6. Probabilistic analysis of the steel technology segments

The reactor and the bubble condenser-reinforced structures with steel liner represent the critical structures of the NPP hermetic zone [3]. Among the critical technology structures, the reactor hermetic covers and the reactor-protective hood, belong too [39, 40].

The reactor-protective hood is shown in Figure 17. The protective hood is an all-welded structure consisting of a spherical and a cylindrical part. The spherical part has a manhole of 500 mm in diameter with a ladder. The manhole facilitates equipment maintenance in the concrete cavity without the necessity to remove the protective hood. In order to ensure higher strength of the structure (on a seismic event), the protective hood is reinforced with a pipe (inner Ø712 mm) and six ribs. At the top, the pipe is welded in the canter of the hood spherical part, while the other end covers the ring on the upper block beam. The protective hood is set on a counter-flange and is attached to it with 60 M48 bolts and sealed with packing. The cap structure includes a platform with railing.

The finite element model of reactor cover was created in software ANSYS by the shell, beam, combine and mass elements. The envelope of cover is from layered shell elements (SHELL181). The surface load is defined using three-dimensional (3D) structural surface elements (SURF154). The connection with bolts is modelled by the combine elements (COMBINE14). The element of point mass (MASS21) represents the concentrated masses adequate to local load of the technology, beam elements (BEAM44) for frame and beam connection. The contact element (CE) and links (CP) were used for the joint connection. The upper part of the hood has

Figure 17. Vertical section of the reactor with reactor-protective hood.

Risk Assessment of NPP Safety in Case of Emergency Situations on Technology http://dx.doi.org/10.5772/intechopen.68772 89

Figure 18. FEM model (RCOV) of the reactor-protective hood.

6. Probabilistic analysis of the steel technology segments

88 Recent Improvements of Power Plants Management and Technology

reactor hermetic covers and the reactor-protective hood, belong too [39, 40].

structure includes a platform with railing.

Figure 17. Vertical section of the reactor with reactor-protective hood.

The reactor and the bubble condenser-reinforced structures with steel liner represent the critical structures of the NPP hermetic zone [3]. Among the critical technology structures, the

The reactor-protective hood is shown in Figure 17. The protective hood is an all-welded structure consisting of a spherical and a cylindrical part. The spherical part has a manhole of 500 mm in diameter with a ladder. The manhole facilitates equipment maintenance in the concrete cavity without the necessity to remove the protective hood. In order to ensure higher strength of the structure (on a seismic event), the protective hood is reinforced with a pipe (inner Ø712 mm) and six ribs. At the top, the pipe is welded in the canter of the hood spherical part, while the other end covers the ring on the upper block beam. The protective hood is set on a counter-flange and is attached to it with 60 M48 bolts and sealed with packing. The cap

The finite element model of reactor cover was created in software ANSYS by the shell, beam, combine and mass elements. The envelope of cover is from layered shell elements (SHELL181). The surface load is defined using three-dimensional (3D) structural surface elements (SURF154). The connection with bolts is modelled by the combine elements (COMBINE14). The element of point mass (MASS21) represents the concentrated masses adequate to local load of the technology, beam elements (BEAM44) for frame and beam connection. The contact element (CE) and links (CP) were used for the joint connection. The upper part of the hood has lugs used to handle it. The FEM model (RCOV) consists of 27,824 shell, beam and mass elements with 22,887 nodes (Figure 18).

#### 6.1. Probability and sensitivity nonlinear analysis

The calculation of the probability of the reactor cover failure is based on the results of the nonlinear analysis for various levels of the accident pressure and mean values of the material properties. The critical areas of the technology segments defined from the nonlinear deterministic analysis are the mechanical closures. The CCD method of the RSM approximation is based on 45 nonlinear simulations depending on the six variable input data. The nonlinear solution for a single simulation consists of about 50–150 iterations depending on the scope of the plastic deformations in the calculated structures. The sensitivity analysis gives us the information about the influences of the variable properties of the input data on the output data (see Figures 19 and 20). These analyses are based on the correlation matrixes.

Figure 19. Sensitivity analysis of the safety function of the reactor-protective hood for overpressure Δp = 0.25 MPa and Δp = 0.80 MPa.

Figure 20. Sensitivity and trend analysis of the safety function of the reactor cover for uniform distribution of overpressure.

#### 6.2. Fragility curves of failure pressure

The fragility curve of the failure pressure (see Figure 21) was determined performing 45 probabilistic simulations using the RSM approximation method with the experimental design CCD for 106 Monte Carlo simulations for each model and five levels of the overpressure. Various probabilistic calculations for five constant levels of overpressure next for the variable overpressure for gauss and uniform distribution were taken out. The nonlinear analysis of the steel technology structures was performed considering HMH-plastic criterion with the multilinear kinematic hardening stress-strain relations for various levels of the temperatures and the degradation of the strength. The uncertainties of the input data (Table 3) were

Figure 21. Fragility curves of the reactor-protective hood determined analytically for normal distribution with 5% envelope.

considered in accordance with the JCSS standards [30], NRC [11] and IAEA requirements [9]. The geometric and material nonlinearities of the steel solid and shell-layered elements were considered for the overpressure static loads from 250 to 1000 kPa.
