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Environ Earth Sci (2017) 76:642
DOI 10.1007/s12665-017-6971-4
ORIGINAL ARTICLE
Equivalent-linear site response analysis on the site of the historical
Trakošćan Castle, Croatia, using HVSR method
Davor Stanko1
•
Snježana Markušić2 • Stjepan Strelec1 • Mario Gazdek1
Received: 21 July 2016 / Accepted: 7 September 2017 / Published online: 22 September 2017
Ó Springer-Verlag GmbH Germany 2017
Abstract This paper presents a major extension of seismic
vulnerability research project on the site of Trakošćan
Castle based on the initial horizontal-to-vertical-spectralratio (HVSR) results from Stanko et al. (2016). The estimated HVSR site frequencies and HV amplification at
Trakošćan Castle can only be used as an indication of the
initial soil site frequency and amplification, so-called natural soil model, corresponding to the subsoil profile without the influence of an earthquake. The equivalent-linear
(EQL) site response analysis has been carried out for different earthquake scenarios for a maximum input rock peak
ground acceleration (PGAROCK) that corresponds to return
periods of 95 (0.08 g), 475 (0.18 g) and 1000 years
(0.31 g). The aim of the research is to evaluate structural
seismic design responses and to determine type and degree
of damage caused by local site effect, which is the result of
an alluvial basin and topographic influences. The main
objective of this research is the formation of local microseismic zones based on an EQL analysis: surface spectral
acceleration and amplification maps at the predominant
frequency. Based on the HVSR frequency response of the
core structure of Trakošćan Castle and the Tower itself
(fundamental and higher frequency modes), maps of surface spectral acceleration and soil amplification at different
frequencies (3, 5 and 10 Hz) are developed for different
input PGAROCK levels (0.08, 0.18 and 0.31 g) to evaluate
seismic response of the Castle. Observed amplifications are
& Davor Stanko
dstanko@gfv.hr
1
Faculty of Geotechnical Engineering, University of Zagreb,
Hallerova aleja 7, HR-42000 Varaždin, Croatia
2
Department of Geophysics, Faculty of Science, University of
Zagreb, Horvatovac 95, HR-10000 Zagreb, Croatia
correlated with ground motion polarization and directionality of the ground motion from the alluvial basin to the
hilltop. Shortening of predominant frequencies (lengthening of the period), particularly in the alluvial basin, has
been observed with higher input PGAROCK in the EQL
analysis. This effect is not manifested in the Trakošćan hill,
and predominant frequencies match HVSR frequencies.
The use of certain geophysical survey methods at historical
sites is a big problem, because terrain features (e.g. steep
hills, mountains, ridges, slopes, cliffs) create lack of space
and make it impossible to carry out geophysical investigation. Microtremor measurements at historical sites can
overcome this limitation and provide local seismic
response and vulnerability behaviour of historical monuments without destroying their authenticity. Also, computational modelling can greatly improve the results. The
EQL site response analysis on the site of Trakošćan Castle
has confirmed and improved the results of seismic response
and vulnerability based on HVSR method.
Keywords Local site effects Seismic vulnerability Horizontal-to-vertical spectral ratio Equivalent-linear
analysis Site response analysis Historical monuments
Introduction
Trakošćan Castle (46.25917° N, 15.95000° E) is located in
the far north of the Zagorje Region (a north-western
highland region in Croatia), and its cultural heritage is
protected as an important historical entity by the Republic
Of Croatia.
Seismic vulnerability of Trakošćan Castle is mainly
attributed to the cumulative damage from past earthquakes,
ageing process, progressively reduced the strength of
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642 Page 2 of 21
construction materials, faulty past repairs or restoration
interventions, soil settlement, damage to building foundations and wars. According to Herak et al. (2009), Trakošćan Castle site is located in the Varaždin–Ivančica–
Kozjansko epicentral area and lies in Lepoglava syncline
alluvial sediments of the Bednja River between Mt. Ivančica and Mt. Ravna Gora. A few moderate to strong
earthquakes (ML [ 4) have been reported in the Croatian
Earthquake Catalogue in an area which is approx. 40 km
away from the Castle. On 16 March 1982, the Tower Castle
and part of the second floor were damaged by an earthquake (ML = 4.5) with an epicentre 20 km away from Mt.
Ivančica. This was the only reported serious earthquake
damage to Trakošćan Castle caused by an earthquake in the
past 50 years (Trakošćan Castle Historical Evaluation
1968–2012). After that, the Castle was under significant
structural restoration and conservation until the 2000s. All
that time it was open to visitors, apart from the Castle
Tower.
Local soil conditions (or so-called site effects) and the
site amplification are the key elements that influence the
spatial distribution of the structural damage in earthquakeprone regions. Destructive earthquakes that occurred in the
last 3 decades (Nepal 2015; Christchurch 2011; Chile
2010; Sichuan 2008; Kocaeli 1999; Kobe 1995; Northridge
1994; Loma Prieta 1989, Mexico City 1985) proved that
the effect of local soil conditions on the earthquake damage
distribution is substantial when compared to travel path
effects and the effects induced by the proximity of earthquake sources (Aki and Richards 2002; Kramer 1996;
Panzera et al. 2013; Reiter 1990). The dynamic behaviour
of structures during an earthquake correlates with the
behaviour of the ground underneath. Dynamic resonance
and structural damage can occur if the natural frequency of
a structure is close to the natural frequency of soil (Kramer
1996). In the last 2–3 decades, the microtremor horizontalto-vertical-spectral-ratio (HVSR) methodology was used in
many studies for estimation of local seismic ground
response expressed by natural/fundamental soil frequency
and site amplification, and determination of fundamental
vibration frequencies and vibration characteristics of
structures at different frequencies (e.g. Del Monaco et al.
2013; Nakamura 1989; Nakamura et al. 1999, 2000; Gosar
2012; Herak et al. 2010; Leyton et al. 2013; Panzera et al.
2013).
The estimated HVSR site frequencies and HV amplifications on the site of Trakošćan Castle from Stanko et al.
(2016) can only be used as an indication of the initial soil
site frequency and amplification, so-called natural soil
model corresponding to the subsoil profile without the
influence of an earthquake. Different types of earthquake
intensities will have different impacts on historical structures. A full-scale, one-dimensional (1-D) equivalent-linear
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Environ Earth Sci (2017) 76:642
(EQL) site response analysis (e.g. Bardet et al. 2000; Idriss
and Sun 1992; Kramer 1996; Schnabel et al. 1972) can be
performed for different earthquake scenarios, ranging from
low to high seismicity. Site response analysis, which
computes the propagation of strong ground motions from
the base rock through the overlying soil layers up to the
ground surface, is a powerful tool that assesses and estimates the effect of local soil conditions (local seismic
response) on the ground shaking (e.g. Hashash et al. 2011;
Idriss and Seed 1968; Idriss and Sun 1992; Kramer 1996;
Rathje et al. 2010; Seed et al. 1984; Schnabel et al. 1972).
The paper presents a major extension of a seismic vulnerability research project on the site of Trakošćan Castle
based on initial HVSR results from Stanko et al. (2016).
The aim of this paper is to contribute assessing the seismic
vulnerability of historical Trakošćan Castle to earthquakes
of different intensities using an EQL site response analysis.
The EQL analysis has been carried out for a maximum
input rock peak ground acceleration (PGAROCK) that corresponds to return periods of 95, 475 and 1000 years
(Herak et al. 2011; Markušić et al. 2002). The main
objective of this research is to form local microseismic
zones, as well as to evaluate structural seismic design
responses and to determine the type and degree of damage
caused by local site effect. These zones have been obtained
in order to detect microzones with the same characteristic
seismic parameters such as a peak surface acceleration,
spectral surface acceleration and surface amplification at a
different frequency (predominant/fundamental and higher
modes) in order to compare with HVSR results in the free
field and inside Trakošćan Castle, primarily the Tower
Castle.
