April 26, 2019 Performance-Based Geotechnical Seismic Design Steve - - PowerPoint PPT Presentation

Performance-Based Geotechnical Seismic Design Steve Kramer

Professor of Civil and Environmental Engineering University of Washington Seattle, Washington

G.A. Leonards Lecture April 26, 2019

Acknowledgments

Pacific Earthquake Engineering Research (PEER) Center Washington State Department of Transportation University of Washington Pedro Arduino Roy Mayfield HyungSuk Shin Kevin Franke Yi-Min Huang Sam Sideras Mike Greenfield Andrew Makdisi

Arduino Mayfield Shin Franke Huang Sideras Greenfield Makdisi

Outline

Introduction Geotechnical Design Seismic Design Historical Approaches Code-Based Approaches Performance-Based Design Response-Level Implementation Damage-Level Implementation Loss-Level Implementation Advancing Performance-Based Design Consideration of Capacity Load and Resistance Factor Framework Demand and Capacity Factor Framework Application to Pile Foundations Summary and Conclusions

Geotechnical Design

The design process

Define performance objectives Characterize loading Select design approach Preliminary design Analysis Are performance

• bjectives

met? Revise design Construction No Yes

The design process

Define performance objectives Characterize loading Select design approach Preliminary design Analysis Are performance

• bjectives

met? Revise design Construction No Yes

Geotechnical Design

The design process

Define performance objectives Characterize loading Select design approach Preliminary design Analysis Are performance

• bjectives

met? Revise design Construction No Yes

What do we mean by “performance?” Demand exceeding capacity (force, stress-based)? Factor of safety Predictability of demands? Predictability of capacities? Minimum allowable FS value?

Geotechnical Design

The design process

Define performance objectives Characterize loading Select design approach Preliminary design Analysis Are performance

• bjectives

met? Revise design Construction No Yes

What do we mean by “performance?” Demand exceeding capacity (force, stress-based)? Excessive deformations? Vertical, horizontal, tilting, rotation Predictability of deformation demands? Predictability of deformation capacities? Maximum allowable deformations?

Geotechnical Design

The design process

Define performance objectives Characterize loading Select design approach Preliminary design Analysis Are performance

• bjectives

met? Revise design Construction No Yes

What do we mean by “performance?” Demand exceeding capacity (force, stress-based)? Excessive deformations? Excessive physical damage? Cracking, spalling, hinging, etc.? Catastrophic damage (e.g., collapse)? Characterization of physical damage Predictability of physical damage?

Geotechnical Design

The design process

Define performance objectives Characterize loading Select design approach Preliminary design Analysis Are performance

• bjectives

met? Revise design Construction No Yes

What do we mean by “performance?” Demand exceeding capacity (force, stress-based)? Excessive deformations? Excessive physical damage? Excessive losses? High repair costs Extended loss of service (downtime) Casualties

Geotechnical Design

Historical Approaches to Seismic Design

Pseudo-Static Retaining walls

Mononobe and Matsuo (1926) Okabe (1926)

Pseudo-Static Retaining walls

Okabe (1926) Mononobe and Matsuo (1929)

Historical Approaches to Seismic Design

Force-based

Pseudo-Static Retaining walls Slopes

Historical Approaches to Seismic Design

Force-based

Pseudo-Static Retaining walls Slopes Foundations

Historical Approaches to Seismic Design

Force-based

Results expressed in terms of factor of safety

Displacement-based Newmark analysis

Historical Approaches to Seismic Design

Displacement-based Newmark analysis Makdisi-Seed (1978)

Historical Approaches to Seismic Design

Displacement-based Newmark analysis Makdisi-Seed (1978) Travasarou and Bray (2007)

Historical Approaches to Seismic Design

Displacement-based Newmark analysis Makdisi-Seed (1978) Bray and Travasarou (2007) Rathje and Saygili (2009)

Historical Approaches to Seismic Design

Displacement-based Newmark analysis Makdisi-Seed (1978) Bray and Travasarou (2007) Rathje and Saygili (2009) Stress-deformation analysis Slopes

Historical Approaches to Seismic Design

Displacement-based Newmark analysis Makdisi-Seed (1978) Bray and Travasarou (2007) Rathje and Saygili (2009) Stress-deformation analysis Shallow foundations

Historical Approaches to Seismic Design

Displacement-based Newmark analysis Makdisi-Seed (1978) Bray and Travasarou (2007) Rathje and Saygili (2009) Stress-deformation analysis Deep foundations

