ground motion intensity measures for performance-based earthquake engineering
DESCRIPTION
Ground Motion Intensity Measures for Performance-Based Earthquake Engineering. Hemangi Pandit Joel Conte Jon Stewart John Wallace. Earthquake Database Seismological Variables Ground Motion Parameters. MDOF Nonlinear Finite Element Model. SDOF Structural Model - PowerPoint PPT PresentationTRANSCRIPT
Ground Motion Intensity Measures for Performance-Based Earthquake
Engineering
Hemangi PanditJoel ConteJon Stewart
John Wallace
Proposed Vector of Ground Motion Intensity Measures
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
InverseAnalysis
DirectAnalysis
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
MDOF NonlinearFinite Element Model
NonlinearResponse HistoryAnalysis
MDOF Response/Demand Parameters
Statistical Study• Marginal Statistics• Correlation Analysis
Regression between Proposed Nonlinear SDOF-Based Intensity Measures andMDOF Response Parameters
Simplified and Efficient Methodsto evaluate PEER Hazard Integralfor MDOF Inelastic Models ofR/C Frame buildings
didd)i(f)i|(fEDP|fD|0IP0IP MMM M
MMii II|EDPD EDP I
EDP|DLSLSannual
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.
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
Selection criteria for records
Hz 10.0FrequencyFilter Pass LowHz 0.2FrequencyFilter PassHigh
g 0.1PGA
Final set of 881 qualified records • 689 from PEASM and additional records 159 from Taiwan, 1999, and 33 from Turkey, 1999
Seismological Variables Ground Motion Parameters
• Magnitude• Closest Distance (R)• Faulting Mechanism• Local Site Condition• Rupture Directivity Index
• PGA, PGV, PGD• Duration• Mean Period Tmean
• Arias Intensity ,Ia,max
• Spectral Acceleration Sa(T0, = 5%)• Average scaled spectral acceleration [ from Sa (T0, ) to Sa (2T0, )]
aS
Ground Motion Database
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
) () ( rev
) ( *max,PL
) (N rev,y
) (N y)ve(
) (E*end,I
) (E*h
) (P*max,I
) (P*max,H
Nonlinear SDOF Analysis
System Parameter
• Initial Period T0
• Damping Ratio
• Normalized Strength Cy = Ry /(mg)
• Strain Hardening Ratio
p
up1
up2
u
R
1k0
Uy
Ry 1 kp
up3
Bilinear Inelastic Model
up1
up2
u
R
1
k 0
Uy
Ry 1 kp
Clough’s Stiffness Degrading Model
up1
up2 u
R
1 2
34
56
8
9 10
117
1k0
Uy
Ry 1 k
up3
Slip Model
Ground Motion Intensity Measures
Primary Intensity Measure: Sa(T0, ) 84-percentile Sa level
Median Sa level
16-percentile Sa level
Secondary Intensity Measures:
• Proposed Intensity Measures• Maximum Value of 1• Measures of damage effectiveness
of a given ground motion record• Obtained using Bilinear Inelastic
SDOF system with = 0
• 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 3.0Factor Scale3.0
T0 [sec]
Sa [g]
C
CF 1
y
yN
N
rev,y
rev,y
C
CF 0P
y
Py
P *max,H
*max,H
*max,H
FF
FFS
I
P
N
E
a
M
*max,H
rev,y
*h
recordmotion ground same theto elasticlinear remain tostructurefor that requiredStrength
recordmotion groundgiven a tolevel responsenonlinear specified a develop tostructure SDOFan for requiredStrength
sponseReF
C
CF 0E
y
Ey
E *h
*h
*h
CC
F 1y
y
Statistical Correlation Analysis Results
PGV [in/sec] Duration [sec]
Cy
Good correlation as measured bya high correlation coefficient
Poor correlation as measured bya low correlation coefficient
Cy
T0 = 0.2 sec; = 0.05 ; = 0 ; = 8 ;
Model: Bilinear Inelastic
Inverse Analysis:
Cy
R [km]
Medium correlation as measured by a medium correlation coefficient
Statistical Correlation Analysis Results
Magnitude
T0 = 0.2 sec.; = 0.05; = 0; Cy= = ; Model: Bilinear Inelastic
PH*
,maxFEh 100*
Direct Analysis:
Response - Seismological Variable Correlation
Response - SDOF-Based Intensity Measure Correlation
Inter-Response Correlation
8y |C~
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 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.
