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Modification of Empirical Strong Ground Motion Attenuation Relations to Include the Amplitude and Duration Effects of Rupture Directivity

Authors:

Abstract

Rupture directivity effects cause spatial variations in ground motion amplitude and duration around faults and cause differences between the strike-normal and strike-parallel components of horizontal ground motion amplitudes, which also have spatial variation around the fault. These variations become significant at a period of 0.6 second and generally grow in size with increasing period. We have developed modifications to empirical strong ground motion attenuation relations to account for the effects of rupture directivity on strong motion amplitudes and durations. The modifications are based on an empirical analysis of near-fault data. The ground motion parameters that are modified include the average horizontal response spectral acceleration, the duration of the acceleration time history, and the ratio of strike-normal to strike-parallel spectral acceleration. The parameters upon which the adjustments to average horizontal amplitude and duration depend are the fraction of the fault rupture that occurs on the part of the fault that lies between the hypocenter and the site, and the angle between the fault plane and the path from the hypocenter to the site. Since both of these parameters can be derived from the hypocenter location and the fault geometry, the model of rupture directivity effects on ground motions that we have developed can be directly included in probabilistic seismic hazard calculations. The spectral acceleration is larger for periods longer than 0.6 second, and the duration is smaller, when rupture propagates toward a site. For sites located close to faults, the strike-normal spectral acceleration is larger than the strike-parallel spectral acceleration at periods longer than 0.6 second in a manner that depends on magnitude, distance, and angle. To facilitate the selection of time histories that represent near-fault ground motion conditions in an appropriate manner, we provide a list of near-fault records indicating the rupture directivity parameters that each contains.
EFFECTS OF RUPTURE DIRECTIVITY ON
PROBABILISTIC SEISMIC HAZARD ANALYSIS
Norman A. Abrahamson
1
ABSTRACT
For long period structures such as bridges that are near faults with high activity rates,
it can be important to explicitly include directivity effects in the attenuation relations for
either probabilistic or deterministic analyses. There are two rupture directivity effects. The
first effect is a change in strength of shaking of the average horizontal component of motion,
and the second effect is the systematic differences in the strength of shaking on the two
horizontal components oriented perpendicular and parallel to the strike of the fault. The new
San Francisco Oakland Bay Bridge is used as an example to show the effects of including
rupture directivity in probabilistic seismic hazard analysis. For this example, including both
effects results in about a 30% increase in the T=3 second spectral acceleration for a 1500
year return period as compared to traditional analyses.
Introduction
Rupture directivity effects can lead to large long period pulses in the ground motion.
Recently, models have been developed to quantify the directivity effect (e.g. Somerville et
al, 1997). With these models of the rupture directivity effect, directivity can be included in
either deterministic or probabilistic seismic hazard analyses. This paper demonstrates the
effect of rupture directivity on probabilistic seismic hazard analyses.
Attenuation Relations and Rupture Directivity
For design of long-period structures such as bridges, characterization of long-period
motion is essential. Attenuation relations commonly used in California do not explicitly
include rupture directivity effects but they can adjusted to account for near-fault directivity
effects using the Somerville et al. (1997) fault-rupture directivity model. The Somerville et
al. (1997) model comprises two period-dependent scaling factors that may be applied to
horizontal attenuation relationship. One of the factors accounts for the change in shaking
intensity in the average horizontal component of motion due to near-fault rupture directivity
effects (higher ground motions for rupture toward the site and lower ground motions for
rupture away from the site). The second factor reflects the directional nature of the shaking
intensity using two ratios: fault normal (FN) and fault parallel (FP) versus the average (FA)
1
Pacific Gas and Electric Company, 245 Market Street, Mail Code N4C, San Francisco, CA 94105
Proceedings of the Sixth International Conference on Seismic Zonation (6ICSZ)
EERI November 12-15, 2000 Palm Springs CA
component ratios. The fault normal component is taken as the major principal axis resulting
in an FN/FA ratio larger than 1 and the fault parallel component is taken as the minor
principal axis with an FP/FA ratio smaller than 1. The two scaling factors depend on
whether fault rupture is in the forward or backward direction, and also the length of fault
rupturing toward the site.