A structural response analysis is beyond the scope of
this study.
Previous study: HVSR and local seismic response
Between 2013 and 2015, the Trakošćan Castle Museum
Master Plan was devised and it included significant future
works, such as finalization of earthquake damage repairs,
static stabilization of the structure of the Castle and full
reconstruction and strengthening of the Castle Tower, so
that it could be opened to the public. Considering the extent
of the work, a seismic vulnerability study was required in
order to reduce the risk of structural damage or ruining in
case of an earthquake. For this purpose, in Stanko et al.
(2016), the application of non-destructive horizontal-tovertical-spectral-ratio (HVSR) method was used to estimate the local seismic response and vulnerability analysis
of the historical Trakošćan Castle.
With a growing interest in the protection of historical
monuments, the usage of a quick and non-invasive
Environ Earth Sci (2017) 76:642
microtremor HVSR methodology with no environmental
impacts started to become more and more popular (e.g. Del
Monaco et al. 2013; Ditommaso et al. 2010; Fäcke et al.
2006; Fiaschi et al. 2012; Gentile and Saisi 2007; Moisidi
et al. 2004; Nakamura et al. 1999, 2000; Stanko et al.
2016). It is the easiest and cheapest way to understand
structural behaviour without doing any harm to a structure.
In a short period of time, it provides several information
including natural frequency, amplification and vibration
characteristics of structures at different frequencies
(Nakamura et al. 1999). Historical monuments, especially
castles, were often built at the top of hills or other places
where they could use some natural features of the land to
help them defend from low-level attacks. The use of certain
geophysical investigation methods which require long
profile is a big problem, because this kind of terrain (steep
hills, mountains, ridges, slopes, cliffs, etc.) creates lack of
space and makes it impossible to carry out geophysical
investigation. Over the past few years, the microtremor
HVSR method has been widely used in the studies of
seismic microzonation and seismic site effects and can
overcome the terrain features limitation at such sites (e.g.
Bard et al. 2010; Del Gaudio et al. 2014; Del Monaco et al.
2013; Gosar 2012; Haghshenas et al. 2008; Herak et al.
2010; Lachetl and Bard 1994; Leyton et al. 2013; Moisidi
et al. 2012; Nakamura 1989; Panzera et al. 2013; Paolucci
et al. 2015; SESAME guidelines 2004; Stanko et al. 2016).
Trakošćan was built on a rocky hilltop in the late-thirteenth century as a small observation fortress within the
Croatian north-western defence (see Fig. 1). Geological
characteristics of the site on which Trakošćan Castle was
built are described in Stanko et al. (2016). It would be a big
challenge to use certain geophysical methods there, especially on the hill where Trakošćan Castle stands. To
overcome this problem, in Stanko et al. (2016) microtremor
measurements were taken in the free field and in the Tower
Castle for the purpose of detecting local seismic response
and structural seismic vulnerability of the weak points of
the Castle. Valuable information, e.g. fundamental soil
frequencies, amplification factors, shear wave velocity
distribution, estimated bedrock depth and directional (polarization) effects on the ground motion help to identify the
main damage mechanism regarding the 1982 earthquake
(see Fig. 2).
Site effects may be defined as a modification of the
characteristics of and incoming wave field (amplitude,
frequency content and duration) as a result of several
physical phenomena such as multiple reflections, diffractions, focusing, resonance which incoming seismic waves
are subjected due to topographic and morphological features, typology and geometry of sediments and possible
presence of water-bearing strata, landslides, structural
discontinuities and cavities (Aki and Richards 2002;
Page 3 of 21
642
Fig. 1 a Historical Trakošćan Castle (T18 and T24) built on a rocky
hilltop—view from the air. b Topography map with marked elevation.
Free-field measurements are marked with green circles. Some
measurement points are marked in the upper figure to demonstrate
terrain features
Kramer 1996; Reiter 1990). Topographic amplification of
seismic energy occurs when seismic waves entering the
base of a topographic ridge are partially reflected back into
the rock mass and diffracted along the free surface. Seismic
waves are progressively focused upwards and the constructive interference of their reflections and the associated
diffractions increases towards the ridge crest, giving rise to
enhanced ground accelerations on topographic heights (e.g.
Meunier et al. 2008). For example, during the 1987
Whittier Narrows (California) earthquake, the amplitude of
seismic waves recorded at the crest of Tarzana Hill, a
60-m-high feature located 44 km from the epicentre, was
ten times greater than that observed on the surrounding
plains. On the same hill, instruments recorded a peak
horizontal acceleration of 1.78 g, during the 1994 Northridge earthquake (Meunier et al. 2008). The highest peak
horizontal acceleration ever recorded in Croatia was
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642 Page 4 of 21
Environ Earth Sci (2017) 76:642
Fig. 2 Results of free-field microtremor measurements on the site of
Trakošćan Castle (Stanko et al. 2016). a Map of fundamental soil
frequencies, b map of HV amplitudes, c map of VS30 distributions,
d map of estimated bedrock depth. Free-field measurements are
marked with yellow circles
0.64 g. It occurred during a devastating earthquake that
was in 1996 (ML = 6.0) with an epicentre 16 km from the
town of Ston. The ancient town of Ston (Croatia) lies at the
foothills of the Bartolomija and Supava hills (Herak et al.
2010).
Regarding the 1982 earthquake, similar effects have
been observed on the site of Trakošćan Castle, and based
on HVSR results (Stanko et al. 2016) concluded that the
most damage occurred due to the amplification of the
seismic energy through the alluvial basin (local soil conditions), trapping of seismic waves, focusing of the seismic
energy directly to the top of Trakošćan hill (topographic
effects), and the improper way the Tower Castle was
constructed in the past and the reconstructed after the
earthquake.
123
Equivalent-linear site response analysis
During past earthquakes, ground motions on soft soils sites
(e.g. alluvial basins, soft sediments) are larger than those of
nearby rock outcrops due to local soil conditions, as it has
Environ Earth Sci (2017) 76:642
been reported in the literature dealing with the issue of
geotechnical earthquake engineering (e.g. Idriss and Seed
1968, Kramer 1996; Vučetić and Dobry 1991). Amplifications of soil site conditions on ground shaking are
assessed through dynamic simulations of wave propagation
called seismic site response analysis.
EQL methodology background
A one-dimensional (1D) equivalent-linear (EQL) site
response analysis using input rock motions was first
introduced by Idriss and Seed (1968) and implemented by
Schnabel et al. (1972) in SHAKE and by Idriss and Sun
(1992) in SHAKE91. Users prefer applying it to assess the
effect of soil conditions on the ground shaking because
vertically propagating and horizontally polarized waves
dominate the earthquake ground motion wave field of
engineering interest. An EQL site response analysis is
based on one-dimensional, linear elastic wave propagation
through multilayered media, and soil nonlinearity is
incorporated through strain-compatible soil properties (i.e.
shear modulus G and damping ratio D) for each soil layer.
Strain-compatible soil properties model the shear modulus
reduction (G/Gmax) and damping ratio (D) to be consistent
with the shear strains generated in each layer that are
consistent with the level of shear strain induced by earthquake. Gmax is calculated from geophysical tests. Shear
wave velocity (VS) is a valuable indicator of the dynamic
properties of soil and rock because of its relationship with
Gmax: Gmax = qV2S.
An equivalent-linear model is an approximation to the
nonlinear behaviour of soil under cycling loading (e.g.
Seed et al. 1984). The theoretical basis of an EQL
methodology is very well described in the literature dealing
with the issue of geotechnical earthquake engineering (e.g.
Bardet et al. 2000; Bolisetti et al. 2014; Hashash et al.
2011; Idriss and Seed 1968; Idriss and Sun 1992; Kramer
1996; Ordonez 2009; Rathje et al. 2010; Seed et al. 1984;
Schnabel et al. 1972), so it won’t be mentioned here.
