Civil Engineering Reference
In-Depth Information
Wavelet-based
probabilistic analysis
It was seen in Chapter 5 how system nonlinearity affects structural responses.
The structure, in most of the cases, is supported on a soil medium that may
behave nonlinearly, and this may affect the structural responses to a signifi-
cant extent under the action of moderate to severe seismic ground motions.
Several researchers have studied the influence of material nonlinearity of
soil on the responses of a structure in the form of a nonlinear stress-strain
relationship, transfer function analysis to obtain effective shear wave veloc-
ities in soil, a nonlinear load-displacement relationship, etc. [34-38]. The
nonlinearity in the system (e.g. in case of slipping foundations) has been
studied in the past [40] in the wavelet domain, extending the technique of
equivalent linearization [38]. There is a general approach to model system
nonlinearity using a hysteretic force-displacement relationship. However,
in doing so to model large deformations, the area under the curve also gets
larger, and hence a 'fat' hysteresis loop may be considered. In such cases,
it is always worth modelling the effect of the hysteresis loop instead of
representing the system stiffness by a backbone curve and an equivalent
viscous damping mechanism (to represent dissipation of energy). In this
chapter, the wavelet analytic technique is used to solve the system dynamics
in the case of a tank supported on nonlinear soil. However, to keep things
simpler, the force-deformation curve, in this case, is assumed to follow
an elasto-perfectly-plastic (EPP) path, and subsequently a methodology for
obtaining a nonstationary stochastic seismic response of a storage tank is
described.
6.1 MODEL AND SOIL NONLINEARITY
In order to demonstrate the use of wavelets in solving the problems related
to material nonlinearity, a structural model is considered similar to the
one described in Chapter 3. The user may use the same concept for other
structures as well. A rigid, right circular cylindrical tank is assumed to
be supported on a thick circular foundation mat. This model, shown in
Figure 6.1, is the same as that used in Chapter 3. However, the system now
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