Transactions on the Built Environment vol 15, 1995 WIT Press, ISSN

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1 Foundation effect on the dynamics of Hagia Sophia A.S. Cakmak, M.N. Natsis, C.L. Mullen Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ 08544, USA Abstract Finite element studies of the Hagia Sophia, a sixth century masonry edifice, in Istanbul, Turkey, provide insight to the structure's response to dynamic loads. The church contains four great brick arches springing from stone piers that offer primary support for a 31-meter diameter central dome and two semidomes. Stone and brick masonry material properties for the numerical model are adjusted to match system mode shapes and frequencies identified from measured response to a recent low-intensity earthquake. The calibrated model is used to predict the measured responses, and the effect of soil-structure interaction is demonstrated. Stresses under simulated severe earthquake loading are estimated at the critical locations in the arches. 1 Introduction Begun in 532 as the principal church of the Byzantine Empire (and converted to a royal mosque after the fall of the Empire in 1453), Hagia Sophia in Istanbul held the record as the world's largest domed building for some 800 years. In order to preserve this historical structure, it is necessary to understand the earthquake response in its present condition. This paper addresses aspects of the present day dynamic behavior of the primary dome support structure under recorded and likely earthquake excitation. Early development of a numerical model for eigenvalue analysis of Hagia Sophia has been discussed by ^akmak et ap. A very good match was attained in the first three natural frequencies measured during an ambient vibration survey of the actual structure (see Erdik et ap). A low-level event of magnitude 4.8 occurred on March 22, 1992, with epicenter at Karabacey, Turkey, about 120 km south of Hagia Sophia. Strong motion acceleration time histories recorded for this event have been analyzed in both the time and frequency domains. System identification performed on this data has been discussed by Qakmak et ap. The first three mode shapes correspond to simple horizontal translation (modes 1 and 2) and a complex form of torsional rotation (mode 3) of the entire primary structure system. Here we

2 4 Dynamics, Repairs & Restoration compare earthquake response of the numerical model and the identified system and extend the model to improve the predictions and provide estimates of severe earthquake responses. 2 System Properties and Measured Response The primary structure supporting the main dome of the Hagia Sophia and its orientation are illustrated in a cutaway view in Figure 1. The main dome is spherically shaped and rests on a square dome base. Major elements include the four main piers supporting the corners of the dome base and the four main arches that spring from these piers and support the edges of the dome base. The instrumentation array described by Erdik et al * has been designed to capture the motion of the major elements comprising the main dome support structure during earthquake events. The main piers are comprised of stone masonry. The stone blocks are almost rigid, whereas the mortar is relatively compliant. The main arches and dome are comprised of brick masonry. The mortar used in the brick masonry may be considered to be a form of concrete with tensile strength approaching 3.5 MPa. The bricks may be thought of as providing stiffness rather than strength as is the case in present day construction. The mass density of the composite is about 1500 kg/nr* which is lighter than present day concrete. Figure 2 shows the earthquake induced N-S (Y), E-W (X), and vertical (V or Z) acceleration component time histories recorded during the 1992 Karacabey event. The three components for each response location are Figure 1. Main dome support structure and strong motion instrument array.

3 Dynamics, Repairs & Restoration 5 displayed in a plan arrangement oriented to the view seen from the entrance to the basilica. In all cases the records indicate a nonstationary process acting with three approximately stationary time intervals. The first interval extends from 2 to 12 s and corresponds to the action of compressional waves; the second from 15 to 25 s corresponds to the arrival of shear waves; and, the third from 30 to 40 s corresponds to a period of decay in the energy of the input motion and will not be emphasized here. N-S motion tends to dominate the response motion with particularly intense N-S motions at locations 4 and 6. The peak displacement at location 4 is estimated as.071 cm which is double that of the locations 2,3, and 5. Similarly, the peak displacement at location 6 is estimated to be.13 cm which is almost double that at location 8. Figure 3 shows the experimental linear system transfer functions, RXX, and Hyy, obtained for thefirsttwo modes using the procedure described by Cakmak et ap. EXX relates X (E-W) response motion to X (E-W) input motion at thefloorlevel, and Hyy, the Y (N-S) response caused by Y (N-S) input at the floor level. Using the second interval, the observed mode 1 and mode 2 frequencies given in Table 1 are obtained. Top of NE Pier Top of E Arch Top of SE Pier ""' *+ #W*t" * ;i * ~i & i i i Top of N Arch Base of NE Pier Top of S Arch 1 4hm# Top of NW Pier Top of W Arch Top of SW Pier '""""*"## H -w- ]" / "" ^ - ;1 ^"#"#'*' '""- ;i tt la. 1 Z ' ' I Figure 2. Measured accelerations for March 22, 1992, Karacabey earthquake.

4 Dynamics, Repairs & Restoration 8-i 5?- 9- a) Arches 0-10s (N) (E) 6(S) 3-1 c) Arches 0-10s (N) (E) 6(S) ^ Frequency (Hz) b) Arches s 6(S) 7 (W) 8<N) 9(E) Frequency (Hz) d) Arches s 3-, 38- H 2- Frequency (Hz) s Frequency (Hz) Figure 3. Transfer functions forfirstand second mode responses. Two characteristics of the measured response are not captured by the numerical models discussed in (^akmak et ap. First, as seen in Figure 3, the system responds primarily at 1.85 Hz in the second interval, a 10 percent reduction in the mode 2 frequency relative to the ambient vibration frequency of 2.09 Hz. The first interval indicates mode 2 response at 2.00 Hz, a 5 percent reduction relative to the ambient vibration. Second, the SW main pier and the arches that spring from it respond at higher amplitudes in mode 2 motion than the other piers and arches. Similar behavior is also noted for mode 1 response. TABLE 1. Earthquake Calibration* Mode Observed Simulation^ Fixed Base Soil Springs Dominant Motion ,.57 1, All frequencies are in Hz Fixed Ba,se=hsdyntc9, Soil Springs= hsdynss E-W (X-axis) translation N-S (Y-axis) translation Torsional (Z-axis) rotation

