THE FEDERAL ENVIRONMENTAL, INDUSTRIAL AND NUCLEAR
SUPERVISION SERVICE
____________________________________________________________________
Approved by
The Order of the
the Federal Environmental, Industrial
and Nuclear Supervision Service
No. 33, dated February 01, 2017
SAFETY GUIDE FOR
THE USE OF ATOMIC ENERGY
"BASIC RECOMMENDATIONS FOR ELABORATION OF THE NPP Unit Level
1 PROBUBILISTIC SAFETY ANALYSIS OF INITIATING EVENTS RESULTED
FROM SEISMIC EFFECTS"
(RB-123-17)
In force since February 01, 2017.
Moscow, 2017
2
Safety Guide for the use of atomic energy "Basic recommendations for elaboration of
the NPP Unit Level 1 probabilistic safety analysis of initiating events resulted from
seismic effects" (RB-123-17)
The Federal Environmental, Industrial and Nuclear Supervision Service, Moscow,
2017
The Safety Guide for the use of atomic energy "Basic recommendations for
elaboration of the NPP Unit Level 1 probabilistic safety analysis of initiating events
resulted from seismic effects" (RB-123-17) (hereinafter - Safety Guide) was developed in
compliance with Article 6 of the Federal Law No. 170-FZ “On the use of atomic energy”
of November 21, 1995 for the purpose of promoting observance of requirements of
paragraphs 3.12, 6.1.5, 6.1.8 of the federal rules and regulations in the field of the use of
atomic energy "General Provisions for Safety Assurance of Nuclear Fuel Cycle
Facilities" (NP-016-05) approved by the Order of Federal Environmental, Industrial and
Nuclear Supervision Service dated December 2, 2005, No.11 and paragraphs 1.2.9,
1.2.17 of the federal rules and regulations in the field of the use of atomic energy
"General provisions for ensuring safety of nuclear power plants" (NP-001-15) approved
by the Order of Federal Environmental, Industrial and Nuclear Supervision Service dated
December 17, 2015, No.522.
This Safety Guide contains recommendations of the Federal Environmental,
Industrial and Nuclear Supervision Service (hereinafter referred to as Rostechnadzor) on
elaboration of PSA of NPP power units with various reactor types for initial events
resulted from seismic effects.
This Safety Guide recommendations cover aims, scope, content, procedure, quality
assurance, content of certain tasks (sections) and content of documentation of PSA for
initial events resulted from seismic effects.
This Safety Guide is intended for the use by:
1) Operating organization when doing safety analysis of the NPP units,
2) Rostechnadzor when reviewing the NPP safety analysis documents.
First issued.1
I.
General Provisions
1. The Safety Guide for the use of atomic energy "Basic recommendations for
elaboration of the NPP Unit Level 1 probabilistic safety analysis of initiating events
resulted from seismic effects" (RB-123-17) (hereinafter - Safety Guide) was developed in
1
Elaborated by the team of authors: D.E. Samokhin T.V. Noskov V.A. Berg M.A. Bredova E. G. Nazhitkov I.V. Bugaev (FBE
SEC NRS) Kalinkin (JSC Atomenergoproekt)
3
compliance with Article 6 of the Federal Law No. 170-FZ “On the use of atomic energy”
of November 21, 1995 for the purpose of promoting observance of requirements of the
federal rules and regulations in the field of the use of atomic energy "General Provisions
for Safety Assurance of Nuclear Power Plants" (NP-001-15) approved by the Order of
Federal Environmental, Industrial and Nuclear Supervision Service dated December 17,
2015, No.522 as well as for the purpose of promoting observance of requirements of the
federal rules and regulations in the field of the use of atomic energy "General
Requirements for the Probabilistic Safety Analysis for Nuclear Power Plants" (NP-09515) approved by the Order of Federal Environmental, Industrial and Nuclear Supervision
Service dated Wednesday, August 12, 2015, No.311.
2. This Safety Guide contains recommendations of the Federal Environmental,
Industrial and Nuclear Supervision Service of Russia for elaboration of the NPP Unit
Level 1 Probabilistic Safety Analysis for initiating events caused by seismic effects
(hereinafter - seismic PSA).
The list of abbreviations in this Safety Guide is presented in Appendix No.1, terms
and abbreviations – in Appendix No.2, recommended composition of the seismic PSA
reporting documentation – in Appendix No.3, recommended sequence and interrelation
of seismic PSA tasks – in Appendix No.4, recommended approaches to carrying out the
seismic hazard probabilistic analysis – in Appendix No.5, recommended approaches to
carrying out the element seismic damage rate analysis – in Appendix No.6, recommended
approaches to carrying out analysis of the systems, aggregate probability of severe
accidents due to seismic loads and evaluation of uncertainties – in Appendix No.7,
examples of elements exclusion criteria – in Appendix No.8 to the present Safety Guide.
3. This Safety Guide contains recommendations, implementation of which
ensures acceptable quality of seismic PSA.
4. The Safety Guide is intended for the use by design agencies, operating
organizations and Rostechnadzor for design, and operation of NPP Units, for supervision
over safety of NPP Units, elaboration and implementation of measures for ensuring
safety at the NPP Units.
5. The seismic PSA is a part of the full-scale Level 1 PSA to be developed for all
categories of IEs and for all possible operating conditions of NPP Units under
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construction and operation, with various types of reactors.
6. The seismic PSA can be conducted by means of other methods than those
stipulated in this Safety Guide, if it is justified that using such methods is safe.
7. This Safety Guide contains recommendations regarding aims, scope,
composition, content and sequence of completing certain tasks as well as composition
and scope of the reporting documentation.
II.
General Information
8. The main tasks of the seismic PSA are the following:
assessment of probability of NPP Unit-level severe accidents caused by seismic
loads;
assessment of the NPP Unit seismic margin as the ability to resist to seismic events
exceeding SSE;
identification of NPP Unit deficiencies including those when the seismic impact
exceeds the SSE level.
9. The main objectives of the seismic PSA are the following:
collection of information specific to the NPP Unit;
probabilistic analysis of the NPP site seismic hazards;
preliminary analysis of seismic impacts, development of a list of systems
(elements) to be analyzed;
probabilistic analysis of buildings (civil structures) response to seismic impacts;
seismic walk down of the Unit;
analysis of seismic damage rate of elements under seismic loads;
human reliability analysis;
modeling of accident sequences;
system analysis;
analysis of uncertainties, sensitivity, importance;
analysis of the seismic PSA results and assessment of the NPP Unit safety level.
10. The seismic PSA is recommended for NPP Units that are under construction
and in operation. Recommended sequence and interrelation of seismic PSA objectives are
5
given in Appendix No. 4 to this Safety Guide.
For NPP Unit under construction:
"The probabilistic seismic hazard analysis" is recommended to be carried out
within the seismic PSA using the simplified method described in Appendix No.5 to this
Safety Guide;
"The seismic walk down of the Unit" is recommended not to be carried out within
the seismic PSA;
when carrying out "The analysis of seismic damage rate of elements under seismic
loads" task within the seismic PSA, it is recommended to use results of the seismic
resistance report of equipment and buildings (structures) implemented for NPP units'
prototypes, information from the integrated data base and expert assessments.
11. The seismic PSA is recommended to be carried out based on information from
the NPP units' Safety Analysis Report and NPP PSA of level 1 for internal IE.
12. Recommendations of the "Provisions for the Basic Recommendations for
Elaboration of Level 1 Probabilistic Safety Analysis for Internal Initiating Events under
all the Operating Modes of a NPP Unit" approved by Order of the Federal
Environmental, Industrial and Nuclear Supervision Service of Russia No. 519 of
09.09.2011 (hereinafter referred to as RB-024-11) apply to the seismic PSA insofar as
they do not conflict with this Safety Guide.
Recommendations of the Safety Guide "Basic recommendations for elaboration of
level 1 probabilistic safety analysis of nuclear power plants for initiating events caused
by on-site fires and floods," (RB-076-12) approved by Order of the Federal
Environmental, Industrial and Nuclear Supervision Service of Russia No. 496 of
September 05, 2012, apply to the seismic PSA insofar as they do not conflict with this
Safety Guide.
Recommendations of the Safety Guide "Basic recommendations for elaboration of
level 1 probabilistic safety analysis of nuclear power plants for initiating events caused
by external natural and man-induced factors," (RB-021-14) approved by Order of the
Federal Environmental, Industrial and Nuclear Supervision Service of Russia No. 396 of
August 28, 2014, apply to the seismic PSA insofar as they do not conflict with this Safety
6
Guide.
13. It is recommended to analyze the possibility of the combined effect of seismic
loads and other external effects caused by seismic loads (for example, fire, floods, fall of
crane, etc. resulting from seismic loads) on the NPP unit.
14. The seismic PSA is recommended for the following IEs:
nuclear fuel in the reactor core;
nuclear fuel at the spent fuel storage facilities (for example, spent fuel/refueling
pool, spent fuel assembly drum);
15. When carrying out the seismic PSA, it is recommended to substantiate the
time interval, for which the systems (elements) of the NPP Unit reach the state to be
analyzed after seismic IEs occurred.
III.
Acquisition of information specific to nuclear power plant unit
16. For this seismic PSA task, the scope and composition of information required
for the analysis are determined, and appropriate information is collected. It is
recommended to collect the following data:
NPP general plan;
assessment results of the global seismic risk as applied to the site area under
consideration;
earthquake catalogs for the NPP site (area);
works performed earlier in the course of the analysis of NPP site seismic hazards,
geological, seismotectonic, seismological features of the area; structure and position of
PSFs, seismic sources, applied attenuation laws models;
site seismic analysis results regarding geodynamic data;
information on soil basements of the site buildings and structures including
geotechnical, geotechnical, dynamic characteristics of the soil basement elements, test
results and research results of the soil basement stability;
time history monitoring study of small earthquakes, settlements and tilts of site
basements and analysis of compensating measures;
unit prototype seismic resistance data bases and seismic walk-down results.
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17. When conducting the seismic PSA, it is recommended to use:
design documentation;
operation documentation;
operation experience as regards all the Units of the NPP in question, as well as
operation experience as regards prototypes, including information about the seismic
effects occurred;
the seismic PSA carried out for NPP Units prototypes.
NPP Unit PSA Level 1 for internal IEs;
available research results related to NPP seismic safety analysis;
verification analyses as regards seismic effects on equipment and structures
including supporting, anchoring and foundation structures of safety important equipment;
programs and results of seismic tests of equipment from the seismic list;
3D-model of the NPP Unit buildings (if available);
NPP Unit safety analysis reports;
state-of-the-art science and technology methodical recommendations described, for
example, in IAEA and other organizations' documentation.
IV.
Probabilistic seismic hazard analysis of the NPP site
18. The PSA "Probabilistic seismic hazard analysis of the NPP site" task is
determining seismic hazard curves giving information on exceedance frequencies of
various seismic intensity on the NPP site.
19. To define exceedance frequencies of various intensity seismic effects, it is
recommended to use a seismotectonic model of the NPP site area developed as part of the
NPP design (or as part of other activities) for definition of site and area seismicity
containing results of processing of geotechnical, geophysical, geotechnical and
seismological information, results of seismic and geodynamic monitoring performed in
the course of design and research activities, construction and operation of NPP.
It is recommended to include the following components into the site
seismotectonic model:
geometrical models of seismic sources (point, linear, areal, 3-D);
earthquake recurrence laws (stochastic models) for seismic sources, including peak
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magnitude assessment;
laws of attenuation of intensity depending on distance.
20. The probabilistic seismic hazard analysis is recommended to be carried out
with due regard to local ground conditions of the NPP site. It is recommended to take
into consideration influence of soil basement dynamic characteristics, including variation
of properties of watered ground levels, on the seismic hazards analysis results.
21. To define seismic hazard curves, it is recommended to define a minimal value
of seismic impact frequencies (within the time interval of a year) with due regard to the
integrated probability of severe beyond design accidents calculated in the course of
elaboration of PSA-1 for internal initiating events.
22. It is recommended to perform analysis of uncertainty of the NPP site seismic
hazard assessments. It is recommended to consider the following sources of uncertainty:
various models of laws of attenuation of intensity parameters from the sources;
various assessments of impact maximum magnitudes;
various types of movements in the seismic focus (shift, fault, overstep, or a
combination thereof);
various statistical laws of event occurrences;
other sources of epistemic uncertainty.
It is recommended to perform the uncertainty analysis using the logic tree, which
allows obtaining seismic hazard curves for various fractiles. The uncertainty, the sources
of which are listed in paragraphs 2  6 of item 22 of this Safety Guide, is assessed by
means of building a logic tree, fragment of which is shown in fig. 6.2 of Appendix No.5
to this Safety Guide as an example.
23. Results of the probabilistic analysis of NPP site seismic hazard are advised to
be presented in the form of the seismic hazard curves for spectral acceleration fractiles of
vibrations of various periods up to the zero period.
24. Results of the probabilistic seismic hazard analysis of the NPP site are advised
to be presented in the form of the seismic hazard curves for fractiles of peak accelerations
of the zero period specifying the form of the response spectrum specific to each level of
recurrence (annual frequency) of these curves.
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25. The recommended methods of performing the probabilistic analysis of NPP
site seismic hazard are given in Appendix No.5 to this Safety Guide.
V.
Preliminary analysis of seismic initiating events. Elaboration of a list of
systems (elements) to be analyzed
26. Preliminary analysis of seismic IEs of various intensity shall be performed for
the following purposes:
determination of IEs caused by seismic effects;
elaboration of accident sequence models;
elaboration of a preliminary list of systems (elements) potentially subject to
seismic effects.
The result of the seismic IEs preliminary analysis shall be a list of IEs as well as a
tree of seismic IEs establishing interrelations between various seismic IEs and failures of
buildings, systems and equipment. The sample matrix of a tree of seismic IEs is given in
Appendix No. 7 to this Safety Guide.
27. The list of systems (elements) in the seismic PSA (hereinafter referred to as 
seismic list of elements) shall be elaborated to account for their failures when modeling
accident sequences for IEs resulted from seismic effects.
28. The seismic list of elements should be elaborated phase by phase with due
regard to the information from:
analysis results of the site where the NPP Unit is located;
analysis
of
stability
of
the
soil
basement
where
NPP Unit is located;
PSA model for internal initiating events;
NPP Unit seismic walk-down results;
the seismic damage rate analysis of the elements from the seismic list.
29. The seismic list of elements should include:
all elements considered in the PSA model for internal IEs;
the
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passive elements of process systems that are not included into the PSA model for
internal IEs by various reasons, failure of which under seismic loads may affect
performance of safety functions considered in PSA (tanks, heat exchangers, volumes,
distribution systems components);
passive civil engineering structures, fastening elements to support other elements
from the seismic list specified in the design appendixes;
buildings and facilities encompassing systems (elements) included into the PSA
model for internal initiating events;
hydraulic engineering structures and elements that, once damaged due to seismic
loads, can lead to flooding of the NPP site or failure in operation of systems responsible
for heat removal to ultimate sink;
other elements added to the seismic list as a result of the NPP Unit seismic walkdown that, once damaged due to seismic loads, can lead to seismic spatial interaction
with other elements from the seismic list.
30. To elaborate the final list of elements, it is recommended to exclude elements
from the preliminary seismic list. Exclusion of elements from the preliminary seismic list
should be made:
by results of the NPP Unit seismic walk-down based on the simplified assessment
of seismic margin performed;
based on assessment of seismic margin of the elements from the preliminary
seismic list using available calculations;
based on similarity with the elements from the integrated data base, for which the
lower value of seismic margin of the element is known;
based on assessment of the seismic damage rate of the elements from the seismic
list performed.
31. The seismic list of elements is recommended to be presented in the table form
with the following information:
serial number of the element in the table;
description of the element;
process system, to which it belongs;
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code name of the element in the NPP design;
building, in which it is located;
facility, in which it is located;
elevation mark;
seismic category according to the federal norms and regulations in the field of the
use of atomic energy "Design Rules for Aseismic Nuclear Power Plants"(NP-031-01),
approved by Decree No.9 of Gosatomnadzor of Russia dated October 19, 2001
(hereinafter referred to as NP-031-91);
position of the element's axis (once the axis is defined for the element) relative to
the building's axes.
The list of buildings and structures is recommended to present as a separate table
with the following information:
serial number of the building (structure) in the table;
name of the building (structure);
code name of the building in the NPP design;
number of element on the NPP general plan.
VI.
Probabilistic analysis of buildings (civil structures) response to seismic effects
32. The probabilistic analysis of buildings (civil structures) response to seismic
effects is recommended to perform in order to assess loads on the elements from the
seismic list in the form of mean and standard deviations of seismic forces and/or response
spectra. For this purpose, it is recommended to build realistic mechanical models of
buildings together with the soil foundations and to perform dynamic calculations taking
into account mechanical interaction of the soil foundation and the building under seismic
loads.
33. When performing the building seismic response analysis (for example,
accelerograms), one should take into account local soil foundation properties (thickness
and order of location of ground levels as well as dynamic characteristics).
34. When making dynamic calculations of the "soil-building" system, it is
recommended to take into account mean values and characteristics of the aleatory and
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epistemic uncertainties for:
mechanical dynamic characteristics of the building and the soil foundation
(rigidity, inertia, damping);
geometrical kinematic features and force of the input seismic action (input
response spectra on the free surface, phase composition of the spectrum).
35. It is recommended to perform the dynamic calculations of the "soil-building"
system using one of the following methods:
direct dynamic method of motion equations connected system integration;
dynamic method of modal superposition;
dynamic method of integral transformation complex functions.
36. Mean values of buildings (structures) response characteristics and their
standard deviations should be determined using one of the following methods under
seismic loads with 10-4 1/year recurrence by the mean seismic hazard curve (for the mean
