design maps for bridge structures were last updated over 10 years ago. Since
that time, several developments have taken place that should be considered when
updating the seismic design values used for bridge design. Among the issues to
be considered as part of this RNS are: (1) Updated mapped values; (2)
Alternative definitions for site coefficients; (3) Direct definition of
displacement spectra (including corner point period models); (4) and Response
spectra definition (i.e. value of NN for RotDNN).
Updated Mapped Values
Seismic Hazard Maps (NSHM) provide expected levels of ground shaking at
specified probabilities based on the best available science; which refers to
findings validated and accepted by the scientific community (Petersen et al.,
2014; 2015). Advances in the assessment of seismic hazards in the US are
considered by periodic updates to the NSHM conducted by the United States
Geological Survey (e.g., Algermissen and Perkins 1976; Frankel et al. 1996,
2000, 2002; Petersen et al. 1996, 2008, 2012, 2014). Such advances may include,
but are not limited to updated databases and earthquake catalogs, new source
and ground motion models, and new ground motion weighting information for
epistemic uncertainty characterization. These maps are instrumental to the
development of seismic-design regulation for buildings and critical
infrastructure such as bridges and nuclear power plants.
development of NSHM requires the implementation of appropriate ground motion
models (Bommer et al., 2010; Cotton et al., 2006; Petersen et al., 2014). In
2014, the next generation attenuation relationships research program (i.e.
NGA-West2) led by the Pacific Earthquake Research Center (PEER), provided a new
set of ground motion prediction equations (GMPEs) for shallow crustal
earthquakes in active tectonic regions (Bozorgnia et al., 2014). The intensity
measure (IM) provided by these GMPEs is SaRotD50, which was
originally proposed by Boore (2010), and refers to the median spectral
acceleration of the rotated orientation-independent, period-dependent combined
horizontal components (Shahi and Baker, 2012; Bozorgnia et al., 2014). Values
of SaRotD50 can be converted to maximum spectral acceleration
observed in any orientation of two-component horizontal ground motion (i.e. SaRotD100)
by implementing the model proposed by Shahi and Baker (2013, 2014). Such
conversion is desirable given that SaRotD100 is the IM adopted by
the US building code (Bozorgnia et al., 2014; Stewart et al., 2011). A
discussion on potential implications of using SaRotD100 versus SaRotD50
for seismic design is provided in later sections of this research needs
important feature of the 2014 updated NSHM (and the 2008 version) is that they
were generated for a reference site condition corresponding to a uniform firm
rock with a time-averaged shear wave velocity over the top 30 m (Vs30)
of 760 m/s (i.e., B/C site class boundary; Petersen et al., 2014). Typically,
site-amplification factors provided by the National Earthquake Hazards
Reduction Program (NEHRP) Provisions (e.g., BSSC 2009) are used in engineering
practice to accommodate the influence of local geologic conditions on the
expected ground shaking initially estimated for a reference rock site (Stewart
and Seyhan, 2013). For low intensity ground motions, site factors in current
NEHRP Provisions are derived empirically; while for stronger ground shaking,
they rely on numerical simulations of soil nonlinear behavior (Stewart and
Seyhan, 2013). The Provisions Update Committee of the Building Seismic Safety
Council has approved revised site factors, which appear in the 2015 version of
the NEHRP Provisions (Stewart and Seyhan, 2013). Such revisions followed the
identification of discrepancies between the NEHRP site factors and site
amplifications obtained from the NGA-West models (Stewart and Seyhan, 2013;
Seyhan and Stewart, 2014). The seismic design maps for bridge structures should
promptly adopt at least the aforementioned fundamental updates or consider
using the maps to be generated for various site classes which will be included
in the 2020 NEHRP Provisions. Moreover, practitioners and the scientific
community would benefit from further exploring the predictive power of other
site response parameters (Rodriguez-Marek et al., 1999; Stewart et al., 2013),
for example the fundamental period of the profile, depth to bedrock, etc.
Additional insights on this topic are provided in the following section.
NSHM considered information from external projects such as the NGA-East and a
new Electric Power Research Institute (EPRI) study on Central and Eastern US
(CEUS) ground motions as additional guidance to define weights for the characterization
of epistemic uncertainty in ground motion models applicable to stable tectonic
regions (Rezaeian et al., 2015). In future updates of the maps, NGA-East
advances and proposed ground motion models must be explicitly considered.
Likewise, site factors specific for CEUS should be developed to account for
unique effects of local geologic conditions on ground shaking in that region.
Other relevant aspects to contemplate in the development of future NSHM
versions include updated ground motion models for subduction zones (i.e.