Instead of that, the focus is on an analysis procedure and
presentation of output results expressed by spectral acceleration on the ground surface and site amplification factors.
The main advantages of traditional 1D EQL site
response analysis are: (1) it requires a small number of soil
parameters (i.e. shear wave velocity, unit weight, shear
modulus and damping curves), (2) it has fast and efficient
computation, (3) it has been heavily tested, and (4) a
variety of codes are available. The disadvantage of the
EQL approach includes the need for a large suite of input
motions and potentially biased estimates of site amplification, particularly at large input intensities.
For an EQL site response analysis, an outcropping rock
acceleration time history is specified, propagated through
Page 5 of 21
642
the soil to the ground surface, and the time history of
surface motion is used directly to compute the acceleration
response spectrum on the ground surface. The most widely
used outcome of 1D EQL site response analysis is the sitespecific response spectrum expressed by spectral acceleration on the ground surface and the site amplification factor
that represents the ratio of the soil surface spectral acceleration (SaSURF) to rock spectral acceleration (SaROCK) as a
function of frequency (f):
AFðf Þ ¼
SaSURF ðf Þ
:
SaROCK ðf Þ
ð1Þ
EQL analysis procedure
DEEPSOIL, a one-dimensional site response analysis
program (Hashash et al. 2011), has been used to conduct
numerical analyses for the EQL site response analysis with
the purpose of investigating the effect of local soil properties on the characteristics of ground motions transferred
to the surface and the resulting demand on structures.
An EQL analysis procedure consists of three steps: (1)
definition of shear wave velocity soil profiles, (2) selection
of appropriate soil shear modulus reduction and damping
curves and (3) specification of input rock motions (e.g.
Bardet et al. 2000; Hashash et al. 2011; Idriss and Seed
1968; Idriss and Sun 1992; Kramer 1996; Schnabel et al.
1972).
Shear wave velocity profiles based on HVSR results
Shear wave velocity can be measured in a field using
geophysical methods (e.g. Spectral Analysis of Surface
Waves—SASW, Multichannel Analysis of Surface
Waves—MASW, Seismic Refraction—RF, Refraction
Microtremor—ReMI, Down-hole and Cross-Hole). Trakošćan Castle was built on a rocky hilltop, which makes it
difficult to use certain geophysical investigation methods
that require long profile. Due to the lack of space, it is
impossible to carry out such geophysical investigation. The
application of quick and non-invasive microtremor HVSR
methodology was used in Stanko et al. (2016) to overcome
this problem. In comparison to other geophysical methods,
this method has a lot of advantages. It is fast, measurements are much denser and it provides a non-invasive
estimation of seismic site effects, e.g. soil fundamental/natural frequency and amplification, determination of
potentially dangerous seismic zones in a particular area at
especially reasonable costs. The only limitation of HVSR
method compare to geophysical methods is that it does not
directly provide shear wave velocity structure. This can be
done by HV modelling of spectral ratio curve (Herak 2008;
Micromed 2009).
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642 Page 6 of 21
Original definition of microtremor HVSR method is
based on a simple soft layer over bedrock half-space subsurface, where the peak of HVSR curve represents the
fundamental soil frequency (e.g. Nakamura 1989; Kramer
1996). Recently, HV modelling routine became available
to derive multilayer shear wave velocity soil profile (Bignardi et al. 2016; Castellaro and Mulargia 2009; Del
Gaudio et al. 2014; Gosar et al. 2008; Herak 2008;
Micromed 2009). The HV modelling is found to be capable
of detecting deviations from 1D subsoil geometry over the
length of a few metres, the correctness of which was
confirmed by direct drilling (Castellaro & Mulargia 2009;
Del Gaudio et al. 2014). If the soil profile is known
(borehole, geophysical method), it can be compared with
theoretical and observed HVSR. In the case that soil profile
is unknown, like at Trakošćan site, most likely soil profile
model can be obtained by inverting observed HVSR curve
to find synthetic HVSR curve by random perturbation of
soil model parameters (shear wave velocity, density and
Poisson ratio) (Bignardi et al. 2016; Gosar et al. 2008;
Herak 2008; Micromed 2009). The HVSR is fitted with a
synthetic curve using the independently known thickness of
a superficial layer of the subsoil as a constraint. The limitation of HV modelling inversion procedure is that independent constraints, i.e. depth of the bedrock or the VS of
the first layer, are known (Bignardi et al. 2016; Micromed
2009). As we did not have direct information’s about
bedrock depth and VS of sedimentary cover, we followed
the works of Di Giacomo et al. (2005) and Luzi et al.
(2011) where the bedrock depths and shear wave velocity
of sediments are estimated from correlations between the
fundamental soil frequency, average shear wave velocity
and depth of the bedrock.
The whole inversion process is based on initial model
described by four soil layers used in the HV modelling
routine: first surface layer: VS \ 180 m/s (low-quality
surface clay, sandy silt, artificial fill), second layer:
180 \ VS \ 360 m/s (sand and gravel, artificial fill), third
layer: 360 \ Vs \ 520 m/s (soft rocks—marly sandstone),
fourth layer: bedrock VS [ 520 m/s (sedimentary rocks—
sandstone). Figure 3 (left figures) shows an example of the
HV modelling routine for stratigraphic purpose to derive
multilayer shear wave velocity soil profile. Every iteration
randomly perturbates soil model parameters until the soil
model reproduces the synthetic HVSR curve (blue line)
which is comparable with the observed HVSR curve (red
line). Usually, assumed multilayer soil model is described
based on observed number of HVSR peaks. To reproduce
one HVSR peak, two soil layers are sufficient and to
reproduce number N of HVSR peaks, N ? 1 layers are
needed (Micromed 2009).
Uncertainty of HV modelling and average values provided in this study exists due to assumed soil model and the
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Environ Earth Sci (2017) 76:642
presence of shear wave velocity inversion which could
affect the average values. The presence of velocity inversion can be detected by strong de-amplification of the
HVSR curve between two peaks usually over layer of
anthropogenic fill, rigid conglomerates and thick layer of
sediments above bedrock (Di Giacomo et al. 2005). We did
not consider such cases since, although they can be noticed
from observed and synthetic HVSR curves, there were
simply not enough supporting evidences to confirm that. If
the information from boreholes or geophysical survey is
known, one can include them into HV modelling to provide
more exact and detailed soil model which can be extended
at greater depths. Geophysical methods (e.g. MASW,
Seismic Refraction) provide depths up to 20–30 metres of
range, while passive methods can exceed greater depths
(e.g. passive MASW, HV modelling). A comparative test
of active and passive multichannel analysis of surface
waves (MASW) methods and microtremor HVSR method
by Gosar et al. (2008) provides a conclusion that microtremor data can provide a good estimate of one-dimensional shear wave velocity profile.
All 29 shear wave profiles have been extracted from the
HV modelling routine for the stratigraphic purpose based
on microtremor measurement points. Figure 2c shows a
map of VS30 distributions at the site of Trakošćan Castle
based on a HV modelling routine from microtremor measurements. According to Eurocode 8 (EC8), the soil at
Trakošćan site may be classified as ground types B
(360 B VS30 B 800 m/s) (hilltop and slopes of the hill) and
C (180 B VS30 B 360 m/s). Due to the uncertainty in HV
modelling and assumed soil models, some sites can be
classified as a ground type A (VS30 [ 800 m/s).
For the EQL site response analysis in a DEEPSOIL,
shear wave velocity soil profiles from HV modelling routine for the stratigraphic purpose were used. Soil column
has been divided into individual layers, each of which is
characterized using the corresponding soil properties (shear
wave velocity and unit weight). The input rock motion is
applied at a fixed bedrock base (VS = 1100 m/s, unit
weight = 2.6 kN/m3, damping ratio 2%), and the surface
motion is recorded as the seismic waves travel vertically to
the surface.