response spectrum of the equal exceedance frequency 10-4 1/year):
statistic modeling using the Monte-Carlo method and variations thereof for
variation of parameters specified in item 34 of this Safety Guide, and dynamic
calculations of the "soil-building" system;
deterministic analysis of the "soil-building" system response at realistic values of
the model parameters with further assessment of every factor specified in item 34 of this
Safety Guide important for deviation from the obtained response value and a general
deviation as a whole;
scaling of the "soil-building" system calculations available in the NPP Unit design
with the purpose of accounting for the difference between the response characteristics
and the mean values and reasonable assignment of values obtained from calculations for
the two previous models to the deviation characteristics.
The choice of method for analyzing buildings' (structures') response should be
made depending on available input data and a method selected for assessment of
elements' damage rates specified in part VIII of this Safety Guide.
VII. Seismic walk-down of the unit
37. The seismic walk-down of the unit at NPP in operation or in commissioning
13
should be done for confirmation of information available in the NPP Unit design and
obtaining the following additional information:
exact location of elements on the site (buildings, rooms, elevation marks,
orientation with regards to the building axes);
compliance of elements in question to the design documentation requirements
regarding reliability of elements' fixation during assembly and operation, condition of
fixing devices, condition of adjoining distribution systems' elements (pipelines, cables,
air ducts);
possibility of seismic spatial interactions of the element with adjoining equipment
and civil engineering structures.
During the NPP Unit seismic walk-down, additional information is collected to
conduct the damage rate analysis of elements from the seismic list.
38. It is recommended to form walk-down groups for the Unit seismic walk-down.
The following people should be included into the walk-down groups:
PSA specialists;
specialists of the seismic damage rate analysis of elements;
NPP Unit personnel.
39. The NPP Unit seismic walk-down should be done in three steps:
step 1  analysis of the technical documentation (process charts, fault trees from
PSA for internal IEs, seismic list of elements, available load calculations, response
spectra, strength and seismic resistance calculations, seismic resistance test results,
equipment specifications) and preparation of walk-down reports; walk-down groups
should be formed on step 1;
step 2 – walk-down and inspection of the site, buildings, civil structures and
premises of the NPP Unit; documenting of results – filling in walk-down report forms,
taking pictures, making sketches, calculation models;
step 3  formation of data base for the seismic elements using walk-down results.
40. The following information should be included into the walk-down reports:
name and marking of the building, premises, elevation mark, description of
system, element, assigned seismic class;
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information characterizing element from the seismic list regarding condition of
anchoring, fixing elements, welded joints to embedded parts, condition of threaded
connections, supports, hanger frames, distribution systems pallets;
information characterizing possible failures of the element due to seismic
interaction with:
civil structure elements and other elements due to close position (impact
effect, falling);
distribution systems (cables, pipelines, air ducts) insufficient fastening;
vessels, tanks, reactor plant vessel equipment, damage of which under
seismic loads leads to element failure caused by flooding;
graphics (pictures, sketches, photos) completing the information included into the
premises walk-down report.
VIII. Seismic damage rate analysis of elements
41. The objective of the seismic damage rate analysis of elements is assessment of
element failure conditional probability depending on the seismic force on the free surface
of site soil (peak or spectral (for fixed frequency range) acceleration) for various
confidence levels. Seismic load force parameter should be selected to be correspondent to
the one that was used for presenting results of the probabilistic analysis of NPP site
seismic hazard.
42. The seismic damage rate analysis of elements should be performed in several
steps:
step 1  selection of criteria (types) of element failure;
step 2  assessment of seismic damage rate of elements for every type of failure;
step 3  building of the seismic damage rate curve for the element.
43. It is recommended to consider the following types of element failures:
functional elasticity failures (spurious actuations of relays and switches, seizure of
drives, elastic instability of vessel walls, extreme fan blades deflection, extreme mutual
displacement of supports on the civil structure);
brittle failures (breaking off and cutting of anchor bolts and studs, break across
15
welded joint);
failures resulting from reaching the limit states of plasticity (reaching plastic
moment in cross sections of pipelines, bodies, plastic deformations of cable trays and
racks).
44. When selecting failure criteria, it is recommended to use design criteria,
seismic test results, failures of similar elements revealed after earthquakes as guidelines.
45. The recommended methods of performing the probabilistic analysis of seismic
damage rate of elements are given in Appendix No.6 to this Safety Guide.
To detect elements that are of most importance for the NPP Unit seismic safety
characteristics, one should ignore elements of insignificant importance. To exclude
elements that are insignificant for the unit seismic safety characteristics, one should
elaborate criteria for exclusion of elements by their seismic margins. It is recommended
to form a list of elements excluded by accepted criteria. Examples of element exclusion
criteria are given in Appendix No.8 to this Safety Guide.
IX.
Human reliability analysis
46. The personnel reliability analysis within the seismic PSA objective is to
determine and assess different factors of seismic effects upon the personnel performing
the accident management activities (higher stress level, reduced time for work
performance, false alarm, loss of information in the MCR).
47. It is recommended to carry out PRA within the framework of the seismic PSA
using a method similar to the method used in the NPP PSA-1 for internal initiating events
and considering the seismic effects.
48. It is recommended to accept the list elaborated within the PSA-1 for internal
initiating events as the basic list of the personnel erroneous actions. When additional
emergency scenarios are detected in the seismic PSA, it is recommended to detect new
human erroneous actions and to estimate their probability.
49. The factors important for probability of human errors during accident
management considered in the NPP PSA-1 for internal IEs should be used as the basic
list for the seismic PSA.
50. When conducting PRA, one should consider additional seismic-caused factors
16
affecting the probability of human accident management actions. It is recommended to
consider the following factors affecting performance of the required actions by the
personnel:
high stress;
reduced time for performance of the action;
impossibility of the action in-situ due to conditions that prevent from performance
of the action;
decreased information support in the MCR.
X.
Analysis of systems and modeling of accident sequences
51. It is recommended to elaborate the accident sequences model of the seismic
PSA on the basis of the available accident sequences models of PSA for internal IEs. It is
recommended to use event trees and fault trees from models of PSA for internal IEs as
the basis for the PSA model being developed including any necessary additional events
and/or changes in system models related to dependent failures in systems due to seismic
effects. It is recommended to take into account the fact that types and consequences of
failures at various seismic force levels can vary, and differ from those considered in PSA
for internal IEs for one and the same element.
52. It is recommended to include elements from the final seismic list into the
probabilistic model.
53. It is recommended to consider various levels of seismic effect according to the
seismic hazard curve that can influence the aggregated probability of severe accidents
with fuel melting. Consideration of various levels of seismic effect is recommended by
imposing specific boundary conditions.
54. Using AS models elaborated within NPP PSA of level 1 for internal IEs can be
possible when developing scenarios of seismic effects to account for specific seismic
effect consequences (multiple failures and spurious actuations). In these cases it is
recommended to develop new AS models upon condition that the principles of modeling
and basic assumptions accepted in the NPP PSA of level 1 for internal IEs are kept.
17
55. It is recommended to consider both system (element) failures caused by
seismic loads and failures from the PSA model for internal IEs caused by other than
seismic factors in the AS models. At the same time, it is recommended to consider
failures of passive elements (for example, pipelines, air ducts, cable routes, tanks,
construction elements). Consideration of the above mentioned passive elements in the
probabilistic models should be substantiated.
56. To reveal IEs caused by seismic effect, it is recommended to develop seismic
event trees at the stage of the preliminary analysis of seismic effects and the stage of AS
modeling.
57. It is recommended to take into account the logical cause-and-effect
relationship of events associated with the seismic effect scenario progress and to make
necessary changes in the seismic PSA model. It is recommended to take into account the
fact that the Unit shall be shutdown by the self-protection signal when the seismic effect
reaches the level envisaged in the design.
58. When elaborating an AS model, one should take into account the fact that a
consequence of the seismic effects of great intensiveness can be problems for personnel
accessing some specific areas of NPP for managing the accident.
59. It is recommended to take into account differences in probabilities of
recovering elements of internal and external effect models. For SSE- and higher level
seismic effects, the possibility for recovering the element can be low or null. It is
recommended to assess the probability for recovering systems (elements) with due
account for the force of the seismic loads.
60. When elaborating an AS model, one should take into account dependency of
element failures due to simultaneous seismic impact on such elements when they are
located at the same or close elevation marks, construction lines and positioned in one
direction. When elaborating the probabilistic model, one should consider the mentioned
dependencies by modeling common-cause failures of elements caused by seismic loads.
61. When analyzing AS, it is recommended to consider NPP site seismic hazard
features as well as characteristics of failure conditional probabilities (damage rate) within
the range of seismic effects of various intensity and recurrence defined in the NPP site
seismic hazard analysis.
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62. It is recommended to use mean values of seismic damage rate and mean
characteristics of the site seismic hazards (mean seismic hazard curves, mean spectra of
equal exceedance frequency) for definition of the mean probability of severe accidents
caused by seismic effects for NPP Unit probabilistic model elements. It is recommended
to use the mean value of integrated (for all seismic loads) probability of severe accidents
over one year for one NPP unit as the probabilistic safety indicator estimated within the
seismic PSA.
XI.
Analysis of uncertainty, sensitivity, importance of seismic PSA results and
assessment of the NPP Unit safety level
63. The analysis of uncertainty, sensitivity, importance in the course of
implementation of some seismic PSA tasks should be performed in accordance with the
recommendations of RB-024-11.
64. The analysis of the seismic PSA results and assessment of the NPP Unit safety
level should be conducted in compliance with the recommendations of RB-024-11.
_______________
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APPENDIX No.1 to the Safety Guide
for the use of atomic energy
"Basic recommendations for elaboration of
the NPP Unit Level 1 probabilistic safety
analysis of initiating events resulted from
seismic effects", approved by the Order of
the Federal Environmental, Industrial and
Nuclear Supervision Service of Russia
No. _________ of "___"
________________ 20
List of Abbreviations
EP
 Emergency Protection
HRA
 Human Reliability Analysis
AS
 Accident Sequence
NP
 Nuclear plant
MCR
 Main Control Room
PSA
 Probabilistic Safety Analysis
PSF
 Possible Seismic Focuses
HEP
 Human Error Probability
ID
 Radiation Source
IE
 Initiating Event
OHL
 Overhead Lines
IAEA
 International Atomic Energy Agency
SSE
 Safe Shutdown Earthquake
NO
 Normal Operation
PE
 Personnel errors
OSY
 Outdoor Switchyard
DBE
 Design Basis Earthquake
_______________
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APPENDIX No.2 to the Safety Guide
for the use of atomic energy
"Basic recommendations for elaboration of
the NPP Unit Level 1 probabilistic safety
analysis of initiating events resulted from
seismic effects", approved by the Order of
the Federal Environmental, Industrial and
Nuclear Supervision Service of Russia
No. _________ of "___"
________________ 20
Terms and definitions
Аccelerogram – time dependence of vibration accelerations
Аnalog accelerogram (selected) – accelerogram recorded during the real earthquake
and assumed for the seismic resistance design with due regard to its compliance with
the seismotectonic and ground conditions within the NPP area.
Earthquake accelerogram – accelerogram of free-surface ground acceleration
during earthquakes.
Response accelerogram – structure accelerogram obtained from calculation of
forced vibrations under seismic effect.
Floor-by-floor accelerogram – response accelerogram for certain elevations of
structures, on which equipment is mounted.
Synthesizing accelerogram – Analytical accelerogram based on statistical
processing and analysis of a series of accelerograms and/or spectra of real
earthquakes with due regard to the local seismic conditions.
Aleatory spread (uncertainty), R – spread of event parameter values due to its
random (stochastic) nature. The aleatory spread is considered in the parameter
modeling as a random value in the probabilistic model. In most cases, the aleatory
spread cannot be reduced by collecting additional data (conducting additional
material tests), obtaining additional information.
Site response analysis – determination of crustal motion induced by earthquakes
21
using the plane wave propagation theory taking into consideration local ground
conditions. The ground profile is modeled as a ground column of finite depth with
infinite horizontal extension. The earthquake waves extend upward the ground
column showing ground movement on the surface.
Element seismic damage rate analysis – a method of determination of types of
failures and seismic damage rate curves for the seismic list of elements.
Probabilistic seismic hazard analysis – a probabilistic method combining
alternative models of focuses, recurrence periods and dependencies of damping of
strong motion, as well as explicit and random uncertainties in the probabilistic model
of seismic hazards for assessing probability of exceedance of the specified ground
motion level.
Conditional probability (in the damage rate analysis) – probability of a considered
event depending (under condition) on achieving a fixed peak acceleration value of
ground free-surface a in free fall acceleration fractions g – P(a). Other characteristics
of intensity of impact on ground free-surface can be used instead of acceleration a.
Interaction of the ground-structure system – mechanical interaction of civil
structures with the soil basement of the structure under external loads with account of
propagating falling and reflected waves or external impacts on the structure.
Seismic margin (HCLPF - High-Confidence-of-Low-Probability-of-Failure) of
an element – value of acceleration (in free fall acceleration fractions g) on the
ground free-surface, at which the conditional possibility of element failure does not
exceed 5 % with the confidence level of 95 %. For the seismic damage rate mean
curve, at the combined uncertainty being within the limits of 0.5, the seismic margin
acceleration value corresponds approximately to the seismic damage rate of 0.01 (1
%).
Seismic margin of the NPP Unit – value of acceleration (in free fall acceleration
fractions g) on the ground free-surface, for which the estimated mean value of
conditional probability of severe core damage does not exceed 1 %.
Movement of the site free surface – ground motion occurring directly on the free
22
surface or near the surface on a specific site in the absence of a structure (a
construction project). It is defined by analyzing the site response to the seismic loads.
Deaggregation – calculation of most possible earthquake magnitudes and distances
from the focus to the site prevailing in the seismic danger probability analysis at a
given recurrence period and time of vibration.
Viscous damping (attenuation) – type of damping that occurs when a body moves
in the viscous medium. Under the viscous damping, the medium resistance force is
proportional to the body vibration velocity.
Structural, material, hysteresis damping – type of damping where the energy
dissipation occurs due to internal friction forces.
Seismic event tree – flow chart reflecting the logic of a certain intensity seismic
effect evolution used for modeling the IE occurrence.
Law of attenuation of intensity depending on the distance to the focus –
dependency of intensity, peak or spectral acceleration values (for various vibration
periods) on the specific distance to the earthquake focus. The law parameters can be
motion characteristics in the focus of the site soil foundation.
Earthquake recurrence law – linear dependence of the earthquake number
logarithm in a certain region for a certain time period on the magnitude.
Zone of PSF – earthquake source zones.
Seismic initial event – initial event caused by the seismic impact.
Viscous damping factor – coefficient of proportionality between the medium
viscous resistance force and the body movement velocity.
Damping factor (fraction, percentage of the critical value) – relation of the current
value of the viscous damping oscillator damping coefficient to the critical value of its
damping factor presented in fractions or percentage.
Seismic hazard (seismic risk) curve – plot of multiple values of frequencies
exceeding seismic effects of given intensity versus the assumed seismic impact
intensity parameter. Seismic hazard curves are built for various confidence levels in
the probability analysis.
23
Seismic damage rate curve – plot of element failure conditional probability values
versus the NPP site free surface peak acceleration values (or another intensity
parameter if seismic damage rate curves are built with the help thereof).
Seismic hazard curves for fractiles – set of seismic hazard curves used for carrying
out the uncertainty analysis to assess frequencies and intensity events that correspond
to various confidence levels.
Critical damping (attenuation) – value of the viscous damping oscillator damping
coefficient, at which its oscillatory movement becomes aperiodic.
Magnitude – measure of the earthquake force associated with the energy released in
the form of seismic waves. The magnitude is presented as a numerical value on a
standard scale (Richter scale, surface waves, moment magnitude, etc.)
Maximum (peak) acceleration of the ground surface – peak acceleration of the
accelerogram occurring on the free ground surface during the earthquake.
Logic-tree method – probabilistic method of accounting for uncertainties in
modeling. This method employs a tree-like structure of nodes and branches that
represent decision points and alternative models respectively. Branches emanating
from each node are assigned weights. The sum of weights of each node equals 1. The
resulting logic tree is either sampled exhaustively or probabilistically to determine
statistics.
Earthquake focus  geological environment, where rock burst and elastic stress
release occur. The size of the focus and the value of released elastic stresses are
responsible for the seismic wave energy and earthquake magnitude. The focus size
measure is also a seismic moment - a product of the rock shift and the burst area and
the shift amplitude. A point in the focus where the burst starts is called a hypocenter
(focus) of the earthquake, whereas its projection on the earth surface is called an
epicenter. The focus can be identified as a shift, fault, overstep, or a combination
thereof.
Combined spread (uncertainty),
and epistemic (model)


