-
SAHC2014 – 9thStructural Analysis of Historical
Constructions
International Conference on
F. Peña & M. Chávez (eds.) Mexico City, Mexico, 14–17
October 2014
NUMERICAL INVESTIGATION OF THE SEISMIC BEHAVIOUR OF ANCIENT
COLUMNS
Konstantinos Papadopoulos1, and Elisabeth Vintzileou2 1 Hellenic
Ministry of Culture, Technical team of the Committee for the
Preservation of Apollo Epi-
kourios temple Archaeological site of Bassai, Andritsaina -
27061, Greece
e-mail: [email protected]
2
Keywords: Ancient Temples, Multi-drum Columns, Rocking Response,
F.E. Simulations.
National Technical University of Athens, Faculty of Civil
Engineering 9 Heroon Polytechneiou Str., Zografos, Athens - 15780,
Greece
e-mail: [email protected]
Abstract. This paper presents a numerical study of the response
to earthquake actions of five multi-drum columns from ancient-Greek
temples constructed in the archaic and classical pe-riod. These
columns are of different size and slenderness, and have various
numbers of drums. The numerical analyses were conducted using the
finite element software Abaqus. In order to verify the efficiency
of the software and to calibrate the basic characteristics of the
simula-tions, a preliminary, but comprehensive, investigation was
carried out, in which data derived from shaking table tests taken
from two experimental programmes were compared with the respective
numerical predictions from the simulation of the tests. As the
results of the prelimi-nary investigation were satisfactory, the
study continued in its second phase, in which 3-dimentional models
of the five abovementioned ancient columns were seismically
excited, us-ing records of four earthquakes occurred in Greece with
different frequency content. The records were scaled by factors of
increasing magnitude, from low intensity levels to the levels that
induced collapse to all the models of the columns. From the
parametric analyses, estima-tions for the instability threshold of
the columns were derived, provided that the columns are in vertical
position, on rigid base and with drums and contacts in good
condition. Moreover, the numerical results show that the various
numbers of drums of the columns did not alter significantly their
dynamic response and that the effect of the size of the columns on
their in-stability threshold is of great significance, as the
larger column presented the strongest resis-tance to deformation
and collapse, despite that it is more slender than the other
columns.
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Konstantinos Papadopoulos and Elizabeth Vintzileou
2
1 INTRODUCTION The columns in monumental buildings of antiquity
are dry-stone structural elements con-
sisting of limited in number stone elements (the drums and the
capital). The stone pieces were almost perfectly cut; thus, in most
cases, full stone-to-stone contact was ensured. In contrast to
their rather simple structural system, their seismic behavior is
extremely complicated and highly non-linear. The free-standing
columns are responding to strong seismic motions with continuous
displacements over the height and rotations or rocking of
individual drums or of groups; thereof, large part of the induced
energy is consumed thanks to the friction mobilized along
interfaces of stone pieces. After the end of the seismic excitation
and provided that the overall stability of the column is preserved
(i.e. partial or total collapse are prevented) the col-umn returns
to calm, in damped free oscillation. Naturally, permanent relative
displacements of the drums are associated with this behaviour.
However, because the above-described dynamic response mechanism
of the ancient col-umns is hard to be modelled analytically, due to
the fact that the governing equations of mo-tion are different for
each of the numerous possible schemes of vibration, after the
earlier [1] and the following analytical studies [2–5] based on the
dynamics of rigid blocks, the research has been directed to
experimental investigations [6–8] as well as to alternative
numerical stu-dies [9–13]. Relative analytical approaches from the
recent years should also be mentioned [14, 15]. The basic
conclusions drawn from these studies are the following: The seismic
re-sponse of multi-drum columns is very sensitive to geometrical
parameters, material properties and seismic action characteristics.
The probability of a column to collapse under seismic exci-tation
increases with the increase of its slenderness ratio or the
decrease of its size for the same proportions and, naturally, with
the increase of the amplitude of the excitation. During the seismic
event, the motion that dominates the response of ancient columns is
rocking of drums. The columns residual displacements are not
necessarily proportional to the maximum displacements induced by
the seismic event.
