Ground Motion Intensity Measures for
Performance-Based Earthquake
Engineering
Hemangi Pandit
Joel Conte
Jon Stewart
John Wallace
Earthquake
Database
• Seismological
Variables
• Ground Motion
Parameters
SDOF Structural Model
• System Parameters
• Hysteretic Model
Parameters
Hysteretic Models • Bilinear Inelastic
• Clough’s Stiffness Degrading
• Slip Model
Inverse
Analysis
Direct
Analysis
SDOF Response/Demand Parameters
Statistical Analysis
• Marginal Probability Distributions
• Second-Order Statistics
Correlation and Regression Analysis
• New Intensity Measures vs. Ground Motion Parameters
• Nonlinear SDOF Response vs. New Intensity Measures
Proposed Vector of Ground Motion Intensity Measures
MDOF Nonlinear
Finite Element Model
Nonlinear
Response History
Analysis
MDOF Response/
Demand Parameters
Statistical Study
• Marginal Statistics
• Correlation Analysis
Regression between
Proposed Nonlinear SDOF-Based
Intensity Measures and
MDOF Response Parameters
Simplified and Efficient Methods
to evaluate PEER Hazard Integral
for MDOF Inelastic Models of
R/C Frame buildings
Project Vision
PEER Framework Equation:


P annual I LS i  0  



 P I LS i  0 | D M    f DM |EDP  | EDP     f EDP |I M ( | i )  f I M (i )d  d  di
DM EDP I M
• 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.
Ground Motion Database
Source of ground motion records • Pacific Engineering and Analysis Strong Motion (PEASM)
Database including Northridge and Kobe earthquakes
• Big Bear, Hector Mine, Petrolia and Northridge aftershocks
• 1999, Chi-chi,Taiwan and 1999, Ducze and Kocaeli, Turkey,
earthquakes
Shallow crustal earthquakes in active tectonic regions
 0.1 g
 High Pass Filter Frequency  0.2 Hz
 Low Pass Filter Frequency  10.0 Hz
Selection criteria for records
 PGA
Final set of 881 qualified records
• 689 from PEASM and additional records
159 from Taiwan, 1999, and 33 from Turkey, 1999
Seismological Variables
• Magnitude
• Closest Distance (R)
• Faulting Mechanism
• Local Site Condition
• Rupture Directivity Index
Ground Motion Parameters
• PGA, PGV, PGD
• Duration
• Mean Period Tmean
• Arias Intensity ,Ia,max
• Spectral Acceleration Sa(T0, x = 5%)
• Average scaled spectral acceleration Sa
[ from Sa (T0, x) to Sa (2T0, x)]
Nonlinear SDOF Analysis
 u p3,
R
 up1,
Ry
R
kp
1
R
 u p1,
Ry
1
kp
Ry
2
1
9
10
1
k0
1
k0
k0
u
1 Uy
1
 up2,
u
7
Uy
4
3 8
11
u
Uy
 u p1,  up3,
6
 up2,
Bilinear Inelastic Model
5
 u p2,
Clough’s Stiffness Degrading Model
Key Response/Demand Parameters
• Displacement Ductility (  )
• Residual Displacement Ductility ( rev )
*
• Maximum Normalized Plastic Deformation Range ( PL,max )
• Number of Positive Yield Excursions ( N( ve ) y )
• Number of Yield Reversals ( N y,rev )
*
• Normalized Earthquake Input Energy (EI,end )
*
• Normalized Hysteretic Energy Dissipated (E h )
*
• Maximum Normalized Earthquake Input Power (PI,max )
*
• Maximum Normalized Hysteretic Power (PH,max )
Slip Model
System Parameter
• Initial Period T0
• Damping Ratio x
• Normalized Strength
Cy = Ry /(mg)
• Strain Hardening Ratio a
kp
Ground Motion Intensity Measures
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 0.3  Scale Factor  3.0
84-percentile Sa level
Sa [g]
Median Sa level
16-percentile
Sa level
Secondary Intensity Measures:
T0 [sec]
Strength required for an SDOF structure to develop a specified
nonlinear response level to a given ground motion record
FRe sponse 
Strength required for that structure to remain linear elastic
to the same ground motion record
F 
Cy
F N y ,rev 
Cy 1
*
FE*h 
CEyh
*
CEyh  0
y ,rev
CN
y
Cy 1
*
F P*H ,max 
CPy H ,max
CPy H ,max  0
*
• 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
 Sa 


