Measured eigenfrequencies for four stonemasonry bridges.
Abstract
The structural performance of old stonemasonry bridges is examined by studying such structures located at the NorthWest of Greece, declared cultural heritage structures. A discussion of their structural system is included, which is linked with specific construction details. The dynamic characteristics of four stone bridges, obtained by temporary in situ instrumentation, are presented together with the mechanical properties of their masonry constituents. The basic assumptions of relatively simple threedimensional (3D) numerical simulations of the dynamic response of such old stone bridges are discussed based on all selected information. The results of these numerical simulations are presented and compared with the measured response obtained from the in situ experimental campaigns. The seismic response of one such bridge is studied subsequently in some detail as predicted from the linear numerical simulations under combined dead load and seismic action. The performance of the same bridge is also examined applying 3D nonlinear numerical simulations with the results used to discuss the structural performance of stonemasonry bridges that either collapsed or may be vulnerable to future structural failure. Issues that influence the structural integrity of such bridges are discussed combined with the results of the numerical and in situ investigation. Finally, a brief discussion of maintenance issues is also presented.
Keywords
 stonemasonry bridges
 structural performance
 in situ measurements
 numerical simulations
1. Introduction
This chapter focuses on stonemasonry bridges that were built in Greece during the last 300 years and most of them survive today (Figure 1a and b).
The use of the stonemasonry arch that is utilized in forming stonemasonry bridges was extensively used in the times of the Roman Empire as part of the transportation system that was established and linked to various provinces of the Roman Empire. Evidence of stonemasonry arch bridges prior to Roman times is not known although stonemasonry structures in the East Mediterranean area for other uses date to prehistoric times. A wellknown use of arch/vault stonemasonry structural form is the one that can be seen at the royal tombs, which have been excavated during the last 200 years in many places in Greece. In Figure 2, the royal tomb of Atreus at Mycenae, Greece, is depicted where stone masonry is employed to form an undergroundvaulted structure with a diameter at its base of 14.60 m and a height of 13.30 m constructed with 33 subsequent series of stone masonry along the height.
The use of such vaulted stonemasonry structures demonstrates the efficient utilization of this structural form in order to bear efficiently the dead loads as well as the weight of the overlying soil volume in a state of stress dominated by compression (Figures 2 and 3a). On the contrary, the main gate of the royal palace walls at Mycenae in Peloponnese of Southern Greece (dated 1325 B.C. to 1200 B.C. and excavated 150 years ago), known as the gate of the lions (Figure 3b), uses the simplesupported beamtype structural system that characterizes most of the prehistoric and classical ancient Greek stonemasonry construction for abovetheground structures. The use of the stonemasonry arch/vaulttype formation is also evident in the structural system of the royal tombs of the Macedonian kings at Vergina in Northern Greece, dated from 350 B.C. and excavated during the last 30 years (Figure 3c and d).
Despite the use of arch/vaulted stonemasonry structural formations for these underground Macedonian royal tombs at Vergina in Northern Greece, there is no evidence of such structural formations being used for bridges at that time. Figure 4a shows the location of the Macedonian royal palaces at Vergina and Pella in Northern Greece (red arrows).
In the same figure, the location of the remains of an ancient Roman bridge (blue arrow) is also indicated. These remains correspond today to only one main arch with a span of 15 m and a height of 7.5 m (Figure 4b). This surviving part of a Roman stonemasonry bridge is dated between 50 A.D. and 150 A.D. and, as can be seen in the map of Figure 4a, is located at a close distance (25 km) from the Macedonian palaces of Vergina and Pella as well as for the important cities of Thessaloniki and Dion (30–40 km). An inventory of Roman stonemasonry bridges is given by O’Connor [1]. These structures survive today, located in many European countries, having been in many cases preserved in good condition (Figure 5a and b) or partially collapsed in other cases (Figure 5c and d).
2. Geometric characteristics of the stonemasonry bridges located at NorthWest Greece
In what follows, a brief review is given of the basic geometric and construction characteristics of the stonemasonry bridges located at the far NorthWestern part of Greece called Ipiros. Bridges of similar geometric and construction characteristics are also located in other parts of Greece. The present study has selected the stonemasonry bridges that are located in Ipiros as they are numerous and are located in a relatively confined area that facilitates their temporary
A considerable number of relatively small stonemasonry bridges can be found in this region with a span smaller than 10 m as the ones depicted in Figure 6a and b. However, stonemasonry bridges with a much larger total span have also been constructed. Relatively longspan stone bridges with a single central span are relatively few in number. The longest stone bridges with one main central arch are the ones in Konitsa (Figure 7a and b) and the one in Plaka (Figure 7c and d). These stonemasonry bridges are very similar in the dimensions of the central arch, although the Arachthos river crossing by the Plaka Bridge is longer (75m total span) due to adjacent additional arches at both ends (Figure 7c), whereas the main arch of the Konitsa Bridge is supported directly at the nearby slopes of the rocky Aoos river gorge. As will be presented briefly in Chapter 9 (see also figures 10g and 11 as well as section 7.3), the Plaka Bridge collapsed almost a year ago (31 January 2015). As can be seen in Figure 7b and d, the main central arch of both the Konitsa and the Plaka stone bridges has a clear span of nearly 40 m and a rise of 20 m.
Apart from the Plaka and Konitsa stone bridges, three more bridges will be examined in the present study. These stone bridges are depicted in Figure 8a–f and are namely the Kokorou Bridge, the Tsipianis Bridge and the Kontodimou Bridge. As can be seen in Figure 8b and d, the main central arch of the Kokorou Bridge has a clear span of 24.69 m and a rise of 12.71 m, whereas the Tsipianis Bridge has a clear span of 26.00 m and the rise 13.65 m. As can be seen, the central main arch of these two bridges has similar dimensions. Finally, the clear span of the Kontodimou Bridge is 14.50 m and the rise 7.40 m.
Thus, the present study covers stone bridges that are all dominated by a central main arch with a span/rise varying from 40.00/20.00 to 14.50/7.40 m. As can be seen in all cases, the clear span over rise ratio is close to 2.0 and the width is close to 3.0 m. In the cases of the longest span, the width of the structure increases as the arch approaches the foundation (Konitsa and Plaka Bridges). A distinct difference between the examined bridges is the fact that in the case of Konitsa, Kokorou and Kontodimou Bridges, the main arch is founded on abutments that are very close to the rocky slopes of the river gorge whereas for the Plaka and Tsipianis Bridges there is a midpier that is founded on the river bed together with adjacent smaller arches (Figures 7d and 8d).
3. Construction characteristics
The construction characteristics of the various parts of these bridges are thought to bear some significance in the effort to understand the static, dynamic and earthquake behaviour of these structures. One can distinguish the following main structural components:
The main primary central arch is founded on abutments at either end of the bridge. These abutments are extensions of the rocky part of the river bank (Figure 9a). In the case of a midpier, which was constructed on the dry part of the river bed, a separate foundation footing is constructed at a certain depth that is not easy to estimate. In case of relatively large river widths, the main arch was founded on right and left midpiers that were also supporting adjacent arches as is seen in Figure 9b. A wooden formwork was employed to support the main arch during construction (Figure 9c).
The construction of the main central arch was preceded by the construction of its foundation at both ends together with the construction of the abutments that were raised up to a certain height in order to resist the thrust of the central arch.
The construction of the main central arch was followed in many cases with the construction of a secondary central arch on top of the main central arch (Figures 9d and 10a–f).
Finally, the mandrel walls were constructed above the abutments in order to form together with the arches the main passage (deck) at the top of the bridge. In certain cases, this passage is protected at both sides at the deck level by an inbuilt continuous stone parapet that rises approximately 0.5 m above the deck level (Figures 7a, c and 8a, c). In the case of the Kontodimou Bridge, this parapet is formed by individual stones inbuilt at intervals of approximately 1.6 m.
The thickness of the primary and secondary arches of the main span varies considerably. The primary arch for the Konitsa Bridge with a clear span of 40 m has a thickness of 1.30 m And The Secondary Arch A Thickness of 0.59 m (Figures 7b and 10a). The primary arch of the Plaka Bridge again with a clear span of 40 m has a thickness of 0.73 m and the secondary arch a thickness of 0.68 m (Figures 7d and 10b). The primary arch of the Kokorou Bridge with a clear span of 24.69 m has a thickness of 0.81 m and the secondary arch a thickness of 0.35 m (Figures 8b, 10c and d). The primary arch of the Tsipiani Bridge with a clear span of 26 m has a thickness of 0.50 m and the secondary arch a thickness of 0.40 m (Figure 8d). Finally, the primary arch of the Kontodimou Bridge with a clear span of 14.5 m has a thickness of 0.70 m and the secondary arch a thickness of 0.30 m (Figures 8f, 10e and f). These thickness values are approximate and correspond to the arch thickness at the maximum rise; in some cases, the primary and the secondary arch thicknesses vary having an increased thickness in the areas where these arches join the abutments.
The construction of both the primary and secondary main central arches as well as the rest of the arches was constructed with stones that were shaped in a very regular prismatic shape. In this way, the mortar joints of the masonry construction for these arches are relatively very small. The same holds for the foundation and the abutments up to a certain height. For these structural parts, according to oral tradition, special attention was paid for the quality of the stone and mortar to be employed.
On the contrary, neither the shape nor the quality of the stones or the mortar was of equal importance for the mandrel walls. As can be seen in Figure 10g that depicts the remaining part of the Plaka Bridge, these mandrel walls were internally constructed with some form of rubble. However, in order to protect these parts from the weather conditions, the mandrel walls were also encased within facades of goodquality stone masonry (Figure 10g).
Because the primary and secondary main arches were constructed at different construction stages, there is a continuous cylindrical joint that lies between them (see Figure 10a–f). As revealed by the remains of the collapsed Plaka Bridge, wooden beams with iron inserts were employed to connect the primary and secondary arches at certain intervals.
Iron ties were also used to connect the two opposite faces of the primary arch in many bridges. These iron ties are visible in the photos of the main central arch of the Plaka Bridge before its collapse and they are still in place at the parts of the arch that were salvaged after its collapse (Figures 11 and 12). The iron ties were also used to connect the opposite faces of the primary arch of the main span in Tsipianis Bridge (Figure 13) and in Voidomatis bridge at Klidonia (Figure 14).
4. In situ measurements of the dynamic characteristics of stone bridges
4.1. Four studied stone bridges
In measuring the dynamic response of four stone bridges, two types of excitation were mobilized. The first, namely ambient excitation, mobilized the wind, despite the variation of the wind velocity in amplitude and orientation during the various tests. Due to the topography of the areas where these stone bridges are located, usually a relatively narrow gorge, the orientation of the wind resulted in a considerable component perpendicular to the longitudinal bridge axis (Figures 15a, 17a, 18a and 19a). This fact combined with the resistance offered to this wind component by the façade of each bridge produced sufficient excitation source resulting in small amplitude vibrations that could be recorded by the employed instrumentation. For this purpose, the employed SysCom triaxial velocity sensors had a sensitivity of 0.001 mm/s and a SysCom data acquisition system with a sampling frequency of 400 Hz. All the obtained data were subsequently studied in the frequency domain through available fast Fourier transform (FFT) software [4, 5]. This wind orientation relative to the geometry of each bridge structure coupled with the bridge stiffness properties could excite mainly the first symmetric outofplane eigenmode, as can be seen in Figure 16c for the Konitsa Bridge. The variability of the wind orientation could also excite, although to a lesser extent, some of the other inplane and outofplane eigenmodes (see Figure 16c for the Konitsa Bridge).
The second type of excitation that was employed, namely vertical inplane excitation, was produced from a sudden drop of a weight on the deck of each stonemasonry bridge [6, 7]. This weight was of the order of approximately 2.0 kN that was dropped from a relatively small height of 100 mm, so as to avoid even the slightest damage to the stone surface of the deck of each bridge. Again, the level of this second type of excitation was capable of producing mainly vertical vibrations and exciting the inplane eigenmodes of each structure that could be captured by the employed SysCom triaxial velocity sensors with a sensitivity of 0.001 mm/s and a SysCom data acquisition system with a sampling frequency of 400 Hz. All the obtained data were subsequently studied in the frequency domain through available FFT software. In Figure 15c, the velocity measurements are depicted along the three axes (
Measured eigenfrequencies (Hz) for the 

