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  ABSTRACT: This paper gives the results of the risk-based safety analysis of the seismic resistance of the NPP (Nuclear Power Plants) in Slovakia. The probabilistic assessment of NPP safety analysis is presented. On the base of the geophysical and seismological monitoring of locality the peak ground acceleration and the uniform hazard spectrum of the acceleration was defined for the return period 10 000 years using the Monte Carlo simulations. There is showed summary of calculation models and calculation methods for the probability analysis of the structural safety considering load, material and model uncertainties. The numerical simulations were realized in the system ANSYS. The results from the reliability analysis of the NPP structures are presented. KEY WORDS: Earthquake; NPP; Probability; Safety; ANSYS. 1   INTRODUCTION The IAEA (International Atomic Energy Agency) set up a  program [4 - 6] to give guidance to its member states on the many aspects of the safety of nuclear power reactors. The risk of the NPP performance from the point of the safety must be calculated by consideration of the impact of the all effects during plant operation. The PSA (Probabilistic Safety Analysis) is one from the effective methods to analyze the safety and reliability of the NPP. The international standard  NUREG-1150 [19] defines the principal steps for the calculation of the risk of the NPP performance by LHS  probabilistic method ã   Accident frequency (systems) analysis ã   Accident progression analysis ã   Radioactive material transport (source term) analysis ã   Offsite consequence analysis ã   Risk integration. The accidents caused by the earthquake even are the critical emergencies from the point of the NPP performance. This  paper gives the experiences from the seismic analysis of the operated NPP in Slovakia [7, 8, 9, 10, 11, 12, 13, 14, 15 and 22]. The earthquake resistance analysis of NPP buildings in Slovakia were based on the recommends of international organization IAEA in Vienna to get international safety level of the nuclear power plants [5]. Seismic safety evaluation  programs of the NPP structures should contain three important  parts [12] ã The assessment of the seismic hazard as an external event, specific to the seismic-tectonic and soil conditions of the site, and of the associated input motion; ã The safety analysis of the NPP resulting in an identification of the selected structures, systems and components appropriate for dealing with a seismic event with the objective of a safe shutdown; ã The evaluation of the plant specific seismic capacity to withstand the loads generated by such an event, possibly resulting in upgrading. 2   SEISMIC SAFETY METHODOLOGY On the base of the experience from the re-evulation programs in the membership countries IAEA in Vienna the seismic safety standard No.28 was established at 2003 [6]. Seismic safety evaluation programs should contain three important parts ã   The assessment of the seismic hazard as an external event, specific to the seismo-tectonic and soil conditions of the site, and of the associated input motion; ã   The safety analysis of the NPP resulting in an identification of the SSSCs (Selected Structures, Systems and Components) appropriate for dealing with a seismic event with the objective of a safe shutdown; ã   The evaluation of the plant specific seismic capacity to withstand the loads generated by such an event, possibly resulting in upgrading. 2.1   Seismic Hazards The assessment of the seismic hazards specific to the seismo-tectonic conditions at a site is performed on the following  bases: ã   IAEA Safety Guides [4-6], ã   Use of current internationally recognized methods and criteria [12, 19, 20, 21], ã    New data [2 and 16]. Two levels of the seismic load are defined in the standards [4]. SL-1 (First level) is coincident with the design earthquake and SL-2 (second level) corresponds to the maximum design earthquake. On the base of the IAEA requirements the NPP structures of the first category have been resistance due to seismic level SL-2. This seismic level [4] should be updated in accordance with the above bases in the event that a reason for this has appeared since the evaluation of the SL-2 design level and should be used in the evaluation. In particular, the PGA (Peak Ground Acceleration) of the RLE (Review Level of Earthquake) should not be less than 0.1g. The level of the seismic risk is characterized by the probability level (return Risk-Based Safety Analysis of the Seismic Resistance of the NPP Structures Juraj Králik  1 1  Department of Structural Mechanics, FCE, STU Bratislava, Radlinského 11, 813 68 Bratislava email: Proceedings of the 8th International Conference on Structural