Predictive design relationships for near-fault pulse amplification of seismic demands in inter-storey-isolated buildings: regression of amplification and displacement-correction factors on bearing period, damping, and substructure flexibility, and the role of pulse arrival timing

Inter-storey isolation (ISI) places seismic isolation bearings at an intermediate storey so that the upper storey block is isolated while the lower storey block behaves as a massive tuned mass damper. Saha and Mishra (2021) showed that near-fault pulse-type ground motions amplify ISI design demands — with 84th-percentile amplification factors up to about 3.3 for upper-block displacement and roughly three-fold increases in bearing hysteretic energy — and that the FEMA-450-type closed-form displacement estimate requires an empirical correction factor $C_r$ that they could tabulate only per configuration. The surviving open problem is: design-usable predictive relationships for pulse-induced amplification — above all the regression of $C_r$ (and of amplification factors) as continuous functions of bearing period, effective damping, and upper/lower-substructure relative flexibility, statistically validated over an expanded frame/bearing/record database — together with a systematic account of how pulse arrival timing (early versus late) governs mobilization of the isolation/tuned-mass-damper mechanism and the resulting amplification. A 2025 follow-up by the first author delivered empirical prediction equations for inter-storey drift and floor-acceleration demands, partially resolving one item of the source's future-work list, but the displacement-correction regression and the pulse-timing question remain unaddressed in the literature to date.

Background

Seismic isolation decouples a building from the horizontal components of ground shaking by interposing flexible, energy-dissipating bearings between the structure and the ground. In inter-storey isolation (ISI), a strategy proposed for taller buildings, the isolation layer is moved from the base to an intermediate storey: the bearings separate an upper storey block (USB) from a lower storey block (LSB), so that the USB is isolated from earthquake input while the LSB, driven through the bearings, behaves like a tuned mass damper (TMD) — a vibration-control device in which a mass attached through springs and dampers counteracts structural motion — here a 'non-conventional TMD' whose mass ratio (USB mass to LSB mass) can approach 100%, far above the few-percent ratios of classical TMDs. The bearings most studied for ISI are high-damping rubber bearings (HDRBs), laminated rubber-steel composites whose horizontal force-deformation response exhibits pre-yield stiffness, post-yield hardening, and a secondary stiffening branch at large shear strains.

Near-fault ground motions produced by forward directivity — rupture propagating toward the site — contain a coherent long-period velocity pulse, typically with a period of one to several seconds, whose energy can coincide with both the isolation period and the natural periods of tall buildings; pulse-like records are conventionally identified, and their pulse period $T_p$ extracted, with Baker's wavelet-based classification algorithm (Baker, 2007). For conventional base isolation it has long been known that such pulses degrade isolation performance; whether the mass partitioning and lower-block flexibility of ISI filter out or instead transmit and amplify the pulse energy was, before the source study, unquantified.

Saha and Mishra (2021) addressed this with 2,744 nonlinear time-history analyses of six steel special moment-resisting frame configurations (designated B1–B4, with storey-partition variants), four HDRB parameterizations (HDRB-A to HDRB-D), and suites of 25 near-fault pulse records drawn from Baker's database against a comparable near-fault non-pulse suite, amplitude-scaled to design-basis and maximum-considered-earthquake levels. They reported 84th-percentile amplification factors — the ratio of the 84th-percentile response under the pulse suite to that under the non-pulse suite — of roughly 1.7 to 3.3 for peak floor displacement at the top of the USB, and about three-fold increases in bearing hysteretic energy dissipation. They further showed that the closed-form isolation-bearing displacement estimate used in the NEHRP provisions (FEMA-450), $D_d=(g/4\pi^2)(S_d T/B)$ — with $g$ the gravitational acceleration, $S_d$ the 5%-damped spectral acceleration ordinate at 1 s, $T$ the bearing vibration period, and $B$ the damping-reduction coefficient for the bearing's effective viscous damping — systematically underestimates the simulated pulse-driven bearing displacement in ISI configurations, and introduced an empirical correction factor $C_r=D_{ISI}/D_d$ (the ratio of simulated peak ISI bearing displacement to the closed-form estimate), tabulated per frame/bearing combination at its median and 84th percentile. Raising the USB/LSB mass ratio toward 100% and the bearing effective damping toward about 20% were identified as the principal mitigation levers.