– uncertainty consisting of aleatory (random)

spread (uncertainty). The spread measure in the form of the
24
lognormal standard deviation is defined as 𝛽с = √𝛽𝑅2 + 𝛽𝑈2 .
Seismic hazard (in the seismic hazard probabilistic analysis) – is presented as
expected (within the given time period) exceedance frequencies of various intensity
seismic effects on the NPP site. The impact intensity is characterized by the
parameter (peak acceleration of the ground surface, spectral acceleration of the
ground surface at a given frequency and a damping factor, etc.) The time period is set
a year as a rule, while the assessed frequency is called the annual frequency impact.
Seismic damage rate of an element (civil structure, equipment or part thereof)
under seismic loads of assigned intensity – assumed probability of element failure
when the assigned seismic impact level is achieved on the free ground surface. The
seismic impact level can be assigned by the response (reaction) spectrum of this
impact on the site free surface. The seismic damage rate does not depend on the
seismic hazard of the site of the object under consideration but takes into
consideration the impact spectral structure.
Seismic source – generic term pertaining to the domains (geological medium of
internal physical homogeneous nature and dissipated seismic features) and tectonic
structures (discontinuous and folded motions) that can cause vibrations and tectonic
deformations of the surface. Impact frequency characteristics versus earthquake
magnitudes must be assigned in the seismic hazard probabilistic analysis for seismic
sources.
Seismic walk down of the Unit – visual inspection of buildings, constructions and
the NPP site, where the seismic list elements are physically located, with the purpose
to determine:
compliance
with
assembling
procedures
and
design
documentation
requirements, conditions of element fixation;
exact location of elements on the site (buildings, rooms, elevation marks,
orientation with regards to the building axes);
possible seismic spatial interactions.
Seismic list of elements – a list of NPP elements and soil basements, for which the
25
seismic damage rate analysis shall be done.
Seismic spatial interaction – mechanical interaction of the equipment, elements of
distribution systems, civil structures with the element from the seismic list located
nearby, which may cause malfunctioning of this element and failure to perform the
intended function.
Response (reaction) spectrum – sum of absolute values of peak response
accelerations of the linear oscillator under the load defined by the accelerogram with
due regard to the natural frequency and damping parameter of the oscillator.
Response spectrum of the equal exceedance frequency – a response spectrum
determined so that the exceedance frequency (within the assigned time interval) of
the spectral value (acceleration, velocity, movement) is equal for all values of
vibration frequency (vibration period) of such spectrum. The time period is set a year
as a rule.
Spectral acceleration – the response spectrum acceleration corresponding to the
assigned frequency (period).
Response spectra of the equal exceedance frequencies for fractiles – a set of
response spectra of the equal exceedance frequencies with different confidence levels
used for the uncertainty analysis in assessments of event frequency and intensity.
Zero period acceleration – spectral acceleration in asymptotic (solid) spectrum area
that lies usually within the frequency range of more than 33 Hz (peak acceleration of
the response spectrum accelerogram).
Frequency of exceedance of the assigned seismic intensity on the NPP site – the
estimated value of probability of exceedance of the assigned seismic parameter on the
NPP site surface over the time interval of one year.
Epistemic spread (uncertainty),U – a spread reflecting uncertainty due to
insufficient knowledge of the considered event, which prevents from modeling this
event with high accuracy. The epistemic uncertainty is present in the parameter value
variation range, possibility of using various models, level of modeling details,
different experts assessments and in statistical confidence level. The epistemic
26
uncertainty can be reduced by obtaining additional information, however, often, this
is not reasonable due to time, financial, technical limitations.
____________
27
APPENDIX No.3 to the Safety Guide
for the use of atomic energy
"Basic recommendations for elaboration of
the NPP Unit Level 1 probabilistic safety
analysis of initiating events resulted from
seismic effects", approved by the Order of
the Federal Environmental, Industrial and
Nuclear Supervision Service of Russia
No. _________ of "___"
________________ 20
Recommended scope of the seismic PSA report
I. General Information
The Chapter gives information about characteristics of the radiation sources,
operational states, missions, scope of investigations and objectives to be performed
within the scope of the seismic PSA investigations and objectives, states the main
suggestions and restrictions assumed in the analysis.
It is recommended to give references to expert reviews, which confirm quality
of the NPP PSA of level 1 for internal initiating events used as the basis for
elaboration of the seismic PSA.
Recommended sequence and interrelation of the seismic PSA objectives are
given in Appendix No. 4 to this Safety Guide. The seismic PSA reporting
documentation should include detailed information about the NPP site, brief
information about the reactor facility, NPP unit control and management, main and
emergency power supply systems, cooling systems of the main equipment and
systems involved in the safety functions. It is recommended to give references to
respective sources containing more detailed information.
The seismic PSA reporting documentation should include brief characteristics
of the procedures, guides and software programs used for all the tasks and objectives
considered within the seismic PSA.
II. Collection of information specific to the NPP Unit
28
The seismic PSA reporting documentation should include all information about
the NPP Unit used for elaboration of the seismic PSA. It is recommended to submit
initial data to the extent required for validity and completeness of the analysis.
When preparing initial seismic PSA data, it is recommended to give references
in the reporting documentation to the information about the NPP and the analyses,
results of which have been used for the seismic PSA.
III. Probabilistic analysis of NPP site seismic hazard
It is recommended to submit the NPP seismic hazard analysis with the
following information:
earthquake catalogs of the region;
data of investigations regarding the seismotectonic conditions of the territory of
construction, namely location and depth of possible earthquake focuses, recurrences,
magnitude, and minimal epicentral distance;
PSF zone models, geometric characteristics of seismic sources;
attenuation relations defining peak magnitudes, variants of relations (epistemic
uncertainty);
laws of earthquakes recurrence for PSF zones;
logical trees for seismic hazard analysis;
seismic hazard analysis results (seismic hazard curves for peak and spectral
accelerations, response spectra);
information on accounting local soil conditions in the seismic hazard
characteristics.
IV. Preliminary analysis of seismic initiating events. Elaboration of a list of
systems (elements) to be analyzed
It is recommended to submit a list of items of equipment, construction
elements, distribution systems elements with the following information:
serial number of the element;
description;
process system, to which it belongs;
building;
29
room;
elevation mark;
seismic category as per NP-031-01;
position of the element's axis relative to the building's axes.
V. Probabilistic analysis of buildings (civil structures) response to seismic
effects
It is recommended to present the following information within the seismic PSA
reporting documentation:
results of the seismic probabilistic analysis of structures in the form of
response spectra;
models of soil foundations used in the "soil-structure" interaction calculation;
results of the site response analysis, comparison of the seismic spectral
characteristics in the design analyses with those obtained from the site response
calculation;
information on performed calculations accounting variation of rigidity and
inertial characteristics.
VI. Seismic walk-down of the unit
It is recommended to submit the following information on the seismic walkdown of the unit:
reports of walk-down of premises;
a final table with the main walk-down results (recommendations, information
on spatial interactions, seismic margin assessment);
justification of seismic margin of elements by indirect methods (if available).
VII. Seismic damage rate analysis of elements
This chapter should present the following information about the element
damage rate analysis performed:
a method used to perform the element damage rate analysis;
types and criteria of failures;
criteria of exclusion;
30
characteristics of seismic damage rate of the elements that were not excluded
Am, U, R,c.
VIII. Human reliability analysis
The seismic PSA reporting documentation should present the results of the
personnel reliability analysis, including: brief description of the HRA methods, list of
considered human errors and their identifiers, results of the analysis for human error
selection, results of the analysis for determination of HEP, results of the analysis for
assessment of PE dependencies.
The seismic PSA reporting documentation should present the basic list of
personnel actions and a list of actions obtained as a result of analysis of additional
scenarios associated with seismic effects.
It is recommended to submit the final HRA results for the seismic PSA
considering seismic factors affecting the human actions.
It is recommended to submit results of assessment of probabilities for the
personnel actions that are used in the seismic PSA.
It is recommended to show the analysis of dependent human errors and results
of their assessment.
IX. Modeling of accident sequences
It is recommended to present results of AS including:
seismic event trees;
brief description of PSA model for internal IEs;
modified and newly developed event trees and fault trees for consideration of
various level seismic effects;
frequencies of seismic IEs and failures for various ranges of effects;
AS modeling results, list of minimal cross sections, probability of the severe
core damage for each IE in question.
X. Analysis of uncertainty, sensitivity and importance
The seismic PSA reporting documentation should present the results of the
analysis of uncertainty, sensitivity and importance.
31
XI. Analysis of seismic PSA results and assessment of the NPP Unit safety
level
The seismic PSA reporting documentation should give recommendations on
improving the NPP Unit safety developed on the basis of the seismic PSA results and
probabilistic assessments of their efficiency including technical and organizational
measures.
________________________________________
32
APPENDIX No.4 to the Safety Guide
for the use of atomic energy
"Basic recommendations for elaboration of
the NPP Unit Level 1 probabilistic safety
analysis of initiating events resulted from
seismic effects", approved by the Order of
the Federal Environmental, Industrial and
Nuclear Supervision Service of Russia
No. _________ of "___"
________________ 20
Recommended sequence and interrelation of seismic PSA objectives
Probabilistic analysis of
NPP site seismic hazard
Preliminary analysis of seismic
effects. Elaboration of a list of
systems (elements) to be analyzed
1
2
Probabilistic analysis of
buildings (civil
structures) response to
seismic impacts
3
Seismic walk-down of the
unit
4
Analysis of damage rate of
elements under seismic
loads
5
Personnel reliability analysis.
analysis of systems and simulation of
accident sequences
6
Analysis of uncertainties, sensitivity
and importance
7
____________
33
APPENDIX No.5 to the Safety Guide
for the use of atomic energy
"Basic recommendations for elaboration of
the NPP Unit Level 1 probabilistic safety
analysis of initiating events resulted from
seismic effects", approved by the Order of
the Federal Environmental, Industrial and
Nuclear Supervision Service of Russia
No. _________ of "___"
________________ 20
Recommended approaches to carrying out the seismic hazard probabilistic
analysis
Basic stages of the probabilistic seismic hazard analysis are given in fig. 6.1.
The specified stages are supplemented with the probabilistic analysis performed by
the method of logic tree given in fig.6.2.
It is allowed applying data cards of seismic zoning for estimation of the
construction site seismic hazards when elaborating the seismic PSA at the stage of
NPP Unit construction. The basic provisions of this method are specified in Appendix
No. 5 of RB-006-98.
1. Schematization of sources
At this stage, a model simplification of focus zones to simple geometric forms
(point, linear, 2D and 3D objects) is implemented depending on the available
information. Usually when determining possible PSF zones, it is assumed that
earthquakes occurrence inside any zone segment is equiprobable (equal distribution).
However, such assumption is not mandatory, and other distribution can be selected if
information on unequal distribution of activity in the zone is available.
The result of this stage is the density of distribution f R (r) , and the function of
distribution of distance to the potential source r, in the form
r
P( R  r) 