As the vast majority of the preserved structures of antiquity
are buildings in ruinous state, consisting only of isolated columns
or colonnades, and are located mostly in regions of signif-icant
earthquake activity (Eastern Mediterranean), the study of the
seismic behaviour of an-cient columns is an essential engineering
component concerning the preservation of the architectural
heritage. This paper presents a numerical study of the response to
earthquake actions of five multi-drum columns from three
ancient-Greek temples; the two out of the three ancient monuments
are being currently restored. The study was conducted using the
finite element software Abaqus [16], after a preliminary
investigation in which the efficiency of this code was verified.
The objective of the study is to reach quantitative results, even
as rough approximations, concerning the various instability
thresholds of the aforementioned columns. As the five selected for
examination columns are of different size and slenderness, and have
various numbers of drums, a secondary aim of the present work is to
draw conclusions, through comparisons, about the influence on the
instability of the columns of their different geometrical
characteristics.
2 CHECKING THE ADEQUACY OF THE SELECTED NUMERICAL TOOL TO
PREDICT THE ROCKING RESPONSE OF DRY-STONE STRUCTURES
2.1 Brief review of the experimental data As mentioned in the
Introduction, in order to verify the efficiency of the computer
code
used in the present work to predict the seismic behaviour of
ancient columns, a preliminary
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Numerical Investigation of the Seismic Behaviour of Ancient
Columns
3
investigation was carried out, in which data derived from
shaking table tests of two broad ex-perimental studies were
compared with the respective results from the simulation of the
tests.
The first experimental study was carried out at the National
Laboratory of Civil Engineer-ing of Portugal, and in this study, it
was investigated the dynamic behaviour of single blocks, and
assemblies of two and three blocks structures. The aforementioned
structures were sub-jected to three different base motions: free
rocking, harmonic and random excitations at the seismic table of
the Laboratory. More specifically, the experimental tests were
carried out on four single blue granite stones (referred as
Specimen 1-4), on two stacked blue granite stones (referred also as
bi-block structure), and on a three-block portico (referred as
trilith) also made of blue granite (Figure 1a). The stones had
different dimensions (Table 1) and were manufac-tured with a small
cut of 45o at their bases, with the aim of reducing the continuous
degrada-tion of their corners. A foundation of the same material
was used as the base where the blocks were free to rock. Details
about the experimental study and its various results can be found
in Peña et al. 2007 [17], 2008 [7].
Results used in the present work were taken also from an
experimental study which was conducted at the Laboratory for
Earthquake Engineering of the National Technical University of
Athens, Greece. This study was focused on the seismic response of a
multi-drum column model, and is presented in details in Mouzakis et
al. 2002 [6]. The column model was a 1:3 scale replica of a column
from the Pronaos (Porch) of the Parthenon (Acropolis, Athens). It
was composed of 12 drums of equal height (0.26m) and a capital of
0.22 m high (Figure 1b). The diameter of the model was decreasing
its height, and no flutes were provided to the drums. The model was
resting on a marble base fixed on the shaking table. Nineteen tests
were per-formed at N.T.U.A., under base excitations simulating
three seismic events which occurred in Greece and cover a wide
range of characteristics of ground motions. In three experiments
the displacements of the capital were registered.
(a) (b)
Figure 1: (a) Test specimens of blue granite [7]: Single blocks
(left), bi-block structure (middle) and trilith; and (b) sketch of
the multi-block column tested at N.T.U.A. [6].
Table 1: Dimensions of granite specimens.
Block Specimen Width (m) Height (m) Thickness (m) Mass (kgr)
Single # 1 0.250 1.000 0.754 503 Single # 2 0.170 1.000 0.502 228
Stacked (top) 0.150 0.600 0.400 97 Stacked (bottom) 0.200 0.600
0.550 178 Trilith (columns) 0.220 0.800 0.650 305 Trilith (lintel)
1.020 0.150 0.650 265 Base 1.000 0.250 0.750 500
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Konstantinos Papadopoulos and Elizabeth Vintzileou
4
2.2 The numerical simulations of the experiments The simulations
of the various experiments on the granite stones and of the test on
the
marble column were conducted using the commercially available
computer code ABAQUS/Explicit (version 6.9), which is an explicit
dynamics finite element program, suita-ble for highly nonlinear
problems involving changing contact conditions. With this code 3-D
numerical models were created, following as close as possible the
geometry of the tested spe-cimens (Figure 2a). Each stone was
modelled as a discrete component block. For the discreti-zation of
the models, 8-nodes hexahedra elements were used, with moderate
density of the meshes, as initial results of the investigation
suggested this kind of approach. The conse-quence of using this
meshing approach was that the shaft of the N.T.U.A. column specimen
in the numerical model to have a polygonal cross-section, instead
of a round one, as the real col-umn. It must be noted, also, that
the detail of the small cuts at the corners of the granite blocks
was included in the models of the bi-block structure and the
trilith (Figure 2b), whereas in the simpler models of the two
single–block specimens was ignored, as of insignificant
influence.