The same authors' companion studies extended intensity-measure-based demand prediction for ISI under near-fault motions (a vector-valued intensity measure, 2021) and consequence modeling (fragility, expected annual loss, and resilience, 2022). A 2025 follow-up by the first author proposed empirical prediction equations for the inter-storey drift ratio and peak floor acceleration of ISI frames under near-fault pulse motions, built on recorded motions and a calibrated equivalent mathematical pulse model, with pulse amplitude, pulse period, oscillatory characteristics, phase angle, moment magnitude, and source distance as predictor concepts and a coefficient of determination above 0.80. No published work yet provides the design-usable regression of the displacement-correction factor — or of pulse amplification generally — on the isolation design parameters themselves, and no systematic treatment of pulse arrival timing for ISI systems exists; timing effects have so far been studied only for fixed-base single-degree-of-freedom systems and reinforced-concrete frames.

Problem Statement

Establish design-usable predictive relationships for near-fault pulse-induced amplification of seismic demands in inter-storey-isolated (ISI) buildings, as left open by Saha and Mishra (2021) and not resolved by subsequent literature. As used here, 'design-usable' means a relationship expressed directly in the isolation design parameters, accompanied by an explicitly reported validated range and a quantitative accuracy or dispersion measure, and adequate to replace configuration-specific tabulated values in the corresponding design check. The problem has two jointly necessary components serving one objective — a validated, design-usable predictive account of pulse amplification for ISI buildings — each of which must be statistically validated over an explicitly defined parameter and record space:

(1) Predictive regression relationships, continuous in the principal isolation design parameters — bearing (isolation) period $T$, effective damping $\beta$, and a measure of relative flexibility between the upper storey block (USB) and the lower storey block (LSB), such as the ratio of their effective periods or stiffnesses — for the amplification of design demands under pulse-type near-fault motions relative to non-pulse near-fault motions. The mandatory members of component (1) are the empirical correction factor $C_r=D_{ISI}/D_d$ that converts the FEMA-450-type closed-form displacement estimate $D_d$ into the pulse-amplified bearing displacement demand of ISI configurations, together with the corresponding amplification-factor regressions for the other design demands quantified by the source study — the peak floor displacement at the top of the USB and the bearing hysteretic energy. The relationships must be statistically validated over a database of building frames, bearing designs, and pulse/non-pulse record suites that exceeds the source study's scope in frame/bearing breadth and record count — the source study's six frame configurations, four HDRB parameterizations, and roughly 25-record suites being explicitly acknowledged by its authors as insufficient for generalization — and the validated parameter ranges and a quantitative goodness-of-fit or dispersion measure must be reported.

(2) A systematic account of pulse arrival timing — early- versus late-arriving pulses — covering how timing governs mobilization of the isolation/non-conventional-tuned-mass-damper mechanism and the resulting amplification of the design demands, carried far enough to yield design-useful criteria rather than illustrative examples.

The source's further extensions — multi-directional excitation, alternative bearing technologies, and combined pulse-plus-fling-step hazards — are recorded as desirable future work beyond the scope of this problem; likewise, the drift- and floor-acceleration demand prediction equations already published for ISI under near-fault pulses (Saha, 2025) do not by themselves resolve component (1), which requires regression relationships continuous in the isolation design parameters.

References

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2. Arijit Saha (2025). Seismic Demand Prediction Models for the Inter-Story Isolated Building Frame Subjected to Near-Fault Pulse-Type Ground Motions. The Structural Design of Tall and Special Buildings 34(17):e70103. DOI: 10.1002/tal.70103. https://doi.org/10.1002/tal.70103
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