rmin
f R (r) dr .
(6.1)
34
Linear and point sources
Site
Zones
Magnitude
Relations for earthquake recurrence
Motion parameter
of free surface of soil
recurrence of 1/year
Schematization of potential sources
Distance
Decrease of intensity with distance (Relations of
attenuation)
Spectral acceleration
Recurrence of the site surface motion (seismic
hazard curves for spectral accelerations)
Fig. 6.1. Basic stages of the probabilistic seismic hazard analysis of the site.
2. Relations for earthquake recurrence
At the second stage, characteristics of the earthquake recurrence in the sources
are established.
The general approach is the Gutenberg-Richter relations of earthquake
recurrence:
35
lg λ m  a  b  m,
(6.2)
where:
m
 mean annual recurrence of exceedance of magnitude m;
a and b  parameters obtained by regression using source seismic nature data.
There are several methods of magnitude estimation (local magnitude ML of
Richter, body wave magnitude mb, surface wave magnitude (MS, MLH, MLV), moment
magnitude MW). It is required to ensure compliance of magnitude indicators in
recurrence relations and attenuation relations when implementing the probabilistic
seismic hazard analysis.
In relation (6.2), the magnitude it not limited, which contradicts the practice,
that is why relation (6.2) is corrected in the form:

m
  0
exp  m  m   exp  m
1  exp  m  m 
 m

,
(6.3)
where:
ν 0  exp(α-β  m ); 
ν 0  impact recurrence with the lower boundary of magnitude m;
α  ln(10)  a;
β  ln(10)  b;
m  upper boundary of magnitude values;
m  lower boundary of magnitude values.
Determination of the upper and lower magnitude value boundaries is a separate
research, performance of which increases credibility of the probabilistic seismic
hazard analysis, and results of which provide for most realistic assessments. Absence
of the realistic assessments of the above mentioned values is the cause for
consideration of this epistemic uncertainty by the logic tree method.
36
Determining the magnitude distribution function by density f M (m) as:
P  M  m m  m  m  
m
 f  μ  dμ
M
(6.4)
m
we can get
 m