There are several aspects of the empirical model for the average horizontal
component scale factors developed by Somerville et al that needed to be modified to make
the model applicable to a probabilistic hazard analysis. As published, the directivity model
is independent of distance. The data set used in the analysis includes recordings at distances
of 0 to 50 km. A distance dependent taper function was applied to the model that reduces
the effect to zero for distances greater than 60km.
T
d
(r) = 1 for r < 30 km
1 - (r-30)/30 for 30 km < r < 60 km (1)
0 for r > 60 km
As published, the model is applicable to magnitudes greater than 6.5. A magnitude taper
was applied that reduces the effect to zero for magnitudes less than 6.0.
T
m
(m) = 1 for m = 6.5
1 - (m-6.5)/0.5 for 6 = m < 6.5 (2)
0 for m < 6
The empirical model uses two directivity parameters: x and θ where x is defined as
the fraction of the fault length that ruptures toward the site and θ is the angle between the
fault strike and epicentral azimuth (see Somerville et al for details). The worst case is x=1
and θ=0. The empirical model uses a form that increases a constant rate as x increases from
0 to 1. There is little empirical data with x cos(θ) values greater than 0.6, and the
extrapolation of the model to larger x cos(θ) values is not well constrained. Based on an
evaluation of empirical recordings and numerical simulations, the form of the directivity
function is modified to reach a maximum at x cos(θ) =0.4. The slope is greater than the
Somerville model, but it flattens out at a lower level. The T=3 second value is used to guide
the adjustment of the model at all periods. The resulting model is given by
y
Dir
(x,θ,Τ) = C
1
(T) + 1.88 C
2
(T) x cos(θ) for x cos(θ) = 0.4 (3)
C
1
(T) + 0.75 C
2
(T)
for
x cos(θ) > 0.4
where C
1
(T) + C
2
(T) are from Somerville et al. (1997), and are listed in Table 1.
Table 1. Model Coefficients for the Modified Somerville et al. (1997) Directivity
Effects for the Average Horizontal Component
Period (sec) C1 C2
0.60 0.000 0.000
0.75 -0.084 0.185
1.00 -0.192 0.423
1.50 -0.344 0.759
2.00 -0.452 0.998
3.00 -0.605 1.333
4.00 -0.713 1.571
5.00 -0.797 1.757
Finally, including the directivity effect should results in a reduction of the standard
deviation of the attenuation relation. Based on an evaluation of the empirical data, at T=3
seconds, there is a reduction of the standard deviation of about 0.05 natural log units due to
adding the directivity term into the ground motion model. The period dependence of the
reduction was approximated by the period dependence of the slope of the directivity effect.
To account for the reduction in the standard deviation due to including the directivity effect
as part of the model, the standard deviations for the published attenuation relations were
modified for use in the hazard analysis using the following relation:
σ
dir
(M,T) = σ (M,T) - 0.05 C
2
(T)/1.333 (4)
where C
2
(T) is given in Table 1 and σ(M,,T) is the standard deviation from the published
attenuation relation (without directivity effects). The final modified Somerville model for
the average horizontal component for strike-slip faults is given by
ln Sa
dir
(M,r,x,θ,Τ) = ln Sa(M,r) + y
Dir
(x,θ,Τ) T
d
(r) T
m
(m) (5)
where Sa(M,r) is an empirical attenuation relation without directivity. This modified model
is shown in Figure 1a. The FN/Avg ratios are shown in Figure 1b for the modified
Somerville et al. (1997) model.
Incorporating Rupture Directivity Into Probabilistic Seismic Hazard Analysis
It is straightforward to include rupture directivity into a probabilistic hazard analysis.
The main change is that the location of the hypocenter on the rupture area needs to be
included as an additional source of (aleatory) variability (Figure 2).
