An Assessment of the Seismic Performance of the Historic Tigris Bridge

Turkey is a country that is vulnerable to earthquakes and has experienced many major earthquakes that completely destroyed or caused significant damage to numerous historic structures. Today, using computer software, it is important to numerically model and analyze historic structures that need significant restoration and strengthening, to evaluate them from a perspective of seismic resistance, and to reinforce them without altering their originality. In this study, a finite element model of the historic Tigris Bridge on the Tigris River was created. First, the stresses and deformation caused by its own weight were determined. Subsequently, dynamic analyses were performed in the time domain using past earthquake ground motion records. Displacement and stress values obtained for each earthquake record in these time domain analysis were compared to each other to evaluate the seismic behavior of the bridge comparatively. The seismic performance of the bridge was determined on the basis of the “Guidelines on the Management of Earthquake Risks for Historic Structures” published by the Directorate General of Religious Foun-dations in Turkey.


Location and History of the Bridge
The historic Tigris Bridge in Diyarbakır is an important and prominent structure in terms of its size and architecture and has become a symbol of the said city. The bridge is 3 km from the city center and is located at a point that links the center of the city to the Township of Bağıvar and several villages. Several

Architectural Review of the Bridge
The Tigris Bridge is considered to fall in the category of multi-span flat-top bridges. The bridge is 172 m long. Its width varies between 5.45 and 6.24 m over the first five spans and increases to the range 9.69 -10.20 m from the fifth span on. The road over the bridge is currently covered with the original paving stones following restoration. The parapet height is 85 cm at the end and rises to as much as 155 cm near the middle (Figure 1).
The capstones are nine capped pyramidal flood splitters [fender piles] stand on the north (upstream) side of the bridge. Flood splitters 1, 2, 3, and 4 (S1, S2, S3, S4) are lower in height than the others. Also, the spandrel walls of the spans 6,7,8,9, and 10 retain their original construction features up to half their heights. However, different masonry work has been applied to the spandrel walls of the spans 1, 2, 3, 4, and 5 as shown in Figure 2 and Figure 3.   Unlike the north side, the southern (downstream) side of the bridge does not feature a flat facade wall. The arches of the spans 1, 2, 3, 4, and 5 are recessed by around 4 m. Following a study of traces left on the current bridge, it was determined that this section collapsed after [it was initially built] and that it was built with recesses during repairs ( Figure 4).
The bridge features 29 different masons' marks in the form of different symbols. In addition to these, two different arrays of markings are inscribed as blocks. One of these is an array where the Latin characters K, O, and E are listed one below the other. The other consists of blocks of points arrayed vertically, horizontally, and diagonally. The masons' marks may be interpreted as signifying the purpose of the construction, the calculation of the stones mined from quarries, differentiation of different types of marbles, identification of marble traders, and identification of the artisans who hewed the stones [4].

Determination of the Material Properties of the Bridge
The determination of structural behaviors and material properties is an important step in engineering studies conducted for the purpose of transferring historic structures to future generations. Because materials used in masonry construction work are of a composite nature and because similar elements exhibit different material properties, the determination of the material properties of a structure is often quite difficult. In general, basalt, a local material, was used in the construction of the Tigris Bridge. Smoothly cut basalt stone was used in the spans 6, 7, 8, 9, and 10 up to half the height of the bridge until the arched sections. However, rubble stone was used for repairs of the arch keystones and sometimes from the joist hanger above the arch to the wall capstone. Material parameters for use in the finite element analysis of the Tigris (Ten Span) Bridge in Diyarbakir were determined from previous studies on the bridge, and the analysis was performed based on these values (Table 1).

Modeling and Analysis of the Structure
The historic bridge was modeled using "Finite Element Analysis", which facilitates the definition of cross-sectional and material properties of structural elements with different geometries, on the computer program SAP2000 (Version 15). Static analysis was used to determine the behavior of the structure due to its own weight; modal analysis was used to determine the mode shapes and natural periods of the structure; and linear analysis in the time domain was used to determine the behavior of the structure under dynamic loads using acceleration data for the March 13, 1992 Erzincan Earthquake.

Creation of the Three-Dimensional Finite Element Model of the Bridge
In finite element modeling, the geometry of the structure or structural elements

Gravity Load Analysis
Gravity load analysis is important in terms of observing the distribution of  weights of the materials in this study. Live loads and snow loads were not included in the calculations. The static analysis results showed that the largest displacements occurred in the vertical axis 3 (z-axis) direction in the arch footings and masonry infill walls, particularly in the arches and footings associated with the wider and taller spans 3, 4, and 5. The largest displacement was found to be 0.852 mm. The distribution of maximum compressive stresses obtained from the static analysis shows that the largest stresses occur at the points where stone arches meet the footings of the bridge and at the bottoms of the footings. The largest stress was found to be 0.618 MPa ( Figure 6).

