Investigation of Structural Performance of Historical Amasya Hundi Hatun Bridge
Online veröffentlicht: 09. Aug. 2022
Seitenbereich: 109 - 120
Eingereicht: 27. Mai 2021
Akzeptiert: 04. Feb. 2022
DOI: https://doi.org/10.2478/acee-2022-0019
Schlüsselwörter
© 2022 Burçin Şenol ŞEKER et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
There are many historical stone bridges from the Roman, Byzantine, Seljuk, and Ottoman periods in Anatolian geography, partially because the area has served as a transition route between the Asian and European continents. Many of these structures have survived until today because of restorations and improvements. The most important characteristic of these structures was their role in facilitating trade and military transportation. In addition, they can be considered water structures, because they were built on rivers and thus exposed to hydraulic loads. These historical stone bridges were generally constructed according to three main architectural types: i) the type with continuous arches that have arch spans and peak regions in the sequence at the same or nearly the same level, ii) the type with an odd number of bays that rise towards the top elevation of the bridge and have the largest arch bay in the middle, iii) the type with an even number of bays that rise towards the top elevation of the bridge and have the largest arch bay in the middle. The bridge analyzed in this paper is an example of the third type [5].
There are primarily two different types of research on historical bridges. In the first group of studies, the structural behaviors of bridges are modeled in a finite element environment by performing a detailed analysis of the bridges’ building materials. Then the bridges’ deformation patterns and crack and stress distributions are determined by performing static and dynamic analyses on the models [2, 10, 14, 17, 23, 24, 25]. In the second group of studies, deteriorations and deformations on historical bridges are determined through observations, and the improvement and restoration work required to eliminate these defects are examined in detail [1, 16, 20, 21, 26, 40]. In one study, Altunisik, Kanbur, and Genc [6] examined the effects of varying thicknesses of arches (one of the main load-bearing elements of a historical bridge) on the structural behavior of the bridge. In another study, Oliveira, Lourenço, and Lemos [22] examined 59 different historical bridges. After reviewing the bridges’ historical design formulas, they determined the load-carrying capacities of 8 reference bridges. The results of their research indicated that bridge arch thickness and the physical properties of fill material are important parameters. A different study collected detailed information on a historical bridge by using photometric, laser scanning, and radar scanning examination techniques, which allowed the researchers to observe the damage occurring over time and make appropriate restoration interventions [27]. The authors of another study investigated the possibility of increasing the axle load of a historical railway bridge from 200 to 250 kN. To determine this possibility with accuracy, the necessary measurements were made on the bridge to calibrate a 3D model created in a computer environment. The results indicated that this load increase was possible [8]. In the present study, a 3D model of the historical Hundi Hatun Bridge was created in a finite element environment and then subjected to static and dynamic analyses to determine the potential damage areas of the structure. Moreover, the analyses determined the plastic joint points that could occur on the bridge under different traffic loads.
Figure 1 shows the construction details of a typical historical bridge. As can be seen from the figure, bridge elements consist of a main load-carrying arch, spandrel, and wing walls. To provide arch stability and increase strength, non-cohesive fill material was used in the inner region. On the bridges, cutwaters are used to reduce the impact of upstream water, and parapet elements are used for pedestrian safety.
Figure 1.
The Yeşilırmak river flows in the southwest-northeast direction and divides the city of Amasya (Fig. 2) into two regions. Therefore, bridges have been built in various places on the river to connect these two separate regions. One of these bridges, the Hundi Hatun Bridge, is located on the Yeşilırmak River in the eastern region of the city. The Bayezid Pasha Mosque is located in the south and the Büyük Ağa Madrasah in the north. The Hundi Hatun Bridge was built by Sultan Mesut’s daughter, Hundi Hatun. It was repaired in 1900 and 1959. It has four bays and flat, circular arches. It is 67 m long, 8 m wide, and 10.50 m high [12]. The general view of the bridge is shown in Fig. 3.
Figure 2.
Figure 3.
Historical artifacts are structures built with a combination of different materials. Some parts of the structures can be made of stone, while other parts can be built with brick. Mortar is usually used as the binding material. Detailed micro modeling, simplified micro modelling, and macro modeling techniques are used to model all these different material types in a finite element environment. These techniques are shown in Figure 4.
Figure 4.
In detailed micro modeling, the mechanical properties of masonry elements and mortar are discussed separately. This technique is widely used to determine the behavior of masonry walls. Because of the long analysis times required for micro modeling, it is appropriate to use this method to analyze small-scale structures or for small regions of large-volume structures where detailed information is required.
