Concept of Asynchronous Multi-Point Seismic Excitation as an Equivalent of Incident Surface Rayleigh Wave

Rayleigh surface waves play a significant role in the seismic impact on extended and high-rise buildings, inducing substantial inertial effects and internal forces. However, modern approaches to modeling the seismic performance of buildings often neglect the wave nature of the surface-wave propagation, which may lead to underestimation of the dynamic response of structures. Therefore, it is relevant to develop engineering methods that can correctly reproduce the spatiotemporal structure of the Rayleigh-wave field in computational models.

Purpose: The aim is to develop and theoretically substantiate the concept of replacing the displacement field of incoming Rayleigh surface wave with an equivalent asynchronous multipoint (multi-support) kinematic excitation applied to the building supports. Measurement of the main parameters and design of algorithm for practical implementation in standard software.

Methodology: The study is based on solving Navier equations for a linear-elastic isotropic half-space. The pure temporal-shift property of the Rayleigh-wave field is utilized for the free surface. A dimensionless asynchrony parameter is introduced, relating the building geometry, the wave phase velocity, and the dire of the wave incidence. The applicability of this approach is evaluated as well as the error of the plane-wave approximation, and the influence of wavefront curvature are analyzed.

Research findings: An engineering formulation is proposed and rigorously justified that allows to replace the continuous Rayleigh surface-wave field by a set of kinematic excitations at the building supports with deterministic time shifts. The key result is the introduction of the asynchrony parameter, which serves as a criterion for distinguishing between the synchronous and substantially asynchronous excitation. An upper bound for the influence of wavefront curvature is obtained, defining the applicability limits of the equivalent replacement.

Practical implication: The developed approach provides a correct account for the wave incidence direction and building dimensions, as well as the computational efficiency by generating excitations at all supports from a single baseline record.

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