Historical Approaches to Seismic Design

Displacement-based Newmark analysis Makdisi-Seed (1978) Bray and Travasarou (2007) Rathje and Saygili (2009) Stress-deformation analysis Macro-elements

H V M M H V

Pecker (2004)

Historical Approaches to Seismic Design

Displacement-based Newmark analysis Makdisi-Seed (1978) Bray and Travasarou (2007) Rathje and Saygili (2009) Stress-deformation analysis Macro-elements

After Hutchinson et

• al. (2002)

Correia et al. (2012)

Historical Approaches to Seismic Design

Code-Based Seismic Design

• a minor level of shaking without damage (non-structural or

structural),

• a moderate level of shaking without structural damage (but

possibly with some non-structural damage), and

• a strong level of shaking without collapse (but possibly with

both non-structural and structural damage). Early building codes – first edition of SEAOC Blue Book: Intended that structure be able to resist:

Code-Based Seismic Design

• a minor level of shaking without damage (non-structural or

structural),

• a moderate level of shaking without structural damage (but

possibly with some non-structural damage), and

• a strong level of shaking without collapse (but possibly with

both non-structural and structural damage). Early building codes – first edition of SEAOC Blue Book: Intended that structure be able to resist:

Multiple levels of seismic loading

Code-Based Seismic Design

• a minor level of shaking without damage (non-structural or

structural),

• a moderate level of shaking without structural damage (but

possibly with some non-structural damage), and

• a strong level of shaking without collapse (but possibly with

both non-structural and structural damage). Early building codes – first edition of SEAOC Blue Book: Intended that structure be able to resist:

Multiple levels of seismic loading Multiple performance objectives

Discrete hazard level approach Vision 2000 – mid-1990s

• Multiple ground motion return periods
• Different performance objectives for each return period

Earthquake Design Level

Vision 2000

Earthquake Performance Level

Fully Operational Operational Life Safe Near Collapse Frequent (43 yrs) Occasional (72 yrs) Rare (475 yrs) Very Rare (975 yrs)

Code-Based Seismic Design

Earthquake Losses

Process leading to losses Ground motion Loss Physical damage System response PGA, Sa(To), Ia, CAV dh, dv, f Crack width, spacing Deaths, dollars, downtime

Deaths, Injuries, Repair cost, Downtime, etc. Concrete spalling, Column cracking, etc.

Losses

Interstory drift, Plastic rotation, Ground deformation, etc.

Physical Damage

Peak acceleration, Spectral acceleration, Arias intensity, etc.

System Response Ground motion Ultimately, we are interested in …

Performance-Based Design

Response model Damage model Loss model

Losses Physical Damage System Response Ground motion Ultimately, we are interested in …

Performance-Based Design

Response model Damage model Loss model

29

IM

Intensity measure

EDP

Engineering demand parameter

DM

Damage measure

DV

Decision variable

Losses Physical Damage System Response Ground motion Ultimately, we are interested in …

Performance-Based Design

Response model Damage model Loss model

30

IM

Intensity measure

EDP

Engineering demand parameter

DM

Damage measure

DV

Decision variable Response given ground motion Damage given response Loss given damage

EDP | IM DM | EDP DV | DM All are uncertain !!!

Performance-Based Design

31

Uncertainty exists – can’t ignore it

• Uncertainty in ground motions varies from location to location
• Uncertainty in response varies from site to site
• Uncertainty in damage varies from structure to structure
• Uncertainty in loss varies with location (material costs, labor

costs, …) and time (inflation, interest rates, etc.) Ignoring uncertainty, or assuming it is uniform, leads to:

Performance-Based Design

32

Uncertainty exists – can’t ignore it

• Uncertainty in ground motions varies from location to location
• Uncertainty in response varies from site to site
• Uncertainty in damage varies from structure to structure
• Uncertainty in loss varies with location (material costs, labor

costs, …) and time (inflation, interest rates, tweets, …) Ignoring uncertainty, or assuming it is uniform, leads to:

• Inaccurate performance predictions

Performance-Based Design

33

Uncertainty exists – can’t ignore it

• Uncertainty in ground motions varies from location to location
• Uncertainty in response varies from site to site
• Uncertainty in damage varies from structure to structure
• Uncertainty in loss varies with location (material costs, labor

costs, …) and time (inflation, interest rates, tweets, …) Ignoring uncertainty, or assuming it is uniform, leads to:

• Inaccurate performance predictions
• Inconsistent levels of safety from one project to another

