PSI - Issue 78

Alvaro Lopez et al. / Procedia Structural Integrity 78 (2026) 807–814

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3. Loading Protocol and Ground Motion Selection All specimens were tested under quasi-static, displacement-controlled loading using three distinct protocols: (1) a conventional symmetric cyclic sequence, (2) a long-duration subduction history (LD), and (3) a spectrally equivalent short-duration history (SD). A conventional symmetric three-cycle load history was first applied, as is standard for evaluating the seismic performance of structural components. However, prior studies have demonstrated that such protocols do not accurately replicate the demands imposed by real earthquakes, which typically involve numerous small inelastic cycles and only a few large cycles prior to collapse (Kunnath et al., 1997; Ou et al., 2013). The load history began with elastic cycles at increments of the analytically predicted first yield displacement ( ∆′ = 5.5 ): (1/4) Δ ′ , (1/2) Δ ′ , (3/4) Δ ′ and Δ ′ . This yield displacement was calculated from the relationship ∆ = ℎ 2 /3 , where ℎ = 1750 is the height of the free cantilever wall, and is the estimated yield curvature (Massone et al., 2012). The experimental first yield displacement is determined as the average displacement at the onset of first yield in both push and pull directions. The equivalent yield displacement, used to define displacement ductility levels ( Δ1 =1×Δ ) , was computed as Δ =Δ ′ ( / ′ ) . Testing then proceeded with three symmetric cycles at increasing ductility levels: 1, 1.5, 2, 3, 4, 6, 8, 10, 12, etc. A 10% increase was applied to account for loading frame flexibility, based on prior calibration tests. Nonlinear time-history protocols were developed to reproduce realistic inelastic demand. A library of subduction zone records — from the 1985 Valparaíso, 2007 Sumatra, 2010 Maule and 2011 Tohoku earthquakes, all with epicentral distances exceeding 100 km — was supplemented by far-field crustal events selected from the FEMA P695 suite including events with moment magnitudes above 6.5 and distances exceeding 10 km from the fault (FEMA P695, 2009). Significant duration measure (5−75) , the interval between 5 % and 75 % of cumulative Arias Intensity, was adopted as the duration metric (Trifunac & Brady, 1975), and motions with (5−75) ≥ 25 seconds were classified as long-duration (Chandramohan et al., 2016; Foschaar et al., 2012). To isolate duration effects, sixty long-/short-duration record pairs were identified by minimizing the sum of squared errors between their geometric-mean spectra over periods 0.05 – 6 s (Chandramohan et al., 2016). Each acceleration record was scaled to match the elastic spectral demand of the standard protocol at a target ductility of =3. Top-wall displacement histories were then extracted from OpenSees NLTHA runs and amplitude-adjusted to preserve the number and amplitude of inelastic cycles, directional symmetry, and peak-to-peak displacements. The three loading histories — standard (W1-ST), short-duration NLTHA (W2-SD) and long-duration NLTHA (W3-LD) — were applied to the respective specimens. The actuator displacement commands are illustrated in Fig. 2. 4. Numerical Modeling and Parameter Calibration The RC walls were modeled in OpenSees (McKenna, 2011) using ForceBeamColumn elements with fiber sections to capture the nonlinear axial behavior of concrete and steel. Concrete fibers employed the Concrete04 material, while steel reinforcement was modeled with a trilinear HystereticMaterial for cyclic behavior. Shear deformations were included through an elastic material and coupled via the Section Aggregator command (Pugh et al., 2015). Bond-slip effects at the wall base were incorporated using a zero-length section with Bond_SP01 material (Zhao & Sritharan, 2007), given evidence that slip may contribute up to 30% of total lateral displacement (Tran & Wallace, 2015). Model calibration was based on five experimental tests from Tran (2015). A constrained optimization algorithm in MATLAB (2019) was used to calibrate the hysteretic parameters governing cyclic degradation and pinching. The best fitting parameters are presented in Table 1.

Table 1. Selected parameter values for Hysteretic Material. Parameters PinchX PinchY Damage1 Damage2 Beta Value 0.2 0.6 0.00275 0.075 0.275