Ground Motion Intensity Measures for PerformanceBased Earthquake Engineering

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Ground Motion Intensity Measures for
Performance-Based Earthquake Engineering

• Hemangi Pandit
• Joel Conte
• Jon Stewart
• John Wallace

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• Earthquake
• Database
• Seismological
• Variables
• Ground Motion
• Parameters

MDOF Nonlinear Finite Element Model

• SDOF Structural Model
• System Parameters
• Hysteretic Model
• Parameters

Nonlinear Response History Analysis
MDOF Response/ Demand Parameters
Hysteretic Models

• Bilinear Inelastic
• Cloughs Stiffness Degrading
• Slip Model

Inverse Analysis
Direct Analysis

• Statistical Study
• Marginal Statistics
• Correlation Analysis

SDOF Response/Demand Parameters

• Statistical Analysis
• Marginal Probability Distributions
• Second-Order Statistics

Regression between Proposed Nonlinear SDOF-Based
Intensity Measures and MDOF Response Parameters

• Correlation and Regression Analysis
• New Intensity Measures vs. Ground Motion
  Parameters
• Nonlinear SDOF Response vs. New Intensity
  Measures

Simplified and Efficient Methods to evaluate PEER
Hazard Integral for MDOF Inelastic Models of R/C
Frame buildings
Proposed Vector of Ground Motion Intensity
Measures
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Project Vision
PEER Framework Equation

• A critical issue in the PEER probabilistic
  framework is the choice of ground motion
  intensity measures, either a single intensity
  measure or a vector of intensity measures
• The choice of this vector has a profound impact
  on the simplifying assumptions and methods that
  can be used to evaluate accurately and
  efficiently the PEER hazard integral for actual
  R/C frame buildings.

Primary objective of this project

• Identify a set of optimum ground motion
  intensity measures that can be used in the PEER
  framework equation to assess the performance of
  R/C frame building structures.

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Nonlinear SDOF Analysis

• Key Response/Demand Parameters
• Displacement Ductility
• Residual Displacement Ductility
• Maximum Normalized Plastic Deformation Range
• Number of Positive Yield Excursions
• Number of Yield Reversals
• Normalized Earthquake Input Energy
• Normalized Hysteretic Energy Dissipated
• Maximum Normalized Earthquake Input Power
• Maximum Normalized Hysteretic Power

• System Parameter
• Initial Period T0
• Damping Ratio x
• Normalized Strength
• Cy Ry /(mg)
• Strain Hardening Ratio a

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Ground Motion Intensity Measures
84-percentile Sa level
Primary Intensity Measure Sa(T0, x)

• Ground Motions scaled to three levels of Sa
  Median Sa, 16-percentile and 84-percentile.
• Distortion of earthquake records minimized by
  restricting the scale factors to reasonable
  values, namely

Sa g
Median Sa level
16-percentile Sa level
Secondary Intensity Measures
T0 sec

• Proposed Intensity Measures
• Maximum Value of 1
• Measures of damage effectiveness of a given
  ground motion record
• Obtained using Bilinear Inelastic SDOF system
  with a 0

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Statistical Correlation Analysis Results
Good correlation as measured by a high
correlation coefficient r
Poor correlation as measured by a low correlation
coefficient r
Medium correlation as measured by a medium
correlation coefficient r
Cy
Cy
Cy
PGV in/sec
R km
Duration sec
T0 0.2 sec x 0.05 a 0 m 8 Model
Bilinear Inelastic
Inverse Analysis
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Statistical Correlation Analysis Results
Inter-Response Correlation
Response - Seismological Variable Correlation
Response - SDOF-Based Intensity Measure
Correlation
m
m
m
Magnitude
T0 0.2 sec. x 0.05 a 0 Cy
0.125 Model Bilinear Inelastic
Direct Analysis
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Three Steps To Determine Effectiveness /
Optimality of Proposed Intensity Measures
STEP I Good Correlation with SDOF response
parameters obtained from the same hysteretic
model as that used to determine
, namely the Bilinear
Inelastic Model. STEP II Good Correlation with
SDOF response parameters obtained from other
hysteretic models, namely Cloughs Stiffness
Degrading Model and Slip Model. STEP III Good
Correlation with MDOF response parameters
obtained from nonlinear finite element models of
RC building or bridge structures.
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Correlation analysis to evaluate optimum
intensity measures STEP-I
Response Parameters computed using Bilinear
Inelastic Model
SDOF-based Intensity Measures (IM) computed using
Bilinear Inelastic Model
Option 1
r Response vs. IM
T0 1.0 sec x 0.05 a 0 Cy 0.028
Option 2
r Response vs. IM
T0 1.0 sec x 0.05 a 0 Cy 0.028
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Correlation analysis to evaluate optimum
intensity measures STEP-II
Response Parameters computed using Slip Model
SDOF-based Intensity Measures (IM) computed using
Bilinear Inelastic Model
Option 1
r Response vs. IM
T0 1.0 sec x 0.05 a 0 Cy 0.028
Option 2
r Response vs. IM
T0 1.0 sec x 0.05 a 0 Cy 0.028
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Relative Correlation of Response Parameter, here
Ductility (m), to Various Candidate Intensity
Measures
r m Vs. IM (T0 0.2 sec)
Strength Cy 0.125
r m Vs. IM (T0 1.0 sec)
Strength Cy 0.028
r m Vs. IM (T0 3.0 sec)
Strength Cy 0.005

