Determination of dynamic parameters of double-layered brick arches

Masonry arches assume a very important role in construction industry, and we find them in many historical structures all over the world. Dynamic parameters, frequency, and damping of masonry arches are defined in this paper using the Experimental Modal Analysis (EMA). Double-layered arches were built using standard hollow bricks and traditional Horasan mortar. The brick arches were tested with an impact hammer, and the arch response was measured using a laser vibrometer. Experimental tests were compared with numerical modelling in order to verify adequacy of physical models.


Introduction
Structures are nowadays generally made of modern construction materials such as reinforced concrete or steel.However, most ancient structures are made of masonry materials such as stone or brick.Masonry structures generally maintain their initial performance, which points to the complexity of their structural behaviour.Understanding structural behaviour of masonry structures is a very complex and obscure issue.An appropriate information about structural components of masonry structures is required to understand their structural behaviour.Although masonry structures have many different structural components, their vital elements are arches, domes, walls, and foundations.Masonry structures are exposed to many different external and internal effects throughout their useful lives.Although these structures are very durable, some historical structures have unfortunately deteriorated, suffered damage, collapsed, or failed due to various effects.Recent studies show that masonry structures are vulnerable to earthquakes.Seismic effects have been among the most important reasons for the collapse of masonry structures [1][2][3][4][5].Hence, many historical structures are at risk with regard to seismic events, and their capability to resist seismic loads is poor.Although scientists have studied masonry structures and their structural behaviour, the dynamic behaviour of their structural components has rarely been investigated [6][7][8].The prediction of the response of structures to dynamic effects such as earthquakes is very important in terms of seismic safety.Therefore, dynamic parameters such as frequency, mode shape, and damping ratio, must be determined.In this study, modal parameters of all arches were determined through experimental modal analysis (EMA).EMA, also known as the frequency response function test, is one of the most important experimental tests.It is based on the measurement of vibration response following the impact applied onto the structure.Therefore, dynamic parameters such as frequency, mode shape, and damping ratio of the double-layered masonry arch, were determined in this study using the EMA procedure.

Traditional Horasan mortar
Traditional Horasan mortar used to be a preferred brick bonding material and was therefore used in many historical structures.Horasan mortar, also known as the "Horasan concrete", is the traditional mixture that was used in buildings originating from Byzantine, Seljuk, and Ottoman periods.This mortar is generally made of binding lime, fine sand, and brick powder, and it is as strong as stone and concrete [9].Horasan mortar had been widely used in Ottoman structures in Anatolia.In addition, this mortar is the basis for the present-day concrete.Hydraulic lime is currently used as binding material in Horasan mortar because of its cement-free feature, high deformation capacity, and porosity.Therefore, hydraulic lime based mortar is used as Horasan mortar in this study.Stone powder, fine sand, lime paste, brick powder, and Albaria Calce Albazzana® bonding material (supplied by BASF Chemical Company) were mixed in equal proportion by weight (Figure 1) to obtain the mortar.Albaria is a cement-free natural hydraulic lime that is burnt at 900 °C in traditional oven, [10].

Masonry hollow bricks
Standard hollow bricks, 90 mm x 190 mm x 50 mm, were used in this study.In the first step, newly manufactured bricks were cleaned with water in order to remove any contamination and dust from the brick surfaces, and to enable an effective adherence between the brick and mortar.After surface cleaning, masonry bricks were dried at room temperature for two days (Figure 2).

Masonry brick arches
Double-layered semi-circular arches 1000 mm in internal span, 500 mm in rise, and 180 mm in thickness, were prepared in the scope of this study (Figure 3).The arches were built on timber shutters, and were removed two days after arch construction.Subsequently, all arches were allowed to cure for ten weeks (Figure 3).GRAĐEVINAR 67 (2015) 2, 123-130 Determination of dynamic parameters of double-layered brick arches

Mechanical characteristics of materials
The most important mechanical properties of masonry units are compressive strength and tensile strength.Therefore, compressive and tensile tests were conducted in this study to determine mechanical parameters of construction materials.Mechanical parameters for masonry materials were obtained from test samples (Figure 4).Compressive strength values were determined from compression tests conducted on five cubes (50 mm× 50 mm× 50 mm) according to TS 699, Turkish Building Code [11] (Table 1).In addition, tensile strength values were obtained from three-point bending tests conducted on five prisms (50 mm × 100 mm × 200 mm) according to Turkish Building Codes, TS EN 1467 and 1469 (Table 1) [12,13].Mortar strength was defined by the compression and three-point bending tests of mortar samples at 28 days.Mechanical properties of materials were obtained by testing samples at laboratories of the Department of Civil Engineering at Ataturk University, Erzurum, Turkey.