(a) (b) Figure 2: (a) The numerical models and their
discretization of the tested specimens (axis-symmetric
drawing);
and (b) enhanced details showing cuts in corners of the bi-block
structure model (left) and the trilith model.
The materials of the specimens, were modeled as isotropic and
elastic, using the mechani-cal properties of granite (ρ= 2670
kgr/m3, Ε = 53000 MPa, ν = 0.20), and marble (ρ= 2700 kgr/m3
In the models of the granite specimens, 0.50 friction
coefficient was defined, whereas in the model of the pentelic
marble column 0.70, on the basis of the known mechanical
proper-ties of the two materials. Regarding the damping
coefficient, it was not introduced in the models of the
single-block specimens and the bi-block structure, because initial
analyses
, Ε = 80000 MPa, ν = 0.26). The interfaces between discrete
blocks were modelled us-ing a ‘hard’ contact model for the
direction normal to the interfaces, in combination with a classical
friction model applied in the tangential direction of the
interfaces. According to the ‘hard’ contact model, when two
surfaces are in contact, compressive stresses can be transmit-ted
by the interface, whereas, when the surfaces separate, transferred
stresses are reduced to zero. On the other hand, the friction model
provides a relationship between the shear (fric-tional) stress
along an interface and the normal pressure on the interface, thus,
allowing to es-timate the critical shear stress at which sliding
along the interface is initiated, correlated with the friction
coefficient at the interface. Moreover, the software allows the
introduction of a damping model that calculates forces resisting
the relative motions of the contacting surfaces, with the
definition of a damping coefficient as a constant directly
proportional to the rate of relative motion between the surfaces.
The damping coefficient remains at the specified con-stant value
while the surfaces are in contact and at zero otherwise.
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Numerical Investigation of the Seismic Behaviour of Ancient
Columns
5
showed that the simulation of a free-rocking test of
single-block specimen 1 leads to almost identical results
regardless if the damping coefficient is equal to zero or 0.05 or
0.10 (Figure 3 left). On the contrary, in the model of the thrilith
and of the multi-block marble column, where the interfaces are
several, parametric analyses showed that damping behaviour must be
taken into account, as it influences notably the numerical
predictions (Figure 3 right). In these parametric analyses, the
examined damping coefficients were zero, 0.005, 0.01 and 0.02, and
the best results (presented in the following paragraph) were
derived from the simulations where the damping coefficient was
equal to 0.01.
The various dynamic loadings were applied to each numerical
model, by determining the time histories of the three components of
displacement of their base imposed during each test.
Figure 3: Numerical results showing the influence of the
introduction of damping model in various simulations.
2.3 Comparison of the numerical results with the experimental
data The experimental results from the study of the Portuguese
research team, which were se-
lected for comparison with respective numerical predictions,
are: (i) the time history of rock-ing angle of specimen 1, after
being deflected by 3o in a free rocking motion test (see Figure 4
left); (ii) the time history of rocking angle of specimen 2, after
being deflected by 6.5o in a free rocking motion test (Figure 4
right); (iii) the maximum rocking angle of the top block from four
tests on bi-block structure, subjected to constant sine of 4.0 Hz
and gradually in-creasing amplitude from 2 to 5 mm (Figure 5 left);
and (iv) the time histories of principal ho-rizontal displacement
of the two pillars and the lintel from the test where the trilith
was subjected to constant sine 3.3 Hz and 5 mm amplitude (Figure 5
middle and right).
It is obvious from the comparisons that the software predicted
accurately the free rocking motion of the two single-block
specimens (Figure 4). In regards to the response of the two stacked
blocks under increasing harmonic excitations, the numerical results
were satisfactory also, because they follow, although
underestimated, closely the variation of the maximum rocking angle
of the top block as the magnitude of the excitation increases
(Figure 5 left). Quite satisfactory results were derived also from
the simulation of the experiment with the trilith. More
specifically, the comparison between experimental data and
numerical results in this more complex case, regarding the
horizontal displacement of the two pillars (Figure 5 middle),
denote that the frequency content was successfully predicted by the
software, as were the maximum values of displacement at the early
stage of the excitation and the gradually in-creasingly slips of
the pillars at the later stages of the test. Only in the comparison
concerning the horizontal displacement of the lintel there is a
notable difference between observed and predicted response (Figure
5 right), and it is due to fact that in the numerical analysis the
slip-page was initiated not immediately after the early stage of
the excitation, but little later; how-ever the rest characteristics
of the response were predicted quite accurately, as for the
pillars.
