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Research Paper
Earthquake Spectra
1–27
ÓThe Author(s) 2023
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DOI: 10.1177/87552930231179493
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Seismic response prediction
using intensity measures:
Graphite nuclear reactor core
model case study
Tansu Gokce, M.EERI , Rory E White, Adam J Crewe,
Matt Dietz, Tony Horseman, and Luiza Dihoru
Abstract
Seismic response analyses of structures have conventionally used the peak ground
acceleration or spectral acceleration as an intensity measure to estimate the engi-
neering demand parameters. An extensive shaking table test program was carried
out on a quarter-sized advanced gas-cooled reactor (AGR) core model to investigate
the global dynamic behavior of the system with degraded graphite components while
subjected to seismic excitation. Evaluation of the most widely considered intensity
measures, with respect to their capability for predicting the seismic response of an
AGR core–like structure, is performed. Twenty intensity measures of 16 distinct
seismic input motions are formulated and correlated, with experimental measure-
ments describing the dynamic response of the reactor core model. Linear correla-
tions are constructed for each intensity measure to statistically determine the best
metric for predicting the seismic response of the AGR core model, and statistical
analysis indicates that the acceleration spectrum intensity (ASI) is best suited to char-
acterize and describe the structural demand of an AGR core-like structure when
subjected to seismic loading. A response prediction tool is developed, based on
empirically derived linear correlations, to estimate column distortions and determine
the critical input motion for further experimental and numerical studies. Statistical
analysis indicates that predicted column distortions, compared against direct experi-
mental displacements, are significant, repeatable, and accurate.
Keywords
Advanced gas-cooled reactor, seismic testing, earthquake response, stacked column,
seismic resilience
Date received: 27 September 2022; accepted: 12 May 2023
Earthquake and Geotechnical Engineering Research Group, Faculty of Engineering, University of Bristol, Bristol, UK
Corresponding author:
Tansu Gokce, Earthquake and Geotechnical Engineering Research Group, Faculty of Engineering, University of Bristol,
University Walk, Bristol BS8 1TR, UK.
Email: tansu.gokce@bristol.ac.uk
Introduction
In 1978 and 1979, a series of low-magnitude earthquakes occurred near the Virgil C.
Summer Nuclear Power Station in South Carolina, USA, which exceeded the operating
basis earthquake (OBE) design response spectrum at frequencies greater than 10 Hz.
Similarly, an earthquake near the Perry Plant in Ohio also exceeded the OBE and safety
shutdown earthquake (SSE) design response spectrum in 1986 (Reed and Kassawara,
1990). After these seismic events, the Electrical Power Research Institute (EPRI) initialized
a research framework developing a rational criterion for determining when the OBE design
limit has been exceeded at a nuclear power plant (NPP). This was essential to determine
when further action is required in accordance with US Nuclear Regulatory Commission
(USNRC) Reg. 10 CFR 100, Appendix S (USNRC, 1973). In EPRI (1988), multiple para-
meters, typically used in the literature to characterize earthquake ground motions, were
reviewed to assess the validity of each intensity measure (IM), for example, peak ground
acceleration (PGA) and Arias intensity. A new IM was proposed, the cumulative absolute
velocity (CAV), to quantify the damage threshold of earthquakes for NPPs. EPRI (1988)
recommends a two-level criterion for determining when an earthquake motion at the site
has exceeded the OBE at an NPP. This constitutes a qualitative check of the response spec-
trum of the input ground motion followed by quantifying the CAV. The computational
algorithm for CAV was further refined and standardized as CAV
STD
in EPRI (1991) to
exclude the contribution of non-damaging portions of long-duration, small-amplitudes
acceleration records that extend for a long time after the strong ground motion.
Nguyen et al. (2020) performed a series of time history analysis for both non-isolated
and base-isolated numerical models of an NPP structure and monitored the floor accelera-
tion, floor displacement, and shear deformation of the lead–rubber bearings. Many IMs
were evaluated to identify which best estimated the seismic damage of the NPP structure
being studied. A series of non-linear time history analyses were performed to determine
the efficient IMs representative of seismic performance and fragility evaluation of the reac-
tor containment building (RCB) in the advanced power reactor 1400 (APR1400). Nguyen
et al. (2021) identified the acceleration spectrum intensity (ASI) measure as one of the best
metrics for RCB structures.
In March 2011, the Great East Japan Earthquake resulted in the automatic shutdown
of 11 reactor units operating at the time of the earthquake in Fukushima Daiichi. The seis-
mic damage indicating parameters of the acceleration time-history measurements at the
plant sites were calculated and analyzed by Grant et al. (2017). It is suggested that the cur-
rent CAV
STD
threshold may be conservative by more than a factor of 10, indicating the
potential for raising the threshold without introducing any significant additional risk to
the US nuclear fleet. Reducing the conservatism in the shutdown criterion can prevent
costly and unnecessary plant shutdowns due to non-damaging ground motions.
Campbell and Bozorgnia (2011) proposed a new IM, characterizing the CAV as
CAV
DP
, which is an altered version of CAV
STD
. A prediction algorithm was developed
between CAV
DP
, and the geometric mean horizontal component of CAV, referred to as
CAV
GM
. Furthermore, a relationship between the CAV
DP
, Japan Meteorological Agency
and modified Mercalli (MMI) instrumental seismic intensities were empirically derived to
correlate CAV
DP
with the qualitative descriptions of damage in the corresponding macro-
seismic intensity scales (Campbell and Bozorgnia, 2012).
Advanced gas-cooled reactors (AGRs) are the United Kingdom’s second-generation
reactor design and generate approximately 20% of the electricity supplied in the United
2Earthquake Spectra 00(0)
Kingdom. Construction of the first AGR nuclear power station began in 1965, with seven
further AGR stations being commissioned between 1976 and 1989 (Nonboel, 1996). The
seismic assessment, performance, validation, and serviceability of these NPPs are critical
factors for their operational lifespan. The AGR core reactors are now reaching the end of
their operational lives (Bonivento et al., 2008). An AGR core consists of thousands of
interlocking hollow cylindrical graphite bricks. The 16-sided reactor core is formed from
vertical fuel, control, and cooling gas channels, which are typically composed of a stack of
11 graphite bricks and allow for the insertion of the fuel assemblies, the control rods, and
the circulation of the carbon dioxide coolant. The graphite bricks not only provide struc-
tural integrity to the core but also act as the reaction moderator (Bradford and Steer,
2008). The bricks are interconnected with graphite keys to provide the core with signifi-
cant stability, while maintaining the vertical alignment of the columns of stacked bricks.