Inplane  First asymmetric 5.176 Hz  Second symmetric 7.715 Hz  Third symmetric 12.549 Hz 
Outof plane  First symmetric 2.539 Hz  Second asymmetric 4.883 Hz  Third symmetric 7.129 Hz 
Measured eigenfrequencies (Hz) for the 

Inplane  First asymmetric 7.275 Hz  Second symmetric 10.059 Hz  Third symmetric 17.139 Hz 
Outof plane  First symmetric 4.541 Hz  Second asymmetric 7.471 Hz  Third symmetric 10.303 Hz 
Measured eigenfrequencies (Hz) for the 

Inplane  First asymmetric 6.934 Hz  Second symmetric 8.549 Hz  Third symmetric 14.209 Hz 
Outof plane  First symmetric 3.320 Hz  Second asymmetric 6.348 Hz  Third symmetric 12.207 Hz 
Measured eigenfrequencies (Hz) for the 

Inplane  First asymmetric 11.621 Hz  Second symmetric 16.934 Hz  Third symmetric 22.00 Hz 
Outof plane  First symmetric 7.860 Hz  Second asymmetric 16.846 Hz  Third symmetric 24.023 Hz 
The same process was followed for measuring the dynamic characteristics of another three stonemasonry bridges (Kokorou, Tsipianis and Kontodimou) using both the wind and the drop weight excitations, as shown in Figures 17–19 where the position of the employed velocity sensors is indicated. Next, by utilizing all these vibration measurements of the dynamic response of each of these studied bridges for either type of excitation, it was possible to extract the relevant eigenfrequencies that are listed in Table 1. At least measurements of three repetitive sampling sequences for each type of excitation, either wind or drop weight, for each bridge (Konitsa, Kokorou, Tsipianis and Kontodimou) were measured. The eigenfrequency values listed in Table 1 are values representing an average from corresponding values that were obtained by analysing the measured response from all tests.
4.2. Additional field measurements for the Konitsa Bridge
To gain more confidence in the
Shown in Figure 21 are the postwind gust bridge response (vertical acceleration) and the corresponding power spectrum associated with the trace segment between 12 and 16 s of the record [4]. The power spectrum associated with the decay segment clearly delineates (a) the symmetric vertical mode (7.75 Hz).
Figure 22 depicts the horizontal (outofplane) acceleration time histories recorded simultaneously at two locations on the Konitsa Bridge deck and their corresponding power spectrum with dominant frequency of 2.56 Hz (first outoutof plane eigenmode). Comparing the eigenfrequency values obtained for the
5. Laboratory tests for the stone masonry
A laboratory testing sequence was performed having as an objective to study in a preliminary way the mechanical characteristics of the basic materials representative of the materials employed to build the studied stonemasonry bridges [4]. For this purpose, stone samples were selected from the neighbourhood of the collapsed Plaka Bridge as well as from a quarry near the Kontodimou and Kokorou Bridges. Moreover, stone samples were also taken from the river bed of the Kontodimou Bridge. Furthermore, it was possible to take a mortar sample from the collapsed Plaka Bridge. From both the stone and mortar samples collected
Code name of sample 
Cross section (mm^{2}) 
Height (mm) 
Maximum load (KN) 
Compressive strength (MPa) 
Slenderness ratio^{*}/correction coefficient 
Compressive strength (MPa) with correction due to slenderness^{*} 

River 1a  58.5 × 48.5  74.0  310.2  124.0  1.383/0.82  101.7 
River1b  61.5 × 48.3  61.0  230.5  77.6  1.111/0.70  54.3 
River 2a  56.3 × 45.0  59.5  225.6  89.0  1.175/0.73  65.0 
River 2b  59.0 × 45.0  65.5  363.0  136.0  1.260/0.77  104.7 
River 2c  33.0 × 65.0  59.0  220.7  102.9  1.205/0.75  77.2 
Quarry 1a  55.0 × 45.5  70.0  416.9  166.6  1.394/0.82  136.6 
Quarry 1b  52.0 × 46.0  73.5  230.5  96.4  1.500/0.90  88.8 
Quarry 2a  44.8 × 44.8  84.5  193.3  96.3  1.886/0.95  91.5 
Quarry 2b  47.0 × 44.8  43.5  313.9  149.0  0.948/0.65  96.9 
Code name of sample 
Width (mm) 
Height (mm) 
Span (mm) 
Maximum vertical load (kN) 
Tensile strength (MPa) 
Young’s Modulus from flexure (MPa) (DCDT) 

River 1  60.0  46.5  135.0  24.98  23.41  2875 
River 2  60.0  45.0  135.0  22.66  25.18  1545 
Quarry 1  54.0  46.5  135.0  12.875  14.89  11,205 
Quarry 2  45.0  44.5  135.0  13.647  20.67  15,345 
Code name of sample  Cross section (mm^{2})  Height (mm)  Maximum load (kN)  Compressive strength (MPa)  Slenderness ratio^{*}/correction coefficient  Compressive strength (MPa) with correction due to slenderness^{*} 

Specimen A  61.0 × 68.0  93.0  264.9  63.9  1.442/0.87  55.6 
Specimen B  67.5 × 62.0  89.0  443.4  106.0  1.375/0.82  86.9 
Code name of sample  Width (mm) 
Height (mm) 
Span (mm) 
Maximum vertical load (kN) 
Tensile strength (MPa) 
Young’s Modulus from flexure (MPa) (S.G.) 

Specimen A  52.0  52.0  180.0  14.75  18.88  33,330 
Specimen B  52.0  52.0  180.0  12.13  15.52  36,360 
Code name of sample  Cross section (mm^{2})  Height (mm)  Maximum load (kN)  Compressive strength (MPa)  Slenderness ratio^{*}/correction coefficient  Compressive strength (MPa) with correction due to slenderness^{*} 

Specimen 1  27.5 × 57.0  66.0  3.228  2.06  1.562/0.91  1.875 
6. Numerical simulation of dynamic characteristics
In this section, the dynamic characteristics of the four studied stonemasonry bridges will be predicted through a numerical simulation process. Initially, this numerical simulation will be based on elastic behaviour, assuming the stone masonry as an orthotropic continuous medium and limiting these numerical models at approximately the interface between the end abutments and the rocky river banks, thus introducing boundaries at these locations [10]. For simplicity purposes, the bulk of these numerical simulations are made in the 3D domain representing these bridge structures with their midsurface employing thickshell finite elements [11]. The various main parts of these stonemasonry bridges, that is, the primary and the secondary arches, the abutments, the deck, the mandrel walls and the parapets, were simulated in such a way that narrow contact surfaces could be introduced between them, representing in this way a different ‘softer’ medium. All available information, measured during the
Measured/predicted eigenfrequencies (Hz) for the 

Inplane  First asymmetric 5.176/6.724  Second symmetric 7.715/7.076  Third symmetric 12.549/10.065 
Outof plane  First symmetric 2.539/2.432  Second asymmetric 4.883/4.478  Third symmetric 7.129/7.275 
Measured eigenfrequencies (Hz) for the 

Inplane  First asymmetric 7.275/10.212  Second symmetric 10.059/11.134  Third symmetric 17.139/15.125 
Outof plane  First symmetric 4.541/4.035  Second asymmetric 7.471/7.065  Third symmetric 10.303/11.545 
Measured eigenfrequencies (Hz) for the 

Inplane  First asymmetric 6.934/7.106  Second symmetric 8.549/10.029  Third symmetric 14.209/12.742 
Outof plane  First symmetric 3.320/3.090  Second asymmetric 6.348/5.734  Third symmetric 12.207/9.248 
Measured eigenfrequencies (Hz) for the 

Inplane  First asymmetric 11.621/11.893  Second symmetric 16.934/12.389  Third symmetric 22.000/20.155 
Outof plane  First symmetric 7.860/5.664  Second asymmetric 16.846/13.117  Third symmetric 24.023/21.988 
Measured/predicted eigenfrequencies (Hz) for the 

