Effect of the Drum Height on the Seismic Behaviour of a Free-Standing Multidrum Column

&e results of a shake-table study on the effect of the drum height on the seismic behaviour and bearing capacity of small-scale free-standing multidrum columns are presented. Columns of equal height with one, three, and six drums through their height were considered for the case of their self-weight only and for the case with an additional weight on the top of the column. &e columns were exposed to a horizontal base acceleration of three accelerograms by successively increasing the maximum acceleration to their failure. &e characteristic displacements and accelerations of the column were measured. It was concluded that an increase in the number of blocks in the column can significantly increase or decrease its ultimate bearing capacity, depending on the type of the applied accelerogram. It is expected that the experimental database can be useful in the validation of nonlinear numerical models for the dynamic analysis of multidrum columns.


Introduction
Multidrum stone columns are important structural elements of historic buildings.eir behaviour during an earthquake depends on numerous parameters, such as the number of blocks, boundary conditions at the top and bottom of the column, the type and processing of joints, the level of gravitational stresses, stone quality, interaction with possible walls, slenderness, precision of construction, foundation deformability, local effects, and earthquake type.
Because of the great importance of historical buildings, the studies regarding the seismic behaviour of stone structures, especially multidrum stone columns, are still up to date.
Unfortunately, only a small number of numerical and especially experimental investigations of multidrum stone columns under an earthquake have been conducted to date.In doing so, only some parameters that affect their seismic response and bearing capacity have been investigated.Several of these studies are briefly listed below.
Contemporary numerical studies on the seismic behaviour of multidrum columns are mainly based on the discrete element method.Using this method, Sarhosis et al. [1] analysed the colonnade of the Forum in Pompeii; Papaloizou and Komodromos [2] analysed multidrum ancient columns and colonnades; Komodromos et al. [3] investigated ancient columns; Konstantinidis and Makris [4] considered a multidrum classical column; Psycharis et al. [5] analysed part of the Parthenon Pronaos; Papantonopoulos et al. [6] analysed classical columns; Sarhosis et al. [7] performed threedimensional modelling of ancient colonnade structural systems subjected to harmonic and seismic loading; and Asteris et al. [8] analysed historic masonry structures.
Contemporary experimental studies regarding the seismic behaviour of multidrum columns are based on shake-table testing.us, Drosos and Anastasopoulos [9] studied a free-standing reduced-scale multidrum column; Drosos and Anastasopoulos [10] investigated an ancient Greek temple; Mouzakis et al. [11] analysed a marble model of a classical column; and Krstevska et al. [12] analysed a model of the Antonina column in Rome.e abovementioned numerical and experimental studies have not been described more closely because they are not considered in this article.
is paper presents the experimental study results regarding the effect of the number of blocks in a multidrum column on its seismic behaviour.e behaviour of smallscale free-standing multidrum columns without and with the mass at the top was studied by shake-table testing.e columns were exposed to the horizontal base acceleration of three di erent accelerograms.Columns made from one, three, and six blocks per their height with stone powder joints were considered.In addition to the new insights of the e ect of the drum height on the seismic behaviour of multidrum columns, one of the aims of this study was to create an experimental database for the possible validation of nonlinear numerical models for the seismic analysis of such columns.e main conclusions of the study are given at the end of the article.According to the authors' knowledge, such research has not been performed to date.It is believed that the given conclusions can be applied to multidrum columns in practice.
Summarized ndings of the study are as follows: (i) An important e ect of the number of blocks in the multidrum column on its seismic response was investigated, which has not been investigated yet.(ii) A reliable experimental approach to research considered problem with the shake-table has been adopted, which can be easily repeated.(iii) Column models were tested to the failure on different earthquake types, with and without mass at their top.(iv) e results of the research are applicable in practice.(v) Generated experimental database can be useful in verifying numerical models for seismic analysis of multidrum columns.

