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# Numerical simulation of basin effects on long-period ground motion

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We simulate long-period (0-0.5 Hz) ground motion time histories for a suite of sixty scenario earthquakes (Mw 6.3 to Mw 7.1) within the Los Angeles basin region. Fault geometries are based upon the Southern California (SCEC) Community Fault Model, and 3D seismic velocity structure is based upon the SCEC Community Velocity Model. The ground motion simulations are done using 5 different 3D finite difference and finite element codes, and we perform numerous cross-check calculations to insure consistency among these codes. The nearly 300,000 synthetic time histories from the scenario simulations provide a resource for ground motion estimation and engineering studies of large, long-period structures, or smaller structures undergoing large, nonlinear deformations. By normalizing spectral accelerations to those from simulations performed for reference hard-rock models, we characterize the source-averaged effect of basin depth on spectral acceleration. For this purpose, we use depth (D) to the 1.5 km/s S velocity isosurface as the predictor variable. The resulting mean basin-depth effect is period dependent, and both smoother (as a function of period and depth) and higher in amplitude than predictions from local 1D models. The main requirement for the use of the results in construction of attenuation relationships is determining the extent to which the basin effect, as defined and quantified in this study, is already accounted for implicitly in existing attenuation relationships, through (1) departures of the average "rock" site from our idealized reference model, and (2) correlation of basin depth with other predictor variables (such as Vs 30).
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NUMERICAL SIMULATION OF BASIN EFFECTS ON LONG-PERIOD GROUND
MOTION
S. M. Day1, J. Bielak2, D. Dreger3, R. Graves4, S. Larsen5, K. B. Olsen1, A. Pitarka4, and L.
Ramirez-Guzman2
ABSTRACT
We simulate long-period (0-0.5 Hz) ground motion time histories for a suite of
sixty scenario earthquakes (Mw 6.3 to Mw 7.1) within the Los Angeles basin
region. Fault geometries are based upon the Southern California (SCEC)
Community Fault Model, and 3D seismic velocity structure is based upon the
SCEC Community Velocity Model. The ground motion simulations are done
using 5 different 3D finite difference and finite element codes, and we perform
numerous cross-check calculations to insure consistency among these codes. The
nearly 300,000 synthetic time histories from the scenario simulations provide a
resource for ground motion estimation and engineering studies of large, long-
period structures, or smaller structures undergoing large, nonlinear deformations.
By normalizing spectral accelerations to those from simulations performed for
reference hard-rock models, we characterize the source-averaged effect of basin
depth on spectral acceleration. For this purpose, we use depth (D) to the 1.5 km/s
S velocity isosurface as the predictor variable. The resulting mean basin-depth
effect is period dependent, and both smoother (as a function of period and depth)
and higher in amplitude than predictions from local 1D models. The main
requirement for the use of the results in construction of attenuation relationships is
determining the extent to which the basin effect, as defined and quantified in this
study, is already accounted for implicitly in existing attenuation relationships,
through (1) departures of the average “rock” site from our idealized reference
model, and (2) correlation of basin depth with other predictor variables (such as
Vs30).
Introduction
We apply 3D numerical modeling to improve understanding of the effects of sedimentary
basins on long-period ( ~2 seconds) earthquake ground motion. The study employs both finite
element (FE) and finite difference (FD) methods to compute ground motion from propagating
earthquake sources in the Southern California Earthquake Center (SCEC) Community Velocity
Model (CVM), a 3D seismic velocity model for southern California (Magistrale et al., 2000).
1Dept. of Geological Sciences, San Diego State University, San Diego CA 92182
2Dept. of Civil and Environmental Engineering, Carnegie-Mellon University, Pittsburgh PA 15213
3Berkeley Seismological Laboratory, University of California, Berkeley, Berkeley CA 94720
5Lawrence Livermore National Laboratory, Livermore CA 94550
Previous work (Day et al, 2001; 2003) documented the mathematical soundness of the five
simulation codes used for the project by comparing results from a set of test simulations. The
comparisons show that all five codes are accurate for the class of problems relevant to this study
(Day, 2003). These tests also demonstrated the validity of putting a lower threshold on the
velocity model to exclude S wave velocity values in the CVM that fall below 500 m/s. The tests
confirmed that imposing this threshold (for the sake of computational efficiency) had negligible
effects within the target bandwidth of 0-0.5 Hz. Validations of these numerical modeling
procedures using recorded strong ground motions for the 1994 Northridge, California,
earthquake are reported in Olsen et al. (2003).
