Page 146 - Dynamic Loading and Design of Structures

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Topography effects
Topography of the site can also have a noticeable effect on amplification of ground motion.
The strong motion shown in Figure 4.3 was recorded on a rocky ridge connected to the
Pacoima Dam, and is characterized by a peak acceleration of 1.17g, one of the highest ever
recorded. Many people argued that this was mainly the result of a topographic amplification,
although other interpretations were also suggested (Reiter, 1991).
The major parameter of the problem appears to be the steepness of the ridges; it can be
shown that the displacement amplification at the crest of an essentially triangular hill is equal
to 2/v, where vπis the angle formed by the ridges; therefore the amplification increases as the
ridge becomes steeper. Observed amplifications at the crest (with respect to the base) range
from 2 to 20, whereas theoretical predictions are generally much less (3 to 4), possibly due to
the influence of three-dimensional effects and ridge to ridge interaction. Topography effects
are discussed, among others, by Finn (1991) and Kramer (1996). Due to the complexity of the
subject, it is generally considered as not mature enough to be included in code provisions. The
Recommendations of the French Association for Earthquake Engineering (AFPS, 1990)
appear to be the only document of regulatory character that has adopted rather detailed rules
for the calculation of the topographic amplification factor.

Spatial variability of ground motion
While the smallest dimension of common structures such as buildings is usually small enough
that the ground motion can be assumed to be the same along the entire plan of the structure, in
elongated structures, such as long bridges and pipelines, a rather significant variability of the
ground motion may occur, particularly whenever the large plan dimensions are combined with
irregularities in the soil profile. The local spatial variation or incoherence of ground motion is
mainly due to
●travelling wave effects, wherein non-vertical seismic waves reach different points of the
structure at different times (time delay effect);
●scattering (reflection, refraction) of seismic waves caused by inhomogeneities along the
travel path;
●local soil filtering and amplification of the motion.

The coherency of two ground motions is a measure of correlation of amplitudes and phase
angles at different frequencies. Ground motions recorded by dense arrays of accelerographs
have shown that coherency decreases with increasing distance and increasing frequency of
motion (Clough and Penzien, 1993; Kramer, 1996).

4.2.5 Assessment of seismic hazard
Analysis of seismic hazard (resulting from strong motions) is the basis for defining seismic
loading for design purposes, more particularly for deriving the design response spectrum,
discussed in more detail in Section 4.3.2.