Fractional order optimal intensity measures for probabilistic seismic demand modeling of extended pile-shaft-supported bridges in liquefiable and laterally spreading ground

Abstract

In performance-based earthquake engineering, probabilistic seismic demand models of structures are essential components that provide probabilistic estimates of earthquake-induced demands as a function of a variable(s) called the ground motion intensity measure (IM). Uncertainties in these models are often dependent on the IM used. Extending from traditional integer order IMs, this study assesses the performance of fractional order (FO, order of α) IMs on the probabilistic seismic demand modeling of extended pile-shaft supported bridges sited in liquefiable and laterally spreading ground. Uncertainties in structural and geotechnical material properties as well as geometric parameters of the bridges are considered in finite element models to achieve comprehensive scenarios. The FO IMs considered include peak ground response (PGRα), cumulative absolute response (CARα) and its modified version (CAR5α), spectral acceleration at 2.0 s for a fractionally damped single degree of freedom (SDF) system (Sad-20α) and for a conventional SDF system with fractional response (Sar-20α), spectrum intensity for a fractionally damped SDF system (SIdα), as well as for a conventional SDF system with fractional response (SIrα). Metrics such as efficiency, practicality, proficiency and sufficiency are measured to assess the optimal α with respect to different demand parameters. Results show the advantages of FO IMs as they increase confidence in demand models compared to traditional integer order IMs. In particular, the proposed fractional spectrum intensities (SIdα and SIrα) with their optimal α values produce significant improvements in practicality, efficiency and proficiency, while maintaining sufficiency. Therefore, FO IMs can provide more reliable demand models for probabilistic seismic demand analysis of extended pile-shaft supported bridges in liquefiable and laterally spreading ground.