Seismic Consequence Abstraction Rev 00, ICN 00
MDL-WIS-PA-000003
August 2003
1. PURPOSE
The purpose of this model report is to develop abstractions for the response of engineered barrier
system (EBS) components to seismic hazards at a geologic repository at Yucca Mountain,
Nevada, and to define the methodology for using these abstractions in a seismic scenario class
for the Total System Performance Assessment - License Application (TSPA-LA). The seismic
hazards addressed herein are vibratory ground motion, fault displacement, and rockfall due to
ground motion. The EBS components are the drip shield, the waste package, and the fuel
cladding. The TSPA-LA is concerned with the postclosure performance of the repository. The
requirements for development of the abstractions and the associated algorithms for the seismic
scenario class are defined in Technical Work Plan for: Engineered Barrier System Department
Modeling and Testing FY03 Work Activities (BSC 2003a).
The development of these abstractions will provide a more complete representation of flow into
and transport from the EBS under disruptive events. The results from this development will also
address portions of integrated subissue ENG2, Mechanical Disruption of Engineered Barriers,
including the acceptance criteria for this subissue defined in Section 2.2.1.3.2.3 of Yucca
Mountain Review Plan, Final Report (NRC 2003).
1.1 SCOPE
The scope of this report is limited to abstracting the mechanical response of EBS components to
seismic hazards during the postclosure period and defining algorithms for the seismic scenario
class. The abstractions are based on the results from structural response calculations of EBS
components to vibratory ground motion, from analyses for fault displacement, and from analyses
of rockfall induced by vibratory ground motion. The structural response calculations and
rockfall calculations are not described in this report; rather, the results from these design
calculations and scientific analyses provide the inputs that the abstractions are based on. The
major design calculations and scientific analyses that provide input information for the
abstractions are identified in Section 6.1.2.
The damage abstractions for EBS components include both model abstractions and scientific
analyses. The abstractions for damage to the waste package and drip shield in response to
vibratory ground motion and rockfall are treated as models because they rely on analyses of
structural response over a range of ground motions that is wider than covered by standard
engineering practices. These model abstractions have been validated to the requirements in
AP-SIII.10Q, Models, through an independent technical review. The abstractions for damage to
the cladding and for damage from fault displacement are considered scientific analyses because
they are based on standard statistical techniques that bound the component response.
This report does not address the performance of naval spent nuclear fuel (SNF) during seismic
events. A planned classified Naval Nuclear Propulsion Program Addendum to the License
Application will provide the seismic analysis for naval SNF.
1.2 LIMITATIONS
The major limitations of the postclosure abstractions for the seismic scenario class are as
follows:

The structural response calculations include degradation of the waste package and drip
shield over a 20,000-year time frame, which includes the initial 10,000-year regulatory
period. The 20,000-year duration for the seismic analyses is designed to demonstrate that
repository performance remains robust well after the 10,000-year regulatory period has
ended. Calculations of the seismic scenario class beyond 20,000 years will require new
structural response calculations with additional levels of structural degradation.

Coupled effects from multiple seismic events are not considered because seismic hazards
with the potential to have a significant impact on engineered barriers are anticipated to
occur very rarely, if at all, during the 10,000-year regulatory period. More specifically,
seismic hazards with the greatest potential to damage the engineered barriers correspond to
large disruptive events with annual exceedance frequencies much less than 10-4 per year
(see Sections 5 and 6 of this report), so there is only a very small probability that multiple
events with the potential to induce significant damage will occur over a 10,000-year or
20,000-year period.

Spatial variability has not been represented in the damage abstractions for EBS components
under ground motion. In other words, damage to the waste package and drip shield from
vibratory ground motion is assumed to be constant throughout the repository. Spatial
variability for the damage abstraction for the drip shield under rockfall is limited to
variability between the lithophysal and nonlithophysal zones of the repository; the damage
abstraction for the drip shield from rockfall is constant throughout each zone.

Structural response calculations for the drip shield and waste package do not include any
initial backfill around the drip shield at the time of the seismic event. This representation is
consistent with the present design that does not include engineered backfill but may
become invalid if long-term fatigue of the tuff rock causes drift degradation and substantial
collapse before the seismic hazard occurs.

The abstraction for damage to the waste package from vibratory ground motions is based
on engineering calculations that cover a range of peak ground velocity (PGV) of 1 m/s to
6 m/s and have a maximum damage of less than 2 percent of the surface area of the waste
package. Similarly, the abstraction for damage to the drip shield from vibratory ground
motions is valid within a range of PGV from 1 m/s to 6 m/s. This is a reasonable approach
if sensitivity studies for the TSPA-LA calculations indicate that the maximum risk occurs
within this range of PGV values.

Damage to the waste package from rockfall is not included in the model abstraction for the
waste package. This is a reasonable approach for the intact EBS components because an
intact drip shield can deflect large rock blocks away from the waste package. However, if
separation of drip shields occurs for very high amplitude ground motions and if natural
backfill is not present, the shields will no longer protect the waste packages from direct
impact under rockfall during a second seismic event. Multiple hazards occur with a very
low probability, as noted previously, so this is a reasonable approach for TSPA-LA.