Soil shear modulus reduction and damping curves
An integral component of a site response analysis (Kramer
1996) is the characterization of the stress–strain behaviour
of soils. Soil undergoes inelastic strains under the very
small level of ground shaking, and nonlinear soil behaviour
of soil needs to be taken into account. Due to the fact that
most soils have a curvilinear stress–strain relationship, the
shear modulus is usually expressed as the secant shear
modulus (Gsec) determined by the extreme points on a
Environ Earth Sci (2017) 76:642
Page 7 of 21
642
Fig. 3 Left figures: Example of HV modelling routine for the
stratigraphic purpose for three free-field microtremor points: T11—
alluvial basin of Bednja river, T14—in-between alluvial basin and the
hill on which Trakošćan Castle stands, T24—the backyard of
Trakošćan Castle (hilltop). The average HVSR curve is represented
by a red line and synthetic HV model by blue line. Castle frequencies
range (fundamental and first higher mode) is marked with yellow box
(from Stanko et al. 2016). Right figures: Presentation of the change of
the PGA (red, blue and green curves) along soil profile depth for three
input PGAROCK levels: 0.08 g (95-year return period), 0.18 g (475year return period) and 0.31 g (1000-year return period). Shear wave
velocity soil model representing synthetic HV model is represented
with thick black curve
hysteresis loop, while the damping ratio (D) is proportional
to the area inside the hysteresis loop. Iteration is required to
determine the appropriate equivalent secant shear modulus
that is compatible with the amount of strain that develops
during the modelling process. The equivalent damping is
defined as a function of the shear strain level. It is
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642 Page 8 of 21
determined from strain-controlled laboratory tests, and it is
used in the modelling process (e.g. Kramer 1996; Seed
et al. 1984; Schnabel et al. 1972; Vučetić and Dobry 1991).
Shear modulus (G) of soils is highly dependent upon
strain level. The small-strain shear modulus (Gmax or G0) is
typically associated with strains in the order to 10-3 % or
less. Provided that Gmax is known, shear response at various levels of strain can be estimated using soil modulus
reduction curves (G/Gmax) that have been published before.
Like the shear modulus reduction behaviour, damping is
influenced by the plasticity of soil. Damping ratios of highplastic soils are lower than those of low-plastic soils.
Generic soil shear modulus reduction and damping curves
used in this study are based on soil types used in HV
modelling: (a) sand and gravel (Seed et al. 1984), (b) clay
(Vučetić and Dobry 1991), (c) rock (Schnabel et al. 1972).
Typical values of unit weight for the mentioned type of
soils have been used (Seed et al. 1984; Vučetić and Dobry
1991).
Input rock motions
The study of seismic vulnerability at Trakošćan Castle has
been conducted for earthquakes of different intensities
since they have a different impact on the structure of the
historical Castle. Considering the fact that it dates from the
thirteenth century, the EQL analysis has been carried out
for maximum input rock design peak ground acceleration
(PGAROCK) that corresponds to return periods of 95
(0.08 g), 475 (0.18 g) and 1000 years (0.31 g) (Herak et al.
2011; Markušić et al. 2002). A few moderate to strong
earthquakes (ML [ 4) have been reported in an area which
is approx. 40 km away from the Castle. They correspond to
a
range
of
horizontal
peak
accelerations
ag,h & 0.06–0.09 g by attenuation relation (Markušić et al.
2002) derived for Croatia.
Depending on how seismic energy travels from the
hypocentre to the site and the area of the fault, the ground
motion duration can vary significantly for an earthquake of
the same magnitude. Ground motion duration is particularly important for historical structures since they have to
withstand intense cyclic shaking that can last for several
seconds and longer. An EQL analysis with multiple input
rock motions of different durations can provide valuable
information about possible degradation of a structure during an earthquake event (Kramer 1996). The description of
earthquakes in seismically active regions is relatively
straightforward, because observed records exist to physically constrain and validate the estimation of future
earthquakes. In regions of low to moderate seismicity, such
as the area of Trakošćan Castle, there is little information
about real earthquakes, particularly for the ones that are
interesting to engineers. The input ground motions (GM)
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Environ Earth Sci (2017) 76:642
used in this study have been taken from previously recorded rock motions at stations with VS,30 [ 800 m/s from
PEER NGA-WEST2 database (http://ngawest2.berkeley.
edu/). A list of 82 ground motions employed in the 1D EQL
analyses are shown in Table 1. Due to the uncertainty
about the characteristics of input rock motions (frequency
and duration), none of the ground motions have been
eliminated and all motions with VS,30 [ 800 m/s have been
used to obtain a statistically stable estimate of the median
surface response spectrum and soil amplification factors.
Selected input rock motions were scaled to the corresponding PGAROCK according to a return period.
Figure 3 (right figures) shows the change of the maximum acceleration along soil profile depth for input
PGAROCK levels: 0.08 g (a 95-year return period), 0.18 g
(a 475-year return period) and 0.31 g (a 1000-year return
period) at three microtremor measurement points (T11,
T14 and T24). The maximum acceleration change for input
acceleration occurs at the T11 point (situated in the alluvial
basin). It is deeper than those on the shallower T14 and the
T24 (hilltop), where VS is higher and less amplification is
observed.
Results
Site response analyses have been done for all 29 soil profiles, and they have been extracted from HVSR results
which have been subjected to the corresponding scaled
input rock motions by PGAROCK equal to 0.08 g, 0.18 g,
and 0.31 g, respectively. Each seismic event is characterized by different ground motion which can be defined
through a site-specific seismic response spectrum which
plots the peak ground-level acceleration as a function of the
frequency of shaking for that event (Kramer 1996). A
seismic surface response spectrum describes vibration
intensities of different frequencies, and for a particular site,
they vary with local soil condition. Output results are
presented in the form of response spectrum expressed by
surface spectral acceleration (SaSURF) and soil amplification factors (AF), in Eq. (1).
Based on the individual EQL analysis and the output
results, the objective of the survey is to derive maps of
surface spectral accelerations and amplification factors in
order to characterize local microseismic zones on the site
of Trakošćan Castle.
Surface spectral acceleration and amplification
factor
An example of an EQL analysis is shown in Fig. 4. A suite
of 82 input rock motions (red lines) with different durations
from PEER database (Table 1) is used to estimate a
Environ Earth Sci (2017) 76:642
Page 9 of 21
642
Table 1 Ground motions (horizontal components) from PEER database used in 1-D EQL site response analysis. Source: (http://ngawest2.
berkeley.edu/)
Nr
Record
sequence
number
Earthquake
Year
Station
Vs,30
(m/s)
Mw
PGA (g)
Hyp.
depth
(km)
8
Epic.
dist.
(km)
1
23
San Francisco, USA
1957
Golden Gate Park
874
5.28
0.0863
2
43
Lytle Creek, USA
1970
Cedar Springs, Allen Ranch
813
5.33
0.0429
8
18.87
20.5
3
59
San Fernando, USA
1971
Cedar Springs, Allen Ranch
814
6.61
0.0180
13
100.39
101.23
4
72
San Fernando, USA
1971
Lake Hughes #4
822
6.61
0.1786
13
24.18
27.46
5
80
San Fernando, USA
1971
Pasadena—Old Seismo Lab
969
6.61
0.1450
13
39.17
41.27
6
98
Hollister, USA-03
1974
Gilroy Array #1
1428
5.14
0.1053
11.08
12.66
7
143
Tabas, Iran
1978
Tabas
767
7.35
0.8125
5.75
55.24
55.54
8
146
Coyote Lake, USA
1979
Gilroy Array #1
1428
5.74
0.1059
9.6
12.56
14.9
6.11
11.13
Hyp.
dist.
