Discrete element modelling of the archaeological colonnade in Pompeii

9th International Masonry Conference 2014 in Guimarães

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International Masonry Conference, Guimarães 2014 1

Discrete element modelling of the archaeological colonnade in Pompeii

GIAMUNDO, VINCENZO1; SARHOSIS, VASILIS2; LIGNOLA, GIAN PIERO3; COSENZA, EDOARDO4

ABSTRACT: In this paper the seismic vulnerability analysis of a magnum opus of the architectural

heritage residing in the ancient city of Pompeii in Italy is presented. Pompeii is a Roman city destroyed during a catastrophic eruption of the Vesuvius volcano in 79 a.C.. Nowadays, Pompeii is one of the biggest tourist sites in Southern Italy and since 1997 it is a UNESCO world heritage site. During its life, the city suffered many earthquakes, and the ruins of the ancient city show several partially collapsed buildings. The peculiarity of the analysed colonnade is an “innovative solution” adopted to avoid long span beams over its slender columns: short segments were built up providing opposing inclined patterned edges. Distinct element analyses outcomes are discussed to evaluate the current seismic vulnerability of the colonnade, in order to preserve the safety of the structure and to study the effects of degradation of the archaeological material.

Keywords: Archaeological ruins, DEM, Parametric analysis, Pompeii, colonnade

1 INTRODUCTION

The archaeological site of Pompeii in Italy is a Roman city destroyed during a catastrophic eruption of the Vesuvius volcano in 79 a.C. As a consequence of the eruption the city was buried providing a complete picture of the city as well as of the daily life at that period. Since 1997 the ancient city of Pompeii has been enrolled among the world heritage sites by UNESCO. Nowadays Pompeii is one of the most popular tourist attractions in Southern Italy. Therefore, due to the large number of visitors, the historical value and the original cultural meaning, the safety of such cultural site is crucial. During its life, the city suffered many earthquakes. In particular, a strong earthquake hit the city in 62 a.C. and reconstruction works were not concluded before the catastrophic eruption. Moreover, after its rediscovery in 1749 other earthquakes hit Pompeii. The last earthquake to hit the city, which produced damages in the whole archaeological site, was in 1980. Furthermore, the structural safety of archaeological structures seems, currently, more and more endangered by rapid deterioration of the archaeological material [1]. In the archaeological site of Pompeii, masonry buildings were surrounded by temples and public places presenting slender columns and typical shapes of marble overlaying blocks. The analysed structure is a two storey colonnade of the Forum. The colonnade was erected in the main square of the ancient city adopting an “innovative solution” for the trabeation. In order to prevent long span beams over the columns, a segmented trabeation was built up made of short

1) PhD Candidate, University of Naples Federico II, Dept. of Structures. for Eng. and Arch., [email protected]

2) Research Associate, Cardiff University, Civil Engineering, [email protected]

3) Assistant Professor, University of Naples Federico II, Dept. of Structures. for Eng. and Arch., [email protected]

4) Full Professor, University of Naples Federico II, Dept. of Structures. for Eng. and Arch., [email protected]

Giamundo, V.; Sarhosis, V.; Lignola, G. P.; Cosenza, E.

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segments providing opposing inclined patterned edges. The basic concept is that small blocks are able to mutually support each other without any tensile capacity. The examination of the methods employed by the ancient builders revealed the continuous research and evolution in design of structures against earthquakes [2,3]. Such “innovative solution”, however, was conceived in order to simplify the construction phases avoiding the use of long and heavy blocks.

2 RESEARCH SIGNIFICANCE

The colonnade represents a classical example of a structure made of discrete rigid blocks and can be successfully analysed by means of Discrete Element Methods (DEM). Large-scale experimental tests for such structures are not possible; consequently, it is necessary to use numerical methods to simulate the dynamic behaviour and seismic response. The paper focuses on the effect of joint cracking and opening to include the potential risk induced by rapid degradation. This kind of study, in fact, potentially supports both the work of historians (for instance in understanding if the collapsed structures can be related to earthquakes before the great eruption or the catastrophic eruption itself) and today’s governors who intends to achieve preservation of archaeological sites and artistic values along with the safety of the high number of tourists daily. The paper in particular evaluates the static conditions of the colonnade under gravity loads and assesses the seismic vulnerability of this block based frame.

