Multidrum Stone Columns at the Pompeii Archaeological Site: Analysis of Geometrical Properties and State of Preservation

: The seismic vulnerability of ancient free-standing multidrum stone columns is an important issue for the preservation of Greek and Roman archaeological sites. Such elements show a complex and highly non-linear dynamic behavior, requiring specific and sophisticated structural analysis. Different numerical studies on the dynamic behavior of ancient multidrum stone columns found that their seismic response is sensitive to their geometrical parameters, as well as to the material elastic properties, the kinetic coefficient of friction and the amplitude and frequency of the seismic action. Therefore, in the present research, a detailed survey of free-standing multidrum stone columns representative of a wide range of elements at the Pompeii Archaeological site was developed to provide a primary evaluation of the seismic vulnerability of such elements based on their geometrical properties. The study focuses on 103 multidrum grey-tuff columns, from four areas at the site: tetrastyle atrium of Casa del Fauno at Regio VI and Quadriportico dei Teatri, Foro Triangolare and Palestra Sannitica at Regio VIII . Grey tuff was a typically locally sourced natural stone, used as a building material in ancient Pompeii. The research areas included both private ( Casa del Fauno ) and public buildings ( Quadriportico dei Teatri, Foro Triangolare and Palestra Sannitica ). The mean overall geometrical properties affecting the seismic behavior of the columns in each research area and the discussion of the collected results are herein presented.