In the simplified micro modeling technique, new masonry elements are obtained by adding a half thickness of the mortar layer to the masonry elements. The masonry units are separated from each other by interface lines. It is accepted that the cracks in the structure will occur at these interfaces.
In the macro modeling technique, masonry unit elements and mortar are composite materials, and new mechanical properties are assigned to this new element depending on the strength of the units. This technique is the preferred method for large-scale structures because it decreases the amount of analysis time required in the digital environment [29]. In this study, analyses were carried out using the macro modeling technique.
The Hundi Hatun Bridge’s main material is sandstone, which was used for the arches and wing walls. The inner region contains filling material. Since this is a historical structure there is no permission for these types of historical structures to examine in detail with destructive experimental methods from the government. So, to get an information about the reaction of the structure to external loads, the material characteristics given in the literature is used. These values are obtained from the restoration works of similar historical structures constructed in the same region in the same dates. So, these values can be used. The test results for the material used in another historical bridge in the same city were used to determine the mechanical properties of the material used in the Hundi Hatun Bridge. According to these test results, the average compressive strength for the stone was 41.46 MPa, while its density was 2646 kg/m³ [2]. For the fill material, the elasticity modulus (E) was 800 MPa, Poisson’s ratio was 0.23, and the density was 1800 kg/m³ [29].
In one study [23], the equation given to determine a wall’s characteristic compressive strength is:
Accordingly, E is calculated as:
where
| Bridge Region | Elasticity Modulus (MPa) | Poisson’s Ratio | Density (kg/m3) | Mean Compressive Strength (MPa) | Mean Tensile Strength (MPa) |
|---|---|---|---|---|---|
| Arches and Wing Walls | 8810 | 0.15 | 2646 | 8.810 | 0.881 |
| Fill | 800 | 0.23 | 1800 | 0.8 | 0.08 |
Software generating solutions using the finite element method are widely implemented today to examine historical buildings with quite complex geometric and material properties. The general behaviors and critical regions of historical buildings under static and dynamic loads can be determined. The three-dimensional bridge model created in this study was subjected to linear and non-linear analyses in an ANSYS environment [7]. For the linear analysis, a Solid 186 element type with three degrees of freedom at each node was used. The finite element model of the historical Hundi Hatun Bridge is shown in Figure 5.
Figure 5.
An analysis of the bridge under its weight was used to determine the principal stress, total deformation, and shear stress distributions of the bridge. The maximum values in the principal stress distribution (shown in Figure 6) occur on the road surface at the peak points of the regions between the bridge arches. Considering that the tensile strength for stone and filling material is very low, cracks should be expected in these regions. However, in ancient artifact building techniques, this problem was eliminated by connecting stone elements with iron clamps. The maximum principal stress value was found to be 1.2909 MPa.
Figure 6.
In modal analysis, the free vibration periods and mode shapes of the structure are determined by using elastic material properties. Thus, preliminary information about the dynamic behavior of the structure can be obtained. Figure 8 shows the structure’s modal shapes with the highest mass participation ratios, while their periods and mass participation ratios are shown in Table 2. As given in Table 2, first and second mode shapes are in the X direction that is transversal direction. The third longitudinal mode shape is in the Y direction. All of the mode shapes’ directions are in the ortogonal plane.
| Mode | Period (s) | Mass Participation Ratios | |
|---|---|---|---|
| X - direction | Y - direction | ||
| 1 | 0.10027 | 0.254380 | ~0.00 |
| 2 | 0.086250 | 0.109023 | 0.160643 |
| 3 | 0.085595 | ~0.00 | 0.228147 |
Figure 7.
Figure 8 shows that the first, second and fifth modes, which were effective in the X-direction of the bridge, occurred in the arch regions. The maximum deformation values were high up in the upper points of the arches because the arch springer points were fixed support. High stress and deformation values are expected in these regions under the effects of an earthquake.
Figure 8.
Earthquakes are natural and unpredicted disasters. Because earthquakes are a vibration of the earth’s crust, they damage structures by creating a time-dependent deformation movement. The formation of earthquakes is explained by plate tectonics. The crust on the mantle layer in the center of the earth is made up of many mobile plates. During the movements of these plates, energy accumulates at the edges and inside the plates, and when the strength of the crust is overcome, energy is released, and earthquakes occur.
Turkey has experienced severely destructive earthquakes because of its geography and tectonic structure. There are African and Arabian plates in southern Turkey. Both plates move northwards and compress the Anatolian block. The compression rate of the Arabian plate is high, while the rate of the European-Asian Plate in the north, also called the Eurasian Plate, is very low. As a result of this phenomenon, the Anatolian Block has to move westwards; accordingly, the North Anatolian Fault Zone and the East Anatolian Fault Zone are formed (see Figure 9). Highly destructive earthquakes occur on these fault lines [11]. Therefore, it is important to examine the seismic behavior of the structures in Turkey, which is in such a fragile geographic region, by considering both the structure’s historical heritage and its subjection to strong dynamic effects, like earthquakes.
