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 opinions have been expressed about the date when the bridge was first built. According to Van Bercheh and Albert Gabriel, another bridge stood in the current location of the Tigris Bridge in ancient times [1] . An epitaph stating that in Diyarbakır, which came under Islamic rule in 639, Umayyad Caliph Hisham started repairing a collapsed bridge in 742 - 743 and that the construction work stopped after his death. It is also known that the eastern armies of the Roman Empire besieged Diyarbakir unsuccessfully in 974 and that they destroyed this bridge when they withdrew [2] .

The bridge is believed to have been destroyed and rebuilt partially or completely several times. The most recent and most accurate known construction date of the bridge is based on the inscription marked on the bridge. According to this inscription, the bridge was built in 457 A.H. (1065 AD).

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] .

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).

In finite element modeling, the geometry of the structure or structural elements is determined by a finite number of nodes. To determine the behavior of the structure accurately, a large number of nodes were used in creating a finite element model of the Tigris Bridge. Specifically, 12,937 solid elements and 17,541 nodes were used in the finite element model created. For this study, the degrees of freedom at the base of the bridge were assumed to be fixed. The finite element model created for the Tigris Bridge is shown in Figure 5.

Gravity load analysis is important in terms of observing the distribution of stresses and deformations caused by the weight of the structure. In general, although structures are expected to carry vertical loads safely, any potential problems and deficiencies can be easily seen and the necessary countermeasures taken through such analysis. Dead loads were defined through the specific

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).

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.

The masonry walls in the structure are made up of mostly pitch-faced and cut stones. The material mechanical properties table provided in the Structural Modeling and Assessment section of the “Turkish Guidelines on the Management of Earthquake Risks for Historic Structures” was used to determine the compressive strength of cut stone. The table recommends a compressive strength of 1.1 to 1.6 MPa (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.

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.

f v k = f v k o + 0.4 σ d ≤ 0.10 f b

where, f_vk is the characteristic wall shear strength using vertical stresses on the wall, f_vko is the characteristic shear strength when no axial stresses are present, σ_d is the vertical compressive stress calculated under the combined effect of vertical loads multiplied by load coefficients and earthquake loads and f_b is the standardized average compressive strength of masonry element (equivalent to non-dim- ensionalized 100 × 100 mm sample).

The characteristic shear strength (f_vk) when axial stresses are not present must be determined based on Turkish Building Earthquake Regulation (Table 5).

Shear strengths for stones are given in 0.10 MPa = 100 kN/m². Effective shear stresses in the walls were obtained from maximum compressive stresses (σ_d) in the structure based on the results of the analysis under vertical loads Shear stresses calculated in walls in time domain analyses were compared to calculated shear strengths (Table 6).

(*) The mortars are labeled such that the number following the letter M indicates the characteristic compressive strength in MPa.

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.