Dynamics, EURODYN 2011Leuven, Belgium, 4-6 July 2011G. De Roeck, G. Degrande, G. Lombaert, G. M¨uller (eds.)ISBN 978-90-760-1931-4 292   period) and the peak ground accelerations values, which are the typical free field zero period acceleration values at the ground surface. The comparison of the ground motion input level for new plants is presented in the Table 1. Table 1. Comparison of the PGA in various countries Probability/ Return Period Peak Ground Acceleration* Bulgaria 10 -4  0,20g Canada 10 -3  to 10 -4  Czech Republic 10 -4  0,10g Germany 10 -4  to 10 -5  0,10g - 0,20g Japan S1 10 -4  0,20g - 0,45g S2 0,38g - 0,60g Korea 10 -3  to 10 -4  Slovak Republic 10 -4  0,14g - 0,34g Sweden 10 -3  Schwitzerland 10 -4  UK 10 -4  US Design 0,30g Margin 0,50g The practice/guidance [12] that was referred to by a number of countries generally fall under the broad headings of a number of organizations, specifically ASME, IAEA, IEEE,  NRC, and, in some cases, local national regulations, as  presented in Table 2. Table 2. Practice/Guidance use in re-evaluation process ASME IAEA IEEE NRC National Belgium ☺   Bulgaria ☺   Czech Repub. ☺   ☺   Slovak Repub. ☺   ☺   Spain ☺   Schwitzerland ☺   ☺   ☺   ☺   US ☺   Existing nuclear facilities throughout the world are being subjected to investigation of their safety in the event of an earthquake. In the United States, there have been several licensing and safety review issues for which industry and regulatory agencies have cooperated to develop rational and economically feasible criteria for resolving the issues. Currently, all operating nuclear power plants in the United States are conducting an Individual Plant Examination of External Events, including earthquakes beyond the design  basis. Western European countries also have been re-evaluating their older nuclear power plants for seismic events often adapting the criteria developed in the United States. With the change in the political systems in Eastern Europe, there is a strong emphasis from their Western European neighbors to evaluate and upgrade the safety of their operating nuclear power plants. Finally, nuclear facilities in Asia are also being evaluated for seismic vulnerabilities. 3   SEISMIC RE-EVALUATION PROGRAM IN SR A re-assessment of the seismic hazard specific to the seismo-tectonic conditions at the site was considered by the SAV (Slovak Academy of Sciences) based on IAEA NUSS SO-SG-S1 and S8 [4]; US NRC-RG 1.60 and NUREG/CR-0098 [18]. IAEA is providing technical assistance to the Slovak regulatory authorities for reviewing the work results. Therefore the RLE (Review Level Earthquake) should correspond to the SL-2 level (Second Seismic Level), directly related to ultimate safety requirements. This is a level of extreme ground motion that shall have a very low probability of being exceeded during the plant lifetime and represents the maximum level of ground motion to be used for design and re-evaluation purposes. For the probability of occurrence a typical value of 10 -4 /yr is usually used and for the ground response spectra an elastic one is selected. As formulated by the Slovak authorities, the main objective of the seismic re-evaluation programs of NPP is to enhance the seismic safety of the plant to the level generally accepted  by the international community and in compliance with the valid standards and recognized practice. These programs should have three important components: (i)   the re-assessment of the seismic hazard as an external event, specific to the site seismo-tectonic conditions; (ii)   the evaluation of the plant specific seismic capacity to withstand the loads generated by such event; (iii)   upgrading if necessary. Regarding the first component (i), the geological stability and the ground motion parameters should be assessed according to specific site conditions and in compliance with criteria and methods valid for new facilities. In relation to the second component of the programs (ii) and considering that the plant has been srcinally designed for an earthquake level lower than the one would preliminarily be established for the site in compliance with IAFA NUSS 50-SG-S1 [4]. On the  base of the results of the seismic analysis of the structure capacity the upgrade concept (iii) will be designed. 