The reactor core contains 332 fuel channels and is surrounded by a graphite reflector and
a steel shield. The graphite structure is held in position by a steel restraint tank that sur-
rounds the graphite. This is supported by a system of steel plates (Nonboel, 1996).
Due to the nuclear reaction process, neutron and gamma radiation is generated, which
bombard the graphite affecting its mechanical characteristics and properties, such as
reducing the mass, stiffness, and tensile and compressive strengths (Young et al., 2019).
The decay of such mechanical properties of the graphite bricks may result in crack propa-
gation (Steer, 2005). This is one of the key issues that determine the operational life of a
nuclear station (Bonivento et al., 2008). To ensure that reactors are still safe for operation,
the reactor core is routinely monitored during planned outages. The cracking of graphite
bricks due to fast neutron irradiation, temperature, and radiolytic oxidation observed dur-
ing inspections of AGRs at later ages in their lifespan could potentially lead to increased
distortion in the fuel and control rod channels during seismic events. The vertical align-
ment of these channels is important for the safe operation, maintenance, and shutdown of
the core by maintaining the ability to insert control rods (Cowell and Steer, 2017). To sup-
port the seismic assessments of the graphite cores, an extensive experimental program was
carried out in the Earthquake and Large Structures (EQUALS) Laboratory at the
University of Bristol. A multi-layered array (MLA), experimentally simulating/represent-
ing a quarter-sized AGR core-like structure, was designed, developed, and tested under
seismic excitations to provide validation evidence for the computational methods used in
the seismic assessments. A number of build configurations with different types and distri-
butions of cracked brick were tested to simulate/represent potential degraded core states.
In this study, the correlations between the seismic input motions and dynamic responses
of instrumented stacked brick columns, representing a 50% cracked configuration (a close
to end-of-life scenario) of a quarter-sized AGR reactor core–like model, are constructed
using direct experimental measurements. Twenty earthquake IM metrics are evaluated,
qualitatively and quantitatively, comparing each one to identify which measure best char-
acterizes and represents the structural demand of the AGR core model structure. A soft-
ware tool is developed to predict the column displacement deformations of stacked brick
columns typically housed in an AGR core structure when subjected to seismic loading.
After an earthquake, the tool could be used to make a rapid determination of the degree
of severity of the seismic event in terms of assessing the response of the AGR reactor core
and determining the damage potential.
This article aims to answer the following research questions: (1) Which seismic/earth-
quake IM, currently used in the literature and in practice, best characterizes the structural
Gokce et al. 3
damage/demand of an AGR core–like structure? and (2) Is it possible to predict the global
column displacement distortions/profiles using empirically derived linear prediction maps?
MLA of AGR core and the shake table tests
Description of the test specimen
To study the seismic performance of a degraded AGR, a quarter-sized model of an AGR
core, namely the MLA, was developed in the EQUALS Laboratory at the University of
Bristol. The design, construction details, keying system, and rocking features of the MLA
can be found in Dihoru et al.’s study (2017). Miniaturized sensor technology was employed
to capture and monitor the intricate nonlinear dynamical response of the MLA when sub-
jected to dynamic loading. The acquired experimental measurements have been used to
verify and validate software tools that are capable of predicting AGR core behavior.
The MLA has dimensions of 2.497 m 32.497 m 31.731 m (b 3w3h) and a mass
of 8.5 tons. It comprised eight layers representing the inner 10 octagonal rings of an AGR
core. The base layer is fixed to a restraint frame. The outer octagonal ring, compromised
of restraint bricks, is fastened to the restraint frame, which is build-up as a practically rigid
aluminum Warren truss (Figure 1). The restraint frame has a natural frequency above
35 Hz, so it behaves rigidly at the seismic test frequencies (0.01–25 Hz) and transmits the
motion of the underlying shaking table to the internal components both horizontally
(across the base) and vertically (up the walls). The bricks in the nine central rings and the
top seven layers of the MLA are interconnected through a radial keying system. In an
AGR core, this allows free radial movement of the bricks during thermal expansion and
contraction of the surrounding steel structures and provides reaction forces to lateral
movement once the clearances between the keys and the keyways have been taken up. The
MLA is designed to reproduce the dynamic behavior of the lower eight layers of an AGR
core–like structure. For the MLA, the model fuel bricks are referred to as lattice bricks,
while the keyed and unkeyed interstitial bricks are referred to as interstitial and filler
bricks, respectively. A plan view of the MLA is displayed in Figure 2a. A vertical section
and detail are also shown to demonstrate the keying system and integration of the intersti-
tial and lattice columns in Figure 2b. The MLA model comprises 301 interstitial and 284
lattice columns. A lattice column comprises seven vertically stacked lattice bricks on top
of each other. Six of these are full-sized bricks, while the top layer brick is two-thirds in
Figure 1. Quarter-sized reactor core model: (a) restraint frame and (b) MLA model on the shaking table.
4Earthquake Spectra 00(0)
brick height. Interstitial brick columns are stacked alternately with individual filler and
interstitial bricks to form the full interstitial column height. Seven interstitial bricks, six
full-size filler bricks, and a hybrid brick, a slightly shorter filler brick due to the geometric
constraints of the base plate, make up a single interstitial column.
Graphite bricks age and degrade because of neutron irradiation, temperature, and radi-
olytic oxidation. This ultimately causes bricks to crack later in the life of AGR cores which
are starting to approach the end of their design lifespan. To include the effects of cracking
in the seismic response of the quarter-sized MLA model, various types of cracked brick
models were developed. These simulate different severities in cracking that a brick may
exhibit over time, to cover a broad range of cracking scenarios. The designed and devel-
oped cracked brick types used in the MLA are (1) doubly crack bricks (DCBs), (2) sym-
metric/asymmetric triply cracked bricks (TCBs), and (3) symmetric/asymmetric quadruply
cracked bricks (QCBs). These are shown in Figure 3.
The quarter-sized MLA model allows the testing of a variety of degradation scenarios
including various types of cracked bricks observed during the routine inspection of the
core. In this study, a 50% cracked array configuration was used as an extreme end-of-life
scenario. A total of 570 cracked bricks were used for this MLA build configuration. The
cracked bricks comprised of 341 DCBs, 157 TCBs, and 72 QCBs which were distributed
over layers 4–7. This corresponds to a breakdown of 50% intact bricks, 30% DCBs, and
20% multiply cracked bricks installed over the active layers of the array.
Input motions
A number of seismic input motions were applied to the MLA during the experimental cam-
paign of the 50% cracked array build configuration. The site-specific earthquake motions
Figure 2. MLA dimensions: (a) plan view and (b) layout of interstitial and lattice columns.