(km)
13.7
9
455
Morgan Hill, USA
1984
Gilroy Array #1
1428
6.19
0.0771
8.5
38.63
39.55
10
643
Whittier Narrows, USA-01
1987
LA—Wonderland Ave
1223
5.99
0.0465
14.6
28.48
32.01
11
663
Whittier Narrows, USA-01
1987
Mt Wilson—CIT Seis Sta
822
5.99
0.1599
14.6
19.56
24.41
12
680
Whittier Narrows, USA-01
1987
Pasadena—CIT Kresge Lab
969
5.99
0.1034
14.6
13.85
20.12
13
703
Whittier Narrows, USA-01
1987
Vasquez Rocks Park
996
5.99
0.0650
14.6
54.21
56.14
14
15
715
765
Whittier Narrows, USA-02
Loma Prieta, USA
1987
1989
Mt Wilson—CIT Seis Sta
Gilroy Array #1
822
1428
5.27
6.93
0.1500
0.4332
13.3
17.48
18.75
28.64
22.98
33.55
16
788
Loma Prieta, USA
1989
Piedmont Jr High
895
6.93
0.0759
17.48
92.21
93.85
17
789
Loma Prieta, USA
1989
Point Bonita
1316
6.93
0.0735
17.48
103.91
105.37
18
795
Loma Prieta, USA
1989
SF—Pacific Heights
1250
6.93
0.0545
17.48
96.34
97.91
19
797
Loma Prieta, USA
1989
SF—Rincon Hill
873
6.93
0.0786
17.48
94.31
95.92
20
804
Loma Prieta, USA
1989
So. San Francisco, Sierra Pt.
1021
6.93
0.0812
17.48
83.53
85.34
21
879
Landers, USA
1992
Lucerne
1369
7.28
0.7272
7
44.02
44.58
22
925
Big Bear, USA-01
1992
Rancho Cucamonga—Deer Can
822
6.46
0.0433
13
69.09
70.31
23
943
Northridge, USA-01
1994
Anacapa Island
822
6.69
0.0536
17.5
77.39
79.34
24
946
Northridge, USA-01
1994
Antelope Buttes
822
6.69
0.0534
17.5
63.95
66.31
25
957
Northridge, USA-01
1994
Burbank—Howard Rd.
822
6.69
0.1427
17.5
23.18
29.05
26
1011
Northridge, USA-01
1994
LA—Wonderland Ave
1223
6.69
0.1408
17.5
18.99
25.82
27
1021
Northridge, USA-01
1994
Lake Hughes #4—Camp Mend
822
6.69
0.0758
17.5
49.93
52.91
28
1033
Northridge, USA-01
1994
Littlerock—Brainard Can
822
6.69
0.0683
17.5
61.26
63.71
29
30
1041
1060
Northridge, USA-01
Northridge, USA-01
1994
1994
Mt Wilson—CIT Seis Sta
Rancho Cucamonga—Deer Can
822
822
6.69
6.69
0.1894
0.0661
17.5
17.5
45.77
89.83
49
91.52
31
1091
Northridge, USA-01
1994
Vasquez Rocks Park
41.9
32
1108
Kobe, Japan
1995
Kobe University
33
1161
Kocaeli, Turkey
1999
34
1165
Kocaeli, Turkey
35
1245
Chi-Chi, Taiwan
36
1366
37
38
996
6.69
0.1540
17.5
38.07
1043
6.9
0.2962
17.9
25.4
31.08
Gebze
792
7.51
0.1932
15
47.03
49.68
1999
Izmit
811
7.51
0.1939
15
5.31
16.86
1999
CHY102
804
7.62
0.0456
8
70.48
70.93
Chi-Chi, Taiwan
1999
KAU034
1010
7.62
0.0088
8
148.42
148.46
1371
Chi-Chi, Taiwan
1999
KAU042
807
7.62
0.0116
8
203.36
203.52
1378
Chi-Chi, Taiwan
1999
KAU051
1005
7.62
0.0088
8
165.73
165.92
39
1432
Chi-Chi, Taiwan
1999
TAP046
817
7.62
0.0623
8
169.36
169.56
40
1440
Chi-Chi, Taiwan
1999
TAP065
1023
7.62
0.0305
8
173.44
173.62
41
1442
Chi-Chi, Taiwan
1999
TAP067
808
7.62
0.0389
8
147.48
147.70
42
1452
Chi-Chi, Taiwan
1999
TAP075
887
7.62
0.0408
8
144.22
144.44
43
1518
Chi-Chi, Taiwan
1999
TCU085
1000
7.62
0.0584
8
106.87
107.16
44
1571
Chi-Chi, Taiwan
1999
TTN016
826
7.62
0.0079
8
166.26
166.45
45
46
1613
1645
Duzce, Turkey
Sierra Madre, USA
1999
1991
Lamont 1060
Mt Wilson—CIT Seis Sta
782
822
7.14
5.61
0.0414
0.2345
10
12
44.4
6.46
46.55
13.63
123
642 Page 10 of 21
Environ Earth Sci (2017) 76:642
Table 1 continued
Nr
Record
sequence
number
Earthquake
Year
Station
47
1649
Sierra Madre, USA
1991
Vasquez Rocks Park
996
48
1672
Northridge, USA-03
1994
Sandberg—Bald Mtn
822
49
1691
Northridge, USA-06
1994
Anacapa Island
822
5.28
0.0104
50
1696
Northridge, USA-06
1994
Burbank—Howard Rd.
822
5.28
51
1709
Northridge, USA-06
1994
LA—Griffith Park Observatory
1016
5.28
52
1715
Northridge, USA-06
1994
LA—Wonderland Ave
1223
5.28
53
1727
Northridge, USA-06
1994
Rancho Cucamonga—Deer Can
822
5.28
0.0124
13.09
82.76
83.78
54
1943
Anza, USA-02
2001
Idyllwild—Keenwild Fire Sta.
845
4.92
0.0372
15.2
29.07
32.81
55
2107
Denali, Alaska
2002
Carlo (temp)
964
7.9
0.0900
8.9
67.67
68.25
56
2111
Denali, Alaska
2002
R109 (temp)
964
7.9
0.0799
8.9
61.96
62.59
57
2207
Chi-Chi, Taiwan-02
1999
CHY102
804
5.9
0.0114
8
87.21
87.57
58
2328
Chi-Chi, Taiwan-02
1999
TAP046
817
5.9
0.0087
8
150.54
150.75
59
2334
Chi-Chi, Taiwan-02
1999
TAP067
808
5.9
0.0092
8
129.36
129.61
60
2339
Chi-Chi, Taiwan-02
1999
TAP068
888
5.9
0.0142
8
126.06
126.31
61
62
2396
2508
Chi-Chi, Taiwan-02
Chi-Chi, Taiwan-03
1999
1999
TCU085
CHY102
1000
804
5.9
6.2
0.0095
0.0193
8
7.8
89.14
67.28
89.5
67.73
63
2633
Chi-Chi, Taiwan-03
1999
TCU085
1000
6.2
0.0041
7.8
109.25
109.53
64
2753
Chi-Chi, Taiwan-04
1999
CHY102
804
6.2
0.0552
18
44.71
48.20
65
2989
Chi-Chi, Taiwan-05
1999
CHY102
804
6.2
0.0594
10
78.79
79.42
66
3094
Chi-Chi, Taiwan-05
1999
KAU051
1005
6.2
0.0068
10
166.79
167.09
67
3135
Chi-Chi, Taiwan-05
1999
TAP067
808
6.2
0.0096
10
139.73
140.09
68
3145
Chi-Chi, Taiwan-05
1999
TAP068
888
6.2
0.0170
10
136.43
136.79
69
3194
Chi-Chi, Taiwan-05
1999
TCU085
1000
6.2
0.0131
10
100.36
100.86
70
3318
Chi-Chi, Taiwan-06
1999
CHY102
804
6.3
0.032
16
80.39
81.97
71
3479
Chi-Chi, Taiwan-06
1999
TCU085
1000
6.3
0.0075
16
96.35
97.66
72
3548
Loma Prieta, USA
1989
Los Gatos—Lexington Dam
1070
6.93
0.4438
17.48
20.35
26.83
73
3718
Whittier Narrows, USA-02
1987
LA-Wonderland Ave
1223
5.27
0.0184
13.3
26.18
29.37
74
3799
Hector Mine, USA
1999
LA-Griffith Park Observatory
1016
7.13
0.0161
14.8
194.40
194.96
75
3893
Tottori, Japan
2000
HYG004
835
6.61
0.0188
12.5
113.18
113.87
76
77
3895
3920
Tottori, Japan
Tottori, Japan
2000
2000
HYG007
OKYH02
761
1047
6.61
6.61
0.0358
0.0300
12.5
12.5
109.71
88.29
110.42
89.17
78
4167
Niagata, Japan
2004
FKSH07
829
6.63
0.098
10.6
58.35
59.31
79
4247
Niagata, Japan
2004
TCGH14
849
6.63
0.033
10.6
109.30
109.81
80
4312
Umbria, Italy-03
1984
Gubbio
922
5.6
0.050
9
17.08
19.31
81
4438
Molise, Italy-02
2002
Sannicandro
865
5.7
0.0387
25.2
58.33
61.64
82
4926
Chuetsu-oki, Japan
2007
AKTH05
829
6.8
0.008
9
226.21
226.39
statistically stable median (black thick line) of the rock
(SaROCK) and surface (SaSURF) response spectrums and the
soil amplification factors (AF). The results of an EQL
analysis are usually shown in terms of period (0.01–10 s),
but for convenience and comparison with the HVSR results
from Stanko et al. (2016), the frequency term is used (inverse to period, 0.1–100 Hz). Values of the specific peak of
Sa and AF at the predominant frequency and at PGA are
indicated in the figures to better understand meaning of the
123
Vs,30
(m/s)
Mw
PGA (g)
Hyp.