For the current investigation, we compute long-period ground motion in the SCEC CVM
for a suite of 60 earthquake scenarios. The 3-component ground motion time histories from these
scenarios are saved on a grid of 1600 sites covering the Los Angeles region, including sites in the
Los Angeles, San Fernando, and San Gabriel basins, as well as rock sites in the intervening
areas. The results from the current study take 2 forms: (1) We have saved and archived a library
of time histories from the 60 scenarios. In cooperation with the SCEC Community Modeling
Environment project, these time histories are available online, through a web interface
specialized to engineering applications (http://sceclib.sdsc.edu/LAWeb). These long-period time
histories capture basin amplifications, rupture-propagation-induced directivity, and 3D seismic
focusing phenomena. They are suitable for the engineering analyses of large, long-period
structures, and smaller structures undergoing large, nonlinear deformations. (2) The results of the
simulation suite have been analyzed to estimate response spectral amplification effects as a
function of basin depth and period. The resulting mean response has been characterized
parametrically and provided to the Next Generation Attenuation (NGA) project to guide
development of attenuation relations in the empirical (NGA-E) phase of the project.
Earthquake Scenarios
We model sources on ten different faults, or fault configurations (for example, the Puente
Hills fault is modeled in 3 different segmentation configurations). For each fault, we simulate 6
sources, using combinations of 3 different static slip distributions and 2 hypocenter locations.
These are kinematic simulations: rupture velocity, static slip, and the form of the slip velocity
function are all specified a priori.
The areal coverage for the 3D models is the 100 km x 100 km region outlined by the green
box in Figure 1. In all simulations, the boundaries of the computational domain (i.e. absorbing
boundaries) lie at or outside of this area and extend to a depth of at least 30 km. For the uniform
grid FD modelers, a grid spacing of 200 m was used. The FE grid uses a variable element size,
with near-surface elements as small as 30 m in dimension.
We use the 10 faults listed in Table 1 for the scenario calculations. The surface
projections of these faults are also shown in Figure 1. The longitude and latitude coordinates in
this table refer to the geographic location of the top center of the fault, that is, the point on the
surface that is directly above the midpoint of the top edge of the fault. Strike, dip and rake
follows Aki and Richards' (1980) convention. Length, width and depth are all given in km. The
depth refers to the depth below the surface of the top edge of the fault (0 corresponding to a
surface-rupturing event).
For each of the fault geometries, we generate 3 random slip distributions, as realizations
of a stochastic model, for use in the simulations. The slip distributions are generated following
some empirical rules for the size and distribution of asperities as given by Somerville et al.
(1999). The slip values on the fault are drawn from a uniformly distributed random variable, then
spatially filtered to give a spectral decay inversely proportional to wavenumber squared, with a
corner wavenumber at approximately 1/L, where L is fault length. Finally, the slip values are
scaled to the target moment of the scenario. The two hypocenter locations are defined as follows
for each fault: Hypocenter 1 is located at an along-strike (AS1) distance of 0.25 of the fault length
and at a down-dip (DD1) distance of 0.7 of the fault width (measured within the fault plane from
the top edge of the fault, not the ground surface). Hypocenter 2 is located at an along strike (AS2)
distance of 0.75 of the fault length and at a down-dip (DD2) distance of 0.7 of the fault width.
Figure 1. Map of scenario events and model region. See Table 1 for fault names
and event magnitudes.
The slip velocity function for each simulation is an isosceles triangle with a base of
duration Tr. The value of Tr is magnitude dependent and given by the empirically derived
expression (Somerville et al., 1999):
log10(Tr) = 0.5(Mw + 10.7) + log10(2.0 x10–9) , (1)
where log10 is base 10 logarithm and Mw is moment magnitude. Rupture velocity is constant for
all faults and all slip models. This value is set at 2.8 km/s. The rupture starts at the hypocenter
and spreads radially outward from this point at the specified velocity. The simulated duration for
each scenario is 80 seconds.
All simulations use the SCEC CVM, Version 2, except for modifications described below
to impose a lower limit on the velocities and add anelastic attenuation. The unmodified model is
described in Magistrale et al. (2000). The SCEC model is modified as follows: Replace the
SCEC model S velocity with the value 500 m/s whenever the SCEC model value falls below 500
m/s. Whenever this minimum S velocity is imposed, the P wave velocity is set equal to 3 times
the S velocity (1500 m/s in this case). Density values follow the SCEC model without
modification. The quality factors for P and S waves, respectively, Qp and Qs, are set to the
preferred Q model of Olsen et al. (2003).
The 3-component time histories are saved on a 2 km x 2 km grid covering the inner 80
km x 80 km portion of the model area. No filtering is applied to the output. The result is 1600
sites (4800 time histories) for each scenario simulation. For all 60 scenarios, and all sites, we
compute response spectral acceleration (Sa), for 5% damping, as a function of period, for each
component of motion. This is done for 26 periods in the range 2-10 seconds: spectral
acceleration is computed at 0.2 second intervals between 2 and 5 second, and at 0.5 second
intervals between 5 and 10 seconds.
