FINITE ELEMENT MODEL UPDATING EFFECT ON EARTHQUAKE BEHAVIOUR OF MASONRY STRUCTURES

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1 FINITE ELEMENT MODEL UPDATING EFFECT ON EARTHQUAKE BEHAVIOUR OF MASONRY STRUCTURES ABSTRACT: A.C. Altunışık 1, A.F. Genç 2, F.Y Okur 3, M. Günaydın 4, S. Adanur 1 1 Assoc. Prof., Department of Civil Engineering, Karadeniz Technical University, Trabzon 2 Research Assistant, Department of Civil Engineering, Karadeniz Technical University, Trabzon 3 M.Sc., Department of Civil Engineering, Karadeniz Technical University, Trabzon 4 Asst. Prof., Department of Civil Engineering, Gümüşhane University, Gümüşhane ahmetcan@ktu.edu.tr, ahmetcan8284@hotmail.com Although the masonry structure basically consists of stone, brick, mortar and filling materials, it has a very complicated structure in terms of structural and especially dynamic behavior such as earthquake. In order to determine the earthquake behavior of the masonry structures as close to reality as possible, it is of great importance to update the finite element models created by general engineering software with the help of nondestructive experimental measurement data and to use the updated models in the calculations. Within the scope of this study, it is aimed to investigate the dynamic behaviors of the historical masonry structure, which is called Zağanos Burcu in the province of Ortahisar in Trabzon. Firstly, the three dimensional finite element model of the building was constructed by taking into account the obtained geometrical measurement data and analysis parameters, and the dynamic characteristics were obtained numerically as a result of the modal analysis. Secondly, in order to verify the obtained numerical results, Operational Modal Analysis tests have been performed on the structure and dynamic characteristics have been determined by using Enhanced Frequency Domain Decomposition (EFDD) and Subspace Structural Identification (SSI) methods. The dynamic characteristics obtained numerically and experimentally are compared with each other and the differences detected at nearly 28% levels are reduced to 3% with the finite element model updating. In this way, finite element model that reflects the actual state of the building has been constructed and it has been demonstrated that the analyzes to be made through this model will give more appropriate results. In order to support the given phenomenon, dynamic analysis is performed on the updated finite element model and maximum displacement, principal stress and principal strain contour diagrams are obtained. KEYWORDS: Operational modal analysis, dynamic response, dynamic characteristics, modal analysis, historical masonry structure, finite element model updating TARİHİ YAPILARIN DEPREM DAVRANIŞINA SONLU ELEMAN MODEL İYİLEŞTİRMESİNİN ETKİSİ ÖZET: Yığma yapı basitçe taş, tuğla, harç ve dolgu malzemelerinden oluşmasına karşın, yapısal ve özellikle deprem gibi dinamik davranış açısından oldukça karmaşık bir yapıya sahiptir. Yığma yapıların deprem davranışlarını gerçeğe en yakın şekilde belirlemek amacıyla, genel mühendislik yazılımları kullanılarak oluşturulan sonlu eleman modellerinin hasarsız deneysel ölçüm verileri yardımıyla iyileştirilmesi ve hesaplamalarda iyileştirilen modellerin kullanılması büyük önem arz etmektedir. Bu çalışma kapsamında, Trabzon İli, Ortahisar İçesinde