In a standard hazard calculation, the hazard is given by:
ν
i
(A > z) = N
i
(M
min
)
Ey
1
Ex= 0
1
RA =0
f
m
i
(m) f
W
i
(m,W) f
RA
i
(m,RA)f
Ex
i
(x)f
Ey
i
(m,x)
m=M
min
M
max
i
W= 0
P(A > z | m,r
i
(x,y,RA,W))dWdRAdxdydm
(6)
where N
i
(M
min
) is the rate of earthquakes with magnitude greater than M
min
from the i
th
source; m is magnitude; M
max
i
is the maximum magnitude (for the i
th
source); f
m
(m),
f
W
(m,W), f
RA
(m,RA), f
Ex
, and f
Ey
are probability density functions for the earthquake
magnitude, rupture width, rupture area, location of the center of rupture along strike and
location of the center of rupture down dip, respectively; and P(A>z|m,r,ε) is the probability
that the ground motion exceeds the test level z for a given magnitude and distance.
Including directivity effects for strike-slip faults, the hazard is given by
where r, X, and θ are computed from the rupture location and the hypocenter location. In
this calculation, we need to define and additional probability density function for the
location of the hypocenter on the rupture, f
hx
(h
x
). Here, I have assumed uniform
distributions for the hypocenter location (e.g. no preferred locations for the nucleation of the
rupture).
It could be argued that the effect on directivity on the average horizontal component
is already included in the standard deviation of the ground motion of the published
attenuation relations. There are two reasons why the published standard deviations do not
adequately account for directivity effects. First, the standard deviation of most attenuation
relations is averaged over all distances. As a result, the standard deviation of the near fault
ground motion is underestimated by the average standard deviation over all distances.
Second, the size of the directivity effect can vary significantly for different locations that are
the same distance away from the fault. That is, a particular site-fault geometry may be more
likely to experience forward directivity effects than other sites.
Example Calculation
As an example, the probabilistic seismic hazard is computed with and without
directivity. As discussed above, we can consider the effects of directivity on the average
horizontal component or on the individual components oriented parallel and perpendicular
to the strike of the fault. The base case is using the attenuation relations as published.
These are for the geometric mean of the two horizontal components. This case is label as
“without directivity” in Figure 3. Including just the effect of directivity on the average
horizontal component increases the hazard at return periods greater than 500 years. The
hazard with directivity can be deaggregated in terms of the rupture directivity parameter,
Xcos(θ). The deaggregation at the 1500 year return period is shown in Figure 4. This figure
shows that most of the long period ground motion hazard is from forward directivity cases.
ν
i
(A > z) = N
i
(M
min
)
hx= 0
1
Ey
1
Ex= 0
1
RA =0
f
m
i
(m) f
W
i
(m,W) f
RA
i
(m,RA)f
Ex
i
(x) f
Ey
i
(m,x)
m=M
min
M
max
i
W= 0
f
h
x
(h
x
)
P(A > z | m,r,X,
θ
)dW dRAdx dydh
x
dm
(7)
Deaggregation on the directivity can guide the selection of time histories in terms of
selecting forward directicity time histories vs neutral or backward directivity time histories.
Conclusions
Rupture directivity has not been included in most probabilistic seismic hazard
calculations. To accurately estimate the hazard from long period ground motions, directivity
should be directly included in the hazard analysis as one of the important sources of
variability of the long period ground motion. I believe that including rupture directivity will
soon become the standard of practice for computing the hazard for long period ground
motions near active faults.
References
Somerville, P. G., N. F. Smith, R. W. Graves. and N. A. Abrahamson (1997). Modification
of empirical strong ground motion attenuation relations to include the amplitude and
duration effects of rupture directivity, Seism. Res. Let, Vol. 68, 199-222.
QGa
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Directivity Model
Xcos(Theta)
Modified Somerville et al.
(1997) directivity model
0
0.05
0.1
0.15
0.2
0.25
0.3
0 102030405060708090
Ln(FN/Avg)
Theta
Somerville et
al. (1997)
FN/Average
Horizontal
Model
1a.
1b.
Figure 1. Modified Somerville et al. (1997) rupture directivity model.
QGa
15
10
5
0
0 102030405060708090100
Depth (km)
Distance (km)
Figure 2. Example of the variability in hypocenter location over the rupture surface for a single rupture
location. The heavy line defines the rupture area of an earthquake scenario, the circle indicates the center of
the rupture, and the stars indicate the range of hypocenters.