The potential coupling of seismic consequences with thermal processes has not been
included in the model abstractions. The presence of rubble about the drip shield after drift
collapse could cause changes in the thermal environment in the EBS if a seismic event
occurs relatively soon after repository closure, while the waste package and drip shield are
at elevated temperatures. However, the irregular and coarse nature of the rubble is
expected to allow sufficient convective heat transfer that the temperature histories
calculated for the nominal scenario class may reasonably be used to approximate
conditions following a seismic event during the thermal period. Because potential changes
in temperature due to the presence of rubble are not expected to be significant, the possible
associated changes in temperature-dependent solubility and corrosion rate have not been
included in TSPA-LA.
2. QUALITY ASSURANCE
The preparation of this model report and its supporting technical activities have been performed
in accordance with the appropriate requirements of the quality assurance program because the
abstractions and algorithms for the seismic scenario class are direct inputs for performance
assessment. This document is prepared in accordance with the applicable technical work plan
(BSC 2003a), which directs the work identified in work package AEBM04. The technical work
plan was prepared in accordance with AP-2.27Q, Planning for Science Activities. All input
information for this model report are identified and tracked in accordance with AP-3.15Q,
Managing Technical Product Inputs. No qualified software is used to develop the abstractions
documented in this report, so AP-SI.1Q, Software Management, is not applicable. The model(s)
and scientific analyses in this document are not structures, systems, or components so the quality
level classification from AP-2.22Q, Classification Criteria and Maintenance of the Monitored
Geologic Repository Q-List, is not applicable. The methods used to control the electronic
management of data, as required by AP-SV.1Q, Control of the Electronic Management of
Information, are identified in Section 8 of the technical work plan.
This document is prepared in accordance with AP-SIII.10Q, Models, and reviewed in accordance
with AP-2.14Q, Review of Technical Products and Data, as directed in the technical work plan.
3. USE OF SOFTWARE
3.1 QUALIFIED SOFTWARE
No qualified software is used to develop the seismic consequence abstractions. These
abstractions are based on the results of rockfall calculations and structural response calculations
that are performed with qualified software and that have been documented in separate scientific
analyses and design calculations. This qualified software is not directly used in the abstraction
process and hence is not listed here.
3.2 EXEMPT SOFTWARE
3.2.1 Microsoft Excel
Microsoft Excel for Windows, Version 97 SR-2, has been used to develop the abstractions for
damage from seismic hazards. The standard functions in Excel, including its statistical package,
are sufficient for all analyses. No macros, codes, or software routines are required or developed
during this work. Relevant Excel files are included as attachments to this report. Microsoft
Excel 97 SR-2 is an exempt software product in accordance with Sections 2.1.1 and 2.1.6 of
AP-SI.1Q, Software Management.
The formulas, listing of inputs, and listing of outputs for the Excel spreadsheets are presented in
Attachments I, II, IV, and VII of this model report.
4. INPUTS
4.1 DATA AND PARAMETERS
Table 1 presents the direct input information and Table 2 presents the corroborating information
for abstraction of damage to EBS components from seismic hazards. The information in Tables
1 and 2 have been categorized into six areas that are relevant to the abstractions in this report:
(1)
seismic failure criteria, (2) damage to the waste package from vibratory ground motion,
(3)
damage to the cladding from vibratory ground motion, (4) damage to the drip shield from
vibratory ground motions and from rockfall, (5) rockfall induced by ground motion, and
(6)
damage to the waste package and drip shield from fault displacement. Table 3 summarizes
the input information for the seismic scenario class and the sources for this information. When a
Data Tracking Number (DTN) is the source for a technical product input, its value is listed in
Tables 1 or 3 with the same number of significant figures as in the source. The technical product
inputs identified in Tables 1, 2, and 3 are appropriate for the development of model abstractions
and scientific analyses for the seismic scenario class.
Section 6.11.1 identifies the uncertainties in input information and parameters for the damage
analyses of EBS components and explains how these uncertainties are propagated into the
abstractions for the seismic scenario class.
Table 1. Direct Input Information for Seismic Consequence Abstractions
Input Information Value Source
Damage to the Waste Package From Vibratory Ground Motion:
Damage statistics for the waste package, based on a
sampling of vibratory ground motions at the 10-6 per year
hazard level
See Table 16 in
BSC 2003c
BSC 2003b, Table 6.1.4-2;
BSC 2003c, Table 16
Damage statistics for the waste package, based on a
sampling of vibratory ground motions at the 10-7 per year
hazard level
See Table 17 in
BSC 2003c
BSC 2003b, Table 6.2.4-2;
BSC 2003c, Table 17
Damage to the Cladding From Vibratory Ground Motion:
Maximum peak acceleration of fuel assemblies due to See Table 14 in BSC 2003d, Table 4;
waste package-to-waste package impacts BSC 2003e BSC 2003e, Table 14
Table 1. Direct Input Information for Seismic Consequence Abstractions (Continued)
Input Information Value Source
Average peak acceleration of fuel assemblies due to waste See Table 15 in BSC 2003d, Table 5;
package-to-waste package impacts BSC 2003e BSC 2003e, Table 15
Damage to the Drip Shield from Vibratory Ground Motion and Rockfall:
Damage statistics for the drip shield, based on a sampling
of vibratory ground motions at the 10-6 per year hazard
level
See Table 4 in
BSC 2003f BSC 2003f, Table 4
Damage to the drip shield due to impact by single rock
blocks from the 10-6 per year ground motion hazard level
See Table 2 in
BSC 2003f
BSC 2003g, Table 6-2;
BSC 2003f, Table 2
Damage to the drip shield due to impact by the maximum
rock block from the 10-7 per year ground motion hazard
level
See Table 3 in
BSC 2003f
BSC 2003g, Table 6-3;
BSC 2003f, Table 3
Rockfall Induced by Ground Motion:
Rockfall statistics in the nonlithophysal zone, based on a
sampling of vibratory ground motions at the 10-6 per year
hazard level
See Attachment
XI in BSC 2003h
BSC 2003h, Attachment XI;
DTN: MO0305MWDNLRKF.001
Rockfall statistics in the nonlithophysal zone, based on a
sampling of vibratory ground motions at the 10-7 per year
hazard level
See Attachment
XI in BSC 2003h
BSC 2003h, Attachment XI;
DTN: MO0301MWD3DE27.003
Length of the drip shield 5805 mm BSC 2003f, Table 1
Tunnel length for rockfall calculations 25 meters BSC 2003h, Section 6.3.1
Damage to the Waste Package and Drip Shield from Fault Displacement:
Drift Diameter 5.5 m BSC 2003i, Figure 1
Invert Thickness (maximum) 806 mm BSC 2003i, Figure 2
Drip Shield Height - Exterior 2885.62 mm BSC 2003f, Table 1
Drip Shield Height - Interior 2715.62 mm BSC 2003f, Table 1
44-BWR Waste Package Diameter 1674 mm BSC 2003j, Table 1
24-BWR Waste Package Diameter 1318 mm BSC 2003j, Table 1
21-PWR Waste Package Diameter 1644 mm BSC 2003j, Table 1
12-PWR Waste Package Diameter 1330 mm BSC 2003j, Table 1
Naval-Long Waste Package Diameter 1949 mm BSC 2003j, Table 1
Naval-Short Waste Package Diameter 1949 mm BSC 2003j, Table 1
5 DHLW-Short Waste Package Diameter 2110 mm BSC 2003j, Table 1
5 DHLW-Long Waste Package Diameter 2110 mm BSC 2003j, Table 1
2-MCO/2-DHLW Waste Package Diameter 1814 mm BSC 2003j, Table 1
44-BWR Waste Package Length 5165 mm BSC 2003j, Table 1
24-BWR Waste Package Length 5105 mm BSC 2003j, Table 1
21-PWR Waste Package Length 5165 mm BSC 2003j, Table 1
12-PWR Waste Package Length 5651 mm BSC 2003j, Table 1
Naval-Long Waste Package Length 6065 mm BSC 2003j, Table 1
Naval-Short Waste Package Length 5430 mm BSC 2003j, Table 1
5 DHLW-Short Waste Package Length 3590 mm BSC 2003j, Table 1
5 DHLW-Long Waste Package Length 5217 mm BSC 2003j, Table 1
2-MCO/2-DHLW Waste Package Length 5217 mm BSC 2003j, Table 1
Emplacement Drifts Intersected by the Sundance Fault in
Lower Lithophysal Zones 1-6, 1-7, and 1-8 DTN: LL030704623122.031,
tspa03.mesh03-150w
3-1, 3-2, 2-5W,
Emplacement Drifts Intersected by the Drill Hole Wash 2-6W, 2-7W, DTN: LL030704623122.031,
Fault in Lower Lithophysal Zones 2-8W, 2-9W, and tspa03.mesh03-150w
2-10W
Table 1. Direct Input Information for Seismic Consequence Abstractions (Continued)
Input Information Value Source
Emplacement Drifts Intersected by the Drill Hole Wash
Fault in Other Zones
2-9E, 2-10E,
2-11E, 2-12E, 213E,
2-14E, 215E,
2-16E, and
2-17E
DTN: LL030704623122.031,
tspa03.mesh03-150w
Emplacement Drifts Intersected by the Pagany Wash Fault
in Lower Lithophysal Zones
2-1W, 2-2W,
2-1E, 2-2E, 2-3E,
2-4E, and 2-5E
DTN: LL030704623122.031,
tspa03.mesh03-150w
Emplacement Drifts Intersected by the Pagany Wash Fault
in Other Zones 2-6E and 2-7E DTN: LL030704623122.031,
tspa03.mesh03-150w
Emplacement Drifts Intersected by the Sevier Wash Fault
in Lower Lithophysal Zones 2-2E DTN: LL030704623122.031,
tspa03.mesh03-150w
Fault Displacement Hazard at Site 3  on the Drill Hole
Wash Fault See file for data DTN: MO0004MWDRIFM3.002,
file ./displ/tot_haz/s3.frac_mean.gz
Fault Displacement Hazard at Site 5  on the Sundance
Fault See file for data DTN: MO0004MWDRIFM3.002,
file ./displ/tot_haz/s5.frac_mean.gz
Fault Displacement Hazard at Site 7a  a generic
repository location, approximately 100-meters east of the
Solitario Canyon Fault, with a hypothetical small fault with
2-meter offset
See file for data DTN: MO0004MWDRIFM3.002,
file ./displ/tot_haz/s7a.frac_mean.gz
Fault Displacement Hazard at Site 8a  a generic
repository location, midway between the Solitario Canyon
and Ghost Dance Faults, with a hypothetical small fault
with a 2-meter offset
See file for data DTN: MO0004MWDRIFM3.002,
file ./displ/tot_haz/s8a.frac_mean.gz
Fault Displacement Hazard at Sites 7b and 7c  generic
repository locations, approximately 100-meters east of the DTN: MO0004MWDRIFM3.002,
Solitario Canyon Fault. Site 7b has a hypothetical shear See files for data files ./displ/tot_haz/s7b.frac_mean.gz
with 10-cm offset and site 7c has a hypothetical fracture
with no cumulative displacement.
and ./displ/tot_haz/s7c.frac_mean.gz
Fault Displacement Hazard at Sites 8b and 8c  generic
repository locations, midway between the Solitario Canyon DTN: MO0004MWDRIFM3.002,
and Ghost Dance Faults. Site 8b has a hypothetical shear See files for data files ./displ/tot_haz/s8b.frac_mean.gz
with 10-cm offset and site 8c has a hypothetical fracture
with no cumulative displacement.
and ./displ/tot_haz/s8c.frac_mean.gz
Number of 21 PWR Waste Packages with Absorber Plates 4299 BSC 2003k, Table 11
Number of 21 PWR Waste Packages with Control Rods 95 BSC 2003k, Table 11
Number of 12 PWR Long Waste Packages with Absorber
Plates 163 BSC 2003k, Table 11
Number of 44 BWR Waste Packages with Absorber Plates 2831 BSC 2003k, Table 11
Number of 24 BWR Waste Packages with Absorber Plates 84 BSC 2003k, Table 11
Number of 5 DHLW Short/1 DOE SNF Short Waste
Package 1147 BSC 2003k, Table 11
Number of 5 DHLW Long/1 DOE SNF Long Waste
Package 1406 BSC 2003k, Table 11
Number of 2 MCO/2 DHLW Waste Package 149 BSC 2003k, Table 11
Number of 5 DHLW Long/1 DOE SNF Short Waste
Package 31 BSC 2003k, Table 11
Number of HLW Long Only Waste Package 679 BSC 2003k, Table 11
Number of Naval Short Waste Package 144 BSC 2003k, Table 11
Number of Naval Long Waste Package 156 BSC 2003k, Table 11
Table 2. Corroborating Input Information for Seismic Consequence Abstractions
Input Information Value Source
Seismic Failure Criteria:
Residual stress threshold for initiation of stress corrosion
cracking on a smooth surface of Alloy 22
90% of the yield strength
of Alloy 22
BSC 2003l, Section 6.2.1, end of
3rd paragraph
Residual stress threshold for initiation of stress corrosion
cracking on a smooth surface of Titanium Grade 7
50% of the yield strength
of Titanium Grade 7
BSC 2003l, Section 6.2.1, end of
3rd paragraph
Damage to the Waste Package from Ground Motion:
Preliminary damage statistics for the waste package,
based on a sampling of vibratory ground motions at the
10-5 per year hazard level
See Table XI-2 in BSC
2003b
BSC 2003b, Table XI-2;
BSC 2003m, Table 58
Damage to the waste package for the single vibratory
ground motion at the 510-4 per year hazard level No damage BSC 2003b, Section 6.3, last
paragraph
Damage to the Cladding from Ground Motion:
Statistics for axial impact velocities between adjacent
waste packages, based on a sampling of vibratory
ground motions at the 10-6 per year hazard level
See Tables 6.1.2-1
through 6.1.2-15
BSC 2003b, Tables 6.1.2-1 to
6.1.2-15;
BSC 2003n, Tables 28 to 42
Statistics for axial impact velocities between adjacent
waste packages, based on a sampling of vibratory
ground motions at the 10-7 per year hazard level
See Tables 6.2.2-1
through 6.2.2-15
BSC 2003b, Tables 6.2.2-1 to 6.2.2-
15; BSC 2003n, Tables 43, 44, and
45; BSC 2003m, Tables 46 to 57
Axial impact velocity between adjacent waste packages
for the single vibratory ground motion at the 510-4 per
year hazard level
Relative displacement of
waste package and pallet
nodes is less than 0.01
mm
BSC 2003b, Figures 10 and 11
Damage to the Drip Shield from Ground Motion:
Damage statistics for the drip shield, based on a
sampling of vibratory ground motions at the 10-7 per year
hazard level
Drip shield separates for
all ground motions BSC 2003f, Calculation Results I
Damage to the drip shield for the single vibratory ground
motion at the 510-4 per year hazard level No damage BSC 2003f, Calculation Results I
Rockfall Induced by Ground Motion:
Rockfall statistics in the nonlithophysal zone, based on a
single vibratory ground motion at the 510-4 per year
level
See Table 19 BSC 2003h, Table 19
Damage statistics for a tunnel in the lithophysal zone,
based on a sampling of vibratory ground motions at the
10-6 per year level
Tunnel collapses for all
ground motions BSC 2003h, Section 6.4.1.1
Damage to a tunnel in the lithophysal zone for the single
vibratory ground motion at the 510-4 per year hazard
level
No rockfall for rock mass
categories 2-5; minor, low-
energy rockfall for rock
mass category 1
BSC 2003h, Section 6.4.1.1
Damage to the Waste Package and Drip Shield From Fault Displacement:
Fault Displacement Hazard at Site 2  on the Solitario
Canyon Fault
See Figure 8-3 in
CRWMS M&O 1998 CRWMS M&O 1998, Figure 8-3
Fault Displacement Hazard at Site 4  on the Ghost
Dance Fault
See Figure 8-5 in
CRWMS M&O 1998 CRWMS M&O 1998, Figure 8-5
Fault Displacement Features of the Sevier Wash
Fault and the Pagany Wash Fault
Similar to Drill Hole
Wash Fault Menges and Whitney 1996
Seismic hazard frequency for drift collapse in lower
lithophysal 1e-06 BSC 2003h, Section 6.4.1.1
Subsurface facility layout and numbering of
emplacement drifts Figure 1 BSC 2003o
Alternate conceptual model for probability-weighted
number of waste package failures from fault
displacement
1.9110-4 to 1.9110-6 Waiting et al. 2003
Alternate conceptual model for number of fault
intersections with emplacement drifts 191 Waiting et al. 2003
Seepage Change Due to Drift Collapse:
Seepage abstraction if seismic hazard is large enough to
collapse the drifts See Table in DTN DTN: LB0307SEEPDRCL.002
Table 3. Direct Input Information for the Seismic Scenario Class
Input Information Value Source
Horizontal PGV at Point B for the 10-6 per year mean
annual exceedance frequency 2.44 m/s DTN: MO0303DPGVB106.002
Horizontal PGV at Point B for the 10-7 per year mean
annual exceedance frequency 5.35 m/s DTN: MO0210PGVPB107.000
Mean hazard curve for horizontal PGV at Point A, a
reference rock outcrop at the repository elevation
See file
h_vel_extended.
frac_mean in the
DTN
DTN: MO03061E9PSHA1.000
4.2 CRITERIA
General programmatic requirements for this document are listed in Technical Work Plan for:
Engineered Barrier System Department Modeling and Testing FY03 Work Activities (BSC
2003a). The technical work plan specifies that this document and all analyses described herein
must adhere to the requirements of AP-SIII.10Q, Models. The technical work plan specifies that
this document must discuss the barrier function of the EBS components (waste package, drip
shield, and emplacement pallet) that may be affected by seismically induced hazards. The
technical work plan also specifies that the acceptance criteria in Yucca Mountain Review Plan,
Final Report (NRC 2003) must be addressed.
4.2.1 Project Requirements and Yucca Mountain Review Plan Acceptance Criteria
Project Requirements Document (Canori and Leitner 2003) contains the high-level technical
requirements for the Yucca Mountain Project. These requirements provide a basis for criteria
relevant to the seismic consequence abstractions. The requirement that pertains to this model
report and its link to 10 CFR Part 63, is defined in Section 3.4 of Project Requirements
Document (Canori and Leitner 2003) as follows:
 PRD-002/T-015: Requirements for Performance Assessment
10 CFR 63.114, specifies technical requirements to be used in a performance assessment to
demonstrate compliance to 10 CFR 63.113. It includes requirements for calculations,
including data related to site geology, hydrology, and geochemistry; the need to account for
uncertainties and variabilities in model parameters, the need to consider alternative
conceptual models, and technical bases for inclusion or exclusion of specific FEPs,
deterioration or degradation processes of engineered barriers, and all the models used in
performance assessment.
The acceptance criteria that are relevant to requirement PRD-002/T-015 for seismic consequence
abstractions are found in Section 2.2.1.3.2.3 of Yucca Mountain Review Plan, Final Report
(NRC 2003). The five general acceptance criteria in Section 2.2.1.3.2.3 follow, along with the
subcriteria that are applicable to development of the seismic consequence abstractions.
 Acceptance Criterion 1: System Description and Model Integration Are Adequate.
The subcriteria applicable to the seismic consequence abstractions are (1), (3), (4), and (5).
 Acceptance Criterion 2: Data Are Sufficient for Model Justification.
Subcriteria (1), (3), and (4) are applicable to the seismic consequence abstractions.
 Acceptance Criterion 3: Data Uncertainty Is Characterized and Propagated Through
the Model Abstraction.
Subcriteria (1), (2), and (3) are applicable to the seismic consequence abstractions.
 Acceptance Criterion 4: Model Uncertainty Is Characterized and Propagated
Through the Model Abstraction.
Subcriteria (2), and (3) are applicable to these model abstractions.
 Acceptance Criterion 5: Model Abstraction Output Is Supported by Objective
Comparisons.
The applicable subcriteria are (1), (2), and (3).
Section 6.11 provides a detailed discussion of how the seismic abstractions and the seismic
scenario class meet the applicable acceptance criteria from Yucca Mountain Review Plan, Final
Report (NRC 2003).
4.3 CODES AND STANDARDS
No codes and standards are applicable to the development of the seismic consequence
abstractions. The regulation that is applicable to the development of these abstractions is
10 CFR Part 63, specifically 10 CFR 63.114 and 10 CFR 63.115.
5. ASSUMPTIONS
5.1 DAMAGE THRESHOLD FROM VIBRATORY GROUND MOTION LIES
BETWEEN MEAN ANNUAL EXCEEDANCE FREQUENCIES OF 10-4 PER YEAR
AND 10-5 PER YEAR
Assumption: There is no damage to EBS components until the repository experiences ground
motions larger than those for the 10-4 per year annual exceedance frequency. More specifically,
the abstractions for damage to the drip shield and cladding from vibratory ground motion assume
that damage becomes nonzero between the 10-4 and 10-5 per year annual exceedance frequencies.
Basis: Structural analyses for the waste package and drip shield have been performed using a
single set of vibratory ground motions (with two horizontal components and one vertical
component) for an annual exceedance frequency of 510-4 per year. The results of these
analyses demonstrate that the response of the waste package and drip shield are always in the
elastic regime for the 5  10-4 per year ground motion (BSC 2003b, Section 6.3; BSC 2003p,
Section 6.1), with no damage to the structures. There will also be no failure of the cladding
because waste package displacements are very small (BSC 2003p, Section 6.3), with no impacts
or significant acceleration that could fail the cladding.
The drip shield may also be damaged by tunnel collapse in the lithophysal zones or from rock
blocks in the nonlithophysal zones. For the 5  10-4 per year ground motion, tunnels in the
lithophysal zones have no damage for higher values of rock compressive strength and only minor
damage (but no collapse) at the lowest level of compressive strength (BSC 2003h, Section
6.4.1.1). For the nonlithophysal zones, a series of 25 analyses have been performed to determine
the range and number of blocks ejected by the 5  10-4 per year ground motion (BSC 2003h,
Section 6.3.1.2.5). This set of analyses is a skewed sample because it is based on the 25 fracture
patterns that produce the most rockfall for the 10-6 per year level ground motions. Fourteen of
the calculations have no rockfall (BSC 2003h, Table 19). When rockfall does occur, the median
energy of the blocks is near 3,000 Joules (BSC 2003h, Figure 70), which produces very minor
damage (see Table 12 in Section 6.6.1.2 of this report). Considering that 85 percent of the
repository is in lithophysal rock, with no damage to the drip shield, and that the remaining 15
percent of the drifts may have only very minor damage based on a skewed sampling of fracture
patterns, it is reasonable to assume that damage to the drip shield from rockfall at the 5  10-4 per
year ground motion level is negligible.
The seismic consequence abstractions for TSPA-LA assume that damage to EBS components
from vibratory ground motion becomes nonzero between the 10-4 and 10-5 per year annual
exceedance frequencies.
Confirmation Status: This assumption is designated To Be Verified (TBV), pending the results
from structural response calculations and rockfall calculations for ground motions at the 10-4 per
year and 10-5 per year mean annual exceedance frequencies. The TBV number for this
assumption is TBV-5106.
Use In Model: The abstraction for damage to the waste package in Section 6.5 uses a linear fit so
that the maximum damage goes to zero for a value of PGV that lies between the 10-4 per year
and 10-5 per year annual exceedance frequency. This assumption is also used in Section 6.7 to
set the lower bound for damage to the cladding. The assumption for damage to the drip shield
from rock blocks in the nonlithophysal zone is used in developing the abstraction in
Section 6.6.1. More specifically, the abstraction for damage to the drip shield assumes that there
is no damage for the 5  10-5 per year ground motion level (Section 6.6.1.4).
5.2 PAGANY WASH AND SEVIER WASH FAULT DISPLACEMENTS
Assumption: The fault displacement hazard curves for the Pagany Wash Fault and for the Sevier
Wash Fault are identical to the fault displacement hazard curve for the Drill Hole Wash Fault.
Basis: The assumption of equivalency is justified by the results of field investigations that are
summarized by Menges and Whitney (1996). The reasoning that supports the assumption of
equivalency is as follows:
1.
The best available field data for the three faults comes from cores on the Drill Hole Wash
Fault, so it is reasonable to use the response of the Drill Hole Wash Fault as the basis for
the seismic hazard.
2.
None of the faults suggest displacement in Quaternary alluvial terraces, so it is appropriate
to assume a low probability of significant displacement for all three faults.
3.
The scale of cumulative vertical displacement is less than 5 to 10 meters for each structure,
consistent with a maximum displacement of approximately 2 meters for a single low
probability event.
4.
Total fault length, an important factor in seismic hazard assessment, is similar for the three
faults and ranges from 2 km for the Drill Hole Wash Fault to 4 km for the other faults.
5.
Spatial orientation to the Solitario Canyon and Bow Ridge Faults, also an important factor
in a hazard assessment, is similar for the three faults. Spatial orientation to more distant
seismic sources is also similar.
6.
Previous geologic studies have consolidated discussion of the three faults based on similar
characteristics and apparent similarity in fault development in response to the extensional
environment.
It is, therefore, reasonable to treat the Drill Hole Wash fault, the Sevier Wash fault, and the
Pagany Wash fault in a similar manner with regard to the potential seismic hazard, barring any
evidence to the contrary.
Confirmation Status: This assumption does not require confirmation. Probabilistic Seismic
Hazard Analyses for Fault Displacement and Vibratory Ground Motion at Yucca Mountain,
Nevada (CRWMS M&O 1998) defines fault displacement hazards at 15 faulting conditions
within the immediate vicinity of Yucca Mountain. Closely spaced secondary faults are not
characterized separately because their displacements during a seismic event are expected to be
similar.
Use In Model: This assumption is used in Section 6.8.3.
5.3 RESIDUAL STRESS ABOVE THE SEISMIC FAILURE CRITERION RESULTS IN
FLOW PATHWAYS THROUGH THE WASTE PACKAGE AND DRIP SHIELD
Assumption: If the residual stress from mechanical damage exceeds the residual stress threshold
for the barrier, then the affected area(s) are considered to have failed as a barrier to flow and
transport.
Basis: The seismic damage abstractions for the waste package and drip shield make use of a
residual stress threshold as a failure criterion. Application of this criterion is non-mechanistic, in
the sense that detailed calculations of the actual rates of general corrosion, stress corrosion
cracking, or localized corrosion are not being used to determine the actual failure time after a
seismic event. Rather, it is acknowledged that the potential exists for one or several of these
processes to occur with such rapidity that the entire damaged area ceases to function as an
effective barrier to flow and transport. Once the barrier fails, advective flow and transport and
diffusive transport can occur through the damaged area.
Confirmation Status: This assumption does not require confirmation because it is a conservative,
bounding approach that ignores the potential for a network of tight cracks to limit advective flow
because of surface tension within a crack and because of precipitation within a crack.
Use In Model: This assumption is used in Sections 6.3 and 6.10.2.
5.4 DERIVING THE FORMULA FOR MEAN DOSE
Assumption: In deriving the formula for mean dose, the dose is assumed to be a function of the
time of occurrence and the amplitude of the PGV for the seismic hazard (see Attachment VIII).
The dose time histories for the reasonably maximally exposed individual at time t from a seismic
event occurring at a time, t, prior to t depends only on the time of occurrence of the event and on
PGV at the waste emplacement drifts associated with the seismic event.
Basis: This assumption simplifies the mathematical derivation for mean dose presented in
Attachment VIII without being overly restrictive.
Confirmation Status: This assumption does not require confirmation.
Use In Model: This assumption is used in Attachment VIII.
5.5 RANDOMNESS OF SEISMIC EVENTS
Assumption: Seismic events occur in a random manner, following a Poisson process, over long
periods of time.
Basis: The assumption that the behavior of the earth is generally random (Poisson process) is the
underlying assumption in all probabilistic hazard analyses. In other words, all earthquakes are
considered as independent events with regard to magnitude, time and location. Although there
may be cases where sufficient data and information exists to depart from this assumption, the
Poisson process is generally an effective representation of nature and represents a compromise
between the complexity of natural processes, availability of information, and the sensitivity of
results of engineering relevance. This assumption is identical to Assumption 6.4.2 in
Characterize Framework for Seismicity and Structural Deformation at Yucca Mountain, Nevada
(CRWMS M&O 2000a).
Confirmation Status: This assumption does not require confirmation because it is a common,
engineering assumption in risk assessments and because it is an implicit assumption in the
development of hazard curves.
Use In Model: This assumption is used in Section 6.10 and Attachment VIII.
5.6 MAJOR ASSUMPTIONS IN SUPPORTING CALCULATIONS
The seismic consequence abstractions are based on the results from analyses for the structural
response of EBS components to vibratory ground motion and on the results from analyses of
rockfall induced by vibratory ground motion. The structural response calculations and rockfall
calculations are not described in this report; rather, the results from these design calculations and
scientific analyses provide the input information that the abstractions are based on. These
supporting calculations include several major assumptions that are not directly used in the
abstraction process, but are noteworthy enough to deserve repeating here.
The structural response calculations for the waste package and drip shield incorporate
assumptions for structural thickness and for material properties of Alloy 22 and of Titanium
Grade 7. The thicknesses of the drip shield plates and the waste package outer shell have been
reduced by 2-mm in these calculations to represent the potential degradation of these structures
by general corrosion over the first 10,000 years after repository closure. The material properties
of Alloy 22 and of Titanium Grade 7 have been evaluated at an elevated temperature (150C)
that provides conservative values for mechanical properties over most (97 percent) of the
10,000-year duration. The rationale for these assumptions is provided in several design
calculations (BSC 2003b, Assumptions 3.20 and 3.21; BSC 2003g, Assumptions 3.7 and 3.10).
The rockfall calculations for the lithophysal and nonlithophysal zones also make several key
assumptions. In the lithophysal zone, the block size distribution is assumed to be a function of
the inter-lithophysal fracture density and the lithophysae spacing (BSC 2003h,
Assumption 5.2.2). This assumption is relevant to the abstraction process because it limits the
potential damage to the drip shield from tunnel collapse in the lithophysal zone, as discussed in
Section 6.6.2 of this document.
6. MODEL DISCUSSION
6.1 INTRODUCTION
6.1.1 Background
The U.S. Department of Energy (DOE) is implementing a comprehensive seismic evaluation
strategy for a geologic repository at Yucca Mountain. This strategy began during the Site
Recommendation period with a probabilistic seismic hazard analysis for the repository site. In
the probabilistic seismic hazard analyses, the DOE has developed (1) ground motion hazard
curves for the Yucca Mountain site, and (2) fault displacement hazard curves for fifteen faulting
conditions mapped within the immediate vicinity of Yucca Mountain (CRWMS M&O 1998,
Sections 7 and 8).
The results from Probabilistic Seismic Hazard Analyses for Fault Displacement and Vibratory
Ground Motion at Yucca Mountain, Nevada (CRWMS M&O 1998) were used to support
screening decisions for features, events, and processes (FEPs) relevant to potential seismic
effects on the repository. With the exception of seismic ground motion effects on fuel rod
cladding, FEPs related to ground motion were screened out of the Total System Performance
Assessment for the Site Recommendation (TSPA-SR) on the basis of median ground motion
hazard (CRWMS M&O 2000b, Section 6.2.6). A key assumption for the TSPA-SR screening
decision was that the median hazard curve, rather than the mean hazard curve, was appropriate
for the analysis. The ground motions and fault displacement amplitudes from the median hazard
curves were low enough that their expected damage to the engineered barriers was not
significant, even down to the lowest annual exceedance frequency of 10-8 per year. This result
supported the decision to screen out seismic effects, except for fuel rod cladding, from
TSPA-SR.
The Nuclear Regulatory Commission (NRC) subsequently expressed concern about the potential
impacts of larger (less frequent) earthquakes on EBS components during the postclosure period.
These concerns resulted in agreements that were reached between the NRC staff and the DOE
during the NRC/DOE Technical Exchange and Management Meeting on the Key Technical Issue
of Structural Deformation and Seismicity, October 1112, 2000 (Gardner 2000).
The DOEs seismic analysis approach for the License Application is outlined in a letter report,
Approach to Postclosure Seismic Analyses for a Potential Geologic Repository at Yucca
Mountain, Nevada (Brocoum 2001, enclosure). The strategy outlined in the letter report
responds to the NRCs concerns on seismic issues. Specifically, the DOE agreed to either
provide technical justification for the use of median fault displacement and ground motion
hazard curves as the basis for screening seismic FEPs for the TSPA-LA, or to adopt mean values
as the basis for screening seismic FEPs, or to evaluate and implement an alternative approach.
The DOE has adopted mean hazard curves for vibratory ground motion and for fault
displacement in screening FEPs for TSPA-LA and in developing the seismic consequence
abstractions for TSPA-LA.
6.1.2 Information Sources and Outputs
This report presents the abstractions for damage to EBS components due to seismic hazards.
These abstractions are the output from this model report. The intended use of this output is to
define the abstractions and associated computational algorithms for the seismic scenario class for
TSPA-LA. The report includes discussion of:

The criteria for determining the failed areas of the waste package and drip shield under
vibratory ground motions

The abstraction of these failed areas as a function of the seismic hazard

Damage to EBS components from fault displacement

The abstraction of cladding failure in response to waste package impacts

The algorithms for including the damage abstractions in the seismic scenario class

Post-seismic event changes in seepage due to tunnel collapse and in EBS flow pathways
due to accelerated localized corrosion of Alloy 22.
Figure 1 illustrates the major components of the EBS in a typical emplacement drift.
Figure 1. Schematic Diagram of the EBS Components in a Typical Emplacement Drift
Mathematically, the hazards included in the seismic scenario class can be represented by the
following vector:
r r
A = ( fWPA , d , v , t |VfDSA , |VfDSARF , |VfCLD , nPWRFD , |DnBWRFD , aPWRFD , |D, aBWRFD ,
V
nHLWFD|DcSPFLX , aLHLWFD , ), cSPFLX ,
V t
(Eq. 1)
Where t is the time (year) after repository closure when the seismic hazard occurs;
v is the amplitude of the ground motion, measured as horizontal PGV (m/s);
r
d is a vector of displacements for faults that intersect emplacement drifts (m);
fWPA|V is the fraction of waste package surface area damaged by ground motion. The
abstraction for damage to the waste package is defined in Section 6.5, based on
information in Structural Calculations of Waste Package Exposed to Vibratory
Ground Motion (BSC 2003b);
fDSA|V is fraction of drip shield surface area damaged by ground motion. The
abstraction for damage to the drip shield from ground motion is defined in
Section 6.6.3, based information in Structural Calculations of Drip Shield
Exposed to Vibratory Ground Motion (BSC 2003p);
fDSARF|V is the fraction of drip shield surface area damaged by rockfall in the
nonlithophysal zone. The abstraction for damage to the drip shield from rockfall
(induced by ground motion) is defined in Section 6.6.1, based on information in
Drift Degradation Analysis (BSC 2003h) and in Drip Shield Structural Response
to Rock Fall (BSC 2003g);
fCLDV is the fraction of cladding perforated by the vibratory ground motion. The
abstraction for damage to the cladding is defined in Section 6.7, based on
information in Maximum Accelerations on the Fuel Assemblies of a 21-PWR
Waste Package During End Impacts (BSC 2003d) and in Structural
Calculations of Waste Package Exposed to Vibratory Ground Motion (BSC
2003b);
nPWRFD|D is the number of PWR waste packages failed due to fault displacement. The
abstraction for the number of failed waste packages is defined in Section 6.8,
based on information from design and from the mean hazard curves
in the probabilistic seismic hazard analyses (CRWMS M&O 1998;
DTN: MO0004MWDRIFM3.002);
aPWRRD is the failed area (m2) on PWR waste packages and their associated drip shield
and cladding resulting from fault displacement. The abstraction for failed area
and for damage to drip shield and cladding is defined in Section 6.8.5;
nBWRFD|D is the number of BWR waste packages failed due to fault displacement. The
abstraction for the number of failed waste packages is defined in Section 6.8,
based on information from design and from the mean hazard curves
in the probabilistic seismic hazard analyses (CRWMS M&O 1998;
DTN: MO0004MWDRIFM3.002);
aBWRRD is the failed area (m2) on BWR waste packages and their associated drip shields
and cladding resulting from fault displacement. The abstraction for failed area
and for damage to drip shield and cladding is defined in Section 6.8.5;
nHLWFD|D is the number of HLW waste packages failed due to fault displacement. The
abstraction for the number of failed waste packages is defined in Section 6.8,
based on information from design and from the mean hazard curves
in the probabilistic seismic hazard analyses (CRWMS M&O 1998;
DTN: MO0004MWDRIFM3.002);
aHLWRD is the failed area (m2) on HLW waste packages and their associated drip shields
resulting from fault displacement. The abstraction for failed area and for
damage to drip shields is defined in Section 6.8.5;
cSPFLXV is an indicator variable (-) for the change in seepage flux in the lithophysal zone
after the seismic hazard; and
cSPFLXt is an indicator variable for the change in flux splitting on the waste package (i.e.,
the fraction of seepage flux that enters a waste package after passing through an
opening in the drip shield) after the seismic hazard.
In the above notation, a subscript |V or |D indicates a parameter that has a distribution that is
r
conditional on (i.e., is a function of) v or d , respectively. The subscripts v and t indicate
variables that are functions of v and t, respectively.
The levels of ground motion and fault displacement are based on the mean hazard curves defined
in Probabilistic Seismic Hazard Analyses for Fault Displacement and Vibratory Ground Motion
at Yucca Mountain, Nevada (CRWMS M&O 1998). The response of the EBS components
incorporates an allowance for corrosion and degradation of the waste package and drip shield
over the 10,000-year regulatory period for the repository. The seismic scenario class has been
designed to adequately represent the seismic hazards that cause significant structural damage,
and considers hazards with an annual exceedance probability of 10-8 per year or greater, per
10 CFR 63.114(d).
6.1.3 Terminology
The terminology for the seismic hazard curves, for the suite of ground motions corresponding to
a given exceedance frequency, and for a comparison of the damage abstractions in this report
with a response surface requires a brief explanation.
A mean hazard curve defines the relationship between the mean estimate of the annual frequency
of exceedance and the amplitude of the vibratory ground motion (measured by PGV) or the
amplitude of the fault displacement (measured by a vertical displacement). The mean annual
exceedance frequency represents the mean value with which a seismic event will exceed a given
value of the PGV or fault displacement.
The mean annual exceedance frequency spans many orders of magnitude, from a minimum of
10-8 per year to a maximum of 1 per year (or greater). The mean frequency is defined as the
number of observed events, divided by the time interval of observation. It varies randomly from
one observation to the next. We use the mean of this random number as a measure of how likely
it is over the next year. When the mean annual exceedance frequency is much less than 1, the
mean annual exceedance frequency and the annual exceedance probability are essentially equal.
This report uses the term exceedance frequency because it is more general, although the
exceedance frequency and exceedance probability are interchangeable for the seismic hazards
considered in this study. All hazard curves in this report are based on the mean annual
exceedance frequency.
A suite of 15 three-component ground motions have been developed for the 10-6 per year (mean)
annual exceedance frequency to support the postclosure performance assessment. This suite of
ground motions has been sampled in order to represent the temporal variability and uncertainty
from the ground motions in the structural response calculations and rockfall calculations that
support the damage abstractions for the seismic scenario class. These ground motions are
collectively referred to as the ground motions at the 10-6 per year mean annual exceedance
frequency, or more simply the 10-6 ground motion level. Similarly, the suite of 15 three-
component ground motions at the 10-7 per year (mean) annual exceedance frequency is referred
to as the 10-7 ground motion level.
Finally, the damage abstractions for EBS components are defined in a different manner than the
typical response surface for a seismic fragility analysis. A typical response surface represents
the mean damage (or mean probability of failure) and its standard deviation, often as normal or
lognormal distributions whose parameters are functions of the amplitude of the ground motion or
fault displacement. The damage abstractions for the seismic scenario class are often uniform
distributions that provide a conditional distribution of the range of damage as a function of the
seismic amplitude. Typically, the upper bound of the uniform distribution is a function of the
amplitude of the ground motion and the lower bound of the uniform distribution is usually zero
damage. While the use of a uniform distribution is not typical for fragility analyses, this
approach does provide a simple and transparent approach for representing the variability and
uncertainty in seismically induced damage via Monte Carlo sampling for TSPA-LA.
6.1.4 Corroborating Information
The abstractions for damage to EBS components from seismic hazards are based on the direct
input information in Tables 1 and 3 of Section 4.1 and on the corroborating information in
Table 2 of Section 4.1.
6.2 RELEVANT FEPS FOR THE SEISMIC SCENARIO CLASS
The development of a comprehensive list of features, events, and processes (FEPs) potentially
relevant to post-closure performance of the potential Yucca Mountain repository is an ongoing,
iterative process based on site-specific information, design, and regulations. The approach for
developing an initial list of FEPs, in support of Total System Performance Assessment for the
Site Recommendation (CRWMS M&O 2000c), was documented by Freeze et al. (2001). The
initial FEP list contained 328 FEPs, of which 176 were included in TSPA-SR models (CRWMS
M&O 2000c, Tables B-9 through B-17). To support TSPA-LA, the FEP list was re-evaluated in
accordance with Section 3.2 of The Enhanced Plan for Features, Events, and Processes (FEPs)
at Yucca Mountain (BSC 2002).
The seismic scenario class is based on a single modeling case, with a single seismic event that
occurs at a randomly chosen time in each realization of the TSPA-LA. The focus here is on
seismic events with frequencies less than 10-4 per year because the associated ground motions
and fault displacements have the potential to cause damage to the EBS components (see
Assumption 5.1). The response of the drip shield, waste package, and cladding to this single
seismic event is represented through damage abstractions for the EBS components under
vibratory ground motion and fault displacement. The failed areas on the EBS components define
pathways for flow and transport through the engineered barriers. Once radionuclides are
released from the EBS, flow and transport in the unsaturated zone and the saturated zone are
based on the same models and algorithms as for the nominal scenario class, with the exception of
the seepage model in the lithophysal zones of the repository and the flux splitting for the waste
package if accelerated localized corrosion can occur. Biosphere calculations and parameters for
the seismic scenario class are also unchanged from those for the nominal scenario class.
The damage abstractions for the drip shield, waste package and cladding provide the
representation for TSPA-LA of the FEPs that can cause damage to the engineered barriers from
seismic hazards. Table 4 identifies the TSPA-LA FEPs that are relevant to the seismic scenario
class and the seismic consequence abstractions. Table 4 also identifies how these FEPs are
represented in TSPA-LA.
Table 4. Included FEPs Relevant to Seismic Consequence Abstractions and Their Disposition in TSPA-LA
FEP # FEP Name Summary TSPA-LA Disposition
Damage to the waste package from fault displacement is included in the
seismic scenario class for TSPA-LA. The expected numbers of damaged
waste packages on four secondary faults are evaluated for a range of annual
exceedance frequencies, based on the mean hazard curves for the
Sundance Fault, the Drill Hole Wash, the Pagany Wash Fault, and the Sevier
Wash Fault, on the clearances between various types of waste packages
and the drip shield, and on the expected numbers of waste packages that lie
on these four faults. The clearances between the waste package packages
and drip shield are based on a simple representation for damage to the
invert from fault displacement. The approximation is made that the
emplacement pallet collapses into the invert on the elevated side of the fault.
No credit is taken for the potential increase in clearances due to further
shifting of the ballast in the invert or due to failure of the steel framework in
the invert. Further details are provided in Section 6.8.1.
1.2.02.03.0A
Fault Displacement
Damages EBS
Components
Damage to the waste package is sampled from a uniform distribution with a
lower bound of 0% and an upper bound given by the area of the waste
package lid. The uniform distribution is a simple approximation to the upper
and lower damage bounds in lieu of detailed structural response
calculations. The upper bound is a reasonable estimate for a severely
crimped waste package that loses its lid because of cracking in the welds
holding the lid in place. The lower bound is a reasonable estimate for a
waste package this is minimally damaged, either because fault displacement
slightly exceeds the available clearance or because the shear occurs at the
opposite end of the waste package from the lid.
Crimping is viewed as the main damage mechanism for the waste package
because the package is a very robust, thick-walled cylinder that will not be
damaged by tilting or minor displacements. In addition, the ability of the
waste package to move on the pallet makes it unlikely that a large enough
bending moment or torsion can be applied to result in failure.
Damage to a drip shield from fault displacement is 100% if it surrounds a
damaged waste package or 0 if it does not. Similarly, cladding in a waste
package is 100% perforated if it is in a damaged waste package or
undamaged if its waste package is not affected by fault displacement.
Section 6.8 defines the damage abstraction for the EBS components in
response to fault displacement. Step 8 in Section 6.10.2 provides an
algorithmic description and definition of output parameters for the fault
displacement damage abstraction for the EBS components. Table 30
summarizes the 20 output parameters for TSPA-LA that specifically relate to
damage from fault displacement.
Table 4. Included FEPs Relevant to Seismic Consequence
Abstractions and Their Disposition in TSPA-LA (Continued)
FEP #
FEP Name
Summary TSPA-LA Disposition
Damage to the waste package, the drip shield, and the cladding is included in
the seismic scenario class for TSPA-LA. Structural response calculations for
the waste package and drip shield are the basis for predicting failed areas for
advective flow and transport. The criteria for failure are based on a residual
stress threshold of between 80% and 90% of the yield strength for Alloy 22 and
of 50% of the yield strength for Titanium Grade 7. The residual stress
thresholds are based on an analysis of experimental data for stress corrosion
cracking, as described in Stress Corrosion Cracking of the Drip Shield, the
Waste Package Outer Barrier, and the Stainless Steel Structural Material (BSC
2003l, Section 6.2.1); this analysis is summarized and extended in Section 6.3
of this report. Failed areas occur in response to impact of the waste package
on the emplacement pallet and to end-to-end impacts of adjacent waste
packages. Because damage to the waste package is always much less than
100%, the failed areas are abstracted as a uniform distribution with a lower
bound of 0 and an upper bound that is a function of PGV. The uniform
distribution has also been compared to an alternate conceptual model based
on a lognormal distribution of damage. This alternate conceptual model
provides insights into the conservatism or nonconservatism of the original
uniform distribution. In fact, the upper bound of the uniform distribution has
been increased to ensure conservatism with respect to the lognormal
distribution over a PGV range of 1 m/s to 6 m/s.
To determine the functional dependence on PGV, vibratory ground motions are
defined at annual exceedance frequencies of 10-6 per year, 10-7 per year, and
5  10-4 per year. Fifteen sets of three-component ground motions are
sampled to capture the variability in the temporal details of the ground motions
at the 10-6 per year and 10-7 per year PGV levels. A single set of three-
component ground motions, originally developed for preclosure design,
represents ground motion at the 5  10-4 per year level. The variability in the
ground motions is a major uncertainty for structural response.
Seismic Ground
The structural response calculations do not represent the dynamic response of 1.2.03.02.0A
Motion Damages
the invert to the ground motion. The invert is represented as an elastic body
EBS Components
whose surface responds instantaneously and uniformly to the given ground
motion. This is a reasonable approach for small amplitude ground motions
because the invert is compacted under the weight of the waste packages and
drip shield and because any remaining steel framework in the invert will tend to
provide some integrity, resulting in an invert that tends to move as a single unit.
For high amplitude ground motions, the ballast is likely to be thrown up and
redistributed, allowing the heavy EBS components to settle on the bottom of
the drift, directly in contact with the rock floor. In this case, applying the ground
motions directly to the surface of the invert is again a reasonable approach.
Sections 6.5.1 and 6.6.3 define the damage abstractions for the waste package
and drip shield, respectively, in response to vibratory ground motion. Steps 3
and 4 in Section 6.10.2 provide an algorithmic description and definition of
output parameters, for the damage abstractions for these two barriers.
Table 30 summarizes the 4 output parameters for TSPA-LA that specifically
relate to damage to the waste package and the 4 output parameters for TSPALA
that relate to damage to the drip shield from vibratory ground motion.
Damage to the cladding is also included in the seismic scenario class for
TSPA-LA. Structural response calculations for end-to-end impacts of adjacent
waste packages define the axial loads on fuel assemblies. These loads are
compared to fuel rod failure criteria based on Euler buckling for various fuel pin
designs. Comparison of axial loads with the failure criteria indicates that most if
not all fuel pins will fail under vibratory ground motions at the 10-6 per year and
the 10-7 per year levels. Cladding will not fail from the vibratory ground motion
at the 5  10-4 per year level.
Section 6.7 defines the damage abstraction for the cladding under vibratory
ground motion. Step 7 in Section 6.10.2 defines the algorithm for the damage
abstraction for cladding in TSPA-LA. Table 30 identifies the single output
parameter for the abstraction of cladding damage.
Table 4. Included FEPs Relevant to Seismic Consequence
Abstractions and Their Disposition in TSPA-LA (Continued)
FEP # FEP Name Summary TSPA-LA Disposition
Damage to EBS components from seismically induced rockfall is included in
the seismic scenario class for TSPA-LA. Vibratory ground motions can
cause failure of the host rock around the emplacement drifts. In the
nonlithophysal zones, large rock blocks can be ejected from the walls of the
drift at high velocity. Rock blocks are ejected for the 10-6 per year and the
10-7 per year ground motion levels; relatively few blocks are ejected at the
5  10-4 per year ground motion level. The damage to the drip shield from
large rock blocks is abstracted for TSPA-LA as a function of the PGV. The
effects of large rock blocks on the drip shield are discussed in
FEP 2.1.07.01.0A.
Structural response calculations for the drip shield are the basis for
predicting failed areas for advective flow. The criteria for failure are based
on a residual stress threshold of 50% of the yield strength for Titanium Grade
7. The residual stress threshold is based on the analysis of experimental
data for stress corrosion cracking, as described in Stress Corrosion Cracking
of the Drip Shield, the Waste Package Outer Barrier, and the Stainless Steel
Structural Material (BSC 2003l, Section 6.2.1); this analysis is summarized in
Section 6.3 of this report. Failed areas occur in response to the combined
impacts of the rock blocks on the drip shield.
In the lithophysal zones, the rock mass can shatter into small fragments,
completely collapsing the drift for the 10-6 per year and the 10-7 per year
ground motion levels; the probability of collapse is small at the 5  10-4 per
year ground motion level, with a small volume of rubble generated by
rockfall. The effects of drift collapse on EBS components are discussed in
FEP 2.1.07.02.0A.
1.2.03.02.0B
Seismic Induced
Rockfall Damages
EBS Components
Sections 6.6.1 and 6.6.2 define the damage abstraction for the drip shield in
response to rockfall induced by vibratory ground motion. Step 5 in
Section 6.10.2 provides an algorithmic description and definition of output
parameters for the damage abstraction from rockfall. Table 30 summarizes
the 6 output parameters for TSPA-LA that specifically relate to drip shield
damage from rockfall in the nonlithophysal zones.
Rockfall induced by vibratory ground motion can alter the hydrologic and
thermal environment in the drifts after the seismic event. The collapse of
drifts from high amplitude ground motion in the lithophysal zones can fill the
drifts with rubble, altering the hydrologic and thermal environment around the
EBS components. The change in the seepage abstraction in response to
drift collapse in the lithophysal zones is based on results from Abstraction of
Drift Seepage (BSC 2003q, Section 6.5.1.5). There is no change in the
seepage abstraction in the nonlithophysal zones because the rockfall does
not completely fill the tunnels at the ground motion levels of interest.
The presence of rubble about the drip shield could cause changes in the
thermal environment in the EBS if a seismic event occurs relatively soon
after repository closure, while the waste package and drip shield are at
elevated temperatures. However, the irregular and coarse nature of the
rubble is expected to allow sufficient convective heat transfer that the
temperature histories calculated for the nominal scenario class may
reasonably be used to approximate conditions following a seismic event
during the thermal period. If the seismic event occurs when the conditions
are satisfied for initiating accelerated localized corrosion on the waste
package, then the flux splitting algorithm for the waste package is modified in
an appropriate manner (see Section 6.9). Because potential changes in
temperature due to the presence of rubble are not expected to be significant,
the possible associated changes in temperature-dependent solubility and
corrosion rate have not been included in TSPA-LA.
Table 4. Included FEPs Relevant to Seismic Consequence
Abstractions and Their Disposition in TSPA-LA (Continued)
FEP # FEP Name Summary TSPA-LA Disposition
Damage to the drip shield from large rock blocks in the nonlithophysal zones
is included in the seismic scenario class for TSPA-LA. Rockfall calculations
define the ranges in mass, velocity, and frequency of rock blocks that are
ejected from the tunnel walls. The rockfall analysis considers the
uncertainties associated with fracture geometry and vibratory ground
motions. To determine the functional dependence on PGV, vibratory ground
motions have been defined at annual exceedance frequencies of 10-6 per
year, 10-7 per year, and 5  10-4 per year. Fifteen sets of three-component
ground motions have been sampled to capture the variability in the temporal
details of the ground motions at the 10-6 per year and 10-7 per year PGV
levels. A single set of three-component ground motions, originally developed
for preclosure design purposes, represents the 5  10-4 per year level.
Structural response calculations for the drip shield are the basis for
predicting failed areas for advective flow. (There is no transport through the
drip shields because they are upgradient from the waste packages.) The
criterion for failure is based on a residual stress threshold of 50% of the yield
strength for Titanium Grade 7. The residual stress threshold is based on an
analysis of experimental data for stress corrosion cracking in Stress
2.1.07.01.0A Rockfall (Large
Blocks)
Corrosion Cracking of the Drip Shield, the Waste Package Outer Barrier, and
the Stainless Steel Structural Material (BSC 2003l, Section 6.2.1); this
analysis is summarized in Section 6.3 of this report. Failed areas are
calculated for individual rock blocks that span the range of mass, energy,
and impact location (top, side and corner) observed in the rockfall
calculations. The damaged area for a complex sequence of rock blocks is
then evaluated by interpolation and summation of the damage values for
individual rock blocks.
Damage is abstracted as two stochastic parameters: (1) a probability that no
damage occurs, and (2) a log-triangular distribution if damage does occur.
The probability that no damage occurs and the mode of the log-triangular
distribution are functions of PGV.
Section 6.6.1 defines the damage abstraction for the drip shield due to rock
blocks in the nonlithophysal zones. Step 5 in Section 6.10.2 provides an
algorithmic description and definition of output parameters for the damage
abstraction for the drip shield in the nonlithophysal zones. Table 30
summarizes the 6 output parameters for TSPA-LA that specifically relate to
drip shield damage from rockfall in the nonlithophysal zones.
Damage to the waste package or cladding from rock blocks is screened out
of the seismic scenario class for TSPA-LA. The drip shield remains intact
until a seismic event occurs during the first 10,000 to 20,000 years after
repository closure. In its intact state, the drip shield will deflect blocks away
from the waste package without collapsing, even for the largest blocks.
Hence damage to the waste package or cladding from rock blocks is
negligible and this damage mechanism is screened out of TSPA-LA.
Table 4. Included FEPs Relevant to Seismic Consequence
Abstractions and Their Disposition in TSPA-LA (Continued)
FEP # FEP Name Summary TSPA-LA Disposition
Damage to the EBS components from drift collapse is included in the seismic
scenario class for TSPA-LA. The direct effects from drift collapse in the
lithophysal zones on EBS components are not included in abstractions for
TSPA-LA. In the lithophysal zones, the rock mass is relatively weak and
often permeated with large void spaces. This weak rock mass can collapse
into small fragments under the load imposed by a large vibratory ground
motion. These smaller fragments have little capability to damage the drip
shield, either from individual impacts or from their static load, as discussed in
Section 6.6.2. Damage to the waste package and cladding will also be
insignificant because the drip shield remains intact until a major seismic
event occurs, deflecting the rock away from the waste package.
The indirect effects from drift collapse may be more significant for EBS
performance in lithophysal zones after the seismic event. Drift collapse
alters the shape of the drift and fills it with a natural backfill. These indirect
changes can affect a variety of processes:
2.1.07.02.0A Drift Collapse
(i)
(ii)
Seepage may increase because of the irregular drift shape;
Temperature of the drip shield and waste package will increase
(relative to an unfilled drift) because the backfill provides an insulating
blanket on top of the drip shield;
(iii) The general corrosion rate, glass dissolution rate, and some
radionuclide solubility limits will increase with increasing temperature.
The indirect effect on seepage is included in the seismic abstractions by
modifying the seepage flux after a seismic event in the lithophysal zone,
based on results from Abstraction of Drift Seepage (BSC 2003q,
Section 6.5.1.5) (see Section 6.9 of this report). The indirect effect from
accelerated localized corrosion is included in TSPA-LA by modifying the flux
splitting algorithm on the waste package if the waste package temperature is
above the threshold for accelerated corrosion at the time of the seismic
event. The indirect effects from thermal changes are screened out of TSPALA
because the temperature histories calculated for the nominal scenario
class may reasonably be used to approximate conditions following a seismic
event during the thermal period, as discussed under FEP 1.2.03.02.0B.
The FEPs in Table 4 differ from the FEP list in Technical Work Plan for: Engineered Barrier
System Department Modeling and Testing FY03 Work Activities (BSC 2003a). The differences
are as follows:

The title of FEP 1.2.02.03.0A has been changed from Fault Movement Shears Waste
Container to Fault Displacement Damages EBS Components. This FEP has been redefined
to address the potential for a variety of failure mechanisms for EBS components due to
fault movement, rather than limiting discussion to shear failure of waste containers.

The description of FEP 1.2.03.01.0A, Seismic Activity, is redundant with other seismic-
related FEPs, and has been deleted for TSPA-LA.

The title of FEP 1.2.03.02.0A has been changed from Seismic Vibration Causes Container
Failure to Seismic Ground Motion Damages EBS Components. The FEP description is
split to separately address the effects of ground motion and rockfall on all of the EBS
components, in addition to the waste packages.

A new FEP, 1.2.03.02.0B, Seismic-Induced Rockfall Damages EBS Components, is added
for TSPA-LA. The description of FEP 1.2.03.02.0A is split to address ground motion and
rockfall separately and to identify damage to all of the EBS components.
6.3 FAILED AREA CRITERIA FOR THE WASTE PACKAGE AND DRIP SHIELD
Mechanical processes that occur during a seismic event can result in permanent structural
deformation and residual stress in EBS components. These mechanical processes include
impacts between adjacent waste packages, between the waste package and its emplacement
pallet, between the waste package and the drip shield, between the drip shield and emplacement
pallet, and between the drip shield and invert. The presence of residual stress may result in local
barrier degradation from enhanced general corrosion, enhanced stress corrosion cracking, and/or
enhanced localized corrosion (pitting and/or crevice corrosion). Once the barriers degrade,
seepage can flow through the drip shield and into the waste package, resulting in advective flow
and transport through the EBS. If seepage is not present, diffusive transport will occur from the
waste package into the unsaturated zone.
If the residual stress from mechanical damage exceeds the residual stress threshold for the
barrier, then the affected area(s) are considered to have failed as a barrier to flow and transport.
Application of this criterion is non-mechanistic, in the sense that detailed calculations of the
actual rates of general corrosion, stress corrosion cracking, or localized corrosion are not used to
determine the actual failure time after a seismic event. Once the barrier fails, advective flow and
transport and diffusive transport can occur through the damaged area (see Assumption 5.3). This
is a conservative approach because surface tension can limit advective flow through a network of
tight cracks and because precipitation of dissolved salts has the potential to reduce the flow area
through these cracks, if not seal them entirely.
The residual stress thresholds for seismic response are similar to the criteria for initiation of
stress corrosion cracking on smooth surfaces of Alloy 22 and Titanium Grade 7 (BSC 2003l,
Section 6.2.1). The use of a stress corrosion cracking initiation criterion is appropriate for
seismic analysis because regions where the residual stress from mechanical damage exceeds the
failure criterion are expected to be severely cold-worked and, hence, potentially subject to
enhanced general and localized corrosion in addition to stress corrosion cracking. If detailed
models of stress corrosion cracking initiation, stress corrosion cracking propagation, and
enhanced local and general corrosion are developed and applied, not only would failures occur at
a later time than the seismic event, but the failed openings would be smaller than those resulting
from this simplified failure criterion. A conservative approach is used here because: (a) it is
consistent with other failure criteria (BSC 2003l, Section 6.2.1), (b) the residual stress failure
criterion is transparent, and (c) it is easily applied to the output from detailed structural response
calculations.
6.3.1 Residual Stress Damage Threshold for the Waste Package
The residual stress threshold for failure of the waste package is represented by a uniform
distribution with a lower bound of 80 percent of the yield strength of Alloy 22 and an upper
bound of 90 percent of the yield strength of Alloy 22. The upper bound of 90 percent is based on
experimental data and incorporates a safety factor of 2.2 because of the very long lifetime of the
waste package (BSC 2003l, Section 6.2.1, third paragraph). The lower bound of 80 percent is
introduced to evaluate the sensitivity of damaged area to residual stress threshold for the seismic
scenario class. Alloy 22 is the outer shell material for the waste package, where most of the
mechanical damage would occur.
This residual stress criterion (80 to 90 percent of the yield strength) is consistent with the failure
criterion for stress corrosion cracking initiation in other waste package analyses. For example,
the same criterion is used for the initiation of stress corrosion cracking in FY 01 Supplemental
Science and Performance Analyses, Volume 1: Scientific Bases and Analyses (BSC 2001a,
Section 7.3.3.3.3).
In practice, the damage to the waste package has been evaluated at the extremes of the uniform
distribution. The results from each structural response calculation are post-processed to
determine the elements in the outer shell of the waste package whose residual stress exceeds
80 percent of the yield strength of Alloy 22 and to determine the elements in the outer shell of
the waste package whose residual stress exceeds 90 percent of the yield strength of Alloy 22.
The failed elements are then converted into a failed area and the failed areas for both the 80 and
90 percent criteria are reported in Section 6.5. The failed areas at intermediate values of the
residual stress threshold can then be defined by linear interpolation between the extremes. The
elements that exceed 90 percent of the yield strength are always a subset of the elements that
exceed 80 percent of the yield strength. In other words, the damaged area for the 90 percent
residual stress threshold is always less than or equal to the damaged area for the 80 percent
residual stress threshold.
6.3.2 Residual Stress Damage Threshold for the Drip Shield
For the drip shield barrier, the residual stress threshold for failure is represented by a fixed lower
bound of 50 percent of the yield strength of the drip shield plate material (Titanium Grade 7)
(BSC 2003l, Section 6.2.1, third paragraph). The following discussion is abridged from this
report. References to the experimental data and technical basis for this threshold can be found in
Stress Corrosion Cracking of the Drip Shield, the Waste Package Outer Barrier, and the
Stainless Steel Structural Material (BSC 2003l).
There is a significant experimental data base for Titanium Grade 7 that justifies the use of
50 percent of yield strength as a stress corrosion cracking initiation criterion. These data include
long-term constant load tests in a concentrated J-13 brine environment (~15 percent Basic
Saturated Water) at 105oC with specimens loaded to stresses of 110 to 140 percent of the yield
strength. Some specimens failed relatively early (=168 hours) at applied stresses in excess of
110 percent of yield strength. At 110 percent of yield strength, there is a mixture of failure and
non-failure runout times from about 200 hours for first failure to greater than 7,000 hours
without failure. These data are consistent with a failure threshold that is less than 110 percent of
yield strength.
A second source of information regarding the stress corrosion cracking initiation criterion for
Titanium Grade 7 comes from U-bend tests. Initiation of stress corrosion cracking is not
observed in fixed deflection U-bend tests on Titanium Grade 7 exposed for one year and
Titanium Grade 16 (an analogous titanium/palladium alloy) exposed for five years to a range of
relevant aqueous environments at 60 and 90oC in the Lawrence Livermore National Laboratory
Long Term Corrosion Test Facility. These U-bend tests are more representative of secondary
residual stress loading that might result from deformation following seismic loadings. These
U-bend specimens are deflected and then restrained to give apex strains (cold work level) of
greater than 10 percent, which results in sustained stress levels significantly over yield strength.
A very conservative value of 50 percent of yield strength is selected as a threshold criterion for
Titanium Grade 7, even though the initiation of stress corrosion cracking is not observed for
residual stresses greater than yield strength.
6.4 GROUND MOTION AMPLITUDES AT THE EMPLACEMENT DRIFTS
Structural damage from a seismic effect, such as vibratory ground motion, is usually abstracted
as a function of the level or amplitude of the ground motion, rather than its annual exceedance
frequency. The amplitude of the ground motion is often expressed as PGV or as peak ground
acceleration (PGA). This approach has the advantage that the damage abstraction can be defined
independently of the geologic properties that influence the propagation and attenuation of ground
motions at a specific site. Stated differently, the damage abstraction is independent of the hazard
curve at a specific site.
The choice of PGV or PGA for the magnitude of the ground motion is based on engineering
judgment as to which parameter will more closely correlate with structural damage. The
abstractions in this document use the horizontal PGV as the measure of the amplitude of the
ground motion. PGV is appropriate for the response of a rock mass to dynamic loading because
the change in stress across a weak compression wave is directly proportional to the particle
velocity. PGV is also appropriate for structural damage caused by sliding or impact under
earthquake loads (Newmark and Rosenblueth 1971, Sections 11.3.5 and 11.4). As a result, PGV
has been selected as the appropriate measure for these abstractions.
The horizontal PGV values have been calculated for the 10-6 per year and 10-7 per year mean
annual exceedance frequencies at the emplacement drifts (called Point B in the probabilistic
seismic hazard analyses). The horizontal PGV value for the 10-6 per year ground motions is
2.44 m/s (DTN: MO0303DPGVB106.002). The horizontal PGV value for the 10-7 per year
ground motions is 5.35 m/s (DTN: MO0210PGVPB107.000). The location of Point B is
illustrated in Figure 2.
TSPA requires a mean hazard curve at the emplacement drifts (Point B) for a wide range of
exceedance frequencies. The two values of horizontal PGV that are available at Point B are
insufficient to define the hazard curve over its full range, which is typically 10-4 per year to 10-8
per year. A solution to this problem is to scale the Point A (a reference rock outcrop at the
repository elevation, as shown in Figure 2) hazard curve so that it minimizes the sum of the
squares of the residuals with respect to the two known values at Point B. This approach, known
as a least square fit, is reasonable because it preserves the shape of the Point A hazard curve
while reproducing the known values at Point B within a small error. The shape of the hazard
curves at Points A and B will be approximately the same if the deaggregation of earthquake
sources over the frequency range of interest remains similar at the two points. This is a
reasonable approximation over the frequency range of interest.
The scaling analysis is presented in Attachment I, based on the Point A hazard curve defined by
the probabilistic seismic hazard analyses expert elicitation (DTN: MO03061E9PSHA1.000, file
h_vel_extended.frac_mean). A scaling factor of 0.7963 results in an error of +7.6 and
-1.7 percent with respect to the two known values at Point B. The scaled hazard curve at Point B
is illustrated in Figure 3. PGV values at other annual exceedance frequencies can be determined
by interpolation, with the resulting values shown in Table 5.
PoiSoilRock
Rock
Point A nt B
Point C
Point D
Point E
Repository
Modified from CRWMS M&O 1998
LEGEND
Point A - Reference rock outcrop
Point B - Repository elevation
Point C - At rock surface
Point D - At surface of significant soil layer over rock
Point E -At surface of shallow soil layer over rock
Figure 2. Schematic Diagram Showing Locations of Points A and B
0
/)
(1/y
Poiili1.00E-08
1.00E-07
1.00E-06
1.00E-05
1.00E-04
500 1000 1500
Horizontal PGV (cmsecAnnual Exceedance Frequencynt A Hazard Curve
Scaled Hazard Curve for Pont B
Known Vaues at Pont B
Calculation in Attachment I
Figure 3. Hazard Curve for Point B is Generated by Scaling the Point A Hazard Curve
Table 5. Calculated Values of PGV on the Point B Hazard Curve
Annual Frequency of Occurrence
(1/yr)
Horizontal PGV a
(cm/s)
510-4 18.1
10-4 38.8
510-5 55.0
10-5 106.7
10-6 262.4 b
10-7 525.8 b
10-8 1073.
NOTES: a All values calculated in Attachment I.
b
These calculated values have an error of +7.6 and -1.7 percent
with respect to the known values at Point B of 244 cm/s for 10-6
per year and 535 cm/s for 10-7 per year, respectively.
6.5 FAILED AREA ABSTRACTION FOR THE WASTE PACKAGE
6.5.1 Initial Abstraction for Damage from Vibratory Ground Motion
This abstraction defines the damage to the waste package from vibratory ground motion. To this
end, structural response calculations have been performed to determine the damage from
impact(s) between the waste package and emplacement pallet and from impact(s) between
adjacent waste packages. The potential for damage from impacts between the waste package and
drip shield is included in the analysis, but produces negligible damage because the drip shield is
unrestrained and can move freely.
In this section, the term damage is synonymous with a failed area that exceeds the residual
stress threshold for Alloy 22, allowing advective flow through the waste package and
radionuclide transport from the waste package. Permanent structural deformation does not
always result in damage because the residual stress may be below the threshold for Alloy 22.
No damage is equivalent to 0 percent failed area on the surface of the package, so there is no
flow through or transport from the waste package. Full damage is equivalent to 100 percent
failed area, wherein all the incident flux passes through the waste package.
6.5.1.1 Structural Response Calculations
A set of 15 calculations for dynamic waste package structural response are performed for the
suite of ground motions with a PGV of 2.44 m/s, corresponding to the 10-6 per year mean annual
exceedance frequency at Point B. A similar set of calculations is also performed for a PGV of
5.35 m/s, corresponding to the 10-7 per year mean annual exceedance frequency at Point B (BSC
2003b). The stochastic (uncertain) input parameters for the 15 simulations are the 15 sets of
three-component ground motion time histories, the metal-to-metal friction coefficient, and the
metal-to-rock friction coefficient. A Monte Carlo sampling scheme defines the appropriate
combinations of ground motion and friction coefficients (BSC 2003r, Section 6.4) for each PGV
level. The same sets of ground motion time histories (accelerograms) are also used for the
analyses of drip shield damage from vibratory ground motions described in Section 6.6.1 and for
the analyses of rockfall induced by vibratory ground motion.
The structural response calculations do not represent the dynamic response of the invert to the
ground motion. The invert is represented as an elastic body whose surface responds
instantaneously and uniformly to the given ground motion. In other words, the ground motion
time histories for the three components of motion are applied directly to the surface of the invert.
This is a reasonable approach for small amplitude ground motions because the invert is
compacted under the weight of the waste packages and drip shield and because any remaining
steel framework in the invert will tend to provide some integrity. These effects will result in an
invert that tends to move as a single unit. For high amplitude ground motions, the invert ballast
is likely to be thrown up and redistributed, allowing the heavy EBS components to settle on the
bottom of the drift, directly in contact with the rock floor. In this case, applying the ground
motions directly to the surface of the invert is again a reasonable approach.
The damage to the waste package is determined by comparing the residual first principal stress
on the waste package outer shell to the failure criterion defined in Section 6.3. More
specifically, two residual stress thresholds are used to define the damaged area on the outer shell
of the waste package. The two stress thresholds are 80 and 90 percent of the yield strength of
Alloy 22. These values correspond to the lower and upper bound of the uniform distribution for
the residual stress threshold defined in Section 6.3. The area on the outer shell of the waste
package for which the residual first principal stress exceeds the residual stress threshold is
referred to as the damaged area or failed area throughout this document.
6.5.1.2 Waste Package Damage
The damaged areas for 14 different realizations at an annual frequency of occurrence of 10-6 per
year are summarized in Table 6 (BSC 2003b, Table 6.1.4-2; BSC 2003c, Table 16). The results
for realization 8 are not presented in Table 6 because an input error was discovered for this
calculation during the checking process. The mean damage and standard deviation of the
damage is also presented in this table. The mean damage for the 80 percent residual stress
threshold is approximately twice as large as the mean damage for the 90 percent residual stress
threshold. Note also that the variability in damage (i.e., the ratio of the maximum damage to the
minimum damage for a given ground motion level) from the ground motions is approximately a
factor of 10 at a given residual stress threshold. The uncertainty in damage is dominated by the
uncertainty in ground motion, rather than the uncertainty in the residual stress threshold.
The results in Table 6 also demonstrate that the cumulative damage area is dominated by the
contribution from end-to-end impacts of adjacent waste packages. In particular, the damaged
area from waste package to pallet impacts is much smaller than the damage due to the end-to-end
impacts of adjacent waste packages, with the exception of realization number 14. The damage
from end-to-end impacts is the dominant contribution to total damage because the adjacent waste
package is conservatively represented as an essentially rigid wall anchored to the invert. The
rigid wall is used for computational simplicity, but results in overestimating the damage from
end-to-end impacts. The damage from multiple end-to-end impacts may also be overestimated
because the potential for stress waves caused by a late impact to relax the residual stress
generated by earlier impacts is ignored in estimated to total damaged area.
The damaged areas for 14 different realizations at an annual frequency of occurrence of 10-7 per
year are summarized in Table 7 (BSC 2003b, Table 6.2.4-2; BSC 2003c, Table 17). The results
for realization 2 are not presented in Table 7 because the kinematics of the waste package are
such that the impacts between package and pallet occur outside the finely meshed region of the
outer shell. The mean damage for the 80 percent residual stress threshold is again approximately
twice as large as the mean damage for the 90 percent residual stress threshold. The variability in
damage from the ground motions is the dominant uncertainty because it is more than a factor of
10 at a given residual stress threshold. Finally, the damaged area from waste package to pallet
impacts is much smaller than the damage due to the end-to-end impacts of adjacent waste
packages, with the exception of realization numbers 1, 4, and 14.
Table 6. Damaged Area from Vibratory Ground Motion at the 10-6 Annual Exceedance Frequency
Realization
Ground
Motion
Damaged Area on the Waste Package
Waste Package to Pallet
Interaction
(m2; % of total OS area)
Waste Package to Waste
Package Interaction
(m2; % of total OS area)
Cumulative
(m2; % of total OS area)
80% Yield 90% Yield 80% Yield 90% Yield 80% Yield 90% Yield
Number Number Strength Strength Strength Strength Strength Strength
1 7 0.0029;
0.010
0.0014;
0.0050
0.023;
0.082
0.012;
0.043
0.026;
0.092
0.013;
0.046
2 16 0; 0 0; 0 0.017;
0.060
0.0089;
0.032
0.017;
0.060
0.0089;
0.032
3 4 0.0050;
0.018 0; 0 0.19; 0.67 0.083; 0.29 0.20; 0.71 0.083; 0.29
4 8 0.030; 0.11 0.0064;
0.023 0.12; 0.43 0.061; 0.22 0.15; 0.53 0.067; 0.24
5 11 0.0015;
0.0053 0; 0 0.15; 0.53 0.066; 0.23 0.15; 0.53 0.066; 0.23
6 1 0.025;
0.089
0.0028;
0.0099 0.15; 0.53 0.063; 0.22 0.18; 0.64 0.066; 0.23
7 2 0.017;
0.060 0; 0 0.11; 0.39 0.057; 0.20 0.13; 0.46 0.057; 0.20
9 10 0.0035;
0.012 0; 0 0.12; 0.43 0.062; 0.22 0.12; 0.43 0.062; 0.22
10 9 0; 0 0; 0 0.014;
0.050
0.0071;
0.025