FandF,F,F PNE *max,Hrev,y
*h
)(
rev
)
(*
max
,
PL
) ( N
rev
,y
)(
)(
N
yve
)(
)(
* ,
Een
dI
) ( P
*m
ax,I
) ( P
*m
ax,
H
) ( E
* h
)(
rev
)
(*
max
,
PL
) ( N
rev
,y
)(
)(
N
yve
)(
)(
* ,
Een
dI
) ( P
*m
ax,I
) ( P
*m
ax,
H
) ( E
* h
[Response vs. IM]
8FIM 25N rev,yFIM
T0 = 1.0 sec = 0.05 = 0Cy = 0.028
Response Parameters computed using Bilinear Inelastic Model
SDOF-based Intensity Measures (IM) computed using Bilinear Inelastic Model
100E*h
FIM
)(
rev
)
(*
max
,
PL
) ( N
rev
,y
)(
)(
N
yve
)(
)(
* ,
Een
dI
) ( P
*m
ax,I
) ( P
*m
ax,
H
) ( E
* h
[Response vs. IM]
Correlation analysis to evaluate optimum intensity measures: STEP-I
T0 = 1.0 sec = 0.05 = 0Cy = 0.028
Option 1:
Option 2:
FS
I100E
aM
*h
FFS
I25 N
8
a
M
rev,y
)(
rev
)
(*
max
,
PL
) ( N
rev
,y
)(
)(
N
yve
)(
)(
* ,
Een
dI
) ( P
*m
ax,I
) ( P
*m
ax,
H
) ( E
* h
)(
rev
)
(*
max
,
PL
) ( N
rev
,y
)(
)(
N
yve
)(
)(
* ,
Een
dI
) ( P
*m
ax,I
) ( P
*m
ax,
H
) ( E
* h
[Response vs. IM]
8FIM 25N rev,yFIM
T0 = 1.0 sec = 0.05 = 0Cy = 0.028
Response Parameters computed using Slip Model
SDOF-based Intensity Measures (IM) computed using Bilinear Inelastic Model
100E*h
FIM
)(
rev
)
(*
max
,
PL
) ( N
rev
,y
)(
)(
N
yve
)(
)(
* ,
Een
dI
) ( P
*m
ax,I
) ( P
*m
ax,
H
) ( E
* h
[Response vs. IM] T0 = 1.0 sec = 0.05 = 0Cy = 0.028
Option 1:
Option 2:
FS
I100E
aM
*h
FFS
I25 N
8
a
M
rev,y
Correlation analysis to evaluate optimum intensity measures: STEP-II
Relative Correlation of Response Parameter, here Ductility (to Various Candidate Intensity Measures
PGA
PGV
PGD
I a,m
ax
Dur
T mea
n
Mag
R F =
2F
= 4
F =
6
F =
8
F25
E* h
F5
E* h
F50
E* h
F10
0E
* h
Vs. IM] (T0 = 3.0 sec)
Vs. IM] (T0 = 1.0 sec)
Vs. IM] (T0 = 0.2 sec)
Candidate Intensity Measures (IM)
System Parameters and Model:Damping ratio () = 5%Strain hardening ratio () = 0Model: Clough’s Stiffness Degrading Model
Strength: Cy = 0.125
Strength: Cy = 0.028
Strength: Cy = 0.005
PGA
PGV
PGD
I a,m
ax
Dur
T mea
n
Mag
R F =
2
F =
4
F =
6
F =
8
F25
E* h
F5
E* h
F50
E* h
F10
0E
* h
Candidate Intensity Measures (IM)
System Parameters and Model:Damping ratio () = 5%Strain hardening ratio () = 0Model: Clough’s Stiffness Degrading Model
vs. IM]
(T0 = 0.2 sec)
*max,PL
vs. IM]
(T0 = 1.0 sec)
*max,PL
vs. IM]
(T0 = 3.0 sec)
*max,PL
Relative Correlation of Response Parameter, here Max. Plastic Deformation ( to Various Intensity Measures *
max,PL
Strength Cy = 0.125
Strength Cy = 0.028
Strength Cy = 0.005
Total number of ground motion records = 550
Total number of ground motion records = 210
Total number of ground motion records = 91
Sa = 0.416 g (Median Sa)