2 bulunan ve Zağanos Burcu olarak adlandırılan tarihi yığma yapının dinamik davranışlarının incelenmesi amaçlanmaktadır. İlk olarak, binanın üç boyutlu sonlu eleman modeli elde edilen geometrik ölçüm verileri ile analiz parametreleri dikkate alınarak oluşturulmuş olup, modal analizler sonucunda dinamik karakteristikler sayısal olarak elde edilmiştir. İkinci olarak, elde edilen sayısal sonuçları da doğrulamak amacıyla, yapı üzerinde çevresel titreşim testleri gerçekleştirilmiş olup, dinamik karakteristikler Geliştirilmiş Frekans Tanım Alanında Ayrıştırma (GFTAA) ve Stokastik Altalan Belirleme (SAB) yöntemleri kullanılarak belirlenmiştir. Sayısal ve deneysel olarak elde edilen dinamik karakteristikler birbirleriyle karşılaştırılmış, %28 seviyelerinde tespit edilen farklılıklar sonlu eleman model iyileştirmesi ile birlikte %3 seviyelerine indirilmiştir. Böylelikle, binanın gerçek durumunu yansıtan sonlu eleman modeli oluşturulmuş olup, bu model üzerinden yapılacak analizlerin daha uygun sonuçlar vereceği ortaya konulmuştur. Belirtilen olguyu desteklemek amacıyla, iyileştirilmiş sonlu eleman modeli üzerinden dinamik analizler yapılmış olup, maksimum yerdeğiştirme, asal gerilme ve asal şekildeğiştirme kontur diyagramları elde edilmiştir. ANAHTAR KELİMELER: Deprem, Dinamik davranış, Dinamik karakteristik, Modal analiz, Operasyonel Modal Analiz, Sonlu eleman model iyileştirmesi, Tarihi yığma yapı. 1. INTRODUCTION Obtaining exact results by numerical calculations depends on true input parameters such as boundary conditions, material properties, geometric dimensions etc. of the problem. It may be easy to determine the input parameters for some problems but it is not easy for solving large problems such as masonry structures. Therefore these problems should be support by experimental data. Today finite element (FE) method is widely used to determine the structural behavior of the historical masonry structures. However these structures are very difficult to determine the exact structural behavior due to unknown material properties, boundary conditions and geometric dimensions. Therefore authors use nondestructive experimental testing methods which are convenient for historical structures. Nondestructive experimental methods such as operational modal analysis (OMA) can allow obtaining dynamic characteristics of the structure such as natural frequencies, damping ratios and mode shapes. With the help of experimental dynamic characteristics finite element model of the structures can be updated and more reliable results can be obtained. In the literature, many studies were made related to investigation of structural behavior of the historical masonry structures with using finite element method and nondestructive experimental methods. Some of them are related to masonry arches (Sevim et al. 2011), masonry tower (Preciado 2015), masonry mosque (Çakir et al. 2015), masonry monuments (Atamturktur and Laman 2012) and other masonry structures (Foti et al. 2012; Altunışık et al. 2016; Lacanna et al. 2016; Torres et al. 2017) etc. Operational modal analysis is the base of the health monitoring and damage detection. Therefore this investigation area has been enhanced day by day by the researchers. In this paper, updating effects on the seismic behavior of an ancient bastion is investigated using linear analyses. Experimental and numerical dynamic characteristics of the bastion were obtained by OMA and FE analyses. To eliminate the differences between experimental and numerical dynamic characteristics, FE model of the bastion was updated. To determine the updating effect, linear FE seismic analyses were carried out using initial and updated FE models.

3 2. APPLICATIONS The Zağanos bastion is placed at on the middle part of the Trabzon castle. Structural system of the bastion consists of load-bearing walls, vaults and arches. In the last century lift, RC floor and cement base mortar were added to bastion. The bastion has approximately 17m height, 15m width and 10m depth. The thicknesses of bastion walls are approximately 2.55m for up to middle point of the bastion from ground and 1.25m from the middle points of the bastion to top points. The bastion has two main stores which have vault roofs and they were divided into two with RC floors so four stores were occurred. Some views of the bastion are given in Fig Experimental Dynamic Characteristics Fig. 1 Views of Zağanos Bastion Operational modal analysis was performed on the bastion to determine its dynamic characteristics such as natural frequencies, mode shapes and damping ratios. In the test, the frequency range was selected as 0-15Hz and eight accelerometers were located at the top of the bastion in the transverse and longitudinal direction. In addition test was carried out for 45 minutes. The dynamic characteristics of the bastion were extracted using both EFDD and SSI techniques after signal processing. Singular values of spectral density matrices (SVSDM) of the data set and the average of auto spectral densities (AASD) of the data set obtained by EFDD technique for the bastion are given in Fig. 2. The dynamic characteristics were also identified using SSI technique. The first three mode shapes are given in Fig. 3. Fig. 2 SVSDM and AASD of the data set