Gokce et al. 5
primarily considered in the computation of input motions have a 10
–4
probability of occur-
rence per annum. They are referred to as Hinkley Point B (HPB), Heysham 2/Torness
(HYB/TOR), and Hartlepool (HRA). These are a few of the several AGR core power sta-
tions located in the United Kingdom. The secondary response acceleration time histories
have been extracted at the base level of the reactor cores from the finite element models,
which include a representation of the pre-stressed concrete pressure vessel (PCPV) and the
soil structure interface. The time history of the resulting secondary response at the core
boundary was quarter-scaled by reducing the time intervals by half to comply with the
quarter scale model geometry. The HPB input motion, with 0.4 g peak acceleration, was
scaled to forcing amplitudes of 0.5–0.7 g to investigate the core response for higher seismic
excitation levels. An input motion which is compatible with the required response spectrum
(RRS) in BS EN 1998-1 (European Committee for Standardization (CEN), 2004) is also
included.
Principia Mechanica Ltd (PML) spectra were developed for use as broad-band spectra
in the design of UK critical facilities by PML in 1981. They are developed from the knowl-
edge of the anticipated PGA at the site and the ground conditions. For this study, this
motion has been anchored to the 10
–4
per annum probability of exceedance PGA values.
PML input motions are computed to investigate a range of core boundary excitations
based on the updated Hinkley Point B and Hunterston B (HNB) power plants’ PCPV. A
range of different properties for the springs and dampers representing the rock–structure
interaction (RSI), bearings pads, and fill are considered. The lower-bound (LB), best-
estimated (BE), and upper-bound (UB) properties were assigned for all three parameters
and used to calculate the secondary response at the base of the reactor core. The INT-1
motion was computed from the UB properties for RSI and bearing parameters and the LB
properties for the fill. In addition to this, some factored input motions were computed for
the UB model by increasing the stiffness with a coefficient and decreasing the damping
properties. In total, 16 input motions were used to excite the MLA to provide the responses
considered for analysis and seismic characterization in this study. These input motions are
representative of the motions used for AGR seismic assessments, and they contain key fea-
tures which are detrimental to the array, promoting key disengagement. The motions are
summarized in Table 1, providing the associated PGA, velocity, and displacements of the
input excitation.
Figure 3. Degraded crack brick types used in the experimental multi-layered array: (a) doubly cracked,
(b) triply cracked, and (c) quadruply cracked.
6Earthquake Spectra 00(0)
The acceleration response spectra (5% damping), S
a
, of the input motions over the fre-
quency bandwidth of 0.1–100 Hz are shown in Figure 4. Frequencies greater than 10 Hz
are considered to be high frequency in EPRI (2007, 2017). Furthermore, OBE exceedance
is only checked for spectral values below 10 Hz in Regulatory Guide 1.166 (USNRC,
1997), recognizing that energy content above 10 Hz is non-damaging. In this study, 10 Hz
is therefore considered as the threshold between low- and high-frequency content on the
spectral acceleration (SA) plot, so the selected input motions have been grouped as
containing low- and high-frequency content and high-frequency content only. This wide
range of input motions, their associated frequency content, and observed peak accelera-
tions enabled the exploration of the fundamental dynamic behavior of the AGR core
model. Moreover, they provided good insight into the response mechanics of the physical
system.
Table 1. Input motion data set
# Input motions PGA (g) PGV (mm/s) PGD (mm)
1 Revised HPB 0.14 46.9 4.7
2 RRS (Eurocode compatible) 0.41 129.5 12.0
3 HYB/TOR at support skirt 0.45 81.9 7.0
4 HRA Core Support Plate 0.46 78.9 12.6
5 HPB 10
–4
0.41 92.5 4.5
6 HPB 10
–4
(scaled at 0.5 g) 0.56 127.1 6.3
7 HPB 10
–4
(scaled at 0.6 g) 0.64 152.2 8.1
8 HPB 10
–4
(scaled at 0.7 g) 0.72 179.4 9.8
9 PML—LB 0.12 61.8 4.6
10 PML—BE 0.19 50.7 4.8
11 PML—UB 0.26 49.4 4.1
12 PML—INT1 0.22 58.4 4.4
13 PML—1.7UB 0.39 55.5 3.7
14 PML—2UB 0.39 48.4 3.7
15 PML—4UB 0.25 43.5 3.7
16 PML—8UB 0.26 36.7 3.9
PGA: peak ground acceleration; PGV: peak ground velocity; PGD: peak ground displacement; HPB: Hinkley Point B;
RRS: required response spectrum; HYB/TOR: Heysham 2/Torness; HRA: Hartlepool; PML: Principia Mechanica Ltd.
(a) (b)
Figure 4. Response spectra of the input motions: (a) low- and high-frequency content and
(b) high-frequency content only.
Gokce et al. 7
Measurement systems
Eight interstitial and six lattice columns were instrumented to record the 6-degrees-of-free-
dom (DoF) motion of the vertically stacked brick columns acquiring measurements at the
brick-to-brick interfaces under seismic loading. For this purpose, several interface mea-
surement techniques and systems were developed (Dihoru et al., 2021; Oddbjornsson
et al., 2021). An interstitial column comprises 7 filler bricks and 7 interstitial bricks, consti-
tuting 13 brick-to-brick interfaces. These interfaces are denoted J0x and J5x for the top of
the interstitial and the top of the filler bricks, respectively, where x is the layer number (see
Figure 2b). To enable measurement of the interstitial brick interface motion in 6 DoF, a
set of two bi-axial Hall effect sensors were mounted in three corners on both the top and
bottom faces of each filler brick. Opposing magnets were installed in the corresponding
three corners of the interstitial bricks. Such a configuration, consisting of six bi-axial Hall
effect sensors and three magnets, produces sensor voltages that can be converted into
6 DoF of the filler-to-interstitial brick interface (Figure 5). Refer Oddbjornsson et al.’s
study (2021) for full details on the calibration procedure and evaluation of 6 DoF motions
at an interstitial brick interface.
A lattice column consists of seven active lattice bricks corresponding to seven brick-to-brick
interfaces, J02-J08, in Figure 2b. Four linear conductive potentiometric transducers were
employed on the bottom face of the instrumented lattice bricks to measure the relative interface
motions. This configuration enables the evaluation of the local roll and pitch rotational motion
at each brick interface using the single-axis displacement recorded by the linear conductive
potentiometers (LCP) (Figure 6). Mean vertical displacement measurement is computed using
all four LCP sensors.
The local brick interface displacement measurements are converted into a global frame
of reference, corresponding to the shaking table coordinate system illustrated in Figure 2,
using an Euler mechanics procedure. This converts the rotational contributions, at each
brick interface, to translational axes/DoFs (x, y, z) and sums these up in the column. This
enables the column shape distortion profiles to be evaluated. Refer White et al.’s study
(2022) for details on the column shape distortion profile procedure.