Tested Columns.
e small-scale free-standing multidrum columns (Figure 1) with approximately equal height formed from one, three, and six blocks per column height were tested.e columns S1, S3, and S6 (Figure 1(a)) were loaded only by self-weight, and the identical columns S1m, S2m, and S6m (Figure 1(b)) were loaded with additional weight at their top.e columns have a circular cross section with a 192 mm diameter.ese columns were supported on a shake table indirectly over a 50 mm thick, rigid concrete plate xed to the shake table. in joints (1-3 mm) from stone powder were formed between the blocks, between the block and the bottom plate, and between the block at the top of the column and mass (m).Such joints were used to reduce the stress concentration in the nonideal at dry joint, that is, to ensure an equal adjustment of the contact surfaces between the blocks and an equal transmission of vertical and horizontal stresses in the joint, as well as to simplify the column construction.e type of the joint also a ects the behaviour of the multidrum columns.
is issue was investigated by Buzov et al. [13] for static loads.e height of the columns was approximately 1200 mm, and their slenderness l was approximately 35. e mass at the top of the column (m 500 kg), which is centrally positioned in relation to its axis, was formed from a rigid concrete block with dimensions of 0.8 × 0.8 × 0.33 m.
e columns S1 and S1m were formed from one 1200 mm high block, the columns S3 and S3m from three 400 mm high blocks, and the columns S6 and S6m from six 200 mm high blocks.e blocks were made of concrete with a compressive strength of 53.55 MPa, obtained on the cylinder according to [14].Although the subject of this study is stone columns, concrete blocks were used instead of stone blocks for several reasons [13,15]: (i) unreliability of the uniformity of the stone quality (the probable presence of anomalies in the stone), (ii) great similarity of stone and concrete properties (arti cial stone), (iii) low level of maximum stress in the blocks (the collapse of a column is due to the loss of its stability), and (iv) lower research costs.is approach did not greatly inuence the given conclusions of this study.1. e signi cant e ect of the number of blocks in the column and the mass at the column top on T 1 is evident.By increasing the number of blocks, T 1 increases, that is, the column sti ness decreases.e mass at the top of the column also increases T 1 .e relation of the basic period for the columns S1, S3, and S6 is 1 : 1.33 : 2.82, and the relation for the columns S1m, S3m, and S6m is 1 : 1.30 : 2.8.

Applied Accelerograms.
e tested columns from Figure 1 were subjected to a horizontal base acceleration of the three accelerograms according to Figure 2: (i) the arti cial accelerogram (Figure 2(a)) generated from the elastic response spectrum in accordance with [16] for type 1 and soil type A; (ii) the N-S horizontal component of the Petrovac earthquake [17], Montenegro (Figure 2(b)); and (iii) the N-S horizontal component of the Ston earthquake [17], Croatia (Figure 2(c)).
e spectral values of the adopted accelerograms are presented in Figure 3.
e arti cial and Petrovac accelerograms are characterized by long-lasting action, where the predominant period of the Petrovac accelerogram is somewhat longer.e Ston accelerogram is characterized by a short impact action with a short predominant period.By considering the basic periods of the columns from Table 1 and the spectral values of the applied excitations from Figure 3, it is expected that the arti cial and Petrovac accelerograms are more unfavourable than the Ston accelerogram.However, due to the possibility of the occurrence of nonlinearities in the joints (sliding and rotation), it is di cult to predict which accelerogram would be the most unfavourable for each column in Figure 1.
All the accelerograms in Figure 2 were applied with a successive increase in the maximum acceleration a gmax , Advances in Materials Science and Engineering until the collapse of the column.For the arti cial accelerogram and the Petrovac accelerogram, the increment in the acceleration Δa gmax was adopted as 0.2 ms −2 , and Δa gmax for the Ston accelerogram was employed as 0.5 ms −2 .Although only three di erent base accelerations were adopted to shorten the research, it is believed that this has no practical in uence on the given conclusions.

Measured Quantities and Equipment.
e horizontal displacements u i of the top and bottom of the blocks (5 mm from their edges) for each tested specimen were measured according to Figure 4, as well as the horizontal acceleration a i in the middle of the drum height.e motion of the columns during base excitation was recorded by a precise video camera.
e shake table at the University of Split, Faculty of Civil Engineering, Architecture and Geodesy, was used.A QuantumX MX840A system (HBM) was used to record the data from the sensors.Analogue displacement sensors PB-25-S10-NOS-10C (UniMeasure) were used for the measured displacements, and the accelerations were measured by a type 4610 piezoelectric high-frequency accelerometer (MS).

