Keywords: fragility curves, historical structures, masonry structures, seismic vulnerability, probabilistic analysis.

A methodology for the probabilistic evaluation of seismic vulnerability of historical structures and monuments is proposed. Namely, both the chaotic character of earthquakes, as well as the random character of the structures' mechanical properties, implies the necessity of a probability-based design approach. The evaluation of the susceptibility of a structure to damage, is assumed to comprise three sets of input information: those concerning the intensity of the seismic event, those describing critical properties for the structure's capacity and those defining the quantification of the structural performance. Seismic vulnerability of structures is associated with their expected performance when subjected to a single seismic event, through the definition of a correlation function between the earthquake action and the probability of exceeding a certain response level. Random values of a selected structural property, referred to as the observation parameter, are considered.

In this paper, estimation of structural response to the accidental action is based on an analysis process, see [3]. Iterative analyses and statistical processing leads to the illustration of structure vulnerability through a fragility curves diagram. The methodology is adapted to masonry structures [2] and it is demonstrated through a case study, an existing historical building.

The seismic intensity index (SII), describing the magnitude of the seismic activity and its value range, is used to define the seismic hazard. The Peak Ground Acceleration (PGA) is employed to represent the SII, see [1]. Its range value is determined according to [6]. The Observation Parameter (OP) expresses the random character of a structural properties influencing structural capacity. The OP selected should influence determinatively the response of the structure. Its value range should be consistent with the real structure. The seismic impact is quantified by implementation of a measurable structural response parameter (RP). The methodology proposes a Damage Index (DI) established on the basis of the ratio of failed area to total area of wall surface of the structure (A_fail/A_tot). Threshold values of the DI calibrate the RP indices.

Iterative parametric stress and failure analysis follows. Masonry systems are sufficiently simulated by finite element models. The program "FAILURE", as developed in [5], to provide analysis data, elaborates stress analysis data implementing a modified Von Mises failure criterion, as described in [4]. Values of the DI are obtained.

Statistical data processing involves the use of the proper Probability Density Function (PDF) to obtain the cumulative probability of exceedence of each damage rank, for each seismic excitation level, by integration along the DI boundaries. The developed fragility curves diagram illustrates the correlation between the damage level and the magnitude of the seismic event.

The case study refers to a masonry structure, a Byzantine monastery called "Moni Kaisarianis". The OP is selected to be the masonry's strength in tension. Stress and failure analyses take place. Statistical processing employs normal and lognormal distribution. The fragility curves diagram is constructed providing evidence that extensive damage to the structure is most probable, when a PGA greater than 0.24g occurs.

1

M. Shinozuka, Q.M. Feng, J.H. Lee, T. Nagamura, "Statistical analysis of fragility curves", Proceedings of the Asian-Pacific Symposium on Structural Reliability and its Application (APSSRA 99), 2003.

2

K. Marinelli, C. A. Syrmakezis, A. K. Antonopoulos, "Structural Response of Masonry Historical Structure Using Fragility Curves", Proceedings of the third European Conference on Structural Control, Vienna University of Technology, Vienna, Austria, 2004.

3

T. Rossetto, A. Elnashai, "Derivation of Vulnerability Functions for RC Buildings based on Observational Data", Engineering Structures, Volume 25, Issue 10, 1241-1263, 2003. doi:10.1016/S0141-0296(03)00060-9

4

C.A. Syrmakezis, P.G. Asteris, "Masonry Failure Criterion under Biaxial Stress State", Journal of Materials in Civil Engineering, ASCE, 58-64, 2001. doi:10.1061/(ASCE)0899-1561(2001)13:1(58)

5

C.A. Syrmakezis, P.G. Asteris, A.A. Sophocleous, "Earthquake Resistant Design of Masonry Tower Structures", Proceedings, 5th STREMA Conference on Structural studies, Repairs and Maintenance of Historical Buildings, Vol. 1, 377-386, St. Sebastian, Spain, 1997.

6

F. Casciati, L. Faravelli, "Stochastic Nonlinear Controllers", Proc. IUTAM Symposium, NonLinearity-Stochastic Structural Dynamics, Madras, Kluwer, 2001.

7

F. Casciati, and H.J. Lagorio, "Urban Renewal Aspects and Technological Devices in Infrastructure Rehabilitation", Proc.1st European Conference on Structural Control, Barcelona, 173-181, 1996.

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