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Konstantinos Papadopoulos and Elizabeth Vintzileou
6
Figure 4: Comparison between experimental and numerical results,
regarding free-rocking motion tests.
Figure 5: Comparison between experimental and numerical results,
regarding tests with harmonic excitation.
From the experimental results related to the seismic response of
the marble column tested by the Greek research team, the results of
the test named EQ17 (which is one out of the three tests where the
displacements of the capital were registered) were selected for
comparison with corresponding numerical results. More specifically,
the results regard the three compo-nents of displacement of two
characteristics points in the capital of the column, K2 and K3 (see
Figure 1b). EQ17 was the test with the larger column deformation
and the larger capital displacements. In this experiment the Griva
earthquake of 1990 (as recorded in the city of Edessa), scaled by a
factor of 2.00, was used for the excitation of the shaking table.
Thereof, the maximum acceleration of the shaking table in the two
horizontal directions and in the ver-tical direction were 0.26g,
0.15g, and 0.09g, respectively.
The comparison between experimental and numerical results for
experiment EQ17 is shown in Figure 6. Regarding point K2, it is
clear that the software succeeds in estimating the shape of the
oscillation, and the maximum and residual values of displacement,
in nearly all cases. The only noteworthy difference is in the
maximum displacements in the longitudinal direction, but the
residual longitudinal displacements of the point are almost
identical, as are its maximum and residual displacements in the
transverse direction. Regarding point K3, si-milarly to K2, the
numerical analysis was able to predict roughly, but quite
accurately, the shape and magnitude of the oscillation observed in
the experiment. Here, again, the only sig-nificant difference is in
the longitudinal direction, where the residual slips are of
opposite signs; however, the frequency contents are quite similar,
and the offsets of the point occurred simultaneously and are almost
equal.
It is worth adding that the residual displacements of the drums
predicted by the simulation of experiment EQ17 are the same, in
qualitative terms, with the deformations observed by the
researchers during the experiments where the Edessa seismic record
was used [6]: in almost
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Numerical Investigation of the Seismic Behaviour of Ancient
Columns
7
every contact of the drums residual slippages and large
rotations around the vertical axis oc-curred (Figure 7).
0 5 10 15 20 25Time (sec)
-150
-75
0
75
150
Dis
plac
emen
t (m
m) K2 - U1
EQ17Abaqus
0 5 10 15 20 25
Time (sec)
-30
-15
0
15
30
Dis
plac
emen
t (m
m) K2 - U2
EQ17Abaqus
0 5 10 15 20 25
Time (sec)
-150
-75
0
75
150
Dis
plac
emen
t (m
m) K2 - U3
EQ17Abaqus
0 5 10 15 20 25Time (sec)
-150
-75
0
75
150
Dis
plac
emen
t (m
m) K3 - U1
EQ17Abaqus
0 5 10 15 20 25
Time (sec)
-30
-15
0
15
30D
ispl
acem
ent (
mm
) K3 - U2EQ17Abaqus
0 5 10 15 20 25
Time (sec)
-150
-75
0
75
150
Dis
plac
emen
t (m
m) K3 - U3
EQ17Abaqus
Figure 6: Comparison between experimental and numerical results,
regarding the absolute displacement of points K2 (top) and K3
(bottom) of the capital of the multi-block column during experiment
EQ17, in the longitudinal
direction (left), the vertical direction (middle) and the
transverse direction (right).
(a) (b)
Figure 7: Final position: (a) of the column after an experiment
at N.T.U.A.; and (b) of the numerical model of the column, after
its excitation with the input motion of experiment EQ17.