QGa
0.0001
0.001
0.01
0.1
1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Annual Probability of Exceedance
Spectral Acceleration (g)
Ave Horizontal without Directivity
Fault Parallel Component
Average Horizontal Component
Fault Normal Component
Figure 3. Effects of directivity on the hazard for T=3 seconds spectral acceleration for the new San
Francisco Bay Bridge.
Figure 4. Deaggregation of the hazard for a spectral period of 3.0 seconds at the 1500 year return period.
KCampbell@eqecat.com
To "Gilles Bureau" <gbureau@geiconsultants.com>
03/03/200510:12
AM
ee
john_barneich@geopentech.com,
kcampbell@absconsulting.com,
Nancy
_ Collins@urscorp.com,
bee
Subject Re: Correction for fault normal
I fault parallel effects
Gilles,
Note
that
there
is
an
error
in
the
strike-slip
equation
that
Norm
gives
in
his
paper
(personall
corom.,
2003).
The
equation
(in
different
format)
should
be:
(Embedded
image
moved
to
file:
pic03902.jpg)
Ken
Kenneth
W.
Campbell,
PhD
Vice
President
EQECAT
Inc
(503)
533-4359
(503)
533-4360
(fax)
kcampbell@eqecat.com
http://www.eqecat.com
"Gilles
Bureau"
<gbureau@geiconsu
Itants.com>
To
<kcampbell@absconsulting.com>,
03/03/2005
08:55
<KCampbell@eqecat.com>,
AM
<john_barneich@geopentech.com>,
<Phalkun_Tan@geopentech.com>,
<yoshi_moriwaki@geopentech.com>,
<Nancy_Collins@URSCorp.com>
<Paul_Somerville@URSCorp.com>
Subject
Re:
Correction
for
fault
normal
/
fault
parallel
effects
To
all:
Thank
you
for
the
paper
and
for
clarifying
this
situation.
I
have
deeply
appreciated
the
fast
response
from
Paul
and
Ken,
after
learning
one
was
on
Australia
and
the
other
in
Italy.
cc
Best
regards,
Gilles
Gilles
Bureau,
P.E.,
G.E.
Senior
Consultant
GEl
Consultants,
Inc.
2201
Broadway,
Suite
321
Oakland,
CA
94612-3017
510-835-9838
x
105
510-835-9842
(fax)
gbureau@geiconsultants.com
»>
<Nancy_Collins@URSCorp.com>
3/1/2005
5:07:18
PM
»>
Gentlemen:
Attached
is
the
Abrahamson
paper
of
which
Paul
speaks
below
(See
attached
file:
Abrahamson_6lCSZ.pdf)
Nancy
F.
Collins,
Project
Scientist
URS
Corporation
566
EI
Dorado
Street,
Suite
200
Pasadena,
CA
91101
(626)
449-7650;
FAX
(626)
449-3536
Forwarded
by
Nancy
Collins/Pasadena/URSCorp
on
03/01/2005
04:52
PM
Paul
Somerville
To:
KCampbell@eqecat.com,
robert_graves@urscorp.com,
03/01/2005
yoshi_moriwaki@geopentech.com,
PM
john_barneich@geopentech.com
<gbureau@geiconsultants.com>,
01:54
nancy_collins@urscorp.com,
cc:
"Gilles
Bureau"
kcampbell@absconsulting.com,
naa2@pge.com,
paul_somerville@urscorp.com
fault
normal/fault
parallel
Subject:
effects
Re:
Correction
for
Gilles
et
al.
Ken
has
correctly
described
the
situation.
My
assistant
Nancy
Collins
is
going
to
fax
you
the
paper
by
Norm
Abrahamson
that
describes
the
tapering
of
the
model
for
small
magnitude
and
large
distance.
Paul
I,
Paul
Somerville
To: KCampbell@eqecat.com, robert-.9raves@urscorp.com,
:td::~t-
nancy-collins@urscorp.com, yoshi_moriwaki@geopentech.com.
