Cloud Capacity Spectrum Method: Accounting for record-to-record variability in fragility analysis using nonlinear static procedures

This paper investigates a number of computational issues related to the use of nonlinear static procedures in fragility analysis of structures. Such approaches can be used to complement nonlinear dynamic procedures, reducing the computational and modelling effort. Specifically, this study assesses the performance of the Capacity Spectrum Method (CSM) with real (i.e. recorded) ground motions (as opposed to code-based conventional spectra) to explicitly account for record-to-record variability in fragility analysis. The study focuses on single-degree-of-freedom systems, providing a basis for future multi-degree-of-freedom system applications. A case-study database of 2160 inelastic oscillators is defined through parametric backbones with different elastic periods, (yield) base shear coefficients, values of the ductility capacity, hardening ratios, residual strength values and hysteresis rules. These case studies are analysed using 100 real ground motions. An efficient algorithm to perform the CSM with real spectra is proposed, combined with a cloud-based approach (Cloud-CSM) to derive fragility relationships. Simple criteria to solve the issue of multiple CSM solutions (i.e. two or more points on the backbone satisfying the CSM procedure) are proposed and tested. It is demonstrated that the performance point selection can be carried out based on a particularly efficient intensity measure detected via optimal intensity measure analysis. The effectiveness of the proposed Cloud-CSM in fragility analysis is discussed through extensive comparisons with nonlinear time-history analyses, the code-based N2 method, and a simple method involving an intensity measure as a direct proxy for the performance displacement. The Cloud-CSM provides errors lower than ±20% in predicting the median of the fragility curves in most of the analysed cases and outperforms the other considered methodologies in calculating the fragility dispersion.