Figure 9.
Turkey has been divided into five distinct regions in terms of earthquake hazard by considering fault lines and previous earthquakes. The first-degree seismic zone indicates the most dangerous zone, while the fifth-degree seismic zone indicates the zone with the lowest hazard. The most hazardous areas are shown in red (see Fig. 10). The map of Turkey in Fig. 10 reveals that only a small area in the middle region has a very low earthquake hazard, while all of the other regions have a high risk of earthquakes. The first-degree seismic zone includes the North Anatolian Fault (which starts at Lake Van and extends to the Marmara Sea and the Dardanelles) and the active faults affecting the Aegean Region. The most active fault in Turkey is the North Anatolian Fault, which is located in the northern region of Turkey and is 1,500 kilometers long. The number of earthquakes on this fault line increased after the great Erzincan earthquake in 1939. Historically, earthquakes of 7 or higher magnitude occur in Turkey approximately every three or four years. Since 1900, nearly 100,000 people in Turkey have died in an earthquake, which demonstrates the fragility of the region to earthquakes [11].
Figure 10.
In the linear and nonlinear analyses described in this section, the 1992 Erzincan seismogram was used. The seismogram of the earthquake accelerated in the north-south direction, which is in the same direction as the Hundi Hatun Bridge. The maximum acceleration in this direction was 0.47 g. The time step was 0.005 and the damping ratio was 0.05. A full Newton-Raphson method was used in the analyses as the solution algorithm. The analysis results were used to calculate the stresses and deformations in the structure. Earthquake acceleration values are shown in Fig. 11.
Figure 11.
Linear and nonlinear seismic analyses of the historical Hundi Hatun Bridge were performed with the ANSYS Workbench software. The Drucker-Prager and Mohr-Coulomb nonlinear material models have been used in the analyses of masonry structures in many studies [4, 9, 30]. In this study, the Mohr-Coulomb model was used for the material properties of the stone and fill material.
The Mohr-Coulomb failure criterion (see Fig. 12) is based on the principle that failure occurs because of the shear in a plane where the boundary shear stress is exceeded. The boundary shear stress is the sum of intergranular adhesive strength, (cohesion,
Figure 12.
The Mohr-Coulomb failure criterion is a two-parameter model. When the parameters c and ϕ are known, the failure surface can be defined. The given envelope equation can also be written in terms of principal stresses. The Mohr-Coulomb failure criterion is defined independently from the median principal stress. With the appropriate mathematical transformations, the Mohr-Coulomb failure criterion can be determined in a triaxial principal stress environment (see Figure 13) [13]. To give the nonlinearity to a brittle masonry material in the finite element environment, we use the Mohr Coulomb or Drucker Prager material model. There are a lot of studies that has been accepted in the literature. So, with the consistent values of ϕ and c, this material model can be used to investigate the behaviour of these historical structures. This model is quite good and suitable for this type of study as can be seen in the literature [3, 10, 15, 18, 19, 28, 31]. The c and ϕ parameters used for the stone and fill regions in this study are shown in Table 2.
Figure 13.
| Bridge | Cohesion (C) (MPa) | Friction Angle (ϕ) |
|---|---|---|
| Arches and Wing Walls | 0.15 | 30 |
| Fill | 0.05 | 20 |
The maximum deformation values obtained from the linear time history analysis are shown in Fig. 14. The highest deformation occurs at the peak of the arch on the far right, which has the highest flatness. The maximum deformation value in the linear time history analysis was 2.13 mm in transversal direction. The maximum tensile principal stresses are shown in Figure 15. The maximum values are observed at the support points of the arch on the far left on the downstream side. The maximum tensile principal stress value was 2.82 MPa. The maximum equivalent (von Mises) stresses are shown in Fig. 16. The maximum equivalent stresses occur at the support points of the arch located at the far right on the upstream side. The maximum equivalent stress value was 2.89 MPa.
Figure 14.
Figure 15.
Figure 16.
The deformation value distribution obtained from the nonlinear time history analysis is shown in Fig. 17. The maximum deformation values occur at the peak of the main arch in the middle. The absolute maximum deformation value was 8.19 mm in transversal direction. Fig. 18 shows the maximum plastic strain propagation. The maximum plastic strains were observed at the support points of the abutments on which the middle arch sits.
Figure 17.
Figure 18.