F



I M   F E*h 


F
N
 y ,rev 
 F P*

 H ,max 
Statistical Correlation Analysis Results
Medium correlation as
measured by a medium
correlation coefficient r
PGV [in/sec]
Inverse Analysis:
Poor correlation as
measured by
a low correlation
coefficient r
Cy
Cy
Cy
Good correlation as
measured by
a high correlation
coefficient r
R [km]
T0 = 0.2 sec; x = 0.05 ; a = 0 ;  = 8 ;
Model: Bilinear Inelastic
Duration [sec]
Statistical Correlation Analysis Results
Response - SDOF-Based
Intensity Measure Correlation
Magnitude
Direct Analysis:
Inter-Response Correlation



Response - Seismological
Variable Correlation
FE*h 100
~
T0 = 0.2 sec.; x = 0.05; a = 0; Cy = C y |8 = 0.125;
Model: Bilinear Inelastic
*
PH ,max
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 F , FE*h , FN y,rev and FP*H ,max ,
namely the Bilinear Inelastic Model.
STEP II: Good Correlation with SDOF response parameters obtained from other
hysteretic models, namely Clough’s 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.
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
IM FE* 100
 Sa 

Option 1: IM 

FE*h100
 S

a



Option 2: IM  F 8 


FN y , rev 25
(E*h )
*
(PI,max )
(P*H , max)
(E*I ,end )
( Ny, rev )
( N(  ve ) y )
r [Response vs. IM]
()

( rev )
( *PL ,max )
T0 = 1.0 sec
x = 0.05
a=0
Cy = 0.028
h
IM FN y,rev 25
IM F 8
(P*H ,max )
(E*h )
(P*I,max )
(E*I ,end )
( Ny, rev )
( N(  ve ) y )
()
( rev )
( *PL ,max )
(E*h )
*
(PI,max )
(P*H , max)
(E*I ,end )
( Ny, rev )
( N(  ve ) y )
T0 = 1.0 sec
x = 0.05
a=0
Cy = 0.028
()
( rev )
( *PL ,max )
r [Response vs. IM]
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
IM FE* 100
 Sa 
Option 1: IM  

* 100
F
 Eh

 S

a



Option 2: IM  F 8 


FN y , rev 25
(E*h )
*
(PI,max )
(P*H , max)
(E*I ,end )
( Ny, rev )
( N(  ve ) y )
r [Response vs. IM]
()