Performance-Based Design

34

Uncertainty exists – can’t ignore it

• Uncertainty in ground motions varies from location to location
• Uncertainty in response varies from site to site
• Uncertainty in damage varies from structure to structure
• Uncertainty in loss varies with location (material costs, labor

costs, …) and time (inflation, interest rates, tweets, …) Ignoring uncertainty, or assuming it is uniform, leads to:

• Inaccurate performance predictions
• Inconsistent levels of safety from one project to another
• Inefficient use of resources for seismic retrofit/design

Divide IMs, EDPs, DMs, and DVs into finite number of ranges Consider all combinations Account for conditional probabilities

Discrete Hazard Level Approach

IM1 IM2 IM3 IM4 IM5

Discrete Hazard Level Approach

EDP1 EDP2 EDP3 EDP4 EDP5 IM1 IM2 IM3 IM4 IM5

Divide IMs, EDPs, DMs, and DVs into finite number of ranges Consider all combinations Account for conditional probabilities

Discrete Hazard Level Approach

EDP1 EDP2 EDP3 EDP4 EDP5 IM1 IM2 IM3 IM4 IM5 DM1 DM2 DM3 DM4 DM5

Divide IMs, EDPs, DMs, and DVs into finite number of ranges Consider all combinations Account for conditional probabilities

Discrete Hazard Level Approach

EDP1 EDP2 EDP3 EDP4 EDP5 IM1 IM2 IM3 IM4 IM5 DM1 DM2 DM3 DM4 DM5 DV1 DV2 DV3 DV4 DV5

Divide IMs, EDPs, DMs, and DVs into finite number of ranges Consider all combinations Account for conditional probabilities

Discrete Hazard Level Approach

EDP1 EDP2 EDP3 EDP4 EDP5 IM1 IM2 IM3 IM4 IM5 DM1 DM2 DM3 DM4 DM5 DV1 DV2 DV3 DV4 DV5

Divide IMs, EDPs, DMs, and DVs into finite number of ranges Consider all combinations Account for conditional probabilities

Discrete Hazard Level Approach

EDP1 EDP2 EDP3 EDP4 EDP5 IM1 IM2 IM3 IM4 IM5 DM1 DM2 DM3 DM4 DM5 DV1 DV2 DV3 DV4 DV5

DV2-4-3-5 = DV5 DV = S DVi-j-k-l Summing over all paths Divide IMs, EDPs, DMs, and DVs into finite number of ranges Consider all combinations Account for conditional probabilities P[IM2|eq] P[EDP4|IM2] P[DM3|EDP4] P[DV5|DM3]

Discrete Hazard Level Approach

EDP1 EDP2 EDP3 EDP4 EDP5 IM1 IM2 IM3 IM4 IM5 DM1 DM2 DM3 DM4 DM5 DV1 DV2 DV3 DV4 DV5

Divide IMs, EDPs, DMs, and DVs into finite number of ranges Consider all combinations Account for conditional probabilities For this case, 5 x 5 x 5 x 5 = 625 paths With 100 values for each . . . 100 million paths

Covers entire range of hazard (ground motion) levels Accounts for uncertainty in parameters, relationships PEER framework



 ) ( ) | ( ) | ( ) | ( ) ( IM IM EDP EDP DM DM DV DV   d dG dG G

Integral Hazard Level Approach

Loss model

Loss curve – Cost vs Cost Seismic hazard curve – Sa vs Sa Fragility curve – interstory drift given Sa Fragility curve – crack width given interstory drift Fragility curve – repair cost given crack width

PSHA Response model Damage model

Covers entire range of hazard (ground motion) levels Accounts for uncertainty in parameters, relationships PEER framework



 ) ( ) | ( ) | ( ) | ( ) ( IM IM EDP EDP DM DM DV DV   d dG dG G

Integral Hazard Level Approach

$2.7M $5.8M

Risk curve – Cost vs Cost Seismic hazard curve – Sa vs Sa Fragility curve – interstory drift given Sa Fragility curve – crack width given interstory drift Fragility curve – repair cost given crack width

PSHA Response model Damage model Cost model

Covers entire range of hazard (ground motion) levels Accounts for uncertainty in parameters, relationships PEER framework



 ) ( ) | ( ) | ( ) | ( ) ( IM IM EDP EDP DM DM DV DV   d dG dG G

PEER Performance-Based Framework

Alternative design

$1.6M $3.9M

Modular – response, damage, loss components

PEER Performance-Based Framework

IM log IM DM log DM EDP log EDP DV log DV PGA Settlement Floor slab cracking Repair cost

Modular – response, damage, loss components

PEER Performance-Based Framework

IM log IM DM log DM EDP log EDP DV log DV PGA Settlement Floor slab cracking Repair cost Includes

• all earthquake magnitudes
• uncertainty in ground motion
• uncertainty in response given ground motion
• uncertainty in damage given response
• uncertainty in loss given damage

All levels of shaking are cosidered and accounted for, not just shaking at one return period.

