09-10-2014, 04:31 PM
The interest of an engineer in earthquakes is mainly from the design point of
view. He studies them so that the structures he builds can safely withstand the
sudden earthquake shocks and the associated erratic ground motion. Though
geophysicists have been studying the phenomenon of earthquakes since a long
time, progress engineering-wise has taken place only recently, The first step in
this direction has been the installation of strong motion recorders in seismic areas
to record the ground motion near the epicenter. The importance of this needs no
extra emphasis. Indeed, earthquake engineering essentially is the design of
structures to respond to this ground motion with minimum or no damage. The
designer is here confronted with a situation with serious difficulties. The
irregularity exhibited by the ground motion cannot be quantitatively described
in a simple manner. This induces uncertainly in the behaviour of a structure itself
rendering design decisions doubtful. To crown these, the unpredictability of
future earthquakes introduces extra uncertainty making the problem much more
involved. The only way out of this seems to be by finding a suitable
mathematical model for the ground motion. The development of a mathematical
model for physical and natural phenomenon is not something new to
engineering practice. This is undertaken in almost all fields by studying the
underlying mechanism; for example, the foundation of a rotating machine is
taken to be subjected to a sinusoidal excitation. In the present problem of
modeling ground motion during earthquakes, an accurate analysis of the
fundamental mechanism is beset with many complexities and may even be
intractable. Anyhow, if the basic mechanisms of different earthquakes are similar
one may expect a common pattern to exist among the recordings also. In the
absence of a suitable analysis of the earthquake mechanism, this pattern is to be
searched among a few available accelerograms.
Even a causal look at the past accelerograms will convince one that the most
striking common feature is the randomness present in all the records. Thus the
concepts of probability, statistics and random processes naturally find their way
in an attempt to understand these records. This in turn makes the response
analysis and design of structures also to be carried out in a statistical manner,
applying the stochastic process approach throughout. In the present work
attention is mainly focused on the modeling of ground acceleration as input to
structural systems and the analysis of a single degree-of-freedom system with
such an input. The presentation is as follows: A brief review of literature
pertaining to the field of modeling of earthquakes followed by a discussion is
presented in Chapter 1. Chapter 2 deals with the development of a new model in
three steps. In the first stage many past records are analysed for what seem to be
their particular and general characteristics. Based on the inferences of this
analysis, in the second stage, a non-stationary random process suitable to
simulate the important properties is proposed. In the last step an approximate
method is worked out to estimate the parameters involved in the suggested
model, so as to get quantitative simulation of some of the characteristics fixed
beforehand.
After fitting in a model for such an irregular process it would be interesting as
well as necessary to test it by generating sample functions. Chapter 3 is
concerned with this aspect of the study. Four real records have been simulated
by the above method of parameter estimation and the sample functions are
presented in four ensembles. Response spectrum analysis is also carried out on
all these. The realized results are compared with the expected ones.
The generation of the excitation samples is unnecessary when the response of a
structure can be analysed probabilistically using only the statistical properties of
the input process and the system characteristics. As an example of this approach,
the analysis of a linear single degree-of-freedom system is undertaken in Chapter
4. After a mean square response analysis, an attempt is made to obtain the
highest-peak statistical approximately. This is followed by an analysis of the
response envelope. Numerical results are presented in detail for four types of
earthquake like excitations.
The thesis ends with a chapter on conclusions and suggestions for future
research. The following two papers have been prepared based on the material
presented in this thesis.
1. A Non-stationary Random process model for earthquake accelerograms (To
appear in the June 1969 issue of the Bulletin of the Seismological Society of
America).
2. Probabilistic Response analyses to earthquakes (Sent for publication).