-,
-',
03/01/200501 :54 PM
john_barneich@geopentech.com
cc: "Gilles Bureau" <gbureau@geiconsultants.com>,
kcampbell@absconsulting.com, naa2@pge.com,
pauLsomerville@urscorp.com
Subject: Re: Correction for fault normal
I fault parallel effects
I+/s.o
t/-v
-j>
-PM
I~
UlVI
J
CUA.I
Gilles et al.
1/i-j-
79b-
9/9/
Ken has correctly described the situation.
My
assistant Nancy Collins is going to fax you the paper by
Norm Abrahamson that describes the tapering
of
the model for
small magnitude and large distance.
Paul
Paul G. Somerville
URS Corporation
566
EI
Dorado Street
Pasadena,
CA
91101-2560
Voice: (626) 449-7650; FAX: (626) 449-3536
email: PauLSomerville@urscorp.com
-KCampbell@eqecat.com
wrote: -----
To: "Gilles Bureau" <gbureau@geiconsultants.com>
From: KCampbell@eqecat.com
Date:
03/0112005
11
:42AM
cc: kcampbell@absconsulting.com, naa2@pge.com, pauLsomerville@urscorp.com
Subject: Re: Correction for fault
normal/fault
parallel effects
Gilles,
I was in Italy and unable to respond to your question before now. I have
carefully reviewed the 1997 SRL paper and I believe that I have made a
mistake in representing the directivity model in
my
CRC Handbook (and two
other chapters that I have written). Even though they refer to the
FN
to
FP factor in many places throughout the text, including the equations
themselves, the authors state that the coefficients listed in the tables
are for the FN to
AV
(average) components. I believe that I was confused
by the ambiguity in their statements and I apologize for the error.
Therefore, I believe that
my
Equation (5.106) should not have the 1/2 in
the first two terms, Furthermore, the last term (0) should also apply when
M > 6, according to the authors. I also neglected to put that constraint
in as well. Furthermore, since the FN and FP relationships are not
numerically constrained at M > 6 and Rrup > 50, I would suggest that a
magnitude and distance taper similar
to
the one Norm applied to the spatial
directivity term
(my
f1) should also be applied to my f2 term, except that
the taper should be applied between M
= 5.5 and 6.5, centered on 6.0.
Paul and/or Norm, can you please confirm this and respond to my taper
suggestion?
Ken
cc
Kenneth
W.
Campbell, PhD
Vice President
EQECAT
Inc
(503)
5334359
(503)
5334360
(fax)
kcampbell@eqecat.com
http://www.egecat.com
"Gilles Bureau"
<gbureau@geiconsu
Itants.com>
To
<kcampbell@absconsulting.com>,
02/24/200512:52 <naa2@pge.com>,
PM <pauLsomerville@urscorp.com>
Subject
Correction
for
fault normal 1
fault parallel effects
Gentlemen:
Greetings.
I am facing an issue with the use
of
the correction factor for fault normal
(FN)
I fault parallel effects (FP)
for
ground motion estimates based on
your attenuation equations.
Paul and Norm, in their 1997, paper talk on page 214 (Seismological
Research Letters Vol. 68, No.1) about fitting the strike-normal to
strike-parallel ratio y
(y
being defined as the natural logarithm
of
the
strike-parallel to strike normal ratio
at
a given period), with an equation
of
the form:
y
=cos 2 ?
[ci
+ c2 In(Rrup + 1) + c3(Mw -
6)]
However, elsewhere in the text and in Table 6 and 7
of
the 1977 reference,
the c coefficients are defined for the strike-normal to average ratio.
In
Chapter 5
of
the
CRe
Handbook (2003), Ken uses a similar equation
for
FN
(and specifically refers to Norm's 2000 model) as follows:
f2(Rrup, Mw,
?) =% (cos 2 ?) [c3 +
c4ln(Rrup
+ 1) + c5
(Mw
- 6)] [5.106]
The
c3, c4 and
c5
are defined in Table 5.25 (Campbell, 2003) and are the
very same values as c1, c2 and c3 in the aforementioned Table
7.
Hence, a factor % (half the fault-normal effects) has been introduced in
Equation 5.106. Equation [5.106] also provides an equal in amplitude but
opposite sign correction
(-1/2 etc.) for FP effects when compared with the
average estimates.