Introduction
Columns are typical constructive elements of Greek and Roman architecture, present in many archaeological sites across the Mediterranean area. They had both a structural function and an architectural meaning, according to their role and position in a private or public building. Besides the different architectural orders, building materials, size and proportions, related to the place and time of construction, ancient columns are vertical elements composed of a shaft and a capital. They could be placed on a base, with or without a pedestal, or a stylobate and could support an entablature and a sloped roof. Ancient columns could be monolithic or composed of overlapped natural stone pieces, the drums. In multidrum columns, the drums were dry overlapped, sometimes connected through metallic or wooden elements [1]; this, however, did not prevent relative displacements (rocking and sliding) between the drums, exceeding a certain level of seismic action [2,3].
Nowadays, many ancients columns are free-standing elements with low or zero axial load, due to missing entablature and roofs [4]. Moreover, material decay, due to the time and natural or anthropic phenomena, foundation failures, presence of cracks, missing or misplaced parts, compromise their stability and seismic capacity.
The study of the seismic behavior of ancient Greek and Roman columns is of particular interest due to the significant seismic activity of the Eastern Mediterranean area [4]. Such studies were typically developed in technical literature according to three main approaches: (i) analytical [3,[5][6][7][8], (ii) numerical, with the use of a software [2,4,[9][10][11][12][13][14][15][16][17][18][19], or (iii) experimental [20,21]. The dynamic behavior of a multidrum free-standing column is controlled by rocking, sliding or a combination of the two mechanisms of the single drums or groups of them. This seismic response is complex and highly non-linear [2,4]. Therefore, theoretical approaches initially involved analytical studies based on simplifying assumptions following the landmark study of G. W. Housner [5] and considered single and multiple block structures [3,[5][6][7][8]; then, recent studies were mainly developed with numerical methods [2,4,[9][10][11][12][13][14][15][16][17][18][19]. These studies found that the seismic response of such elements is sensitive to the geometrical parameters of the columns, as well as to the material elastic properties, the coefficient of friction and the amplitude and frequency of the seismic action.
The importance of the main geometrical parameters in the dynamic response of multidrum columns was highlighted at first by G. W. Housner [5]. His study concerned the rocking motion of an inverted-pendulum-type structure considered as a monolithic rigid block, standing on a rigid and horizontal base, with the assumption of infinite compressive strength of the block and no sliding between the block and the base [5]. It was found that the dynamic response of a slender rigid rocking block depended on its size and slenderness and on the type of applied action (three models of the seismic motion were considered: a constant horizontal force, a sinusoidal acceleration and a seismic motion represented by a constant velocity response spectrum). In particular, the 50% probability of overturning a slender block subjected to the seismic motion was defined through the equation: = / , where Sv was a given velocity response spectrum representing the earthquake motion; R was the distance from the center of mass of the block to the perimeter at the base; and α = b/h was the angle between R and the vertical, with h the height of the block and b the base width [5]. This led to defining an "unexpected size effect" according to which a larger block was more stable than a smaller one with the same slenderness. This theory was explained with the fact that the seismic action is not scaled with the dimensions of the block [5]. More recent numerical studies on multidrum columns confirmed this size effect found by Housner and the fact that the absolute dimensions of the columns significantly affect their response. Pappas et al., based on Discrete Element Method (DEM) simulations, defined a preliminary seismic assessment form with the definition of influence factors taking into account all the parameters affecting the seismic response of ancient free-standing multidrum columns (i.e., slenderness, height, number of drums, structural conditions and soil type) [12]. It was found that when keeping the other factors constant when increasing the slenderness, the probability of collapse increased; conversely, when the size of the column was increased, the probability decreased. Likewise, Papadopoulos et al., from the Finite Element Method (FEM) analysis, derived criteria for the seismic stability of ancient free-standing multidrum columns in which, for a given seismic input, lager columns were more stable than smaller ones with the same aspect ratio [4].
The number of drums was found to be another important parameter affecting the seismic response of a column in terms of sliding and energy dissipation due to friction [4,13]. The influence of this parameter depends on the frequency of the seismic action [11]. Literature studies [4,12,13] found that columns with a higher number of drums were less vulnerable compared to columns with few drums and the monolithic ones, when they are on hard soils, while such effect was less noticeable on soft soils due to the lower frequencies produced. Moreover, Papadopoulos et al. found that the presence of entasis at the shaft of the columns did not affect the results of the numerical analysis [4,13]. Meanwhile, the configuration of the base of the columns could affect their seismic response [4]. Indeed, it was found that a column placed on several layers of stone blocks showed higher seismic stability compared to a column placed on a single block, probably due to the higher dissipation of energy through the relative displacement of those additional stone blocks.
As concerns the material properties, the deformability of the drums was considered according to the selected modelling approach, while the coefficient of friction was generally a fundamental parameter (along with the geometry and the density of the material). Relevant numerical studies based on FEM considered the drums as isotropic and elastic elements, taking into account the modulus of elasticity and Poisson ratio of the material [2,4]. In particular, Pitilakis and Tavouktsi found that a degradation of the elastic properties of the material related to ageing (accounted with a reduction of the elastic modulus) could lead to a higher probability of collapse, related to higher inplane and out-of-plane displacements [2]. However, other approaches based on DEM considered the deformability of the drums as negligible compared to the significant displacements produced by strong seismic input and defined them as infinitely rigid elements, in the interest of a lower computational effort [9,12,14]. On the other hand, both in FEM-and DEM-based approaches, the interaction between the drums was mainly modelled based on the Coulomb friction law with zero cohesion [2,4,12,14]. Therefore, the coefficient of friction of the material related the shear and normal stresses on the contact surfaces between the drums and defined the activation of sliding [2,4,14]. It was found that, for lower values of the coefficient of friction, the sliding mode prevails, while, for higher values of the coefficient, the rocking mode prevails [2,14]. Commonly, a single value of the coefficient of friction was set in the analysis, with the kinetic coefficient equal to the static one [2,4], [12]. Indeed, Papadopoulos et al. found that varying the kinetic coefficient of friction with respect to the static one did not affect the results of the analysis with a specific trend. Finally, Konstantinidis and Makris found that the presence of wooden connecting elements between the drums did not affect significantly the dynamic response of the multidrum columns while stiff metallic connections could have an unfavorable impact on their seismic stability [9].
Indeed, according to available literature studies it can be summarized that: (i) in absence of specific damage (cracks, lacking parts, uneven profile), ancient columns can resist significant seismic actions [2,4]; (ii) the number of drums can affect the dynamic behavior of the columns and their influence is also strongly related to the soil properties [4,12,13]; (iii) the higher the slenderness of the column, the higher the probability of failure [2,4]; (iv) for given slenderness, smaller columns have a higher probability of failure [2,4]; (v) the probability of failure is higher for long-period earthquakes than high-frequency ones [2,4,11,13].
As concerns the Pompeii archaeological site, recent studies focused on the static and dynamic assessment of the two-story colonnade at the Civil Forum and evaluated the effect of a rapid degradation due to joint cracking and opening [17][18][19]. This colonnade presented an innovative constructive solution for the entablature made with short horizontal blocks mutually supporting each other over inclined surfaces [17][18][19]. However, these studies specifically concerned that peculiar colonnade, while several ancient columns at the Pompeii archaeological site are free-standing multidrum columns. Therefore, a continuous commitment to consolidate the historical knowledge of such elements, to monitor their state of preservation and to design proper restoration interventions in the respect of the material asset, intangible values and the safety of numerous visitors, is still needed. Moreover, many of these elements are in an advanced state of degradation due to the material decay and successive tampering related to different restoration and consolidation interventions, requiring urgent safety measures, restoration and reconstruction of materials.
To support the monitoring of the state of preservation of the columns at the site and the development of a program of interventions, deep and systematic knowledge extended to the whole site was required. This was the main objective of a scientific collaboration between the Archaeological Pompeii Park (PAP) and the Department of Structures for Engineering and Architecture (DiSt) of the University of Naples Federico II. On-site inspections and a study of bibliographic and archival sources in the historical and scientific archives of the PAP were performed. The study was developed on free-standing multidrum stone columns in four areas of the site representative of typical columntypes (Casa del Fauno at Regio VI and Quadriportico dei Teatri, Foro Triangolare and Palestra Sannitica at Regio VIII). Such columns nowadays present cracks and detachments, which may affect their safety and aesthetics.
The study allowed u to define the mean geometrical properties affecting the dynamic behavior of the columns and to recognize the most common forms of degradation. In the following, the column-types surveyed and analyzed in each research area, the mean geometrical properties affecting their seismic behavior and their state of preservation are described in detail to provide a primary evaluation of the seismic vulnerability of such elements and a useful tool for a future numerical investigation.