2.4 Conclusion of preliminary investigation Taking into
consideration the sensitivity of the rocking response of dry-stone
structures,
the overall agreement between experimental data and numerical
results is considered quite satisfactory. From the investigation
presented above, it was found that the selected for use fi-nite
element software was able to reproduce the key features (the
frequency content, the max-imum displacement and the residual
slippage) of the experimentally observed dynamic response of
various stone-blocks assemblies (including a multi-drum marble
column). More-over, the fact that the numerical predictions came
from simulations in which no significant changes were made to the
basic parameters of the problem (models geometry, surfaces’
inte-raction properties, dynamic loads) suggests that the software
can be employed with confi-dence for the estimation of the dynamic
behaviour of structures made of stone-blocks connected only by
friction, such as free-standing ancient columns, or more complex
column-architrave structural groups.
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Konstantinos Papadopoulos and Elizabeth Vintzileou
8
3 THE SEISMIC STABILITY OF FIVE ANCIENT MULTI-DRUM COLUMNS
3.1 The selected for examination ancient columns and their
numerical models The columns selected for the investigation of
their seismic behaviour are the folowing: i)
The typical column of the archaic Doric temple of Athena at the
Arcadian Alifeira, con-structed around the 500 B.C., of
shell-limestone. The column is 3.365 m high, has 0680 m diameter at
its base, and is composed of four drums and a capital. ii), iii)
and iv) Three Doric columns from the north part of the temple of
Apollo Epikourios at Bassai, built of the local limestone in the
last quarter of the 5th
Column of
century B.C.; these columns are 5.97 high, have 1.16 m base
diameter and are composed by a capital and five, seven and ten
drums. (v) The typical Doric peristyle column of the marble
Parthenon erected at the Athenian Acropolis in 447-438 B.C., which
is 10.435 high, has 1.902 m lower diameter, and is composed of
twelve stone pieces. As the aforementioned columns are of different
size and increasing slenderness (their height to base ratios are
around 4.95 for the Alifeira column, 5.15 for the Bassai columns,
and 5.50 for the Parthenon column) and have various numbers of
drums, they can be considered representative of a broad spectrum of
columns constructed in antiquity, at least of the Doric order.
The investigation was conducted using the software
ABAQUS/Explicit (version 6.9), based on the results of the
preliminary numerical analyses. For each column a 3-D model was
created, and all were part of the general model of the parametric
analyses. The columns were simulated free-standing, in vertical
position, and with separate base blocks. Each column model was
created in such way to correspond with the geometry and actual
dimensions of the respective real column (Table 2), on the basis of
the data that are available in the relative bib-liography [18 –
20], with few adjustments made for simplicity reasons. The only
note-worthy difference, derived by the adjustments, is at the cross
sections of the columns shafts, which in the models were polygonal,
instead of the real circular sections with 20 flutes (Figure
8).
Table 2: The basic dimensions used for the creation of the
numerical models of the five ancient columns.
Athena temple Apollo Epi-kourios temple Apollo Epi-
kourios temple Apollo Epi-
kourios temple the Parthenon
Drum Lower Diam.
(m)
Height (m)
Lower Diam.
(m)
Height (m)
Lower Diam. (m)
Height (m)
Lower Diam.
(m)
Height (m)
Lower Diam. (m)
Height (m)
1st 0.680 0.640 1.160 0.700 1.160 0.595 1.160 0.58 1.902 0.870
2nd 0.641 0.720 1.137 1.300 1.135 1.080 1.136 0.59 1.864 0.870 3rd
0.597 0.765 1.084 1.450 1.090 0.840 1.112 0.67 1.826 0.870 4th
0.551 0.800 1.025 1.420 1.060 0.785 1.085 0.61 1.788 0.870 5th – –
0.968 0.555 1.025 0.750 1.061 0.51 1.750 0.870 6th – – – – 0.995
0.745 1.040 0.55 1.712 0.870 7th – – – – 0.965 0.630 1.018 0.53
1.674 0.870 8th – – – – – – 0.996 0.63 1.636 0.870 9th – – – – – –
0.971 0.38 1.598 0.870 10th – – – – – – 0.955 0.375 1.560 0.870
11th – – – – – – – – 1.522 0.870 Capital 0.502 0.440 0.940 0.545
0.940 0.545 0.940 0.545 1.484 0.865 Abacus 0.9042 x 0.155 1.2452 x
0.210 1.2452 x 0.210 1.2452 x 0.210 2.0002 x 0.350
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Numerical Investigation of the Seismic Behaviour of Ancient
Columns
9
(a) (b)
Figure 8: (a): Axis-symmetric drawing of the models of the five
columns showing the differences in the size of the columns and in
the number of their drums; and (b) the discretization of the model
of the Parthenon column.
