The effect of material and ground motion uncertainty on the seismic vulnerability curves of RC structure

Vulnerability curves are crucial for earthquake loss assessment, linking strong-motion shaking severity (intensity, peak ground parameters, or spectral ordinates) to the probability of exceeding performance limit states (serviceability, damage control, collapse prevention). These curves are integral to regional seismic risk and loss estimation, alongside seismic hazard maps, inventory data, and integration/visualization capabilities. This study focuses on deriving vulnerability curves for a reinforced concrete structure subjected to various ground motion sets, investigating the impact of material uncertainties and ground motion set selection. Additional aspects explored include ground motion duration, limit state definition, damping parameter selection, and statistical manipulation. The goal is to assess the relative influence of material properties and ground motion characteristics on the accuracy and reliability of vulnerability curves, without simplifying assumptions that might obscure the impact of the parameters under investigation. The study uses a three-story ordinary moment resisting reinforced concrete frame (OMRCF) previously subjected to shake-table testing to ensure accurate verification of analytical modeling.

Vulnerability function derivation methods vary significantly, influenced by factors such as ground motion sets, severity indices, limit states, structural damage data sources, modeling methods, analysis platforms, analysis methods, and uncertainty considerations. Vulnerability curves can be categorized into empirical (based on post-earthquake surveys), judgmental (based on expert opinion), analytical (based on simulated damage distributions), and hybrid (combining multiple data sources). Empirical curves, while realistic, often lack statistical viability and generalizability. Analytical curves offer broader applicability but are computationally intensive and limited by modeling capabilities. Previous analytical studies, such as those by Mosalam et al. (using SDOF systems), HAZUS (neglecting structural parameter influence), and Reinhorn et al. (using inelastic spectra), employed simplified methods due to computational constraints, resulting in approximations. This study utilizes inelastic dynamic response-history analysis to avoid these limitations.

The study employs a four-part vulnerability curve derivation process: structure selection, hazard definition, simulation method, and vulnerability analysis (Figure 1). A three-story OMRCOCF, representing a common structure type in the Mid-America region, is selected due to the availability of experimental data for model verification. Ultimate concrete strength and steel yield strength are considered random variables. The analytical model is validated against shake-table test results (Section 6). Inelastic dynamic response-history analysis using ZEUS-NL, a platform capable of handling material and geometric nonlinearities, is adopted. Multi-threading techniques significantly reduce computational time. Nine ground motion sets are used: three based on the a/v ratio (low, intermediate, high) and six artificial ground motions generated for Memphis, TN (Lowlands and Uplands soil profiles). Full combination of ground motion sets and material properties are simulated using Monte Carlo simulation. Limit states are defined based on the first yielding of steel, maximum element strength, and maximum confined concrete strain from adaptive pushover analysis. These are termed 'serviceability', 'damage control', and 'collapse prevention' limit states. The significant duration of strong ground motion is defined using the interval between 0.5% and 95% of the integral of the squared acceleration, velocity, and displacement, accounting for the energy distribution within the ground motion record. Scale factors for PGA are selected based on capacity spectrum method estimations, ensuring sufficient data for curve generation for each ground motion.

The analysis reveals significant differences in vulnerability curves across different ground motion sets (Figure 10), indicating a strong influence of ground motion characteristics on structural response. The discrepancy between curves increases for higher damage limits and with increasing ground motion intensity. The coefficient of variation (COV) of interstory drift also varies significantly among different ground motion sets (Figure 11). The study assesses the impact of material property variability by considering 10 concrete ultimate strengths and 10 steel yield strengths. Results demonstrate a small contribution of material variability to the overall variance of maximum interstory drift (ISDmax), especially at low PGA levels. The influence of material variability, represented by variations in concrete strength and steel yield strength, is less significant than the effects of ground motion characteristics (Figure 12, Figure 13). This is more clearly observed in Figure 13 (a-f) demonstrating the relationship between ISDmax and concrete/steel strength, at both low and high PGA levels, showing that the effect of material variability is minor compared to the effects of the ground motion. The effect of sample size is investigated using ground motion set U-1 with varying numbers of material property combinations (1, 10, 50, 100). The coefficient of variation shows minimal change with increasing sample size (Figure 14), further confirming the dominance of ground motion uncertainty. An SDOF system analysis (Figure 15) visually confirms the minimal impact of material variability on spectral displacement compared to the significant impact of ground motion set variation.

The findings highlight the importance of meticulous ground motion selection and scaling in vulnerability curve derivation. The relatively minor impact of material variability in this study, particularly at lower PGA levels, suggests that focusing efforts on accurately characterizing ground motion uncertainty may yield greater improvements in the accuracy and reliability of seismic vulnerability assessments for this type of RC structure. The use of inelastic dynamic response-history analysis minimizes approximations, providing a more realistic assessment of structural behavior. However, these findings are conditional on the assumption that the analytical model and methods selected reflect the real-world behavior of the structure and material properties.

This study demonstrates the significant effect of ground motion variability on seismic vulnerability curves compared to the comparatively small influence of material property uncertainty, particularly for the specific three-story RC structure examined. Careful ground motion selection and scaling are crucial for reliable vulnerability assessments. Future research could explore the impact of material variability in more complex or irregular structures with potential for spatially uncorrelated material distributions that might lead to different failure modes. Investigating alternate measures of structural damage beyond interstory drift in such cases would be beneficial for expanding the applicability of this work.

The conclusions are specific to the analyzed three-story RC frame and may not generalize to all low-ductility RC structures. The study focuses on aleatory uncertainty (randomness in material and ground motion); epistemic uncertainty (lack of knowledge) is not considered. The definition of limit states and structural response vary with structural configuration, limiting the general applicability of the derived vulnerability curves beyond the specific structure class considered.