Use of exact solutions of wave propagation problems to guide implementation of nonlinear seismic ground response analysis procedures

Annie O.L. Kwok, Jonathan P. Stewart, Youssef M.A. Hashash, Neven Matasovic, Robert Pyke, Zhiliang Wang, Zhaohui Yang

Research output: Contribution to journalArticlepeer-review


One-dimensional nonlinear ground response analyses provide a more accurate characterization of the true nonlinear soil behavior than equivalent-linear procedures, but the application of nonlinear codes in practice has been limited, which results in part from poorly documented and unclear parameter selection and code usage protocols. In this article, exact (linear frequency-domain) solutions for body wave propagation through an elastic medium are used to establish guidelines for two issues that have long been a source of confusion for users of nonlinear codes. The first issue concerns the specification of input motion as "outcropping" (i.e., equivalent free-surface motions) versus "within" (i.e., motions occurring at depth within a site profile). When the input motion is recorded at the ground surface (e.g., at a rock site), the full outcropping (rock) motion should be used along with an elastic base having a stiffness appropriate for the underlying rock. The second issue concerns the specification of viscous damping (used in most nonlinear codes) or small-strain hysteretic damping (used by one code considered herein), either of which is needed for a stable solution at small strains. For a viscous damping formulation, critical issues include the target value of the viscous damping ratio and the frequencies for which the viscous damping produced by the model matches the target. For codes that allow the use of "full" Rayleigh damping (which has two target frequencies), the target damping ratio should be the small-strain material damping, and the target frequencies should be established through a process by which linear time domain and frequency domain solutions are matched. As a first approximation, the first-mode site frequency and five times that frequency can be used. For codes with different damping models, alternative recommendations are developed.

Original languageEnglish (US)
Pages (from-to)1385-1398
Number of pages14
JournalJournal of Geotechnical and Geoenvironmental Engineering
Issue number11
StatePublished - Nov 2007


  • Damping
  • Earthquakes
  • Ground motion
  • Seismic effects
  • Wave propagation

ASJC Scopus subject areas

  • General Environmental Science
  • Geotechnical Engineering and Engineering Geology


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