Each filler and interstitial brick in the instrumented interstitial columns was also
equipped with a three-axis accelerometer, while each lattice brick in the instrumented lat-
tice columns contained two off three-axis accelerometers at the top and bottom of the
bricks (see Figures 5 and 6). The acceleration recordings of the bricks were used to explore
the dynamic properties of the array.
Figure 5. Instrumented interstitial and filler bricks: (a) instrumented interstitial brick with magnets and
(b) instrumented filler brick with micro-data acquisition system.
8Earthquake Spectra 00(0)
Shake table tests
The shaking table tests of the MLA model with 50% cracked bricks in layers 4–7 were con-
ducted on the 6 DoF shaking table in the EQUALS at the University of Bristol. The seis-
mic input motions given in Table 1 were applied as a single-axis motion in 0°,45°, and 90°
directions, corresponding to x, combined x–y and y input motions (see Figure 2 for the glo-
bal shaking table coordinate reference system), to acquire experimental results for compar-
ison against finite-element model outputs such as brick-to-brick displacements and column
profiles. The shaking table acceleration input motion was tracked using seven uni-axial
Setra 141a accelerometers (S) that were mounted on the top surface of the shaking table.
The direction and location of the accelerometers are given in Figure 2. The main objectives
of the experimental studies were to reduce the uncertainty in the numerical modeling tools
developed, while also investigating the interactions between keys and keyways.
In this article, only the x-axis input motion results and analyses are presented, but simi-
lar results were obtained for the input motions in the other directions.
The experimental results of one instrumented interstitial and one lattice column are pre-
sented in this article. Forensic analysis and investigation of each column are performed
and presented. Both columns, which are marked in red in Figure 2, are located in the cen-
tral region of the MLA, where the peak column/brick displacements were measured.
Observations in other instrumented columns, moving from the middle of the array toward
the boundaries, exhibited decreasing displacement amplitude responses. The typical instru-
mented lattice column displacement profile and the interface time histories along the col-
umn height are illustrated in Figure 7 for HPB 10
–4
input motion in the x-direction with a
forcing peak acceleration amplitude of 0.41 g.
The maximum column shape displacement envelopes, for both the instrumented lattice
and interstitial columns, are displayed in Figure 8 for all 16 seismic excitations in the x-
direction. The maximum relative displacement amplitudes of the lattice and interstitial col-
umns were observed between layers six and seven for all input motions. Note that cracked
bricks are located in the MLA between layers 4–7, promoting large displacement responses
of the vertically stacked brick columns.
The stacked brick column displacement response occurs in the same direction as the
input seismic excitation. This corresponds to an input seismic excitation in the x-direction
resulting in significant dynamic responses of the columns in the x-direction. The column
Figure 6. Lattice brick instrumentation configuration: (a) LCP positions at the bottom face of the brick
and (b) side view of the instrumented brick.
Gokce et al. 9
responses in the y-direction were very much smaller. Residual displacement analysis was
performed for each test, comparing the displacements of the columns at the end of the
recorded time histories relative to their initial conditions. The maximum residual displace-
ments in both interstitial and lattice columns were approximately 0.05 mm, corresponding
to 0.5% of the maximum relative displacements. This indicates that the brick columns are
effectively self-centering and return to their initial position after being subjected to seismic
loading.
(a) (b)
Figure 7. Lattice column displacement/distortion profile for HPB 10
–4
x-direction input motion with a
peak acceleration amplitude of 0.41 g: (a) max amplitude envelope curves of the column displacements
representing the column distortion profiles and (b) displacement time histories of the column interface
displacements.
(a) (b)
Figure 8. Column shape displacement profiles on x-direction: (a) lattice column displacements and
(b) interstitial column displacements.
10 Earthquake Spectra 00(0)
IMs
As part of the seismic assessment of an NPP, rapid determination of the degree of severity
of an earthquake is crucial. Ground motion data are required to evaluate whether the plant
must shut down as a result. The reactor core is one of the most important components of
an NPP. Therefore, it is vital to identify the optimal earthquake IM that best characterizes
the seismic loading and the reactor core’s response. This is necessary for efficient and reli-
able decision-making following a seismic event.
Seismic analysis procedures and seismic design codes have commonly used the PGA
and/or SA as the seismic IM for use in the prediction of structural response. These IMs are
also commonly used in the seismic fragility assessment of critical infrastructures such as
bridges, dams, tunnels, and so on. However, in recent decades, questions have been raised
regarding the reliability of the use of these measures and the information they provide
when considered alone (Cao and Ronagh, 2014a, 2014b; Chen and Wei, 2013; Ghayoomi
and Dashti, 2015; Yaghmaei-Sabegh, 2012; Zhang et al., 2015). As an example of this phe-
nomenon, the peak relative interface displacements of lattice and interstitial columns that
were recorded in the shake table tests of the MLA are given in Figure 9 for PM-LB, PM-
BE, and PM-8UB seismic excitations. The peak displacement for the lattice column was
measured as 5.64 mm at the interface between layers 6 and 7 (i.e., interface J06 in Figure
2b) for PM-LB input motion, which has a 0.12 g PGA value. The corresponding peak dis-
placements at the same interface were recorded as 5.52 and 2.45 mm for PM-BE and PM-
8U, which have 0.19 and 0.26 g PGA values, respectively. Similarly, peak displacements in
the interstitial column were recorded as 6.35, 6.25, and 2.89 mm for PM-LB, PM-BE, and
PM-8UB input motions at interstitial interface J07 (see Figure 2b), respectively. This is a
significant indication that the MLA response depends not only on the amplitude of the
input motion but also on the frequency content.
Seismic IMs represent the characteristics of the earthquake-induced ground motion and
can be used as a tool in predicting the response of a structure and any associated damage.
In this study, 20 scalar IMs are considered and evaluated using direct experimental mea-
surements of the input and output responses of the AGR core model. The IM descriptions,
summarized in Table 2, are evaluated to determine the IM which is best capable of accu-
rately predicting the seismic response of the AGR core model.
As these IMs are scalar quantities, linear correlations are constructed, using the experi-
mental measurements, quantifying the correlation for each linear prediction model. These
are presented in Figure 10 for the interface between Layers 6 and 7 (J06) in the instrumen-
ted lattice brick column. Each individual seismic input motion represents a single data
point; hence the 16 input motions create 16 data points which are used to construct the lin-
ear correlations. The displacement values used are the peak displacement values of the col-
umn distortion profile, as illustrated in Figure 9. The correlation coefficient (r) value is
quantified for each linear prediction map constructed and is presented in Figure 10, repre-
senting the accuracy of the IM prediction.