Table 1. List of Fault Rupture Scenarios
Reference Simulations
To aid us in quantifying the effect of sedimentary basins on the computed ground
motions, we perform several auxiliary, or “reference,” simulations. For each of the 10 faults, we
select one rupture scenario, and repeat that simulation using the same source model, but
replacing the SCEC CVM with a horizontally stratified model. The stratified reference model
corresponds to an artificially high-velocity, unweathered hard-rock site. This reference velocity
model was constructed by laterally extending a vertical profile of the SCEC CVM located at (–
118.08333, 34.29167), in the San Gabriel Mountains. As noted, surface S velocities are
artificially high (3.2 km/s) in the resulting model, since this part of the SCEC model does not
account for a weathered layer. The purpose of the reference simulations is solely to provide a
normalization for the results from the simulations done in the full SCEC CMV, as an
approximate means of isolating basin effects from source effects.
Response Spectral Amplifications
Basin amplification effects result from interaction of the wavefield with basin margins,
and depend in a complex, poorly understood manner on period, source location, source distance,
basin geometry, sediment velocity distribution, and site location within the basin. The 60
scenarios provide synthetic data that can be used to improve our understanding of these effects.
We take an initial step in this direction by attempting to isolate the effects of period and local
basin depth. To isolate these 2 effects, we average over sources. As response spectral values vary
much more between ruptures on different faults than between ruptures on a given fault, we have
computed averages using only 1 of the 6 scenarios from each fault, giving us a 10-event subset of
the simulations. This subset misses a small amount of the variability in basin response present in
the full 60-event suite, but allows us to work with spectral values normalized to the reference
structure, without requiring 60 reference-structure simulations. Tests using a small number of
additional events confirm that source effects have been adequately removed by this procedure.
Method
We first bin the sites according to the local basin depth D at a site, with Dj denoting the
depth at site j. For this purpose, we define the depth D to be the depth to the 1.5 km/s S wave
velocity isosurface. Note, however, that in the SCEC CVM, the depths of different S velocity
isosurfaces are strongly correlated, and therefore very similar results are obtained using the 1.0
or 2.5 km/s isosurface instead of the 1.5 km/s isosurface. The binning is represented through a
matrix W. We define Nbin bins by specifying depths
Dq
bin
, q=1, . . . Nbin, at the bin centers, spaced
at equal intervals
!D
(i.e.,
Dq
bin == q!1 2
( )
"D
, and then form W,
Wqj =
1 if Dq
bin ! "D2
( )
#Dj<Dq
bin +"D2
( )
0 otherwise
$% & ' & . (2) For consistency with most empirical attenuation relations, we work with response spectral values averaged over the two horizontal components. For the ith event and jth site, we form the ratio , where Saij (P k) is the absolute spectral acceleration (averaged over horizontal components) from SCEC-CVM event i at site j and period Pk, and Saij ref (P k) is the corresponding quantity for the corresponding reference-model event. Then we form the source-averaged basin response factor B(Dq, Pk) by averaging over all Nsite sites (Nsite=1600), and over all Nev events, where in this case Nev is 10: B(Dq,P k)=Nev Wqj j=1 Nsite ! " #$%
&
'
(1
Wqj Saij (P
k)Saij
ref (P
k)
j=1
Nsite
!
i=1
Nev
!
. (3)
Results
Figure 2 summarizes the results of this procedure for (200 m bins). The upper frame
shows B as a function of depth and period. The lower frame shows basin amplification calculated
by the same procedure, but replacing the spectral acceleration ratio
Saij (P
k)Saij
ref (P
k)
at each
site by the vertically-incident plane-wave amplification factor for that site. The latter factors
were computed using a plane-layered structure specific to each site, and corresponding to the
SCEC-CVM shear wavespeed and density depth-profiles directly beneath that site. The main
results from Figure 2 are the following: (1) Source-averaged basin amplification is period-
dependent, with the highest amplifications occurring for the longest periods and greatest basin
depths. (2) Relative to the very-hard rock reference structure, the maximum amplification is
about a factor of 8. (3) Compared with 1D theoretical predictions, the 3D response is in most
cases substantially higher. (4) The 3D response is also smoother, as a function of depth and
period, than is the 1D prediction, since laterally propagating waves in the former smooth out the
resonances present in the latter.
Figure 2. Top: Basin amplification versus depth and period, calculated from 3D simulations.
Bottom: Basin amplification calculated by same procedure, but replacing the 3D results with 1D
plane-wave amplification factors calculated using the local 1D wavespeed and density profiles
(from the SCEC CVM) at each of the 1600 sites.