Dynamic Analysis
In the finite element model created by macro modeling technique, dynamic analyzes were performed. In the model, the damping ratio is constant 5%. Within the scope of dynamic analysis, modal analysis and time history analysis were performed.

Modal Analysis
In the modal analysis, the first five modes of the Tigris Bridge were considered to calculate mode shapes and natural frequencies, which constitute the dynamic characteristics of the bridge. Table 2 lists the natural period values and mass participation factors. When we look at the mode shapes corresponding to the listed natural frequency values, we find that the first and second modes are y-direction lateral modes, the third and fourth modes are x-direction lateral modes, and the fifth mode is a z-direction vertical mode (Table 2).

Time Domain Analysis
A time domain finite element dynamic analysis was performed on the model that was created using a macro-modeling technique. Acceleration data for the east-west component of the March 13, 1992 Erzincan Earthquake were applied to the model to simulate the behavior of this structure under dynamic loads. The largest acceleration [in the earthquake record] was −470.915 cm/s 2 at 3.395 seconds (Figure 7).
1992 Erzincan Earthquake in cases where the choice of sufficient score and quantity of earthquake records cannot make, simulated ground motions are used considering the local ground conditions. The major seismic activity occurred in the region is the Erzincan Earthquake in 1992. In the linear time history analysis

Determination of the Performance of the Structure
The performance of the structure was determined based on the performance    (Table 3)".

Compressive Strength Safety of the Masonry Wall System
The  (Table 4).
The maximum compressive stress that develops in the structure is 0.618 MPa, which does not exceed the compressive strength specified for masonry walls.

Shear Strength Safety of the Masonry Wall System
According to Section 11 of the Turkish Building Earthquake Regulation, the characteristic wall shear strength, f vk , must be calculated from tests conducted on wall samples or the following equation.  (Table 6). Table 3. Performance level [6].
Performance level Calculation method and limits Limited damage limit condition (LD) 1) Linear calculation method used; a) Calculated strengths subjected to vertical loads and undamped projected earthquakes not exceeded. b) The sidesway ratio under undamped earthquake loading does not exceed the 0.3% limit.
Controlled damage limit condition (CD) 1) Linear calculation method used; a) Calculated strengths subjected to vertical loads and projected earthquakes damped by R a ≤ 3 not exceeded. b) The sidesway ratio under undamped earthquake loading does not exceed the 0.7% limit.
2) Nonlinear calculation method used; a) The sidesway ratio does not exceed the 0.7% limit. b) The deformation capacities of the materials not exceeded.
Pre-collapse limit condition (PC) 1) Linear calculation method used; a) Calculated strengths subjected to vertical loads and projected earthquakes damped by R a ≤ 3 may be exceed to some extent (~1.5 times). b) The sidesway ratio under undamped earthquake loading does not exceed the 1% limit.
2) Nonlinear calculation method used; a) The sidesway ratio does not exceed the 1% limit. b) The deformation capacities of the materials may be exceeded by a limited amount (~1.2 times).

Control of Maximum Drift Ratio in the Structure
The maximum displacement in the structure in analyses performed using earthquake impact was calculated as 2.199 mm. The maximum drift ratio of the structure is 0.02% which is less than the limited damage limit state acceptance criteria described above.

Conclusions
Turkey is an active seismic country. Therefore, earthquakes can be devastating for historical buildings. Damages caused by earthquakes can be manifested by cracks in the arches. Stones are strong in compression and somewhat so in shear, but cannot resist much force in tension, thus masonry arch bridges are designed to be constantly under compression. Furthermore, lateral loads may also be applied to the bridges in addition to vertical loads due to earthquake effects in seismic areas. Consequently, lateral displacements may also occur and cause damage [8].
Maximum potential stresses and displacements in the Tigris Bridge were determined through static and dynamic analysis performed on a finite element model of the historic structure. The performance level of the structure was determined using calculation methods that correspond to performance levels and limit conditions specified in the "Turkish Guidelines for the Management of Earthquake Risks for Historic Structures" based on the findings below. Compressive stresses that were calculated in the static analysis under vertical loads do not exceed the compressive strength. Shear stresses in the X-X direction, determined in an analysis performed under real earthquake loading, exceed the effective shear strength. However, this earthquake loading, was not reduced by a response modification factor "R" factor. Shear stresses in the Y-Y direction, de-