Some of these IMs only consider specific frequency band ranges, such as the ASI and
effective peak acceleration (EPA), which are calculated from 2 to 10 Hz, and the Housner
spectrum intensity, which is calculated from 0.4 to 10 Hz. The first natural frequency of
the quarter-scaled AGR core model (T
1
) was identified as approximately 5 Hz using the
acceleration records from the sensors, which were embedded in the instrumented bricks
(see Figures 5 and 6). Since this fell within the IM bandwidths above, these frequency
ranges were considered to be acceptable. However, if applying these IMs to the full-scale
Gokce et al. 11
AGR reactor, it might be necessary to update these limits, based on the natural frequency
of the full-sized structure.
To identify the relationship between the seismic response of the MLA and earthquake
IMs, Pearson’s correlation coefficient is used. The correlation coefficient given by Ang and
Tang (2007) is defined in Equation 1:
r=P
n
i=1
(xi
x)(yi
y)
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
P
n
i=1
(xi
x2)P
n
i=1
(yi
y)2
sð1Þ
Table 2. Selected intensity measures
No Earthquake intensity measure Definition Reference
1 Peak ground acceleration PGA =maxja(t)j
2 Peak ground velocity PGV =maxjv(t)j
3 Peak ground displacement PGD =maxjd(t)j
4 Peak velocity and
acceleration ratio
vmax
amax
=maxjv(t)j
maxja(t)j
Kramer (1996)
5 Root mean square of
acceleration Arms =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
ttot Ð
ttot
0
a(t)2dt
sDobry et al. (1978)
6 Root mean square
of velocity Vrms =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
ttot Ð
ttot
0
v(t)2dt
sKramer (1996)
7 Root mean square
of displacement Drms =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
ttot Ð
ttot
0
d(t)2dt
sKramer (1996)
8 Arias intensity
Ia=p
2gð
ttot
0
a(t)2dt
Arias (1970)
9 Characteristic intensity Ic=Arms
ðÞ
2=3ffiffiffiffiffiffi
ttot
pPark et al. (1985)
10 Specific energy density SED =Ð
ttot
0
v(t)2dt
11 Cumulative absolute
velocity CAV =Ð
ttot
0ja(t)jdt EPRI (1988)
12 Standardized cumulative
absolute velocity CAVSTD =P
N
i=1
H(PGAi0:025)Ð
i
i1ja(t)jdt
EPRI (1991)
13 Acceleration spectrum
intensity ASI =Ð
0:5
0:1
Sa(j=0:05,T)dT Von Thun et al.
(1988)
14 Housner spectrum intensity HI =Ð
2:5
0:1
PSv(j=0:05,T)dT Housner (1959)
15 Sustained max. acceleration SMA = the third peak of PGA Nuttli (1979)
16 Sustained max. velocity SMV = the third peak of PGV Nuttli (1979)
17 Effective peak acceleration EPA =mean(S0:10:5
a(j=0:05))
2:5
Kramer (1996)
18 Spectral acceleration at T
1
Sa(T1)
19 Spectral velocity at T
1
Sv(T1)
20 Spectral displacement at T
1
Sd(T1)
EPRI: Electrical Power Research Institute; PGA: peak ground acceleration; PGV: peak ground velocity.
a(t), v(t), and d(t) are acceleration, velocity, and displacement time histories, respectively. t
tot
is the total duration of
the record. gis the acceleration due to gravity, and jis the damping ratio. S
a
,S
v
, and S
d
are spectral acceleration,
velocity, and displacement, respectively. PS
v
is pseudo-spectral velocity.
12 Earthquake Spectra 00(0)
where xiare the seismic responses of the MLA, yirepresents the values of the IMs,
xand
y
are the mean of the xiand yivariables, and nis the total number of data points.
The relationship between the engineering demand parameters (EDPs) and the IMs can
be written using a logarithmic transformation as expressed in Equation 2, where a
1
and a
2
are constant coefficients, and e
i
is the residual, representing the error between the com-
puted and estimated values of EDP
i
:
ln(EDPi)=a1+a2ln(IMi)+eið2Þ
‘‘Practicality’’ represents the direct relationship between an IM and EDPs. It is quanti-
fied by the regression parameter, a
2
(i.e., the slope of the regression line), as described in
Equation 2. A lower value for a
2
implies a less-practical IM. Conversely, an IM with a
larger value for a
2
is more practical. Figure 11 shows that the peak ground velocity (PGV),
V
rms
, HI, sustained maximum velocity (SMV), and ASI IMs stand out with high practical-
ity values.
The IM efficiency indicator (b) is evaluated by the dispersion of the regression fit for
EDP. IM efficiency can be evaluated (Baker and Cornell, 2004) by computing the logarith-
mic standard deviation of the residual between the measured (EDPi)and estimated values
of EDP (E^
DPi)(see Figure 12). A lower log standard deviation (i.e., less spread of data
points) means a more efficient IM. The log standard deviations (b) were calculated for
each IM by using Equation 3:
b=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
n1X
n
i=1½ln(EDPi)ln(E^
DPi)
sð3Þ
The evaluated correlation coefficients (r) and log standard deviations (b), for each char-
acteristic IM, are presented in Figures 13 and 14 for both interstitial column interface J07
(in red) and lattice column interface J06 (in blue), respectively. These computations are
(a) (b)
Figure 9. Column displacement/distortion profile for PM-LB (0.12 g), PM-BE (0.19 g), and PM-8UB
(0.26 g) input motions on x-direction: (a) lattice column and (b) interstitial column.
Gokce et al. 13
made at the column interfaces where the maximum horizontal displacements are observed.
In Figure 13, the peak velocity and acceleration ratio (v
max
/a
max
), peak ground displace-
ment (PGD), and the root mean square of the displacement (D
rms
) are observed to have
the lowest correlation coefficient values. These correspond to much higher log standard
deviation values in Figure 14. However, the ASI, EPA, and PGV IMs stand out with low
log standard deviation values, b, and high correlation coefficients, r. The reason for the
good performance of the ASI and EPA measures is related to the fact that both IMs are
based on the frequency content of the SA in the range of 2–10 Hz, and the dominant
response frequency of MLA is also in this bandwidth. The ASI was identified statistically
as the best IM with the highest correlation coefficients, 0.976 and 0.9762 and lowest
Figure 10. Correlations with IMs and the maximum displacements of the lattice column for 16 input
motion on x-direction.
14 Earthquake Spectra 00(0)
standard deviations, 0.128 and 0.158, for lattice and interstitial columns, respectively. This
is evident in the corresponding linear correlation constructed from the experimental mea-
surements in Figure 10 (fourth row far left). In general, the correlation coefficients and log
standard deviations show similar values for both the interstitial and lattice columns, for
each IM, respectively.