Figure 3 presents the results in the form of amplification curves for each of 6 periods. For
depths in the range of roughly 500-1000 m, amplification decreases with period. This is, at least
qualitatively, in agreement with expectations from 1D theory: shallow sediments will have
diminished effect as the wavelength becomes long relative to sediment depth. For depths
exceeding about 1000 m, amplification increases with period. This is a 3D effect: higher-mode
resonances present in the 1D case are smoothed out by lateral scattering, so that the longer-
period resonances dominate.
Figure 3. Basin amplification as a function of depth to 1.5 km/s S wave isosurface.
Parametric Model
It is useful to have a simple functional form that captures the main elements of the
period- and depth-dependent basin amplification behavior observed in the simulations. One
purpose of such a representation is to provide a functional form for representing basin effects in
regression modeling of empirical ground motion data. We constructed a preliminary
representation of this sort to provide immediate guidance to the NGA development team. Our
approximate representation,
!
B D,P
( )
takes the following form:
!
B(D,P)=a0(P)+a1(P) 1 !exp(D300)
[ ]
+a2(P) 1 !exp(D4000)
[ ]
, (4a)
where
ai(P)=bi+ciP, i=0,1,2
, (4b)
The 6 parameters bi, ci were calculated in a two-step procedure. Separate least squares fits at
each period Pk of
!
B D,P
k
( )
to B(Dq,Pk) gave individual estimates of the ai(Pk) values for each
period Pk. Then parameters bi and ci, for each i=0,1,2, were obtained by least-squares fitting of
these 26 individual ai(Pk) estimates. The resulting values are
b0 = –1.06, c0 = 0.124,
b1 = 2.26, c1 = –0.198, (4c)
b2 = 1.04, c2 = 0.261.
The resulting amplification curves are shown in Figure 4. These expressions, despite their
simplicity, represent the mean predictions of the numerical simulations quite well, and can serve
as a starting point for modeling basin effects in empirical studies. In particular, they provide, in
simple form, a physical basis for extrapolation of empirical models to periods greater than 2 or 3
seconds, where reliable data on basin effects are extremely scarce.
Figure 4. Parametric model
!
B
(dashed curves) fit to basin amplification curves B (solid curves)
derived by averaging 3D simulations.
Figure 5 shows the root mean square residual of
Saij (P)Saij
ref (P)
, relative to
!
B D,P
( )
, as
a function of period. That is, the figure depicts R, where
R2P
k
( )
=Nev Wqj
j=1
Nsite
!
"
#
$% & ' (1 Saij (P k)Saij ref (P k)(! B Dj,P k ( ) ) *+ , 2 j=1 Nsite ! i=1 Nev ! . (5) The residuals decrease systematically with period. This period-dependence is what one would expect on the basis of simple physical arguments. Short-period waves are subject to short- wavelength variations due to local focusing and interference effects. Very long-period waves, in contrast, represent oscillations that are coherent over large scale lengths and are influenced principally by large-scale averages of the seismic velocity structure. Figure 5. Root-mean-square residual of spectral acceleration amplification, relative to predictions from parametric model. Discussion and Conclusions We characterize the source-averaged effect of basin depth on spectral acceleration using depth (D) to the 1.5 km/s S velocity isosurface as the predictor variable. The resulting mean basin-depth effect is period dependent, and both smoother (as a function of period and depth) and higher in amplitude than predictions from local 1D models. For example, relative to a reference hard-rock site, sites with D equal to 2.5 km (corresponding to some of the deeper L.A. basin locations) have a predicted mean amplification factor of approximately 5.5 at 2 s period, and approximately 7.5 at 10 s period. The basin amplification estimates described in this report are intended to guide the design of functional forms for use in attenuation relationships for elastic response spectra. In particular, they should be useful guides for extrapolating the period-dependence of basin terms to periods longer than a few seconds, where empirical data provide little constraint. More direct, quantitative use of the results may become possible in the future, however. The main requirement is that we first carefully assess the extent to which the basin effect, as defined and quantified in this study, is already accounted for implicitly in existing attenuation relationships, through (1) departures of the average “rock” site from our idealized reference model, and (2) correlation of basin depth with other predictor variables (such as Vs30). A preliminary assessment of the reference model bias is presented in Day et al. (2005). They find that the reference-model simulations under-predict the rock regression model of Abrahamson and Silva (1997) by a factor of 2 at long period (5 seconds). They argue that at the long periods considered, both source details and Vs30 will have minimal effects, and that this factor of 2 is likely representative of a seismic velocity shift (between the average engineering rock-site and the reference model) extending to depths of the order of half a kilometer or more. The correlation of basin effects with Vs30 is discussed by Choi et al. (2005), who propose data analysis procedures for separating these effects. Acknowledgments This work was supported by Pacific Earthquake Engineering Research (PEER) Center Lifelines Program (Tasks 1A01, 1A02, and 1A03), the National Science Foundation under the Southern California Earthquake Center (SCEC) Community Modeling Environment Project (grant EAR-0122464), and by SCEC. SCEC is funded by NSF Cooperative Agreement EAR- 0106924 and USGS Cooperative