To construct a design spectrum for a particular site, an estimate of earthquake ground motion is necessary. This is based on seismic history in the vicinity of the site.

**Estimating the ground motion**

To construct a design spectrum for a particular site, an
estimate of earthquake ground motion is necessary. This is based on seismic
history in the vicinity of the site. Unfortunately in many regions this
information is not available. Based on limited information, seismic risk
procedures and *attenuation* *relationship *for estimating the peak
ground acceleration (PGA) has been* *developed. From these studies it was
recommended that the ratio of peak velocity to peak acceleration *v*/*a*
be used to estimate the peak ground velocity and ratio of peak acceleration â€“
peak displacement product to the square of the peak velocity (*ad*/*v*^{2})
be used to estimate the peak displacement. A log normal distribution summary of
*v*/*a* and *ad*/*v*^{2} for records on four
different soil conditions is presented in Table 17.6. In the table *L*, *S*
and V denote the larger of two horizontal acceleration, the smaller of two peak
horizontal accelerations and the vertical component of the earthquake motion.
Using the *seismal risk map* and Table 17.6 one can estimate the maximum
ground motion at a site. This information is used to construct a site-specific
spectrum.

Example 17.9

Construct Newmarkâ€“Hall
broad-banded design spectrum for a site. Develop spectrum curves using the
program for damping factors 0.02, 0.05, 0.1. Estimate the maximum horizontal
ground displacement assuming the maximum ground acceleration = 0.4*g*,
assuming group L and 84.1% on 50 m alluvium by bed rock.

Solution

Maximum ground acceleration = 0.4*g*
= 0.4 Ã— 981 cm/s^{2} = 392.4 cm/^{2}
From Table 17.6 *v*/*a* = 117/*g*; *ad*/*v*^{2}=
7.8

*v *= 117* *Ã—* *0.4 = 46.8 cm/s

*d *= 7.8* v*^{2}/*a *=
7.8* *Ã—* *46.8^{2}/392.4
= 43.53 cm

*a *= 392.4
cm/s^{2};* v *= 46.8 cm/s* d *= 43.53 cm

Construct the maximum ground
motion polygon with the values of *a*, *v* and *d*. Apply
appropriate amplification factors to the maximum ground motion* *components
in a manner similar to that described in the next pages.

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Civil : Structural dynamics of earthquake engineering : Estimating the ground motion |

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