• all source-to-site distances

Modular – response, damage, loss components

PEER Performance-Based Framework

IM log IM DM log DM EDP log EDP DV log DV PGA Settlement Floor slab cracking Repair cost Includes

• all earthquake magnitudes
• uncertainty in ground motion
• uncertainty in response given ground motion
• uncertainty in damage given response
• uncertainty in loss given damage

Response, damage, and loss are all explicitly computed – with explicit consideration of uncertainty in each

• all source-to-site distances

Closed-form solution Assume hazard curve is of power law form IM(im) = ko(im)-k

Performance-Based Response Evaluation

IM(im) im edp im

and response is related to intensity as edp = a(im)b with lognormal conditional uncertainty (ln edp is normally distributed with standard deviation sln edp|im)

Closed-form solution Then median EDP hazard curve can be expressed in closed form as

IM(im) im edp im EDP(edp) edp

                      



s 

2 | ln 2 2 / 1

2 exp ) (

im edp k b

• EDP

b k a edp k edp

Performance-Based Response Evaluation

Closed-form solution Then median EDP hazard curve can be expressed in closed form as

EDP(edp) edp

Based on median IM and EDP-IM relationship EDP “amplifier” based

• n uncertainty in

EDP|IM relationship

                      



s 

2 | ln 2 2 / 1

2 exp ) (

im edp k b

• EDP

b k a edp k edp

Performance-Based Response Evaluation

Closed-form solution Example: Slope displacement

Performance-Based Response Evaluation

Combining, with different levels of response model uncertainty …

Closed-form solution Example: Slope displacement

Performance-Based Response Evaluation

Uncertainty in response prediction accounts for half

Closed-form solution Extending to DM and DV, with same assumptions, gives

Performance-Based Loss Evaluation

dv DV(dv)

Median relationship (no uncertainty)

 

                               



   

2 2 2 2 2 2 2 2 2 2 / / 1 / 1

2 exp 1 1 ) (

L D R b k d f DV

f f d f d b k e dv c a k dv

Median relationships Uncertainty amplifier

Response model Damage model Loss model

With response model uncertainty Response and damage model uncertainties Response, damage, and loss model uncertainties Losses

1/TR

Characterization of loading Select IMs – important considerations include: Efficiency – how well does IM predict response?

Displacement (cm)

PGA (g)

Arias intensity (m/s) PGV2 (cm/s)2

Travasarou et al. (2003)

Implementation of Performance-Based Design

Permanent displacement of shallow slides

Characterization of loading Select IMs Efficiency – how well does IM predict response? Sufficiency – how completely does IM predict response?

Implementation of Performance-Based Design

Systematic trend in pore pressure residuals w/r/t Mw

Magnitude scaling factor

Kramer and Mitchell (2003) Deviations from mean excess pore pressure ratio correlation to PGA

Weak trend w/r/t R

ru over- predicted ru under- predicted

Characterization of loading Select IMs Efficiency – how well does IM predict response? Sufficiency – how completely does IM predict response? Predictability – how well can we predict IM?

Intensity Measure, IM Standard error, sln IM Reference

PGA 0.53 – 0.55 Campbell and Bozorgnia, 2008 PGV 0.53 – 0.56 Campbell and Bozorgnia, 2008 Sa (0.2 sec) 0.59 – 0.61 Campbell and Bozorgnia, 2008 Sa (1.0 sec) 0.62 – 0.66 Campbell and Bozorgnia, 2008 Arias intensity, Ia 1.0 – 1.3 Travasarou et al. (2003) CAV 0.40 – 0.44 Campbell and Bozorgnia, 2010

Implementation of Performance-Based Design

Characterization of loading Select IMs Efficiency – how well does IM predict response? Sufficiency – how completely does IM predict response? Predictability – how well can we predict IM?