The correlation coefficients (r) and the log standard deviations (b) were computed for
all interfaces of the instrumented interstitial and lattice columns, shown in Figure 2, and
similar results were obtained.
Padgett et al. (2008) proposed an indicator, namely proficiency, which is a composite
measure of efficiency and practicality. Proficiency considers and balances these two para-
meters when identifying an optimal IM. The proficiency (j) is defined by the ratio of
Figure 11. Practicality of the IMs for the instrumented interstitial and lattice column.
Figure 12. IM efficiency evaluation; data regression and standard deviation.
Gokce et al. 15
dispersion (log standard deviation, b) to the practicality (a
2
), as shown in Equation 4. A
lower value of proficiency (j) indicates a more proficient IM, which has a stronger correla-
tion between the IM and the demand while leading to less dispersion around the median
values:
j=b
a2ð4Þ
Based on the proficiency values shown in Figure 15, the ASI was identified as the opti-
mal IM with the lowest proficiency factors (j), of 0.137 and 0.1812 for the lattice and inter-
stitial columns, respectively.
ASI is identified as the optimal IM correlating the seismic input to the column displace-
ment response for a 50% cracked configuration (a close to end-of-life scenario) of a
quarter-sized AGR reactor core model. However, another IM might be optimal for a com-
paratively rigid or flexible configuration of the AGR core. Thus, it is essential to use exist-
ing numerical or experimental data sets representing the actual behavior of the AGR core
to train the developed algorithm and to identify the optimal IM and corresponding regres-
sion coefficients.
Development of column shape prediction algorithm
Based on the ASI measure, a seismic demand prediction tool has been developed to pre-
dict the steady-state column shape displacement profiles of stacked brick columns typi-
cally housed within AGR cores. This algorithm utilizes the linear correlation procedure
empirically derived for the ASI measure illustrated in Figure 10; see Table 2 for its defini-
tion. This IM was identified statistically as being the optimal metric correlating the seismic
input to the output column displacement response. The linear regression coefficients were
obtained for the brick column displacement responses at each measured interface for the
ASI IM. These coefficients can then be used to estimate the displacement demands of the
Figure 13. Correlation coefficients of the IMs for the instrumented interstitial and lattice column.
16 Earthquake Spectra 00(0)
interfaces for any input motion. To demonstrate the validity and accuracy of the predic-
tion algorithm, 1 of the 16 experimental results, see Table 1, was excluded from the identi-
fication of the linear regression coefficients. The column displacement profiles were then
estimated for the excluded input motion and compared with its actual recorded displace-
ment data, as shown in Figures 16 and 17. This procedure was repeated for all 16 input
motions. Figures 16 and 17 present results for the predicted column shape responses when
subjected to RRS Eurocode compatible, HPB 10
–4
, HPB 10
–4
(scaled at 0.7 g), and PML-
2UB input motions for the interstitial and lattice columns, respectively. The predicted
responses are overlain in red to compare against the measured responses shown in blue.
Using the proposed prediction algorithm, the predicted brick column displacement pro-
file responses compare very well with the experimental data both qualitatively and quanti-
tatively. The same trends in column shape profiles are witnessed for both interstitial and
lattice brick columns for each seismic input motion.
A 95% confidence interval is calculated to define a confidence interval for the predic-
tion algorithm. The prediction algorithm is applied to each of the 16 input motions to gen-
erate the predicted column displacement data for the lattice column. The mean (m) and
standard deviation (s) of the residual between the experimental and predicted column
data for each interface are calculated to generate a confidence interval. The 95% confi-
dence intervals for each layer are presented in Table 3. The obtained maximum standard
deviation is 0.797 mm, and the prediction uncertainty (m62s) is calculated as 1.593 mm,
which corresponds to 11% of the maximum horizontal displacement of that interface.
From these results, it can be surmised that despite the differences between the predicted
and measured interface displacements presented in Figures 16 and 17 and Table 3, a very
good performance was achieved when using the optimal IM to predict the column interface
displacements. Due to the AGR core model system being restrained with a Warren truss,
the physical displacement responses of the columns are ultimately constrained. The MLA
was tested up to the 0.7 g PGA level, which is 1.75 times higher than the site-specific earth-
quake motion with a 10
–4
probability of occurrence (HBP 10
–4
). It can be seen from Figure
8a, that the lattice column displacement responses for HPB motions scaled to 0.6 and 0.7 g
Figure 14. Log standard deviations of the IMs for the instrumented interstitial and lattice column.
Gokce et al. 17
PGA levels are quite similar. So, the physical displacement limit of the lattice column
might be hit for the maximum seismic excitation (HPB 10
–4
scaled at 0.7 g). However, it is
not hit for the interstitial column (see Figure 8b). The performance of the proposed predic-
tion tool is likely to deteriorate if it is used beyond the maximum seismic excitation of the
data set.
Safety shutdown criteria
A set of criteria was adapted from the recommendations of EPRI (1988, 1991) in USNRC
(1997) to evaluate whether an NPP must be shut down for inspection after seismic action.
Figure 15. Proficiency of the IMs for the instrumented interstitial and lattice column.
(c) (d)(a) (b)
Figure 16. Comparisons of predicted and measured interstitial column displacements: (a) RRS
Eurocode compatible motion, (b) HPB 10
–4
motion, (c) HPB 10
–4
(scaled at 0.7 g) motion, and
(d) PML-2UB motion.
18 Earthquake Spectra 00(0)
The determination of the OBE exceedance is based on the recorded data by the acceler-
ometers/seismometers in any one of the three components of the free-field ground motion.
To determine the OBE exceedance, a CAV check and a response spectrum check were
defined in USNRC (1997).
The standardized version of the CAV, denoted as CAV
STD
is defined to make the CAV
value representative of strong ground shaking rather than coda waves (small amplitudes
that can continue for a long time after the strong shaking) in EPRI TR-100082 (EPRI,
1991). The method restricted the integration for computing CAV to 1-s time windows that
have amplitudes of at least 0.025 g. This definition of CAV
STD
is given in Equation 5
(EPRI, 2006):
CAVSTD =X
N
i=1
H(PGAi0:025)ð
ti+1
ti
ja(t)jdt ð5Þ
where Nis the number of 1-s time intervals, PGA
i
is the PGA (g) in the time interval i, and
H(x) is the Heaviside function defined as follows:
(c) (d)(a) (b)
Figure 17. Comparisons of predicted and measured lattice column displacements: (a) RRS Eurocode
compatible motion, (b) HPB 10
–4
motion, (c) HPB 10
–4
(scaled at 0.7 g) motion, and (d) PML-2UB
motion.