My
question is:
How
where the c coefficients developed? Do they relate FN to FP,
or
FN to
average? Is a 0.5 factor correctly applied by Ken, or does it result from
the language ambiguity regarding y in the 1977 paper?
Thank you all very much for clarifying how to correctly apply the FN
correction. Your help will be greatly appreciated.
Best regards
to
all three
of
you,
Gilles.
Gilles Bureau, P.E., G.E.
Senior Consultant
GEl Consultants, Inc.
2201
Broadway, Suite
321
Oakland,
CA
94612-3017
510-835-9838 x 105
510-835-9842 (fax)
gbureau@geiconsultants.com
... In near-fault conditions, two distinct displacement patterns may be observed as a consequence of the rupture process (Sommerville et al. [71]). The first displacement pattern associated with double-sided velocity pulses is generally observed in the fault normal component of strike-slip motions. ...
... In the response spectrum method, generally, an empirical model of rupture directivity effects that utilizes spectral amplification factors, such as those originally proposed by Somerville et al. [71], is considered. Somerville's model uses the length ratio (X = s/L) and width ratio (Y = d/W), respectively, for strike-slip and dip-slip faulting mechanisms. ...
... Abrahamson [2] has modified the model to saturate the directivity effect for X cos θ > 0.4 and to reduce directivity effects through the use of tapers for distances > 30 km and M < 6.5. Despite the presence of more recent models developed with far larger NGA-West 1 and NGA-West 2 datasets, the experience has been that in practice, the Somerville et al. [71] model in conjunction with the Abrahamson [2] modification continues to be applied to analyze directivity effects on response spectral ordinates (PEER, [57]). ...
... Ground motions recorded near a ruptured fault can be significantly different from the usual earthquake ground motions recorded further away from the seismic source. In the proximity of an active fault system, ground motions may be characterized by a high amplitude and longperiod distinctive pulse, which is concentrated in a narrow frequency band and is evident at the beginning of their velocity and displacement time histories (Bray and Rodriguez-Marek, 2004;Somerville et al., 1997). Nearfault ground motions with such pulses impose high input energy on structures at the onset of an earthquake and bring about severe structural damage (Bray and Rodriguez-Marek, 2004;Fang et al., 2018Fang et al., , 2021. ...
... Nearfault ground motions with such pulses impose high input energy on structures at the onset of an earthquake and bring about severe structural damage (Bray and Rodriguez-Marek, 2004;Fang et al., 2018Fang et al., , 2021. Forward-directivity is one of the most prominent characteristics of near-fault ground motions that can be observed when the rupture and slip direction relative to a site coincide, and a significant portion of the fault rupture propagates towards the site with a velocity close to the shear-wave velocity (Somerville et al., 1997). Forwarddirectivity effects generate short-duration ground motions with large amplitude and long-period two-sided velocity pulses (Bray and Rodriguez-Marek, 2004). ...
Article
Fling-step is one of the important characteristics of near-fault ground motions that is caused by a permanent static offset of the ground and appears as a one-sided velocity pulse and a large residual displacement at the end of the motion. Due to baseline errors in many ground motion records, they are processed (processing is a combination of baseline correction and filtering) before adding accelerograms to some earthquake databases whereby the residual displacements (i.e., the permanent static offsets) in the fling records are typically eliminated. It is not clear to what extent the record processing can affect the nonlinear responses of structures subjected to fling-step records. To address this issue, the current study is conducted to investigate the sensitivity of the nonlinear structural responses to record processing. To achieve this goal, the seismic responses of three code-conforming reinforced concrete (RC) special moment-resisting frames with different heights subjected to two versions of fling-step ground motions including a processed version that static offsets are removed, and a baseline-corrected version with static offsets preserved are evaluated. The findings of this assessment indicate that even though the processing procedure does not preserve the static offsets of the fling-step ground motions, the seismic responses of the structures to the processed records may resemble those obtained under only the baseline-corrected ground motions (with static offsets preserved).