( rev )
( *PL ,max )
T0 = 1.0 sec
x = 0.05
a=0
Cy = 0.028
h
IM FN y,rev 25
IM F 8
(P*H ,max )
(E*h )
(P*I,max )
( E*I ,end )
( Ny, rev )
( N(  ve ) y )
()
( rev )
( *PL ,max )
(E*h )
*
(PI,max )
(P*H , max)
(E*I ,end )
( Ny, rev )
( N(  ve ) y )
T0 = 1.0 sec
x = 0.05
a=0
Cy = 0.028
()
( rev )
( *PL ,max )
r [Response vs. IM]
Relative Correlation of Response Parameter, here Ductility (,
to Various Candidate Intensity Measures
r  Vs. IM] (T0 = 0.2 sec)
Strength: Cy = 0.125
r  Vs. IM] (T0 = 1.0 sec)
Strength: Cy = 0.028
r  Vs. IM] (T0 = 3.0 sec)
System Parameters and Model:
Damping ratio (x) = 5%
Strain hardening ratio (a) = 0
Model: Clough’s Stiffness
Degrading Model
PGA
PGV
PGD
Ia,max
Dur
Tmean
Mag
R
F = 2
F = 4
F = 6
F = 8
FE*h 5
FE*h  25
FE*h 50
FE*h 100
Strength: Cy = 0.005
Candidate Intensity Measures (IM)
Relative Correlation of Response Parameter, here Max.
Plastic Deformation ( *PL,max, to Various Intensity Measures
r  *PL,max vs. IM]
(T0 = 0.2 sec)
Strength Cy = 0.125
r  *PL,max vs. IM]
(T0 = 1.0 sec)
Strength Cy = 0.028
r  *PL,max vs. IM]
(T0 = 3.0 sec)
System Parameters and Model:
Damping ratio (x) = 5%
Strain hardening ratio (a) = 0
Model: Clough’s Stiffness
Degrading Model
PGA
PGV
PGD
Ia,max
Dur
Tmean
Mag
R
F = 2
F = 4
F = 6
F = 8
FE*h 5
FE*h  25
FE*h 50
FE*h 100
Strength Cy = 0.005
Candidate Intensity Measures (IM)
Reduction in Dispersion of Normalized Hysteretic Energy (E*h
when F and FNy rev are Specified in Addition to Sa(T0, x)
,
Total number of ground motion records = 550
N
Sa = 0.416 g (Median Sa)
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
N
N
Sa = 0.416 g (Median Sa)
0.24  F  8  0.36
c.o.v. = 0.57
Total number of ground motion records = 91
Sa = 0.416 g (Median Sa)
0.24  F  8  0.36
0.24  F N y ,rev  0.36
c.o.v. = 0.44
Ductility ()
Reduction in Dispersion of Normalized Hysteretic Energy (E*h
when F and FNy,rev are Specified in Addition to Sa(T0, x)
Total number of ground motion records = 550
N
Sa = 0.416 g (Median Sa)
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
N
N
Sa = 0.416 g (Median Sa)
0.09  F  0.14
c.o.v. = 0.41
Total number of ground motion records = 26
Sa = 0.416 g (Median Sa)
0.09  F  0.14
0.03  FN y ,rev  0.05
c.o.v. = 0.33
Ductility ()
Reduction in Dispersion of Normalized Hysteretic Energy (E*h
when F and FNy,rev are Specified in Addition to Sa(T0, x)
Total number of ground motion records = 94
N
Sa = 0.416 g (Median Sa)
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
N
N
Sa = 0.416 g (Median Sa)
0.25  F  0.37
c.o.v. = 0.48
Total number of ground motion records = 27
Sa = 0.416 g (Median Sa)
0.25  F  0.37
0.25  FNy ,rev  0.37
c.o.v. = 0.45
Ductility ()
Reduction in Dispersion of Normalized Hysteretic Energy (E*h
when F and FN ,rev are Specified in Addition to Sa(T0, x)
y
Total number of ground motion records = 84
N
Sa = 0.416 g (Median Sa)
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
N
N
Sa = 0.416 g (Median Sa)
0.19  F  0.29
c.o.v. = 0.48
Total number of ground motion records = 19
Sa = 0.416 g (Median Sa)
0.19  F  0.29
0.25  FNy ,rev  0.37
c.o.v. = 0.45
Ductility ()
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:
 Sa 

IM  *

FEh100
 S

a



IM  F 8 


FN y , rev 25
• 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
Nonlinear Regression Analysis
SMSR subset
LMSR subset
E*h
Log (residuals)
IM F 8
E*h
IM F 8
T0 = 1.0 sec; x = 0.05; a = 0
Cy = 0.028,
Model: Bilinear inelastic
IM F 8
Main regression lines for both subsets
Confidence interval for LMSR subset
Confidence interval for SMSR subset