System Parameters and Model Damping ratio (x)
5 Strain hardening ratio (a) 0 Model Cloughs
Stiffness Degrading Model
PGA
PGV
PGD
Ia,max
Fm 6
Mag
Fm 2
Fm 4
Fm 8
Tmean
Dur
R
Candidate Intensity Measures (IM)
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Relative Correlation of Response Parameter, here
Max. Plastic Deformation ( ), to Various
Intensity Measures
Strength Cy 0.125
r vs. IM (T0 1.0 sec)
Strength Cy 0.028
r vs. IM (T0 3.0 sec)
Strength Cy 0.005
System Parameters and Model Damping ratio (x)
5 Strain hardening ratio (a) 0 Model Cloughs
Stiffness Degrading Model

Fm 6
PGA
PGV
PGD
Ia,max
Fm 2
Fm 8
Mag
Fm 4
Tmean
Dur
R
Candidate Intensity Measures (IM)
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Reduction in Dispersion of Normalized Hysteretic
Energy ( ) when
are Specified in Addition to Sa(T0, x)
and
F
F
m
N
rev
y
,
Total number of ground motion records 550
Sa 0.416 g (Median Sa)
N
c.o.v. 1.09
System Parameters and Model Initial Period (T0)
0.2 sec. Damping ratio (x) 5 Strength Cy
0.125 Strain hardening ratio (a) 0 Model
Bilinear Inelastic
Total number of ground motion records 210
Sa 0.416 g (Median Sa)
N
c.o.v. 0.57
Total number of ground motion records 91
Sa 0.416 g (Median Sa)
N
c.o.v. 0.44
Ductility (m)
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Reduction in Dispersion of Normalized Hysteretic
Energy ( ) when
are Specified in Addition to Sa(T0, x)
and
F
F
m
N
rev
y
,
Total number of ground motion records 550
Sa 0.416 g (Median Sa)
N
c.o.v. 0.67
System Parameters and Model Initial Period (T0)
3.0 sec. Damping ratio (x) 5 Strength Cy
0.005 Strain hardening ratio (a) 0 Model Slip
Total number of ground motion records 201
Sa 0.416 g (Median Sa)
N
c.o.v. 0.41
Total number of ground motion records 26
Sa 0.416 g (Median Sa)
N
c.o.v. 0.33
Ductility (m)
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Reduction in Dispersion of Normalized Hysteretic
Energy ( ) when
are Specified in Addition to Sa(T0, x)
and
F
F
m
N
rev
,
y
Total number of ground motion records 94
Sa 0.416 g (Median Sa)
N
c.o.v. 1.01
System Parameters and Model Initial Period (T0)
0.2 sec. Damping ratio (x) 5 Strength Cy
0.125 Strain hardening ratio (a) 0 Model
Bilinear Inelastic SUBSET LMLR
Total number of ground motion records 39
Sa 0.416 g (Median Sa)
N
c.o.v. 0.48
Total number of ground motion records 27
Sa 0.416 g (Median Sa)
N
c.o.v. 0.45
Ductility (m)
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Reduction in Dispersion of Normalized Hysteretic
Energy ( ) when
are Specified in Addition to Sa(T0, x)
and
F
F
m
N
rev
,
y
Total number of ground motion records 84
Sa 0.416 g (Median Sa)
N
c.o.v. 0.86
System Parameters and Model Initial Period (T0)
0.2 sec. Damping ratio (x) 5 Strength Cy
0.125 Strain hardening ratio (a) 0 Model
Slip SUBSET LMSR
Total number of ground motion records 29
Sa 0.416 g (Median Sa)
N
c.o.v. 0.48
Total number of ground motion records 19
Sa 0.416 g (Median Sa)
N
c.o.v. 0.45
Ductility (m)
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Conclusions

• Performed extensive parametric and statistical
  study of correlation between

• Seismological variables
• Ground motion parameters
• Nonlinear SDOF response parameters

• Defined new nonlinear SDOF-based ground motion
  intensity measures

• Evaluate effectiveness of newly defined nonlinear
  SDOF-based intensity measures at the SDOF level

• Identify promising vectors of intensity measures

• Work in progress Nonlinear regression analysis
  between

• Proposed intensity measures and nonlinear SDOF
  response parameters
• Seismological variables and proposed intensity
  measures

• Future work

• Evaluation of effectiveness of nonlinear
  SDOF-based intensity measures at the MDOF level

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Nonlinear Regression Analysis
SMSR subset
LMSR subset
Log (residuals)
Main regression lines for both subsets
Confidence interval for LMSR subset
T0 1.0 sec x 0.05 a 0 Cy 0.028,
Model Bilinear inelastic
Confidence interval for SMSR subset