λ m  ν 0  1   f M  μ  dμ  .
 m

(6.5)
3. Relations of attenuation
The term "attenuation" here means decrease of seismic effect depending on the
distance from the focus. The seismic effect in general can be determined on the free
site surface or on the free surface of the bedrock. The attenuation laws can generally
consider various parameters of the source (types of motions in the focus, type of
source), the site parameters (parameters of the site soil conditions) and are presented,
as usual, in the form of the mean value of the motion parameter logarithm (for
example, in the form of relation (6.6)) and the standard deviation:
C
ln a  C1  C2  m  C3  m 4  C5  ln  r  C6  exp(C7  m)  
C8  r  φ( s1 , s2 sk )  ψ( p1 , p2  pk ),
(6.6)
where:
С1…С8 – constants of regression (can be equal to zero);
m  magnitude;
r  distance to the source (epicentral, hypicentral);
s1 sk  parameters of the source;
φ()  function for consideration of the source parameters (can be equal to zero);
p1  pk  parameters of the site soil conditions;
37
ψ()  function for consideration of the site soil condition parameters (can be equal to
zero);
The final result of the step will be the conditional probability of exceeding
some value of the motion parameter A for every source in question.
P(A  a | m,r )  1  Ф(ln a, ln a ) .
(6.7)
4. Determination and presentation of results (hazards curves)
The results obtained at the previous stages for all the sources are integrated by
the equation giving the probability (frequency) of motion parameter exceedance per
year:
N
m rmax
v(a )   λ i (m ) 
n 1

f M i (m) f Ri (r ) P( A  a m, r )dmdr ,
(6.8)
m rmin
where index i belongs to i-th source.
The uncertainty, the sources of which are listed in item 20 of this Safety Guide,
is considered by means of building a logic tree, a fragment of which is shown in fig.
6.2 of Appendix No.5 to this Safety Guide.
Calculation of the seismic hazard curves is made for every branch of the logic
tree, and therefor, every final state of the tree has its own seismic hazard curve.
Besides that, every branch of the logic tree is assigned weight calculated for this
branch, with the sum of weights being 1.0. Therefor, every value of the motion
parameter a has n recurrence values, where n  the number of final states. The mean
weighted (with regard for the weight) recurrence value calculated for every registered
acceleration value makes up the mean curve of seismic hazard eventually. Median
values and fractiles of the seismic hazard curves are determined by analogy with
consideration of weights.
38
Подвижка в очаге
Mmovement
in
the focus
Оценка максимальной
Maximum
magnitude
магнитуды
assessment
highest,
наибольшая,
0,2
Закон
затухания
Decay
law
C&B 0,33
B&A 0,33
Model
Модель
А 0,33
uplift,
взброс, 0,2
average,
средняя, 0,6
C&B 0,33
B&A 0,33
Model
Модель А 0,33
lowest,
наименьшая,
0,2
C&B 0,33
B&A 0,33
Модель А 0,33
Model
highest,
наибольшая,
0,2
C&B 0,33
B&A 0,33
Модель
А 0,33
Model
throw, 0,5
average,
средняя, 0,6
сброс, 0,5
C&B 0,33
B&A 0,33
Модель
Model А 0,33
lowest,
наименьшая,
0,2
C&B 0,33
B&A 0,33
Модель
А 0,33
Model
highest,
наибольшая, 0,2
C&B 0,33
B&A 0,33
Модель
А 0,33
Model
average,
средняя, 0,6
C&B 0,33
B&A 0,33
сдвиг, 0,3
displacement, 0,3
Model А 0,33
Модель
lowest,
наименьшая,
0,2
C&B 0,33
B&A 0,33
Модель
А 0,33
Model
Fig. 6.2. Fragment of the uncertainty analysis logic tree
39
It is recommended to present the seismic hazard curve H(a) for convenience
as:
H (a)  K1  a - KH ,
(6.9)
where K1 and KH  constants determined, for example, by the method of least
squares.
If we present the seismic risk curve equation as the logarithm linear function,
we will get:
lg H (a )  lg K1  K H  lg a .
(6.10)
Examples of presentations of the seismic hazard curves for peak and spectral
accelerations are given in fig. 6.3, 6.4, 6.5 and 6.6.
1.00E-02
Средняя
mean
95%
1/year
Recurrence
1/год
Повторяемость,
1.00E-03
84%
16%
1.00E-04
5%
1.00E-05
median
Медиана
1.00E-06
1.00E-07
1.00E-08
0
0.1
0.2
0.3
0.4
Ускорение
нулевого периода,
g
Zero
period acceleration,
g
0.5
0.6
Fig. 6.3. Example of the seismic hazard curves for peak accelerations (or accelerations of
the zero period) and various confidence levels.
40
1.00E-02
1.00E-03
1/year 1/год
Recurrence
Повторяемость,
1.00E-04
Нулевой
период
Zero period
20 ГцHz
1.00E-05
10 ГцHz
1.00E-06
2 Гц
Hz
0.5 Гц Hz
1.00E-07
1.00E-08
0
0.5
1
1.5
Спектральное
ускорение,
Spectral acceleration, gg
2
2.5
Fig. 6.4. Example of the mean seismic hazard curves for spectral accelerations
0.5
Средний
mean
0.45
Медиана
median
0.4
fractile
5% квантиль
Ускорение, g
Acceleration, g
0.35
fractile
16% квантиль
0.3
84% квантиль
fractile
0.25
95% квантиль
fractile
0.2
0.15
0.1
0.05
0
0
10
20
30
Частота,
Гц
Frequency, Hz
40
50
Fig. 6.5. Example of the equal frequencies response mean spectra for the exceedance
frequency 10-4 1/year and various fractiles (5 % of critical damping)
41
1.8
1.6
1.4
Acceleration,
Ускорение,gg
1.2
1.00E-03
1
1.00E-04
0.8
1.00E-05
1.00E-06
0.6
1.00E-07
0.4
0.2
0
0
5
10
15
20
25
30
35
40
45
50
Частота, ГцHz
Frequency,
Fig. 6.6. Example of the equal frequencies response mean spectra for frequencies from 10 -3
to 10-7 1/year (5 % of critical damping)
If multiple sources are involved in the probabilistic seismic analysis, the
analysis of their importance can be performed in the form of deaggregation.
Example 1. Point source (Cornwell models)
Let us consider a model in the form of the point source shown in fig. 6.7. It is
assumed that occurrence of earthquakes from this source is a Poisson random
process.
P  Nt  n 
ν t
 0
n
exp   ν 0  t   number of events within the interval (0, t).
n!
To simplify the model, let us assume:
relations for recurrence (6.3) are only restricted at the left (only for small
amplitudes) thus m+ = ∞;
constants in the decay law (6.6) are equal to С3, C6, C7, C8 = 0; the decay law
spread is not considered C9 = 0. Functions   
thus, the decay law has the following form:
42
Ln  a   C1  C2  m  C5  ln  r  .
Point
Source
r  distance to the source
NPP site
x – distance to the epicenter
h – depth of the focus
Fig. 6.7. Point Source
Relation (6.7) has the deterministic form:
PA  a m, r   1.
This example belongs to determination of only one seismic hazard curve (the
logic tree for uncertainty analysis is not developed). In this case:
λm   0  exp β  m  m  ,
а function of distribution for events with magnitude m:
Fm  m  1  exp β  m  m  ;
f M  m  β  exp  β  m  m   ;
fR  r   δ R  r  ,
where  (∙)  delta (Dirac delta function).
The probability that magnitude Mmax of the most intensive earthquake (t=1) of
the year will exceed m:
43

P  M max  m   1  P  M max  m   1    P  M  m    P  N t  n  
 1  exp   ν 0  exp  β  m  m    .
n
n 0
Because the decay law spread (С9) is not considered, then:
M max 
 Amax

1
 ln 
 r C5  ,
C2
 exp  C1 

where Amax – peak acceleration of the free surface at an earthquake in the point source
of magnitude Mmax.
Then the following is true:
ν  a   P  M max  m   P  Amax  a  

 



a
1
 
 1  exp   0  exp  β   ln 
 r C5   m   .

 

 exp  C1 

 C2
 
After mathematical transformations, we can get:
β
β


C2
C2
γ
γ
ν  a   1  exp   ν 0  d  r  a   ν 0  d  r  a ,




where:
γ  β
C5
;
C2
 C  m  C2 
d  exp  β  1
.
C2


Below is the numerical example.
Let us assume that the site is 30 km from the point source focus that is 10 km
deep. From the seismological information, it follows that the impacts of magnitude
over 4 occur once in 50 years, whereas value 
The decay law for accelerations (in cm/s2) has the following coefficients:
С1 = 7.6 С2 = 0.8 С5 = -2,
then:
44
d = 5.32E+11;
 = 5;
r  30 2  10 2  31,62 km;
0 = 1/50 = 0.02.
Then, for example, for the free surface acceleration 0.1g (98 сm/s2), we will get
frequency:
ν  0,1g   0,02   5.32 1011    31,62   98
5
2,5
 0,0035 (1/year).
For a set of acceleration values, we will get the hazard curve (fig. 6.8) of this
Frequency, 1/year
site with 1 point source.
Acceleration, g
Fig. 6.8. The hazard curve for the point source example
Models, that allow "manual" calculations, only permit making approximate
assessment. It is difficult to account for limiting magnitudes at the right (peak m+),
spread and modern complex forms of attenuation in these models, therefor numerical
methods are used for hazard curves calculations.
Below is the example of main principles of their usage.
45
Example 2. Models with linear, rectangular and point sources
Fig. 6.9 gives the model in consideration.
(5,80)
Source
3
Источник
3
(25,75)
Источник
Source 2 2
(25,15)
(25,125)
Source
1
Источник
1
(0,0)
Площадка
Site
(-15,-30)
Fig. 6.9. Model with three sources
Recurrence law characteristics (6.2) for the sources are given in table 6.1.
Table 6.1
Recurrence law characteristics
Source
Recurrence law
lg λ  m   4  m
Source 1
Source 2
Source 3
lg λ  m   4.5  1.2  m
lg λ  m   3  0.8  m
m
m
4
7.7
4
5
4
7.3
Decay law (6.6) is given in the form suggested by Cornwell:
ln a  6,74  0,859  m  1,80  ln r  25 ,
where:
а – acceleration in cm/s2;
x – distance to the epicenter, km.
46
Standard deviation:
 ln a  C9  0,57 .
We will show how functions f R r  (6.1) and f M m (6.4) can be obtained by
the example of obtaining one summand of the total of expression (6.8).
All the summands should be obtained using computer equipment.
Let us consider the linear source No.1.
Maximum
distance
from
this
source
(point
with
coordinates
(-50;75)) to the site rmax = 90.14 km, minimal distance – rmin = 23.72 km. Let us
divide the source by 1000 equal sections by points. In addition to that, let us divide
the difference rmax  rmin by 100 equal sections, let us take a corresponding radius for
every dividing point and calculate the number of points of the source falling within
the circle between radii  ri , ri 1  , ri   rmin , rmax  .
Relation of the number of points falling into the item to the total number of
points (1000) determines the frequency of falling of the radius for the given interval.
The obtained in this way histogram for source No.1 is shown in fig. 6.9.
km
Fig. 6.9. Approximation of function f R r  for source No.1
For
rectangular
source
No.
2,
minimal
distance
–
rmin = 29.15 km, maximum  rmax = 145.78 km.
Let us divide the distance difference rmax  rmin by 100 equal sections, and take
a corresponding radius for every dividing point. Let us divide the rectangular source
47
by 2500 equal rectangles of (21.2) km each, take the point at the cross of diagonals
of every rectangle, calculate the number of points falling into every section.
Similar to the linear source, let us calculate the approximation of function
f R  r  (fig. 6.10).
Fig. 6.10. Approximation of function f R r  for source No.2
For
the
point
source,
the
approximation
function
is
evident
(see example 1).
From formulas (6.3), (6.5):
fM  m 
β  exp  β  m  m  
1  exp  β  m  m  
.
For every source in the small interval of magnitudes (m1,m2):
m2
 m  m2 
P  m1  m  m2    f M  m dm  f M  1
  m2  m1  .
2
m1


