wdp, and pseudo-static displacement, wps


Requires user to estimate pseudo-static displacements




Vertical displacement








Rocking rotation

Model development

Need to be able to predict dynamic displacements/rotations givenInitial static loadingDynamic loading

Framework Development

sy

dy

sx

dx

s

d

sy

dx

sy

dxdpydpxdpdpdp M

M

M

M

Q

Q

V

V

V

Vfwvu

,

,

,

,

,

,

,

,,, ,,,,,,,,

Letting the loading be represented by pseudo-static load ratios

psypsxpspspsdpydpxdpdpdp wvufwvu ,,,, ,,,,,,,,

or, using pseudo-static displacements

Framework development

Develop probabilistic IM – LM – EDP relationship


Actual pile displacement

Computed pile displacement


Pile properties

Load measure

D

L

EI

My

Qult

Strength-basedPile driving formula-basedWave equation-basedPile load test-based

Soil properties,

Pile-soil int. properties, ,


Develop probabilistic IM – LM – EDP relationship. First – EDP |LM





Pile properties

Soil properties

Pile-soil int. properties

Load measure

FOSM-based collapse


Load measure

, , ,


Load measure


Develop probabilistic IM – LM – EDP relationship. Next – LM|IM


Actual load measure

Computed load measure


Structural properties

FOSM-based collapse


Intensity measure

Foundation stiffness,

Foundation damping,

Intensity measure,

Actual load measure

Intensity measure


Develop probabilistic IM – LM – EDP relationship


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

Documents

Seismic LRFD for Pile Foundation Design Steve Kramer Juan Carlos Valdez University of Washington