Dynamic identification of three 19 th century churches in Turkey

It is of great importance to determine the in-situ wall strength and dynamic characteristics of historic structures by experimental methods before structural analysis. The most effective experimental methods are the flat-jack, shear and vibration tests. After experimental methods, dynamic behaviour of the structures should be checked by the finite element analysis. Dynamic characteristics of three churches constructed in the 19th century in Balıkesir and Bursa provinces, now reduced to load-bearing walls (outer walls) only, are analysed in this study. It was established that, in order to identify dynamic characteristics of such structures, both the whole structure and the individual walls should be tested and evaluated by means of the finite element analysis.


Introduction
Historic buildings, being our cultural legacy for hundreds of years, are extremely important and valuable in terms of cultural heritage. Transferring these structures from today to the future is an inevitable task for us. These structures have been affected over time by fires, earthquakes, wars, and many interventions. Thus, it is important to diagnose the current condition of these structures by in-situ tests and computational analyses so that they can be restored in an appropriate way. The decisions taken by the International Council of Monuments and Sites (ICOMOS) during an international workshop in 2003 constitutes the basis of this study. Before conducting restoration studies, the current condition, construction techniques, interventions, boundary conditions, structural properties and wall strength of the buildings, should be determined by in-situ tests. After this stage, a safety assessment should be performed before defining the intervention techniques [1]. It is of great importance to accurately determine the strength of masonry walls and dynamic characteristics of the real structure before the actual computer analysis. Dynamic parameters can be determined by modal analysis of the finite element models prepared based on boundary conditions and material properties. These parameters may be far from their expected values due to the loss of strength of the building materials over time, workmanship errors at the construction phase, cracks caused by various loads, and fatigue caused by collapse of the structure. Therefore, dynamic parameters of the structure should be determined by experimental and analytical methods [2].
The most effective methods for determining the wall strength are the flat-jack and shear tests. These test methods have been used by researchers for many years to accurately determine the wall strength of historic buildings [3][4][5][6][7][8]. An experimental method known as the Operational Modal Analysis (OMA) has often been used over the last two decades to determine dynamic behaviour of real structures. In this non-destructive test method, vibration tests are performed by placing sensitive accelerometers in perpendicular directions. Natural frequencies, mode shapes, and damping ratios of the structure can be determined by means of this test technique. However, this method has both advantages and disadvantages when applied to historical structures. Thus, it has the following advantages: it is a fast and cheap testing technique, there is no need to use an excitation equipment, the structure can be tested under operating conditions, and it can be used for damage detection of structures. On the other hand, it has the following disadvantages: modal participation factors cannot be computed, modal parameters can be difficult to determine in the presence of spurious harmonics near natural frequencies, use of very long cable transducers, and difficulties with the positioning of accelerometers. To ensure accuracy of dynamic parameters, ambient vibration tests must be considered with modal updating techniques. Repeated tests are important for the evaluation of dynamic parameters. The orthogonality between the modes can be checked using the Modal Assurance Criteria (MAC) and the complexity plots [9][10][11][12][13]. Many studies have so far been made using the Operational Modal Analysis tests to determine dynamic parameters of structures [14][15][16][17][18][19][20]. Dereköy and Aydınpınar churches in Bursa and Ballıpınar Church in Balıkesir, all built in the 19th century, are examined in this paper by means of experimental and finite element analyses. The compressive and shear strength of the walls is calculated using the flat-jack and shear tests. Natural frequencies and mode shapes of the entire structure and individual walls in x direction are analysed by means of the Operational Modal Analysis tests. The data obtained from all experimental approaches are used in the finite element models. The experimental and finite element analysis results are compared.

Architectural features of the churches
As a result of abandon and neglect, the studied churches have not been in use for more than two decades now. The roof of the churches and all timber pillars and beams related to the roof structure collapsed, so that only the load bearing walls (outer walls) are still standing today. Architectural features of the churches were examined in terms of construction dates, material usage, dimensions of the churches, and height of the walls. Aydınpınar Church was built between 1846 and 1870. Brick, rubble stone, and cut stone materials were used in the construction of the walls. Lime mortar was used as binder.   Figure 1 [21,22]. Photographs of the exterior, interior and wall section of the churches are presented in Table 1.

