G.A. Leonards Lecture April 26, 2019

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

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwjWo--dud7ZAhXCzVkKHdhwBoQQjRwIBg&url=https://www.linkedin.com/in/mike-greenfield-561800111&psig=AOvVaw0Un5Vr9rPu_B9_jIaau45d&ust=1520657600919687

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwiDx_Sy5bXZAhVGKGMKHSLEAg8QjRwIBw&url=https://kr.linkedin.com/in/hyungsuk-shin-32168126&psig=AOvVaw2dVMzJfg4qUjWnDjPdipsG&ust=1519260725510362

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

objectives

met?

Revise

design

Construction

No

Yes

The design process




Preliminary design

Analysis

Are

performance

objectives

met?

Revise

design

Construction

No

Yes

Geotechnical Design

The design process




Preliminary design

Analysis

Are

performance

objectives

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




Preliminary design

Analysis

Are

performance

objectives

met?

Revise

design

Construction

No

Yes



Excessive deformations?

Vertical, horizontal, tilting, rotation

Predictability of deformation demands?

Predictability of deformation capacities?

Maximum allowable deformations?

Geotechnical Design

The design process




Preliminary design

Analysis

Are

performance

objectives

met?

Revise

design

Construction

No

Yes




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




Preliminary design

Analysis

Are

performance

objectives

met?

Revise

design

Construction

No

Yes




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)


Force-based

Pseudo-Static

Retaining walls

Slopes


Force-based

Pseudo-Static

Retaining walls

Slopes

Foundations


Force-based

Results expressed in

terms of factor of safety

Displacement-based

Newmark analysis


Displacement-based

Newmark analysis

Makdisi-Seed (1978)


Displacement-based

Newmark analysis

Makdisi-Seed (1978)

Travasarou and Bray (2007)


Displacement-based

Newmark analysis

Makdisi-Seed (1978)

Bray and Travasarou (2007)

Rathje and Saygili (2009)


Displacement-based

Newmark analysis

Makdisi-Seed (1978)



Stress-deformation analysis

Slopes


Displacement-based

Newmark analysis

Makdisi-Seed (1978)




Shallow

foundations


Displacement-based

Newmark analysis

Makdisi-Seed (1978)




Deep

foundations


Displacement-based

Newmark analysis

Makdisi-Seed (1978)




Macro-elements

H

V

M M

H

V

Pecker (2004)


Displacement-based

Newmark analysis

Makdisi-Seed (1978)




Macro-elements

After Hutchinson et

al. (2002)

Correia et al.

(2012)


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:



structural),







Multiple levels of seismic loading



structural),







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

Ea

rth

qu

ak

e D

es

ign

Leve

l

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)


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 …


Response

model

Damage

model

Loss

model

Losses Physical

Damage

System

Response

Ground

motion



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



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 !!!


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:


32






costs, …) and time (inflation, interest rates, tweets, …)


• Inaccurate performance predictions


33









• Inconsistent levels of safety from one project to another


34









• 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


EDP1

EDP2

EDP3

EDP4

EDP5

IM1

IM2

IM3

IM4

IM5





EDP1

EDP2

EDP3

EDP4

EDP5

IM1

IM2

IM3

IM4

IM5

DM1

DM2

DM3

DM4

DM5





EDP1

EDP2

EDP3

EDP4

EDP5

IM1

IM2

IM3

IM4

IM5

DM1

DM2

DM3

DM4

DM5

DV1

DV2

DV3

DV4

DV5





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




P[IM2|eq] P[EDP4|IM2] P[DM3|EDP4] P[DV5|DM3]


EDP1

EDP2

EDP3

EDP4

EDP5

IM1

IM2

IM3

IM4

IM5

DM1

DM2

DM3

DM4

DM5

DV1

DV2

DV3

DV4

DV5




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

)()|()|()|()( IMIMEDPEDPDMDMDVDV ddGdGG

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



PEER framework


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



PEER framework


PEER Performance-Based Framework

Alternative

design

$1.6M $3.9M

Modular – response, damage, loss components


IM

log

IM

DM

log

D

M

EDP

log

E

DP

DV

log

DV

PGA Settlement

Floor slab

cracking Repair

cost



IM

log

IM

DM

log

D

M

EDP

log

E

DP

DV

log

D

V

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



IM

log

IM

DM

log

D

M

EDP

log

E

DP

DV

log

D

V

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)