If for source No.1 the possible range of magnitudes from m- = 4 to m+ = 7.7 is
divided
into
10
sections,
for
the
first
of
them
( β  b  ln 10   1  ln(10)  2,303 ):
P  4  m  4,37  
2,303  exp  2,303   4,19  4  
1  exp  2,303   7,7  4  
 4,37  4   0.556.
The histogram built for 10 magnitude intervals for P(m = M) is given in fig.
6.11.
48
Fig. 6.11. Histogram P(m = M) for 10 magnitude intervals
Therefore,
for
source
No.1,
if
the
distance
to
the
site
and
the magnitude range corresponds to the minimal value, then:
P  r  27,04   0,208
P  m  4,19   0,556 .
For this combination of m and r, according to the accepted decay law, the peak
acceleration logarithm of the free surface
ln  a   3,225 (a = 0.025g).
Assuming that uncertainty (С9) in the decay law (natural acceleration logarithm
on the free surface) has normal distribution with the mean value 3.225 (for the given
values m and r), let us determine the 0.05g frequency occurrence on the free surface:
P  A  a m, r   P  A  0,05g m  4,19r  27,04  1    z  ,
where (∙) – standard function of the normal distribution.
z
ln  0,05  981  3,225
 1.17
0,57
1  1.17  0,121
49
g = 981 cm/s2.
Let us determine the first summand of the formula (6.8):
1(m-) = 1(4) = 1 (the second column, the second raw of table 6.1)
ν11  0,05 g   λ  m   P  A  0,05 g m  4,19r  27,04   P  r  27,04   P  m  4,19  
1
.
год
For obtaining the hazard curve, the following actions should be taken further: for the
 1  0,121  0,208  0,556  0,014
0.05g level, sum up all the values of frequencies for all combinations of m and r
values and for all the sources – by this way, the frequency value for 0.05 g
acceleration exceedance will be obtained. Further on, the described actions for other
values of accelerations should be taken, and frequency values should be determined.
The described calculations should be made with the help of computer equipment.
_____________
50
APPENDIX No.6 to the Safety Guide
for the use of atomic energy
"Basic recommendations for elaboration of
the NPP Unit Level 1 probabilistic safety
analysis of initiating events resulted from
seismic effects", approved by the Order of
the Federal Environmental, Industrial and
Nuclear Supervision Service of Russia
No. _________ of "___"
________________ 20
Recommended approaches to carrying out the analysis of element damage rate
due to seismic loads
Basic characteristics of the lognormal distribution Double lognormal
distribution
The lognormal distribution of random value is determined by density:
f  x 
1
e
β  x  2
 ln x μ 
2β
2
2
, x>0,
depending on the two parameters ,
where:
logarithmic median (or median value of the random value in question);
standard deviation of the random value logarithm.
Mathematical expectation m and standard deviation
distribution can be determined as:
me
 β2 
 μ+ 
2

,


σ N  e2μ β eβ  1 .
2
2
Then, for median
m  Am  e
 β2 
 
 2 
.
Am  eμ the following is true:

for the lognormal
51
At small  (for example <0,4):
m  Am ;
2
σN
 eβ  1  β ,
m
where COV – variation coefficient.
COV 
Function of the lognormal distribution
F  z  P X  z 
1
z
β  2π 0
 ln sμ 
e
s
2
2β 2

ds,0  z   .
The lognormal distribution of value A can be presented in the form:
A  Am  eβZ , where Z is the random value having a standard lognormal
distribution (the mean value is equal to zero, the dispersion is equal to 1).
Let us consider a standard model "load-strength" (fig.7.1).
Failure
region
Область
отказа
Probability density function
fQ(a), fR(a)
Load carrying
Несущая
capacity
способность
Реакция
Response
Q, R
Q(ai)
Q(ai+1) R(a)
Fig. 7.1. The combination of the response values and the seismic damage rate resulting in
the element's failure
For any specified seismic intensity level aQ, the element response will be a
random value conditioned by a set of random factors of the system transferring the
soil surface seismic motion impacts to the element (for example, by the spread of the
soil foundation features, rigidity and mass characteristics of the structural
components, damping). At the same time, the element's load carrying capacity that is
52
the ability to withstand the response forces, is also a random value conditioned by the
spread of material strength and other random parameters of the element's structure
features. Let us suppose that the load and the load carrying capacity are independent
random values distributed by the normal law. In the general case, the procedure of
determination of the element seismic damage rate curve is reduced to determination
of the joint probability density of response of the element and the load carrying
capacity. Fig. 7.1 shows the probability density plot of the random value that is
conventionally called "Response" and the probability density plot of another random
value – "Load carrying capacity". The region formed by the cross of areas under
these curves is the failure region. In a special case, when the calculated values can be
divided into two groups, the first one including the characteristics of the structure
proper, and the second one characterizing the external effects, the failure condition in
the strength calculation tasks appendices will be mathematically expressed by the
inequality:
g  R Q  0,
where Q – response to the load effect;
R – load carrying capacity expressed in the same units as the load effect Q ;
g – operability function or strength margin.
If random values R and Q are independent, the mathematical expectation and
the standard deviation of the strength margin are equal correspondingly to:
mg  mR  mQ ,
σ g  σ 2R  σQ2 ,
where:
mR and σ R – mathematical expectation and the standard deviation of the load
carrying capacity distribution;
mQ and σ Q – mathematical expectation and the standard deviation of the load
carrying capacity distribution;
For the normal distribution of the random values, the failure probability is
determined by the equation:
53
 m m
Q
Pf  1    R
 σ 2R  σQ2


 m m
R
   Q

 σ 2R  σQ2



,


where  – function of the standard normal distribution.
If functions R and Q are distributed lognormally and independent, the above
specified relation can be presented in the form:
 m
 mln R 
ln  Q 
Q 
Pf  P   1  P  ln  Q   ln  R   0    
 σ2  σ2
R 
ln  Q 
 ln R 

,


where:
Q
 load carrying capacity margin (random value);
R
mln( R ) , σln( R )  the mathematical expectation and the standard deviation of the
response natural logarithm;
mln(Q ) , σ ln(Q )  the mathematical expectation and the standard deviation of the
response natural logarithm of the load carrying capacity characteristic.
If Sm and Rm – median values of "load" Q and "strength" R, it the following is
true:
mln( R )  ln  Rm  ;
mln(Q )  ln  Qm  ;
 ln(Q )  βQ ;
 ln( R )  β R ;
βC  β 2R  βQ2 , then, at the earthquake of acceleration a on the free surface, the
random value will be the load on the element in question Q(a), while its madian 
Qm(a).
Then, the following is true for the element in question:
54
  Qm  a   
 ln 

Rm   .


f a  


βC




The specified relation determine the element seismic damage rate curve with
parameters Rm and C. in the general form.
By going from the loads and the load carrying capacity of the element (at the
mark) to the loads and the load carrying capacity of the free surface expressed in
accelerations, we will get a traditional view of the mean seismic damage rate curve:
  a 
 ln 

Am  


,
f a  
 βC 




where Am – median value of the element load carrying capacity expressed in the form
of the acceleration value of the free surface at the earthquake, at which the element's
failure occurs.
The double lognormal distribution is used in the damage rate analysis:
A  Am  eβU  X  eβR Y  Am  εU  ε R ,
where:
U, R – characteristics of aleatory and epistemic uncertainty;
εU  eβU  X , ε R  eβR Y ;
X, Y – random values having the standard normal distribution.
Such form of presentation supposes that alteration of the acceleration limit due
to epistemic uncertainty can be presented in a simple way as a random displacement
of the median value of this acceleration to the zone of less and greater values, while
the aleatory uncertainty determines the form of the "displaced" seismic curve (fig.
7.2).
Method of damage rate (scaling)
The element seismic damage rate expressed by the peak acceleration on the
55
soil free surface, at which the element failure occurs, is presented in the form of the
double lognormal distribution of random value A :
A  Am R U ,
(7.1)
where:
~
Am  median value of the random value A ;
εU ,ε R  lognormally distributed random values with single median and logarithmic
standard deviations U, R. These random values define the spread of the random
value A due to various factors:
ε R – aleatory spread;
εU – epistemic spread;
the seismic damage curve for confidence level Q is determined by the
  a 

1
 ln    βU Ф (Q) 
A
,
following expression: f (a)  Ф   m 


βR




(7.2)
where Ф(∙) and Ф-1(∙)  direct and inverse standard normal distribution functions;
Q  confidence level.
The median curve is obtained from the expression (7.2) by substituting Q=0.5
in (7.2), taking into account that Ф-1(0.5)=0 (or assuming =0, that is without account
of the epistemic uncertainty parameter ).
The curve for the 95% level of confidence is obtained by substituting Q=0.95
in (7.2).
In addition to that, the damage rate can be considered as the mean curve:
A  Am  εC ,
where ε C determines the total spread.
(7.3)
56
Mean (composite) curve is determined by the following relation:
  a 
 ln 

Am  


,
f (a)  Ф
 βC 




(7.4)
where βC  βU2  β 2R  combined uncertainty.
Fig. 7.2 gives an example of the seismic damage rate curves for various
fractiles. The representative points of the curves are: median Am corresponding to the
conditional probability of 0.5 on the median and mean curves, and the point on the
horizontal axis corresponding to the element seismic margin (HCLPF).
The 0.05 probability value on the 0.95 confidence level curve or the 0,01 value
on the mean (composite) curve corresponds to the HCLPF acceleration.
57
Median
Failure conditional probability
Mean (composite)
Peak ground acceleration (PGA), g
Fig. 7.2. Example of seismic damage rate curves
58
Here, relative to the damage curves, the stable term "mean" does not pertain to
the distribution characteristics but to the means of generalization of the seismic
damage curves with various level of confidence. It is more correct to call the mean
curve mean weighted.
~
To determine the seismic damage rate characteristics Am, , , the value A is
written in the form of the product:
A  F  AP ,
(7.5)
where AР – peak acceleration (of the zero period) on the soil free surface of the
earthquake with recurrence of 10-4 1/year according to the mean seismic risk curve (for
the mean spectrum of the equal exceedance frequency 10-4 1/year);
the value AP obtained in the seismic probabilistic analysis is allowed to be
different from the SSE acceleration accepted in the design;
F~ – statistical margin coefficient (random value characterizing the element load
carrying capacity margin coefficient at the earthquake of 10-4 recurrence according to
the mean seismic curve);
F~ – relation of the ultimate load in the element (that is the load due to the
earthquake critical for the element) to the load (response) in the element due to effect
Ар; the factor (random value), by which one must multiply the calculated acceleration to
obtain acceleration (random value) on the free surface, at which the failure occurs.
It is agreed to use the method of variable separation to separately account for
factors impacting the statistical margin coefficient. It is assumed that the element has
already been analyzed for seismic safety in the following scope:
the level of the design earthquake, for example SSE, has been established,
if the element in question is a civil structure, calculation of loads in the civil
structures (response in civil structures) and the element strength analysis have been
performed;
59
if the element in question is equipment, the impact of the structure on the
element, on which the element is fixed (response spectrum) has been determined;
calculation of loads in the element due to the estimated impact and the element
strength analysis have been performed.
The method assumes that at every stage of the load, response and strength
determination, there is a difference of the realistic approach from the conservative
one that is necessary in the safety analysis.
Coefficient F~ can be presented in the following form:
~ ~ ~ ~
F  F1  F2  F3 ,
(7.6)
where:
~
F1
 relation of the destructive load determined using realistic methods to the
allowed load regulated by the norms;
~
F2  relation of the allowed load to the design earthquake (SSE, DBE) load
regulated by the norms;
~
F3
 relation of the design earthquake (SSE, DBE) load regulated by the norms to
the load of the earthquake with 10-4 1/year recurrence according to the mean
seismic risk curve Ар determined by the realistic method.
Equivalent presentation F~ :
for buildings and structures: F  FC  FRS ,
for equipment: F  FC  FRE  FRS ,
(7.7)
(7.8)
where:
~
~ ~
FC  F1  F2 – load carrying capacity margin coefficient (random value);
FRS – building response coefficient (random value);
60
FRE – coefficient of equipment response against the building, in which it is installed
(random value) – relation of equipment response at the design earthquake determined
by the norms to the load due to AP , determined by the realistic method.
Accordingly:
for structures
FRS  F3 ,
for equipment FRE  FRS  F3 .
(7.9)
(7.10)
The margin coefficient FC is presented as a product of the two random values
~
~
FS and F that allow separate consideration of the margin with respect to the forces
obtained by the linear calculation and the margin related to the element structure
working beyond the elasticity limits:
~
~ ~
Fc  FS  F .
(7.11)
The margin coefficient FS is the relation of the critical force (or displacement),
at which, once achieved, the element loses the ability to perform its functions, to the
corresponding force occurring at the design earthquake:
S  PN
F~S 
PT  PN ,
(7.12)
where:
S – ultimate load that the element in question can resist in respect to the failure in
question;
PN – force of the operational load (NO);
PT – aggregated force (seismic effect + NO).
In the general case, these loads are random values having their own statistical
~
characteristics. Then the mean value and the deviation of the coefficient FS can be
determined by the Monte-Carlo method or by any other method (for example, the
first moment).
61
~
Coefficient F accounts for the energy dissipation beyond the elasticity limits.
Method for determining this coefficient are given in the document EPRI TR103959.
~
The structure response coefficient FRS is random value that takes into
consideration the fact that calculations made in the framework of the project are
based on specific (often conservative) deterministic parameters of the structure and
response therein. Depending on the factors influencing the structure response that
must be taken into account, it can be presented as the product of, for example,
corresponding coefficients of random values (IAEA-TECDOC-1487 Annex 1):
FRS   FRSi ,
(7.13)
where various factors can be considered as coefficients:
difference and spread in the response resulting from the difference of the
design spectrum (for example SSE) and the spectrum obtained as a result of the
seismic analysis of the site (in case of mapping the calculations of the seismic
stability performed in the design analysis according to paragraph 3 of item 36 of this
Safety Guide);
incoherency of seismic waves;
difference of the realistic damping from the damping regulated by the norms;
model uncertainty;
methods of natural forms addition;
method of taking into account the combined effect of spatial components of
effect;
effects of "soil-structure" interactions including change of effect intensity
depending on the depth relative to the earth's surface for the buried structures.
Every coefficient, as a random value having the double lognormal distribution,
can have a median and its own epistemic and aleatory spread  and  respectively. In
the general case, they can be determined by either varying the parameters influencing
62
each factor separately with the purpose of defining its median and spreads (method of
variable separation), or by using results of the researches that have been already
completed.
Using the lognormal distribution features, the median value of the coefficient
FRS is determined as:
FRS   FRSm ,
i
(7.14)
where m – index meaning the median values of corresponding coefficients.
Coefficient FRE for equipment can be represented in various ways depending
on the method used for seismic safety analysis of the element.
For rigid equipment (having high natural frequencies), it is enough to take into
account the modeling uncertainties and combined effect of spatial components of
effect.
For equipment having natural frequencies within the range of spectra of the
effects under consideration, one can also take into account differences in the design
and realistic spectral accelerations, differences in damping, errors of the qualification
method (in case of the experimental justification), etc.
Seismic damage characteristics Am,  and  are determined from the relations:
Am  Fm  Ap ,