depth
(km)
Epic.
dist.
(km)
Hyp.
dist.
(km)
5.61
0.1031
12
39.6
41.38
5.2
0.0097
6
45.99
46.38
13.09
85.15
86.15
0.0604
13.09
16.21
20.83
0.0489
13.09
20.53
24.35
0.0527
13.09
15.71
20.45
peak amplitudes and surface amplitudes at PGA. The frequency (or period) at which maximum spectral amplitude
is observed is called predominant frequency (period). An
amplification factor at PGA is the ratio of the input rock
acceleration at the bedrock and acceleration on the top of
surface. (An example is shown in Fig. 3, right.)
For the T11, it can be observed that higher spectral
acceleration (SaSURF) and lower AFs follow higher input
PGAROCK. The same pattern applies for the T24, but with
Environ Earth Sci (2017) 76:642
less amplification. At the T11, peaks are shifted to a lower
predominant frequency (longer period) with higher
PGAROCK, which is not the case for the T24. Beresnev and
Wen (1996) concluded that amplification decreases rapidly
with increasing acceleration and that nonlinear behaviour
of soils can be expected at PGAROCK larger than 0.1 g to
0.2 g. At higher frequencies, nonlinear soil amplification
means that less amplification occurs for larger input
intensities because of increased levels of induced strain and
damping. At lower frequencies, nonlinear soil amplification means that more amplification occurs for larger input
intensities because of increased levels of induced strain and
frequency shortening (period lengthening) effect (e.g.
Bolisetti et al. 2014; Dhakal et al. 2013; Rathje and Ozbey
2006, 2010). A low-intensity input ground motion allows
the soil to respond more in the linear range, thereby significantly reducing the stiffness degradation, which consequently results in the greater surface-to-bedrock
acceleration ratio. On the contrary, high-intensity input
ground motions induce large strains and therefore consequential nonlinear behaviour. This, in turn, significantly
reduces stiffness and increases hysteretic damping, reducing the ability of the soil to transmit force to the surface
and structure above (Bolisetti et al. 2014; Dhakal et al.
2013; Philips and Hashash 2009).
The same procedure of individual analysis of output
results, shown in Figs. 3 and 4, has been applied to all 29
soil profiles. Internal MATLAB scripts have been written
for the purpose of analysis and comparison of the multiple
output results, because DEEPSOIL does not have that
possibility.
Maps of surface spectral accelerations
and amplification factors
From the individual EQL results (SaSURF, AF), maps of
surface spectral acceleration and amplification factors at
predominant frequency have been derived for different
earthquake intensity scenarios (0.08 g, 0.18 g, 0.31 g).
Figure 5 (SaSURF) and Fig. 6 (AF) show two cases of local
microseismic maps: (a) at PGA and (b) at a predominant
frequency (period). (Individual examples are shown in
Fig. 4). SaSURF maps (at PGA) clearly distinct three
microzones of interest that correspond to the alluvial basin
(higher values of SaSURF), transition zone in-between
alluvial basin into the hill, and the hilltop (lower values
SaSURF). In comparison with right SaSURF maps (at predominant frequency), a clear increase in SaSURF is
observed due to soft soil of alluvial basin of Bednja river.
The hilltop (T24) shows little or no variation of SaSURF at
PGA and at the predominant frequency with higher input
PGAROCK.
Page 11 of 21
642
A map of soil amplification (Fig. 6) shows the variation
of range of AF at PGA (left figures) and AF at a predominant frequency (right figures) on the site of Trakošćan
Castle for different input rock motions. The maps clearly
distinct three main microzones of interest: the alluvial
zone, the transition zone and the hilltop. The highest
amplification occurs in the alluvial basin, particularly for
lowest input PGAROCK = 0.08 g. Little or no amplification
is observed at the hilltop in all three cases of input PGA.
Medium to high-plasticity soils (lower VS) have small
damping and a large range of linearly elastic behaviour
which is prone to resonance effect. Such resonance can
amplify the incoming seismic motion. Soils with low (or
none) plasticity (higher VS) exhibit a highly nonlinear
behaviour, they show substantial damping even at very
small shear strains, and their strength can degrade significantly. In such cases, resonance effect is less possible
(Vučetić 1992). From the presented maps, it is clear that
the alluvial basin of Bednja river on the Trakošćan Castle
site is more susceptible to earthquakes due to the fact that
soft soil causes amplification of seismic energy than those
at the hilltop.
Discussion
Trakošćan Castle lies in Lepoglava syncline alluvial sediments of the Bednja River between Mt. Ivančica and Mt.
Ravna Gora (e.g. Tomljenović and Csontos (2001). Based
on the HVSR results (see Fig. 2), it was concluded in
Stanko et al. (2016) that the mechanism of damage to
Trakošćan Castle occurred due to the propagation of the
seismic energy from the epicentre (Mt. Ivančica) through
the alluvial basin of the Bednja river (amplification),
trapping of seismic waves and focusing of the seismic
energy directly to the top of Trakošćan Castle hill on which
Trakošćan Castle stands (topographic effects). Presented
maps (Figs. 5 and 6) of surface spectral acceleration and
amplification factors confirm this conclusion and raise a
question: ‘‘Why was Trakošćan Castle damaged in 1982 if
HVSR show little to none amplification at the hilltop?’’