Inplane  First asymmetric 5.176/6.733  Second symmetric 7.715/7.078  Third symmetric 12.549/10.085 
Outof plane  First symmetric 2.539/2.526  Second asymmetric 4.883/4.759  Third symmetric 7.129/7.706 
Measured eigenfrequencies (Hz) for the 

Inplane  First asymmetric 7.275/10.212  Second symmetric 10.059/11.134  Third symmetric 17.139/15.125 
Outof plane  First symmetric 4.541/4.548  Second asymmetric 7.471/8.408  Third symmetric 10.303/13.733 
Measured eigenfrequencies (Hz) for the 

Inplane  First asymmetric 6.934/7.106  Second symmetric 8.549/10.029  Third symmetric 14.209/12.742 
Outof plane  First symmetric 3.320/3.321  Second asymmetric 6.348/6.257  Third symmetric 12.207/10.012 
Measured eigenfrequencies (Hz) for the 

Inplane  First Asymmetric 11.621/11.905  Second Symmetric 16.934/12.395  Third Symmetric 22.000/20.185 
Outof plane  First Symmetric 7.860/7.643  Second Asymmetric 16.846/17.035  Third Symmetric 24.023/26.362 
The approximation adopted in this study is a process of back simulation [6, 7]. That is, adopting values for these unknown mechanical stonemasonry properties, respecting at the same time all the measured geometric details, which result in reasonably good agreement between the measured and predicted in this way eigenfrequency values. Following this approximate process, two distinct cases of boundary conditions were introduced. In one series of numerical simulations, all the boundaries, either at the river bed or at the river banks, were considered as being fixed in these 3D numerical simulations for all studied bridges. This is denoted in the predicted eigenfrequency values in Tables 7 and 8 and Figures 24 and 25 with the subscript ‘
7. Simplified numerical investigation of the seismic behaviour of the studied stonemasonry bridges
7.1. Simplified dynamic spectral numerical simulation of the seismic behaviour of the Konitsa Bridge
This section includes results of a series of numerical simulations of the Konitsa Bridge when it is subjected to a combination of actions that include the dead weight (D) combined with seismic forces. The seismic forces will be defined in various ways, as will be described in what follows. Initially, use is made of the current definition of the seismic forces by EUROCode 8 [12]. Towards this, horizontal and vertical design spectral curves are derived based on the horizontal design ground acceleration. This value, as defined by the zoning map of the current Seismic Code of Greece [13, 14], is equal to 0.16 g (g is the acceleration of gravity) for the location of the Konitsa Bridge. Furthermore, it is assumed that the soil conditions belong to category A because of the rocky site where this bridge is founded, that the importance and foundation coefficients have values equal to one (1.0); the damping ratio is considered equal to 5% and the behaviour factor is equal to 1.5 (unreinforced masonry). The design acceleration spectral curves obtained in this way are depicted in Figure 26a and b for the horizontal and vertical direction, respectively. In the same figures, the corresponding elastic acceleration spectral curves are also shown derived from the ground acceleration recorded during the main event of the earthquake sequence of 5 August 1996 at the city of Konitsa located at a distance of approximately 1.5 km from the site of the bridge [15]. In Figure 26a and b, the eigenperiod range of the first 12 eigenmodes is also indicated (ranging between the low and the high modal period). For the vertical response spectra, this is done for only the inplane eigenmodes (see also Table 9).
As can be seen in Figure 26a, the EuroCode horizontal acceleration spectral curves compare well with the horizontal component3 of 1996 Earthquake spectral curves for the period range of interest. The EuroCode vertical acceleration spectral curves, depicted in Figure 26b, are approximately 100% larger than the vertical component2 of 1996 Earthquake spectral curves for the period range of interest. Based on these plots, it can be concluded that this bridge sustained a ground motion that in the horizontal direction was approximately comparable to the design earthquake; however, the design earthquake in the vertical direction is shown to be more severe than the one this stonemasonry bridge experienced during the 1996 earthquake sequence.
In Table 10, the base reactions are listed (
Output case Text 
Period s 
Frequency Hz 
Unitless 
Unitless 
Unitless 
Sum Unitless 
Sum Unitless 
Sum Unitless 

Mode 1 (first OOP Symmetric) 
0.396  2.5264  0.3300  0  0  0.33002  0  0 
Mode 2 (second OOP asymmetric) 
0.210  4.7588  0.0004  0  0  0.33043  0  0 
Mode 3 (first IP asymmetric) 
0.149  6.7333  0.0  0.08498  0.00055  0.33043  0.08498  0.00055 
Mode 4 (second IP symmetric) 
0.141  7.0777  0.0  0.00104  0.12769  0.33043  0.08602  0.12825 
Mode 5 (third OOP symmetric) 
0.130  7.7062  0.2271  0  0  0.55753  0.08602  0.12825 
Mode 6 (third IP symmetric) 
0.099  10.0851  0.0  0.0007  0.15393  0.55753  0.08672  0.28218 
Mode 7 (fourth OOP asymmetric) 
0.086  11.6697  0.0  0  0  0.55754  0.08672  0.28218 
Mode 8 (fourth IP asymmetric) 
0.074  13.4317  0.0  0.17916  0.0023  0.55754  0.26588  0.28447 
Mode 9 (fifth OOP symmetric) 
0.065  15.2999  0.08851  0  0  0.64605  0.26588  0.28447 
Mode 10 (fifth IP symmetric) 
0.062  16.0400  0.0  0.23382  0.000014  0.64605  0.49971  0.28449 
Mode 11 (sixth IP asymmetric) 
0.0565  17.6794  0.0  0.0026  0.08175  0.64605  0.5023  0.36624 
Mode 12 (sixth OOP asymmetric) 
0.0522  19.1439  0.00262  0  0  0.64868  0.5023  0.36624 
As can be seen in Table 9, these eigenmodes have modal mass participation ratios that result in sums smaller than 90%. That is, Sum
Loading case description 
Loading type description 
Type limit 
Global (kN) 
Global (kN) 
Global (kN) 