The same assumptions made for the material and interaction
behaviours for the models presented in Section 2.2 were adopted for
this investigation as well. However, only the neces-sary mechanical
properties of marble (ρ= 2700 kgr/m3
3.2 Seismic input motions
, Ε = 80000 MPa, ν = 0.26, n=0.70) were used, like if all five
columns were constructed of this material, in order for the results
to be absolutely comparable. The models were loaded by their own
weight and were seismically excited using various records. The
records were scaled by factors of increasing magnitude, from low
intensity excitations levels to the levels that induced
collapse.
The seismic excitations were imposed to the base block of each
column model. The three components of each motion were imposed
according to the time histories of ground displace-ments taken from
records of four real earthquakes. In each analysis, the three
motion compo-nents were factored. The seismic input motions used in
the study were selected to have quite different characteristics and
to be representatives of the shallow destructive earthquakes in
Greece. The following seismic events were used:
(a) The Kalamata earthquake, 9/13/1986 (MS = 6.2). The
accelerogram was recorded on hard soil at a distance of about 9 km
from the epicenter. The duration of the strong motion is about 6
sec and the maximum horizontal acceleration 0.27g (PGV = 30.9
cm/sec and PGD = 7.1 cm). (b) The Griva earthquake, 12/21/1990 (MS
= 5.9). The accelerogram used in the study was recorded in Edessa,
in a distance of about 31 km from the epicenter, and reflects the
interference of soft subsoil conditions under the station. It shows
an almost sinusoidal motion with a period of about 0.6 sec, with a
maximum horizontal acceleration of 0.10g (PGV = 10.9 cm/sec and PGD
= 1.1 cm). (c) The Aigion earthquake, 6/15/1995 (MS = 6.2). Its
accelero-gram was recorded 18 km away from the epicenter, in the
basement of a two-storey building on rather soft soil and it is
dominated by a 0.5 sec period pulse of approximately 0.54g
ampli-tude (PGV = 48.1 cm/sec and PGD = 6.7 cm); and (d) The Athens
earthquake, 9/7/1999 (MS
3.3 Numerical results
= 5.9). The accelerogram used in the study was recorded on the
one-story RC building of K.E.D.E., 11 km from the epicenter. The
record shows a maximum acceleration of 0.30g (PGV = 16.1 cm/sec and
PGD = 2.1 cm) and a period of about 0.20 sec.
The results concerning the minimum excitations, in terms of PGA,
PGV and PGD, which caused the collapses of the columns models are
presented in Table 3. It must be parenthetical-ly noted that
hereafter the letter G represents the columns bases. Although the
results vary
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Konstantinos Papadopoulos and Elizabeth Vintzileou
10
significantly, as expected, it is very obvious, even from these
raw data, that the most influen-tial parameter was the size of the
columns (as the larger column presented the strongest resis-tance
to deformation and collapse, despite that it is more slender than
the other columns) and that the different number of drums of the
columns had no significant effect on the results (as the derived
instability limits of the three columns of Apollo temple are almost
equal).
In Table 4 the mean values and the standard deviations of the
minimum levels of maxi-mum accelerations, velocities and
displacements of the excitations that caused the collapses of the
columns models are listed. These summated results are the numerical
predictions about the threshold value of PGA, PGV and PGD that
would cause collapse for each examined col-umn, or any other
ancient column with similar geometrical and material
characteristics, pro-vided that the column is standing vertically,
on rigid base, and with intact drums and interfaces. However, it
must be noticed that the simplifying assumptions made in the
simulat-ing process, in combination with the well known
difficulties in predicting the dynamic beha-vior of multi-drums
columns, render these predictions as rough estimations, and, thus,
the derived instability thresholds of the columns can only be
considered as approximations.
Nevertheless, it is quite interesting that the numerical
estimations about the instability thre-sholds of the larger columns
are much higher than the anticipated earthquake actions in the
areas of the two classical monuments [21], whereas for the smaller
archaic column, they are close; these are in accordance with the
preservation state of the three ancient temples, as near-ly all the
columns of the Parthenon and Apollo Epikourios temple are still
standing [19, 20], whereas the columns of Athena temple at Alifeira
are all collapsed [18].
Table 3: Main data of the minimum excitations that caused
collapse of the columns models.