Table 3. Statistical characteristics of a 95% confidence interval for the interfaces of lattice column (mm)
Interface Mean (m) Standard
deviation (s)
95% Confidence
interval (m62s)
Max. horizontal
displacement
Layer 2 0.000 0.157 0.314 1.767
Layer 3 0.000 0.375 0.749 4.959
Layer 4 0.000 0.600 1.200 9.532
Layer 5 0.000 0.784 1.568 12.681
Layer 6 0.000 0.797 1.593 14.681
Layer 7 0.000 0.563 1.126 6.275
Layer 8 0.000 0.329 0.658 3.911
Gokce et al. 19
H(x)= 0,x\0
1,xø0
ð6Þ
The CAV
STD
threshold is defined as 0.16 g s for any of the three directional compo-
nents recorded at a seismometer in USNRC (1997).
In the response spectrum check, the OBE response spectrum is exceeded if any one of
the three components (two horizontal and one vertical) of the 5% damped response spec-
tra is larger than:
The corresponding design response spectral acceleration (OBE spectrum if used in
the design, otherwise, 1/3 of the safe shutdown earthquake (SSE) ground motion
spectrum) or 0.2 g, whichever is greater, for frequencies between 2 and 10 Hz, or
The corresponding design response spectral velocity (OBE spectrum if used in the
design, otherwise 1/3 of the SSE spectrum) or a spectral velocity of 15.24 cm/s,
whichever is greater, for frequencies between 1 and 2 Hz.
If the response spectrum check and the CAV
STD
threshold exceed for any one of the
three directional components recorded at a seismometer, then the OBE exceedance is trig-
gered, and plant shutdown is required.
The CAV
STD
and response spectrum checks according to USNRC (1997) are presented
in Table 4 for the 16 input motions given in Table 1. The calculated values which exceed
the defined thresholds in the regulations are highlighted in gray. Since there is a relatively
weak correlation between the CAV
STD
and spectral measures with the seismic response of
MLA core model (see Figures 10, 11, and 13–15), a new criterion is suggested to be
employed in the evaluation of OBE exceedance for a cracked graphite reactor core which
approaches the end of its operational life. The ASI, which is shown above to be a good
IM to use in the prediction of graphite column displacements, is proposed for use in the
rapid evaluation of OBE exceedance after a seismic action. The maximum horizontal
displacement value was measured as 4 mm for both lattice and interstitial columns in the
middle of the array for the intact array experiments of the MLA core model. This value
corresponds to the physical displacement limit of the mid-array without any crack opening
or key disengagements. Using experimental results and the developed prediction algo-
rithm, an ASI threshold value was determined as 0.09 g s, which corresponds to a 4 mm
maximum horizontal interface displacement for the 50% cracked MLA configuration.
This means that any earthquake motion lower than this threshold will not cause any
significant crack openings or key disengagements in the MLA core model.
According to the criteria given in USNRC (1997), the PML-8UB input motion triggers
the OBE exceedance and requires a plant shutdown, but the PML-LB and PML-BE
motions did not exceed the OBE (see Table 4). However, a different result was obtained if
the suggested criteria (ASI) were used. The maximum column displacement profiles for all
three input motions are given in Figure 9. It can be seen that the PML 8UB, motion which
triggers the OBE exceedance according to the USNRC, resulted in a maximum horizontal
displacement of 3.1 mm. Conversely, the PML-LB and PML-BE shakes resulted in maxi-
mum interface displacements of 5.65 and 5.52 mm but did not exceed the OBE in accor-
dance with USNRC (1997). This shows that a lack of precision in the prediction methods
to evaluate the damage potential of an earthquake may lead to wrong decisions about the
serviceability of an NPP. When the reactor transitions from ‘‘at power’’ to ‘‘at shutdown’’
20 Earthquake Spectra 00(0)
Table 4. Exceedance of shutdown thresholds for USNRC Regulatory and the suggested IM.
USNRC Suggested criteria
Response spectrum check Cumulative absolute
velocity check
Safety shutdown
(OBE exceedance)
USNRC
Suggested IM Suggested safety
shutdown for 50%
cracked arrayInput motion PSA (\0.20 g) PSV (\15.24 cm/s) CAV
STD
(\0.16 g s) ASI (\0.09 g s)
Revised HPB 0.35 10.65 0.126 No 0.08 No
RRS (E.comp.) 1.10 24.50 0.606 Ye s 0.22 Ye s
HYB/TOR 1.48 14.86 0.458 Yes 0.18 Ye s
HRA Core 1.11 18.92 0.442 Ye s 0.18 Ye s
HPB (@0.4 g) 1.10 9.95 0.287 Ye s 0.19 Ye s
HPB (@0.5 g) 1.54 13.73 0.398 Ye s 0.26 Ye s
HPB (@0.6 g) 2.04 17.67 0.522 Ye s 0.35 Ye s
HPB (@0.7 g) 2.49 21.07 0.635 Ye s 0.42 Ye s
PML-LB 0.42 17.18 0.105 No 0.10 Ye s
PML-BE 0.48 10.66 0.146 No 0.10 Yes
PML-UB 0.59 8.82 0.182 Ye s 0.10 Ye s
PML-INT1 0.63 9.78 0.171 Ye s 0.12 Ye s
PML-1.7UB 0.85 8.70 0.294 Ye s 0.11 Ye s
PML-2UB 0.73 8.71 0.321 Ye s 0.11 Ye s
PML-4UB 0.40 7.59 0.158 No 0.06 No
PML-8UB 0.49 7.47 0.179 Yes 0.06 No
USNRC: US Nuclear Regulatory Commission; OBE: operating basis earthquake; IM: intensity measure; ASI: acceleration spectrum intensity; HPB: Hinkley Point B; RRS: required
response spectrum; HYB/TOR: Heysham 2/Torness; HRA: Hartlepool; PML: Principia Mechanica Ltd; PSA: peak spectral acceleration for frequencies between 2 to 10 Hz; PSV: peak
spectral velocity for frequencies between 1 to 2 Hz.
Gokce et al. 21
conditions, the temperature of the core changes. This causes a change in the thermal strain,
which in turn changes the stress experienced by the bricks, increasing the likelihood of
cracking at shutdown (Bond et al., 2018). Using the proposed new criteria, a more precise
prediction of damage potential after an earthquake can be made. In this way, unnecessary
plant shutdowns could be avoided, and the economic losses resulting from an interruption
of service could be prevented. The authors note that the proposed new criteria are identi-
fied for seismic response prediction of the AGR core and may not be valid for the other
critical components of the NPP. Due to an NPP containing various types of critical com-
ponents which have entirely different structural characteristics and dynamic responses, fur-
ther similar studies should be performed for the other critical components to identify the
best IMs to assess their seismic responses.
