P E R Seismic Demands and their Dependence on Ground Motions

2001 PEER Annual Meeting

PPEEEERR Seismic Demands and their

Dependence on GroundMotions

Helmut Krawinkler

Stanford University


What are Seismic Demands?

� Damage Measures� Roof and story drifts� Local deformations (e.g., plastic hinge rotation)� Floor acceleration and velocity� Cost-related damage indices� Cumulative damage measures (e.g., energy)

� Design Parameters� Story shear forces and overturning moments� Relative strength of fuses (strong column concept)


Purpose of Demand Evaluation

� Understanding of Behavior� Rigorous Probabilistic Performance

Assessment in the Presence of Uncertainties� Approximate Performance Assessment� Conceptual Design (Strength and Stiffness

Requirements)


PPEEEERR Probabilistic Performance

Assessment in the Presenceof Uncertainties


Incremental Dynamic Analysis (IDA)

� Spectral Acceleration Hazard

� Incremental Dynamic Analysis Curves

� Probability Distribution of Drift given Sa

� System Drift Capacity Data Points

� Probability Distribution of CapacityCornell/Jalayer

Maximum Interstory drift Angle,qmax HSa(sa) = Pr [Sa > sa ]

sa1

sa2

Sa a

t T

1

Median Capacity

δ C HSa(sa1)

δ D

qmax |Sa2

qmax = a Sa b


Accuracy of IDA Depends on

� Description of return period dependent hazard� Intensity measure

� Frequency content

� Duration

� Description of structural properties, includingdeterioration

� Analytical modeling and analysis tool

� Method of prediction (analysis method)


PPEEEERR

Description of return perioddependent hazard


Frequency Effects, T1 = 0.5 sec.

ELASTIC STRENGTH DEMAND SPECTRAScaled Records (T=0.5 s), LMSR, ξ = 0.05

0

0.5

1

1.5

2

0 1 2 3 4 5

T (s)

S a (

g)

Median84%NEHRP 94 Soil D


Frequency Effects, T1 = 2.0 sec.

ELASTIC STRENGTH DEMAND SPECTRAScaled Records (T=2.0 s), LMSR, ξ = 0.05

0

0.5

1

1.5

2

0 1 2 3 4 5

T (s)

S a (

g)

Median84%NEHRP 94 Soil D


Near-Fault Effects

Elastic SDOF Velocity Demands15-D* vs. Recorded Near-Fault, ξ = 2%

0

200

400

600

800

0 0.5 1 1.5 2 2.5 3 3.5 4

T (sec)

Sv (c

m /

sec)

LP89lgpc LP89lexEZ92erzi LN92lucrNR94rrs NR94sylmKB95kobj KB95tato15-D* (mean)


NF Response of Strong Structures

Story Ductility Demands15-D* vs. Recorded Near-Fault, T = 2.0 sec, γ = 0.40

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

Story Ductility Ratio, µi = δmax,i / δy,i

Rel

ativ

e H

eig

ht

LP89lgpcLP89lexEZ92erziLN92lucrNR94rrsNR94sylmKB95kobjKB95tato15-D* (mean)


Story Ductility Demands15-D* vs. Recorded Near-Fault, T = 2.0 sec, γ = 0.15

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10 12

Story Ductility Ratio, µi = δmax,i / δy,i

Rel

ativ

e H

eig

ht

LP89lgpcLP89lexEZ92erziLN92lucrNR94rrsNR94sylmKB95kobjKB95tato15-D* (mean)

NF Response of Weak Structures


Improvement of Intensity Measure

Figure 5 � IDA plot of IDR versus (left) Sa(T1) and (right) SaRsaα

IDRMAX

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

SaR

Saα

0

1

2

3

α = 0.9TF = 1.8T1

IDRMAX

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

Sa (T

1,5%)

0

1

2

3

4

5

6IV79-A6 LP89-LG LP89-LX EZ92-EZ NR94-NH NR94-RS NR94-SY KB95-JM

Tp/T1 > 1

Tp/T1 < 1

(a) Intensity Measure = Sa(T1) (b) Intensity Measure = SaRsaα

Cordova/Deierlein


PPEEEERR Description of structural

properties, includingdeterioration


Basic Modes of Deterioration

Normalized Deformation (%)

