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

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 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 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

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

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

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

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

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

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

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

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

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

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

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 zero FN

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 zero FP

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 zero UP

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Thank you You’re welcome