Earthquake Input Motion - Fundamentals of Earthquake Engineering - page 129

Table 3.5 Values of coeffi cients for equation (3.13).

Soil type Shear wave velocity, v S (in m/s) S A S S

Rock v s > 750 0 0

Stiff soil 360 < v s ≤ 750 1 0

Soft soil 180 < v s ≤ 360 0 1

Very soft soil v s ≤ 180 0 1

( ) =− log PGA 0 659 . + 0 202 . M − 0 0238 . d + 0.020 S + 0 029 . S (3.13)

S A S

h

in which the epicentral distance d is in km; the scatter σ is 0.214. Coeffi cients S A and S S account for
the effects of soil condition. Four soil categories were considered (rock, stiff soil, soft and very soft
soil); they are classifi ed on the basis of the average shear wave velocity to 30- m depth v S,30 . Values
can be obtained from Table 3.5. Focal depths h are not greater then 20 km (1 ≤ h ≤ 19 km). The value
of PGA in equation (3.13) is expressed in m/sec 2 .
Equation (3.13) assumes decay associated with anelastic effects due to large strains. Consequently,
in the above relationships, both terms log( d ) and d [ see equation (3.5) , where d = R ] are not utilized
because their strong correlation does not permit a simple summation.

Problem 3.3

For an earthquake of magnitude M = 7.0 and depth 25 km, calculate the peak ground acceleration
at a site 50 km from the epicentre using the attenuation relationships for Europe, Japan and western
North America (randomly oriented horizontal components). The fault mechanism is normal and the
seismic waves travel through a thick layer of rock ( v s = 780 m/sec). Compare the results with the
prediction of the worldwide attenuation relationship. Plot the curve of the above attenuation relation-
ships for M = 7 and comment on the plots.

3.4 Earthquake Spectra
3.4.1 Factors Infl uencing Response Spectra
The shape of earthquake (acceleration, velocity or displacement) spectra is infl uenced by a number
of factors, which are similar to those affecting earthquake ground- motion characteristics, outlined
below:

(i) Magnitude;
(ii) Source mechanism and characteristics;
(iii) Distance from the source of energy release;
(iv) Wave travel path;
(v) Rupture directivity;
(vi) Local geology and site conditions.

Some factors are more infl uential than others and therefore are selected for discussion hereafter. The
three fundamental parameters infl uencing spectra are magnitude, distance and site conditions. Ideally,
strong motions used to derive uniform hazard spectra should be uniformly distributed in the space of