3.1   Safety Aspects The decision should be made early on whether either the SPSA (Seismic Probabilistic Safety Assessment), SMA (Seismic Margin Assessment), or EPRI (Electric Power Research Institute) seismic safety evaluation methods are to  be used [12, 19-21]. These methods have an advantage in that the entire plant may be evaluated as an integrated unit, including system and spatial interactions, common cause failure, human actions, non-seismic failures and operating  procedures. The seismic resistance of the existing building structures as well as the technological equipment can be executed by the SMA method, especially its variant known as CDFM (Conservative Deterministic Failure Margin) depending on HCLPF (High Confidence Low Probability of Failure) determination of the seismic margin values. The CDFM method is based on an assumption that all the building structures and all the technological equipment components were designed properly for any non-seismic loads and conditions. Proceedings of the 8th International Conference on Structural Dynamics, EURODYN 2011  293  3.2    Acceptance Criteria The individual seismic resistance re-evaluation of each  building structure and each single component of NPP, technological equipment needs to be executed in the following way: ã   seismic margin assessment of the equipment structure or component in the existing state, which means the seismic margin HCLPF values determination in the existing state, ã    projection of seismic modifications (measures), if necessary  – if the seismic margin HCLPF value is calculated > ZPA, ã   seismic margin assessment of the equipment structure or component in the so-called fixed state after the projected modifications were executed, which means the seismic margin HCLPF values determination for this state. The HCLPF seismic margin value is calculated for the PGA for the review level of earthquake (RLE = SL-2) and it is defined mathematically as 95% probability that an earthquake will cause violation, SME (Seismic Margin Earthquake), in less than 5% of cases. The condition is to have the SME value greater than RLE (ergo SL-2) value; in other words to gain HCLPF seismic margin values greater than PGA RLE =SL-2. 3.3    High Confidence Low Probability of Failure The concept of the HCLPF (High Confidence Low Probability Failure) capacity is used in the SMA (Seismic Margin Assessment) reviews to quantify the seismic margins of NPPs. In simple terms it corresponds to the earthquake level at which, with high confidence ( ≥  95%) it is unlikely that failure of a system, structure or component required for safe shutdown of the plant will occur (< 5% probability). Estimating the HCLPF seismic capacity of a system, structure and component requires an estimation of the response, conditional on the occurrence of the RLE. Two candidate procedures to determine the HCLPF seismic capacities for NPP's structures and equipment components have been developed: (1) the Fragility Analysis (FA), and (2) the Conservative Deterministic Failure Margin (CDFM) method. The HCLPF approach or an equivalent method may be used to verify the seismic capacity of Mochovce NPP. The general criteria for CDFM approach is contained in [1]. The value of the HCLPF parameter depends on the equipment structure or component resistance (  R ) and the corresponding effect of action (  E  ) using elastic or inelastic  behavior. The following equation follows for the strength and response (  R/E  ) in respect to linear elasticity (  R/E  ) el  =  R / [(  E  Si 2  +  E  Sa2 ) 1/2  +  E   NS  ] (1) where  E  Si , or  E  Sa  is the seismic response to RLE (SL-2) inertial actions, or corresponding different seismic support movement, respectively, calculated according to linear elasticity. Then  E   NS   is a total response to all the co-incidental non-seismic bearings in the given combinations. Analogically, considering the elastic-plastic effect (  R/E  ) ep  =  R  / {[(  E  Si  / k   D ) 2  + (  E  Sa  · k   D ) 2 ] 1/2  +  E   NS  )} (2) where k   D  is ductility coefficient ( k   D  1.0). The partial seismic response  E  Sa  in equation (2) is really multiplied, not divided,  by the ductility coefficient. If SME is greater than RLE (SL-2), then (  R/E  ) ep  is greater than 1.0 and vice-versa. However, the (  R/E  ) el  and (  R/E  ) ep  ratios do not define the multiplication factors for RLE (SL-2) to gain the HCLPF seismic margin value. These factors are calculated as follows: ( FS  ) el  = (  R - E   NS  ) / (  E  Si 2  +  E  Sa 2 ) 1/2  (3) ( FS  ) ep  = (  R - E   NS  ) / (  E  Si  / k   D ) 2  + (  E  Sa  · k   D ) 2 ] 1/2  (4) The equation (4) is valid provided that ( FS  ) ep  > ( FS  ) el  and it can be significantly simplified if the  E  Sa   response to different seismic support movement as a result of RLE (SL-2) is negligible or it does not need to be considered. Then ( FS  ) ep  = ( FS  ) el  · k   D   (5) Generally it follows HCLPF (CDFM) = (FS)ep · PGA RLE =SL-2 (6) and this value must always be  HCLPF   > PGA . The HCLPF seismic margin value can also be determined via a non-linear elastic-plastic calculation (e.g. limit analysis defined in the ASME BPVC Section III (ed. 92) – Mandatory Appendix XIII). Generally, such calculation needs to be repeated several times before the seismic margin value is reached. No ductility coefficient is used in these non-linear calculations, of course (ductility coefficients are used only in linear elastic calculations). 