NUMERICAL INVESTIGATION OF THE SEISMIC BEHAVIOUR OF … · 2014. 7. 31. · Numerical Investigation of the Seismic Behaviour of Ancient Columns . 3 investigation was carried out,

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]

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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.

Konstantinos Papadopoulos and Elizabeth Vintzileou

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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

Numerical Investigation of the Seismic Behaviour of Ancient Columns

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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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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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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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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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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)

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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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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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(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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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


Apollo Epikourios



Apollo Epikourios



the Parthenon



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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

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NUMERICAL INVESTIGATION OF THE SEISMIC BEHAVIOUR OF … · 2014. 7. 31. · Numerical Investigation of the Seismic Behaviour of Ancient Columns . 3 investigation was carried out,