3 DEM MODELLING OF THE COLONNADE

Ancient columns of archaeological importance in high seismicity areas are made of stone blocks that lie on top of each other usually without connecting material in between. A simulation of the individual rocks blocks, in the same way as they are actually built, as distinct bodies, can be performed using DEM. This method has already been used to simulate ancient monuments with good results [4,5]. The analysis of the seismic behaviour of such colonnade is scientifically interesting, as it involves complex rocking and sliding phenomena of the individual rock blocks. Finite Element Methods (FEM) can use interface elements to model discontinuities in the material. However, interface elements application is restricted due to many reasons (e.g. difficulties in the implementation of many intersecting interfaces and in the recognition of different evolving contacts; awkward evaluation when many joints and large displacements occur etc). To overcome some of these restrictions, the DEM was originally proposed in early ‘70s as a way to solve problems of rock mechanics [6], using distinct elements to simulate discontinuous rock masses. The method assumes an assembly of discrete blocks, where the interfaces between distinct bodies, named joints are discontinuities treated as boundary conditions. Tracing the displacements (potentially they are unlimited translations and rotations) of the blocks, the contact forces and displacements at the interfaces are established, associating the normal and the shear forces to displacements. The interactions between two bodies can be simulated by recently detected contacts, existing contacts, or relative displacements and rotations between bodies in contact. This method is preferably applied when the behaviour is dominated by the discontinuities hence the structure is an assembly of discrete blocks [7].

3.1. Model description

2D numerical analyses have been conducted by means of the UDEC software. In UDEC, each drum of the column and block of the trabeation was modelled by deformable blocks, characterized by density and elastic properties. Interaction between blocks was represented using a zero thickness interface and characterised by an elastic normal stiffness (JKn), a shear stiffness (JKs) and the angle of friction (Jfric). Furthermore, the joints had no tension and cohesion. Tables 1 and 2 resume the adopted UDEC modelling parameters.


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Table 1. Parameters used for the blocks in the UDEC model

Density [kg/m3] E [GPa] G [GPa] Bulk Modulus [GPa] ν [-]

2680 40 16 27 0.25

Table 2. Parameters used for the interface in the UDEC model (in brackets values used for sensitivity analysis)

JKn [GPa/mm] JKs [GPa/mm] Jfric [DEG]

4 (0.4) 2 (0.2) 15.0°, 26.6°, 36.9°

It was not authorized to perform mechanical tests on archaeological materials, hence no data were available for constituent materials. Reasonable properties for ancient blocks frictional joints were assumed on safe side. In particular, to simulate potential modern degradation effects, a reduced stiffness was considered as well (one tenth of the benchmark value assuming direct contact of blocks) and also a tangent of friction angle of 15° (in all the analyses), instead of a benchmark value ranging between 26.6° (tanφ=0.5) and 36.9° (tanφ=0.75). The base of the model has been fixed and the model was brought initially at equilibrium (static gravity loads). Then, external loading has been applied by increasing horizontal accelerations.

4 STATIC CONDITIONS (GRAVITY LOADS)

The results for the joint properties combinations are discussed for the static conditions under gravity loads. Comparisons are made with respect to stresses, vertical displacement, maximum joint opening and horizontal displacement of a control point (the top left upper column, as it will be discussed for seismic analyses). Since the continuity of the beam is lost, the arch mechanism provides thrust, hence the sliding and opening of the horizontal blocks. Even if stability is granted, the opening of the joints allows water and other polluting agents to attack the hidden surfaces of the marble elements. Maximum joint opening reduces as the joint friction angle and joint stiffness increases, and it ranges between 0.08 mm and 0.51 mm under static conditions. This clearly means that joint degradation should be considered in particular to analyse the seismic vulnerability. The focus of this work is the analysis of the “innovative solution” (for that period) of segmented trabeation. However, the unavoidable need of a single longer block over the first two columns, allows to directly compare the “classical” Greek solution (between third and fourth columns in Figure 1) and the “innovative” Roman one (between first and third columns in Figure 1). The thick yellow lines in Figure 1 show the arch shaped path of stress that is deeper in the left case and flat in the right side. The continuous beam has the common flexural stress field with traction at the bottom (see continuous line circle in Figure 1) and compressions at the top of the overlapped elements. Conversely the left layout provides a “flat-arch” hence having almost negligible tractions (see dashed line circles in Figure 1) and widespread compression stresses. Like as in the case of joint opening, stress intensities are reducing as the joint friction angle and joint stiffness increases. Since joint degradation implies a mechanical reduction of properties, this means that both joint opening and stresses tend to increase with this phenomenon hence aggravating it. Maximum compressive stresses, varying the mechanical properties of joints, range between 0.27 MPa and 0.56 MPa, while maximum tensile stresses are quite lower and ranging between 0.10 MPa and 0.25 MPa. These values corroborate the idea that blocks are almost rigid and no failure can be expected inside them (the strength is expected to be at least one order of magnitude higher, both in tension and in compression), conversely damage and attention should be on joints. Furthermore the application of gravity loads let the top of upper columns to move on the left, hence