1  DEAD (D)  Linear Static  0  0  35,853  
2  1996 Comp 2 RS Ver IP  Linear Resp. Spectral 1996 EQ  Max  0  179  1499 
3  1996 Comp 3 RS Hor 
Linear Resp. Spectral 1996 EQ  Max  3130  0  0 
4  1996 Comp 3 RS Hor 
Linear Resp. Spectral 1996 EQ  Max  0  2552  230 
5  Combination 1  Dead + 1996 EQ RS ( 
Max  4825  5574  40,406 
6  Combination 1  Dead + 1996 EQ RS ( 
Min  −4825  −5574  31,299 
7  EuroCode RS Hor 
Linear Resp. Spectral EuroCode  Max  3725  0  0 
8  EuroCode RS Hor 
Linear Resp. Spectral EuroCode  Max  0  2224  193 
9  EuroCode RS Ver 
Linear Resp. Spectral EuroCode  Max  0  443  3426 
10  Combination 7  Dead + EuroCode RS ( 
Max  5742  5640  45,597 
11  Combination 7  Dead + EuroCode RS ( 
Min  −5742  −5640  26,109 
In Figure 27a and b, the numerically predicted deformation patterns of Konitsa Bridge are depicted for load combination 1 and 7, respectively. As can be seen, this stonemasonry bridge develops under these combinations of dead load and seismic forces relatively large outofplane displacements at the top of the main arch. As expected, the deformations for the EuroCode design spectra reach the largest values attaining at the crown of the arch a maximum value equal to 30.6 mm. In Figure 28a–h, the numerically predicted state of stress (max/min S11, max/min S22), which develops at Konitsa Bridge for load combinations 1 and 7, is depicted. Again, as expected, the most demanding state of stress results for the load combination 7 that includes seismic forces provided by EuroCode [12]. The largest values of tensile stress S11 (3.46 MPa, Figure 28b) develop at the bottom fibre of the crown of the arch. This is a relatively large tensile stress value that is expected to exceed the tensile capacity of the stone masonry of this bridge [16]. The largest value of tensile stress S22 (1.5 1 MPa, Figure 28f) develops at the area where the primary arch joins the foundation block. Again, this is a relatively large tensile stress value that is expected to exceed the tensile capacity of the stone masonry of this bridge. Both these remarks indicate locations of distress for this stonemasonry bridge predicting in this way the appearance of structural damage. On the contrary, the largest value of compression stress equal to S11 = −4.3 MPa (Figure 28d, for combination 7) is expected to be easily met by the compression capacity of the stone masonry for this bridge [16].
7.2. Dynamic elastic timehistory numerical simulation of the seismic behaviour of the Konitsa Bridge
An additional linear numerical simulation was performed. This time, apart from the dead load (D, row 1, Table 11), the Konitsa Bridge was subjected to the horizontal component (Comp3) and/or the vertical component [17] of the 1996Konitsa earthquake record (Figure 29) in the following way. The bridge was subjected only to the vertical (Comp2Ez, rows 2 and 3 of Table 11) or only to the horizontal component of this record in the out ofplane direction (Comp3Ex, rows 4 and 5 of Table 11). Alternatively, the bridge was subjected to the horizontal component of this record in the inplane horizontal direction (Comp3Ey, rows 6 and 7, Table 11) [15].
The solution this time was obtained through a stepbystep time integration scheme assuming a damping ratio equal to 5% of critical. In these analyses, only the first most intense 6 s of this 1996Konitsa earthquake record were used [15]. In Table 11, the base shear values in the
Loading case description 
Loading type description  Type limit 
Global (kN) 
Global (kN) 
Global (kN) 


1  DEAD  Dead Load (D) Linear Static  0  0  35,853  
2  Comp 2 TH Ver 
Konitsa 1996 Comp 2 THist. Ver InPlane (Ez) 
Max  0  128.6  2651.2 
3  Comp 2 TH Ver 
Konitsa 1996 Comp 2 THist. Ver InPlane (Ez) 
Min  0  −140.2  −2380.5 
4  Comp 3 TH Hor 
Konitsa 1996 Comp 3 THist. Hor OutofPlane (Ex) 
Max  5254.6  0  0 
5  Comp 3 TH Hor 
Konitsa 1996 Comp 3 THist. Hor OutofPlane (Ex) 
Min  −5786.6  0  0 
6  Comp 3 TH Hor 
Konitsa 1996 Comp 3 THist. Hor InPlane (Ey) 
Max  0  4608.7  88.2 
7  Comp 3 TH Hor 
Konitsa 1996 Comp 3 THist. Hor InPlane (Ey) 
Min  0  −6456.7  −81.9 
8  COMB9  Dead + Ex + Ez  Max  5254.6  128.6  38,504.2 
9  COMB9  Dead + Ex + Ez  Min  −5786.6  −140.2  33,472.5 
10  COMB10  Dead + Ey + Ez  Max  0  4737.3  38,592.4 
11  COMB10  Dead + Ey + Ez  Min  0  6596.9  33,390.7 
12  COMB11  Dead + Ex + Ey + Ez  Max  5254.6  4737.3  38,592.4 
13  COMB11  Dead + Ex + Ey + Ez  Min  −5786.6  −6596.9  33,390.7 
Figure 31a and b depict the envelop of the limit (maximum/minimum) values of the S11 stress distribution in the Konitsa Bridge for load combination 11 that includes the dead load, the application of Comp3 of the Konitsa earthquake record in both the horizontal inplane and outofplane direction as well as Comp2 of the Konitsa earthquake record in the vertical inplane direction. By examining the displacement and stress response, it could be concluded that the application of the horizontal component of the Konitsa 1996 in the horizontal
7.3. Simplified numerical simulation of the seismic behaviour of the Plaka Bridge
This section includes results of a series of numerical simulations of the Plaka Bridge when it is subjected to a combination of actions that include the dead weight (D) combined with seismic forces. The seismic forces will be defined as was done in Section 7.1 by making use of the current definition of the seismic forces by EUROCode 8 [12]. Towards this, horizontal and vertical design spectral curves are derived based on the horizontal design ground acceleration. This value, as it is defined by the zoning map of the current Seismic Code of Greece, is equal to 0.24 g (g is the acceleration of gravity) for the location of the Plaka Bridge [13, 14]. Furthermore, it is assumed that the soil conditions belong to category A because of the rocky site where this bridge is founded, that the importance and foundation coefficients have values equal to one (1.0), the damping ratio is considered equal to 5% and the behaviour factor is equal to 1.5 (unreinforced masonry). The design acceleration spectral curves obtained in this way are depicted in Figure 32a and b for the horizontal and vertical direction, respectively. In Figure 32a and b, the eigenperiod range of the first 12 eigenmodes is also indicated (ranging between the low and the high modal period). For the vertical response spectra, this is done for only the inplane eigenmodes (see also Table 11). By comparing these design spectral acceleration curves (of Figure 32a and b) for the Plaka Bridge with the corresponding spectral curves for the Konitsa Bridge (Figure 26a and b), it becomes apparent that the former represent a more demanding seismic force level than the latter.
For the Plaka Bridge, the modal mass participation ratios and the base reactions are listed in Tables 12 and 13, respectively. The base reactions are
Output Case  Period  Frequency  Sum 
Sum 
Sum 