Research Significance
Relevant analytical and numerical studies found that the seismic behavior of ancient multidrum columns is greatly affected by their main geometrical parameters. These parameters are: the diameter at the base, d, the total height, H, the distance from the center of mass of the column to the circumference of its base, R, and the aspect ratio of the column, H/d, that is a measure of its slenderness. However, the absolute dimensions of a column and its slenderness cannot be considered individually and in an absolute manner. Indeed, larger columns were found to be in general less vulnerable to the seismic action compared to the smaller ones, in certain cases even with higher slenderness.
Based on these fundamental findings, systematic and detailed knowledge of the geometrical properties and state of preservation of free-standing multidrum stone columns in archaeological sites with a considerable number of such elements may be a useful tool to: (i) identify representative geometrical properties of the columns; (ii) identify columns being potentially more vulnerable than others; (iii) provide basic information for further investigation on the seismic assessment of such structural elements.

Stone Columns at the Pompeii Site
The built asset at the Pompeii archaeological site provides a wide range of columns typologies of different sizes, architectural style and building materials. In terms of materials, the ancient Pompeian building techniques were mainly based on the use of locally sourced materials, and columns were typically realized with natural stone drums. Limestone and tuff were the most common materials used for the realization of columns, and, less frequently, marble was used [1]. Masonry columns were also present at the site. They were made of bricks and mortar or with building techniques typically used for the realization of walls (i.e., the use of opus reticulatum alternating with bricks and mortars at Villa dei Misteri), then covered with a thick layer of plaster.
In the present investigation, a wide number of columns representative of typical column types at the site were studied. Indeed, 103 multidrum grey-tuff columns from four different areas at the site, including private and public buildings, were studied.