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indicating a non-symmetry of the structure and the effect of unbalanced horizontal thrust, even under vertical gravity loads only.

5 SEISMIC VULNERABILITY

Apart static safety, this cultural heritage structure should be checked against seismic actions too. The vulnerability should include fully the nonlinear behaviour, hence sliding and/or rocking failure of the blocks, and for this reason an incrementally nonlinear analysis was performed up to the collapse of the colonnade. Code earthquakes for the site (based on ITACA database seismic data [8]) are considered and seismic intensity is expressed, according to Italian Building Code [9], in terms of return period or probability of occurrence in a reference period of 50 years. Preliminary modal analyses [10] gave an estimation of the dynamic response of the colonnade, but in the elastic field. Table 3 reports the first natural frequencies in the in-plane and out-of-plane.

Table 3. Natural Frequencies, periods and damping ratios for first six modes for in-plane and out-of-plane

Mode In-plane Out-of-plane

Frequency [Hz] Period [s] Frequency [Hz] Period [s]

1 18.1 0.055 7.40 0.135

2 25.3 0.040 27.4 0.036

3 25.5 0.039 71.5 0.014

4 27.6 0.036 104 0.010

5 104 0.010 159 0.006

6 111 0.009 111 0.005

Figure 1. Geometry (in-plane) of the colonnade and map of principal stress directions

Principal stresses (JKn=4GPa/mm and Jfric=15°)

Minimum = -0.55MPa (compression)

Maximum = 0.24MPa (tension)


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The colonnade is stiff. The seismic vulnerability was analysed, according to Italian seismic code, hence substantially according to Eurocode8 [11], by means of characteristic force – displacement relationship of the Multi-Degree-Of-Freedom (MDOF) system. An incremental analysis was performed applying a constant gravity load at the beginning and then incrementally increasing horizontal loads were applied according to a “uniform” layout. In this way the structure was pushed (positive direction) and pulled (negative direction) up to its failure when equilibrium was no more achieved. In this way the full nonlinear behaviour was accounted for. The “uniform” layout provided on lateral actions proportional to the mass regardless of the elevation (i.e. uniform response acceleration according to Eurocode8 [11]). The nonlinearity involved again mainly the joints rather than the blocks. In this case, the force and the displacement are: the base shear and the displacement of a control point on top columns at the upper level, respectively. The equivalent Single-Degree-Of-Freedom (SDOF) system was determined (according to a bi-linearized curve having the same initial stiffness and area under the curve), as shown in Figures 2 and 3 where capacity diagrams are plotted in Acceleration-Displacement (ADSR) plane, both for in-plane and out-of-plane. Similarly, the seismic demand is expressed in terms of an equivalent SDOF system. A spectral displacement demand represents a target displacement for the structure. For structures in the short-period (i.e. lower than upper corner period of the constant acceleration region of the elastic spectrum) the elastic spectral demand is properly increased (according to [9,11]) and displacement capacity of the structure, to be safe should exceed the demand. The structure is not symmetric so that both positive and negative lateral accelerations were considered. Dissimilar performance was found (see Figure 1 for in-plane and Figure 2 for out-of plane). According to different friction angles for joints, the behaviour is different in each direction, too. Highest scatter is found mainly in the in-plane direction, where the effect of joint opening and sliding is more significant, on displacement capacity while the lateral strength is almost comparable (Figure 2).

