Page 147 - Dynamic Loading and Design of Structures

Page 123

If seismic hazard is to be estimated in a deterministic way, an appropriate earthquake
scenario has to be defined. This involves identifying the source (fault) which will give the
most critical motion for the site under consideration, estimate the maximum magnitude that
can be produced by this source, and then estimate the maximum PGA at the site using an
appropriate attenuation relationship (similar to eqns 4.4, 4.5). This PGA can then be used for
scaling or ‘anchoring’ a fixed spectral shape, with due allowance for site effects, in order to
produce the design spectrum (see Sections 4.3.2, 4.3.4). Such a procedure (whereas not
uncommon) suffers from various drawbacks. One problem is the difficulty in identifying the
critical source (different sources can produce motions that may be critical for a particular type
of structure), another one is the difficulty in predicting the ‘maximum credible earthquake’
associated with a source. Even if this earthquake is reliably estimated, it is generally
uneconomical to design structures against it. These and other problems are the reason why
today all major seismic hazard studies are carried out using a probabilistic approach.
The various components of a probabilistic hazard analysis are shown in Figure 4.6 (EERI
Committee, 1989). The first step is the identification of all sources, which can be point
sources or line sources (faults), or area sources. Then, for each type of source the recurrence
of earthquakes has to be defined, mainly on the basis of historical data. Despite (or because
of) its simplicity, the most commonly used recurrence relationship is the one proposed by
Gutenberg and Richter back in 1944

(4.7)

where N is the (cumulative) number of earthquakes greater than or equal to a given magnitude
M, that are expected to occur during a specified period of time, typically taken equal to 1 year.
The coefficients a and b have to be determined from regression analysis of available data.
Usually an upper bound on magnitude is placed, based on the characteristics of the source
and/or the maximum historical earthquake.
Design seismic loads for a structure are based on the ground motions having a desired
probability of exceedance during the lifetime of the structure (about 50 years for usual
buildings, higher for other types of structures); this probability is commonly taken equal to 10
per cent for buildings of usual importance. The probability p of an earthquake exceeding a
certain magnitude M during the lifetime can be calculated if an appropriate statistical model is
assumed, as shown in Figure 4.6(top left). For simplicity a Poisson process is assumed,
wherein the various ‘events’ (i.e. that the magnitude M is exceeded within a certain time) are
independent. This is equivalent to assuming that earthquake activity has no memory, which is
not true, but the resulting error is not large. Using the definition of the Poisson distribution,
this probability is

(4.8)

where L is the lifetime of the structure. Hazard assessment can then proceed by selecting a
number of values of a strong motion parameter (e.g. Ai), calculate the