4 Fig. 3 The mode shapes of the bastion Experimental identified dynamic characteristics of the bastion are given in Table 1. It can be seen from the Table 1 that, there is significant agreement between the natural frequencies with the maximum error of 0.77% in the second mode. However, there is no significant agreement between the damping ratios. Table 1 Modal Parameters of the bastion for the EFDD and SSI Mode Frequency (Hz) Damping Ratios (%) EFDD Diff.(%) SSI EFDD Diff.(%) SSI Initial Finite Element Model Finite element model of the Zağanos bastion is modeled using ANSYS software (ANSYS, 2015). SOLID186 element type is used for analyses. The FE model (Fig. 4) of the bastion has four different structural elements namely masonry walls, masonry arches and vault, reinforced concrete (RC) floors, steel columns.

5 Fig. 4 Finite element model of bastion Initial material properties of the bastion are given in Table 2. In the model, the supports of the bastion are assumed to be fixed. Table 2 Linear material properties of the bastion for initial FE model Elements Material Properties Modulus of Elasticity (N/m 2 ) Poisson Ratio (-) Density (kg/m 3 ) Masonry walls 2.4E Masonry Arches and vault 4.0E RC floors 2.5E Steel column 2.0E FE modal analysis is carried out for the bastion to obtain the natural frequencies and mode shapes numerically. The first three natural frequencies are obtained as Hz, Hz and Hz respectively. The first three modes are translational modes in the transverse and longitudinal direction and torsional mode. Experimental and numerical mode shapes are similar. Comparisons of the experimentally and numerically identified natural frequencies for the bastion are given in Table 3. As shown, there is no clear agreement between the experimental and numerical frequencies. A maximum error between the experimental and numerical frequencies is calculated as 27.86%. Due to this high differences, initial FE models must be updated according to the experimental frequencies. Table 3 Experimental and initial FE natural frequencies Mode Frequency (Hz) EFDD SSI Max. Difference (%) Initial Model

6 2.3. Finite Element Model Updating The selecting of updating parameters is of the most important steps in model updating procedure. Because of the geometric simplicity, boundary condition and structural geometry were not taken into account in the updating process. FE model has the same geometry with the constructed models. The elasticity modulus is selected as updating parameter to minimize the errors between experimental and numerical results. The manual updating process was achieved by changing of elasticity modulus of masonry walls and arches. With the updating process, the modulus of elasticity values changed from 2.40E9 to 1.32E9 and 4.00E9 to 2.55E9 for masonry walls and masonry arches-vaults respectively. A significant agreement is obtained between the obtained frequencies after model updating. The natural frequencies before and after model updating are given in Table 4. Table 4 Comparison of the experimental and updated frequencies Mode Frequency (Hz) EFDD SSI Diff. (%) Updated Seismic Analysis In this study, linear seismic performance was examined for initial and updated FE models using time-history analysis. The seismic load is selected as Kocaeli earthquake (1999), station of Duzce (KOCAELI_DZC270) (PEER, 2016). In the analysis, only five second between the 5-10 seconds of the record, which is the most effective duration, is taken into account because of the computational demand of this method and less time consuming. Accelerations are subjected to the bastion along the x direction where the first mode shape was obtained. Initial FE model analysis results are given below with contour diagrams. Updated FE model analysis results are given in Table 5. The maximum displacement contour diagram of the bastion is given in Fig. 5. The maximum displacement occurs at upper part of the bastion with the value of 7.8mm. Also, the displacements decrease towards to lower part of the bastion. The maximum tensile stresses contour diagram of the bastion is given in Fig. 6. The maximum tensile stress occurs on the RC floor locally as a value of 4.56MPa. But this value does not reflect the real behavior of the bastion because the RC floor is not main component of the bastion. Maximum tensile stress occurred on masonry components is 2.63MPa and occurs on a local point of arch. Except this local stress, the maximum tensile stresses are generally obtained as 0.93MPa on the bastion. The compressive stresses contour diagram of the bastion is given in Fig. 7. The maximum compressive stress occurs at on the RC floor locally with the value of 6.04Mpa. Also, the maximum compressive stress on the masonry components occurs as 5.0MPa.The main structural elements of the bastion have approximately 0.90MPa compressive stress. The maximum tensile strain contour diagram of the bastion is shown in Fig. 8. The maximum strain occurs at between masonry arch and lift wall. Maximum tensile strain obtained is 10.59E-4.