Figure 2. In-plane pushover analysis in positive and negative directions and bilinearization


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Conversely in the out-of-plane direction, where the effect of global rocking/overturning is more significant, displacement capacity is comparable, while the lateral strength is different (Figure 3). In previous figures different friction angles are plotted with different colours, while different stiffness is recognized by line hatch style.

5.1. In-plane Behaviour

Horizontal in-plane actions yield to dissimilar behaviours depending on the friction angle and joint stiffness. In the positive direction lower friction angles yield to an almost linear behaviour up to failure, while in the case of highest friction angle (i.e. 36.9°) a reduced nonlinear plastic behaviour is observed, being the strength almost the same. Failure mechanism in fact, according to the bi-linearized response occurs at an acceleration slightly lower than 0.20 g. Even considering the lower joint stiffness, the behaviour is almost similar. In the negative direction, even if the strength is almost similar (in fact for the higher friction angles the maximum acceleration is again close to about 0.20 g), however the nonlinear behaviour is remarkably different. A very large pseudo ductility is found, being the maximum displacement almost three to five times higher than in the positive direction. Fig. 4 reports the pushover curves for the average friction angle of 26.6° and the benchmark joint stiffness. According to the adopted performance evaluation, in each case, the structure is able to resist an expected earthquake if the displacement capacity exceeds the displacement demand. Dotted vertical lines represent the SDOF target displacements for different levels of ground motions. The colonnade is able to satisfy a design earthquake with a return period of about 200 years, or about 22% in 50 years (i.e. expected PGA is ag=0.10 g), both in the positive and negative direction, and this performance is provided being the structure still in its elastic branch. In this sense the behaviour is totally overlapping in the two directions. In the elastic branch the check can be limited also to a strength capacity check, since the capacity curve exceeds the spectral curve. Conversely, in the negative direction, where the structure exhibits a pseudo ductile behaviour, the spectral displacement

Figure 3. Out-of-plane pushover analysis in positive and negative directions and bilinearization


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is properly amplified to account for the reduced strength of the colonnade, hence accounting for its displacement capacity in the nonlinear field. In the negative direction the colonnade is able to resist an earthquake with a return period of more than 2475 years, or 2% in 50 years (i.e. expected PGA higher than ag=0.22 g), whose target displacement is about 0.46 mm. It is worth to recall that other assumptions on the colonnade in terms of stiffness, friction angle, hence of strength and pseudo-ductility, would provide different target displacements for the same return periods. Deformed shape clearly shows the evolution versus the mechanism (still highly magnified in Figure 5): blocks partially lose their geometrical support and sliding occurs, coupled to rocking, yielding to in-plane failure condition.

-0,25

-0,15

-0,05

0,05

0,15

0,25

-0,60 -0,50 -0,40 -0,30 -0,20 -0,10 0,00 0,10 0,20

Displacement [mm]

ag/g [-]

Return period 475 years (10% in 50 years)





Return period 475 years (10% in 50

years)


Figure 4. Comparison of the bilinearized curve (average friction angle 26.6°) in-plane with expected seismic demands.

Figure 5. Magnified deformed shape, seismic in-plane condition.


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The effect of seismic accelerations, at the peak force is shown in the stress plots in Figure 6. From a stress point of view, compression stresses are lower than 0.8 MPa (in all the analysed cases). Even though they exceed the stresses under static conditions, they are still lower than expected material strength, so not causing particular concern. Similarly tensile stresses are lower than 0.4 MPa. This means that no internal block failure is expected, but sliding and rocking each other.

5.2. Out-of-plane Behaviour

Horizontal out-of-plane actions, conversely, yield to similar behaviours whatever the friction angle and joint stiffness. Failure mechanism in fact, according to the bi-linearized response occurs at acceleration slightly lower than 0.20 g in the positive direction and 0.15 g in the negative direction. This result, confirmed for the lower joint stiffness, is coupled to a clear pseudo ductility and is due to the trabeation protruding on the left side (hence in the negative horizontal direction). Fig. 7 reports the pushover curves for the average friction angle of 26.6° and the benchmark joint stiffness. The colonnade is able to satisfy a design earthquake with a return period of more than 475 years, or about 10% in 50 years (i.e. expected PGA higher than ag=0.13 g), both in the positive and negative direction. A design earthquake with a return period of 72 years, or 50% in 50 years (i.e. expected PGA is ag=0.06 g) is expected to stress the structure still in its elastic branch. It is worth noting that during November 1980 an earthquake hit the area shaking the ground with a PGA close to that expected for such an earthquake, and effectively the damage was almost negligible. In the negative direction the colonnade, even if showing lower strength, is able to resist an earthquake whose target displacement is higher due to its higher pseudo-ductility. Since other assumptions on the colonnade in terms of stiffness, friction angle provide similar strength and pseudo-ductility, almost the same seismic risk can be estimated. Deformed shape clearly shows the evolution versus the mechanism (still highly magnified in Figure 8): blocks partially lose their geometrical support and sliding occurs, coupled to rocking, yielding to out-of-plane failure condition.

