Application of mathematical functions for seismic increment fragility determination

The goal of this paper is to determine a mathematical function which most accurately and efficiently models the time-dependent fragility data representing seismic vulnerability for deteriorating bridge pier columns subjected to ground motions rather than the logistic function that has been commonly used for this application while making as many or fewer assumptions. In this paper, three other functions, including the Gompertz function, the Ricker's growth function, and a power function, are considered and compared against the logistic one. All of these functions are analogous to the logistic one with deviations. The deviating characteristics include the location of the inflection point, the existence of inverted symmetry, and the asymptotic nature of the logistic function. As part of the best function determination procedure, the initial step of a general assessment of a bridge column's vulnerability to seismic damage is to employ time-dependent fragility data and fit the data to an appropriate curve. Inaccurately fitting the data could result in incorrect assumptions in the assessment, which could lead to miscalculated hazards and cost inefficiencies. For a proper fit, the model should be simplistic so as to make as few assumptions about reality as possible while still reasonably fitting the data. The standard function used to fit the fragility data is the logistic curve due to its well-studied nature and simplicity, but the logistic function may not be ideal. Key findings reveal that the Gompertz function better fits the fragility data and does not make any more assumptions. The Ricker's growth function and power function do not fit the fragility data well.