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8.5 Ground Motion Estimates**

Ground motion attenuation equations are used to determine the level of acceleration as a function of distance from the source as well as the magnitude of the earthquake. Correlations have been made between peak acceleration and other descriptions of ground motion with distance for various events. These equations allow the engineers to estimate the ground motions at a site from a specified event. They also allow engineers to find out the uncertainty associated with the estimate. There are a number of attenuation equations that have been developed by various researchers. Donovan and Bornstein (1978), developed the following equation for peak horizontal acceleration.

Where,

Several methods for evaluating the effect of local soil conditions on ground response during earthquakes are now available. Most of these methods are based on the assumption that the main responses in a soil deposit are caused by the upward propagation of horizontally polarized shear waves (SH waves). These waves are propagated from the underlying rock formation. Analytical procedures based on this concept incorporating linear approximation to nonlinear soil behavior have been shown to give results in fair agreement with field observations in a number of cases. The analytical procedure generally involves the following steps:

(a) Determining the characteristics of the motions likely to develop in the rock formation underlying the site. The maximum acceleration, predominant period, and effective duration are the most important parameters of an earthquake motion. Empirical relationships between these parameters and the distance from the causative fault to the site have been established for earthquakes of different magnitudes.

(b) Determining the dynamic properties of the soil deposit. Average relationships have been established to estimate dynamic shear modulus as a function of shear strain and static properties for various soil types (Seed and Idriss, 1970). Average relation between the damping ratios of soils as functions of shear strain and static properties have also been established. Thus a testing program to obtain the static properties for use in these relationships will often serve to establish the dynamic properties with a sufficient degree of accuracy.

(c) Computing the response of the soil deposit to the base rock motions. A one-dimensional method of analysis can be used if the soil structure is essentially horizontal.