Figure 6. In-plane seismic actions at peak load: map of principal stress directions





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The stress plot, at the peak force is shown in the Figure 8: as in the in-plane case, compression stresses and tensile stresses are comparably low as in previous cases, so that elastic response, therefore no failure is expected.

Figure 7. Comparison of the bilinearized curve (average friction angle 26.6°) out-of-plane with expected seismic demands.

Figure 8. Out-of-plane seismic actions at peak load: magnified deformed shape and map of principal stress directions





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5.3. Discussion on nonlinear lateral behaviour

The behaviour of the colonnade both in-plane and out-of-plane through non-linear pushover analyses substantially shows that, compared to out-of-plane, in-plane capacity is quite higher only in the negative direction, while in the positive direction a brittle failure occurs. This result is on safe side because it was assumed the worst numerical outcome where the displacement capacity in the positive in-plane direction was the smallest one. In the other examined cases the displacement capacity is enough to withstand a design earthquake with a return period comparable to the others (namely 475 years, or about 10% in 50 years) The basic idea for ancient builders was to conceive an innovative construction technique where short segments were built up providing opposing inclined patterned edges in order to avoid long span beams over the columns and to simplify the construction phases. The blocks mutually supporting each other over inclined surfaces induce horizontal thrust in the structure to carry loads without any tensile capacity. In the structure (when possible) each block pushes over the other two contiguous blocks and this load is counteracted. The corners of the colonnade, where there is no symmetric, mutual interaction, however, become the critical location. As a solution to that static issue the builders at that time did not used the reduced size blocks at the end of the colonnade. Basically, instead of placing a block over each column, they placed a longer block on the first two extremity columns. The use of long block at the end of the colonnade provides for the required horizontal thrust balance. In particular, the horizontal thrust, not counteracted by a contiguous block, which was missing, was counteracted by two columns. Such thrust potentially could overturn a single extremity column. Another critical point of this static scheme could concern the potential swing of the blocks. In particular, the first block, supported over two columns can be considered as fixed, then a portion of this first block overhangs and works as a suspended support for the contiguous block. The block in between two columns is simply supported, but the block on the subsequent column is not fixed like the first one, because it is simply supported on a single column, so it can potentially swing. In order to prevent the potential swing, a second row of smaller, but longer blocks was simply placed on the main blocks with inclined sides. Their joints were staggered with respect to the other blocks to prevent any weak planes, and to reduce the rotation of the “suspended” blocks in between two columns. On the other hand, this solution did not prevent tensile stresses at the inclined joint locations. However, despite the joints tend to slide and to open, the geometrical configuration guarantees a certain degree of stability. It is worth noting that, even if the stability is granted in spite of small opening of the inclined joints, these opening are considered detrimental for the structure. This occurs because joint openings may lead to dangerous water leakage and lubrication of the potentially sliding planes. These points have been studied in detail numerically by means of Distinct Element Modelling (DEM). It is worth noting that nowadays the partially collapsed colonnade presents higher vulnerability because the system of horizontal thrust is not perfectly balanced on a side, hence providing non-symmetric behaviour and higher vulnerability. A potential strengthening intervention should improve the in-plane horizontal behaviour by balancing the horizontal thrust at the first column on the left hand side.