0.014;
0.050
0.0071;
0.025
11 5 0.012;
0.043
0.0037;
0.013 0.074; 0.26 0.032; 0.11 0.086; 0.30 0.036; 0.13
12 6 0.0039;
0.014 0; 0 0.073; 0.26 0.036; 0.13 0.077; 0.27 0.036; 0.13
13 12 0; 0 0; 0 0.032; 0.11 0.016;
0.057 0.032; 0.11 0.016;
0.057
14 14 0.010;
0.035
0.0043;
0.015
0.0056;
0.020
0.0029;
0.010
0.016;
0.057
0.0072;
0.026
15 3 0.0078;
0.028
0.0015;
0.0053
0.020;
0.071
0.010;
0.035
0.028;
0.099
0.012;
0.043
Mean Value 0.310% 0.136%
Standard Deviation 0.237% 0.097%
Minimum Value 0.050% 0.025%
Maximum Value 0.710% 0.136%
Source: BSC 2003c, Table 16
NOTES:  Only 14 realizations are presented in this table. Results for realization 8 are not presented because
of an error in the input file for this calculation.
 Calculations are performed with 15 ground motions numbered 1, 2, 3, , 14, and 16. Time history
15 is not used because it has an anomalous response spectrum.
 Mean, standard deviation, minimum and maximum damage areas are calculated in Attachment II.
OS = outer surface of waste package.
Table 7. Damaged Area from Vibratory Ground Motion at the 10-7 Annual Exceedance Frequency
Ground
Damaged Area on the Waste Package
Waste Package to Pallet
Interaction
(m2; % of total OS area)
Waste Package to Waste
Package Interaction
(m2; % of total OS area)
Cumulative
(m2; % of total OS area)
Realization Motion 80% Yield 90% Yield 80% Yield 90% Yield 80% Yield 90% Yield
Number Number Strength Strength Strength Strength Strength Strength
1 7 0.20; 0.71 0.17; 0.60 0.16; 0.57 0.086;
0.30 0.36; 1.28 0.26; 0.92
3 4 0.096; 0.34 0.083; 0.29 0.42; 1.49 0.17; 0.60 0.52; 1.84 0.25; 0.89
4 8 0.12; 0.43 0.096; 0.34 0.11; 0.39 0.050;
0.18 0.23; 0.82 0.15; 0.53
5 11 0.093; 0.33 0.071; 0.25 0.18; 0.64 0.080;
0.28 0.27; 0.96 0.15; 0.53
6 1 0.046; 0.16 0.024; 0.085 0.42; 1.49 0.15; 0.53 0.47; 1.67 0.17; 0.60
7 2 0.038; 0.13 0.028; 0.099 0.32; 1.13 0.14; 0.50 0.36; 1.28 0.17; 0.60
8 13 0.095; 0.34 0.068; 0.24 0.32; 1.13 0.14; 0.50 0.42; 1.49 0.21; 0.74
9 10 0.0052; 0.018 0.0035; 0.012 0.034; 0.12 0.017;
0.060 0.039; 0.14 0.021;
0.074
10 9 0.16; 0.57 0.14; 0.50 0.33; 1.17 0.15; 0.53 0.49; 1.74 0.29; 1.03
11 5 0.0016; 0.0057 0; 0 0.30; 1.06 0.11; 0.39 0.30; 1.06 0.11; 0.39
12 6 0.062; 0.22 0.041; 0.15 0.10; 0.35 0.044;
0.16 0.16; 0.57 0.085; 0.30
13 12 0.027; 0.096 0.018; 0.064 0.12; 0.43 0.053;
0.19 0.15; 0.53 0.071; 0.25
14 14 0.020; 0.071 0.016; 0.057 0.0077; 0.027 0.0040;
0.014
0.028;
0.099
0.020;
0.071
15 3 0.0045; 0.016 0; 0 0.29; 1.03 0.14; 0.50 0.29; 1.03 0.14; 0.50
Mean Value 1.036% 0.530%
Standard Deviation 0.560% 0.298%
Minimum Value 0.099% 0.071%
Maximum Value 1.84% 1.03%
Source: BSC 2003c, Table 17
NOTES:  Only 14 realizations are presented in this table. Results for realization 2 are not presented because the
kinematics of the waste package are such that the impacts between package and pallet occur outside the
finely meshed region of the outer shell.
Mean, standard deviation, minimum and maximum damage calculated in Attachment II.
OS = outer surface of waste package.
6.5.1.3 Initial Abstraction for Waste Package Damage
The failure criterion for Alloy 22 is defined as a uniform distribution between 80 and 90 percent
of the yield strength (see Section 6.3.1). In other words, there is uncertainty in the value of the
appropriate residual stress threshold for Alloy 22. Tables 6 and 7 present damage values at the
two extremes (80 and 90 percent) of the residual stress threshold. Since the failed area is defined
by the elements of the finite-element grid whose residual stress exceeds the value of the residual
stress threshold, it follows that the failed area for the 90 percent threshold is always less than or
equal to the failed area for the 80 percent threshold.
The residual stress threshold could be retained as a stochastic parameter whose value is sampled
for TSPA-LA. In this situation, the damage at intermediate values of the residual stress
threshold could be defined by linear interpolation between the damage at the extreme values.
However, the uncertainty in damaged area is dominated by the ground motions, rather than the
residual stress threshold, as discussed above. In this situation, it is reasonable to simplify the
damage abstraction for the waste package by averaging the failed areas at the two extremes (80
and 90 percent). In effect, this corresponds to a failure criterion for the average (85 percent)
value of the residual stress thresholds. The use of the average or mean value is consistent with
the release limits for the repository at Yucca Mountain, which are expressed in terms of the mean
of the distribution of projected dose to the reasonably maximally exposed individual, per 10 CFR
63.303 and 63.311. The average damage values are calculated in Attachment II.
A number of distributions are considered as potential fits to the damage area for the
14 realizations with damage information. A normal distribution provides a reasonable fit to the
results at the 10-7 per year annual exceedance frequency, although it must be truncated for the
10-6 per year annual exceedance frequency because the mean and standard deviation are
approximately equal. The magnitude of the mean is only 30 to 40 percent greater than the
standard deviation, implying a significant fraction of negative damage values for a normal
distribution.
A uniform distribution provides an excellent description of the damage, is simple to implement
in a Monte Carlo sampling scheme, and does not need to be truncated. Figure 4 compares the
damage results for the 10-7 per year ground motion level to the cumulative distribution function
for a uniform distribution, which is simply a straight line. In comparing the damage results to
the cumulative distribution function, the damage values have been sorted in ascending order and
each point is assigned equal probability.
R2
(-)
iiily = 69.959x - 0.048
= 0.9685
0.0
0.2
0.4
0.6
0.8
1.0
0.0% 0.2% 0.4% 0.6% 0.8% 1.0% 1.2% 1.4% 1.6%
% Damaged Area on Waste Package
Cumulative ProbabilityData
CDF for Unform Distrbuton
Calcuation in Attachment II
Figure 4. Comparison of Damage Results for the 10-7 per Year Ground Motion Level to the Cumulative
Distribution Function for a Uniform Distribution
The straight line for the least squares fit to the results has been determined by Excels statistical
package. This straight line provides an excellent fit to the results, judging by the fact that the
square of the residuals, r2, is 0.9685. As a reminder, an r2 value of 1.0 is a perfect correlation
and a value of 0.0 is no correlation. The fact that a straight line provides an excellent fit to the
results confirms that a uniform distribution is a reasonable representation for the damage
abstraction.
A uniform distribution also provides a very good description of the damage results for the 10-6
per year ground motion level. Figure 5 compares the damage results for the 10-6 per year ground
motion level to the straight line for the least squares fit. The square of the residuals with the
straight line, 0.946, is slightly less than that in Figure 4 but still quite close to 1.0. Again, a
uniform distribution is a reasonable representation of these damage results.
R20.0
0.2
0.4
0.6
0.8
1.0
(-)
iiiiy = 174.65x + 0.111
= 0.946
0.0% 0.1% 0.2% 0.3% 0.4% 0.5% 0.6%
% Damaged Area on Waste Package
Cumulative ProbabilityData
CDF for Unform Distrbuton
Calculaton in Attachment II
Figure 5. Comparison of Damage Results for the 10-6 per Year Ground Motion Level to the Cumulative
Distribution Function for a Uniform Distribution
The upper and lower bounds of the uniform distribution must span the range of damage values
shown in Figures 4 and 5. Estimation of the upper bound of a uniform distribution from sampled
results (especially when the number of samples is small) requires careful consideration.
Rossman et al. (1998) describe a Bayesian procedure for calculating the 95 percent upper
confidence limit (UCL) for the upper bound of a uniform distribution as follows:
1
-
95%UCL =a n-1 max( X) (Eq. 2)
where a is the significance level (i.e., 0.05 at the 95 percent confidence level), n is the sample
size, and X is the uncertain quantity of interest (i.e., the damaged area). Using Equation 2, the
Bayesian upper bound for the uniform distribution of damaged area is calculated to be
0.630 percent at the 10-6 per year hazard level and 1.744 percent at the 10-7 per year hazard level.
This formula for calculating the Bayesian upper bound uses the so-called flat prior, which
indicates maximal uncertainty about the upper bound based on the sampled values. Other prior
distributions tend to represent increased prior certainty about the value of the parameter, and thus
produce lower posterior estimates (Rossman et al. 1998). The selection of the flat prior can thus
be justified as a conservative choice.
Estimation of the lower bound of the uniform distribution also must be considered carefully.
Figure 4 shows that the least squares fit for the 10-7 per year ground motion level has a minimum
damage value of less than 0.1 percent at a cumulative probability of 0.0. This minimum damage
value is about a factor of 15 less than the damage of 1.5 percent at a cumulative probability of
1.0. Figure 5 shows that the least squares fit for the 10-6 per year ground motion level has a
negative damage at a cumulative probability of 0.0. This is physically impossible, and is
probably caused by the cluster of six points with damage values between 0.0 and 0.1 percent.
In this situation, it is reasonable to set the lower bound of the uniform distribution at 0 percent at
all ground motion levels. Zero percent is clearly the minimum value for the least squares fit at
the 10-6 per year ground motion level. A zero percent minimum value produces a minor error in
the minimum value for the least squares fit at the 10-7 per year ground motion level. Zero
percent is also a reasonable lower bound for the preliminary damage results at the 10-5 per year
ground motion level presented in the next section (Section 6.5.2). However, it is difficult to
extrapolate the behavior for ground motions significantly greater than those at the 10-7 per year
ground motion level.
The damage abstraction for the TSPA-LA calculations is a relationship between the Bayesian
upper bound and the corresponding seismic hazard level, as measured by horizontal PGV. The
PGV levels corresponding to the 10-6 and 10-7 per year hazard levels are 2.44 m/s and 5.35 m/s,
respectively (see Section 6.4). A linear fit to the Bayesian upper bounds calculated earlier and
these PGV values produces the following linear relationship:
Dub = MAX(0.0, 0.383  PGV  0.305) (Eq. 3)
where Dub = Bayesian upper bound of the uniform distribution of the percent of damaged area
on the surface of the waste package at a given PGV. The MAX function ensures that the value
of Dub cannot be less than 0 percent. These calculations are documented in Attachment II.
Figure 6 compares the results for percent damaged area on the surface of the waste package with
the linear fit to the Bayesian upper bound at the 95 percent confidence limit from Equation 3.
Percent of Failed Area Per WP (-)
3.0%
2.5%
2.0%
1.5%
1.0%
0.5%
0.0%
1e-6 ground motion level
1e-7 ground motion level
upper bound values
Linear Fit to Upper Bound
02468
Peak Ground Velocity (PGV) (m/s)
Calculation in Attachment II
NOTE: The lower bound is 0 percent.
Figure 6. Linear Fit to Upper Bound of Damage Distribution
The damage to the waste package is applied to all waste packages in the repository, except for
those packages that experience a juvenile failure. There is no spatial variability for damage to
the waste package.
6.5.2 Corroborating Information from the 10-5 Per Year Ground Motion Level
Three simulations have been performed using approximate ground motions for the 10-5 per year
annual exceedance frequency, corresponding to a PGV value of 1.067 m/s. These simulations
provide added confirmation that the upper bound for the damage, as shown in Figure 7, is
tending to zero in a linear fashion. The approximate ground motions are created by scaling the
three acceleration components of each 10-6 per year ground motions by the ratio of the PGV for
the 10-5 per year level to the PGV for the 10-6 per year level. This procedure is not exact because
the deaggregation of seismic sources for the 10-5 and 10-6 per year ground motion levels is
different. However, it provides a reasonable approach for calculations that can corroborate the
abstraction in Figure 6. The scaling factor, 0.4066, is calculated in Attachment I of this report.
Ground motions number 1, 2, and 10, corresponding to realizations 6, 7, and 9, respectively, are
scaled for these calculations. These three ground motions are characterized by the highest
intensity (energy) among the set of 15 10-6 per year ground motions and have high levels of
damage, although not the maximum damage (for example, see Table 6). The damage results for
these three ground motions (BSC 2003b, Table XI-2; BSC 2003m, Table 58) are summarized in
Table 8.
The damage results for these three additional points, at a PGV of 1.067 m/s corresponding to the
10-5 per year ground motion level (see Table 5), can be added to the abstraction in Figure 6. The
Bayesian upper bound at the 95 percent confidence limit can also be calculated for the three
points in Table 8, and results in a value of 0.114 percent. Figure 7 shows that the linear equation
for the upper bound, based on the results at PGVs of 2.44 m/s and 5.35 m/s, is a reasonable fit at
the 10-5 per year ground motion level, and that a lower bound of 0 percent damage is reasonable
at this level. While there are only three results at a PGV of 1.067 m/s, these points do provide
additional confidence in the extrapolation of the abstraction for waste package damage to values
of PGV of 1 m/s and below.
Table 8. Damaged Area from Vibratory Ground Motion at the 10-5 Annual Exceedance Frequency
Realization
Number
Ground
Motion
Number
Damaged Area
(m2 ; % of total OS area)
80% Yield Strength 90% Yield Strength Average Yield Strength
6 1 0.0060; 0.021 0; 0 0.0030; 0.0105
7 2 0; 0 0; 0 0; 0
9 10 0.0106; 0.038 0.0037; 0.013 0.00715; 0.0255
Source: BSC 2003b, Attachment XI, Table XI-2; BSC 2003m, Table 58
OS = outer surface of waste package.
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
0 2 4 6 8
i () ()
i(-)
il
il
iil
lli iPeak Ground VeloctyPGVm/sPercent of Faled Area Per WP
1e-6 ground moton leve1e-7 ground moton leveupper bound values
Linear Ft to Upper Bound
1e-5 ground moton leveCacuatonn Attachment II
Figure 7. Comparison of Linear Fit to Bayesian Upper Bound of Damage Distribution at PGVs of 2.44
m/s and 5.35 m/s with the Results for the 10-5 per Year Ground Motions
6.5.3 Independent Technical Review of Model Abstraction
An independent technical review of this model abstraction has been performed by Dr. Robert P.
Kennedy of RPK Structural Mechanics Consulting. The result of Dr. Kennedys review is
presented in Attachment III and briefly summarized here.
Dr. Kennedy presents an alternate analysis of the damage information for the waste package.
This alternative analysis is structured around a fragility approach. In a fragility approach, one
often asks: What is the exceedance probability that the damage will exceed a given level for a
given value of PGV? Following this approach, a lognormally distributed approximation of the
damage surface is fit by trial and error. The following lognormal distribution provides a good fit
to the damage results in terms of exceedance probability (Equation III-9 in Attachment III):
Median: PGV50 = (5.7 m/s)D0.5
Log. Std. Dev.:  = 0.28D-0.5 = 0.8
Truncation Point: EP = 1 %
A comparison of the lognormal distribution at PGV of 2.44 m/s and 5.35 m/s with the uniform
distribution in Section 6.5.1 identifies values of D (in the units of percent damaged area) where
the uniform distribution is nonconservative with respect to the lognormal distribution. For a
PGV of 5.35 m/s, the uniform damage surface provides a good approximation for D less than
about 1.67 percent. Above this damage level the uniform damage surface estimate of
exceedance probability becomes seriously nonconservative. For a PGV of 2.44 m/s, the uniform
damage surface significantly overestimates exceedance probability (is conservative) for damage
between 0.06 and 0.56 percent. However, a more significant issue is that the uniform damage
surface significantly underestimates exceedance probability for damage greater than
0.60 percent.
The nonconservatism at higher damage values can be easily corrected by changing Equation 2 to
slightly increase the linear upper bound for damage, Dub. The nonconservatism can be
eliminated if Dub is defined as:
Dub = 0.436(PGV)  0.305 (Eq. 4)
instead of using Equation 3. Dub has the units of percent damage, so that a PGV of 5.35 m/s
results in damage of 2.0 percent. Details of the comparison between the lognormal distribution
and the uniform distribution are presented in Attachment III. Figure 8 compares the modified
upper bound for the lognormal fit to the original upper bound for the uniform distribution.
0 2 4 6 8
) (m/s)
(-)
il
il
iil
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
Peak Ground Velocity (PGVPercent of Failed Area Per WP1e-6 ground moton leve1e-7 ground moton leveupper bound values
Linear Ft to Upper Bound
1e-5 ground moton leveUpper Bound - Lognormal Dist.
Calculation in Attachment II
Figure 8. Comparison of Upper Bounds Based on a Lognormal Distribution (Blue Curve) with the
Bayesian Upper Bound
6.5.4 Final Abstraction for Damage from Vibratory Ground Motion
Without additional data for PGV values below 2.44 m/s or above 5.35 m/s, it is prudent to
choose the more conservative fit (Equation 3) for the upper bound of the uniform distribution for
waste package damage for TSPA-LA. Additional structural response calculations at a PGV of
1 m/s (corresponding to the 10-5 per year ground motion level) can provide additional insight into
the appropriateness of a uniform versus a lognormal distribution for the damage to the waste
package. In addition, activities related to defining the maximum amplitude ground motion that
can propagate through Yucca Mountain will also assist in bounding the potential damage at PGV
values greater than 6 m/s.
6.6 FAILED AREA ABSTRACTION FOR THE DRIP SHIELD
Vibratory ground motion has the potential to damage the drip shield as a barrier to flow. This
damage may occur due to the mechanical response of the drip shield to impacts from the waste
package, emplacement pallet or invert. Damage may also occur due to the mechanical response
of the drip shield to impacts from rock blocks or rockfall that are induced by the ground motions.
In addition to damage caused by impact, it is also possible that adjacent drip shields will be
separated during a high amplitude ground motion. Separated drip shields could allow seepage to
fall directly on a waste package(s), and therefore have the same effect as damage caused by
impact. Both mechanisms (damage due to impact and separation) have been observed in the
structural response calculations for ground motions at the 10-6 per year and 10-7 per year levels.
In this section, the term damaged area is synonymous with a failed area that exceeds the
residual stress threshold for Titanium Grade 7, allowing advective flow through the drip shield.
Permanent deformation of the drip shield does not always result in damage if the residual
stress is below the threshold. No damage is equivalent to 0 percent failed area on the surface, so
there is no flow through the drip shield. Full damage is equivalent to 100 percent failed area,
wherein all the incident flux passes through the drip shield.
6.6.1 Abstraction for Damage from Rockfall in the Nonlithophysal Zone
Vibratory ground motions have the potential to eject large rock blocks in the nonlithophysal
zone. The mechanical response of the drip shield to impact by a large rock block has the
potential to damage the drip shield as a barrier to flow. This damage could also occur because of
separation between two adjacent drip shields from vibratory ground motions.
Development of an abstraction for damage to the drip shield due to rockfall induced by vibratory
ground motion in the nonlithophysal zone involves the following steps. Figure 9 presents a
flowchart of these steps, which are described in detail in the following sections.
iliiliieli)
Select indivdual rock bock sizes and
velocities that span range of kinetic energy
Calculate the sequence of rock blocks
ejected in the nonlithophysal zone
Generate ground motion time histores and
synthetic fracture patterns
Calculate damage from multiple rock
blocks by interpolating and summng
Caculate damage to drp shd from
these indivdual rock blocks as function of
impact location (top, corner and side
damage for the full sequence of blocks
ilAbstract total faed area
Figure 9. Flow chart of the Drip Shield Damage Abstraction Methodology