Good predictability Poor predictability

Implementation of Performance-Based Design

Characterization of loading Select IMs Efficiency – how well does IM predict response? Sufficiency – how completely does IM predict response? Predictability – how well can we predict IM? Example:

Implementation of Performance-Based Design

EDP Hazard Curves

Worse predictability, worse efficiency Better predictability, better efficiency Worse predictability, better efficiency Better predictability, worse efficiency

Implementation of Performance-Based Design

Characterization of loading Select IMs Efficiency – how well does IM predict response? Sufficiency – how completely does IM predict response? Predictability – how well can we predict IM? Example:

Typical predictability, typical efficiency

50-yr exceedance probabilities

Implementation of Performance-Based Design

Characterization of loading Select IMs Efficiency – how well does IM predict response? Sufficiency – how completely does IM predict response? Predictability – how well can we predict IM? Example:

Predictability and efficiency both affect response for a given return period

Performance characterized in terms of response variables

Response-Level Implementation

Inferred from computed response Inferred from inferred damage

Loss

Probabilistic response model needed – must account for uncertainty in EDP|IM

Performance characterized in terms of response variables

Response-Level Implementation

Site response

) ( ] | [ ) (

r IM r s S s IM

im d im im IM P im

R S

 





 





  ) ( ] | [ ) (

r IM r r s s IM

im d im im im AF P im

R S

 

Rock hazard curve Soil hazard curve Uncertainty in amplification behavior Integrating over all rock motion levels

Performance characterized in terms of response variables

Response-Level Implementation

Site response Empirical Analytical

Performance characterized in terms of response variables

Response-Level Implementation

6 m

Distributions of M at all hazard levels considered

Liquefaction (Kramer and Mayfield, 2007) FSL hazard curves

TR = 5000 yrs TR = 50 yrs

Lateral Spreading – Franke and Kramer (2014) Reference soil profile

(N1)60

Displacement hazard curves

Response-Level Implementation

Post-liquefaction settlement (Kramer and Huang, 2010) Performance characterized in terms of response variables

Response-Level Implementation

Assuming soil is susceptible, liquefaction is triggered, and neglecting maximum volumetric strain Considering maximum volumetric strain Considering susceptibility

Hypothetical site in Seattle, Washington

Settlement hazard curves

Considering triggering

Slope instability (Rathje et al., 2013) Performance characterized in terms of response variables

Response-Level Implementation

PGA (g)

Displacement hazard curves

Displacement (cm)

Slope instability (Rathje et al., 2013) Performance characterized in terms of response variables

Response-Level Implementation

Displacement hazard curves

PGA (g) Displacement (cm)

Vector IM cuts displacement in half

PGV (cm/sec)

Uncertainties from different sliding block models Performance characterized in terms of response variables

Response-Level Implementation

Flexible sliding mass model PGA and Mw PGA and PGV

Performance characterized in terms of damage measures

Damage-Level Implementation

Requires: Characterization of allowable levels of physical damage Damage model How much settlement is required to crack a slab? How much lateral displacement is required to produce hinging in a concrete pile? in a steel pile?

Inferred from damage

Continuous DM scales Fragility curve approach Some damage states (e.g., collapse) are binary Insufficient data available for others Discrete DM scales Damage probability matrix approach Performance characterized in terms of damage measures

Damage-Level Implementation

Damage State, DM Description EDP interval edp1 edp2 edp3 edp4 edp5

dm1 Negligible X11 X12 X13 X14 X15 dm2 Slight X21 X22 X23 X24 X25 dm3 Moderate X31 X32 X33 X34 X35 dm4 Severe X41 X42 X43 X44 X45 dm5 Catastrophic X51 X52 X53 X54 X55

Probability that response in EDP interval 2 produces severe damage

Performance characterized in terms of damage measures

Damage-Level Implementation

N = None S = Small M = Moderate L = Large C = Collapse Ledezma and Bray, 2010

Fragility curve approach Continuous DM scales difficult to quantify Some damage states (e.g., collapse) are binary Insufficient data available for others Damage probability matrix approach

Pile-supported bridge founded on liquefiable soils

Performance characterized in terms of damage measures

Damage-Level Implementation

Ledezma and Bray, 2010

Fragility curve approach Continuous DM scales difficult to quantify Some damage states (e.g., collapse) are binary Insufficient data available for others Damage probability matrix approach

Performance characterized in terms of damage measures

Damage-Level Implementation

Ledezma and Bray, 2010

Fragility curve approach Continuous DM scales difficult to quantify Some damage states (e.g., collapse) are binary Insufficient data available for others Damage probability matrix approach