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

IM(im)

im

edp

im

EDP(edp)

edp

s 2|ln2

2/1

2exp)( imedp

kb

oEDPb

k

a

edpkedp



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

on uncertainty in

EDP|IM relationship

s 2|ln2

2/1

2exp)( imedp

kb

oEDPb

k

a

edpkedp



Example: Slope displacement


Combining, with different levels of response model uncertainty

…


Example: Slope displacement


Uncertainty in response

prediction accounts for half


Extending to DM and DV, with same assumptions, gives

Performance-Based Loss Evaluation

dv

DV(dv) Median relationship (no uncertainty)

222222

222

2

//1

/1

02

exp11

)(LDR

bkd

f

DV ffdfdb

k

e

dv

cakdv

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?

Dis

pla

cem

ent

(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


Select IMs


Sufficiency – how completely does IM predict response?


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


Select IMs



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



Select IMs




Good predictability

Poor predictability



Select IMs




Example:


EDP Hazard Curves

Worse predictability, worse efficiency

Better predictability, better efficiency

Worse predictability, better efficiency

Better predictability, worse efficiency



Select IMs




Example:

Typical predictability, typical efficiency

50-yr exceedance probabilities



Select IMs




Example:

Predictability and efficiency both

affect response for a given

return period

Performance characterized in terms of response variables


Inferred from

computed

response

Inferred from

inferred

damage

Loss

Probabilistic response

model needed – must

account for uncertainty

in EDP|IM



Site response

)(]|[)(0

rIMrsSsIM imdimimIMPimRS

0

)(]|[)( rIMr

r

s

sIM imdimim

imAFPim

RS

Rock

hazard

curve

Soil

hazard

curve

Uncertainty in

amplification

behavior

Integrating over

all rock motion

levels



Site response

Empirical

Analytical



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


Post-liquefaction settlement (Kramer and Huang, 2010)



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)



PGA (g)


Displacement (cm)

Slope instability (Rathje et al., 2013)




PGA (g) Displacement (cm)

Vector IM cuts

displacement in half

PGV

(cm/sec)

Uncertainties from different sliding block models



Flexible sliding

mass model

PGA and Mw

PGA and PGV

Performance characterized in terms of damage measures


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



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



N = None

S = Small

M = Moderate

L = Large

C = Collapse

Ledezma and

Bray, 2010


Continuous DM scales difficult to quantify




Pile-supported

bridge founded on

liquefiable soils



Ledezma and

Bray, 2010


Continuous DM scales difficult to quantify




Example: Caisson quay wall (Iai, 2008)

Life cycle cost as decision variable, DV


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



5 m widening with

deep mixing

Fragility curve approach – Kramer et al. (2009)

Pile-supported bridge on liquefiable soils




1

10-2

10-4

10-6

Repair cost ratio, RCR

0.0 0.2 0.4 0.6 0.8 1.0 Me

an

an

nu

al ra

te o

f e

xce

ed

an

ce

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


1

10-2

10-4

10-6

Repair cost ratio, RCR

0.0 0.2 0.4 0.6 0.8 1.0 Me

an

an

nu

al ra

te o

f e

xce

ed

an

ce

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)'


475-yr losses


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



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



Effects of uncertainty in capacity

Response hazard curve

i

N

i

ijjEDP imIMPimIMedpEDPPedpIM

1

|)(

s 2|ln2

2/

|2

1exp)( IMEDP

bk

oCEDPb

k

a

ckc

0

| )()()( dccfcedp CCEDPEDP

ss 2

ln2

2

2|ln2

2

2

1exp

2

1exp)()( ln

CIMEDPIMEDPb

k

b

kimc C

Let C = capacity (response corresponding to given damage state)