NGA-subduction project) as well as induced seismicity (Petersen et al, 2014). The latter has proven
to be rather challenging to address given the unique characteristics of
earthquakes caused by fluid injection as compared to natural earthquakes
(Petersen et al., 2014). Recent research efforts aim to better characterize
these events and have provided preliminary insights on how to assess the
suitability of current GMPEs to estimate motions from induced earthquakes
(e.g., Atkinson and Assatourians, 2017).
multi-period design response spectra were suggested as part of the report on
issues and research needs from the 2015 NEHRP provisions, prepared by the
Provisions Update Committee of the National Institute of Building Sciences Building
Seismic Safety Council (Gosh et al., 2015). The development of multi-period
spectral parameter data and spectra also constitutes one of the main objectives
of Project 17. The idea is to cover a broad natural period range, while
accounting for relevant site conditions such as deep basin effects and the
nonlinear behavior of different types of soils.
Alternative Definitions for Site Coefficients
conditions can significantly affect the intensity of ground shaking as observed
in past earthquakes, such as the 1985 Mexico City (Seed et al., 1987) and 1989
Loma Prieta (Seed et al., 1991) earthquakes. Ground motion recordings from the
aforementioned seismic events have particularly led to improvements in the
assessment of site effects within seismic design recommended procedures. As
described in the previous section, site coefficients are used in practice to
adjust the ground shaking intensity estimated for reference rock conditions in
NHSM, in accordance with the characteristics of near surface deposits.
One of the
main areas that could benefit from further research is the assessment of site
amplification in the context of probabilistic seismic hazard assessment. The
first attempt to consider the influence of local geologic conditions in GMPEs
included a binary classification; rock versus soil. Nowadays, GMPEs and
building codes rely on values of Vs30 as a proxy for site response.
For instance, the proposed models in the NGA-West2 project include site terms
which are a function of Vs30 (Bozorgnia et al., 2014).
The effect of
site conditions on the characteristics of ground motions is a complex function
of multiple factors, such as the depth to bedrock (or the thickness of the soil
deposit), the stiffness of the materials, and damping. Due to soils’ nonlinear
behavior, seismic site response is also dependent on the intensity of ground
shaking. This nonlinear stress-strain behavior also varies with soil type
(e.g., Vucetic and Dobry, 1991; Darendeli, 2001; Menq, 2003). Cementation and
geologic age may also play a role on soils’ nonlinearity, but their effects
have not been rigorously considered yet (Rodriguez-Marek et al., 1999).
parameters have been considered in the literature as site response predictors,
mostly based on their ability to capture the aforementioned key characteristics
of the site. Values of Vs30 provide a measure of the stiffness of
near surface materials, while the natural period of the site combines the
effect of Vs and the soil thickness, site-specific κ values (i.e., κ0)
as proposed by Anderson and Hough (1984) can reflect near-surface attenuation
characteristics at a site (Ktenidou et al., 2013; 2015). The 1976 version of
the seismic code contemplated the natural period of the site as a site response
proxy (Rodriguez-Marek et al., 1999), but recent updates have chosen Vs30
instead. Most of the debate around such decision focuses on the ability of Vs30
to properly characterize site response because it is based only on information
from near-surface deposits.
and Pezeshk (2013) analyzed nonlinear site amplification factors using deep
soil profiles from the Mississippi Embayment and found that “the amplification
(or de-amplification) at various frequencies implied by the depth of sediment
was greater than that implied just by site classification based on Vs30
values”. Rodriguez-Marek et al. (1999) also noted that site coefficients and/or
site classification based solely on Vs30 overlook the potential
influence of the depth to bedrock. However, Stewart et al., (2013) did not
found any other site response proxy that could perform as well as Vs30
for GMPEs applications. Other researchers have investigated the predictive
capabilities of other parameters such as average velocities over different
depth ranges, depth to specific Vs horizons, maximum impedance ratio
(e.g., Kaklamanos et al., 2013), and even the topographic slope (Wald and
Allen, 2007). More recently, Rezaeian et al. (2015) identified κ (Anderson and
Hough, 1984) as a relevant parameter in ground motion modeling, especially for
stable tectonic regions such as CEUS. It would be worth exploring whether it is
the combination of different site proxies what could provide the answers to
some of the unresolved issues in the prediction of the effects of local geology
on ground motions.
Direct Definition of displacement spectra
In order to
facilitate the implementation of design approaches such as Direct-Displacement
Based Design, direct definition of the displacement spectral ordinates from
mapped values would be useful. Currently, engineers wishing to apply such an
approach convert values of pseudo-spectral to displacement response spectra by
dividing by the circular frequency squared. Direct definition of mapped values
that are consistent with ground motion models would eliminate the need to do
such calculations. However, obtaining such displacement values directly from
ground motions has proven to be a rather challenging task (e.g.,
Facciolli et al., 2004; Douglas 2006; Akkar and Bommer 2007, Campbell and Bozorgnia, 2008). For instance, the NGA-West2 project opted to
exclude peak ground displacement (PGD) as part of their model outcomes because
PGD values are more sensitive to frequency-filtering parameters and record
processing (Campbell and Bozorgnia, 2008).
as part of the definition of displacement spectra, additional investigation
into corner point period models should be conducted. Corner point period models
are absent from the LRFD and guide spec, although maps are available in ASCE-7.