Example: Caisson quay wall (Iai, 2008) Life cycle cost as decision variable, DV

Loss-Level Implementation

Performance characterized in terms of decision variables

Construction Costs Indirect Losses Direct Losses Life-Cycle Costs Options A: Foundation compaction only B: Foundation cementation C: Foundation and backfill compaction (1.8 m spacing) D: Foundation & backfill compaction (1.6 m spacing) E: Foundation compaction & structural modification

Options:

A: Foundation compaction only B: Foundation cementation C: Foundation and backfill compaction (1.8 m spacing) D: Foundation and backfill compaction (1.6 m spacing) E: Foundation compaction and structural modification

Example: Expressway embankment widening (Towhata, 2008) Life cycle cost as decision variable, DV

Loss-Level Implementation

Performance characterized in terms of decision variables

5 m widening with deep mixing

Fragility curve approach – Kramer et al. (2009) Pile-supported bridge on liquefiable soils Performance characterized in terms of decision variables

Loss-Level Implementation

Loss-Level Implementation

1 10-2 10-4 10-6 Repair cost ratio, RCR 0.0 0.2 0.4 0.6 0.8 1.0 Mean annual rate of exceedance 1,000 yrs 100 yrs Return period Repair cost losses only Doesn’t include losses due to downtime Doesn’t include losses due to casualties

0.16 0.47

Loss-Level Implementation

1 10-2 10-4 10-6 Repair cost ratio, RCR 0.0 0.2 0.4 0.6 0.8 1.0 Mean annual rate of exceedance 100 yrs 1,000 yrs Return period Repair cost losses only Doesn’t include losses due to downtime Doesn’t include losses due to casualties

0.05 0.20

Liquefaction No Liquefaction

Impacts on bridge structure PBEE framework allows deaggregation of costs

'Temporary support (abutment)' 'Furnish steel pipe pile' 'Joint seal assembly' 'Column steel casing' 'Structure excavation' 'Aggregate base (approach slab)' 'Elastomeric bearings' 'Other' 'Structure backfill' 'Bar reinforcing steel (footing, retaining wall)'

Loss-Level Implementation

475-yr losses

Advancing Performance-Based Design

Improved Characterization of Capacity How should we characterize physical damage? How much ground movement can structures tolerate? Bird et al. (2005; 2006) Analyses of RC frame buildings subjected to ground deformation Four damage states: None to slight – linear elastic response, flexural or shear-type hairline cracks (<1 mm) in some members, no yielding in any critical section Moderate – member flexural strengths achieved, limited ductility developed, crack widths reach 1 mm, initiation of concrete spalling Extensive – significant repair required to building, wide flexural or shear cracks, buckling of longitudinal reinforcement may occur Complete – repair of building not feasible either physically or economically, demolition after earthquake required, could be due to shear failure of vertical elements or excess displacement LS1 LS2 LS3

Advancing Performance-Based Design

Improved Characterization of Capacity How should we characterize physical damage How much ground movement can structures tolerate? Bird et al. (2005) Analyses of structures subjected to ground deformation

Horizontal Vertical

High uncertainty

Rational, quantified fragility curves for R/C frame buildings

Advancing Performance-Based Design

Improved Characterization of Capacity Effects of uncertainty in capacity Response hazard curve

  



i N i i j j EDP

im IM P im IM edp EDP P edp

IM

    

1

| ) (  

            



s 

2 | ln 2 2 / |

2 1 exp ) (

IM EDP b k

• C

EDP

b k a c k c







|

) ( ) ( ) ( dc c f c edp

C C EDP EDP

               s s  

 2 ln 2 2 2 | ln 2 2

2 1 exp 2 1 exp ) ( ) (

ln

C IM EDP IM EDP

b k b k im c

C

Let C = capacity (response corresponding to given damage state) Integrating over distribution of capacity Assuming lognormal capacity distribution

Capacity uncertainty amplifier

Advancing Performance-Based Design

Improved Characterization of Capacity Effects of uncertainty in capacity Accurate characterization of uncertainty in capacity nearly as important as uncertainty in response Increasing uncertainty in capacity

Can PBEE concepts be used to develop load and resistance factors associated with predictable rate of limit state exceedance, LS? Capacity

Advancing Performance-Based Design

Can PBEE concepts be used to develop load and resistance factors associated with predictable rate of limit state exceedance, LS? Let LM = load measure = aIMb lm

LM (lm)

b k LM

a lm k lm

/

) (



                    



 

2 2 2 /

2 exp ) (

L b k LM

b k a lm k lm

No uncertainty Uncertainty in loading Capacity

Advancing Performance-Based Design

Can PBEE concepts be used to develop load and resistance factors associated with predictable rate of limit state exceedance, LS? Let LM = load measure = aIMb lm

