Validating the governing role of the pulse-to-interacting-system period ratio: seismic drift demands of soil–MDOF structure systems under recorded near-fault ground motions and realistic nonlinear soil–foundation models

Khoshnoudian and Ahmadi (2013) established, using idealized sinusoidal mathematical pulse models of forward-directivity and fling-step type applied to soil–MDOF systems with a Cone-model elastic half-space and bilinear shear-building superstructures, that the higher-mode contribution to interstory drift demands is governed by the pulse-to-interacting-system period ratio $T_p/T_{ssi}$ rather than the pulse-to-fixed-base ratio, and that forward-directivity pulses are more severe than fling-step pulses. Whether these conclusions transfer to recorded near-fault ground motions, nonlinear and flexible soil–foundation models (soil yielding, foundation uplift, embedment with kinematic interaction), component-level structural nonlinearity, and pulse period and duration parameter ranges beyond those adopted in the study has been only partially established: later studies used real records with single-degree-of-freedom superstructures or with different demand endpoints, while nonlinear soil–foundation studies used idealized pulses or non-pulse records. The open problem is to establish which dimensionless parameters govern near-fault seismic drift demands of realistic soil–MDOF systems — validating, revising, or replacing the idealized-pulse parametric law, including the forward-directivity-versus-fling-step severity ordering under recorded motions that contain genuine fling.

Background

Near-fault (near-field) ground motions, recorded close to a rupturing fault, differ from ordinary ground motions in that they can contain a large, coherent velocity pulse. Two source mechanisms produce such pulses. Forward directivity arises when the rupture front propagates toward the site and the slip direction aligns with it, concentrating seismic energy into a sharp, two-sided velocity pulse that is most pronounced in the fault-normal component. A fling step is the permanent tectonic ground offset across the fault, which appears in recordings as a one-sided displacement step accompanied by a unipolar velocity pulse, most pronounced in the fault-parallel component. The dominant period of such a pulse is the pulse period, $T_p$. When a structure is founded on deformable soil, the foundation translates and rocks relative to the free field, the system's fundamental period lengthens from the fixed-base period $T$ to a longer period of the coupled system, conventionally denoted $T_{ssi}$, and energy radiates into the soil; collectively these effects are called soil–structure interaction (SSI). A standard practical SSI idealization is the cone model, in which the soil beneath the foundation is replaced by frequency-independent springs and dashpots (a lumped-parameter model) approximating a homogeneous elastic half-space, making broad parametric studies cheap. Superstructures are commonly modeled as nonlinear multi-degree-of-freedom (MDOF) shear buildings — a stack of stories, each with a bilinear hysteretic force–displacement law — with the interstory drift ratio (relative displacement of adjacent floors normalized by story height) as the standard engineering demand measure. Because a building's dynamic response contains contributions from its higher vibration modes in addition to the fundamental mode, higher-mode effects denote the amplification of demands, especially in upper stories, beyond what an equivalent single-degree-of-freedom (SDOF) representation would predict. In SSI parametric studies the governing dimensionless parameters are conventionally the non-dimensional frequency (a structure-to-soil stiffness ratio), the aspect ratio of the superstructure (height to foundation radius, controlling foundation rocking), and the structural target ductility ratio (the prescribed maximum inelastic deformation). Combining these ingredients, Khoshnoudian and Ahmadi (2013) applied idealized sinusoidal pulse models of forward-directivity and fling-step type, scaled to a design spectrum, to soil–MDOF systems whose soil was represented by the cone model beneath a rigid circular foundation. They demonstrated that the contribution of higher modes to the response of the soil–structure system depends on the pulse-to-interacting-system period ratio $T_p/T_{ssi}$ rather than on the pulse-to-fixed-base period ratio $T_p/T$; that increasing target ductility brings first-mode domination; that SSI makes higher-mode effects more significant than for fixed-base structures; and that forward-directivity pulses activate higher modes more severely than fling-step pulses. Since the interacting system resonates when the pulse period matches its fundamental period, testing the governing-ratio law requires coverage of $T_p/T_{ssi}$ approaching and exceeding unity. The question this problem poses is whether their parametric conclusions — the controlling role of $T_p/T_{ssi}$, the amplification of higher-mode effects by soil–structure interaction, and the greater severity of forward directivity relative to fling step — survive the removal of these idealizations: recorded motions with complex, multi-peaked frequency content and extraction-based pulse periods; nonlinear, stratified, and flexible soil–foundation models with yielding, uplift, and embedment; component-level structural nonlinearity; and pulse period and duration parameter ranges beyond those adopted in the study.

Problem Statement

Determine whether the governing law established for idealized pulses — seismic drift demands and higher-mode participation of soil–MDOF structure systems controlled by the pulse-to-interacting-system period ratio $T_p/T_{ssi}$, with higher-mode effects more significant when soil–structure interaction is taken into account, and with forward-directivity pulses more severe than fling-step pulses — transfers to realistic conditions. The single scientific objective is to establish which dimensionless parameters govern the interstory drift demands of soil–MDOF systems when the idealizations of Khoshnoudian and Ahmadi (2013) are removed, specifically: (i) excitation by recorded near-fault ground motions with complex, multi-peaked frequency content, including motions containing genuine fling steps, with pulse periods identified by established extraction methods (wavelet-based or comparable time-domain procedures) rather than by idealized sinusoidal pulses; (ii) soil–foundation models with nonlinear and stratified soil behavior, flexible shallow foundations including soil yielding and foundation uplift, and embedment with kinematic interaction, in place of the elastic cone model under a rigid foundation; (iii) superstructure models with component-level nonlinearity, such as plastic-hinge softening and strength degradation, beyond bilinear story hysteresis; and (iv) pulse period and duration parameter ranges beyond those adopted in the 2013 parametric study, ensuring in particular coverage of $T_p/T_{ssi}$ approaching and exceeding unity (the interacting-system resonance regime). The problem is answered when it is established, with stated evidence and parameter coverage, whether each source conclusion — the controlling role of $T_p/T_{ssi}$, the SSI-induced amplification of higher-mode effects, and the directivity-versus-fling severity ordering — holds under these realistic conditions, and in what quantitative form. The three source conclusions are the independently refutable sub-claims of this one objective, and the condition classes (i)–(iv) jointly delimit the target realistic conditions rather than being four separately mandatory deliverables; a resolution therefore adjudicates each of the three conclusions and states which idealizations it removes, which it retains, and the parameter ranges it covers, since any residual idealization or uncovered range limits the scope of the verdict.

References

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