# Probabilistic Modeling of Containment Severe Accident Response

The analysis efforts described previously were deterministic in that they computed the response of the containment given one set of assumptions. The assumptions used for each analysis included the level of detail in the model, the material properties, the failure criterion used for steel and concrete, and the boundary conditions among others. Often, there is a large amount of uncertainty in many of these assumptions, and “best estimate” values are used to assess the containment’s behavior. However, studies have attempted to account for these uncertainties through probabilistic modeling. As discussed earlier in this chapter, fragility curves were developed for use in probabilistic risk assessments [3] and in the IPE [4] studies. Following those efforts, more sophisticated research programs explored methods to develop fragility curves using computational finite element analyses. One study by Ellingwood and Cherry [48] examined the development of fragility curves using these techniques. Ellingwood and Cherry accounted for two types of uncertainty in their study. The inherent randomness for the most part focuses on material property uncertainty, while the knowledge- based uncertainty centers on finite element modeling assumptions, the failure criterion, and the extrapolation of material test data for use in the models. The uncertainties were defined for these parameters using test data and engineering judgment as available. A number of techniques were available to develop the fragility curves including classical Monte Carlo; however, Monte Carlo approaches would require a large number of samples to be developed. For each sample, a complete finite element analysis must be performed. Since this would not be practical, Ellingwood and Cherry utilized a Latin Hypercube sampling (LHS) [49] technique to develop the set of input parameters for each finite element analysis. The use of the LHS greatly reduced the number of samples required in order to develop the fragility curve. Ellingwood and Cherry performed 14 finite element analyses of a PWR Ice Condenser with a steel shell containment. In each of these analyses, the material properties and other uncertainty parameters were varied as defined by the LHS process. After conducting the finite element analyses and computing the failure (e.g., leak or rupture) pressure for each analysis, the failure pressures were rank ordered and plotted on the log-normal plot shown in Fig. 6.20. The

**FIG. 6.20**

**FRAGILITY CURVES FOR A PWR ICE CONDENSER [48]**

plot also includes the IPE fragility developed for the plant (e.g., Sequoyah) used as the basis for the PWR Ice Condenser finite element model. For most of the probability range, the Ellingwood and Cherry estimates show higher failure probabilities at the same pressure relative to the IPE values.

This method of developing fragility curves can be, and has been, used for input into PRA models in order to include the uncertainty in the containment performance in the severe accident assessment. The following section includes a description of a study that uses this technique to develop containment fragility curves to assess the effects of degradation (e.g., corrosion) on the severe accident response.