... A distinct velocity pulse with a long period often characterizes near-fault earthquake ground motions. Such pulse is typically observed at the beginning of the fault-normal (FN) ground velocity time-history and has a probability of occurrence that depends on the site-tosource geometry, earthquake magnitude and other parameters [1][2]. Starting from the pioneer studies of Veletsos and Newmark [3] and Bertero et al. [4], the response of yielding singledegree-of-freedom systems subjected to near-fault earthquake ground motions has been extensively studied by many researchers [5-6 and references therein]. ...
... The term "directivity" as used in the literature is a catch-all term meant to describe all the factors that cause ground motion amplitudes and polarization to vary at a constant distance from an earthquake rupture (Spudich et al. 2013). In general, directivity produces larger amplitude velocity pulses in the ground motion time histories when rupture occurs towards the site of interest and smaller amplitude when rupture propagates away from the site (Somerville et al. 1997). The PSHA is the international standard practice on which the optimized seismic risk assessment is based and requires the state-of-the-art specification of its three key elements, (1) earthquake fault locations and sizes, their (2) seismic activity, and (3) the ground motion models (GMM). ...
Book
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Proceedings of the NorthQuake 2022 workshop on Earthquakes in North Iceland, held in Húsavík, North Iceland, 19-23 October, 2022.
... They may be determined empirically, by a regression of recorded ground motion, or theoretically, using seismological models to generate synthetic ground motions that account for the source, site, and path effects. Theoretical attenuation relations between various source parameters are used to estimate source parameters for earthquakes that have not yet occurred, or for which parameters of interest are unknown (e.g., Geller 1976;Oth et al. 2007;Somerville et al. 1997). The other approach uses empirical relations between source parameters compiled for a huge number of earthquakes (e.g., Wells and Coppersmith 1994). ...
... The pulse-like ground motions are related to the fault rupture direction [33,34]. For example, the pulse-like ground motions caused by the directivity effects and the fling step effects generally appear in the fault-normal and fault-parallel orientation, respectively [35,36]. ...
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The near-fault pulse-like ground motion is of practical importance since it tends to cause severer damage to structures than ordinary ground motion in engineering and helps characterize the seismic source and the kinematic characteristics of the geological fault in seismology. However, previous investigations mainly focus on single-pulse ground motion. As one of the particular seismic records in the near-fault earthquake, the multi-pulse ground motion is rarely considered caused by the absence of an effective identification method. Hence, a generalized continuous wavelet transform (GCWT) method is proposed by combining convolution analysis with evaluation parameters to facilitate wider studies on multi-pulse ground motion. In identification, the proposed method requires each pulse in the multi-pulse ground motion to satisfy the same criteria and excludes the effects of attenuation component. In methodology, the proposed method overcomes the limitations of the classical CWT method that requires a wavelet basis and provides a workable and flexible framework for pulse-like ground motion identification. Based on the method, single- and multi-pulse ground motions from two typical near-fault earthquakes on the PEER NGA-West2 database were identified. The effects of the pulse model and ground motion orientation on identification are discussed. Besides, the 5\% damped spectral velocity of multi-pulse ground motions potentially contain multiple peaks in the high-period range. This phenomenon implies that the risk would be underestimated for the response spectrum-based seismic hazards and risk analysis if the multi-pulse features are not, or are insufficiently taken into account.
... Such shortduration/long-period pulses are capable of imposing severe damage on structures. They emanate from the rupture zone and propagate toward the site at a velocity that is close to the shear wave velocity [1]. Furthermore, near-fault earthquake records are rich in high frequencies. ...