3.4   Seismic Input Data The seismic response can be calculated in the frequency (spectrum response analysis) or time domain (transient analysis) [12]. Figure 1. Comparison of the horizontal acceleration response spectrum NUREG and GRS. Figure 2. Comparison of the horizontal acceleration response for various probability values. Proceedings of the 8th International Conference on Structural Dynamics, EURODYN 2011  294  Also, hence the earthquake input must be specified in terms of free-field ground motion accelerograms for time-history dynamic analyses [1]. The foundation of the reactor building  NPP can be embedded into the subsoil. This embedment has generally two effects on the dynamic analysis of the building: ã   In comparison to a surface foundation the dynamic behavior of the foundation is different. In the case of rock these differences are minimal. The impedance analysis results in stiffness parameters and damping ratios for the foundation soil system, which are higher than those for a surface foundation. ã   The second effect is that the acceleration time histories at foundation level are different from the control motions specified at the surface of the free field. In the case where structure and soil are idealized in only one Finite Element System or a consistent substructuring analysis the control motion is specified at the top of the surface and the effect of the embedment on both impedance and free field motion are automatically taken into account. 3.5    Response Spectrum Compatible Accelerogram To provide input excitations to structural models for sites with no strong ground motion data, it is necessary to generate the synthetic accelerogram. It has long been established that due to parameters such as geological conditions of the site, distance from the source, fault mechanism, etc. different earthquake records show different characteristics. Based on Kanai's investigation regarding the frequency content of different earthquake records, Tajimi proposed the following relation for the spectral density function of the strong ground motion with a distinct dominant frequency [12]: ( ) ( )( ) ( ) 220222 1414 ggggg SS  ξ ω ω ω ω ω ξ ω ω  ⎡ ⎤+⎢ ⎥⎣ ⎦=⎡ ⎤− +⎢ ⎥⎣ ⎦  (7) Here ξ  g  and ω g are the site dominant damping coefficient and frequency, and S  0  is the constant power spectral intensity of the bed rock excitation. The FORTRAN program COMPACEL has been developed  by Králik [12] for generate synthetic ground motion accelerogram assuming the site effect and requirement of standard. The requirements for the synthetic ground motion accelerogram according to standard ASCE 4/98 [1] are following: 1. The mean of the zero-period acceleration (ZPA) values shell equal or exceed the design ground acceleration, 2. In the frequency range 0,5 to 33 Hz, the average of the ratios of the mean spectrum to the design spectrum, where the ratios are calculated frequency by frequency, shall be equal to or greater than 1. 3. No one point of the mean spectrum (from the time histories) shall be more than 10% below the design spectrum. 4. The three components of motion in the orthogonal directions shall be statistically independent (with mean correlation smaller than 0,3), and the time histories shall be different. The program COMPACEL was created by J.Kralik to generate synthetic accelerograms. The comparison of the synthetic acceleration spectrum and GRS spectrum in the case of three and one accelerograms is showed in Figure 3 and 4. Using three accelerograms for the calculation of spectrum response the calculation results is less conservative than for one accelerogram. Figure 3. The spectrum compatible design horizontal accelerograms. Figure 4. The spectrum compatible design vertical accelerograms. Figure 5. Comparison of the synthetic acceleration spectrum and GRS spectrum. 4   CALCULATION MODEL OF NPP STRUCTURE The NPP WWER 440 building consists of six objects - reactor  building, bubbler tower, air-conditioning centre, turbine  building, and lengthwise side electrical building and cross side electrical building [12]. The foundation plate (75,0/43,0m) under building on part V-D/10-22 is on two levels -8.5m. The foundation plate (39,5m/27,0m) under bubbler tower on part D-E/10-17 is on level -8.5m too. The foundation strip and foot under columns are in the cross side electrical building and turbine building. The global geometry of the NPP structures in Jaslovské Bohunice and Mochovce is identical, Proceedings of the 8th International Conference on Structural Dynamics, EURODYN 2011  295
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