GROUND MOTION INTENSITY MEASURES
THAT CORRELATE TO
ENGINEERING DEMAND PARAMETERS
Jonathan Bray and Thaleia Travasarou
University of California, Berkeley
PEER IM Working Group:
Abrahamson, Bray, Conte, Cornell, Deierlein, Kramer,
Krawinkler, Porter, Silva, Somerville, Stewart, Stojadinovic
Pacific Earthquake Engineering Research Center
SHAKING-INDUCED
DAMAGE to
Bridges and Buildings
Moehle
Seismic Displacement
LIQUEFACTION-INDUCED DAMAGE
EERC Slide Collection
EERC Slide Collection
PRIMARY PEER EARTHQUAKE ENGINEERING ISSUES
•
Building or Short Bridge, including site response and SSI
•
Long-Span Bridge, including site response and SSI
•
Networks with Multiple Structures
•
Liquefaction and Lateral Spreading
•
Seismic Slope Instability and Permanent Ground Deformations
BUILDING OR SHORT BRIDGE, INCLUDING SITE RESPONSE AND SSI
Engineering Damage Parameters (EDP):
Story Drift, Base Shear, Input Energy, and Floor Acceleration
Drift, Max. Curvature, Column Curvature or Displacement Ductility
Intensity Measures (IM):
Sa(T1), PGV, PGD, SPGA, Sa(T1)[Sa(2T1)/Sa(T1)]0.5
Other combinations by Cornell involving Sa(T1) and Sa(T2)
Vectors by Conte or Krawinkler
Tpulse, D 5-95, Ia
LONG-SPAN BRIDGE, INCLUDING SITE RESPONSE AND SSI
Engineering Damage Parameters (EDP):
Drift, Max. Curvature, Column Curvature or Displacement Ductility
Intensity Measures (IM):
Sa(T1), PGV, PGD
Vector by Hutchinson et al.
D 5-95, CAV, Ia
NETWORKS WITH MULTIPLE STRUCTURES
Engineering Damage Parameters (EDP):
The IM (e.g. PGA)
Intensity Measures (IM):
PGA
Sa(T1)
PGV
Ia
LIQUEFACTION AND LATERAL SPREADING
Engineering Damage Parameters (EDP):
Factor of Safety Against Liquefaction (FSl)
Pore Pressure Ratio (ru)
Intensity Measures (IM):
Cyclic Stress Ratio (CSR) or PGA
CAV5
Ia
Equivalent Number of Uniform Stress Cycles or D 5-95
Combination or Vector
SEISMIC SLOPE INSTABILITY AND PERMANENT GROUND
DEFORMATIONS
Engineering Damage Parameters (EDP):
Permanent Ground Displacement (U)
Intensity Measures (IM):
Ia
Sa(T1)
PGV or EPGV
Response Spectrum Intensity (SI)
Characteristic Intensity (Ic)
Combination or Vector
Notes on the Intensity Measure Breakout Session - PEER Annual Meeting - Jan. 17, 2002
· Testbeds will not provide definitive answers as to the best single IM for all future use.
· The preferred way to compare IMs is to use “stripes”. (i.e., for each IM, scale records to
the same IM level, do nonlinear runs, and compare their dispersions, with secondary
recognition of possible difficulties with respect to “sufficiency”). The most efficient solution is
to use the same runs on records scaled to the same first-mode Sa to test all IMs. However,
it is not yet clear that such runs can be effectively used to study other IMs.
· Another solution is to provide the same records in their original unscaled condition, and
then apply the “cloud” method (i.e., a regression of response on IM) to estimate the
dispersion. This is equally applicable to all IMs, but it will take one additional set of runs for
all records.
· For each record, it should contain the list of IM values and the list of EPD outputs.
Standard IM values (e.g., Sa, Ia) can probably be provided by an individual; other more
exotic IM values should be provided by the proponent.
· The lists of preferred IMs and EDPs to be studied for each testbed need to be compiled.
· A standardized procedure for evaluating efficiency and sufficiency of IMs needs to be
agreed to and documented for others to use.
PEER IM-EDP Meeting of April 26, 2002
Overall Objective:
Identify ground motion Intensity Measures that “best”
correlate to meaningful Engineering Demand
Parameters
• develop a refined list of promising IMs
• standardize the manner in which IMs will be evaluated
• resolve some of the difficult issues identified at
January's meeting.
PRIMARY PEER EARTHQUAKE ENGINEERING ISSUES
Original
•
Building or Short Bridge, including
site response and SSI
•
Long-Span Bridge, including site
response/SSI
•
Networks with Multiple Structures
•
Liquefaction and Lateral Spreading
•
Seismic Slope Instability and
Permanent Ground Deformations
Revised
• Short-period systems, Ia
• Long-period systems, SI
• Specific Systems, Sa(T1) or
more sophisticated IMs
PERIOD-INDEPENDENT INTENSITY MEASURES
Peak Ground Acceleration
Peak Ground Displacement
PGA
PGD
Arias Intensity (Arias, 1970)
 
