Along the west coast of the United States, reinforced concrete core wall systems are commonly selected as seismic force resisting systems for tall buildings. During strong ground shaking, core wall systems are intended to dissipate energy by yielding of coupling beams, followed by flexural yielding at the wall base. Although the wall behavior is governed by flexure, the wall design is often governed by shear, as the walls experience high shear demands, usually up to the ACI318-11 code limiting shear stress of 8∙√(f'c ) psi over a significant wall height. The high shear demands are due to a lack of redundancy in tall buildings, as the wall lengths are limited to the perimeter of the elevator core.
Design of tall buildings is typically conducted using performance-based design procedures recommended by Los Angeles Tall Buildings Structural Design Council (LATBSDC, 2014) or Pacific Earthquake Engineering Research Center Tall Buildings Initiative (PEER TBI, 2010). Provisions in these two documents recommend shear design per acceptance criterion Fuc ≤ κi ϕ Fn,e, where Fuc is 1.5 times the mean shear demand resulting from a suite of ground motions, Fn,e is the nominal strength computed from expected material properties, κi is the risk reduction factor based on risk categories, and ϕ is the uncertainty in Fn,e. The 1.5 factor applied to the mean shear demand is referred to as the demand factor, γ. Although shear failure can be fatal due to its sudden and brittle nature, the reliability of this shear design acceptance criterion has not yet been thoroughly researched.
To assess seismic reliability of structural wall shear design acceptance criterion, dispersion in structural responses, specifically for shear demands, must be quantified. Dispersion in structural responses (referred to as engineering demand parameters, EDPs) primarily results from three sources, namely, record-to-record (RTR) variability, modeling and/or model parameter uncertainties, and design uncertainties. To study how these uncertainties contribute to dispersion in tall building EDPs, eleven input random variables (expected to be the most relevant) were selected. Specifically, uncertainties in scaled ground motions, unconfined and confined concrete compressive strengths, reinforcing steel yield strength, shear modulus, coupling beam strength, seismic mass, dead and live gravity loads, damping, and shear wall design variations were considered. A series of 20 and 30-story nonlinear models for reinforced-concrete core wall systems were built and Monte Carlo simulations were utilized to assign values for random variables and to perform nonlinear response history analyses. Analyses were performed at five seismic hazard levels corresponding to return periods of 25, 43, 475, 2495, and 4975 years, until an adequate convergence in dispersion measure was reached. Selected EDPs (base shear, roof drifts, coupling beam rotations, and structural wall boundary element axial strains) were evaluated and statistical parameters were quantified. Results show that dispersion in EDPs was the largest for coupling beam rotations and shear wall axial strains. Total dispersion, measured in coefficient of variation, ranged between 0.15 and 0.85, considering all EDPs at all five hazard levels. The relative contributions from RTR variability and model parameter/design uncertainties accounted for 72-98% and 2-28% of the total dispersion, respectively. Fitted probability distributions were either normal or lognormal for all EDPs and using correlated random variables for model parameter uncertainties resulted in changes in dispersion of -6% to 5% compared with using independent random variables.
Using the measured dispersion values, the current recommendations in Los Angeles Tall Buildings Structural Design Council (LATBSDC, 2014) were reviewed for shear design of structural walls in tall reinforced-concrete core wall buildings (Fuc ≤ κi ϕFn,e). Both closed-form solutions using full distribution methods and Monte Carlo simulation results were used to assess reliability of the current shear design acceptance criterion. Statistical parameters were established for shear demand by using measured dispersion values from nonlinear response history analyses of tall reinforced-concrete core wall buildings, and experimental test results from shear-controlled walls were used to establish statistical parameters for shear capacity. A range of reliability results were computed for various shear demand and capacity statistical parameters. The current shear design acceptance criterion using γ=1.5 and ϕ=1.0 resulted in 94.2% reliability for structural walls with f’c < 8ksi and 96.5% reliability for structural walls with f’c ≥ 8ksi. Minimum values for the demand factor, γ, are tabulated for various risk categories defined per ASCE7-10.
Results suggest that the use of ϕ=1.0, along with appropriate expected material properties, produce an acceptable probability of failure. Per Pacific Earthquake Engineering Center Tall Buildings Initiative (PEER TBI, 2010), the recommended use of ϕ=0.75 appears excessively conservative. However, due to a lack of experimental tests on possible shear strength degradation in walls that yield in flexure, limitations on curvature ductility or plastic rotation demands are recommended in the plastic hinge regions. Moreover, since this study is based on variations of results from two prototype tall core wall buildings; to reduce the potential conservatism in the current guidelines, a comprehensive reliability study including a larger population of tall buildings is further needed to calibrate γ and ϕ factors.