Agreement 02HQAG0008. References Abrahamson, N. A., and W. J. Silva (1997). Empirical response spectral attenuation relations for shallow crustal earthquakes, Seism. Res. Lett. 68, 94-127. Aki, K., and P. G. Richards (1980). Quantitative Seismology, Theory and Methods, W. H. Freeman and Co., New York. Choi, Y., J. P. Stewart. And R. W. Graves (2005). Empirical model for basin effects accounts for basin depth and source location, Bull. Seism. Soc. Am., Vol. 95, 1412-1427, doi: 10.1785/0120040208. Day, S. M., J. Bielak, D. Dreger, R. Graves, S. Larsen, K. Olsen, and A. Pitarka (2001). Tests of 3D elastodynamic codes: Final report for Lifelines Project 1A01, Pacific Earthquake Engineering Research Center. Day, S. M., J. Bielak, D. Dreger, R. Graves, S. Larsen, K. Olsen, and A. Pitarka (2003). Tests of 3D elastodynamic codes: Final report for Lifelines Project 1A02, Pacific Earthquake Engineering Research Center. Day, S. M., J. Bielak, D. Dreger, R. Graves, S. Larsen, K. Olsen, and A. Pitarka (2005). 3D ground motion simulation in basins: Final report for Lifelines Project 1A03, Pacific Earthquake Engineering Research Center. Magistrale, H., S. M. Day, R. Clayton, and R. W. Graves (2000). The SCEC southern California reference three-dimensional seismic velocity model version 2, Bull. Seism. Soc. Am., 90, S65-S76. Olsen, K. B., S. M. Day, and C. R. Bradley (2003). Estimation of Q for long-period (>2 s) waves in the Los Angeles Basin, Bull. Seism. Soc. Am., 93, 627-638. Somerville, P.G., K. Irikura, R. Graves, S. Sawada, D. Wald, N. Abrahamson, Y. Iwasaki, T. Kagawa, N. Smith and A. Kowada (1999). Characterizing crustal earthquake slip models for the prediction of strong ground motion, Seism. Res. Lett. 70, 59-80. ... Linear SSI analysis using the DRM was performed in LS-DYNA and results can be found in Bolisetti and Whittaker [8]. The DRM has been successfully used for large-scale SSI simulations in computational seismology [15,40,41,44,45,47] and can be used for site-response and SSI analyses such as those presented in this paper. However, because the scope of this study is limited to vertically propagating shear waves, the direct method is used here Fig. 2. ... Article Soil-structure interaction (SSI) analysis is generally a required step in the calculation of seismic demands in nuclear structures, and is currently performed using linear methods in the frequency domain. Such methods should result in accurate predictions of response for low-intensity shaking, but their adequacy for extreme shaking that results in highly nonlinear soil, structure or foundation response is unproven. Nonlinear (time-domain) SSI analysis can be employed for these cases, but is rarely performed due to a lack of experience on the part of analysts, engineers and regulators. A nonlinear, time-domain SSI analysis procedure using a commercial finite-element code is described in the paper. It is benchmarked against the frequency-domain code, SASSI, for linear SSI analysis and low intensity earthquake shaking. Nonlinear analysis using the time-domain finite-element code, LS-DYNA, is described and results are compared with those from equivalent-linear analysis in SASSI for high intensity shaking. The equivalent-linear and nonlinear responses are significantly different. For intense shaking, the nonlinear effects, including gapping, sliding and uplift, are greatest in the immediate vicinity of the soil-structure boundary, and these cannot be captured using equivalent-linear techniques. ... Bimaterial fault interfaces also influence ground motion during an earthquake [Ben-Zion, 2001]. Therefore, this result is vital to assess ground motion level from potential earthquake scenarios mainly on the EPGF not only because this fault still remains a major seismic threat for the nearby cities in southern Haiti [Calais et al., 2010;Douilly et al., 2015;Prentice et al., 2010;Symithe et al., 2013] but also because sedimentary basin could trap the energy and significantly amplify the ground shaking [Day et al., 2006;Olsen, 2000;Wald and Graves, 1998]. As an example, Komatitsch et al. [2004] used a spectral element method to simulate ground motion in the Los Angeles basin and their results uncover large amplification within the basin for their 3-D simulation with respect to their 1-D case. ... Article Full-text available We investigate 3D local earthquake tomography for high-quality travel time arrivals from aftershocks following the 2010 M7.0 Haiti earthquake on the Léogâne fault. The data were recorded by 35 stations, including 19 ocean bottom seismometers, from which we selected 595 events to simultaneously invert for hypocenter location and 3D Vp and Vs velocity structures in southern Haiti. We performed several resolution tests and concluded that clear features can be recovered to a depth of 15 km. At 5 km depth we distinguish a broad low velocity zone in the Vp and Vs structure offshore near Gonave Island, which correlate with layers of marine sediments. Results show a pronounced low velocity zone in the upper 5 km across the city of Léogâne, which is consistent with the sedimentary basin location from geologic map. At 10 km depth, we detect a low velocity anomaly offshore near the Trois Baies fault and a NW-SE directed low velocity zone onshore across Petit-Goâve and Jacmel, which is consistent with a suspected fault from a previous study and that we refer to it in our study as the Petit-Goâve-Jacmel fault (PGJF). These observations suggest that low velocity structures delineate fault structures and the sedimentary basins across the southern peninsula, which is extremely useful for seismic hazard assessment in Haiti. ... The Southern California