7 The compressive strain contour diagram of the bastion for the seismic analysis is shown in Fig. 9. The maximum strain occurs at between masonry arch and RC floor as a value of 19.47E-4. In addition, the value of 8.60E-4 compressive strain is obtained between side rampart and bastion area. Fig. 5 Maximum displacements contour diagram of the bastion for seismic analysis

8 Fig. 6 Tensile stresses contour diagram of the bastion for seismic analysis

9 Fig. 7 Compressive stresses contour diagram of the bastion for seismic analysis

10 Fig. 8 Tensile strain contour diagram of the bastion for seismic analysis

11 Fig. 9 Compressive strain contour diagram of the bastion for seismic analysis 2.5. Comparison of Initial and Updated FE Model Results To determine the updating effects, linear seismic analyses of initial and updated Fe models are compared in Table 6. It can be seen from the table, there is significant differences between initial and updated results. Table 6 Comparison of the results Parameters Initial Diff.(%) Updated Maximum Displacement(mm) Tensile Stress (MPa) Compressive Stress (MPa) Tensile Strains 10.59E E-3 Compressive Strains 19.47E E-3

12 3. CONCLUSIONS İn this study, updating effect on the seismic behavior of a masonry bastion was examined. Operational modal analysis, numerical modal analysis, updating process and linear seismic analyses were made for this purpose. According to study following conclusions can be drawn. The first three experimental frequencies are attained within 4-7Hz for SSI and EFDD. However the first three numerical frequencies are identified within 5-10Hz. The maximum difference between the experimental and numerical frequencies is obtained as nearly 28%. Despite the natural frequencies, the numerical and experimental mode shapes are the same. After manual FE model updating the differences between numerical and experimental frequencies are decreased 28% to 3%. The differences between seismic analyses of initial and updated FE model are approximately 92%, 52%, 48%, 93% and 95% for displacement, tensile stress, compressive stress, tensile strain and compressive strain respectively. As seen from the results that updating process affects the results of seismic analysis importantly. REFERENCES Altunışık, A.C., Adanur, S., Genç., A.F, Günaydın, M. and Okur, F.Y. (2016). Non-destructive testing of an ancient masonry bastion. Journal of Cultural Heritage, 22, ANSYS (2015), Swanson Analysis System, Pennsylvania, USA. Atamturktur, S. and A. Laman, J. (2012). Finite element model correlation and calibration of historic masonry monuments: review. The Structural Design of Tall and Special Buildings 21, Cakir, F., Seker, B.S., Durmus, A., Dogangun, A. and Uysal, H. (2015). Seismic assessment of a historical masonry mosque by experimental tests and finite element analyses. KSCE Journal of Civil Engineering 19, Foti, D., Diaferio, M., Giannoccaro, N.I. and Mongelli M. (2012). Ambient vibration testing, dynamic identification and model updating of a historic tower. NDT&E International 47, Lacanna, G., Ripepe, M., Marchetti, E., Coli, M. and Garzonio, C.A. (2016). Dynamic response of the Baptistery of San Giovanni in Florence, Italy, based on ambient vibration test. Journal of Cultural Heritage 20, PEER (2016), Pacific Earthquake Engineering Research Center. University of California, Berkeley, CA, USA. Preciado, A. (2015). Seismic vulnerability and failure modes simulation of ancient masonry towers by validated virtual finite element models. Engineering Failure Analysis 57, Sevim, B., Bayraktar, A., Altunişik, A.C., Atamtürktür, S. and Birinci, F. (2011). Finite element model calibration effects on the earthquake response of masonry arch bridges. Finite Elements in Analysis and Design 47, Torres, W., Almazán, J.L., Sandoval, C. and Boroschek, R. (2017). Operational modal analysis and FE model updating of the Metropolitan Cathedral of Santiago, Chile. Engineering Structures 143,