6 CONCLUSIONS

Numerical analyses checked both the gravity condition and the seismic vulnerability of one of the masterpieces in the archaeological city of Pompeii, a UNESCO World cultural heritage site in Italy, the colonnade of the forum. The seismic vulnerability analyses were performed in both the cases of in plane direction (in order to highlight the suitability of the segmented trabeation), and out-of-plane direction (where a higher vulnerability can be expected due to slenderness of the structure). By means of a static nonlinear analysis, useful outcomes were derived and knowledge for a methodical conservation. This case study represents one of the most suitable structures to be analysed by means of Discrete Element Method, because it is really made of discrete blocks (mainly rigid due to the high stiffness and very reduced stress levels) dominated by the presence of discontinuities, or interfaces,


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representing the joints between the blocks. Hence nonlinearities were taken into account mainly in the joints. The loads inside the structure were sufficiently low so that only interfaces performed nonlinearly while blocks remained almost in their elastic field. In this situation Finite Element Analysis reveals to be cumbersome only. The values of the joint parameters, which are used in the numerical analysis, play an important role to the response and they should be assigned carefully, according to the material properties. In the present case the knowledge on Archaeological material is inadequate and the analysis presented here could potentially be strongly affected by this uncertainty. For this specific reason, a sensitivity analysis was performed on the stiffness of the joints and on the frictional performance. After the analysis of a benchmark situation, stiffness of the joints was strongly reduced to simulate the presence of a weaker filling material, e.g. a mortar, still having no tensile strength. Therefore the uncertainty on the friction angle was analysed. Three values were considered. It was in fact recognized that even under gravity loads, stability was granted but joints open. Joint opening helps the income of dangerous agents, degrading the hidden marble surfaces. This provides further reduction in the mechanical performance of the joints, hence emphasizing these phenomena, implementing a vicious circle. However, by examining the capacity of this multi-drum colonnade, the simulations reveal that the capacity is adequate to positively withstand medium earthquakes as those expected in the area where it is built. This structure passed almost thirty years ago a natural test, withstanding, with negligible damages, an earthquake hitting the area in 1980, having an intensity comparable to a design earthquake with a return period of 72 years, or 50% of probability of occurrence in 50 years.

ACKNOWLEDGEMENTS Prof. G. de Martino is gratefully acknowledged for his architectural and historical key contribution to expand the understanding of the structure for conservation of this UNESCO cultural heritage site, both to preserve the artistic and historical value along with the safety of all-time visitors.

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Archeological Sites: the case of Pompeii. 8th International Conference on Structural Analysis of Historical Constructions, SAHC 2012. J.Jasienko (Ed.), vol. II: 1386-1394.

[2] Maiuri A. 1942, L’ultima fase edilizia di Pompei. Istituto di Studi Romani, Roma:25-30 (In italian)

[3] Adam J.P. 1989, Osservazioni tecniche sugli effetti del terremoto di Pompei del 62 d.C. In Guidoboni E. (Ed.) I terremoti prima del Mille in Italia e nell’area mediterranea. SGA, (In italian)

[4] Papaloizou L., Komodromos P. 2010. Investigating the seismic response of ancient multi-drum colonnades with two rows of columns using an object-oriented software, Journal of Computers & Structures

[5] Papantonopoulos C., Psycharis I., Papastamatiou D., Lemos J., Mouzakis H.. 2002. Numerical prediction of the earthquake response of classical columns using the distinct element method Earthq Eng Struct Dynam, 31, pp. 1699–1717

[6] Cundall PA. Computer model for simulating progressive large scale movements in blocky rock systems. Proceedings of the Symposium of International Society of Rock Mechanics, Vol. 1, Paper No. II-8, Nancy, France, 1971

[7] Sarhosis V. 2012. Computational modelling of low bond strength masonry. PhD thesis. University of Leeds, Leeds, UK.

[8] The ITACA website. 2014. Available online: http://itaca.mi.ingv.it/

[9] NTC’08 Ministero delle Infrastrutture. 2008. DM 14 gennaio 2008, Norme tecniche per le costruzioni, Suppl. or. n.30 alla G.U. n.29 del 4/2/2008. (In Italian)

[10] de Martino G., Giamundo V., Lignola G.P. 2012. Seismic vulnerability of the marble blocks colonnade of ancient forum in the archaeological site of Pompeii. In 15th World Conference on Earthquake Engineering”. Lisbon, Portugal. Paper 4323:1-10.

[11] EN 1998-1 2004. Eurocode 8: Design of Structures for Earthquake Resistance, CEN, Brussels.

Discrete element modelling of the archaeological colonnade in Pompeii

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