Earthquake Center (www.scec.org) and its research team have made significant progress over the course of the past decade at simulating rupture and the resultant wave fields for large magnitude earthquakes in Southern California [e.g., Taborda and Bielak (2011), Day et al. (2006) and Restrepo et al. (2011. These petascale simulations can predict site-specific wave fields, including body and surface waves, at frequencies of 1 Hz and lower. ... Article The Nuclear Regulatory Commission (NRC) regulation 10 CFR Part 50 Appendix S requires consideration of soil-structure interaction (SSI) in nuclear power plant (NPP) analysis and design. Soil-structure interaction analysis for NPPs is routinely carried out using guidance provided in the ASCE Standard 4-98 titled “Seismic Analysis of Safety-Related Nuclear Structures and Commentary”. This Standard, which is currently under revision, provides guidance on linear seismic soil-structure-interaction (SSI) analysis of nuclear facilities using deterministic and probabilistic methods. A new appendix has been added to the forthcoming edition of ASCE Standard 4 to provide guidance for time-domain, nonlinear SSI (NLSSI) analysis. Nonlinear SSI analysis will be needed to simulate material nonlinearity in soil and/or structure, static and dynamic soil pressure effects on deeply embedded structures, local soil failure at the foundation-soil interface, nonlinear coupling of soil and pore fluid, uplift or sliding of the foundation, nonlinear effects of gaps between the surrounding soil and the embedded structure and seismic isolation systems, none of which can be addressed explicitly at present. Appendix B of ASCE Standard 4 provides general guidance for NLSSI analysis but will not provide a methodology for performing the analysis. This paper provides a description of an NLSSI methodology developed for application to nuclear facilities, including NPPs. This methodology is described as series of sequential steps to produce reasonable results using any time-domain numerical code. These steps require some numerical capabilities, such as nonlinear soil constitutive models, which are also described in the paper. Article Full-text available The main objective of this study is to understand the dependency of basin amplification on-site and source parameters employing high computational numerical simulations. This study mainly addresses the effect of fault dip, size of the basin, site classification, and position of the basin on wave amplification. Two dip angles are considered, 7 and 9 degrees in this study to estimate the factor of amplification. Amplifications observed at the basin center and basin edge station for three different sizes of the basin are analyzed. Simulation results obtained from three different models with the ASCE site class C, D, and E basin sediment specifications are compared. To analyze the effect of basin relative position on amplification, we studied a model with two different basins embedded in bedrock, back and forth of the fault. This study observed multiple peaks at different time periods in response spectra drawn to amplification ratio versus time periods. Data Full-text available This file provides the list of references for Technical report MCEER-15-0002. Article Strong ground motions from earthquakes are shaped by the energy radiated from the fault and by the Earth structure in the region. The finite size of the fault and the spatial and temporal details of its slip during the earthquake have first-order effects on nearby ground motions. The near-surface geology, including structures such as basins and mountain ranges, contribute in many complex ways to modify the amplitude, duration, and frequency content of the radiated energy. The test of understanding all these phenomena is the ability to combine their effects, using the representation theorem, to generate realistic synthetic ground motions. Conference Paper The first fundamental complete plane strain (CPS) problem for an infinite one-dimensional hexagonal quasicrystals body containing a doubly-periodic array of cracks in periodical and aperiodical plane is considered. Employing the superposition principle of force, the complete plane strain state, which is a special three-dimensional elastic system, is resolved into two linearly independent two-dimensional (plane) elastic systems, one is the generalized plane strain state, and another is the longitudinal displacement state. Using a technique that based on the complex potential function of Kolosov and Muskhelishvili, solving this problem are transferred into seeking analytic functions which fit certain boundary value problems. Furthermore, the general representation for the solution is constructed, under some general restrictions the boundary value problem is reduced to a normal type singular integral equation with a Weierstrass zeta kernel along the boundary of cracks, and the unique solvability of which is proved. Conference Paper Seismic analysis of nuclear power plants is routinely carried out using guidance provided in “Seismic Analysis of Safety-Related Nuclear Structures and Commentary (ASCE 4, 1998).” This document, which is currently under revision, provides detailed guidance on linear seismic soil-structure-interaction (SSI) analysis of nuclear facilities using deterministic and probabilistic methods. However, a new Appendix in ASCE 4-2013 (draft) is being added to provide guidance for nonlinear time domain SSI analysis. Nonlinear seismic SSI analysis may be needed to model the following behaviors: material nonlinearity (in soil and/or structure), rocking or sliding of the foundation, static and dynamic soil pressure effects on deeply embedded