Rockfall calculations have been performed for 15 ground motion time histories at each
annual exceedance frequency (10-6 per year and 10-7 per year), sampling a suite of 105
synthetic fracture patterns.

Potential results of the rockfall calculations are summarized in terms of the block mass,
relative impact velocity, impact angle, impact momentum, and impact energy associated
with each individual block that impacts the drip shield.

A set of representative rocks that span the block energy distribution and impact location are
selected in order to optimize the structural response calculations. For each representative
block and impact location, a structural response calculation is performed to determine the
damage to the drip shield. The residual stress from these calculations is interpreted as a
failed area on the drip shield, and collated into a catalog of damage areas as a function of
block energy and impact location.

This catalog is used as the basis for estimating (by interpolation) the impact from multiple
rockfall events at intermediate kinetic energy values and impact locations. The damage
from a multi-block rockfall is estimated as the sum of the effects from individual blocks.

The distribution of failed area (caused by the 15 ground motion time histories and synthetic
fracture patterns) is generated for the 10-6 and 10-7 per year annual exceedance frequencies.
This distribution is parameterized in terms of a log-triangular distribution, and also
characterized in terms of the fraction of no-fail cases.

The resulting damage abstractions for: (a) mode of log-triangular distribution of the failed
area as a function of PGV, and (b) fraction of no-fail cases, as a function of PGV are
characterized in terms of best-fit curves. The parameters of these curves are the
abstractions for drip shield failure due to rockfall induced by vibratory ground motion.
6.6.1.1 Rockfall Calculations
Analysis of rockfall in the nonlithophysal zone requires ground motion time histories, fracture
geometries, and fracture properties as input parameters or boundary conditions for the
calculations. To ensure adequate representation of uncertainty and variability, individual
rockfall calculations are sampled from 15 ground motions at each probability level (10-6 and 10-7
per year) and from 105 synthetic fracture patterns. The synthetic fracture patterns (BSC 2003h,
Section 6.1.6) are based on a random sampling of 105 centroid locations within a cube of rock
that is 100-meters on a side. A Monte Carlo sampling scheme provides the appropriate
combinations of ground motion and synthetic fracture pattern (BSC 2003r, Sections 6.1 and 6.2).
A total of 76 3DEC simulations are performed for the 10-6 per year annual exceedance frequency
(BSC 2003h, Section 6.3.1.2.3 and Attachment XI; DTN: MO0305MWDNLRKF.001).
Approximately 33 percent of the simulations predict no rockfall. A total of 281 rock blocks,
with a total volume of 101.8 m3, have been identified from the analyses. The associated impact
parameters for these rock blocks include the following:

Rock block volume falling on the drip shield

Relative impact velocity of rock block to the drip shield

Impact location.
The impact momentum and impact energy, both functions of block mass and impact velocity, are
also calculated as functions of the block mass and impact velocity. Summary statistics for these
parameters are provided in Table 9. The maximum predicted mass of an individual rock block is
21.42 tons, while the median block mass is 0.23 tons. The predicted results all show large
variance and high skewness with the exception of impact velocity.
Table 9. Summary of Rock Block Statistics for the 10-6 Annual Exceedance Frequency
Block Mass
(MT)
Relative ImpactVelocity (m/s)
Impact Angle
(degree)
Impact
Momentum
(kg  m/s)
Impact Energy
(Joules)
Mean 0.87 3.39 132 2747 5267
Median 0.23 3.49 120 663 902
Standard Deviation 1.97 1.61 81 6209 12941
Skewness 6.04 0.04 1.12 6.23 7.52
Range 21.39 7.54 355 68836 163083
Minimum 0.02 0.02 5 4 0
Maximum 21.42 7.56 360 68840 163083
Sum 245.55 NA NA 771861 1479888
Source: BSC 2003h, Table 14
NOTES:  Not Applicable;  MT = Metric Ton = 1,000 kg.
A similar number of 3DEC simulations are also performed for the 10-7 per year exceedance
frequency (BSC 2003h, Section 6.3.1.2.4). Approximately 21 percent of the simulations predict
no rockfall. A total of 380 blocks (with a total volume of 151.2 m3) have been identified
from the analyses. As before, information about individual rockfall events (e.g., rock
block volume falling on the drip shield, relative impact velocity of rock block to the drip
shield, impact location, impact momentum and impact energy) are documented in
DTN: MO0301MWD3DE27.003.
Summary statistics for these parameters are provided in Table 10 (BSC 2003h, Table 16). The
maximum rockfall block mass predicted is 21.42 tonnes, same as predicted for the 10-6 annual
exceedance frequency ground motions. The median block size is 0.23 tonnes, also the same as
predicted for the 10-6 per year exceedance frequency. The median impact momentum and energy
predicted for rockfall impact on the drip shield for the 10-7 annual exceedance frequency are
approximately two times the values predicted for those parameters at the 10-6 annual exceedance
frequency.
Table 10. Summary of Rock Block Statistics for the 10-7 Annual Exceedance Frequency
Block Mass
(MT)
Relative ImpactVelocity (m/s)
Impact Angle
(degree)
Impact
Momentum
(kg  m/s)
Impact Energy
(Joules)
Mean 0.96 5.03 139 4169 11459
Median 0.23 4.63 127 980 2440
Standard Deviation 2.04 2.78 87 8489 27461
Skewness 5.01 1.00 1.06 4.64 6.73
Range 21.39 17.67 356 89485 348170
Minimum 0.02 0.07 1 18 4
Maximum 21.42 17.74 357 89502 348174
Sum 364.58 NA NA 1584186 4354385
Source: BSC 2003h, Table 16
NOTES: Not Applicable; MT = Metric Ton = 1,000 kg.
MDL-WIS-PA-000003 REV 00 49 of 118 August 2003
A minor discrepancy has been found between the final version of Drift Degradation Analysis
(BSC 2003h, Attachment XI; DTN: MO0305MWDNLRKF.001) and the rockfall information
used in Attachment IV of this report. For rockfall from ground motions at the 10-6 per year level,
two blocks associated with case #42 are missing from the rockfall 1e-6 and impact
information worksheets in Attachment IV of this report. The material impact of this omission
on the abstractions for drip shield damage due to rockfall is negligible. The rationale for this
viewpoint is as follows:

Only 2 out of 281 rockfall events are inadvertently missing from the analysis.

The rock masses for these two blocks are 0.69 MT (metric tons) and 0.04 MT. By way of
comparison, the mean of the entire distribution of 281 blocks is 0.87 MT, the median is
0.23 MT, and the minimum is 0.02 MT (see Table 9).

The kinetic energy for these two blocks is 10,654 Joules and 307 Joules, whereas the 95th
percentile for the entire distribution of 281 events is 24,052 Joules, the median is 902
Joules, and the 5th percentile is 42 Joules.