Research Areas
The present study focuses on grey-tuff free-standing columns in four areas of the site: Casa del Fauno at Regio VI and Quadriportico dei Teatri, Palestra Sannitica and Foro Triangolare at Regio VIII ( Figure 1). Casa del Fauno was one of the largest private houses at the ancient Pompeii, dated to the second century B.C., occupying an entire Insula at the Regio VI. The main excavation of the house is dated between 1829 and 1833. The name of the house came from a statue of a mythological figure, namely Fauno, found in the house, whose copy is nowadays in the main atrium. The study focused on four Corinthian columns of the tetrastyle atrium at the south-east side of the house, one of which showed significant degradation and needed safety devices.
Quadriportico dei Teatri, Palestra Sannitica and Foro Triangolare at Regio VIII were all public buildings. Quadriportico dei Teatri occupied a large part of the "theaters area" of Pompeii in the southwest area of the site. It originally had the function of the foyer for the Large Theatre, then, after the earthquake of 62 A.D., it became a barracks for gladiators. Among the 74 Doric columns composing the building, the 54 free-standing ones were selected and analyzed in the present study, while the remaining 30 columns were not involved in the present study since they bore a sloped roof realized in the last decades. Palestra Sannitica, located to the north-west of the Quadriportico dei Teatri was a stadium dated back to pre-Roman times in the second century B.C. All the 19 Doric columns of the three remaining sides of the original colonnade were studied. Foro Triangolare, located to the southwest of the Quadriportico dei Teatri, took its name from its triangular shape, dating the second century B.C. The 26 grey-tuff columns remaining of the external colonnade that surrounded the area of the Doric Temple were analyzed in the present study. These research areas at Regio VIII were mainly brought to light in the second half of the XVIII century.
It is known, from the technical archives of PAP, that consolidation interventions were carried out after the Irpinia earthquake of 1980 on the columns at Quadriportico dei Teatri, Palestra Sannitica and Foro Triangolare, and probably involved the four columns at Casa del Fauno. Moreover, further consolidation interventions were carried out in 1991 on the columns at Quadriportico dei Teatri.
For each area, a progressive number was assigned at each column, so that they were uniquely identified through an alphanumeric code structured as follows: P_RIA_CX where:  P is the initial letter of the site (i.e., Pompeii);  R stands for the number of the Regio, in Roman numerals;  I stands for the number of the Insula;  A indicates the name of the research area (i.e., CF stands for Casa del Fauno, QT stands for Quadriportico dei Teatri, PS stands for Palestra Sannitica and FT stands for Foro Triangolare);  C is the initial letter of the structural element (i.e., column);  X is the assigned number within each area.
As an example, column 10 at the Quadriportico dei Teatri was identified by the code: P_VIII7Q_C10. Figure 2reports the plan of each research area with the numbers of the studied columns.

Geometrical Survey
According to what was found in previous numerical studies [2,3,12], the definition of the overall main geometrical properties of multidrum stone columns could provide a very useful tool for the primary evaluation of their seismic vulnerability. Therefore, an extensive geometrical survey aimed at defining the mean overall geometrical properties of the studied columns was performed. The following data were collected related to columns and drums: (i) the column overall height, H, (ii) the diameter of the drum at the base, d, (iii) the drum height, hi, (iv) the drum diameter at the bottom, dinf, and (v) the drum diameter at the top, dsup. Thus, the aspect ratio Η/d and the distance from the center of mass of the column to the circumference at the base, R, were also evaluated ( Figure 3).

Complete and Incomplete Columns
In each one of the four research areas, several incomplete columns were found, i.e., columns where one or more drums or the capital are missing. Indeed, as part of the excavation work and/or later restoration intervention, many columns were only partially re-erected, due to missing or damaged drums and capitals. Figure 4 shows examples of completely re-erected columns (i.e., all the parts from the base to the capital are present today) and partially re-erected ones (i.e., with missing parts). In the tetrastyle atrium of the Casa del Fauno, three out of four columns are complete, while only the capital is missing in the remaining one.

Overall Geometrical Properties
The mean overall geometrical properties of complete columns in each investigated area (i.e., total height, H, diameter at the base, d, and the size R) are reported in Figure 6 along with the corresponding standard errors. Columns at Casa del Fauno had larger geometrical properties compared to columns at the other areas, related to both the different architectural styles and the different functions (i.e., a private Corinthian tetrastyle atrium instead of public Doric colonnades). In the other areas, the mean overall properties were comparable; columns at Palestra Sannitica showed the smallest dimensions and columns at Foro Triangolare showed the largest ones. From the collected mean overall geometrical properties, four column types could be provided to be representative of each investigated area (Figure 7). For each column, the mean geometrical and physical properties are summarized in Table 1: total height, H; diameter at the base, d; mass, Μ; aspect ratio, Η/d; distance from the center of mass to the circumference at the base, R; quote of the center of mass, yCM; volume, V. Note that the positions of the center of mass and the mass of the columns were evaluated based on the assumption of the columns being homogeneous solid of grey tuff with density ρ= 2600 kg/m 3 .