The dominant frequency of an earthquake event and the
natural frequency of a structure and soil are vital factors
(Kramer 1996). Dynamic resonance and structural damage
can occur if the natural frequency of a structure is close to
the natural frequency of soil. The dynamic behaviour of a
building in the elastic domain can be useful to assess its
vulnerability (Nakamura et al. 1999, 2000). The application
of a microtremor HVSR methodology has been used to
determine the natural frequency of historical monuments
(e.g. Del Monaco et al. 2013; Ditommaso et al. 2010;
Fäcke et al. 2006; Fiaschi et al. 2012; Gentile and Saisi
123
642 Page 12 of 21
Environ Earth Sci (2017) 76:642
PGAROCK = 0.08 g (95 yrp)
T11
T11:
SaSURF (pf)= 0.53 g (4.2 Hz)
SaSURF (PGA)= 0.19 g
AF(pf)= 3.54 (3.95 Hz)
AF(PGA)= 2.30
T14:
SaSURF (pf)= 0.43 g (9.4 Hz)
SaSURF (PGA)= 0.13 g
AF(pf)= 3.26 (11.4Hz)
AF(PGA)= 1.65
T24:
SaSURF (pf)= 0.21 g (17.6 Hz)
SaSURF (PGA)= 0.94 g
AF(pf)= 1.98
AF(PGA)= 1.17
T14
T24
PGAROCK = 0.31g (1000 yrp)
T11
T11:
SaSURF (pf)= 1.75 g (3.3 Hz)
SaSURF (PGA)= 0.60 g
AF(pf)= 2.89 (3.28 Hz)
AF(PGA)= 1.91
T14
T14:
SaSURF (pf)= 1.78 g (9.4 Hz)
SaSURF (PGA)= 0.55 g
AF(pf)= 3.06 (9.4 Hz)
AF(PGA)= 1.78
T24:
SaSURF (pf)= 0.94 g (15.5 Hz)
SaSURF (PGA)= 0.38 g
AF(pf)= 2.14 (17.6 Hz)
AF(PGA)= 1.22
123
T24
Environ Earth Sci (2017) 76:642
b Fig. 4 Example of EQL analysis for sites T11, T14 and T24
(Trakošćan Castle, hilltop) for input PGAROCK levels: 0.08 g (95-year
return period) and 0.31 g (1000-year return period) represented by
input rock response spectrum (SaROCK) on the left side. Surface
response spectrum (SaSURF) and amplification factor (AF) are
presented on the right side. Red lines indicate results of EQL analysis
for individual ground motions. Thick black line indicates median
results for all ground motions. Thin black dash lines indicate 95%
confidence interval. Blue line marks peak values of SaROCK, SaSURF
and AF at predominant frequency (pf). Dashed blue line marks values
of SaROCK at input PGAROCK, and SaSURF and AF at peak ground
acceleration (PGA). Values of the specific peak (SaSURF, AF) at
predominant frequency (pf) and at the peak ground acceleration
(PGA) are shown on the left side
2007; Moisidi et al. 2004; Nakamura et al. 1999, 2000,
Stanko et al. 2016). Microtremor ambient noise measurements have been taken to detect potential weak points in
the structure of Trakošćan Castle, primarily the construction of the Castle Tower due to earthquake damage and
improper reconstruction (Stanko et al. 2016). The results of
the HVSR frequency response of Trakošćan Castle were:
(a) the fundamental frequency of the Tower Castle ranges
from 2.41 up to 3.13 Hz, (b) the fundamental frequency of
the core structure of the Castle ranges from 4.25 up to
5.31 Hz, and (c) observed higher frequency modes of the
structure of the Castle (first and second floor) ranges from
approx. 8 Hz up to 12 Hz.
Based on the observed HVSR frequency response of the
core structure of Trakošćan Castle and the Tower itself
(fundamental and higher modes), maps of surface spectral
acceleration and soil amplification at different frequencies
(3 Hz, 5 Hz and 10 Hz) have been developed for different
input PGAROCK (0.08 g, 0.18 g and 0.31 g) to evaluate the
seismic response of the Castle. Maps are shown in Fig. 7
(SaSURF) and Fig. 8 (AF). Surface spectral accelerations
and amplification factors are mostly expressed at 5 Hz,
particularly in the alluvial basin, and the frequency corresponds to the core structure of Trakošćan Castle. With the
change of frequency (from 3 Hz to 10 Hz), it is obvious
that highly amplified seismic energy (SaSURF and AF)
focuses from the alluvial basin of the Bednja river directly
to the right side of the Castle structure (fundamental and
higher modes). Seismic waves polarized through mountain
topography are subjected to localized (de)amplification due
to diffraction and interference, affecting the pattern of
PGAROCK (Meunier et al. 2008). Recent studies (e.g.
Burjanek et al. 2014) observed site effects at sites with
pronounced topography. In general local soil conditions are
considered in terms of subsurface velocity structure;
amplification is controlled by the subsurface velocity
structure; i.e. weak amplification (\ 2) at some rock sites
(EC8 class A) and systematic frequency-dependent
amplifications for the non-EC8 class A sites. Burjanek
et al. (2014) observed that amplifications are correlated
Page 13 of 21
642
with ground motion polarization and directionality in the
both ambient noise vibrations and earthquake recordings at
sites with pronounced topography. Although strong
amplification at hilltop is not observed like in recent studies
(e.g. Burjanek et al. 2014), amplification factor maps at
PGA and predominant frequency (Fig. 7) and at 10 Hz
(Fig. 8), indicate topographic effects due to pronounced
polarization and directionality of simulated ground motion.
In our previous study (Stanko et al. 2016), this effect was
not clearly observed from HV amplification map (Fig. 2d)
and the conclusions were drawn based on damage reports
and HVSR results combined with geology and topography
maps at the Trakošćan site. Indirect evidence of topographic effects was drawn from directionality HVSR
polarization effects observed at Trakošćan site controlled
by subsurface faults (geometry) and polarized from alluvial
basin directly to the Castle hilltop (NNE-SSW direction).
The dynamic behaviour of structures during an earthquake correlates with the behaviour of the ground underneath, which can lead to resonance effects. Stiffness and
strength of saturated soils (sand, gravel) may significantly
degrade under cyclic earthquake loads, leading to the
shortening of the original (fundamental) predominant frequency (lengthening of the period) of the soil deposit
(Vučetić 1992). Figure 9 shows maps of predominant frequency variation for different PGAROCK (0.08 g, 0.18 g,
and 0.31 g). The result for PGAROCK = 0.08 g is comparable with HVSR frequencies (Fig. 2a). A slight difference
can be seen at points T22 and T23, whose HVSR frequencies are higher than 30 Hz (a very stiff site). With
higher PGAROCK, shortening of predominant frequencies
(lengthening of the period), particularly in the alluvial
basin, can be observed. This effect is not expressed in the
Trakošćan hill (rock site, higher values of VS), and predominant frequencies match the HVSR frequencies from
Stanko et al. (2016), except for the mentioned T22 and T23
points. Maps of surface spectral accelerations (SaSURF)
(Figs. 5 and 7), i.e. response spectra, indicate that shaking
in the alluvial basin is particularly rich in frequency range
3 – 6 Hz (matches fundamental frequency of the core
structure of the Castle) where the shortening of predominant frequencies is most prominent with higher input
PGAROCK. More interesting is that rich frequency content
of shaking extends towards the Trakošćan Castle hilltop
between 5 Hz and 10 Hz (matches higher frequency modes
of the structure of the Castle) where the effects of shortening of predominant frequencies are not observed. Recent
strong earthquakes in Italy (e.g. L’Aquila, Amatrice)
proved that centuries-old structures are particularly vulnerable to strong earthquakes of longer durations. The
study of Celebi et al. (2010) proved that historical structures due to lack of ductility and structural capacity are
deficient in terms of intense cycling shaking with similar
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Environ Earth Sci (2017) 76:642
b Fig. 5 Left: Surface spectral acceleration (SaSURF) maps at peak
ground acceleration (PGA) for input PGAROCK levels (0.08, 0.18 and
0.31 g). Right: SaSURF maps at predominant frequency (pf) for input
PGAROCK levels (0.08, 0.18 and 0.31 g)
observations as ours. Celebi et al. (2010) conclusions were
drawn from response spectra of recorded motions and
indicate that non-ductile, unreinforced older historical
buildings that were damaged responded with shortening of
structure frequencies (the structure is softening) that corresponds to dominant frequencies of input motions. The
same study Celebi et al. (2010) observed that some
buildings damage or collapse was limited because of short
duration of strong shaking, and that longer duration of
medium- to high-frequency shaking could induce more
damage particularly to old buildings up to six stories
(similar height as Trakošćan Castle Tower). Quantitatively
speaking, longer durations at higher accelerations combined with lack of ductility in historical buildings play a
significant role in the collapse or heavy damage, particularly if the frequency content of given input motion is
similar to the fundamental frequency of the structure.
