Influence of Prior Distributions and Fragility assessment methods in the estimation of the Magnitude of a Historical Seismic Event

Abstract

The production of fragility functions describing the probable behaviour and damage on historical buildings is a key step in a method for the estimation of the magnitude of historical seismic events that uses a Bayes'. The fragilities are estimated by integrating the structural capacity with the seismic demand using either static methods, as the Capacity Spectrum Method (CSM), or dynamic methods, as Incremental Dynamic (IDA) and Multiple Stripes Analysis (MSA). Uncertainties in both resistance, demand, and distance and magnitude models propagate to the posterior magnitude distribution. The present paper studies the effect of uncertainties related both to the production of fragility functions and prior distributions, in the estimation of the magnitude of the 1763 Komárom earthquake (in historical Hungary). In the XVIII century most of the structures in the region were built of earth, adobe, clay or stone masonry, which is complex to model. While micro or detailed macro-modelling strategies are computationally costly, simplified macro-approaches are often more efficient, but require a pre-identification of the failure mode(s) and the determination of the backbone curve. For this study, a simplified macro-model of a Hungarian peasant house archetype is calibrated for CSM and IDA. The physical and geometrical uncertainties are incorporated in the fragilities using Monte-Carlo simulation. Prior magnitude and distance distributions are studied. The final magnitude estimates are presented and discussed.

A methodology for the development of historical building archetypes for seismic performance assessment

“…1), is illustrated here in order to highlight the relevance and aim of the historical archetypes. This application example is detailed in [12] and makes use of the processes developed in [13]. Despite the correct use of methodology, the reliability of the final magnitude estimates is still conditioned by uncertainties related to the model, strength parameters and to the quantification and relation of the building/damage pairs.…”

“…2, center). This process enables the determination of the damage points associated with the damage states dm 1 to dm 4 [12], to which lognormal CDFs, or fragility functions (Fig. 2, right), are fitted.…”

“…The sources, regarding [4], lead us into a dichotomy in structural modeling: still existing affected monumental buildings may guarantee a reliable building/damage relation and are relatively well documented, but fall into modeling complexity and lack representativeness. In [27], initial steps were taken to analyze the church of Zsámbék, which has damage descriptions due to the 1763 earthquake. Another path [13] studies simpler and highly representative (in damage numbers) buildings (dwelling houses, mills, kilns, etc.…”

Cyclic Behaviour, Dynamic Analysis and Seismic Vulnerability of Historical Building Archetypes in Hungary

“…In this context, the 1763 event was a major object of discussion and rejection criteria for the construction of a water power plant at Nagymaros (Eisinger, Gutdeutsche, and Hammerl 1992). These facts led to the investigation of the probable historical seismic intensities and magnitude of the 1763 event, first by historical seismology (Szeidovitz, 1986;Varga et al, 2001), and then by earthquake engineers (Morais, Vigh, and Krähling 2017, 2018a, 2018b) that considered the behaviour and effects on real building structures.…”