Modelling and simulation of spatially varying earthquake ground motions at sites with varying conditions

Kaiming Bi, Hong Hao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

171 Citations (Scopus)


In a flat and uniform site, it is reasonable to assume that the spatially varying earthquake ground motions at various locations have the same power spectral density or response spectrum. If an engineering site with varying soil conditions at different structural supports is considered, this assumption is no longer valid because of different local site amplification effect. This paper presents an approximate method to model and simulate spatially varying ground motions on the surface of an uneven site with non-uniform conditions at different locations in two steps. In the first step, the base rock motions at different locations are assumed to have the same intensity, and are modelled by a filtered TajimiKanai power spectral density function or other stochastic ground motion attenuation models. The base rock ground motion spatial variation is modelled by an empirical coherency loss function. The power spectral density functions of the surface motions on the site with multiple soil layers are derived based on the deterministic 1D wave propagation theory, neglecting the wave scattering on the uneven canyon surface, and assuming that the base rock motions consist of out-of-plane SH wave or in-plane combined P and SVwaves propagating into the site with an assumed incident angle. In the second step, a stochastic method to generate spatially varying time histories compatible with non-uniform spectral densities and a coherency loss function is developed to generate ground motion time histories on an uneven site. Two numerical examples are presented to demonstrate the proposed method. Each generated ground motion time history is compatible with the derived power spectral density at a particular point on the site or response spectrum corresponding to the respective site conditions, and any two of them are compatible with a model coherency loss function.

Original languageEnglish
Pages (from-to)92-104
Number of pages13
JournalProbabilistic Engineering Mechanics
Publication statusPublished - Jul 2012
Externally publishedYes


  • Ground motion simulation
  • Power spectral density function
  • Response spectrum
  • Spectral representation method
  • Wave propagation theory

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Civil and Structural Engineering
  • Nuclear Energy and Engineering
  • Condensed Matter Physics
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering


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