Dynamic resonance of the core structure of Trakošćan
Castle and focused earthquake energy amplified between
5 Hz and 10 Hz were responsible for the structural damage
to the Castle Tower which occurred due to shaking of its
structural core. The small Tower Castle and the core
structure date back to the thirteenth century. Since a higher
Castle Tower was added in the nineteenth century, there is
a certain difference in material. A possible solution to this
problem would be to change the fundamental frequency of
Castle Tower through structural reconstruction. In this way,
it would match the fundamental frequency of the core
structure of Trakošćan Castle. Cracking and other damages
to the structure that occur due to an earthquake or other
disruptions can change its natural frequency and in that
way increase or decrease resonance potential. The principle
of anti-seismic strengthening and repair should be applied
to restore and improve the structural capacity of Trakošćan
Castle in order to increase seismic structural resistance and/
or ductility of certain structural members (the Castle Tower
in particular) within the existing structural core of the
Castle, thus enabling it to absorb seismic energy without
serious damage (e.g. Celebi et al. 2010; Elnashai and Di
Sarno 2008).
Polarization and directionality observed for surface
spectral accelerations and amplifications with the change in
input PGAROCK and at certain frequencies confirm and
enhance conclusions drawn from the previous HVSR study
of seismic response and vulnerability (Stanko et al. 2016)
about the damage to the Tower Castle and part of the
second floor that happened during the earthquake in 1982
Page 15 of 21
642
because of the topographic effects in the NW–SE direction.
Nowadays, the improvement of earthquake resistance and
protection of cultural-historical monuments require
knowledge of the usage and protection of traditional
buildings without destroying their authenticity. When
structural interventions are performed, the original structural system should basically remain unchanged. Conservation is actually one of the most challenging problems
modern civilization faces. This requires a multidisciplinary
cooperation (e.g. seismologists, geotechnical engineers,
geologists, civil construction engineers, structural engineers, archaeologists, restorers, government, monumental
institutions) (e.g. Viggiani 2013). The use of geophysical
methods is usually limited at historical sites due to terrain
features. Microtremor measurements at historical sites can
overcome this limitation and provide local seismic
response and vulnerability of historical monuments. Also,
computational modelling can greatly improve these results.
Conclusion
The improvement of earthquake resistance and protection
of cultural-historical monuments require knowledge of the
usage and protection of traditional buildings without
destroying their authenticity. Historical monuments, such
as castles, were usually built at hilltops or other places
where they could use some natural features of the land to
help them defend from low-level attacks. The use of
certain geophysical survey methods which require a long
profile is a big challenge because this kind of terrain
(steep hills, mountains, ridges, slopes, cliffs, etc.) creates
lack of space and makes it impossible to carry out a
survey. The application of a quick and non-invasive
microtremor HVSR methodology with no environmental
impacts can overcome this limitation and provide a local
seismic response.
Trakošćan Castle is a good example of a historical
monument which is protected as an important historical
entity by the Republic of Croatia. The Tower Castle and
part of the second floor were damaged by an earthquake in
1982 (ML = 4.5). A non-invasive horizontal-to-verticalspectral-ratio (HVSR) method was used to estimate the
local seismic response and to analyse the seismic vulnerability of the Castle. The estimated HVSR site frequencies
and HV amplification at Trakošćan Castle can only be used
as an indication of an initial soil site frequency and
amplification, so-called natural soil model, which corresponds to the subsoil profile without the influence of an
earthquake. A full-scale equivalent-linear (EQL) site
response analysis can be performed for different earthquake scenarios, ranging from low to high seismicity.
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Environ Earth Sci (2017) 76:642
Environ Earth Sci (2017) 76:642
b Fig. 6 Left: Amplification factor maps at peak ground acceleration
(PGA) for input PGAROCK levels (0.08, 0.18 and 0.31 g). Right: AF
maps at predominant frequency (pf) for input PGAROCK levels (0.08,
0.18 and 0.31 g)
This paper presents a continuation of seismic vulnerability research project on the site of Trakošćan Castle based
on initial HVSR results. The aim of this paper is to develop
and enhance the seismic vulnerability of the historical
Trakošćan Castle to earthquakes of different intensities
using an EQL site response analysis. The earthquake scenarios that have been chosen for the EQL analysis are
Page 17 of 21
642
based on maximum input design ground acceleration
PGAROCK that corresponds to return periods of 95 (0.08 g),
475 (0.18 g) and 1000 (0.31 g) years, respectively. Based
on the EQL analysis, maps of spectral acceleration and
amplification have been created at the predominant frequency and at 3 Hz, 5 Hz and 10 Hz. These frequencies
correspond to HVSR frequency response of the core
structure of the Castle and the Castle Tower itself. The
results strongly confirm conclusions from the HVSR
method about the damage to the Tower Castle and part of
the second floor that happened during the earthquake in
1982 due to topographic effects by pronounced
Fig. 7 Maps of surface spectral accelerations (SaSURF) at different frequencies (3, 5 and 10 Hz chosen to match frequency range of Trakošćan
Castle fundamental and higher modes) for input PGAROCK levels (0.08, 0.18 and 0.31 g)
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Environ Earth Sci (2017) 76:642
Fig. 8 Maps of amplification factors (AF) at different frequencies (3, 5 and 10 Hz chosen to match frequency range of Trakošćan Castle
fundamental and higher modes) for input PGAROCK levels (0.08, 0.18 and 0.31 g)
polarization and directionality of the ground motion from
the alluvial basin to the hilltop. Highly amplified seismic
energy from the alluvial basin of the Bednja River was
focused directly on the right side of the structure of the
Castle. Dynamic resonance between the core structure of
the Castle and amplified earthquake energy at 5 Hz and
10 Hz was responsible for the structural damage, which
occurred in the Castle Tower due to the shaking of the
structural core of the Castle.
Different types of earthquake intensities will have different impacts on historical structures. The combination of
123
highly dense microtremor measurements (their advantage
is that they can be taken in a free field and inside a
structure) and computation modelling, such as an EQL
analysis, can help to assess seismic vulnerability to an
earthquake. Since microtremor measurements on the site of
Trakošćan Castle have been taken only at the oldest
structural core and the Tower because of the damage that
occurred during the earthquake in 1982, there are plans to
extend these measurements so that they cover vulnerability
and frequency response of the entire Castle. The results of
the survey (dynamic frequency response of a historical
Environ Earth Sci (2017) 76:642
Page 19 of 21
642
b Fig. 9 Comparison of peak amplification factor predominant fre-
quency map for input PGAROCK levels (0.08, 0.18 and 0.31 g)
structure, surface spectral acceleration, soil amplification,
predominant frequency) provide valuable information for
anti-seismic strengthening and repair which can be used to
restore and improve the capacity of historical structures. In
this way, seismic structural resistance and/or ductility of
certain structural members within the existing structural
system could be increased, thus enabling it to absorb
seismic energy without serious damage.
Acknowledgements We thank to anonymous reviewers for their
constructive criticism that helped us to improve the overall quality of
the manuscript. The study was financed by the Faculty of Geotechnical Engineering, University of Zagreb. We are very grateful to the
Trakošćan Castle Museum for their help with this project study and
for providing us with historical information’s that help us in the
interpretation of our results. We acknowledge A. Filipović, V. Sanković and I. Slukan for their help with microtremor measurements.
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