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

Within performance-based seismic design, structures are expected to exhibit inelastic behavior under design-level earthquakes, necessitating reliable nonlinear analysis to confirm intended failure mechanisms. Despite widespread use of nonlinear time-history analysis in practice, clear modeling guidelines remain limited, and diverse element formulations lead to varied accuracy and computational demands. Blind prediction contests have revealed large dispersion in predicted inelastic responses, underscoring the need for systematic guidance. This study evaluates the applicability and accuracy of commonly used distributed plasticity models for RC frame elements by comparison with a large set of quasi-static tests and by examining the influence of model choice on inelastic dynamic response. The central research questions are: (1) How accurate are different RC element models across failure modes? (2) How does model choice affect predicted seismic responses as a function of structural period and shear demand-capacity? (3) What guidance can be provided to practicing engineers for efficient and reliable modeling?

Prior guidelines and studies include ASCE 41, which prescribes simplified multi-linear backbone curves based on reinforcement ratios and failure modes; Berry and Eberhard’s assessment of lumped vs. distributed plasticity models across 37 tests; Deierlein et al.’s synthesis of nonlinear frame element types and modeling guidance; and Rodrigues et al.’s comparison of fiber models for biaxial RC column behavior. Numerous modeling approaches exist, from lumped plasticity with calibrated hysteretic rules to distributed plasticity fiber and finite element models, each with specific assumptions (plane sections, uniaxial material behavior, confinement models) and varying abilities to capture shear deformation/failure, bond-slip, and degradation. Despite this body of work, a comprehensive comparative assessment of accuracy across many tests and of the impact on seismic performance assessment remained incomplete, motivating the present study.

Five distributed plasticity modeling approaches are evaluated using consistent, physically based input parameters: - OS-FBBC: OpenSees force-based beam-column fiber element with uniaxial material models (Concrete02 with confinement by Mander et al.; Steel02 Giuffré-Menegotto-Pinto with isotropic hardening). Five integration points are used; section discretization for rectangular sections: 20 core fibers + 2 cover fibers in each local direction; for circular sections: 20 circumferential fibers, 10 radial core, 1 radial cover. Only elastic shear deformation is included via a shear spring (K_shear = GA_g/(2(1+ν)L)). No explicit nonlinear shear failure. - OS-PHIM: OpenSees plastic hinge integration method element with elastic midspan and finite-length plastic hinges at ends. Same section and material models as OS-FBBC within hinges. Plastic hinge length l_p/h determined by l_p/h = [0.3 + P/P_o − A_s/A_g − 0.1](L/h) + 0.25 ≥ 0.25. Elastic shear deformation included; no explicit nonlinear shear failure. - VT2-MCFT: VecTor2 2D continuum finite element using Modified Compression Field Theory (MCFT). Concrete modeled with averaged stress-strain, rotating smeared cracks; reinforcement as truss elements; transverse reinforcement smeared. Default material models include compression base curves (Hognestad/Popovics), modified Park-Kent post-peak, Vecchio-1992 compression softening, Bentz-2003 tension stiffening, Mohr-Coulomb cracking, etc. Mesh with rectangular elements (height/width < 2), ≥10 elements transversely. Axial force and cyclic displacement applied via rigid elements to avoid local concentrations. Captures shear deformation and failure. - VT5-MCFT: VecTor5 frame element coupling flexure and shear at section level using MCFT. Global frame analysis iteratively coupled with sectional analyses subdividing the section into 30–40 layers; assumes plane sections for longitudinal strain, parabolic shear strain distribution; discrete longitudinal bars, smeared transverse reinforcement. Default material models as in VT2. - R2K: Response-2000 sectional analysis (monotonic only) with MCFT-based shear integration. Concrete model Popovics/Thorenfeldt/Collins; compression softening Vecchio-Collins (normal strength) or Porasz-Collins (very high strength); Bentz tension stiffening; steel with elastic-plastic-hardening. Includes yield penetration at the loading block via D_p = 0.022 σ_s d_b. Modeling choices avoid heavy calibration (e.g., bond-slip explicitly modeled only in R2K per recommendations; tension stiffening included in MCFT-based models but not in OS models). Validation dataset: 320 PEER RC column cyclic tests (232 rectangular, 88 circular) with reported equivalent cantilever shear force vs. tip displacement histories and specimen details. Statistics: depths (rect.: 152–914 mm, mean 288 mm; circ.: 152–1520 mm, mean 431 mm), aspect ratios (means ≈3.44, 3.80), axial load ratios (mean 0.26 rect., 0.12 circ.), longitudinal and transverse steel ratios. Accuracy measures defined: - Peak strength ratio R_F = F_cal/F_exp (both directions) - Initial stiffness ratio R_K = K_cal/K_exp using secant stiffness at 0.1% drift - Energy dissipation capacity ratio R_E = E_cal/E_exp over the cyclic history Results are binned by shear force demand-capacity ratio I_s = M/(V L) computed per CSA A23.3: I_s < 1 flexure-dominated; I_s > 1 shear-critical. Box plots summarize mean, median, percentile, and spread per bin. Computational effort comparison performed for representative flexure- and shear-critical columns, reporting number of elements/nodes, displacement steps, and wall-clock times on a standard desktop. Parametric dynamic study: Two columns (I_s = 0.59 flexure-critical; I_s = 0.93 near shear-critical) analyzed as SDOF cantilevers with assigned lumped masses tuned to achieve T = 0.1, 0.5, 1.0, 2.0 s, ensuring equal elastic seismic demand between models. Constant axial load maintained. Subjected to 15 ground motions (some scaled) spanning intensity levels (records and scale factors tabulated). Compare peak top displacements versus spectral displacement for OS-FBBC and VT2-MCFT across 240 nonlinear time-history analyses (2 models × 4 periods × 2 columns × 15 motions).