Test Results
. Before the nal tests were performed, the accuracy of the recurrent tests was measured to verify their reliability.Speci cally, for the S3 and S3m columns, three identical tests were performed for the arti cial and Petrovac accelerograms.e maximum di erence in the measured 4 Advances in Materials Science and Engineering values for each test was up to 4.8%.Given the sensitivity of the problem and the possible e ect of di erent parameters (column verticality, inhomogeneity in joints, mass eccentricity at the top of the column, precision of the acceleration application by the shake table, imperfections in the measurement equipment and measurements, etc.), it was suggested that these deviations are within acceptable limits and have no practical in uence on the given conclusions.erefore, because of the simple presentation of the measured values, the nal tests were conducted on a single specimen.
Only some test results are graphically presented and brie y discussed.
e maximum base acceleration a gmax values for the columns S1, S3, and S6 in their limit state are shown in Figure 5, where the full line indicates a gmax at the collapse of the columns and a dotted line indicates a gmax from the previous acceleration increment with the preserved stability of the columns.It is evident that the column bearing capacity depends on the number of blocks in the column and the applied accelerogram.For the arti cial accelerogram, by increasing the number of blocks in a column, its ultimate bearing capacity decreases.For the Petrovac and Ston accelerograms, by increasing the number of blocks in a column, its ultimate bearing capacity increases.Increasing the number of blocks in a column, that is, increasing the number of joints in the column, decreases not only its static sti ness but also its dynamic sti ness.erefore, lower inertial (earthquake) forces are generated, but at the same time, the column also has a lower resistance.e reduction in the bearing capacity of the column by increasing the number of blocks for the arti cial accelerogram can be explained by the fact that this excitation introduced a higher energy in the column.Speci cally, this accelerogram has higher spectral displacements and velocities for a higher T 1 (Figure 3.) than those of the Petrovac accelerogram and especially the Ston accelerogram.
e maximum bearing capacity for the Ston accelerogram can be explained by the fact that this excitation has a short impact activity and introduces the lowest energy of the earthquake in the columns; that is, it has the lowest spectral velocities and displacements for a higher T 1 .
For the columns S1m, S3m, and S6m with a mass at the top, the maximum base acceleration a gmax in their limit state is shown in Figure 6. e full line indicates a gmax at the failure of the columns, and a dotted line indicates a gmax from the previous acceleration increment with the preserved stability of the columns.By comparing Figures 5 and 6, a similar behaviour of the columns with a mass at their top and the columns without mass is notable.However, the bearing capacity of the columns S1m, S3m, and S6m is smaller due to the e ect of the mass at their top (a signi cant increase in seismic forces but also an increase in the stability of the column).e similarity of the columns' behaviour for a particular accelerogram is also noticeable.Namely, for the arti cial accelerogram, the bearing capacity of the column was also reduced with an increase in the number of blocks, while for the Petrovac and Ston accelerograms, an increase in the number of blocks increased the column's bearing capacity.e explanations are analogous to those for the columns S1, S3, and S6.Advances in Materials Science and Engineering e horizontal displacements u 1 and u 2 of the column S1 for the artificial accelerogram for some a gmax are shown in Figure 7.It is evident that there were no major displacements in the column up to approximately a gmax � 1.6 ms −2 .By increasing a gmax , there was ever-increasing reversible and irreversible displacements of the column.At a gmax � 2.8 ms −2 (excitation before the column's collapse), the irreversible horizontal displacement of the column's bottom was approximately 60 mm and that of the column's top was approximately 50 mm (the column remained in an inclined position).e largest relative displacement of the column's top in relation to its bottom for a gmax � 2.0 ms −2 was approximately 80 mm.
Figure 8 shows the horizontal displacements u 1 and u 2 of the column S1m for the artificial accelerogram for several a gmax .At approximately a gmax � 0.6 ms −2 , the column did not demonstrate large displacements.For the larger a gmax values, the column's top displacements were significantly increased.At a gmax � 1.2 ms −2 , there were small irreversible displacements of the column's top and bottom.e largest relative displacement of the column's top in relation to its bottom was approximately 40 mm.e horizontal displacements of the column S3 for the Petrovac accelerogram for some a gmax are shown in Figure 9. e column's displacements were small at approximately a gmax � 1.2 ms −2 .e maximum displacement of the column's top for a gmax � 1.6 ms −2 (approximately 100 mm) was larger than that for a gmax � 2.4 ms −2 (approximately 70 mm).After the strongest excitation for which the column remained in balance (a gmax � 2.4 ms −2 ), there were almost equal permanent displacements of all column blocks (approximately 10 mm), that is, the column remained almost vertical.
Figure 10 presents the horizontal displacements of the column S3m for the Petrovac accelerogram for some a gmax .
e large permanent displacements occurred already at a gmax � 0.4 ms −2 .During the excitation before the column's failure (a gmax � 2.0 ms −2 ), the permanent displacement of the column's top was approximately 18 mm.us, the column's bottom remained in the initial position before testing.Some horizontal displacements of the column S6 for the Ston accelerogram for some a gmax are shown in Figure 11.
e other displacements are not presented for the clear presentation of drawings.e column demonstrated large reversible displacements already at a gmax � 3.0 ms −2 but practically without any permanent displacements.At a gmax � 6.0 ms −2 , the top of the column had a large permanent displacement of approximately 120 mm, and the tallest block exhibited large permanent displacements.
Figure 12 presents several horizontal displacements of the column S6m for the Ston accelerogram at some a gmax .
e permanent displacements of the column occurred  14. Notably, the relative displacements between the blocks were smaller for the column S6m than for the column S6.