Number and Size of Drums
According to [12], the number of drums affects the seismic response of the columns, especially if they are located on soft soils [11,12]. Therefore, the number and size of drums of a column may be a key parameter for the development of exhaustive numerical investigation of its seismic behavior.
Based on a detailed survey of all the investigated columns, inhomogeneous distributions and the size of the drums were found in each research area, probably related to both the original configuration of the columns (depending on the available materials at that time) and post-excavation interventions (re-erection and subsequent alterations of the columns). Concerning complete columns, the ones at the Casa del Fauno had six drums, except for column number 4, with seven drums. In the other areas, the number of drums of the complete columns varied from three to seven at Quadriportico dei Teatri and between four and five at Palestra Sannitica and Foro Triangolare (Figure 8). To provide specific indications for the structural modeling of a column-type representative of each area, the mean dimensions of the drums for complete columns with the most frequent number of drums were calculated: six drums at Casa del Fauno; four drums at Quadriportico dei Teatri and five drums at Palestra Sannitica and Foro Triangolare ( Table 2).  1  104  75  63  137  49  48  94  39  38  82  53  52   drum  2  84  63  62  66  48  46  71  38  37  52  51  105   drum  3  98  62  60  100  46  43  67  37  35  105  51  47   drum  4  79  60  60  39  43  42  59  35  33  73  48  44   drum  5  116  60  59  22  33  32  31  45  45   drum  6  45  51  58   Capital  68  17  18  11

State of Preservation of the Columns
An ideal numerical model shall be representative of the dynamic behavior of an ancient multidrum column based on the assumption that the ancient column is in a satisfactory state of conservation: there are no significant deformations, cracks, detachments, missing portions and the drums are in good contact [4,10]. Indeed, a reduction of diameter in drums due to damaged parts may increase the vulnerability of the column [12] and has to be included in the vulnerability assessment.
Therefore, for a proper assessment of seismic performances, the analysis of geometrical properties and the evaluation of the state of preservation of the columns are crucial for correct structural modeling.
This section presents and discusses the critical issues commonly found in several columns in the research areas. In particular, anthropic and natural phenomena resulted in material damaging and general decay of the columns. They can be summarized as follows, see Figure 9: (i) weathering, cracks and detachment of the building material; (ii) irregular shape (initial tilting and partial lack of contact among the drums); (iii) presence of corroded metallic devices (i.e., ties to connect drums) and too invasive interventions. Figure 9. Critical issues on columns: weathering, cracks and detachment of the building material (a); initial tilting and partial lack of contact among the drums (b); presence of corroded metallic devices and too invasive interventions (c) and (d).
Columns showing significant damages would require more urgent interventions aimed to restore the material integrity and the initial shape (reintegration of lacking parts, reparation of cracks, assessment of foundation failures, reparation or removal of invasive earlier interventions).

Analysis of Relationships between Columns Geometrical Parameters
In order to provide a tool for a primary evaluation of the seismic vulnerability of multidrum columns, the relationship between the mean geometrical parameters of the complete columns affecting their behavior under horizontal actions are reported in the following. The relation between the column mean height and the mean diameter at the base is reported in Figure 10a. Figure 10b reports the trend of data collected concerning the mean aspect ratio, H/d, and the distance from the center of mass of the column to the circumference at the base, R. The aspect ratio varied between 7.27 for columns at the Quadriportico dei Teatri to 8.53 for columns at Palestra Sannitica (with coefficient of variation, CoV = 7%), while the size R varied from 159 cm for Palestra Sannitica to 282 cm for Casa del Fauno (CoV = 28%). According to the size effect defined by G. W. Housner [5] and confirmed by more recent numerical studies [4,[11][12][13], complete columns at Palestra Sannitica would appear the most vulnerable, showing both the highest mean aspect ratio and the smallest size. On the contrary, columns at the tetrastyle atrium of the Casa del Fauno showed a value of the aspect ratio within the range of detected data and the largest dimensions, so they are probably more stable compared to the first columns. Meanwhile, columns at the Quadriportico dei Teatri and columns at Foro Triangolare showed similar geometrical properties. Further specific analysis based on the provided mean geometrical data could be performed in order to verify and extend these primary considerations. To define future scenarios for intervention on incomplete columns, the analysis of their geometrical properties is also reported even if they are clearly not comparable with the complete ones. Except for column 3 at Casa del Fauno, where only the capital is missing, incomplete columns generally had a lower aspect ratio than complete ones, clearly related to lower overall heights with similar diameters at the base (Figure 11a). In particular, their aspect ratio varied from 1.73 to 6.63 at Quadriportico dei Teatri, from 2.26 to 4.45 at Palestra Sannitica and from 2.07 to 7.30 at Foro Triangolare. Columns with an aspect ratio lower than 4 could be considered relatively stable, as stated in [12]; this happens only for 14 out of 48 incomplete columns herein investigated. Thus, the remaining 34 incomplete columns had a significant aspect ratio (i.e., greater than 4) and require specific analysis to properly define their seismic capacity as in the case if complete columns. Figure 11 shows the relationship between H and d and between H/d and R for the incomplete columns.

