10-10-2014, 02:01 PM
The safety of nuclear power plant structures under the seismic loading is one of
the most important design requirements. A major hurdle in fulfilling this
requirement lies in dealing with a significant level of uncertainty associated with
the specification of the seismic load. This uncertainty arises, in turn, because of
the complex nature of the earthquake source mechanism, wave propagation that
affect the intensity of the ground motion at a given site and the effects due to soil
structure interactions. The problem is further compounded by scarcity of
recorded ground motions for different site conditions and focal distances. For
the estimation of seismic responses, the deterministic methods such as response
spectrum and time history methods have been developed with certain
conservative assumptions to take care of the uncertain inputs. In the recent past,
application of random vibration analysis techniques for the estimation of seismic
responses is gaining acceptance in the nuclear industry. Nevertheless, for the
critical structures such as nuclear power plant components, where the responses
are to be estimated with a high degree of confidence, the uncertainties associated
with the seismic loading makes the design an ill posed problem. The
complexities are further enhanced in the case of multiply supported structures
wherein a more detailed specification of the seismic loading at the supports are
required. Also, it is worth noting that quantification of design seismic margins in
the design is currently being carried out using probabilistic methods. The
robustness and accuracy of such methods are open to question due to lack of
available data.
Under such a situation, it is valuable to know what could be the maximum
possible response of a given structure. The subject of critical excitation deals
with this issue and offers a counterpoint to the traditional response spectrum
based methods. Recently a methodology for optimal random process modelling
of multi-support and multi-component earthquake motions has been developed
at Indian Institute of Science. This method, called herein the Critical Cross
Power Spectral Density (C-CPSD) method, has the potential for use in industry
and therefore its performance merits a critical appraisal vis-d-vis the traditional
methods of seismic response analysis. Furthermore, the method, as has been
developed, is inapplicable if structural non-linearitys are to be taken into
account. The present thesis, thus primarily aims at evaluating the performance
of critical seismic excitation modelling in a realistic setting and contributing to
the development of the methodology of critical excitations by extending the
presently available procedures to nonlinear systems.
The thesis is divided into five chapters and the layout of the thesis is as follows.
Chapter I deals with a review of literature on the methods of seismic response
analysis of secondary systems and the existing codes of practice. It brings out
the scope and limitations of the various methods and codes of practice. The need
to know the seismic margins available and the relevance of critical excitations in
such a scenario is discussed.
Chapter 2 deals with the details of a multiply supported primary discharge pipe
of the 500 MWe Prototype Fast Breeder Reactor, that has been selected for the
purpose of the assessment of the C-CPSD method. The details of the finite
element model used, results of the modal analysis and the generation of floor
response spectra at support locations of the primary discharge pipe by time
history and random vibration approaches are presented.
A critical assessment of the C-CPSD method with respect to the estimated
responses such as dynamic stresses and displacements is reported in chapter 3
by comparing the results with those estimated by the conventional methods such
as multiple response spectrum method, multiple time history method and
envelope spectrum method. In the application of the critical excitation method,
the seismic inputs are described in terms of the response spectra at the support
points while the cross correlation between the support motions are taken to be
unknown. The unknown cross correlations are found in such a way that the
response variance at any given location is maximized. The results indicate that
the critical excitations do not produce unduly high responses and they are about
1.3 times higher than the values that are obtained by multiple time history
analysis. Also, the critical excitation method clearly establishes the high degree
of over conservatism associated with the envelope spectrum method. In a multisupport
excitation situation, as per the prevailing codes of practice, the allowable
stresses for the dynamic part of the total stress is smaller than that due to the
support displacements. In view of this, the critical responses were obtained by
maximizing the dynamic part of the total response rather than the total response.
Here, also, the robustness of the critical excitation method was established by
changing the damage variable of interest and comparing the resulting responses
over the structure. The results have indicated that the overall behavior of the
relative response values between any two structural points remains unchanged
irrespective of the response variable with respect to which the critical excitations
have been established. The C-CPSD method uses a simple model for the phase
characteristics between the support motions. It emerges from the present study
that, since the actual cross coherence in a secondary system is more complex,
there is scope for improving the method by allowing for more realistic models
for phase spectra.
Chapter 4 considers the seismic response of a nonlinear, doubly supported,
single degree of freedom system with cubic spring characteristics. The two
supports are subjected to stationary Gaussian support motions. To start with,
the support motions are taken to be completely specified. An equivalent
linearization based random vibration approach for analyzing the system
response is developed and the scope of the method is examined using digital
simulations. A stochastic stability analysis of the approximate solution is also
carried out to examine the validity of the equivalent linear models used.
Subsequently, the problem of determination of the C-CPSD friction is considered
and an approximate solution to this problem base don equivalent linearization is
developed. The numerical results demonstrate the feasibility of the proposed
approach.