However, the source of the mapped values in ASCE-7 is not well understood, and
the values possibly too high (up to 16 seconds). Currently, the EuroCode uses a
constant 2 second period, which is likely too low. Individual researchers
(Faccioli et al, 2004) have proposed magnitude dependent corner point period
models that fall in between those two extremes. These three approaches are
compared in Fig. 1 below (Priestley et al. 2007). Clearly, additional work is
needed in this area such that consensus may be reached.
Comparison of Corner Point Period Models (Priestley et al. 2007)
Response Spectra Definition
Over the last
decade, a debate has been underway in the earthquake engineering community with
regards to the appropriate definition for design response spectra (Stewart et
al., 2011). The essence of the argument relates to the representation of
bi-directional motion via response spectra.
In both the AASHTO LRFD Bridge Design Specifications as
well as the _AASHTO Guide Specifications
for LRFD Seismic Bridge Design _(SGS), response spectra are established by
defining spectral ordinates at 2 or 3 different periods from design maps
developed by USGS for a return period of 1000 years. The resulting spectra is
then adjusted for local site conditions, resulting in the final design spectra.
establishing the design maps for parameters such as Ss and S1, USGS has
traditionally relied upon probabilistic seismic hazard analysis which utilizes
ground motion prediction equations (GMPEs) defined by the geometric mean of the
two principle directions of recorded motion. In 2006, Boore introduced a new
rotation independent geometric mean definition termed GMRotI50 (Boore, 2006).
In 2010, Boore developed a new definition that does not rely upon the geometric
mean termed RotD50 spectra which can be generically expressed as RotDNN spectra
where NN represents the percentile (i.e. 50 is consistent with the median, 0
the minimum, and 100 the maximum). The NGA West2 project GMPEs utilized RotD50
spectra for the ground motion models, however, the 2009 NEHRP provisions
adopted RotD100 as the spectra for the design maps (Stewart et al., 2011).
In order to appreciate the impact of these
choices, a brief discussion of RotDNN spectra is warranted. As described in Boore (2010), for a given recording
station, the two as-recorded orthogonal-component time series are combined into
a single time series corresponding to different rotation angles, as shown in
Combination of Time Series to Generate Rotation Dependent Spectra
The process is repeated for a range of azimuths from 0°
to one rotation-angle increment less than 180°. If the rotation-angle increment
is θ, then there will be
< single time series, as
< corresponding response
spectra. For example, if θ=30°, then 6 single time series will be generated, as
well as 6 response spectra, as shown in
Example rotations for theta = 30
Once the response spectra for all rotation
angles are obtained, then the nnth
percentile of the spectral amplitude over all rotation angles for each period
is computed (e.g., RotD50 is the median value and RotD100 is the largest value
for all rotation angles). For example, at a given period of say 1 second, the
response spectra values for all rotation angles are compared, and the RotD100
value would be the largest value from all rotation angles, while RotD50 would
be the median. Figure 4 shows an example of the displacement spectra for RotD50
and RotD100 for a recorded ground motion.
Sample spectra for a recorded ground motion pair
As can be
seen in the example spectra of Figure 4, the RotD100 spectra represents a
substantial increase in demand when compared to the RotD50 spectra. The main
question facing the bridge community going forward is the appropriate selection
of response spectra definition. This can only be answered by conducting designs
to both the RotD50 and RotD100 spectra which would then be evaluated via
non-linear time history analysis. Such a study will require multiple bridge
configurations and multiple ground motions.
study by Palma and Kowalsky (2019) has aimed to investigate the impact of
response spectra definition on design of RC bridge columns. As of the writing
of this RNS, the study has focused only on SDOF systems, however, clear trends
have been observed which demonstrated that displacements, on average, are 20%
higher for structures designed to ROTD50 vs those designed to ROTD100. A
complete study on MDOF systems is essential before recommendations on
appropriate response spectra definition can be offered.
The written summary in this section refers to response spectra
definitions and its impact on seismic response. Boore et al. (2006) and Boore
(2010) introduced orientation-independent measures of seismic intensity from
two horizontal ground motions. Boore et
al. (2006) proposed two measures of the geometric mean of the seismic intensity,
which are independent of the in situ orientations of the sensors. One measure uses period-dependent rotation
angles to quantify the spectral intensity, denoted GMRotDnn. The other measure
is the GMRotInn, where I stands for period-independent. The ground-motion
prediction equations of Abrahamson and Silva (1997), Boore et al. (1997),
Campbell and Bozorgnia (2003), and Sadigh et al. (1997) have been updated using
GMRotI50 as the dependent variable.
Since more users expressed the desire to use the maximum spectral
response over all the rotation angles without geometric means, Boore (2010)
introduced the measures of ground shaking intensity irrespective of the sensor
orientation. The measures are RotDnn and RotInn, whose computation is similar
to GMRotDnn and GMRotInn without computing the geometric means.
With regards to impact on seismic response the opinion paper by
Stewart et al. (2011), and the work by Mackie et al. (2011) on impact of
incidence angle on bridge response are relevant. Specifically, Stewart et al.
(2011) noted the importance of computational analysis of structures (that had
not been done as of 2011) in proposing appropriate spectra definitions.
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