Flat-jack and shear tests
Average results of two experimental tests (one for each wall in the x and y directions) were registered during the flat-jack and shear tests. Test locations for each church are shown in Figure  2.

Figure 2. Flat-jack and shear test locations: a) Aydınpınar Church, b) Dereköy Church and c) Ballıpınar Church
The compressive stress, elastic modulus, and shear stress values were determined for masonry walls during these tests. A single flat-jack test method was used to determine In this test method, a slot was cut in the mortar layer and a flat jack was placed inside the slot. The stress and displacement values of composite walls were continuously read while the hydraulic oil pressure pump (bar and psi) inflated the flatjack [23]. The method C was used according to ASTM C1531-09 in shear tests [24]. In this method, a small flat jack is horizontally inserted at one end of the test unit. Hydraulic oil pressure is applied until a crack appears or slip occurs. A detailed presentation of the flat-jack and shear test setups, including the displacement measurement, flat-jack placement, and slip surfaces, is given in Figure 3. The calculation of compressive stress, elastic modulus, and shear stress is presented as follows in Eqs. (1) and (2). Compressive stress exp. (1): where K m is a dimensionless constant related to the stiffness and geometrical properties of the flat-jack, K a is the ratio of the area of the flat-jack to the area of the slot and p is the flat-jack pressure, psi or MPa.
The chord modulus at any point i, exp. (2): where f mi is the stress at point i, and e mi is the strain at point i [23].
Elastic moduli of composite walls were calculated using end points of 0.05 and 0.33 chord modulus of elasticity values [25].
The stress-strain diagram of composite walls is presented in Figure 4. The calculation of an average bed joint shear stress is given by equations (3) and (4). Horizontal force: where K m is the dimensionless constant related to the stiffness and geometrical properties of the flatjack, A f is the area of the fiatjack and p is the fiatjack pressure at crack initiation or slip. Shear stress: where P h is the maximum force applied by the hydraulic pump and A j is the gross area of the upper and lower bed joints [24]. Mechanical properties such as compressive stress, shear stress and elastic moduli of church walls calculated by in-situ tests are presented in Table 2. The plaster of the outer walls has fallen off and the open air conditions and moisture made the mortar weak. Therefore, the walls have significantly lost their mechanical properties.

Structural health monitoring tests
The Operational Modal Analysis (OMA) test method was used to obtain dynamic parameters relevant for the studied churches. This non-destructive test method can be used to determine natural vibration frequencies, damping ratios, and mode shapes. This technique can be used to determine dynamic parameters of structures from output-only experimental data. The loads are environmental forces and the modal identification is based on responses only. 2400 mV/g highly sensitive accelerometers were used in the tests. Monoaxial accelerometers having 0.01-200 Hz bandwidths and ±3g measurements range were used in this study. The Testbox 2010 data acquisition device with 8 channels was used in dynamic tests [26]. 30-minute test periods were applied to ensure proper accuracy of the tests. During sensor placement, perpendicular orientations were carefully checked for all church walls. For all churches, tests were performed both on the entire structure and on one of the individual walls in x direction. Accelerometers were placed approximately 1,5 metres under the elevation of the roof. The orientation of sensors and the test setup were the same for all churches, as shown in Figure 5 for Ballıpınar Church. Sensor placement and test equipment are shown in Figure 6. The results for the test setup 1 were examined. It was observed that there were some difficulties in determining frequencies of the entire structure. The main problem was the absence of the roof and the loss of all horizontal connections between the walls. Therefore, it was seen that the walls do not act as a structure but rather as independent walls. The other problem was the non-symmetrical wall construction. The bending mode frequencies of the walls in x direction (north and south wall) were determined by OMA tests with good accuracy. The reason for this is thought to be the symmetrical wall construction and the sufficient test data gain from both walls. On the other hand, the bending mode frequencies of walls of the entrance part and the walls of the apse part in y direction (west and east walls) were determined by OMA tests with poor accuracy because