- Energy dissipation capacity (R_E): For flexure-dominated specimens (I_s ≈ 0–0.25), mean R_E: OS-FBBC 1.23 (SD 0.44), OS-PHIM 1.22 (0.52), VT2-MCFT 1.01 (0.27), VT5-MCFT 1.16 (0.38). As I_s increases toward and above 1, OS-FBBC and OS-PHIM increasingly overpredict dissipated energy (up to ~5× when I_s > 1) due to lack of shear degradation modeling. VT2-MCFT remains within ~0.81–1.30 across I_s bins. - Peak strength (R_F): For 0 < I_s ≤ 0.5, all models predict peak strength well (mean R_F ~0.95–1.19; SD ~0.13–0.26). For I_s ≥ 1.0, OS-FBBC and OS-PHIM overestimate peak strength (mean R_F ≈ 1.33 and 1.26, unconservative). MCFT-based models perform better: VT2-MCFT ≈ 0.95, VT5-MCFT ≈ 1.13, R2K ≈ 0.86. - Initial stiffness (R_K): All models overestimate initial stiffness. For flexure-dominated cases, mean R_K ≈ 1.33–1.81; for I_s > 1, mean R_K ≈ 2.35–3.35 across models. Overestimation has limited impact on nonlinear global response where cracking/yielding dominate, but is critical if using elastic analyses. - Sample comparisons: For a shear-critical column (I_s = 0.93), OS-FBBC/OS-PHIM fail to capture observed strength/stiffness degradation; VT2-MCFT and VT5-MCFT match hysteresis more accurately; R2K captures initial stiffness and peak strength but cannot produce full cyclic loops. - Computational effort (example columns): Flexure-critical: OS-FBBC 15 s; OS-PHIM 13 s; VT2-MCFT 2870 s; VT5-MCFT 898 s; R2K 4 s. Shear-critical: OS-FBBC 17 s; OS-PHIM 14 s; VT2-MCFT 2080 s; VT5-MCFT 514 s; R2K 4 s. VT2-MCFT is orders of magnitude slower due to large meshes (e.g., 792 nodes) vs. frame models (2–9 nodes). - Dynamic parametric study: For flexure-critical columns (I_s = 0.59), OS-FBBC and VT2-MCFT produce similar peak displacements across T = 0.1–2.0 s. For shear-critical columns (I_s = 0.93), differences are significant at short periods (T = 0.1, 0.5 s), with OS-FBBC underestimating response relative to VT2-MCFT; differences diminish at longer periods (T = 1.0, 2.0 s), consistent with the equal-displacement rule.