2
Ia 

a
(
t
)

dt

2g 0

Cumulative Absolute Velocity
CAV5   x a(t )dt
(Kramer 2002; 5 cm/sec2 threshold)
0
Response Spectrum Intensity
2 .5
SI   PSV (  0.05 , T )dt
(Housner, 1959)
0 .1
Peak Ground Velocity
& Pulse Period
PGV
Tv
PERIOD-DEPENDENT INTENSITY MEASURES
Spectral Acceleration
at Fundamental Period
Sa(T1)
Spectral Combination
(Cordova et al. 2000)
Sa(2 T1 )
SaC  Sa(T1 ) 
Sa(T1 )
Spectral Vector
(Conte, 2002)
Sa(T1)
F
E*
h
Spectral Combination
(Luco and Cornell, 2001)

E*
C Yh
E * 0
C Yh
IM1I&2E
Summary of Discussion of April 26, 2002 Meeting:
Participants discussed specific findings from their studies on the ability of various IMs to
estimate important EDPs for their particular problems, which included from bridge response,
nonlinear building response, liquefaction and seismically induced permanent slope
displacements.
Allin Cornell discussed procedures for studying alternative candidate IMs, and his current
recommendations are located at www.peertestbeds.net/Crosscutting.htm Here, efficiency
and sufficiency are discussed. Both the “stripes” method and the direct regression “cloud”
method were found to be acceptable ways of moving forward. Efficiency was determined to be
more tractable and more important than sufficiency. An IM with twice the dispersion requires 4x
as many runs to obtain an equivalent sense of the true median response.
Joel Conte’s work was especially helpful for understanding how a vector of IMs may be
developed (see www.peertestbeds.net/Crosscutting.htm)
Most found that the spectral acceleration at the fundamental period of the system being
analyzed worked well and is the default IM for most problems. Some promising combinations of
spectral acceleration and some vectors containing spectral acceleration for normal cases and
PGV for near-fault cases were also identified.
Several researchers noted the advantage of using a non-system specific IM for studies that
involved many systems of various characteristics (several sites that might liquefy or experience
permanent displacement and network studies of many systems). For problems involving the
response of short period systems, Arias Intensity was found to be promising, and a new
attenuation relationship for this ground motion parameter was distributed at the meeting.
EFFICIENCY
Seismic Displacement:
Ts = 0.3 s, ky = 0.05
EFFICIENCY
Seismic Displacement:
Ts = 1.0 s, ky = 0.05
SUFFICIENCY
ln(D) = a + b ln(Ia) + c ln(Ia)2 + d M+e ln(R)
Ts = 0.3s ky = 0.05
Longitudinal drift ratio
Longitudinal drift ratio
(Mackie and Stojadinovic, 2002)
ln( I a ) 
c1  c2  ( M  6)  c3  ln( M / 6)  c4  ln( R 2  h 2 ) 
( s11  s12  ( M  6))  SC  ( s21  s22  ( M  6))  S D 
f1  FN  f 2  FR
Standard deviation of the random error for different intensity
measures for a M=7.5 strike-slip earthquake at R = 10 km on soil.
Data Set
Standard
Deviation
Travasarou et al. (2002)
1208 records from 76 world
wide shallow crustal events
up to 1999. (4.7  M  7.6)
0.82
PGA (g)
Abrahamson & Silva (1997)
655 records from 58 world
wide shallow crustal events
up to 1994. (4.5  M  7.4)
0.43
SA(T=.5s)
(g)
Abrahamson & Silva (1997)
655 records from 58 world
wide shallow crustal events
up to 1994. (4.5  M  7.4)
0.54
Tp (s)
Rathje et al. (1998)