Experimental Modal Analysis (EMA)
Modal parameters, such as natural frequency and mode shapes, have always been important in the analysis of dynamic behaviour of structures.EMA, also known as frequency response function testing, is a preferred method for dynamic identification of structures in general [14,15].EMA uses the principle of response measurement in relation to the load applied onto the structural system.Modal parameters of the structural system are determined through structural response to the load applied.Hence, EMA is frequently preferred for determination of modal parameters [14,15].Therefore, EMA is applied in this study to assess dynamic parameters.In the first step, all devices in the laboratory were closed, and people were prevented from entering the laboratory in order to isolate unwanted ambient vibrations.All masonry arches were primarily fixed to the floor, and arches were vibrated with an impact hammer (Brüel & Kjaer 8206-002).
The response of arches to these impacts was measured using a Laser Vibrometer (Ometron VH300+).During the test, all data were recorded with a multi-channel data logger (Brüel & Kjaer 3050-B-040) (Figure 5).Following the experimental set-up, the frequencies and damping ratios of the arches were determined using the experimental modal analysis.For this purpose, the arches were vibrated at least five times at the same point, and the linear averaging was applied.
The impact hammer causing vibration of arches was weighted at a certain point between two impact forces for stabilization.After each impact force, the monitoring system was used, and all response functions were visually controlled on the screen in order to better understand the vibration.Thanks to these visual observations, only the structural response to impact hammer was recorded.Outside vibrations and noises were discarded in this manner.In all tests, four different impact points were chosen at the quarter span and middle span of the arches in and out of plane (Figure 6).Moreover, the frequency range of this study was 0-500 Hz.For this frequency range, a rubber impact tip was preferred (Figure 7).Natural frequencies were identified from the peaks of the frequency response functions (FRF).The FRF provides the input and output relations between the impact point and the measurement point on the arch as a function of frequency.The selected peaks in the frequency response function were used to define the modes.Dynamic parameters such as natural frequencies, damping ratios and mode shapes were obtained from a set of FRF curves.In this study, the Peak Picking method was preferred to determine the frequencies.In this method, the narrow peaks in the curve describe high resonances.Figure 8 presents the frequency response function obtained from different impact points, while Table 2 summarizes the frequencies and periods of the structure.

Table 2. Frequencies and periods obtained from EMA
In addition, damping ratios were also determined using FRF graphs.The damping ratios were calculated by the method called half-power bandwidth [15].Figure 9 demonstrates the half-power bandwidth technique.ω 1 and ω 2 are the half-power points of the bandwidth and ω n is the frequency value.The modal damping ratio is calculated with the formula shown below, and Figure 10 shows the damping ratio screen view.The first six frequencies, periods, and damping ratios for the double-layered arch are presented in Table 3.

Numerical analysis
Advances in computer technology have facilitated numerical analysis and examination of structural behaviour via threedimensional models.Thus, the determination of static and dynamic behaviour of masonry structures with the finite element method has recently become one of the most common methods.
A three-dimensional finite element model was developed in this study based on the structural state and geometrical constraints of the arch.The three-dimensional finite element model was analysed for the double-layered arch investigated in the scope of this study.In this respect, the FEA program called ANSYS Workbench was used to analyse the arch with SOLID186 elements, which has 20 nodes and three degrees of freedom per node.In the first model, the double-layered arch was discretized with 7560 solids, corresponding to 37960 nodes (Figure 11).According to the Turkish Earthquake Code (TEC 2007) [18], the modulus of elasticity (E) for masonry units used in masonry construction can be calculated using the formula; E = 200.f,where f is an average compressive strength of masonry unit in MPa.Masonry arches were made of bricks and mortar.According to [17], the modulus of elasticity for the new composite material (brick + mortar) could be obtained based on homogenization procedures as follows: where t m represents the mortar thickness, t u represents the brick height, and ρ represents the efficiency factor with respect to the deficient bond between mortar and brick.Finally, E m and E u represent the modulus of elasticity of mortar and brick, respectively.The thickness of brick used in this study is 50 mm, while the mortar is almost 10 mm in average thickness.The calculated moduli of elasticity for bricks and mortars amount to 3395.2 MPa and 2003.2MPa, respectively.Moreover, the efficiency factor of 0.5 is adopted for masonry structures [17].When all values used in formula ( 1) are taken into account, the calculated elasticity modulus of the new composite material (brick + mortar) amounts to 1521.36 MPa.
Hence, the moduli of elasticity were calculated using the above formula in all three-dimensional finite element models.The Poisson ratio of 0.2 from was taken from similar studies [15], and the mass per unit volume was accepted as an average value of experimental tests.
To get the most appropriate results in the numerical analyses, a single layered reference masonry arch, with previously determined boundary conditions, was taken into consideration in the first step, and the frequency values obtained at the reference masonry arch were compared with frequency values obtained through numeric analyses.Based on these comparisons, it was determined that experimental data differ from analytical data.To eliminate these differences, a calibration study was conducted using the numerical model recommended in literature [15,19,20,21].The comparisons allowed some modifications of material properties so as to obtain an optimum level, without changing boundary conditions.This amendment also enabled consistency between numerical analyses and experimental studies.Technically, numerical models are formed by using the finite element method.Numerical model errors mainly result from assumptions such as: material properties and geometrical constraints.Boundary conditions of the structure defined in the model may not be in accordance with the physical system [22].In this study, mechanical properties of materials were modified as shown in the flowchart given in Figure 12.The numerical analysis was repeated for updated conditions to validate the FEM analysis and the solution.
In this study, the elasticity modulus obtained on the numerical model was changed by about 1.5 %, and it amounted to 1500 MPa instead of 1521.36MPa.The Poisson ratio was 0.20, and the unit weight was 2800 kg/m 3 .Frequency values and mode shapes are presented in Table 4 and Figure 13, respectively.
According to finite element results the first, the second and the fourth modes exhibit a purely bending behavior, whereas the third mode is a torsional one.The fifth and sixth modes are a combination of bending and torsion behaviors.

Conclusion
The determination of modal parameters, such as natural frequency and mode shapes, has always been an important issue in the design of structures in terms of dynamic loading conditions.In this study, the "Experimental Modal Analysis (EMA)" method was applied in order to determine dynamic characteristics of double-layered arches.For this purpose, the dynamic behaviour of the arches was investigated through experimental tests.Only the first six modes were evaluated in this study, and all experimental studies were supported with the finite element model.Moreover, the experimental and numerical studies were merged together, and the consistency between the data was observed.According to the data presented in Table 2 and Table 3, it can be seen that the first period is around 0.25 s, and that the period is below 0.1 in the second mode.This result proves that the double-layered arches investigated in this paper exhibit a more rigid behaviour than the other type of structures.Finally, it is expected that the analyses and results of this study

Figure 13
Figure 13.Mode shapes and directions