structures, local soil failure at the foundation-soil interface, nonlinear coupling of soil and pore fluid, nonlinear effects of gaps between the surrounding soil and the embedded structure, and seismic isolation systems. Guidance is provided in Appendix B on development of finite element meshes, earthquake ground motion input, nonlinear constitutive models, assessment of analysis results, and verification and validation procedures. This paper provides an overview of the proposed Appendix B to ASCE 4. The principles of nonlinear SSI analyses and technical bases for the recommendations on modeling, earthquake ground input motion and constitutive models are discussed. Software codes are available to perform nonlinear SSI analysis such as the NRC ESSI simulator (Jeremic et al. 2012), and commercial codes such as ABAQUS, LS-DYNA, and ANSYS. The paper provides a brief overview of how to apply the guidance in Appendix B of ASCE 4 to perform nonlinear SSI analysis utilizing these codes. Time-domain soil-structure interaction analysis for nuclear facilities. Available from: https://www.researchgate.net/publication/269873946_Time-domain_soil-structure_interaction_analysis_for_nuclear_facilities. Article Full-text available The so called “valley effect” relates to the typical seismic response of basin shaped bedrock filled by quaternary sediments. It is an aspect of the renown “local seismic effect” that shall be taken into account when dealing with microzoning studies. Several experimental surveys and numerical simulations performed worldwide over the last 40 years, confirmed that valley responses under seismic excitations show common features in various geological contexts as far as the sedimentary valleys (e.g. alluvial and lacustrine plains), the intermountain valleys (e.g. alpine valleys) and graben shaped basins. Such features mainly depend on the basin geometry, referred to as the shape ratio SR, and the sediment and basin impedance contrast IC. Although researchers agree on the prominent role of local seismic effects for interpreting erratic damages caused by seismic shaking in urbanized areas, no fully shared strategies have been identified for taking into account valley effect within microzoning studies. In this paper, a numerical simulations on three models of trapezoidal shaped basins have been performed. These valley models relate to sediments and basins detected within the Tuscany Region territory during the VEL project. Results, in terms of the amplification index$\text{ F }_{\mathrm{A}}\$ F A have been provided. Three “valley effect charts” for various SR and IC values have been propose for taking into account the local seismic effects due to the basin amplifications within microzoning maps.
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We propose a model for the effect of sedimentary basin depth on long- period response spectra. The model is based on the analysis of 3-D numerical simulations (finite element and finite difference) of long-period 2-10 s ground motions for a suite of sixty scenario earthquakes (Mw 6.3 to Mw 7.1) within the Los Angeles basin region. We find depth to the 1.5 km/s S-wave velocity isosurface to be a suitable predictor variable, and also present alternative versions of the model based on depths to the 1.0 and 2.5 km/s isosurfaces. The resulting mean basin-depth effect is period dependent, and both smoother (as a function of period and depth) and higher in amplitude than predictions from local 1-D models. The main requirement for the use of the results in construction of attenuation relationships is determining the extent to which the basin effect, as defined and quantified in this study, is already accounted for implicitly in existing attenuation relationships, through (1) departures of the average "rock" site from our idealized reference model, and (2) correlation of basin depth with other predictor variables (such as Vs30). DOI: 10.1193/1.2857545
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We simulate 0- to 0.5-Hz 3D wave propagation through the Southern California Earthquake Center seismic velocity reference model, version 2, for the 1994 Northridge earthquake in order to examine the effects of anelastic attenuation and amplification within the near-surface sediments. We use a fourth-order finite-difference staggered-grid method with the coarse-grained frequency-independent anelastic scheme of Day and Bradley (2001) and a variable slip distribution from kinematic inversion for the Northridge earthquake. We find that the near-surface material with S-wave velocity (Vs) as low as 500 m/sec significantly affects the long-period peak ground velocities, compared with simulations in which the S-wave velocity is constrained to 1 km/sec and greater. Anelastic attenuation also has a strong effect on ground-motion amplitudes, reducing the predicted peak velocity by a factor of up to 2.5, relative to lossless simulations. Our preferred Q model is Qs/Vs = 0.02 (Vs in meters per second) for Vs less than 1–2 km/sec, and much larger Qs/Vs (0.1, Vs in meters per second) for layers with higher velocities. The simple model reduces the standard deviation of the residuals between synthetic and observed natural log of peak velocity from 1.13 to 0.26, relative to simulations for the lossless case. The anelastic losses have their largest effect on short-period surface waves propagating in the Los Angeles basin, which are principally sensitive to Qs in the low-velocity, near-surface sediments of the basin. The low-frequency ground motion simulated here is relatively insensitive to Qp, as well as to the values of Qs at depths greater than roughly that of the 2-km/sec S-wave velocity isosurface.