Conclusions
Based on the results of the performed shake-table study on the behaviour and ultimate bearing capacity of the freestanding small-scale multidrum columns (S1, S3, and S6; S1m, S3m, and S6m) formed from one, three, and six blocks through their height with stone powder joints with variations in the columns gravity load (S1, S3, and S6: only selfweight; S1m, S3m, and S6m: self-weight and 500 kg mass at the top) and three different successively increased horizontal base accelerations (artificial, Petrovac, and Ston accelerograms), the main conclusions given below can be drawn.e number of blocks in the multidrum column significantly affects its stiffness, resistance, and bearing capacity under an earthquake load.
e columns loaded with self-weight only (S1, S3, and S6) and the identical columns with a mass at their top (S1m, S3m, and S6m) had a similar effect to the number of blocks on their bearing capacity.However, the columns with the mass at their top had a lower bearing capacity because of additional seismic (inertial) forces caused by the mass.
e effect of the number of blocks in the column on its bearing capacity was dependent on the applied accelerogram (earthquake type).For an artificial accelerogram, the column's bearing capacity was reduced with the increase in the number of blocks in the column.e ratios of bearing capacity of the columns were approximately S1 : S3 : S6 � 1 : 0.71 : 0.64 and S1m : S3m : S6m � 1 : 0.83 : 0.66.For the Petrovac and Ston accelerograms, by increasing the number of blocks in the column, the column's bearing capacity was increased.e ratios of the bearing capacity for the Petrovac accelerogram were S1 : S3 : S6 � 1 : 1.22 : 1.33 and S1m : S3m : S6m � 1 : 1.42 : 1.57.e ratios of the bearing capacity for the Ston accelerogram were S1 : S3 : S6 � 1 : 1.42 : 1.71 and S1m : S3m : S6m � 1 : 1.16 : 1.16.
e abovementioned relationships are related to the fact that increasing the number of blocks in a column reduces its stiffness and generates earthquake forces but also decreases the column resistance.e artificial accelerogram is characterized by long-lasting action with high spectral velocities and displacements for longer T 1 , that is, the great earthquake energy.is is considered the cause of decreasing the column's bearing capacity by increasing the number of blocks in it, that is, by decreasing its stiffness.
e Petrovac accelerogram has a shorter duration than the artificial accelerogram with lower spectral velocities and displacements for soft structures.e Ston accelerogram has a short impact action with the lowest spectral velocities and displacements, that is, with the lowest earthquake energy.
e abovementioned is the reason why for the Petrovac and Ston accelerograms, an increase in the number of blocks in a column resulted in a greater bearing capacity.
We hope that the obtained experimental database can be useful for the validation of numerical models for the dynamic analysis of multidrum columns.
Although the aforementioned conclusions are based on the experimental study of small-scale models, such an approach may be accompanied with a number of problems and dilemmas.However, it is believed that this experimental approach can reliably be applied to similar full-scale columns because only the relative effect of a single parameter was considered (the number of blocks in a column), while all other influential parameters were kept equal in all the tests.
Further detailed and more comprehensive research of the subject matter is needed to produce more reliable conclusions.e effect of the drum height on the behaviour of multidrum columns exposed to static forces was performed by Buzov et al. [15].

Figure 1 :
Figure 1: Tested free-standing columns: (a) self-weight only and (b) self-weight and mass at the top.

Table 1 :
Fundamental free oscillation period T 1 of the tested columns.