Article
This paper investigates the role of soil-structure interaction (SSI) in the confidence levels of setback steel moment-resisting frames (MRFs) for meeting the structural performance objectives, under the action of the components of pulse-like ground motions. To this end, a group of nine flexible-base 10-story steel MRFs with irregular configurations of the setback type, as well as a 10-story regular frame (for comparison purposes) were subjected to the components of 55 near-fault records containing forward directivity pulses. For investigating the role of near-and far-fault shakings, a group of 32 far-fault ground motions was also applied to the structures. The role of soil-structure interaction was considered by using the beam on nonlinear Winkler foundation theory (BNWF) and results were compared with those from the rigid-base frames in the previous study. The pulse components were extracted from the original records through wavelet analysis so that their capability for representing the original near-field excitation would be assessed to impose severe damage on structures. The pulse components were also categorized into four groups according to the pulse-to-structure fundamental period ratio (T PULSE /T STRUCTURE). The results reveal that SSI has beneficial and destructive effects on the performance-based confidence levels (PBCL) of all the studied structures under near-and far-fault records, respectively. The detrimental effects of SSI on PBCLs are more obvious for setback frames in comparison with the regular ones. Furthermore, using direc-tivity pulses instead of original near-fault motions does not seem reliable while evaluating the PBCL of flexible-base setback structures, unlike the regular MRFs. Finally, it is highly recommended to consider the T PULSE / T STRUCTURE ratio effects on the PBCL of flexible-base structures, especially for setback frames.
Article
Tall buildings suffer from low inherent damping and high flexibility. Therefore, a core‐outrigger system is often used to stiffen such buildings. A modified form, known as the damped outrigger system, wherein vertically oriented dampers are installed between outriggers and perimeter columns, has been recently developed to supplement the damping. This paper studies the efficacy of a viscously damped outrigger system through dynamic analysis of a 60‐story tall building subjected to nonconcurrent earthquake and wind excitations. Two ground motion sets (100 accelerograms) are used for the former and wind tunnel test data for the latter. Effects of three building parameters, namely, (i) the core‐to‐column stiffness ratio, (ii) the outrigger location, and (iii) the damper size, on the dynamic characteristics and seismic and wind responses are evaluated. Effects of damper nonlinearity on seismic and wind responses are also investigated considering energy‐equivalent nonlinear viscous dampers. Finally, the optimum values of these parameters are determined. For example, the optimum outrigger location is found to be between 0.6H$$ 0.6H $$ to 0.9H$$ 0.9H $$, where H$$ H $$ is the height of the building. The results also show that the damped outrigger system significantly outperforms the conventional one for seismic excitation, and it is very effective in reducing the wind‐induced floor accelerations, provided the parameters are chosen appropriately.
Article
Earthquake-induced strong near-fault ground motion is typically accompanied by large-velocity pulse-like component, which causes serious damage to slopes and buildings. Although not all near-fault ground motions contain a pulse-like component, it is important to consider this factor in regional earthquake-induced landslide susceptibility assessment. In the present study, we considered the probability of the observed pulse-like ground motion at each site (PP) in the region of an earthquake as one of the conditioning factors for landslide susceptibility assessment. A subset of the area affected by the 1994 Mw6.7 Northridge earthquake in California was examined. To explore and verify the effects of PP on landslide susceptibility assessment, seven models were established, consisting of six identical influencing factors (elevation, slope gradient, aspect, distance to drainage, distance to roads, and geology) and one or two factors characterizing the intensity of the earthquake (distance to fault, peak ground acceleration, peak ground velocity, and PP) in logistic regression analysis. The results showed that the model considering PP performed better in susceptibility assessment, with an area under the receiver operating characteristic curve value of 0.956. Based on the results of relative importance analysis, the contribution of the PP value to earthquake-induced landslide susceptibility was ranked fourth after the slope gradient, elevation, and lithology. The prediction performance of the model considering the pulse-like effect was better than that reported previously. A logistic regression model that considers the pulse-like effect can be applied in disaster prevention, mitigation, and construction planning in near-fault areas.
elsewhere in the text and in Table 6 and 7 of the 1977 reference, the c coefficients are defined for the strike-normal to average ratio
  • However
However, elsewhere in the text and in Table 6 and 7 of the 1977 reference, the c coefficients are defined for the strike-normal to average ratio.
(half the fault-normal effects) has been introduced in Equation 5.106. Equation [5.106] also provides an equal in amplitude but opposite sign correction (-1/2 etc.) for FP effects when compared with the average estimates
  • Hence
  • Factor
Hence, a factor % (half the fault-normal effects) has been introduced in Equation 5.106. Equation [5.106] also provides an equal in amplitude but opposite sign correction (-1/2 etc.) for FP effects when compared with the average estimates.
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