306 records from 20
earthquakes in active platemargin regions.
(5.7  M  7.3)
0.56
Tm (s)
Rathje et al. (1998)
306 records from 20
earthquakes in active platemargin regions.
(5.7  M  7.3)
0.35
D5_95 (s)
Abrahamson & Silva (1996)
655 records from 58 world
wide shallow crustal events
up to 1994. (4.5  M  7.4)
0.49
IM
Attenuation Relationship
Ia (m/s)
Rel. PGA Sa Ia D5-95 U
Atten 0.50 0.58 0.90 0.49 2.3
DM/IM 1.09 0.96 0.84 2.23 -
Cornell (2002) “Guidance for Evaluating Alternative IMs
- Stripes Analysis: each record within a hazard bin must be scaled to
the same IM value for that hazard level, say Sa(T=1s) and PGAmed;
compare the dispersion of the EDP vs. each IM within a hazard bin
(median should be similar); a dispersion reduction of ~30% implies
that half the number of nonlinear dynamic analyses are required.
Need a new set of runs for each candidate IM
- Regression (Direct/Cloud) Method: use unscaled records; perform
regression of EDP vs. candidate IM, and estimate standard deviation
of the residuals of the fitted model; compare standard deviations of
each candidate IM; but it is a measure of both the variability of the
EDP vs. IM and the regression model used.
Need only one set of runs
- Modified Stripes Analysis: use stripes method to evaluate primary
IM, say Sa(T=1s) and then evaluate scatter of other IMs given that
records have been scaled to Sa(T=1s); implies dependency; Cornell
et al. are currently investigating this approach.
Need only one set of runs
A Vector of Ground Motion Intensity Measures (Conte et al. 2002)
Primary Intensity Measure: Sa(T0, )
• 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 
Testbed Ground Motions
Somerville and Collins (2002)
Uniform Hazard Spectra developed for outcropping soft rock for 50%
in 50 yrs, 10% in 50 yrs, and 2% in 50 yrs level.
Using available recorded ground motion records that represent the
controlling event’s M and R at each hazard level, 10 to 20 ground
motions were selected.
For Humbolt Bay Bridge, M = 7 to 8 and R = 5 to 20 km for Sa(T=1.23s)
All motions provided unscaled and scaled so that each record has Sa
at T=1.23s equal to that of uniform hazard spectra at each hazard level.
For I-880 Bridge, M = 6.6 to 7 and R = 7 km for Sa(T=1s)
All motions provided only unscaled until representative period is
selected. User must transform FN and FP components into
logitudinal and transverse components.
Motion sets inherently contain some forward-directivity and fling
motions.
ENGINEERING DEMAND PARAMETERS
BRIDGES
Drift Ratio, Peak Column Curvature,
Displacement Ductility, Curvature Ductility
Mackie and Stojadinovic (2002) PEER Report:
1.) global response - drift ratio
2.) intermediate response - maximum column moment
3.) local response - material stress
BUILDINGS
Ductility Demand, Residual Ductility Demand
Peak Story Drift, Peak Story Drift Angle
Normalized Hysteretic Energy Dissipated
LIQUEFACTION
Pore Pressure Ratio
Factor of Safety Against Liquefaction
SEISMIC SLOPE STABILITY
Seismically-Induced Permanent Displacements
SUMMARY OF PRIMARY INTENSITY MEASURES
• PGA
• PGD
• PGV & Pulse Period
• Ia
• CAV5
• SI
• Sa(T1)
• Spectral Combination
• Spectral Vector
* Bold IMs have attenuation
relations available