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Empirical relationships are developed to predict amplification factors for 5% damped response spectral acceleration that incorporate basin response effects. The parameters considered are depth to the 1.5 km/sec shear-wave isosurface ( z 1.5 ) as well as the location of the source beneath or outside the perimeter of the basin in which the site is located. Sites located in a basin overlying the source are denoted as having coincident source and site basin locations (cbl) and are differentiated from distinct source and site basin locations (dbl). Amplification factors for cbl and dbl sites are evaluated from simulated data (developed by others) and strong-motion data. Amplification factors derived from strong-motion recordings are taken as residuals of rock attenuation relations coupled with amplification factors for shallow-site conditions. Models relating amplification to z 1.5 were developed separately for the cbl and dbl data groups. The results indicate that the use of basin models is generally worthwhile for periods T ≥ 0.75 sec. At those long periods, residuals are significantly sensitive to z 1.5 for cbl but not for dbl. The standard deviation is also reduced for long periods to an extent that the standard deviations for long and short periods are similar.
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Using a database of 655 recordings from 58 earthquakes, empirical response spectral attenuation relations are derived for the average horizontal and vertical component for shallow earthquakes in active tectonic regions. A new feature in this model is the inclusion of a factor to distinguish between ground motions on the hanging wall and footwall of dipping faults. The site response is explicitly allowed to be non-linear with a dependence on the rock peak acceleration level.
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We describe Version 2 of the three-dimensional (3D) seismic velocity model of southern California developed by the Southern California Earthquake Center and designed to serve as a reference model for multidisciplinary research activities in the area. The model consists of detailed, rule-based representations of the major southern California basins (Los Angeles basin, Ventura basin, San Gabriel Valley, San Fernando Valley, Chino basin, San Bernardino Valley, and the Salton Trough), embedded in a 3D crust over a variable depth Moho. Outside of the basins, the model crust is based on regional tomographic results. The model Moho is represented by a surface with the depths determined by the receiver function technique. Shallow basin sediment velocities are constrained by geotechnical data. The model is implemented in a computer code that generates any specified 3D mesh of seismic velocity and density values. This parameterization is convenient to store, transfer, and update as new information and verification results become available.
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Empirical relationships are developed to predict amplification factors for 5% damped response spectral acceleration that incorporate basin response effects. The parameters considered are depth to the 1.5 km/sec shear-wave isosurface (z 1.5) as well as the location of the source beneath or outside the perimeter of the basin in which the site is located. Sites located in a basin overlying the source are denoted as having coincident source and site basin locations (CBL) and are differentiated from distinct source and site basin locations (DBL). Amplification factors for CBL and DBL sites are evaluated from simulated data (developed by others) and strong-motion data. Amplification factors derived from strong-motion recordings are taken as residuals of rock attenuation relations coupled with amplification factors for shallow-site conditions. Models relating amplification to z 1.5 were developed sepa-rately for the CBL and DBL data groups. The results indicate that the use of basin models is generally worthwhile for periods T 0.75 sec. At those long periods, residuals are significantly sensitive to z 1.5 for CBL but not for DBL. The standard deviation is also reduced for long periods to an extent that the standard deviations for long and short periods are similar.
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This new edition of the classic text by Aki and Richards has at last been updated throughout to systematically explain key concepts in seismology. Now in one volume, the book provides a unified treatment of seismological methods that will be of use to advanced students, seismologists, and scientists and engineers working in all areas of seismology.
Tests of 3D elastodynamic codes: Final report for Lifelines Project 1A01
• S M Day
• J Bielak
• D Dreger
• R Graves
• S Larsen
• K Olsen
• A Pitarka
Day, S. M., J. Bielak, D. Dreger, R. Graves, S. Larsen, K. Olsen, and A. Pitarka (2001). Tests of 3D elastodynamic codes: Final report for Lifelines Project 1A01, Pacific Earthquake Engineering Research Center.