Structural identification for post-earthquake safety analysis of the Fat i ̇ h mosque after the 17 August 1999 Kocael i ̇ earthquake

Abstract

This paper presents the results of the structural identification of a historical structure damaged during the 17 August 1999 Kocaeli earthquake. Results of the structural models and methods are cross-validated in order to identify the reliable dynamic characteristics. Spectral analysis of the eight structural points yields average peak frequencies, respectively at around 2.5, 3.5, 4.3, 5.3 Hz and so on for NW–SE direction. Similarly for the SW–NE direction, peaks are seen at around 2.6, 3.2, 4.5–5 Hz with small differences in amplitudes between different structural points. Among the stations, station 3 behaves differently than the other observation points in low and high frequency regions indicating that the data recorded at station 3 should be examined in more detail. In parametric analysis, (a) the SDOF system as an SISO-ARX model, and (b) the MDOF system as a MIMO-ARX model are adopted and modal deformations are obtained using a state-space model with the OKID technique. The SDOF model captures the important peak frequencies with sufficient accuracy, but magnitudes are arguably small. In MDOF model, responses at the crown stations 1, 2, 3, and 4 display almost the same peak magnitudes at the same frequency, 2.51 Hz for NE–SW direction, but station 3 (which possesses smaller peak amplitude at a smaller frequency, 2.2 Hz) is exceptional and indicative of an anomaly. Similar conclusion with different peak frequency for NE–SW direction is also inferred from the SISO and Spectral analyses, when compared. Station 3 among the crown stations exceptionally yields peak frequency at 1.8 Hz in spectral analysis and around 1.8 Hz in SISO analysis. Natural frequencies of the structure estimated by SDOF and MDOF systems are close to each other, and thus, they can be accepted as global properties of the structure, except station 3. Such inconsistency implies that, for indicative anomaly, there might be a practical avenue through the evaluation of the first mode estimated by spectral, SDOF and MDOF models for a structure with the members of equal importancy in global dynamic behavior and symmetrical in plan and in elevations. Calculated elastic response spectrum of the Fatih record has larger amplitudes at the period of 0.55 s (with broadband characteristic) and larger than the amplitudes of the design spectrum with 10% probability of excedance in 50 years (for new constructions) for North–South direction. These larger local peaks at 0.55 s; (1) verify the 1.8 Hz of the fundamental frequency of the local ground and (2) suggest that, as the minimum requirements for the earthquake resistant design of buildings, in accordance with the strengthening applications in current seismic design code, the 2% probability of exceedance of the 5% damped elastic design acceleration spectrum within a period of 50 years is adequate. First mode of the structure, 2.4 and 2.5 Hz for NS and EW directions respectively, falls into the range of the dominant broadband period of the seismic loading. Such a match points out the resonance possibility, which might have occurred during the earthquake. The duration of the earthquake and following shocks of many small earthquakes in addition to the resonance might be the key contributors to the damage.