A Rate-Dependent and Pinching-Sensitive Constitutive Model for Reinforcing Steel

Abstract

Reinforced concrete structures subjected to seismic loading experience strain rates in the longitudinal reinforcement that are orders of magnitude higher than those applied in standard quasi-static material tests, yet most constitutive models used in nonlinear time-history analysis neglect this rate dependence. This dissertation develops SteelDRCV (Dodd-Restrepo-Carreño-Velásquez), a hysteretic constitutive model for reinforcing steel that extends the SteelDRC formulation with two mechanisms: (i) a nonlinear Voigt-type viscous overstress term that captures rate-dependent strengthening beyond initial yield, and (ii) a quadrant-dependent curvature factor that phenomenologically reproduces bond-slip-induced pinching in cyclic response. Both extensions are implemented in OpenSees and formulated to preserve compatibility with large-scale nonlinear structural analysis.

Strain-rate demands are first characterized from two full-scale shake-table specimens tested at the LHPOST facility at UC San Diego: (i) a circular bridge column and (ii) a seven-story structural wall, quantifying the magnitude, distribution, and amplification of strain rates in longitudinal reinforcement under realistic seismic excitation. High-strain-rate tensile tests then characterize the viscous mechanism and support proposing two nonlinear Voigt-type parameters. A phenomenological curvature formulation is proposed to reproduce bond-slip-induced pinching in cyclic response.

Model calibration follows a two-stage strategy. The first stage identifies the cyclic and pinching parameters from the quasi-static structural response under displacement-controlled conditions. The second employs Bayesian inference to refine the remaining strain-rate, damping, and concrete damage parameters using Gaussian-Process surrogates, variance-based sensitivity decomposition, and Transitional Markov Chain Monte Carlo sampling. The posterior distributions quantify parameter uncertainty and identify which parameters are informed by the dynamic response versus the quasi-static stage. The results also show that, for highly nonlinear structural models with interacting parameters, engineering judgment informed by the physical response remains essential when assessing surrogate-based Bayesian solutions. The calibrated model is validated against an independent seismic simulation. Finally, seismic input energy is decomposed into hysteretic, viscous damping, and strain-rate-dependent contributions. Rayleigh viscous damping and strain-rate-dependent dissipation contribute approximately 5.5% and 5.1%, respectively, corresponding to a combined equivalent viscous damping ratio of approximately 0.9%, compared with the ad hoc 2% conventionally adopted in nonlinear analysis to represent additional dissipation sources not explicitly modeled.