Because kinetic energy is directly related to failed area, the two additional points in the
failed area distribution should be located between the 5th and 50th percentiles (for the 0.04
MT rock) and between the 50th and 95th percentiles for the 0.69 MT rock.
Given this rationale, the deletion of these two blocks from the original distribution of 279 points
is not expected to have any significant impact on the statistics of the distribution because only
two blocks are involved and the mass and kinetic energy of both blocks lie well within the
typical ranges for rockfall. In this situation, no significant impact is anticipated for the resulting
abstraction for damage to the drip shield from rockfall.
6.6.1.2 Drip Shield Damage - Single Block Impact
In order to minimize the number of structural response calculations, a set of five representative
blocks and three representative impact locations are selected to span the range of blocks. The
idea behind this approach is to perform a limited set of calculations that span the range of rock
sizes, rock velocities, rock impact angles and rock impact points on the drip shield. This limited
set of calculations then provides the basis for estimating the response of the drip shield when
multiple blocks are ejected from drift walls during a ground-motion-induced event. This limited
set of calculations is referred to as a catalog of results or simply a catalog.
5
The selection of representative rocks is based on their kinetic energy since the impact energy of a
rock block should provide a direct correlation with damage. The impact energies associated with
the selected rocks correspond to the minimum, maximum, median (50th-percentile),
th-percentile and 95th-percentile of the sorted impact energies for the 10-6 per year exceedance
frequency (BSC 2003h, Attachment XI; DTN: MO0305MWDNLRKF.001). Other
characteristics of these rock blocks are given in Table 11. Note that the variability in ejection
velocity from the host rock sometimes leads to small blocks, with less mass, having a higher
kinetic energy than larger blocks.
Table 11. Characteristics of Selected Rock Blocks for the 10-6 Annual Exceedance Frequency
Rock Block Mass
(MT)
Kinetic Energy
(J)
Vertical Velocity
(m/s)
Lateral Velocity(m/s)
14.5 163083 4.69 0.656
3.3 24712 3.75 0.0824
0.15 902 3.09 0.955
0.11 42 0.202 0.383
0.25 ~0 0.0137 0.0103
DTN: MO0305MWDNLRKF.001
An examination of the rockfall results for the 10-7 per year ground motion level (DTN:
MO0301MWD3DE27.003) reveals that the range of rocks considered in Table 11 would be
adequate for spanning the impact energy range, provided one rock block representing the
maximum possible impact energy level for 10-7 is added to this set. The parameters for this
additional rock block are: block mass = 11.5 MT, kinetic energy = 348174 Joules, vertical
velocity = 7.77 m/s, and lateral velocity = 0.295 m/s.
Damage to the drip shield from impact of individual rock blocks is determined by structural
response calculations. The objective of these calculations is to determine the areas on the drip
shield where the residual stress exceeds the threshold value (50 percent of yield strength) for
Titanium Grade 7. The six representative rock sizes impact the drip shield from three different
angles: vertically downward onto the top of the drip shield, at a 60 angle (with the horizontal)
onto the transition region between the top and side of the drip shield, and horizontally into the
side wall. Table 12 shows the results for the 10-6 and 10-7 per year rockfall on drip shield (BSC
2003g, Section 5.5.1).
Table 12. Damaged Area from Individual Rock Blocks Impacting the Drip Shield
Rock Mass and
Kinetic Energy
(MT and Joules)
Failed Area (m2) and Failed Area as a % of Total Drip Shield Surface Area
Vertical Rockfall
(90 from horizontal)
Rockfall Onto DripShield Corner
(60 from horizontal)
Rockfall Onto DripShield Side-Wall
(40 from horizontal)
11.5 MT Rock 4.304 2.835 1.126
(348174 J) (11.25%) (7.41%) (2.94%)
14.5 MT Rock 3.508 0.612 0.079
(163083 J) (9.17%) (1.60%) (0.21%)
3.3 MT Rock 0.548 0.416 0.0
(24712 J) (1.43%) (1.09%) (0.00%)
0.15 MT Rock 0.0015 0.0091 0.0
(902 J) (0.00%) (0.02%) (0.00%)
0.11 MT Rock 0.0 0.0 0.0
(42 J) (0.00%) (0.00%) (0.00%)
0.25 MT Rock 0.0 0.0 0.0
(~0 J) (0.00%) (0.00%) (0.00%)
Source: BSC 2003f, Tables 2 and 3
6.6.1.3 Drip Shield Damage - Multiple Block Impacts
Using the catalog of damage results for individual rock blocks in Table 12, the failed areas for
multi-block rockfalls at the 10-6 per year and 10-7 per year ground motion levels are calculated by
interpolation. In other words, the information presented in Table 12 is used to estimate the
damage caused for all of the single or multi-rockfall events summarized in Table 9 and Table 10.
In the interpolation process, the impact angle associated with individual rockfall events is
converted to an indicator variable representing either a vertical rockfall, a rockfall into the
transition region between top and side, or a rockfall into the sidewall. The details of the
interpolation process are explained in Attachment IV. Thus, impact energy is the only
interpolating variable. Furthermore, the impact from a multi-block fall is estimated as the sum of
the effects from individual rock blocks. Summary statistics for the failed area corresponding to
these hazard levels are derived in sheet impact information by case of Attachment IV of this
document and given in Table 13.
Table 13. Statistics for Damaged Area from Multiple Rockfalls on the Drip Shield at 10-6 and 10-7
Annual Exceedance Frequencies
Failed Area at the 10-6
Level (%)
Failed Area at the 10-7
Level (%)
Mean 1.698 3.405
Median 0.049 0.941
Standard Deviation 5.165 9.322
Minimum 0 0
Maximum 32.245 63.568
NOTE: Calculation in Attachment IV, sheet impact information by case.
The spread in the failed area reflects: (a) the uncertainty associated with the ground motion time
histories corresponding to a given annual exceedance probability, and (b) the geologic
uncertainty regarding the exact configuration of the fracture system near the emplacement drifts.
This uncertainty is represented in the rockfall calculations through the synthetic fracture pattern.
The distribution of the failed area for the 10-6 annual exceedance frequency is presented in
Figure 10. Approximately 25 percent of the cases do not have any damage (i.e., 0 percent failed
area). A log-triangular fit to the damage distribution is also shown in Figure 10, where the lower
bound is fixed at 0.001 percent (as the logarithm of zero is undefined) and the upper bound is
fixed at 100 percent. The most-likely value (mode) is obtained using a least-squares regression
as 0.197 percent (see Attachment IV). Although fits of similar quality could be obtained using
more complicated distributional forms such as the gamma or extreme value distributions, a log-
triangular distribution is chosen for its simplicity and because it provides a good fit to the results.
Drip Shield Damage at 1e-6 1/yr frequency
0
1
FiData
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Cumulative Probability
tted CDF
-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2
log(Percent Failed Surface Area)
Figure 10. Comparison of Failed Areas for PGV of 2.44 m/s (10-6 per year mean annual exceedance
frequency) with the Fitted Log-Triangular Distribution
The distribution of the failed area for the 10-7 annual exceedance frequency is presented in
Figure 11. Approximately 20 percent of the cases do not have any damage (i.e., 0 percent failed
area). A log-triangular fit to the damage distribution is also shown in Figure 11, where the lower
bound is fixed at 0.001 percent (as the logarithm of zero is undefined) and the upper bound is
fixed at 100 percent. The most-likely value (mode) is obtained using least-squares regression as
5.83 percent (see Attachment IV). A log-triangular distribution is chosen because it provides a
good fit to the results with a simple distribution type, although fits of similar quality could be
obtained using more complicated distributional forms such as the gamma or extreme value
distribution.
Drip Shield Damage at 1e-7 1/yr frequency
0
1
FiData
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Cumulative Probability
tted CDF
-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2
log(Percent Failed Surface Area)
Figure 11. Comparison of Failed Areas for PGV of 5.35 m/s (10-7 per year mean annual exceedance
frequency) with the Fitted Log-Triangular Distribution
MDL-WIS-PA-000003 REV 00 53 of 118 August 2003
6.6.1.4 Abstraction for Drip Shield Damage from Rockfall
Figure 12 shows the abstraction for the mode of the percent failed surface area as a function of
PGV, based on a log-triangular distribution. Figure 13 shows the abstraction for the fraction of
cases with no damage, again as a function of the PGV. The results of the calculations for PGVs
of 2.44 m/s and 5.35 m/s (10-6 and 10-7 per year mean annual exceedance frequencies,
respectively) have been supplemented by an additional point representing the 510-5 per year
exceedance frequency with a PGV of 0.55 m/s. This is consistent with Assumption 5.1, in that
the threshold of damage lies between 10-4 and 10-5 per year exceedance frequencies. For this
latter case, there is zero damage to the drip shield. Thus, the mode is taken to be the same as the
lower bound (i.e., 0.001 percent), and the fraction of no-failure cases is taken to be 1.0.
A power law fit to the mode, M, of the log-triangular distribution is given by the following
relationship:
M = 0.0088  (PGV)3.7767 (Eq. 5)
The numerical parameters in this fit are determined by the Excel fitting function, and are shown
in Figure 12. Similarly, a power law fit to the fraction of cases with no damage is given by:
F = MIN(1.0, 0.601  (PGV)-0.735) (Eq. 6)
where F is the fraction of rockfall cases without failure. The numerical parameters in this fit are
again determined on the Excel fitting function, and are shown in Figure 13. The MIN function
ensures that the value of F cannot be greater than 1.0.
Mode of % Failed Surface Area
10
1
0.1
0.01
0.001
y = 0.0088x3.7767
R2 = 0.9974
0.1 1.0 10.0
Peak Ground Velocity (m/s)
Figure 12. Power Law Fit to the Mode of the Log-Triangular Distribution
1
Fraction of No Fail Cases
y = 0.601x-0.735
R2 = 0.958
0.1
0.1 1.0 10.0
Peak Ground Velocity (m/s)
Figure 13. Power Law Fit to the Fraction of Undamaged Cases
6.6.1.5 Damage Abstraction for Multiple Drip Shields
The rockfall calculations in the nonlithophysal zone are based on a tunnel length of 25 meters
(BSC 2003h, Section 6.3.1). Since the length of an individual drip shield is 5805 mm (BSC
2003f, Table 1), the damage from multiple block impacts will be shared between 25/5.805 = 4.31
drip shields, rather than being applied to a single drip shield. Note that the overlap between
adjacent drip shields is ignored in this calculation because it is a relatively small length
compared to the overall length of the drip shield. Given the presence of multiple drip shields, it
is necessary to reconsider the damage abstraction in Equations 4 and 5.
The power law fit to the fraction of cases with no damage (Equation 6) is unchanged by the
effective number of drip shields exposed to the rock fall. On the other hand, the mode of the
log-triangular distribution (Equation 5) needs to be modified because this damage is distributed
among 4 to 5 drip shields. As a first approximation, it is reasonable to reduce the mode by a
factor of 4.31 to represent the mean damage to each drip shield in the 25-meter length of tunnel.
That is,
M = (0.0088/4.31)  (PGV)3.7767 (Eq. 7)
M = 0.00204  (PGV)3.7767 (Eq. 8)
represents the mode of the log triangular distribution for the damage to each drip shield in the
nonlithophysal zones. The fixed upper and lower bounds of the log-triangular distribution, 0.001
and 100 percent, are not being changed because these bounds are limiting values.
6.6.1.6 Independent Technical Review of Model Abstraction
An independent technical review of this model abstraction has been performed by Dr. Robert P.
Kennedy of RPK Structural Mechanics Consulting. The result of Dr. Kennedys review is
presented in Attachment V and briefly summarized here.
Dr. Kennedys major recommendations are as follows:

A constant residual stress threshold of 50 percent for failure of Titanium Grade 7 is unduly
conservative; a distribution for the residual stress threshold is desirable to represent this
uncertainty in the damaged areas.

The abstraction for damage at a PGV of 2.44 m/s has good agreement with the percent
damaged surface area for values between zero and 30 percent. The abstraction for damage
at a PGV of 5.35 m/s also has good agreement with the percent damaged surface area for
values up to 1.5 percent and becomes very conservative above this value. This could lead
to a significant overestimation of the annual probability of exceeding higher damage
values.

So long as this potential conservatism is acceptable, the damage abstraction is more than
adequate within a range of PGV values between 1.5 m/s and 6 m/s.
Given these recommendations, the TSPA-LA will use the model abstraction defined in
Section 6.6.1.5.
6.6.2 Damage from Rockfall in the Lithophysal Zone
Vibratory ground motions can cause failure of the host rock around the emplacement drifts. In
the nonlithophysal zones, large rock blocks can be ejected from the walls of the drift at high
velocities. The damage to the drip shield from large rock blocks in the nonlithophysal zones is
discussed and abstracted in Section 6.6.1.
In the lithophysal zones, the static loads from a collapsed drift using continuum or discontinuum
representations of the host rock are not expected to collapse the drip shield from the mean value
of the rock mass pressure predicted for the drip shield. Damage to the drip shield from rockfall
in the lithophysal zone is neglected for TSPA-LA on this basis. However, structural response
calculations have not been performed for the most extreme pressures or for the nonuniform
loading predicted by the rock mechanics codes.
In the lithophysal zones, the rock mass has very low compressive strength and is permeated with
void spaces of varying size. Average joint spacing is less than 1 meter, and at certain locations
this spacing is much smaller, on the order of 0.1 meters (BSC 2003h, Section 6.1.4.1). This
weak rock mass is expected to collapse into small fragments under the load imposed by a large
vibratory ground motion. Rockfall calculations demonstrate that drifts in the lithophysal zones
would collapse under the 10-6 per year (and by inference the larger, 10-7 per year) vibratory
ground motions (BSC 2003h, Section 6.4.1.1).
The small fragments from lithophysal failure have little capability to damage the drip shield
because the small mass and energy of the individual fragments cannot cause permanent
deformation of the drip shield. Consider a fragment that (for simplicity) is a cube 0.1-meter
(4-inches) on a side. The volume of this fragment is 0.001 m3 and its mass is approximately
2 kg, assuming a tuff density of approximately 2,000 kg/m3. The velocity of this fragment is
7.7 m/s for a 3-meter drop under gravitational acceleration, and the associated kinetic energy is
59 Joules. Table 13 shows that a 0.11 MT rock with 42 J of kinetic energy does not produce a
failed area on the surface of the drip shield. A comparison of the mass and kinetic energy of the
0.1-meter fragment with the block in Table 13 indicates that there should be no damage from the
impact of this fragment on the drip shield.
A cubic fragment that is 0.3-meters (12 inches) on a side has a mass of 54 kg and a kinetic
energy of 1600 Joules. This fragment is approximately equivalent to the 0.15 MT (150 kg) rock
with 902 Joules of kinetic energy in Table 13. This rock produces no damage for the top and
side impacts, and very small damage (0.02 percent) for the corner impact. Again, the damage for
impact of a cubic fragment 1-foot on a side should be negligible. In summary, the drip shield
will not be damaged by direct impact of small rock fragments in the lithophysal zone.
It is also worth noting that rockfall in the lithophysal zone does not damage the waste package
and cladding. The waste package and cladding are not damaged because the drip shield remains
intact until a seismic event occurs, deflecting any rockfall away from the waste package. If the
duration of the seismic scenario class extends beyond 20,000 years, then the drip shield may be
significantly degraded before the seismic event occurs and may not protect the waste package
from rock blocks or drift collapse.
Drift collapse in the lithophysal zones can impose a static load on the drip shield from the weight
of the natural backfill that fills the drifts as a result of the collapse. The structural response of the
drip shield to the static load from a hypothetical engineered backfill and fallen host rock
generated by tunnel collapse has been evaluated with structural response calculations. The layer
of engineered backfill in these calculations is taken to be 0.9 meters thick or 1.1 meters thick.
The fallen host rock is 5.5 meters thick. The applied pressure from these materials is 143 kPa if
the hypothetical engineered backfill is 0.9-meters thick and 146 kPa if the engineered backfill is
1.1 meters thick (BSC 2003s, Table 5.2-1 and Section 5.2).
The maximum stress in all components of the drip shield is always less than the yield strength
for this combined load (BSC 2003s, Section 6 and Table 6.2). At room temperature, the highest
stress in the drip shield is 43 percent of the yield strength for Titanium Grade 7. At 150C, the
highest stress in the drip shield is 68 percent of the yield strength for Titanium Grade 7. In
addition, the average stress in the large support beams (the peripheral bulkheads) of the drip
shield is far enough below the yield strength of Titanium Grade 24 to alleviate any concern of
buckling. (The drip shield plates are fabricated from Grade 7, while the supporting structure is
fabricated from Grade 24.)
It is important to differentiate between dynamic and static failure of the drip shield. For dynamic
loading of the drip shield due to seismic hazards, an area fails as a flow barrier when the residual
stress exceeds 50 percent of the yield strength of Titanium Grade 7. This failure is a combined
chemical-mechanical response of a cold worked material to dynamic impacts. For static loading,
as discussed in the above paragraph, the failure of the drip shield is determined by mechanical
collapse of the drip shield. In this situation, a local stress of 68 percent of the yield strength of
Titanium Grade 7 does not imply structural failure.
The potential rock loads in the lithophysal zones after complete collapse of the emplacement
drift have been analyzed for 5 cases using a discontinuum representation of the host rock (BSC
2003h, Section 6.4.2.4 and Table 40). The mean pressure on the top of the drip shield is 145
kPa, with a maximum value of 179.2 kPa. The mean pressure on the right side of the drip shield
is 85 kPa, with a single outlier at 220.8 kPa. The mean pressure on the left side of the drip shield
is 86 kPa, with a maximum value of 142.7 kPa. The elastic response of the drip shield for an
applied pressure of 146 kPa clearly indicates that the drip shield will not fail from these mean
rock loads. It is also likely that the drip shield will not fail from the maximum load on the top of
the drip shield, 179.2 kPa. However, the single outlier on the right side of the drip shield, at
220.8 kPa, may require additional analysis. In addition, the pressure contours on individual
segments of the drip shield are quite nonuniform (BSC 2003h, Figure 139), which is not included
in the structural response calculations.
An alternate conceptual representation of the potential rock loads can be based on a continuum
approach. The potential rock loads after the complete collapse of the emplacement drift from
15 ground motions at the 10-6 per year level have been analyzed for the lithophysal rock
(BSC 2003h, Section 6.4.1.1 and Table 38). The mean pressure on the top of the drip shield is
178 kPa, slightly greater than the value of 146 kPa for the static load calculation. This increase,
on the order of 22 percent, is still well below the threshold for yielding.
The largest pressure on the top of the drip shield is 317.1 kPa and the largest pressure on the side
of the drip shield is 507.1 kPa for the 15 cases. This latter value is not realistic because it is due
to a single elastic block of rock that is wedged in place. In reality, this level of stress will
fracture or crush the rock, invalidating the elastic assumption. Local deformation of the drip
shield plates will also reduce the lateral pressure.
6.6.3 Abstraction for Drip Shield Damage from Vibratory Ground Motion
The mechanical response of the drip shield to vibratory ground motions has the potential to
damage the drip shield as a barrier to flow. This loss of integrity could occur because of impacts
between the drip shield and the waste package, empacement pallet or invert or because of
separation between two adjacent drip shields. In fact, all these mechanisms are observed in the
structural response calculations that are performed for ground motions at the 10-6 per year and
10-7 per year levels.
The structural response calculations do not represent the dynamic response of the invert to the
ground motion. The invert is represented as an elastic body whose surface responds
instantaneously and uniformly to the given ground motion. In other words, the ground motion
time histories for the three components of motion are applied directly to the surface of the invert.
This is a reasonable approach for small amplitude ground motions because the invert is
compacted under the weight of the waste packages and drip shield and because any remaining
steel framework in the invert will tend to provide some integrity. These effects will result in an
invert that tends to move as a single unit. For high amplitude ground motions, the invert ballast
is likely to be thrown up and redistributed, allowing the heavy EBS components to settle on the
bottom of the drift, directly in contact with the rock floor. In this case, applying the ground
motions directly to the surface of the invert is again a reasonable approach.
The results of the structural response calculations for ground motions at the 510-4 per year, at
the 10-6 per year and at the 10-7 per year ground motion levels are summarized as follows
(BSC 2003p):

One simulation performed at the 5  10-4 per year ground motion level indicates that there
is no damage to the drip shield (BSC 2003f, Calculation Results I). More specifically, no
area of the drip shield exceeds the residual stress threshold of 50 percent of the yield
strength of Titanium Grade 7. The residual stress threshold is 104.5 MPa at 150C for
Titanium Grade 7.