The conclusions emerging from the above study and a few suggestions for
further research are presented in the Chapter 5.
the most important design requirements. A major hurdle in fulfilling this
requirement lies in dealing with a significant level of uncertainty associated with
the specification of the seismic load. This uncertainty arises, in turn, because of
the complex nature of the earthquake source mechanism, wave propagation that
affect the intensity of the ground motion at a given site and the effects due to soil
structure interactions. The problem is further compounded by scarcity of
recorded ground motions for different site conditions and focal distances. For
the estimation of seismic responses, the deterministic methods such as response
spectrum and time history methods have been developed with certain
conservative assumptions to take care of the uncertain inputs. In the recent past,
application of random vibration analysis techniques for the estimation of seismic
responses is gaining acceptance in the nuclear industry. Nevertheless, for the
critical structures such as nuclear power plant components, where the responses
are to be estimated with a high degree of confidence, the uncertainties associated
with the seismic loading makes the design an ill posed problem. The
complexities are further enhanced in the case of multiply supported structures
wherein a more detailed specification of the seismic loading at the supports are
required. Also, it is worth noting that quantification of design seismic margins in
the design is currently being carried out using probabilistic methods. The
robustness and accuracy of such methods are open to question due to lack of
available data.
Under such a situation, it is valuable to know what could be the maximum
possible response of a given structure. The subject of critical excitation deals
with this issue and offers a counterpoint to the traditional response spectrum
based methods. Recently a methodology for optimal random process modelling
of multi-support and multi-component earthquake motions has been developed
at Indian Institute of Science. This method, called herein the Critical Cross
Power Spectral Density (C-CPSD) method, has the potential for use in industry
and therefore its performance merits a critical appraisal vis-d-vis the traditional
methods of seismic response analysis. Furthermore, the method, as has been
developed, is inapplicable if structural non-linearitys are to be taken into
account. The present thesis, thus primarily aims at evaluating the performance
of critical seismic excitation modelling in a realistic setting and contributing to
the development of the methodology of critical excitations by extending the
presently available procedures to nonlinear systems.
The thesis is divided into five chapters and the layout of the thesis is as follows.
Chapter I deals with a review of literature on the methods of seismic response
analysis of secondary systems and the existing codes of practice. It brings out
the scope and limitations of the various methods and codes of practice. The need
to know the seismic margins available and the relevance of critical excitations in
such a scenario is discussed.
Chapter 2 deals with the details of a multiply supported primary discharge pipe
of the 500 MWe Prototype Fast Breeder Reactor, that has been selected for the
purpose of the assessment of the C-CPSD method. The details of the finite
element model used, results of the modal analysis and the generation of floor
response spectra at support locations of the primary discharge pipe by time
history and random vibration approaches are presented.
A critical assessment of the C-CPSD method with respect to the estimated
responses such as dynamic stresses and displacements is reported in chapter 3
by comparing the results with those estimated by the conventional methods such
as multiple response spectrum method, multiple time history method and
envelope spectrum method. In the application of the critical excitation method,
the seismic inputs are described in terms of the response spectra at the support
points while the cross correlation between the support motions are taken to be
unknown. The unknown cross correlations are found in such a way that the
response variance at any given location is maximized. The results indicate that
the critical excitations do not produce unduly high responses and they are about
1.3 times higher than the values that are obtained by multiple time history
analysis. Also, the critical excitation method clearly establishes the high degree
of over conservatism associated with the envelope spectrum method. In a multisupport
excitation situation, as per the prevailing codes of practice, the allowable
stresses for the dynamic part of the total stress is smaller than that due to the
support displacements. In view of this, the critical responses were obtained by
maximizing the dynamic part of the total response rather than the total response.
Here, also, the robustness of the critical excitation method was established by
changing the damage variable of interest and comparing the resulting responses
over the structure. The results have indicated that the overall behavior of the
relative response values between any two structural points remains unchanged
irrespective of the response variable with respect to which the critical excitations
have been established. The C-CPSD method uses a simple model for the phase
characteristics between the support motions. It emerges from the present study
that, since the actual cross coherence in a secondary system is more complex,
there is scope for improving the method by allowing for more realistic models
for phase spectra.
Chapter 4 considers the seismic response of a nonlinear, doubly supported,
single degree of freedom system with cubic spring characteristics. The two
supports are subjected to stationary Gaussian support motions. To start with,
the support motions are taken to be completely specified. An equivalent
linearization based random vibration approach for analyzing the system
response is developed and the scope of the method is examined using digital
simulations. A stochastic stability analysis of the approximate solution is also
carried out to examine the validity of the equivalent linear models used.
Subsequently, the problem of determination of the C-CPSD friction is considered
and an approximate solution to this problem base don equivalent linearization is
developed. The numerical results demonstrate the feasibility of the proposed
approach.
The conclusions emerging from the above study and a few suggestions for
further research are presented in the Chapter 5.