U


n
i. 1

R


(7.15)
2
U i.
,
(7.16)
n
i. 1  R2
i.
,
(7.17)
Fm  FCm  FRSm  FREm ,
HCLPF  Am  e
1,65 βU β R 
(7.18)
,
(7.19)
where FCm , FRSm , FREm are median values of margin coefficients of the load
carrying capacity, response of structures and equipment respectively.
63
Simplified method of seismic damage rate calculation (hybrid method)
The method is based on generalization of the previous seismic PSA results and
allows simplifying the procedure of the element seismic damage range assessment by
using HCLPF characteristics that are assessed by the deterministic methods or
indirect methods (IAEA-TECDOC-1333, EPRI NP-6041-SL) after seismic walkdown of the unit.
Description
of
the
method
is
given
in
the
technical
document
IAEA-TECDOC-1487.
The hybrid method suggests the following order of actions:
assessing HCLPF for the element in question or assessing the free surface
intensity peak parameter value, at which its conditional probability is equal to 0.01
(or 1%);
assigning lognormal deviation  using the following recommendations:
for civil structures and basic passive mechanical equipment at low
elevations or at the free surface level   in the interval of 0.3 … 0.5;
for active elements located at high elevation marks in buildings

 in
the interval of 0.4 … 0.6;  = 0.4 is used as the conservative assessment;
calculating the median value of the load carrying capacity by the following
equation:
Am  HCLPF  e2.33βC ;
(7.20)
assessing the seismic damage curve by the formula (7.20).
For assessment of the element HCLPF, it is suggested to use the deterministic
method (CDFM) [EPRI NP-6041-SL, EPRI 1019200, IAEA Safety Report 28] or to
use the indirect seismic analysis methods based on the unit walk-down results
(IAEA-TECDOC-1333, EPRI NP-6041-SL).
64
Example
The vertical pump supplying water for cooling is considered. The potential
failure analysis covers various types of failures including anchor structure failures.
One of the potential failure types is the failure of the support structure of the electric
motor transmitting the torque moment to the pump shift, which can lead eventually to
the pump unit failure. In this example, obtaining the seismic damage curve for this
type of failure is considered. The electric motor (fig. 7.3) is fixed on the support
structure having the form of the cylinder with two cutout windows making in fact two
arcs with 120 angles and working as cantilever beams when lateral force is applied.
Electric motor
Motor frame
Coupling
Support motor structure
Support plate
Pump shaft
Fig. 7.3. The pump electric motor fixation layout
Calculation scheme is shown in fig. 7.4.
Electric motor
Электродвигатель
Опорный
Anchor
plate кронштейн
Support
plate
Опорная
Fig. 7.4. Calculation scheme
плита
65
In this example, the coefficients depend on the calculation specifics and can
be different for other cases (with different content).
Load carrying capacity margin coefficient Fc
The support structure is manufactured of steel with the minimal yield strength
σT0,2  250МПа at the design temperature. Let us assume that this value is guaranteed
with the 95 % exceedance level. The variation coefficient value for the carbon steel
yield strength normal distribution is approximately near 0.1.
Using the lognormal distribution properties we will get the epistemic
uncertainty due to lack of knowledge of actual material properties  u1  0,1, and the
material properties median value  300 MPa. Here we agree with the assumption that
the difference of the normal law from the lognormal one in this particular case and in
the practical application zone is not important for this task.
In the calculation, the combined stresses arising from bending and tension
(compression) caused by the horizontal and vertical seismic components are 50 MPa.
The calculation was made especially for determination of the seismic damage rate,
therefore the results can be considered having the median load assessment.
The median value of coefficient Fs can be obtained by the formula (7.12)
ignoring the operation load (dead weight):
FS 
300
 6.
50
It follows from the design statistical analysis that plastic yielding in the support
structure cross section (plastic hinge) is generated with the load increasing by 1.5
higher than the load of the beginning of plastic deformations. It follows from the
operational documentation that such increase can lead to misalignment and damage
of the coupling between the electric motor shaft and the pumping mechanism shaft,
therefore the coefficient F was assumed to be 1.5, while the load carrying capacity
66
margin coefficient
Fc:
Fc  Fμ  FS  1,5  6  9 .
Assuming the value F = 1.5 to be median, and the value equal to one having
the 95 % exceedance level, we will get:
βu2  1 / 1,65   ln 1,5   0, 245 ,
where the value 1.65 corresponds to the value of the inverse standard normal
distribution function at the value 0.95.
According to (7.16), the resulting value epistemic spread for the load carrying
capacity margin coefficient Fc is:
βU  βU2 1  βU2 2  0,12  0,2452  0,26 .
Equipment response coefficient FRE
Response coefficient parameters: calculation method, damping, modeling,
summing up natural forms and combination of earthquake components.
Calculation method
The natural frequency (6.81 Hz) of the discussed vibration mode measured
during the inspection slightly differs from that assumed earlier in the calculation
(4.23 Hz).
67
Расширенный
Extended 2% of2%
critical
damping
критического
демпфирования
acceleration, g
2%2%
Критического
of critical damping
демпфирования
5%5%
критического
of critical damping
демпфирования
Frequency, Hz
Fig. 7.5. Response spectra at the element installation mark
The damping in the calculation was assumed to be 2% of the critical one
according to NP-031-01. The damping median value is considered to be the value at
the condition close to failure that is assessed as 5% of the critical one.
The 2% extended spectrum was used in the calculation performed earlier. The
difference of the spectral acceleration (at frequency of 4.23 Hz) of the design
extended 2% spectrum from the spectral acceleration at frequency 6.81 Hz for the 5%
spectrum (fig.7.5) is estimated as:
FQM 
0,81 g
 1,03.
0,78 g
Uncertainty of the spectrum processing is estimated as the difference of the 2%
extended spectrum from the 2% one at frequency of 6.81 Hz. Considering that the
extension provides for 99% probability of non-exceedance (+2.33), we will get (at
frequency of 6.81 Hz) by the lognormal distribution properties:
βU1 
 1,41 g 
1
ln 
  0,12 .
2.33  1,06 g 
Damping
The design frequency of the electric motor was 4.23 Hz corresponding to the
acceleration  0.81g. It is considered that the 5% damping is median. However, when
68
computing the damping coefficient and its uncertainty ( βU ) one should first correct
the frequency that changed due to the calculation update. Damping was taken into
account when calculating the previous coefficient, therefore FD  1 . Frequency 6.81
Hz is within the zone of response spectra intensification. In this zone, relations of the
spectra (accelerations) with various attenuation coefficients (in fractions of the
critical one) at the selected frequency are approximately inversely proportional to the
square root of the relation of these attenuation coefficients.
It is assumed that the 2% spectrum form the boundary corresponding to the
standard deviation value  2U , while the 5% spectrum is median (U = 0) (such
assumption is suggested in the form of the expert evaluation). In this case:
1
 5% 
U  ln 
  0,23.
2
 2% 
2
Modeling
Possible decrease of the natural frequency due to change of damping and
propagation of non-linear deformation is considered. There are several methods of
taking into account the change of loads on the elements due to the mentioned effects.
Here the expert approach is used as the basis for such accounting.
As mentioned above, the natural frequency 6.81 Hz is within the zone of
response spectra intensification. When the natural frequency decreases, the load on
the support structure will also decrease in accordance with the response spectrum. It
is reasonably to suppose the decrease of the natural frequency by approximately 10%
(median value) due to propagation of the non-linear deformations in the pre-failure
condition. At the same time, (see fig. 7.5, the plot with the 5% critical level) the
possible spread is limited by the "shelf" of the 5% spectrum at frequencies from 4.6
to 5.6 Hz. Let us determine the accounting coefficient as the relation of the actual
load to the decreased one (the calculations use the spectrum with the 5% damping in
critical fractions):
69
FMod 
0,78 g
 1,13.
0,69 g
If we suppose that the lower acceleration value of the spectrum "shelf" (0.6g at
frequencies from 4.6 to 5.6 Hz) ensures the 99% exceedance probability, while the
initial value 0.78g ensures the 99% non-exceedance probability (1% of exceedance
probability), we will get:
βU Mod 
 0,78 g 
1
ln 
  0,056.
2  2,33  0,6 g 
Natural forms addition
The calculations were made by the dynamic analysis method with
decomposition into natural frequencies.
The first frequency were vibrations of the vertical pump structural column
itself, the second – vibrations of the electric motor on the support structure. Other
forms (over 15 Hz) practically do not influence the electric motor response.
Therefore, the natural forms addition effect is absent.
FMC  1.
The aleatory uncertainty is assumed to be minimal at the level:
R = 0.05.
Earthquake component combination
When the addition of components by the square root or by the rule (100-40-40)
(see table П.4.1 НП-031-01) is used, it is assumed that the load value is median:
FECC = 1.
According the EPRI TR-103959 recommendation, let us assume R = 0.18.
The resulting equipment response coefficient FRE:
FRE  FQM  FD  FMod  FMC  FECC  1,03  1,0  1,13  1  1  1,16.
Characteristics of the equipment response coefficient spread are equal to:
βU  0,122  0,232  0,0562  0,265;
R = 0.05.
70
Structure response coefficient
Coefficient components: spectrum profile, damping, modeling, summing up by
profiles and accounting of spatial and asynchronous nature of the external effect on
the structure (incoherency).
Spectrum profile
At the discussed frequency of 6.81 Hz, the relation of the response spectrum
acceleration value (5% of the critical damping) on the free surface used in the earlier
calculations to intensification of the spectrum obtained as a result of the seismic
hazard probabilistic analysis and accounting of the soil foundation local
characteristics is equal to 1.15.
FSS  1,15.
According to the document EPRI TR-103959:
β R  0,2;
βU  0,16.
Damping
At the loads on the pump support close to critical ones, the building structures
are in the elastic stage, therefore the damping equal to 4% is considered as median.
The spread due to uncertainty was estimated as 0.15.
FD  1,0;
βU  0,15.
Modeling
The building modeling and the model-based calculations were done in
accordance with the recommendations of section VI of this Safety Guide. The
building model was assumed to have median characteristics. Varying the
characteristics allows estimating the building natural frequencies spread for assessing
βU  0,1 . The pumping building vibration forms did not vary with the incoming
model parameters variation:
71
FMod  1,0;
βU  0,1.
Combination of natural forms
The building response is determined by one natural form in general. Therefore
the values obtained earlier have the median characteristic. The minimal value for the
aleatory spread is assumed according EPRI TR-103959:
FMC  1,0;
β R  0,05.
Accounting of the spatial and asynchronous nature of the external effect on the
structure (incoherency).
The pumping room has dimensions in the plan 27m55m.
For frequency of 6.81 Hz, the decreasing coefficient to correct the response
spectrum is 1.14. Because it is not taken into account in the design, then the
coefficient FGMI is also 1.14.
It is recommended to select the epistemic spread characteristic U of this
coefficient to ensure that the probability of exceeding the value FGMI1 was
extremely small:
1
1
βU  ln  Fm   ln 1,14   0,065.
2
2
Final structure response coefficient:
FRS  FSS  FD  FMod  FMC  FGMI  1,15  1,0  1,0  1,0  1,14  1,31;
β R  0,22  0,052  0,2;
βU  0,162  0,152  0,12  0,0652  0,25.
Element damage rate characteristics:
The calculated effect on the free surface corresponds to the maximal horizontal
acceleration on the free surface 0.08g.
72
Am  FC  FRS  FRE  ASSE  9  1,16  1,31  0,08 g  1,09 g ;
βU  0,262  0,2652  0,252  0,45;
β R  02  0,052  0,252  0,25;
βC  βU2  β 2R  0,51;
HCLPF  Am  e
1,65 βU β R 
 0,34
or by the approximate formula for the mean (composite) curve and the failure
conditional probability 0.01:
HCLPF  Am  e2,33βC  0,33.
Failure conditional probability
Seismic damage curves are shown in fig. 7.6.
Median
Mean (composite)
Peak ground acceleration (PGA), g
Fig. 7.6. Seismic damage curves for the electric motor support structure.
_____________
73
APPENDIX No.7 to the Safety Guide
for the use of atomic energy
"Basic recommendations for elaboration of
the NPP Unit Level 1 probabilistic safety
analysis of initiating events resulted from
seismic effects", approved by the Order of
the Federal Environmental, Industrial and
Nuclear Supervision Service of Russia
No. _________ of "___"
________________ 20
Recommended approaches to carrying out analysis of the systems, integrated
probability of severe accidents due to seismic loads and evaluation of
uncertainties
The scope of activities recommended to be carried out when performing the
analysis of the systems and the integrated probability of severe accidents due to
seismic loads and evaluation of uncertainties is given below.
1)
Elaboration of event trees and fault trees on the basis of AS model (event
trees) and system models (fault trees) from PSA level 1 for internal IEs taking into
account failures of elements due to seismic effects.
2)
Analysis of possible seismic IEs and elaboration of the seismic event
tree. The following events can be emphasized:
events, development of which leads to IEs that were considered in PSA for
internal initiating events: leaks (failure of the primary circuit equipment and adjacent
systems), blackout (OSY equipment, OHL external supports), other events that could
be considered in the model of PSA for internal IEs (loss of service water and other
initiating events);
additional effect-specific events: failures of structures, foundations, fires and
floods, flying objects, pipeline ruptures; the building and structure failures with
different consequences can be modeled on the seismic event trees (for example,
failure of the reactor compartment building  reactor vessel rupture, failure of EP,
failure of the turbine building).
74
The example of seismic IE tree is given in fig. 8.1
Reactor
Reactor
Seismic event
vessel
Reactor
PG head
building
emergency
Off-site power
Large
Medium
Small
Turbine
Designat
leak
leak
leak
building
ions
protection
Fig. 8.1. Example of seismic IE tree
3)
Grouping events by consequences: for example, OSY-related events are
grouped as events leading to the initiating event – the long-term NPP unit blackout.
To determine probabilities of the functional events (headings of the seismic IEs tree),
additional fault trees can be developed, for example, the reactor plant elements fault
tree of failures leading to events with small leakage at the 0.2g intensity event on the
free surface or the reactor compartment building civil structures fault tree.
4)
Breaking of the discussed seismic curve into ranges by intensiveness, in
which accident development qualitatively differs due to, for example, occurrence of
75
new events with frequencies that were outside the cut off level in a previous range, or
due to transfer of some events to the unconditional grade (for example, blackout at
intensive earthquakes). To obtain the mean value of severe accident probability, the
mean seismic hazard curve is considered.
5)
Calculation of seismic IE frequencies for every range and frequencies of
seismic failures.
Seismic IE frequencies are evaluated taking into account the seismic hazard
curve and the element damage rate curve.
For the seismic hazard curve range (hi, ai)…(hi+1, ai+1), the element damage rate
curve range with corresponding accelerations (fi, ai)…(fi+1, ai+1) is selected.
where:
hi, hi+1  values of the 1/year recurrence on the seismic hazard curve corresponding to
boundaries i -of the range;
ai, ai+1  values of the free soil surface accelerations corresponding to boundaries i -of
the range;
fi, fi+1  values of the element failure conditional probability (damage rate).
Frequency of the event for the n-th element IE nf is determined as:
i
IE nfi  (hi1  hi )  fi ,
where f i

