Vertical Motions and Design Time Histories

J. P. Singh
JP Singh and Associates, California

Note:The following paper and references are taken from part of the lecture notes for "Seismic Loading: Code Versus Site Specific" presented at a "Portland Regional Seminar on Seismic Engineering Issues" in September, 1995. The notes are used by permission of the author.

Vertical Motions

The most commonly used ratio of vertical to horizontal response spectra as a functional period is about two thirds. Recent studies of vertical ground motion have shown that the V/H response spectral ratios are dependent on the distance of site to the seismic source. The ratio is higher in the near-field region and in the high-frequency range of the response spectra. The V/H ratio largely exceeds the commonly assumed ratio of two thirds at short periods in the near-field regions. Based on the studies the following observations can be made:

• The ratio of vertical to horizontal response spectra varies as a functional period, distance to the fault, and earthquake magnitude. The ratio is larger in the near-field region and has a peak at a period of about 0.1 sec.

• In the near-field region, the ratio of vertical to horizontal spectra at short periods is much larger than the ratio of the peak accelerations. In the high-frequency range of spectra, the commonly used ratio of two thirds grossly underestimates the spectral ratio, especially in the near-field region.

• At long periods the vertical to horizontal spectra ratio is less than two thirds. For guidance purposes, the data developed on the vertical to horizontal spectra ratios by Bozorgnia, Niazi, and Campbell (1995) for the 1994 Northridge earthquake, the 1989 Loma Prieta earthquake, and the SMART-1 Array in Taiwan are shown in the figures below.

Design Time Histories

The signature of time histories for use in design must be a reasonable representation of the ground motion anticipated at a given site. In particular, the time histories for design should capture the signal content that reflects the source effects (i.e., type and size of seismic source), distance effects (near field or far field), geological effects (topography, basin geometry, local soil conditions).

• Type and Size of Seismic Source The type and size of seismic source effects the high frequency, long period, and duration of the time histories. For example, the long period and duration content should properly reflect the size of the seismic sources.

• Distance Effects The signature of the ground motion in the near and far field of the seismic sources are quite different. In the near field of the seismic source, the signatures of ground motion show considerable spatial variation related to the speed and direction of rupture propagation of the seismic source. For example, the waves are crowded together in the direction of rupture propagation, producing energetic unidirectional pulse-type motions called "fling" (Singh 1985).

• Geological Effects Local topography has significant effect on ground motion. For example, ridges amplify and valleys de-amplify the ground motion. Similarly, basins have the effect of enhancing the long-period tails and total duration of the ground motion due to reverberation of the waves trapped in the basin. Finally, local soil conditions, in addition to modifying the high-frequency/long-period content of the ground motion can also significantly change the duration of the ground motion.

  Even though the rapid densification of strong-motion stations within the last few years has considerably increased the database of strong-motion records, there are still cases where time histories of actual earthquakes with sufficient duration and signal content are still not available to satisfy the specific needs of many applications. This need has spawned a new science and technology, the synthesis of realistic strong-motion records.

  The synthesis of realistic earthquake records for structural analysis requires adequate consideration of spectrum compatibility as well as all characteristics of strong ground motion that can be expected at the structure site. Synthetic ground motion records can be developed in the frequency domain (Singh 1986) or in the time domain (Lilhanand and Tseng 1988). The effects of source, travel path, and local soil conditions are contained in the Fourier amplitude and Fourier phase spectra. The Fourier amplitude spectra can be modeled using the method suggested by Boore and Brune, a far-field model that assumes that slip occurs simultaneously along the entire fault, corresponding to an infinite rupture velocity. This approach adequately models the frequencies above 1 Hz; the long period part of the spectrum for effects of source directivity and local soil conditions, however, must be modeled empirically. The Fourier phase spectra model the characteristics of the strong-motion accelerograms, and are more complex. These can be preserved using either recorded phase spectra or synthetic phase spectra based on the phase properties of recorded motions.

  References

  Bozorgnia, Y., M. Niazi, and K. W. Campbell. 1995. "Characteristics of Free-Field Vertical Ground Motion in the 1994 Northridge Earthquake." Earthquake Spectra 11,(4): 515-525.

  Bozorgnia, Y., M. Niazi. 1993. "Distance Scaling of Vertical and Horizontal Response Spectra of the Loma Prieta Earthquake."Journal of Earthquake Engineering and Structural Dynamics 22: 695-707.

  Lilhanand, K. and W. S. Tseng. 1988. "Development and Application of Realistic Earthquake Time Histories Comparable with Multiple Damping Design Spectra." Proceeedings of the Ninth World Conference on Earthquake Engineering, Tokyo-Kyoto, Japan, Vol.2,

  Niazi, M., and Y. Bozorgnia. 1991. "Behavior of Near Source Peak Vertical and Horizontal Ground Motion over SMART-1 Array, Taiwan." Bulletin of Seismological Society of America. 81: 715-732.

  Niazi, M., and Y. Bozorgnia. 1992. "Behavior of Near Source Vertical and Horizontal Response Spectra at SMART-1 Array, Taiwan." Journal of Earthquake Engineering and Structural Dynamics 21: 37-50.

  Singh, J. P. 1986. "A Simple Method for Generating Synthetic Time Histories for Design of Base Isolation Systems." Proceedings Applied Technology Council (ATC) Seminar on Base Isolation and Passive Energy Dissipation Devices, March 12&13, San Francisco, ATC-17. Redwood City, Calif.: ATC. 391-402.

  
  

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