When examining the principal stress and equivalent stress (von Mises) distributions in Figs. 19 and 20, the maximum stress values occur around the abutments and decreasingly move towards the upper points of the bridge.
Figure 19.
Figure 20.
In this study, the Hundi Hatun Bridge was analyzed by creating a 3D model in a computer environment and assigning linear and nonlinear material properties to the masonry units constituting the bridge. The macro modeling technique was used, and the units constituting the structure were considered. By analyzing historical structures, their load-carrying system capabilities can be determined according to their strength and strain values. In the strength evaluation, the maximum stresses formed should not exceed the allowable stress value of the deformation evaluation; the ratio of the maximum deformation to the maximum height of the bridge should not exceed a certain value [38]. The Earthquake Risk Management Guide for Historic Structures defines the limits for the maximum deformation ratio allowable for varying performance levels in the context of dynamic effects (see Tab. 4).
| Performance Level | Maximum Deformation / Maximum Height Ratio Limit |
|---|---|
| Limited Damage | 0.003 |
| Controlled Damage | 0.007 |
The performance levels given in Tab. 4 are defined as follows:
Limited Damage: In this damage level, limited nonlinear behavior (damage) occurs in the load-carrying system elements of the structures.
Controlled Damage: In this damage level, the damage only occurs in repairable load-carrying system elements of the structures.
Prevention of Collapse: In this damage level, severe damage occurs in the load-carrying system elements of the structure, and the structure is about to collapse partially or completely, but the collapse is prevented.
The deformation ratio in historical structures is the ratio of the difference in horizontal deformations at different levels to the height difference. Because the foundation of the structures is fixed at the ground, the deformations in this plane are zero. Therefore, the height and deformation differences between the top and bottom points of the bridge are considered in the study.
The bridge height in this study is 10 m. Therefore, the maximum deformation limits according to Tab. 4 are 3 mm for limited damage, 7 mm for controlled damage, and 10 mm for prevention of collapse.
The following results are interpreted according to the above principles:
In the case of linear static loading, maximum compressive and tensile stresses formed at the far-right arch springer points on the upstream side, depending on the bridge arch geometry. Similarly, maximum deformations occurred at the peaks of the far-right arch. The bridge was safe under linear static loads, as it did not exceed allowable values.
Modal deformations occurred in the load-carrying arches perpendicular to the flow direction of the river. The bridge was strained, so it experienced out-of-plane deformation in the direction of its weakest axis. It was determined that these deformations may distort the arch geometry in both orthogonal directions. Therefore, the modal analysis shows that the stones constituting the arch elements should be interlocked.
The linear time history analysis demonstrated that the tensile stresses formed at the support points of the right end arch on the upstream side and exceeded the allowable stress value.
The linear time history analysis also showed that the highest deformation values occurred in the arch with the highest flatness. The highest deformation value obtained in this study was below 3 mm, placing it within the limited damage level.
The nonlinear analysis revealed that the maximum principal and equivalent stresses had high values at all bridge abutments and exceeded the allowable stress values. Plastic deformations occurred at the support points of the far-right arch according to the perspective of the middle arch and upstream side. The nonlinear analysis also indicated that the largest deformations occurred at the peaks of these arches. The displacement value of 8 mm was considerably higher than that obtained by linear analysis, so the bridge exceeded the upper limit value for controlled damage.
In Turkey, bridges of historical importance are currently open to traffic. It is important to examine these structures because they are mostly found in cities and thus must necessarily be used, even under far greater traffic loads than what was expected when they were built. This study evaluates the structural performance of the historical Hundi Hatun Bridge, located in the city center of Amasya. The Hundi Hatun Bridge connects the two separate sides of the river and carries a very heavy traffic load, in addition to its weight and earthquake loads. It was determined because of the analyses that, in the strained regions of the bridge, stones should be joined to each other with iron clamps to eliminate tensile stresses. Furthermore, the sections should be enlarged and wooden elements should be used on the foundations where the abutments of the arches are located, as in the historical bridge construction technique [34, 39] Moreover, this study demonstrated that not only linear analyses but also nonlinear analyses of these types of historical works should be performed, as they can yield very different results. Considering the bridge geometry, it is expected that stress and deformation values will increase on the arch, which has more flatness than other regions of the bridge. It should not be ignored that this method will create a weak zone in the load-carrying system of the bridge. One study state [30] that arches with high flatness cannot be found in the original form of this type of bridge. In other words, the builders and architects who built these ancient structures were aware of this unfavorable situation. Considering all the analysis results, the most important points were the integration of stone elements constituting the bridge and the stability of the bridge abutments. This study’s results are expected to guide future restoration and renovation efforts.