the reduced conditional probability for the range.
To determine the reduced conditional probability, the recurrence range is
divided into intervals, while the reduced frequency is established as the mean
weighted.
100
fi 
 f h
m 1
100
i
 h
m 1
i
m
, where hm 
i
i
m
hi  hi 1 
100
, m = 1…100.
76
6)
To account for the seismic failure consequences, changes are introduced
in the fault trees developed for the internal IEs. In some cases the boundaries of the
discussed systems are revised: the system boundaries are extended by including
support structures and equipment anchoring, pipelines, cabinets for electric and
control systems, panels, to which elements are fixed, that were considered earlier in
PSA for internal IEs, and the distribution system elements.
7)
Conditional common cause failures under seismic loads are accounted.
The dependence is due to the equipment being of one type, the impact being similar
due to location (similar or slightly different response spectra: the systems are close at
each other, at the same or neighboring elevations, in the same location at building's
lines, with the same mounting conditions at the elevation, on the pipeline, etc.),
similar responses to seismic effect will happen. Maximum response characteristics of
such equipment will coincide by time, direction, and if any element fails, then a
similar failure of the similar element can be supposed.
The following methods of accounting of dependence by seismic response have
been used in the earlier elaborated seismic PSA:
similar elements at the same elevation mark responding in the same response
spectrum frequency range are considered absolutely dependent with regard to seismic
response;
similar elements at the same elevation mark responding in different response
spectrum frequency ranges have the response correlation factor 0.5. The difference
from the previous case can be, for example, in different conditions of fixation of
similar elements, which alters the rigidity and, correspondingly, the response
frequency ranges;
similar elements at different elevation marks of the same building but
responding in the same frequency range, have the seismic response correlation factor
0.75;
77
elements installed near the buildings are considered as if they are located at the
lower mark (of the soil surface) of the adjoining building;
similar configurations of the pipeline valves (serial or parallel) of the similar
elements have the seismic response correlation factor 1;
the rest configurations are considered independent.
When using the above described method at the stage of developing the seismic
list of elements and the NPP Unit walk-down, it is recommended to reveal and
register similar elements of equipment as well as similar fixation, installation,
suspension conditions.
8)
The aggregate probability of severe accidents caused by seismic effects
is calculated for every seismic hazard curve range.
Next, the obtained results are summed up for all the ranges.
9)
To conduct the uncertainty analysis, one should take into account
combinations of the seismic hazard probabilistic analyze data and the seismic damage
rate curves for various confidence levels. Because the possible combination of hazard
and damage rate curves can occur extremely large, special software for making the
specified calculations should be used for conducting the uncertainty analysis.
_______________
78
APPENDIX No.8 to the Safety Guide
for the use of atomic energy
"Basic recommendations for elaboration of
the NPP Unit Level 1 probabilistic safety
analysis of initiating events resulted from
seismic effects", approved by the Order of
the Federal Environmental, Industrial and
Nuclear Supervision Service of Russia
No. _________ of "___"
________________ 20
Examples of element exclusion criteria
Examples of exclusion criteria for elements that are insignificant for the NPP
Unit seismic safety are given below.
1) An element can be excluded if its seismic margin obtained by the indirect
method, by the walk-down results, exceeds the value assigned as threshold for
exclusion. The threshold value is substantiated considering the site seismic hazard
characteristics (Section IV of this Safety Guide) and absence of element failure
impact on the mean value of probability of severe accident. For estimating the
seismic margin by the indirect method, one makes the comparison of the considered
element against the class of similar elements, seismic behavior of which is well
known from experience.
2) The element can be excluded if the calculated seismic margin exceeds the
value assigned as threshold for exclusion (see item 1 of Appendix No.8 to this Safety
Guide). When using this criterion, the seismic margin assessment is required. At the
same time, a preliminary assessment of the seismic margin can be made using results
of
the earlier seismic resistance report:
HCLPF 
where:
 S   SНЭ
SМРЗ  НЭ  S НЭ
 aМРЗ ,
79
SНЭ – load at the normal operating conditions;
[S] – allowed load at SSE;
SМРЗ+НЭ – load from NO+SSE;
aМРЗ – peak acceleration of the free surface at SSE in free fall acceleration fractions.
3) The element seismic failure frequency in the entire given range lower by
more than order of two than the severe accident probability mean value (requires
assessment of the damage curve); may require the re-assessment if the severe
accident probability obtained in the seismic PSA differs by less than order of two
from the full annual frequency of element failure.
For determination of the seismic failure frequency HYf it is recommended to
use the full probability formula:


dH (a)
df (a)
HY f  
f a da  
 H a da ,
da
da
0
0
where:
H(a) – mean curve of the seismic hazard;
f(a) – mean curve of the seismic damage rate;
a – maximum horizontal acceleration of the free surface of soil.
When making the numerical integration, the limits zero and infinity in the
given formula can be replaced with the approximate values amin and amax
correspondingly. Then, if the seismic hazard curve can be presented in the form of
relations (6.9), (6.10) from Appendix No.5 to this Safety Guide, for
definition of HYf one can use the approximating formula:
HY 
1
(K H βC )2
2
H0  e
A
( m )K H
A0
,
where:
(H0, A0) – some point of the mean seismic hazard curve corresponding to, for
example, H0 = 10-4 1/year;
80
Am – see Appendix No. 6 to this Safety Guide.
Formulas (6.9) and (6.10) from Appendix No. 5 to this Safety Guide do not
often ensure good approximation of the seismic hazard curve. Therefore a preferable
option to obtain HYf is performing the numerical integration.
Example
The mean seismic hazard rate curve approximation has identifiers K1 = 2.32 1010
and KH = 4.18, acceleration A0 = 0.12g corresponds to frequency H0 = 1.9 10-6
1/year.
Then the full frequency value HYf = 1.57 10-8 1/year corresponds to the mean
seismic hazard rate curve with parameters
Am = 0.53g and = 0.4.
If, for example, it is expected that the probability of seismic event-related
severe
accidents
will
be
20%
of
the
aggregate
allowed
value
of
10-5 1/year for all IEs, then the obtained value HYf is lower by more than order of two
and can be excluded.
_______________