Text  s  Hz  Unitless  Unitless  Unitless  Unitless  Unitless  Unitless 
Mode 1 (first OOP symmetric)  0.484  2.068  0.33622  0  0  0.33622  0  0 
Mode 2 (second OOP asymmetric)  0.250  3.994  0.00003  0  0  0.33625  0  0 
Mode 3 (first IP asymmetric)  0.179  5.583  0  0.10253  0  0.33625  0.1025  0.000008 
Mode 4 (third OOP symmetric)  0.157  6.351  0.24674  0  0  0.58298  0.10253  0.000008 
Mode 5 (second IP symmetric)  0.152  6.573  0  0.00067  0.13444  0.58298  0.1032  0.13445 
Mode 6 (third IP symmetric)  0.111  9.034  0  0  0.16089  0.58298  0.10323  0.29533 
Mode 7 (fourth OOP asymmetric)  0.104  9.463  0.00006  0  0  0.58304  0.10323  0.29533 
Mode 8 (fourth IP asymmetric)  0.0865  11.561  0  0.37475  0.00011  0.58304  0.47797  0.29545 
Mode 10 (fifth IP symmetric)  0.0787  12.706  0  0.10353  0.00049  0.58304  0.5815  0.29594 
Mode 9 (fifth OOP symmetric)  0.0772  12.953  0.0914  0  0  0.67444  0.5815  0.29594 
Mode 11 (sixth IP asymmetric)  0.0687  14.556  0  0.00557  0.09697  0.67444  0.58708  0.39291 
Mode 12 (sixth OOP asymmetric)  0.0609  16.420  0.00186  0  0  0.6763  0.58708  0.39291 
Loading case description 
Loading type description 
Type limit  Global 
Global 
Global 