Finite element analysis of churches
Natural frequencies and mode shapes of the churches were investigated by means of the Algor V20 finite element analysis (FEA) programme [27]. Brick, tetrahedra, wedge and pyramid elements, with three degrees of freedom at every node, were generated in the mesh of FEA models (Figure 9). In the finite   Table 3. The bending frequencies in x direction obtained by OMA tests were compared with the bending frequencies obtained from the finite element modal analysis for the calibration. The frequencies of the first three bending modes of the walls in x direction (north and south wall) of Ballıpınar Church obtained from the OMA test setup 1 and the finite element analysis after the calibration is shown in an example given in Figure 10. In this figure, the bending frequencies obtained from the Finite Element Analysis are presented as FEA, while the frequencies from experimental study are presented as Exp.  The mode frequencies obtained from experimental tests, mode frequencies obtained from finite element analysis, and the error between them, are presented in Table 4. The errors between the results ranged from a minimum or 2 % to a maximum of 8 %.
The frequencies of the first three bending modes of walls in y direction (the wall of the entrance part -south wall, and the wall of the apse part -east wall) of Ballıpınar Church obtained from the finite element analysis after the calibration are shown as an example in Figure 11. It can be seen that the bending mode frequencies of the wall of the entrance and the wall of the apse in y direction differ from each other. The first three bending mode frequencies of the wall of the entrance part and the wall of the apse part of churches in y direction were determined by the finite element analysis. The finite element analysis results can be seen in Table 5.
The mass participation factors of the first three bending modes of the studied churches in x and y directions are presented in Table 6. After the first three bending modes, it can be seen that the mass participation factors for x and y directions are below or close to 50 %. The mass participation factors increase to 95 % percent or over after 50 modes. This shows that at least 50 modes should be taken into account for the static and dynamic structural analysis of the structures.

Conclusion
Dynamic behaviour of three 19 th century churches in the cities of Bursa and Balıkesir were investigated in this study. The flatjack and shear tests were performed to determine mechanical behaviour of the walls. When the vibration test results were   compared with the finite element analysis, it was established that the mechanical properties were determined with a high level of accuracy. The maximum difference between the vibration tests and the finite element analysis ranged between 0 and 21 percent. The vibration tests were conducted in order to determine dynamic characteristics of the structures. Unfortunately, some difficulties were encountered when determining frequencies of the entire structure. The first one was that the walls did not act as a structure but as independent walls due to the loss of the roof and horizontal connections between the walls. The walls in y direction had different vibration frequencies. Unlike the wall of the entrance part, half-domes were used in the construction of the walls of the apse part. On the other hand, the bending mode frequencies of the walls in x direction (south and north walls) were determined by OMA tests with great accuracy. The reason for this is thought to be the symmetrical wall construction and the sufficient test data collected from both two walls. In addition, the first three bending mode frequencies and mode shapes for one of the individual walls in x direction of the churches were obtained from another test setup. The orthogonality between the first three bending modes for both test setups in x direction was checked using the modal assurance criteria (MAC). It was observed in both tests for all churches that the frequencies are very close to each other. After calibration of material properties, the errors between test results and the finite element analyses ranged from a minimum of 2 % to a maximum of 8 %.
The identification of structural and material behaviour of structures is important for the conservation studies. Therefore, it is necessary to diagnose the current condition of structures in detail so as to be able to properly evaluate their safety level. It is clear that the flat-jack, shear and vibration tests have an important role in correct determination of the properties and dynamic behaviour of these structures. In the case of the studied churches that are currently reduced to load bearing walls (outer walls) only, a complete analysis should involve the testing and evaluation of both the individual walls and the entire structure using finite element models.