Integrating over distribution of capacity

Assuming lognormal capacity distribution

Capacity

uncertainty

amplifier



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




Let LM = load measure = aIMb

lm

LM (lm)

bk

LMa

lmklm

/

0)(

2

2

2/

02

exp)(L

bk

LMb

k

a

lmklm

No uncertainty

Uncertainty

in loading

Capacity




Let LM = load measure = aIMb

lm

LM (lm)

bk

LMa

lmklm

/

0)(

2

2

2/

02

exp)(L

bk

LMb

k

a

lmklm

22

2

2/

2

1exp

CL

bk

oLMb

k

a

lmk

No uncertainty

Uncertainty

in loading

Uncertainty in

loading and capacity

Capacity




Let LM = load measure

lm

LM (lm)

LMLC LML LM0

Solving previous equations for LM,

kb

LM

kaLM

/

0

0

2

/

0 2exp L

kb

LML

b

k

kaLM

22

/

0 2exp CL

kb

LMLC

b

k

kaLM

LS





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

0

ˆˆLM

LML

LM

LMC L

LC

L

LC ˆˆ for

L

LCLLC

LM

LM

LM

LMLMLM

0

0

L C





lm

LM (lm)

LS

LMLC LML LM0

0LM

LM LLC

L

LM

LMf

So,

Substituting closed-form LM expressions,

2

2

1exp

Lb

k

f

2

2

1exp

Cb

k

Load factor

Resistance

factor

Uncertainty

in loading

Uncertainty

in capacity


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}

)()|()|()( IMIMLMLMEDPedp ddGGEDP

Closed-form assumptions:

k

IM IMkim )()( 0 baIMLM edLMEDP

Loads and moments

Displacements

and rotations



Closed-form assumptions:

k

IM IMkim )()( 0 baIMLM edLMEDP

22

22

2/

/1

02

exp1

)(RL

bke

EDP eeb

k

d

edp

akedp

Solution:

222

22

2/

/1

02

exp1

)(CRL

bke

EDP eeb

k

d

edp

akedp

Considering capacity:

Uncertainty in LM|IM Uncertainty in EDP|LM

Uncertainty in capacity



edp

No uncertainty

Uncertainty in

loading and

response

Uncertainty in loading,

response, and capacity

bke

EDPd

C

akedp

//1

0

ˆ1)(

22

22

2/

/1

02

expˆ1

)(RL

bke

EDP eeb

k

d

C

akedp

222

22

2/

/1

02

expˆ1

)(CRL

bke

EDP eeb

k

d

C

akedp

EDP (edp)



edp

EDP (edp)

LS

EDPLRC EDPLR EDP0

Solving previous equations for EDP,

22

/

/

0 2exp

RL

kbe

bk

EDPLR e

be

k

akdEDP

222

/

/

0 2exp

CRL

kbe

bk

EDPLRC e

be

k

akdEDP

kbe

bk

EDP

akdEDP

/

/

0

0



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

0

ˆˆEDP

EDPD

EDP

EDPC LR

LRC

LR

LDFCCF ˆˆ or

LR

LRCLRLRC

EDP

EDP

EDP

EDPEDPEDP

0

0



0EDP

EDPDF LR

LRC

LR

EDP

EDPCF

So,

Substituting closed-form LM expressions,

lm

LM (lm)

LS

EDPLRC EDPLR EDP0

)(

2

1exp

222 RL

ebe

kDF

2

2

1exp

Cbe

kCF

Demand factor

Capacity factor


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


LM|IM

Computational approach: Decoupled analyses


LM|IM

p-y t-z

Q-z



LM|IM

p-y t-z

Q-z

EDP|LM



OpenSees pile group model

Vertical settlement due to static plus cyclic vertical load

Vertical settlement due to static vertical load plus cyclic moment



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



Analyzed multiple cases:

)ln(796.0320.0990.0ln364.0191.0ln ynxnynxnnn MMVVQu

749.0ln nus

Normalized

displacement vs.

normalized load


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



San Francisco

Seattle



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



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


•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


•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


Thank you

G.A. Leonards Lecture April 26, 2019

Documents

Transcript of G.A. Leonards Lecture April 26, 2019