1  DEAD (D)  Linear Static  0  0  42,544  
2  EuroCode RS Hor 
Linear Resp. Spectral EuroCode 
Max  6382  0  0 
3  EuroCode RS Hor 
Linear Resp. Spectral EuroCode 
Max  0  5773  311 
4  EuroCode RS Ver 
Linear Resp. Spectral EuroCode 
Max  0  677  6581 
5  Combination 1  Dead + EuroCode RS ( 
Max  9436  11,555  59,823 
6  Combination 1  Dead + EuroCode RS ( 
Min  −9436  −11,555  25,265 
In Figure 33a and b, the numerically predicted deformation patterns of Plaka Bridge are depicted for load combination 1. As can be seen, this stonemasonry bridge develops under this combination of dead load and seismic forces relatively large outofplane displacements at the top of the main arch. As expected, the outofplane displacement response of the Plaka Bridge, when subjected to EuroCode design spectra, reaches the largest value at the crown of the arch with a maximum value equal to 52.84 mm. This maximum outofplane value for the Plaka Bridge is almost twice as large as the corresponding value predicted numerically for the Konitsa Bridge.
In Figure 34a–d, the numerically predicted state of stress (max/min S11, max/min S22), which develops at Plaka Bridge for load combination 1, is depicted. Again, as expected, the most demanding state of stress results is for the load combination 1 that includes seismic forces provided by EuroCode. The largest value of tensile stress S11 (5.73 MPa, Figure 34a) develops at the bottom fibre of the crown of the arch. This relatively large tensile stress value [11, 16] is exceeding by far the tensile capacity of traditionally built stone masonry. The largest value of tensile stress S22 (3.40 MPa, Figure 34c) develops at the area where the toes of the primary arch join the foundation block. Again, this is a relatively large tensile stress value and is exceeding by far the tensile capacity of traditionally built stone masonry. Both these remarks indicate locations of distress for the Plaka stonemasonry bridge, as was done for the Konitsa Bridge predicting in this way the appearance of structural damage. On the contrary, the largest value of compressive stress equal to S11 = −6.14 MPa (Figure 34d, for combination 1) could be met by the compression capacity of the stone masonry for this bridge. The maximum tensile stress values that were numerically predicted for Plaka Bridge are approximately twice as large as the corresponding values obtained for Konitsa Bridge. This is due to the seismic forcing levels, which for Plaka Bridge are by 50% higher than those applied for Konitsa ridge. This is because Plaka Bridge is located in seismic zone II (design ground acceleration equal to 0.24 g) whereas Konitsa Bridge is located at seismic zone I (design ground acceleration equal to 0.16 g). Furthermore, although the main central arches of the two bridges are very similar in geometry (with the deck of the Plaka Bridge being somewhat wider than the deck of the Konitsa Bridge), the Plaka Bridge has a much larger total length than the Konitsa Bridge due to the construction of a midpier and arches adjacent to the main central arch. Thus, Plaka Bridge is more flexible and has a much larger total mass than the Konitsa Bridge. Based on these remarks, it is reasonable to expect for the Plaka Bridge larger seismic displacement values in the outofplane direction and consequently larger tensile stress values, than the corresponding values predicted for the Konitsa Bridge. The final consequence of these remarks is that, according to the results of this simplified numerical approach, the Plaka Bridge has a higher degree of seismic vulnerability than the Konitsa Bridge. A similar simplified numerical study of the performance of the Plaka Bridge could be done when measurements of flow data of the flooding of river Arachthos (31st January 2015) that caused the collapse of this bridge become available.
8. Nonlinear numerical simulation of the seismic behaviour of the Konitsa stonemasonry bridge
A threedimensional finite element model of the Konitsa stone bridge was developed and utilized in the linear (modal and gravity) and nonlinear (earthquake) analyses [18, 19]. The general finite element software TrueGrid (meshing) and LSDYNA (static, modal, earthquake analyses) software were employed [20]. The developed threedimensional model incorporated interface conditions between distinct parts of the structure (i.e. lower and upper stone arches, arches and abutments, etc.) in an effort to capture the interaction between the structural sections as well as differentiate between the building techniques and details that were introduced during the construction of the bridge and thus differentiate between the different failure criteria and mechanisms that may govern the different parts. A modelling approach where the elements (stones) of the arch are represented by solid elements with ‘hybrid’ behaviour was adopted and used throughout. The detailed model developed for this study included 4009 beam elements that formed the steel mesh in the intrados of the bridge rigidly connected to the stone array. The bridge was modelled using four different solid materials with 72,540 elements. As noted above, the different structural components are in ‘contact’ governed by contact interface conditions. The two arches have been modelled with solid ‘hybrid’ elements (stonemortar behaviour) that capture the ‘nonlinearity’ or failure rather than the pure contact between stones, an approach that is closer to the actual conditions in the structure. Specifically, it has been assumed that the ‘hybrid’ element representing mortar and stone behaves as one with the weakness attributed to the mortar part (Modulus and Poisson ratio represent the entire element but critical stresses are dependent on mortar).
The model is assumed to be fixed on competent rock on both sides and no soilstructure interaction (SSI) effects are considered. Figure 35a and b depict the finite element model that was developed and utilized based on
8.1. Modal and static analyses
Before proceeding to the complex nonlinear analyses, a modal analysis was performed as a first attempt utilizing the numerical model depicted in Figure 36a and b. This was done using isotropic elastic material behaviour throughout the numerical model with material properties
8.2. Nonlinear earthquake analysis and damage criteria
For the static analysis and subsequently dynamic (earthquake) analyses where the bridge structure is expected to exhibit nonlinear behaviour and damage, the following material behaviour was adopted in this study.
The mortarstone material was assumed to behave like ‘pseudoconcrete’ according to the Winfrith model. It is controlled by compressive and tensile strength as well as fracture energy and aggregate size.
The compressive strength is considered to be controlled by the stone portion of the hybrid element (30 MPa) and the tensile strength by that of the mortar. The range of the tensile strength assumed in this study for the different sections of the Konitsa Bridge is 0.25–2.1 MPa. The fracture energy assumed in the analysis dissipated in the opening of a tension crack assumed as 80 N/m. Upon formation of a tension crack, no tensile load can be transferred across the crack faces.
An additional failure criterion that controls the detachment of elements from the structure is that of pressure (negative in tension). This criterion is used to simulate the failure of mortar in the hybrid element, which is considered to fail when the negative pressure exceeds a critical value. The pressure threshold assumed in the study was 1.1 MPa.
8.3. Seismic analysis of the Konitsa Bridge
The most recent earthquake in the proximity of the Konitsa Bridge occurred in August 1996 [21]. The epicentre of the 6th August earthquake (
