Numerical models of RC elements and their impacts on seismic performance assessment

Performance-based seismic design necessitates evaluating a structure's behavior under various earthquake intensities, often involving inelastic structural response. Nonlinear analyses, such as static pushover or nonlinear time history analysis, are crucial for assessing this inelastic behavior and verifying intended failure mechanisms. However, accurately modeling inelastic structural elements and performing nonlinear analyses remain challenging. Surveys reveal a lack of adequate guidelines for modeling nonlinear structural elements, leading to inconsistencies in analysis results, even when provided with identical input data (structural details and ground motions). This research addresses this gap by systematically evaluating the applicability of commonly available distributed plasticity models for RC frame elements.

Existing literature offers various nonlinear models for RC frame elements, ranging from early lumped-spring models with calibrated hysteretic rules to more recent distributed plasticity models (finite-length hinge models, fiber-section models, and finite element models). While guidelines exist (e.g., ASCE 41, Berry and Eberhard's work), a comprehensive comparative assessment of their accuracy and influence on seismic performance assessment is lacking. Previous studies have focused on specific model comparisons or aspects of RC element behavior, leaving a need for a broader, systematic evaluation encompassing various model types and considering their implications for seismic design.

The study evaluates five representative distributed plasticity models: 1) OpenSees force-based beam-column (OS-FBBC) element; 2) OpenSees plastic hinge integration method (OS-PHIM) element; 3) VecTor2 modified compression field theory (VT2-MCFT) continuum element; 4) VecTor5 MCFT-based frame element (VT5-MCFT); and 5) Response-2000 section-analysis-based element (R2K). The models' accuracy is assessed using 320 quasi-static experimental results from the PEER column database, encompassing both rectangular and circular columns. Three accuracy measures are employed: peak force ratio (RF), initial stiffness ratio (RK), and energy dissipation capacity ratio (RE). These measures are evaluated against the shear force demand-capacity ratio (Is) to understand the impact of failure mode. A parametric study involving a cantilever RC column with varying natural periods (0.1, 0.5, 1.0, and 2.0 s) subjected to 15 ground motions is conducted using OS-FBBC and VT2-MCFT to investigate the influence of model choice on dynamic response.

The comparison with quasi-static cyclic tests reveals a strong dependence of model accuracy on the shear force demand-capacity ratio (Is). For flexure-critical columns (Is < 0.5), all five models accurately predicted peak strengths (mean RF: 0.95–1.19) and energy dissipation capacities (mean RE: 1.01–1.49), although all overestimated initial stiffness (mean RK: 1.33–1.81). For shear-critical columns (Is ≥ 1), VT2-MCFT and VT5-MCFT exhibited superior accuracy in capturing peak strengths and hysteretic behavior; OS-FBBC and OS-PHIM significantly underestimated these aspects. The parametric study showed that for long-period structures (T ≥ 1.0 s), the choice of numerical model had a minimal impact on the global response. However, for short-period shear-critical structures, the choice significantly affected the predicted global response. OS-FBBC underestimated the response of shear-critical columns with short periods. Detailed statistical parameters (mean, median, percentiles) for each accuracy measure are provided as functions of Is (Figures 8-10).

The findings highlight the importance of considering the shear force demand-capacity ratio and structural period when selecting a numerical model for seismic performance assessment. The superior accuracy of MCFT-based models (VT2-MCFT, VT5-MCFT) in shear-critical scenarios underscores the necessity of explicitly capturing shear deformation and failure in such cases, especially for short-period structures. The insensitivity of global response to model choice in long-period structures aligns with the equal-displacement rule. The overestimation of initial stiffness by all models suggests caution when using linear analysis; however, this effect is less critical in nonlinear analyses due to material nonlinearity. The study's focus on models requiring primarily physical properties, without empirical calibration, enhances its practical relevance for practicing engineers.

The study provides valuable insights for selecting appropriate numerical models for RC elements in seismic performance assessment. The recommendations emphasize the importance of considering the shear force demand-capacity ratio and structural period, favoring more sophisticated models for shear-critical, short-period structures. For flexure-critical structures or long-period shear-critical structures, computationally efficient models are deemed suitable. Further research should focus on refining hysteretic damping modeling in inelastic analysis and conducting more dynamic experiments to improve the accuracy of numerical predictions.

The study's reliance on quasi-static cyclic tests may not fully capture the complexities of dynamic behavior under earthquake loading. The limited number of ground motions in the parametric study could influence the generalizability of the findings. Further investigation into the influence of other parameters (e.g., material properties, reinforcement details) on model accuracy is recommended.