Model of column
from
Seismic record
Scaling factor
PGA (g)
PGV (cm/sec)
PGD (cm)
Result: overturned cap-
ital and
Athena temple at Alifeira
Kalamata 1.29 0.35 40.0 9.16 3 out of 4 dr. Edessa 5.50 0.55
60.0 6.05 1 out of 4 dr. Aigion 1.56 0.84 75.0 10.45 2 out of 4 dr.
Athens 3.73 1.12 60.0 7.83 3 out of 4 dr.
Apollo Epikourios
temple, with 5 drums
Kalamata 1.62 0.44 50.0 11.50 4 out of 5 dr. Edessa 8.72 0.87
95.0 9.59 4 out of 5 dr. Aigion 2.60 1.40 125.0 17.42 4 out of 5
dr. Athens 7.14 2.14 115.0 14.99 2 out of 5 dr.
Apollo Epikourios
temple, with 7 drums
Kalamata 1.78 0.48 55.0 12.64 5 out of 7 dr. Edessa 8.72 0.87
95.0 9.59 3 out of 7 dr. Aigion 2.60 1.40 125.0 17.42 4 out of 7
dr. Athens 6.83 2.05 110.0 14.34 4 out of 7 dr.
Apollo Epikourios
temple, with 10 drums
Kalamata 1.94 0.52 60.0 13.77 9 out of 10 dr. Edessa 8.72 0.87
95.0 9.59 8 out of 10 dr. Aigion 2.60 1.40 125.0 17.42 4 out of 10
dr. Athens 7.14 2.14 115.0 14.99 5 out of 10 dr.
the Parthenon
Kalamata 4.21 1.14 130.0 29.89 2 out of 11 dr. Edessa 12.84 1.28
140.0 14.12 2 out of 11 dr. Aigion 4.26 2.30 205.0 28.54 6 out of
11 dr. Athens 8.39 2.52 135.0 17.62 5 out of 11 dr.
-
Numerical Investigation of the Seismic Behaviour of Ancient
Columns
11
Table 4: Statistical data concerning the excitations that cause
collapse at the columns models.
Model of column from
Critical excitation’s peak base acceleration (g) velocity
(cm/sec) displacement (cm) Mean value
Standard deviation
Mean value
Standard deviation
Mean value
Standard deviation
Athena temple 0.72 0.34 58.75 14.36 8.37 1.88 Apollo temple,
with 5 drums 1.21 0.73 96.25 33.26 13.38 3.50 Apollo temple, with 7
drums 1.20 0.68 96.25 30.10 13.50 3.27 Apollo temple, with 10 drums
1.23 0.70 98.75 28.69 13.94 3.27
Apollo temple (all three) 1.22 0.64 97.08 27.84 13.61 3.04 the
Parthenon 1.81 0.70 152.50 35.24 22.54 7.86
4 CONCLUDING REMARKS • This paper presents a numerical study of
the seismic response of five columns from three
ancient-Greek temples. As these columns have various numbers of
drums and are of dif-ferent size and slenderness, they can be
considered representative of a broad spectrum of columns
constructed in antiquity, at least of the Doric order.
• The numerical study was conducted using the commercially
available F.E. software ABAQUS. In the first step of the study, a
preliminary but comprehensive investigation was carried out, where
the efficiency of the software was verified and the basic
parame-ters of the simulations were calibrated.
• Following the initial investigation, parametric analyses were
conducted in which the models of the five ancient columns were
seismically excited using records of four earth-quakes occurred in
Greece with different characteristics. From these analyses,
estimation were derived about the threshold value of PGA, PGV and
PGD that would cause collapse for each examined column, or any
other ancient column with similar geometrical and ma-terial
characteristics.
• Moreover, the numerical results denoted that the size of the
columns plays the key-role in their capacity to withstand without
collapsing large earthquake actions, whereas the fact that the
columns are composed by various numbers of drums was not found to
influence significantly their dynamic response nor alter their
stability.
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INTRODUCTIONCHECKING THE ADEQUACY OF THE SELECTED numerical tool
TO PREDICT THE rocking RESPONSE OF dry-stone STRUCTURESBrief review
of the experimental dataThe numerical simulations of the
experimentsComparison of the numerical results with the
experimental dataConclusion of preliminary investigation
THE SEISMIC stability OF five ancient multi-drum COLUMNSThe
selected for examination ancient columns and their numerical
modelsSeismic input motionsNumerical results
CONCLUding remarks