A Multi-Surface Plasticity Model for Reinforced Concrete Cracks With Applications to Crack-Based Assessment

Abstract

Concrete crack measurements are central to earthquake damage assessment procedures, yet few analysis models are equipped to handle crack data as direct inputs. To address this need, this work develops a non-associative, multi-surface plasticity model that describes the configuration-dependent response of a reinforced-concrete crack subjected to earthquake loading. The aggregate interlock configuration is controlled by a well-established parabolic yield surface whereas frictional unloading follows a newly proposed hyperbolic yield surface. An extensive experimental review is undertaken to verify the form of the yield surfaces – which are completely parameterized by crack width – and to motivate the development of non-associated flow rules that regulate crack dilation for cyclic loading. Furthermore, ranges for the model's elastic stiffness components and six plasticity parameters are identified from experimental data. Typical model outputs are demonstrated for a mixed-mode, cyclically loaded crack from the experimental literature, for which the model simulates complicated hysteresis behavior accurately. This illustrates the model's potential for analyzing existing cracks under earthquake loads, subject, however, to future calibration and validation of the model's predictive power. A compact vector-representation of the constitutive model is provided to aid implementation into any structural analysis software, for the eventual crack-based assessment of full-scale structures.