The seismic study was conducted in two steps. Specifically, during the first step, the static conditions of the structure were reached by introducing a fictitiously high global damping. Upon stabilization throughout the structure (see yellow arrow in Figure 38a), the earthquake analysis was initiated with the correct damping estimated based on the experimental measurements made during the two campaigns (i.e. global damping of 1.6%, Figure 38b). Figure 39 depicts the stateofstress profile throughout the Konitsa Bridge due to gravity load (Figure 39a depicts principal deviatoric stress, 39b vertical stress around the righthand side (RHS) abutment and 38a vertical stress evolution during the gravity load analysis reaching stabilization for the start of earthquake analysis).
Shown in Figure 40a is the location of the numerical model of Konitsa Bridge where the seismic response is predicted (crown, Loc3, Loc2, Loc1) having as input motion the described seismic excitation throughout all the base points (Base EQ input). Figure 40b depicts the horizontal (inplane and outofplane) and vertical crown displacement seismic response of the Konitsa Bridge predicted using the nonlinear numerical analysis. As can be seen in Figure 40b, the maximum predicted outofplane horizontal crown displacement is somewhat larger than the maximum value predicted by the linear timehistory analysis in Section 7.1 (Figure 30a). The maximum predicted inplane vertical crown displacement (Figure 40b) predicted by this nonlinear earthquake analysis is significantly larger (approximately four times) than the maximum value predicted by the linear timehistory analysis in Section 7.1 (Figure 30a). This must be attributed to the fact that the linear analysis performed in Section 7.1 is threedimensional but employing a numerical model of the bridge that represents its midsurface, whereas the 3D nonlinear simulation utilizes a model where the bridge is simulated with its actual thickness (compare Figure 15 with Figures 35 and 36). Thus, the vertical displacement at the crown (see Figure 40a) predicted by the 3D nonlinear analysis represents the vertical displacement at the façade of the crown cross section of the bridge, which includes a contribution from the outofplane response, and not the vertical displacement of the crown at midsurface, as is the case for the simplified analysis of Section 7.1 (Figure 30a). The inplane horizontal displacement predicted by both the linear and the nonlinear earthquake analyses has relatively very small amplitude. As discussed before, this clearly demonstrates the much larger stiffness of the bridge structure along the horizontal inplane direction than along the outofplane direction. In Figure 41a and b, the absolute velocity response at four locations of the Konitsa Bridge as well as at its base is depicted in the horizontal inplane or outofplane direction, respectively. As can be seen again in these figures, the stiffness of the bridge combined with the applied seismic motion results in very small amplification of this velocity response in the inplane direction than in the outofplane direction between the base and the four Konitsa Bridge locations (Crown, Loc3, Loc2, Loc1). This crown/base velocity response amplification factor in the outofplane direction has a value approximately equal to 2.
In Figure 43, the contours of the effective vonMises stresses are depicted for the Konitsa Bridge subjected to the previously described 1996Konitsa earthquake record. As can be seen in this figure, tensile distress is indicated at the right and left ends of the primary and secondary arches where they join the foundation blocks. This is also shown in some detail in Figure 42a and b in terms of vonMises and vertical stress response in this location. The timehistory plot of the vertical stress at the foundation block (A) at the archtofoundation block interface (B) and at the primary arch (C) clearly indicates that the tensile stress at location C reaches, as expected, the largest value, which is in excess of the tensile capacity of the bridge construction material (see also Section 7.1. and Figure 28e). By comparing the results of the displacement and stress response of the Konitsa Bridge, as obtained by the present 3D nonlinear analysis, with the corresponding timehistory results of the simplified linear analysis of Section 7.1, it can be concluded that the 1996Konitsa ground motion employed in both cases was of such an intensity and frequency content that very limited nonlinearities developed at this 3D advanced nonlinear model of the structure. This conclusion is in line with the observed performance of this bridge during the 1996 main event. As already mentioned before, limited damage was experienced by this bridge in this 1996 earthquake in the form of (a) spalling of the protective cement layer in the bridge intrados that was introduced following upgrades performed few years earlier and (b) loss of parapet sections (Figure 43).
8.4. Seismic vulnerability assessment and code guidance effects
In order to examine the capabilities of the 3D nonlinear numerical simulation performed in the previous section and in an effort to understand the potential influence of the time structure and period content of the exciting earthquake which may be missed when utilizing envelope code spectra (i.e. EuroCode), the Konitsa Bridge was subjected to two (2) additional earthquakes that represent distinct classes, namely nearfield (impulsivetype) and farfield earthquakes. Specifically, the NS component observed at Shiofukizaki site in the 1989 ItoOki earthquake of moment earthquake magnitude 5.3, epicentral distance of 3 km and the depth of the seismic source of 5 km. The record was observed at the surface of basalt rock and has a maximum acceleration of 0.189 g. It has been characterized as a nearfield earthquake and it exhibits remarkable similarity to the Konitsa 1996 earthquake (Figure 44, top).
The second earthquake is the 1940 ElCentro normalized to 0.19 g (Figure 44, bottom) allowing for direct comparison with the similar PGA Konitsa1996 and ItoOki nearfield earthquakes. The direct comparison of the response spectra of the three earthquakes (Konitsa1996, ItoOki and normalized 1940 ElCentro) is shown in Figure 45. The objective of subjecting the Konitsa Bridge to the same PGA but different spectral content earthquakes is to directly compare the damageability potential based on the nonlinear response of the bridge and shed some light on sensitivities to the type of earthquake these type of structures (masonry stone bridges) exhibit. This ultimately will aid in the modification/updating of the seismic codes to capture the unique structural design and response characteristics of large span arch masonry bridges in their provisions. While for the Konitsa1996 earthquake the actual vertical acceleration was used, for the ItoOki and modified 1940 ElCentro the vertical component was assumed as 75% of the employed horizontal component. The results drawn from the three (3) nonlinear analyses (Konitsa1996, ItoOki and 1940 ElCentro) and the comparative damageability potential are very revealing. Specifically, very similar response and bridge damage are observed for the two impulsivetype earthquakes,