Conclusions
A study of free-standing multidrum stone columns at the Pompei archaeological site was developed as a part of a scientific collaboration between the Archaeological Pompeii Park (PAP) and the Department of Structures for Engineering and Architecture (DiSt) of the University of Naples Federico II. The objective of the research was the improvement of the knowledge of such elements, the evaluation of their state of preservation and the preliminary analysis of their seismic vulnerability. Indeed, despite consolidation and restoration interventions performed in the past, several columns nowadays present cracks, detachments and uneven profiles, affecting their safety and aesthetics.
Previous studies on the dynamic behavior of ancient multidrum stone columns showed that their seismic response is mainly sensitive to their geometrical parameters, as well as to the material elastic properties, the kinetic coefficient of friction and the amplitude and frequency of the seismic action. To provide key information for the assessment of the seismic vulnerability of multidrum columns at the Pompeii site, a detailed survey of 103 grey-tuff free-standing multidrum columns from four areas at the site was performed (i.e., tetrastyle atrium of Casa del Fauno at Regio VI and Quadriportico dei Teatri, Foro Triangolare and Palestra Sannitica at Regio VIII). They were selected as representative of a wide range of typical column-type at the site.
From the performed study, the following conclusions may be drawn:  For each research area, the mean overall geometrical properties were provided, representative of a broad spectrum of multidrum stone columns at the Pompeii Archaeological site: the aspect ratio Η/d and the distance from the center of mass of the column to the circumference at the base, R, ranged between 1.73 and 9.99 and between 49 and 167 cm, respectively; complete columns were commonly made by four, five or six drums; the height of the drums varied between 11 and 181 cm, with a most common dimension lying in the range of 80-90 cm;  Relevant numerical studies found that the higher the slenderness of a column, the higher is the probability of failure, and, for a given slenderness, smaller columns have a higher probability of failure; thus, by comparing mean data detected in each area, columns at Casa del Fauno are likely to be more stable than others, showing an intermediate value of Η/d and the largest R; on the contrary, columns at Palestra Sannitica are likely to be the most vulnerable with the highest Η/d and the lowest R;  A relevant number of incomplete columns are present in each investigated area (i.e., 48 incomplete columns out of 103 under investigation);  Despite the lower overall height, several incomplete columns showed a relatively high aspect ratio (i.e., 34 out of 48 incomplete columns showed Η/d > 4) requiring a seismic assessment as well as the complete ones;  The main critical issues that may affect the seismic response of columns under investigation were detected by detailed surveys and can be summarized as follows: (i) weathering, cracks and detachment of the building material; (ii) initial tilting and partial lack of contact among the drums; (iii) the presence of corroded metallic devices to connect drums and/or invasive postexcavation interventions;  Before any assessment of the dynamic behavior of free-standing multidrum stone columns, specific interventions aimed to restore the material integrity and the uneven profile would be required.
The collected information can represent an effective tool for a preliminary evaluation of the seismic vulnerability of such structural elements based on their geometrical properties. The definition of the main overall properties may support further specific numerical analysis of a column-type for each investigated area. Possible future development of this research could involve a parametric evaluation of the different studied parameters (i.e., number and size of the drums, dimensions of incomplete columns). Moreover, expanding the investigation to different areas and column types of the site, it could be possible to define a priority plan of intervention to preserve such elements against decay and seismic actions.