Summary of developed algorithm
The developed algorithm to identify the optimal IM and predict column displacements is
depicted as a flowchart in Figure 18. The basic steps can be summarized in three phases.
The automated process of the developed algorithm was undertaken using MATLAB
(2019).
‘‘Phase 0’’ is the algorithm’s initial step for defining the physical model and gathering
data. The physical features of the AGR core are defined as input in terms of geometric
properties of brick types, the number of layers, the natural frequency of the array, and the
overall dimensions of the AGR core model. AGR core data sets are typically generated
from three sources: (a) numerical models, (b) experimental models, and (c) inspections of
the graphite core components in-situ. A unified data format was designed and developed
to ensure all data types can be processed with a range of input data associated with the
AGR cores. Since the developed algorithm can read a unified data format, it can extract
numerical or experimental data, which represents the actual behavior of the AGR core,
directly from data sets.
‘‘Phase 1’’ is the second step of the algorithm, which assesses the possible IMs that could
be used in the estimation of the earthquake response of the AGR core and determines the
optimal ones. Linear regression coefficients of the IMs are identified for each brick inter-
face, and the IM performances are assessed in terms of efficiency (log standard deviation),
practicality, and proficiency.
ASI, EPA, and HI measures are calculated for specific period ranges. However, these
IMs can be modified by redefining these period ranges to better account for the period
range of the interest of the considered structure (Di Sarno and Pugliese, 2021; Pourmasoud
et al., 2022). Therefore, an optional sensitivity analysis feature, shown in green on the flow-
chart (Figure 18), is introduced for users to modify the period range of these IMs.
To define a confidence interval for the prediction uncertainty whereby a 95%
confidence interval can be determined, one of the input motions and its corresponding
results is excluded from the data set, and the linear regression coefficients are obtained
with the (n21) other motions. Then the column displacement profiles for the excluded
input motion are predicted by using the calculated regression coefficients, and the
predicted displacements are compared with the actual results. This procedure is repeated,
one by one, for all the input motions. The mean (m) and standard deviation (s) of the
residuals between the experimental and predicted column data for each interface are calcu-
lated to generate a confidence interval.
22 Earthquake Spectra 00(0)
‘‘Phase 2’’ is where the column displacement profiles are predicted for any given input
motion using the regression coefficients determined for the selected optimum IM in ‘‘Phase
1.’’ In addition, if there are any pre-defined safety thresholds for the AGR core, the
Figure 18. Flowchart of the developed algorithm.
Gokce et al. 23
predicted displacements are compared with corresponding threshold values, and an alert is
triggered if a threshold is exceeded.
To obtain high accuracy in the predicted displacements, the algorithm needs to be
trained using an existing numerical or experimental data set representing the actual beha-
vior of the AGR core to identify the optimal IM and corresponding regression coefficients
for prediction. The licensee who operates the power plant is responsible for demonstrating
to the Office for Nuclear Regulation (ONR) that the graphite core continues to operate
safely as it ages. This requires the licensee to undertake extensive testing and analysis to
support the safety case for continued operation. Each reactor is periodically shut down
and inspected, as it is necessary to carry out inspections and remove samples of the gra-
phite to determine the level of weight loss and cracking (ONR, 2021). Therefore, each
AGR core has an experimental or numerical data set that represents its actual dynamic
behavior.
Determination of the seismic behavior of an AGR core by experimental methods is
expensive and time-consuming. Similarly, finite-element model analysis of an AGR core
takes a long-time due presence of a large number of nonlinear springs, which represent the
contact behavior of the thousands of bricks and keys. Experimental or numerical results
also require significant post-processing, which may take weeks/months. Considering all
these costly and time-consuming experimental/numerical processes, this prediction algo-
rithm could be used to expand the output of experimental or numerical studies thus saving
time, effort, and cost.
Furthermore, after an earthquake, the developed prediction algorithm could be used to
make a rapid determination of the damage potential of the seismic action on a graphite
nuclear reactor core, in addition to the IMs defined in USNRC (1997).
It was observed from the experiments that large column displacements caused more key
disengagements and crack openings. A higher number of disengaged keys could lead to loss
of core integrity during an extreme earthquake and might have safety implications during
the seismic event, as a severe permanent distortion of the vertical channel profiles, caused
by key disengagement, could block the insertion of the control rods and prevent the safe
shutdown of the reactor. Therefore, column displacements were chosen as an EDP in this
study. However, an extensive research study is ongoing on the measurement of internal
brick forces at the University of Bristol. The developed algorithm could also be used to
predict brick stresses and shear forces, which are also critical EDP for the AGR cores. In
this case, a force measurement data set would be required to train the algorithm.
Conclusion
This article presents the seismic assessment and serviceability of instrumented stacked
brick columns housed within a quarter-sized AGR core model. The correlation between
the seismic input motion and displacement response of instrumented stacked brick col-
umns are evaluated directly from experimental measurements using 20 earthquake IM
metrics. Statistical analysis indicates that the ASI is best suited to characterize and describe
the structural damage/demand of an AGR core-like structure when subjected to seismic
loading. The EPA, root mean square of velocity (V
rms
), SMV, and PGV IMs are also con-
sidered to be good/acceptable metrics for this specific engineering application.
A prediction algorithm/software tool, identifying the optimal IM and utilizing it for the
response prediction, is presented to anticipate the column displacement profiles of stacked
24 Earthquake Spectra 00(0)
brick columns housed within an AGR core–like structure when subjected to seismic load-
ing. Qualitative and quantitative assessment of the measured and predicted displacements
at each brick column interface indicates very good agreement between the two data sets.
The column profile trends are captured very well, demonstrating the excellent performance
and accuracy of the prediction algorithm. Time, effort, and cost savings could be achieved
by using the prediction algorithm to expand the output of further numerical and experi-
mental studies.
This study could be used to improve regulation and industry methods for rapidly evalu-
ating the damage potential of a seismic action for a graphite nuclear reactor core.
Although this study focuses on damage indicating parameters for the AGR core structure
of an NPP, a similar methodology and criterion could also be used to rapidly assess
whether lifeline infrastructures have been damaged after an earthquake to aid in emer-
gency response and loss assessment activities.
Acknowledgments
The experimental studies were carried out in the Earthquake Laboratory (EQUALS) at University
of Bristol. All support is gratefully acknowledged. The views expressed in this paper are those of the
authors and do not necessarily represent those of the EDF.
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/
or publication of this article.
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or
publication of this article: The authors are grateful to EDF for both financial and technical support.
ORCID iD
Tansu Gokce https://orcid.org/0000-0003-1354-3963
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