Nor

mal

ized

Loa

d (%

)

1.0

1.0 5.0


Nor

mal

ized

Loa

d (%

)

1.0

1.0 5.0


Nor

mal

ized

Loa

d (%

)

1.0

1.0 5.0


Nor

mal

ized

Loa

d (%

)

1.0

1.0 5.0

No deterioration Strength deterioration

Strength det. with capping Strength det. with capping & stiff. det


Det. Modes for Pinching System


No

rmal

ized

Lo

ad (

%)

1.0

1.0 5.0


No

rmal

ized

Lo

ad (

%)

1.0

1.0 5.0


No

rmal

ized

Lo

ad (

%)

1.0

1.0 5.0


No

rmal

ized

Lo

ad (

%)

1.0

1.0 5.0

No deterioration Strength deterioration

Strength det. with capping Accelerated stiffness det. with capping


Example of Deterioration Model

A single deterioration parameter:

c

i

jjt

ii

EE

E

−=

∑=1

β

in which βi = parameter defining the deterioration in excursion i

Ei

= hysteretic energy dissipated in excursion

iEt

= hysteretic energy dissipation capacity = γFyδyEj∑

= ηψστερετιχ ενε ργψ δισσιπατεδ ιν αλλ πρεϖιουσ εξχυρσιονσ

c = exponent defining the rate of deterioration


Calibration of Deterioration Model

Pinching Hysteretic Model, Halil-Column 1,P-∆=0, α=0.10,αcap=-0.24,κ=0.5,γk=100,γs=50,γa=30,γc=40,δc=2.3δ

y

-40000

-30000

-20000

-10000

0

10000

20000

30000

40000

-15 -10 -5 0 5 10 15

Displacement

Fo

rce

AnalyticalExperimental


Sensitivity to Deterioration, SDOFR factor vs. Norm. Disp. - NR94hol Pinching Model, T=0.5s

Sa=1, ξ=5% , P-∆=0, α=0.03, αcap=-0.06, δc=4δy, γs,k,c,a=Variable

0

5

10

15

20

0 5 10 15 20δmax/δy

R

R = µ

No Deterioration


Sensitivity to Frequency ContentR factor vs. Norm. Displacement - Pinched System, T=0.5 sOrd. Rec. LMSR, Sa=1, ξ=5%, P-∆=0, α=0.05, αcap=-0.10, δc=4δ

y, No Det

0

5

10

15

20

25

30

0 2 4 6 8 10 12 14 16δ

max/δ

y

R


Deterioration Effect, MDOF System


Analytical Modeling andAnalysis Tool

� Incorporate deterioration models

� Incorporate uncertainty in properties

� Soil-foundation-structure interaction

� Modeling of 3-D effects


Method of Prediction(Analysis Method)

STORY DRIFT ANGLE ENVELOPES Dynamic Analysis, Record LA30 (Tabas): LA 20-Story, Pre-Northridge

1

3

5

7

9

11

13

15

17

19

21

0 0.03 0.06 0.09 0.12 0.15

Story Drift Angle

Flo

or L

evel

Model M2 Model M1A

Model M2A Model M2AK

Model M1 FW Model M1FS

Model M1-NPD Model M1E-PD

Model M1E-NPD Model M1: Collapse


Understanding of Behavior - Walls

20-StoryT = 1.22 sec.


Understanding of Behavior - Walls

µ = 3


PEER Research Activities

� Demand database for many structuralsystems and different ground motion types

� Sensitivity of demands to ground motioncharacteristics (ordinary and near-fault)

� Collapse safety prediction from IDAs

� Improved intensity measures for reducinguncertainties in demand prediction

� Prediction of demand parameters for lossestimation (structural and nonstructural)


PEER Research Activities, cont�d

� Modeling of deterioration

� Evaluation of demand parameters forconceptual design

� Fragility curves for bridge peers andsystems

� Probabilistic demand models for bridges


Ultimate Objective

� Provide knowledge and data needed toimplement a performance assessmentmethodology based on the PEER frameworkequation (short term)

� Provide understanding, knowledge, and dataneeded to develop and implement aperformance-based conceptual designmethodology for retrofitting existing structuresand designing new ones (long range)

Documents

P E R Seismic Demands and their Dependence on Ground Motions