The study addresses the core modeling question by quantifying how element model assumptions interact with failure mode to affect predicted cyclic and dynamic responses. When behavior is flexure-dominated, fiber-section models with uniaxial materials (OS-FBBC, OS-PHIM) reproduce peak strengths and energy dissipation adequately and with high computational efficiency. As shear demand approaches or exceeds capacity (I_s → 1 or >1), models lacking explicit shear deformation/failure (OS-FBBC, OS-PHIM) overpredict strength and energy dissipation and produce unconservative assessments; MCFT-based models that integrate shear (VT2-MCFT, VT5-MCFT) capture degradation and hysteretic behavior more realistically. In dynamic response, model choice matters most for short-period, shear-critical systems where nonlinear shear mechanisms dominate cycle-by-cycle response; here, simplified fiber models underestimate displacements. For longer periods, the global peak response is less sensitive to hysteretic details, and computationally efficient models may suffice provided system stability is not compromised by shear-critical components carrying significant gravity load. The consistent overestimation of initial stiffness by all models suggests caution when using linear elastic analyses, but has limited effect on nonlinear response due to rapid stiffness degradation after cracking/yielding. These findings align with mechanics-based expectations and provide actionable guidance on selecting model fidelity commensurate with failure mode and dynamic characteristics, balancing accuracy and computational cost.

- The applicability of five nonlinear RC element modeling approaches was assessed against 320 quasi-static cyclic tests and through 240 nonlinear time-history analyses. Failure mode, quantified by shear force demand-capacity ratio I_s, governs model accuracy. - Flexure-critical elements (I_s < 0.5): All models accurately predict peak strengths (mean R_F ≈ 0.95–1.19) and energy dissipation (mean R_E ≈ 1.01–1.49), though all overestimate initial stiffness (mean R_K ≈ 1.33–1.81). Computationally efficient fiber-section models are suitable regardless of period. - Shear-critical elements (I_s ≥ 1): MCFT-based VT2-MCFT and VT5-MCFT best capture hysteretic behavior; fiber-section models without explicit shear mechanisms overestimate strength and energy and are unconservative. - Dynamic response sensitivity: For short-period, shear-critical systems, accurate shear modeling materially affects peak response; for long-period systems (T ≥ 1.0 s), differences diminish. - Practical guidance: Use models that capture shear deformation/failure (e.g., MCFT-based elements or fiber models augmented with shear springs/aggregated shear sections) for shear-critical, short-period cases; fiber-section models may be used for flexure-critical cases or shear-critical long-period systems where stability is not jeopardized. Reduce stiffness when performing elastic analyses. - Contributions include statistical accuracy parameters per model, enabling their use in probabilistic seismic assessments. Future work: More dynamic experiments on RC elements and improved modeling of hysteretic damping are needed to validate predictions up to collapse and refine guidance.

- Shear behavior: OS-FBBC and OS-PHIM include only elastic shear deformation; nonlinear shear deformation and failure are not modeled, leading to inaccuracies for shear-critical cases. - Bond-slip and end effects: Explicit bond-slip/strain penetration was not modeled in OS-FBBC/OS-PHIM/VT2/VT5; only R2K included yield penetration per Bentz. This may affect initial stiffness and energy dissipation predictions. - R2K cyclic limitation: Response-2000 provides monotonic sectional response only; full cyclic hysteresis cannot be simulated, limiting its validation scope to peak strength and initial stiffness. - Dataset scope: Validation focused on cantilever columns with available shear vs. displacement data; local strain/crack distributions were not assessed. Generalization to other element types (e.g., beams, walls) and boundary conditions requires caution. - Modeling parameter choices: Mesh densities, integration points, and convergence criteria were selected for reasonable accuracy rather than optimized computational efficiency; times reported are indicative, not absolute. - Damping modeling: Hysteretic damping representation in inelastic analyses remains uncertain; study did not calibrate or vary damping models extensively. - Material model assumptions: OS models excluded tension stiffening; MCFT-based models included it by default, potentially contributing to differences in stiffness/energy predictions.