A strikingly different bridge response and damage potential are observed when Konitsa Bridge is subjected to an excitation with the 0.19g normalized 1940 ElCentro earthquake, which represents a different type (farfield) of seismic event lacking that characteristic dominant velocity pulse (Figure 29). Figures 47 and 48 clearly demonstrate the different damage potential of this type of earthquake on such relatively longspan stonemasonry bridges. Figure 47 depicts the Konitsa Bridge outofplane displacement response when subjected to PGAadjusted (0.19g) 1940 ElCentro earthquake. Figure 48 depicts the variation of tensile stresses together with relevant nonlinear deformations of large amplitude at critical locations of the main arch during certain time windows of the response when these deformations are maximized, thus indicating the collapse potential of that portion of the main arch. This prediction of the main arch performance is in agreement with a similar conclusion reached by the simplified analyses of Section 7.1 when Konitsa Bridge (Figures 27b, 28b and d) and Plaka Bridge (Figures 33 and 34) were subjected to the design spectra as defined employing provisions of EuroCode 8. This large variation in the damageability potential, therefore, should be accounted for in establishing seismic code guidelines for relatively fragile old cultural heritage structures (as the old stonemasonry bridges studied in this chapter) as they apply to these nontypical structures. It should be noted that similar conclusions regarding the damageability of nearfieldtype earthquakes, as compared to their farfield counterparts based on which seismic codes for nuclear structures were deduced, were reached following an International Atomic Energy Agency (IAEA)launched coordinated research project (CRP) experimental study [23] augmented with numerical analysis and response/damage predictions conducted by an international participation.
9. Maintenance issues for stonemasonry bridges
In this section, a brief discussion will be presented dealing with maintenance issues of the stonemasonry bridges that were examined in this chapter. This study focused on the dynamic and seismic response of this type of bridges. However, it was shown by past experience that structural damage can also result from other types of actions such as flooding or traffic when such bridges are used not only for light pedestrian use. Because almost all the stonemasonry bridges in Greece have been built mostly for relatively light live load levels resulting from the crossing of pedestrians or animal flocks, their structural vulnerability due to traffic conditions is not an issue. Instead, flooding of the narrow gorge currents that these bridges cross (Figure 49a) is one of the main structural damage causes, as demonstrated from the Plaka Bridge (see Figure 50a and b). Apart from the hydrodynamic loads that a stonemasonry bridge is subjected to from a flooded current, one of the main sources of distress that may lead to partial or total collapse is the deformability of the foundation. The deformability of the foundation and the potential for subsequent collapse does include not only washout effects from a sudden flooded current but also the cumulative deformability of the foundation in a wider time window as was demonstrated by a recent flooding of Pineios river that caused the tilting of a midpier and the partial collapse of the DiavaKalampakareinforced concrete bridge in Thessaly, Greece (16 January 2016, Figure 49b).
Thus, foundation maintenance seems to be of the utmost importance. The flooding of Arachthos river, which caused the collapse of Plaka Bridge on 31 January 2015, was of considerable proportions. It is of interest to observe the conditions of the midpier of Plaka Bridge after the collapse (Figure 50a and b). As can be seen, the foundation of this pier is almost nonexistent being covered by the remains of the East part of central arch and of part of the adjacent arch and midpier. Thus, it is evident that this midpier was highly distressed leading to this mode of collapse.
Another maintenance issue of considerable importance is the integrity of the stone masonry in parts of the bridge apart from the foundation. It was already discussed in Section 6, when comparing numerically predicted with measured eigenfrequency values, that evidence of washedout mortar joints was present mainly in Kontodimou, Tsipianis and Kokorou Bridges. At the time of
In some cases, these stonemasonry bridges suffered structural damage from human activity. Plaka Bridge is one such example as can be seen in Figure 51a. The red arrow in this figure points to the structural damage suffered by the central arch due to an explosion during World War II. The damaged part was retrofitted in a way that is not known in detail to the authors. This retrofitting is visible in detail in Figure 51b where one can distinguish the difference in the texture of the old stone masonry from the retrofitted part of the secondary arch in this location indicated by the red circle.
This is also visible in Figure 52a where the scaffolding used for additional maintenance works is also visible. However, these works did not prove sufficient to prevent the collapse of this bridge from the severe flooding. It is of great research interest to be able to apply the methodology of
In the brief space of this section, the principles that govern a major retrofitting of such bridges must also be underlined. This is very important not only for the collapsed Plaka Bridge and the plans for its reconstruction but for numerous other bridge structures that have suffered serious structural damage or partial collapse. Figure 52b depicts a stonemasonry bridge in NorthWestern Macedonia, Greece, which underwent major reconstruction. It is worth mentioning that the regions of NorthWestern Macedonia and Ipiros in Greece are the home of stone masons who have been active worldwide. Due to their initiative specific stonemasonry workshops have been established recently in this region in an effort to keep this type of traditional construction as well as its maintenance alive.
10. Conclusions
This structural performance of old stonemasonry bridges is studied following a methodology that utilizes a large number of high fidelity
The numerically predicted bridge deformation and stress state seismic response are in good agreement resulting from either the simple or complex numerical simulations as well as with observed structural performance following actual earthquake occurrence in the proximity of Konitsa Bridge. This offers confidence in the described methodology using (a) detailed modelling which incorporates both field measurements of the dynamic characteristics and (b) laboratory testing on the complex mortarstone mechanical behaviour in its aged/weathered condition.
The high fidelity of the complex nonlinear numerical analyses that were used to predict the vulnerability of these structures to earthquakes and account for new fault information that surfaces in the proximity of these structures should also be underlined. The influence of certain issues that were not included in the current numerical treatment, such as soilstructure interaction, deformability of the foundation, and so on, should also be addressed in the future. This vulnerability analysis demonstrated:
The damage potential of farfield earthquakes on these types of unique structures (longspan masonry stone) is far greater than the damageability of impulsivetype earthquakes. This is confirmed through detailed analysis of the Konitsa Bridge using actual impulsive and farfield seismic records.
The observations on the damageability variation between impulsive and farfield earthquakes confirm previously conducted experimental and numerical studies on nuclear structures.
The above findings should be considered in establishing seismic code guidelines to specifically apply to these structures considering that they are typically constructed to span river beds that are in turn closely related to faulting [25].
Acknowledgments
The assistance of D. Gravas, K. Giouras and C.G. Manos junior in conducting the field experiments and gathering geometric information relevant to the stonemasonry bridges presented here as well as the help of the local people is gratefully acknowledged.
For conducting the laboratory tests, we would like to thank T. Koukouftopoulos and V. Kourtidis from the laboratory of Strength of Materials and Structures of Aristotle University.
Finally, we would also like to thank J. Evison Manou for editing this manuscript.
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