LM (lm)

b k LM

a lm k lm

/

) (



                    



 

2 2 2 /

2 exp ) (

L b k LM

b k a lm k lm

  

            



  

2 2 2 2 /

2 1 exp

C L b k

• LM

b k a lm k

No uncertainty Uncertainty in loading Uncertainty in loading and capacity Capacity

Advancing Performance-Based Design

Can PBEE concepts be used to develop load and resistance factors associated with predictable rate of limit state exceedance, LS? Let LM = load measure lm

LM (lm)

LMLC LML LM0

Solving previous equations for LM,

k b LM

k a LM

/

         

                

2 /

2 exp

L k b LM L

b k k a LM

 

                 

2 2 /

2 exp

C L k b LM LC

b k k a LM

LS

Advancing Performance-Based Design

Can PBEE concepts be used to develop load and resistance factors associated with predictable rate of limit state exceedance, LS? Let LM = load measure lm

LM (lm) LS

LMLC LML LM0

LMLC can be interpreted as median capacity that will be exceeded every TR years, on average, and LM0 as the median load. Then this will occur when ˆ ˆ LM LM L LM LM C

L LC L

  

L C ˆ ˆ     f

• r

L LC L LC

LM LM LM LM LM LM   

L C

Advancing Performance-Based Design

Can PBEE concepts be used to develop load and resistance factors associated with predictable rate of limit state exceedance, LS? Let LM = load measure lm

LM (lm) LS

LMLC LML LM0

LM LM L  

LC L

LM LM  f So, Substituting closed-form LM expressions,

        

2

2 1 exp

L

b k         f

2

2 1 exp

C

b k

Load factor Resistance factor

Uncertainty in loading Uncertainty in capacity

Advancing Performance-Based Design

Extension to foundation displacements Let LM = load measure, EDP = response measure Note that LM = {Q, Vx, Vy, Mx, My} EDP = {w, u, v, qx, qy} Q Vx Vy Mx My w u v

qy qx

Loads (LMs) Deformations (EDPs)

Application to Foundation Design

Extension to foundation displacements Let LM = load measure, EDP = response measure Note that LM = {Q, Vx, Vy, Mx, My} EDP = {w, u, v, qx, qy}



 ) ( ) | ( ) | ( ) ( IM IM LM LM EDP edp   d dG G

EDP

Closed-form assumptions:

k IM

IM k im



 ) ( ) ( 

b

aIM LM 

e

dLM EDP 

Loads and moments Displacements and rotations

Application to Foundation Design



 ) ( ) | ( ) | ( ) ( IM IM LM LM EDP edp   d dG G

EDP

Closed-form assumptions:

k IM

IM k im



 ) ( ) ( 

b

aIM LM 

e

dLM EDP 

 

                    



  

2 2 2 2 2 / / 1

2 exp 1 ) (

R L b k e EDP

e e b k d edp a k edp Solution:

 

                     



   

2 2 2 2 2 2 / / 1

2 exp 1 ) (

C R L b k e EDP

e e b k d edp a k edp

Considering capacity:

Uncertainty in LM|IM Uncertainty in EDP|LM Uncertainty in capacity

Application to Foundation Design



 ) ( ) | ( ) | ( ) ( IM IM LM LM EDP edp   d dG G

EDP

edp

No uncertainty Uncertainty in loading and response

Uncertainty in loading, response, and capacity

b k e EDP

d C a k edp

/ / 1

ˆ 1 ) (



                 

 

                      



  

2 2 2 2 2 / / 1

2 exp ˆ 1 ) (

R L b k e EDP

e e b k d C a k edp

 

                       



   

2 2 2 2 2 2 / / 1

2 exp ˆ 1 ) (

C R L b k e EDP

e e b k d C a k edp

EDP (edp)

Application to Foundation Design



 ) ( ) | ( ) | ( ) ( IM IM LM LM EDP edp   d dG G

EDP

edp

EDP (edp) LS

EDPLRC EDPLR EDP0

Solving previous equations for EDP,

 

              



  

2 2 / /

2 exp

R L k be b k EDP LR

e be k a k d EDP

 

               



   

2 2 2 / /

2 exp

C R L k be b k EDP LRC

e be k a k d EDP

k be b k EDP

a k d EDP

/ / 

         

