The FSI Model methodology also implements the same random variables as the
last methodology. The main advantage of this methodology is to use the fluid-
structure interaction and detailed finite element modeling which can provide
details on the performance of coastal bridges such as wave force variation over the
time, local damages, and stress concentrations. The FSI Model can provide insight
on the forces on bridge super- and substructure, as well as local and global
damages and failure mechanisms.
This section constructs the fragility surface for the case study bridge from
Houston/Galveston Bay area that was defined in Section 4.2.5. This bridge is used
in the next chapter for all the modeling methods to provide a comprehensive
comparison. As it was shown in the previous sections, the observed failure mode is
abrupt; i.e., once deck movement is initiated, significant displacement occurs
which provide combinations of hazard and bridge model parameters for subsequent
fluid-structure interaction simulation. The generated wave and surge profiles cover
the entire reasonable range of hazard by selecting 256 points that span the range of
Hmax and Zc from 0 to 5m and 2m to -2m, respectively. Quasi Monte Carlo
sampling technique was used to generate realizations of random variables. The
sample points are presented in Appendix V. As mentioned for the previous
modeling methodologies, given the abrupt nature of deck response under surge and
wave loads, the outcome of the assessment is not sensitive to this imposed limit
used to categorically distinguish survived and failed cases. The result of the
simulation is shown in Figure 6-5. As it can be seen the results are revealing a
transition zone between the failed and survived region. The FSI Model provides the
most accurate output in comparison to the MCS Static and Dynamic Model;
however, it requires significantly more computational power. For example, each
FSI simulation on a super computer cluster that has quad-core Intel Xeon
processors running at 2.83GHz takes an average of 7 hours to complete. Each
simulation of the Dynamic Model on the same machine takes less than 10 minutes
to complete.
Figure 6-5. Fragility surface of the case study bridge using FSI Model methodology.
6.4. Summary
This chapter presented three distinct modeling methodologies, designated as the
MCS Static Model, Dynamic Model, and FSI Model, for the reliability assessment
of deck unseating mode of failure. The FSI Model is the most accurate, yet
computationally intense strategy. Additionally, it requires a deep understanding of
the intricacies involved in fluid-structure interaction modeling. Therefore, the MCS
Static and Dynamic Models can be used instead of FSI Model for a more efficient
reliability assessment of coastal bridges under hurricane events. All of these models
implement quasi-Monte Carlo sampling technique to generate realizations of
random variables. The results of these models reveal that deck unseating is a
brittle failure mode and can be treated as a binary data of failed and survived
the developed the MCS Static Model is limited to the bridge deck unseating failure
mode. However, the Dynamic and FSI Models can be used to evaluate other failure
modes for retrofitted bridges as illustrated in Chapter 8 and Chapter 9.
It is possible to increase the number of Monte Carlo simulations and also
realizations of hazard intensity measures to a very large number for the MCS
Static Model. However, this approach is not feasible for the Dynamic and FSI
Models due to the limitation on the computational power. Thus, surrogate models
are required to be constructed over the result of different models. After
construction, these surrogate models can provide deck unseating failure probability
for the any hazard intensity measure; even if no simulation result exists. Also, the
accuracy of the different structural analysis methods can be compared with each
other more holistically over the large number of hazard intensity measures
combinations by utilizing the developed surrogate models. Next chapter introduces
appropriate surrogate models for coastal bridges reliability assessment and compare
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Chapter 7
Reliability Assessment of Coastal
Bridges: Surrogate Models
In this chapter, statistical learning techniques are applied to the outcome of
different structural models to develop surrogate models of bridge reliability under
hurricane storm surge and wave loading and thereby derive bridge fragility
surfaces. The representation of the three different structural analysis models output
that have been presented in the previous chapter in a mathematical form is
necessary in order to compare them together. Additionally, the developed surrogate
models can be used to interpolate the probabilities of failure at any point that
there is no simulation result. Different surrogate models that are appropriate for
with each other through goodness-of-fit measures. Also, the performance and
accuracy of different structural analysis methodologies are compared with each
other.