Civil Engineering Reference
In-Depth Information
(iii)
Ray path effect
(or
scattering effect
): caused by refl ection and refraction of waves through the
soil during their propagation, inhomogeneities of soil layers and other differences in local soil
conditions under the various stations.
Spatial variability of earthquakes can be described mathematically either in the time domain (gener-
ally by auto- covariance and cross -covariance) or frequency domain (by coherency functions). It is
beyond the scope of this chapter to discuss analytical techniques employed to defi ne dispersion and
incoherence. The reader may consult one of the textbooks that deal specifi cally with random vibrations
in earthquake engineering (e.g. Manolis and Koliopoulos, 2001, among others). It is noteworthy that
ground motions recorded by dense arrays in several regions worldwide, e.g. USA, Japan and Taiwan,
have shown coherency decreases with increasing distance between measuring points and increasing
frequency of motion (e.g. Clough and Penzien, 1993 ; Kramer, 1996). The coherency of two ground
motions is a measure of correlation of amplitudes and phase angles at different frequencies. Incoherence
(or loss of coherence) is strongly frequency-dependent (Luco and Wong, 1986). The coherence factor
or absolute value of coherency is a measure of the incoherence. More signifi cant effects are observed
at higher frequencies: for frequencies lower than 1.0- 2.0 Hz (periods
T
of 0.5 to 1.0 seconds), the loss
of coherence can be ignored (coherence factor is close to 1.0). Coherence starts to decrease signifi cantly
for higher frequencies. For frequencies higher than 5 Hz (
T
less than 0.2 seconds), the coherence factor
is reduced by more than 40-50%. Several expressions for smooth coherence functions have been pro-
posed for design purposes (e.g. Haricharan and Vanmarcke, 1986; Luco and Wong, 1986; Abrahamson,
1991 ; Oliveira
et al
., 1991 ; Somerville
et al
., 1991; Der Kiureghian, 1996). These relationships typically
depend on the separation distance and frequency.
Dispersion and incoherence of earthquake ground motions do not generally affect short-span struc-
tures, such as buildings, but they may signifi cantly infl uence the dynamic response of long- span struc-
tures, for example medium- to long-span bridges, stadiums and pipelines that extend over considerable
distances. Signifi cant spatial variability may often occur whenever the large plan dimensions are com-
bined with irregularities in the soil profi le along the travel path. For long distances and rather stiff
structures, totally uncorrelated ground motions with appropriate frequency content should be consid-
ered. Loss of coherence can be ignored in all the other cases, although time delay should always be
accounted for.
Problem 1.4
What is the natural period of a layered soil with medium gravel of depth 40 m? Is it safe to build a
multi-storey framed building with fundamental period of vibration equal to 1.5 seconds, as that
displayed in Figure 1.19, on a site with the above soil type? Is this site more suitable for a particular
type of structure shown in Figure 1.19 ?
T=1.5 secs
T = 4.5 secs
T=0.2 secs
V
s
=780 m/sec
T
s
= ?
H=40m
Figure 1.19
Structural systems with different natural periods of vibration