Application to Foundation Design



 ) ( ) | ( ) | ( ) ( IM IM LM LM EDP edp   d dG G

EDP

lm

LM (lm) LS

EDPLRC EDPLR EDP0

EDPLRC can be interpreted as median displacement capacity that will be exceeded every TR years, on average, and EDP0 as the median displacement demand. Then this will occur when ˆ ˆ EDP EDP D EDP EDP C

LR LRC LR

  

L DF C CF ˆ ˆ   

• r

LR LRC LR LRC

EDP EDP EDP EDP EDP EDP   

Application to Foundation Design



 ) ( ) | ( ) | ( ) ( IM IM LM LM EDP edp   d dG G

EDP

EDP EDP DF

LR



LRC LR

EDP EDP CF  So, Substituting closed-form LM expressions, lm

LM (lm) LS

EDPLRC EDPLR EDP0

        ) ( 2 1 exp

2 2 2

 

R L

e be k DF        

2

2 1 exp

C

be k CF

Demand factor Capacity factor

Application to Foundation Design

Example: 5x5 pile group in sand Closed-form expression helps in understanding Actual problem more complicated Five components of load Five components of displacement Components of both may be correlated Relationships not described by power laws Uncertainty may not be lognormal Numerical integration required – in five dimensions

Application to Foundation Design

LM|IM Computational approach: Decoupled analyses

Application to Foundation Design

LM|IM p-y t-z Q-z Computational approach: Decoupled analyses

Application to Foundation Design

LM|IM p-y t-z Q-z

EDP|LM

Computational approach: Decoupled analyses

Application to Foundation Design

OpenSees pile group model Vertical settlement due to static plus cyclic vertical load Vertical settlement due to static vertical load plus cyclic moment

Application to Foundation Design

OpenSees pile group model Analyzed multiple cases: 3 x 3 5 x 5 7 x 7 3 x 5 3 x 7 groups Sand profile Clay profile Linear structure, To = 0.5 sec Linear structure, To = 1.0 sec Nonlinear structure, To = 0.5 sec Nonlinear structure, To = 1.0 sec

Fault normal Fault parallel Vertical

50 three-component motions

Application to Foundation Design

OpenSees pile group model Analyzed multiple cases: ) ln( 796 . 320 . 990 . ln 364 . 191 . ln

yn xn yn xn n n

M M V V Q u      

749 .

ln



n

u

s

Normalized displacement vs. normalized load

Application to Foundation Design

Example: 5x5 group of 60 cm, 20-m-long pipe piles in m. dense sand Static loads Q = 40,000 kN Vx = 10,000 kN Vy = 15,000 kN Mx = 30,000 kN-m My = 20,000 kN-m s = 0.1 ref = 0.3 L = 0.2 C = 0.3 Assumed to be located in: San Francisco Seattle

Application to Foundation Design

Example: 5x5 group of 60 cm, 20-m-long pipe piles in m. dense sand

San Francisco Seattle

Application to Foundation Design

Example: 5x5 group of 60 cm, 20-m-long pipe piles in m. dense sand

San Francisco Seattle

Application to Foundation Design

Example: 5x5 group of 60 cm, 20-m-long pipe piles in m. dense sand

San Francisco Seattle

Uncertainties in forces are relatively low LM hazard curves are close to each other Load and resistance factors vary with TR Load and resistance factors close to 1.0

Application to Foundation Design

Example: 5x5 group of 60 cm, 20-m-long pipe piles in m. dense sand

San Francisco Seattle

Uncertainties in displacements are high EDP hazard curves are far from each other Load and resistance factors not close to 1.0

Application to Foundation Design

• Seismic design has always considered performance, but not always

in rigorous manner

• Performance can be characterized in different ways – response,

damage, loss

• It is important to define performance objectives in clear, quantitative

way

• Design for specified performance level requires consideration of

uncertainties

• For a given return period, response, damage, and loss all increase

with increasing uncertainty

• Geotechnical engineers are able to reduce expected losses by

reducing uncertainty through more extensive subsurface investigation, improved field and laboratory testing, and more rigorous analyses

Summary and Conclusions

• Application of performance-based concepts has increased – usually

implemented in terms of response measures (displacement, rotation, curvature, etc.)

• Performance-based concepts can be implemented for such

structures in LRFD-type format

• Force-based load and resistance factors reflect relatively low

uncertainty in ability to predict forces

• Displacement-based demand and capacity factors reflect high

uncertainty in displacements

• Performance-based earthquake engineering offers a framework for

more complete and consistent seismic designs and seismic evaluations

Summary and Conclusions

Thank you