c.o.v. = 1.09
c.o.v. = 0.57
c.o.v. = 0.44
System Parameters and Model:Initial Period (T0) = 0.2 sec.Damping ratio () = 5%Strength Cy = 0.125Strain hardening ratio () = 0Model: Bilinear Inelastic
N
N
N
Ductility ()
Sa = 0.416 g (Median Sa)
Sa = 0.416 g (Median Sa)
80.24 F 0.36
80.24 F 0.36
36.024.0 FN rev,y
Reduction in Dispersion of Normalized Hysteretic Energy ( when are Specified in Addition to Sa(T0, )
E*hFF N rev,y
and
Total number of ground motion records = 550
Total number of ground motion records = 201
Total number of ground motion records = 26
Sa = 0.416 g (Median Sa)
c.o.v. = 0.67
c.o.v. = 0.41
c.o.v. = 0.33
System Parameters and Model:Initial Period (T0) = 3.0 sec.Damping ratio () = 5%Strength Cy = 0.005Strain hardening ratio () = 0Model: Slip
N
N
N
Ductility ()
Sa = 0.416 g (Median Sa)
Sa = 0.416 g (Median Sa)
Reduction in Dispersion of Normalized Hysteretic Energy ( when are Specified in Addition to Sa(T0, )
E*hFF N rev,yand
14.0F09.0
05.0F03.0 N rev,y14.0F09.0
Total number of ground motion records = 94
Total number of ground motion records = 39
Total number of ground motion records = 27
Sa = 0.416 g (Median Sa)
c.o.v. = 1.01
c.o.v. = 0.48
c.o.v. = 0.45
System Parameters and Model:Initial Period (T0) = 0.2 sec.Damping ratio () = 5%Strength Cy = 0.125Strain hardening ratio () = 0Model: Bilinear InelasticSUBSET: LMLR
N
N
N
Ductility ()
Sa = 0.416 g (Median Sa)
Sa = 0.416 g (Median Sa)
Reduction in Dispersion of Normalized Hysteretic Energy ( when are Specified in Addition to Sa(T0, )
E*hFF N rev,yand
37.025.0 F
37.025.0 F 37.025.0 FN rev,y
Total number of ground motion records = 84
Total number of ground motion records = 29
Total number of ground motion records = 19
Sa = 0.416 g (Median Sa)
c.o.v. = 0.86
c.o.v. = 0.48
c.o.v. = 0.45
System Parameters and Model:Initial Period (T0) = 0.2 sec.Damping ratio () = 5%Strength Cy = 0.125Strain hardening ratio () = 0Model: SlipSUBSET: LMSR
N
N
N
Ductility ()
Sa = 0.416 g (Median Sa)
Sa = 0.416 g (Median Sa)
Reduction in Dispersion of Normalized Hysteretic Energy ( when are Specified in Addition to Sa(T0, )
E*hFF N rev,y
and
29.0F19.0
37.025.0 FN rev,y 29.0F19.0
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:
FS
I100E
aM
*h
FFS
I25 N
8
a
M
rev,y
• 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
Main regression lines for both subsetsConfidence interval for LMSR subsetConfidence interval for SMSR subset
Log
(res
idua
ls)
8FIM
8FIM
E*h
T0 = 1.0 sec; = 0.05; = 0 Cy = 0.028, Model: Bilinear inelastic
Nonlinear Regression AnalysisSMSR subsetLMSR subset
8FIM
E*h