5 Dynamics, Repairs & Restoration 7 Figure 4. P-wave velocity contours obtained by seismic tomography.

6 Dynamics, Repairs & Restoration 3 Simulation Two select attempts at matching the recorded response using linear FE models are discussed here with particular attention paid to accounting for the two characteristics described above. The first model named hsdyntc9h&s been constructed by Davidson'*. It is similar to the linear FE model used by Cakmak et ap for eigenvalue analysis but has more refinement of the mesh in the region of the arches. The elastic properties have been adjusted to match the observed frequency during the second interval of the earthquake response motion. The elastic moduli and density used in this model are the same as those for the eigenvalue model, except the Young's moduli, E, in surcharge and tension areas were not reduced and a ratio of 1.00:0.68 was used for E values of stone and brick masonries, respectively. The second model named hsdynss has been constructed with the same geometry above the floor level as the hsdyntco model. The effect of soil-structure interaction has been incorporated, however, by supporting the portions of the main piers below floor level with linear translational soil springs acting normal to the faces of the piers. Soil spring stiffnesses have been distributed in a manner reflective of expected variations in soil elastic moduli. Such patterns have been obtained from seismic tomography which measured compressional wave velocity of foundation material along a grid of horizontal and vertical planes in the area below and contained by the four main piers. Figure 4 shows representative contours of equal velocity. The frequencies obtained by eigenvalue analysis of the hsdyntco and hsdynss models are given in Table 1. Simulated response of the hsdynss model to the earthquake was calculated using the mode superposition method with input acceleration at all soil spring locations in the model identical to that measured in the corresponding component direction at the Kandilli seismographic station, a nearby bedrock free-field location. A pseudo-nonlinear response has been estimated by selecting different moduli in thefirstand second time intervals of the earthquake response motion. Figure 5 shows a comparison of some of the measured and simulated acceleration time histories. 4 Stress Analysis Static dead load stresses in a model named 10try6 have been calculated using a pseudo-nonlinear procedure described in Davidson*. The procedure attempts to capture intermediate selfweight deformations experienced during a number of major stages of construction. The FE mesh for the lotryg is essentially the same as that used in the hsdyntco model. Using magnitude M=6.5 and M=7.5 earthquake input accelerations generated at the site according to the procedure described by Findell et of.\ response time histories for the hsdyntco model have been simulated. Maximum stresses in the critical crown region of the east and west arches corresponding to the static and dynamic loadings are summarized in Table 2. These results give benchmarks for severe response characteristics and highlight the importance of dynamic response to past and potential failures of the primary support structure.

7 Dynamics, Repairs & Restoration 9 WEST ARCH SW PIER Figure 5. Simulated earthquake response predicted by soil-spring model.

8 10 Dynamics, Repairs & Restoration TABLE 2. Simulated Stresses* for Severe Earthquakes Load Case East Arch West Arch M=6.5 M=7.5 M=6.5 M=7.5 DL 0.80(3.30) 1.21(3.61) EQ 0.60(0.60) 1.72(1.72) 0.51(0.51) 1.48(1.48) TOTAL 1.40(3.90) 2.52(5.02) 1.72(4.12) 2.73(5.09) * All stresses are in MPa. Maximum tensions for hsdyntco are listed with maximum compressions given in parentheses. 5 Conclusion Numerical modeling of the Hagia Sophia has been performed using calibrated linear finite element analyses. System identification from a recent low-intensity earthquake indicate a nonlinear behavior for the masonry structure even at very low response levels. The linear models provide reasonable estimates of overall dynamic characteristics including frequency and primary modes of response. Incorporation of nonlinear behavior and soilstructure interaction may be achieved in an approximate way and improves the low-intensity predictions. Numerical modeling provides an important means of monitoring the earthquake worthiness of Hagia Sophia. As larger intensities are recorded and appreciable damage becomes evident, it will become increasingly important to accurately incorporate in such models the characteristic nonlinear behavior of the masonry construction. References 1. Qakmak A.. Davidson R., Mullen C. L. & Erdik M., Dynamic analysis and earthquake response of Hagia Sophia, in STREMA/93 (ed C.A. Brebbia & R.J.B Frewer), pp , Proceedings of the 3rd Int. Conf. on Structural Studies, Repairs and Maintenance of Historical Buildings, Bath, UK, 1993, CML Publications. Southampton, Erdik M. & Cakti E., Istanbul Ayasofya muzesi yapisal sisteminm ve deprem guvenliginin saglanmasina yonelik tedbirlerin tespiti, 2nd Research Report, Earthquake Research Institute, Bogazici University, November, Erdik M. and Cakti E., Instrumentation of Aya Sofya and the analysis of the response of the structure to an earthquake of 4.8 magnitude, in STREMA/93 (ed C.A. Brebbia & R.J.B Frewer), pp , Davidson R.A., The mother of all churches: a static and dynamic structural analysis of Hagia Sophia, unpublished senior thesis, Civil Engineering and Operations Research Dept., Princeton University, Findell K., Koyliioglu H.U. & Qakmak A.., Modeling and simulating earthquake accelerograms using strong motion data from the Istanbul, Turkey region, Soil Dynamics and Earthquake Engineering, 1993, 12,