Fourteen simulations are performed at the 10-6 per year ground motion level using the set of
three-component ground motion time histories. Table 14 identifies the realization number,
the associated ground motion number, and the drip shield area exceeding the residual stress
threshold for the 14 simulations (BSC 2003f, Table 4).
The mean percent damaged area in Table 14 is 0.70 percent and the maximum percent
damaged area is 2.13 percent. This latter value is an outlier, in the sense that the second
greatest percent damaged area is 1.25 percent, or more than 40 percent below the maximum
damage value. There is no indication of separation of drip shields in the calculations for
the 10-6 per year ground motion level.

Five simulations performed at the 10-7 per year ground motion level indicate separation of
adjacent drip shields (BSC 2003f, Calculation Results I). Separation occurs between
adjacent drip shields because of plastic deformation of the drip shield and because of the
large magnitude of the ground motions. In fact, each of the five simulations demonstrates
that a drip shield rides over its adjacent neighbor, implying that a separation must occur
somewhere in the emplacement drift. The degree to which the drip shield rides over its
neighbor is substantial, on the order of 10 to 25 percent of the length of the drip shield.
A uniform distribution has been selected to represent the damaged area on the drip shield from
vibratory ground motion. The motivation for selection of a uniform distribution is twofold.
First, there are only five realizations for the 10-7 per year ground motion level, and a uniform
distribution is a reasonable representation of the upper and lower bounds with a very limited
number of samples. Second, the use of a uniform distribution is conservative for damage at the
10-6 per year ground motion level because a uniform distribution samples the high damage end
more than a normal or log-normal distribution that incorporates the single outlier at 2.13 percent.
Table 14. Damaged Area from Vibratory Ground Motion at the 10-6 Annual Exceedance Frequency
Realization Number  Ground Motion Number
Damaged Area
(m2; % of Total Area)
1 7 0.113; 0.30
2 16 0.055; 0.14
3 4 0.248; 0.65
4 8 0.105; 0.27
5 11 0.257; 0.67
6 1 0.427; 1.12
7 2 0.479; 1.25
8 13 0.100; 0.26
9 10 0.814; 2.13
10 9 0.192; 0.50
11 5 0.456; 1.19
12 6 0.376; 0.98
14 14 0.0456; 0.12
15 3 0.0989; 0.26
Source: BSC 2003f, Table 4
NOTES: Only 14 realizations are presented in this table. Results for realization 13 are
not presented because a numerical instability occurred during this calculation.
Calculations are performed with 15 ground motions numbered 1, 2, 3, , 14,
and 16. Time history 16 is used in place of 15 because because 15 has an
anomalous response spectrum.
The upper bound of the uniform distribution at the 10-6 per year ground motion level is based on
the damage results in Table 14. The 95 percent UCL for the upper bound of a uniform
distribution can be defined using a Bayesian procedure (Rossman et al. 1998):
1
-
%95 UCL =a n-1 max( X ),
1
-
= (05.0 ) 13 (%),13.2 (Eq. 9)
= %.68.2
where a is the significance level (i.e., a = 0.05 at the 95 percent confidence level), n is the
sample size (i.e., n = 14 entries in Table 14), and X is the uncertain quantity of interest (i.e., the
percent damaged area).
The upper bound of the uniform distribution at the 10-7 per year ground motion level or higher
amplitude ground motions is 50 percent. The rationale for this value is as follows. The five
structural response calculations at the 10-7 per year level demonstrate that a drip shield can cover
or overlap its neighbor by a substantial amount. In an extreme case, each pair of drip shields in
the emplacement drifts could be reduced to one-half their original length if one member of the
pair completely covers the other member of the pair. In this situation, the total length of drip
shield in a drift would be reduced by 50 percent. While more extreme situations are possible,
such as a stack of three or four drip shields that cover one another, these situations seem
extremely improbable. First, a tall pile of drip shields will probably be less stable than a 2-high
stack under vibratory ground motions. Second, increasing structural deformations are required to
add a third or fourth drip shield to a stack that is 2-high. Deformation must increase because the
inner width of the third drip shield in a stack must be greater than the outer width of the second
drip shield, and so on. The complex dynamics of the EBS components in response to ground
motions make these arrangements improbable, given that ground motions are usually coherent
over 10s of meters.
The lower bound of the uniform distribution is defined as 0 percent at all ground motion levels.
In reality, the lower bound around the 10-6 per year level is a small non-zero value that changes
with the ground motion level. Setting the lower bound for damage to 0 percent provides a
reasonable simplification based on the available computational results. The lower bound at the
10-7 per year level is highly uncertain because there is substantial uncertainty in the degree of
separation between adjacent drip shields. This uncertainty is represented in TSPA-LA by
defining the lower bound as 0 percent at the 10-7 per year ground motion level. This choice
provides a range of damage between 0 and 50 percent at the 10-7 per year level, bounding the
potential variability in overlap between adjacent drip shields and passing this uncertainty into
TSPA-LA for sensitivity studies.
Finally, the maximum damage is assumed to go to zero at the 510-5 per year ground motion
level. This approach is consistent with Assumption 5.1, whereby damage from vibratory ground
motion first begins between the 10-4 and 10-5 per year ground motion levels. In other words, the
ground motions greater than those at the 10-4 per year level are required to damage the drip
shield. This approach is also consistent with the zero damage state chosen for the damage
abstraction for the drip shield from rockfall (see Section 6.6.1.4).
In terms of PGV, the abstraction for the upper bound of the uniform distribution is a simple lookup
table defined by the five points in Table 15. The mean annual exceedance frequencies of 10-6
and 10-7 per year have been replaced with the corresponding PGV values in the emplacement
drifts, 2.44 m/s and 5.35 m/s, respectively. The mean annual exceedance frequency for 510-5
per year is replaced with 0.55 m/s, based on the scaled hazard curve for Point B in Table 5.
Table 15. Abstraction for Maximum Damage to the Drip Shield from Vibratory Ground Motion
PGV Value
(m/s)
Damage to Drip Shield
(%)
0.0 0
0.55 0
2.44 2.68
5.35 50
20 50
6.6.3.1 Independent Technical Review of Model Abstraction
An independent technical review of this model abstraction has been performed by Dr. Robert P.
Kennedy of RPK Structural Mechanics Consulting. The result of Dr. Kennedys review is
presented in Attachment VI and briefly summarized here.
Dr. Kennedy presents an alternate analysis of the damage information for the drip shield. This
alternative analysis is structured around a fragility approach. Following this approach, the
damage data at the 10-6 per year ground motion level (PGV = 2.44 m/s) has been fit with a
lognormal distribution. A lognormal distribution with the following parameters provides an
excellent fit to the damage results at 10-6 per year (Equation VI-4 in Attachment VI):
Median: D50 = 0.55%
Log. Std. Dev.:  = 0.85
A comparison of this lognormal distribution with the uniform distribution in Section 6.6.3 shows
that the uniform distribution is very conservative for percent damage areas of 0.50 percent and
greater. This could lead to a significant overestimation of the annual probability of exceeding
the percent damage when the damage is greater than 0.50 percent with a normal distribution.
Dr. Kennedy notes that there are only 5 data points for the damage from ground motions at the
10-7 per year level (PGV = 5.35 m/s). One knows that damage will be large, but it is difficult to
estimate exceedance probability for various percent damage values. He also states that the upper
bound of 50 percent for damage is probably reasonable for PGV = 5.35 m/s; however, the lower
bound should probably be in excess of 10 percent at this level. Given limited data, his primary
conclusion is that the drip shields are likely to be severely damaged at a PGV of 5.35 m/s or
greater.
6.6.3.2 Final Abstraction for Damage from Vibratory Ground Motion
Without additional damage data for PGV values at or above 5.35 m/s, it is prudent to choose the
uniform distribution with an upper bound defined in Table 15 because it is more conservative
than the lognormal distribution. The maximum damage of 50 percent for PGV values of 5.35
m/s or greater is considered a reasonable upper bound. The rationale for this bound is twofold:
(1) the five simulations for the PGV level of 5.35 m/s (10-7 per year) demonstrate that a drip
shield rides over its adjacent neighbor by 10 percent to 25 percent of its axial length, well below
the recommended maximum of 50 percent, and (2) the value of 50 percent corresponds to an
extreme case in which each and every pair of drip shields through the repository is reduced to
one-half of its original length.
However, Dr. Kennedy notes that using a lower bound of zero for the uniform distribution does
not seem conservative for PGV values of 5.35 m/s or greater. In this situation, it seems
appropriate to define a lower bound that is a function of PGV. This lower bound is zero for all
values of PGV that are less than or equal to 2.44 m/s, as discussed in Section 6.6.3. For values
of PGV between 2.44 m/s and 5.35 m/s, there is a linear interpolation between 0 percent damage
and 10 percent damage, respectively. The value of 10 percent is selected because it is the
minimum value for the 5 simulations at the PGV level of 5.35 m/s, and this minimum is
appropriate for a uniform distribution. For values of PGV greater than 5.35 m/s, the lower bound
is based on a linear extrapolation of the damage at 2.44 and 5.35 m/s. In other words, damage
continue to increase with PGV. The data points for the abstraction are summarized in Table 16.
Table 16. Abstraction for Minimum Damage to the Drip Shield from Vibratory Ground Motion
PGV Value
(m/s)
Damage to Drip Shield
(%)
0.0 0
2.44 0
5.35 10%
6.6.4 Combined Abstraction for the Drip Shield
The combined abstraction for damage to the drip shield is a function of the host rock:

In the lithophysal zone, the damage to the drip shield from vibratory ground motion is
determined by the abstraction in Section 6.6.3.2. The damage from vibratory ground
motion is given by a uniform distribution with a lower bound defined by Table 16 and an
upper bound given in Table 15.

In the nonlithophysal zone, the damage to the drip shield is determined by the sum of the
damage abstraction for rockfall, as described in Section 6.6.1.4, and the damage abstraction
for vibratory ground motion, as defined in Section 6.6.3.2. The total damage cannot be
greater than 100 percent.
These levels of damage are applied to all drip shields in the lithophysal zone and to all drip
shields in the nonlithophysal zone. There is no spatial variability within each of these zones.
6.7 FAILURE ABSTRACTION FOR THE CLADDING
The mechanical response of the waste package to vibratory ground motions can produce
dynamic impacts between adjacent waste packages, between the waste package and its
emplacement pallet, and between the waste package and the drip shield. During each of these
impacts, the waste package may experience very high acceleration in the axial and lateral
directions. These accelerations can be transmitted to the the fuel rod assemblies and fuel rods.
The assemblies and fuel rods may impact the lid of a waste package due to the end-on (axial)
impact of adjacent waste packages, or the fuel rods may be pushed sideways, toward the sidewall
of the waste package, during impact with the emplacement pallet or drip shield. Either of these
impacts has the potential to fail the cladding.
As noted in Section 6.5.1.2, the end-on impact between two adjacent waste packages accounts
for 87 percent of the mean damage to the waste package at the 10-6 per year ground motion level
and 92 percent of the mean damage to the waste package at the 10-7 per year ground motion
level. These results imply that the end-on impact of adjacent waste packages produces much
more severe forces and accelerations than the side-on impact between a waste package and the
emplacement pallet or drip shield. These results are consistent with the conservative approach to
the end-on impact calculations, which are based on a waste package impacting an almost rigid
plane of symmetry located midway between two adjacent waste packages.
The maximum waste package velocities from end-on impacts with the 15 ground motions at the
10-6 per year level vary between 1.4 to 4.5 m/s (BSC 2003b, Tables 6.1.2-1 through 6.1.2-15;
BSC 2003n, Tables 28 through 42). In other words, all realizations for the 10-6 per year ground
motions have an impact velocity of at least 1.4 m/s. Similarly, the maximum waste package
velocities for end-on impacts at the 10-7 per year level vary between 1.3 and 6.5 m/s (BSC
2003b, Tables 6.2.2-1 through 6.2.2-15; BSC 2003m, Tables 46 through 57; BSC 2003n,
Tables 43, 44, and 45). That is, all realizations for the 10-7 per year ground motions have an
impact velocity of at least 1.3 m/s. (The minimum value for the 10-7 per year ground motions is
less than that for the 10-6 per year ground motions because of the stochastic variability in the
15 ground motions.)
The resulting fuel assembly accelerations due to this range of impact velocities have been
analyzed using a finite-element representation of the fuel assemblies. The maximum peak
acceleration and the average peak acceleration for all assemblies in a waste package are reported
in Tables 4 and 5 of Maximum Accelerations on the Fuel Assemblies of a 21-PWR Waste
Package During End Impacts (BSC 2003d) and Tables 14 and 15 of Repository Design Project,
RDP/PA IED Typical Waste Package Components Assembly (4) (BSC 2003e). The peak and
average accelerations in this reference have been evaluated for cutoff frequencies of 450 Hertz,
600 Hertz, and 1,000 Hertz. The accelerations for a cutoff frequency of 450 Hertz are repeated
in Table 17.
The finite-element calculations for the fuel assembly accelerations do not include any damping.
Impact calculations with no damping often produce highly transient time histories with peak
accelerations that are influenced by the spatial and temporal discretization of the calculations. In
this situation, the output is typically filtered through a low-pass, Butterworth filter to determine a
more realistic acceleration time history. The cutoff frequency for the filter is a compromise
between damping the extraneous numerical noise while leaving the fundamental modes of the
structure intact. Filtering the output below 400 Hertz dampens the fundamental modes of waste
package and fuel assembly, potentially leading to erroneous results. Filtering the output at
greater than 1,000 Hertz preserves computational noise and can also lead to misleading results.
A cutoff frequency of 450 Hertz dampens the numerical noise but has minimal impact on the
fundamental modes of fuel assembly and waste package (BSC 2003d, Attachment VIII).
Table 17. Fuel Assembly Accelerations from Waste Package-to-Waste Package Impacts for a 450 Hertz
Cutoff Frequency
Parameter
Initial Impact Velocity (m/s)
0.5 1 2 4 6
Maximum Peak Acceleration (gs) 75 144 263 323 506
Average Peak Acceleration (gs) 35 72 115 155 194
Source: BSC 2003d, Tables 4 and 5
The minimum impact velocity for the 10-6 per year and the 10-7 per year ground motions is
1.3 m/s, as noted above. Interpolating on the results in Table 17 for impact velocities of 1 m/s
and 2 m/s, the maximum peak acceleration is 180 gs and the average peak acceleration is 85 gs
at 1.3 m/s with a 450 Hertz cutoff frequency. With a cutoff frequency of 600 Hertz, the average
peak accelerations for 1 m/s and 2 m/s are 99 gs and 147 gs, respectively (BSC 2003d,
Table 4). The interpolated value for the average peak acceleration at 1.3 m/s is then 113 gs for
the 600 Hertz cutoff.
The integrity of fuel rod cladding during cask drop or tipover incidents has been extensively
studied for zircalloy-clad light water reactor spent fuel assemblies (Chun et al. 1987; Sanders
et al. 1992). The work by Chun et al. (1987) is more useful here because it explicitly calculates
g-loads for axial buckling and for yielding due to side drops. The range of g-loads for failure
due to axial buckling varies between 82 gs for the Westinghouse 1717 fuel assembly to 252 gs
for the Combustion Engineering 1616 fuel assembly (Chun et al. 1987, Table 4). The range of
g-loads for yielding due to side drops varies between 63 gs for a Westinghouse 1717 fuel
assembly to 211 gs for a Combustion Engineering 1616 fuel assembly (Chun et al. 1987,
Table 4). The actual g-loads for failure may be lower because: (1) the weight of the fuel pellets
is not transferred to the cladding (Chun et al. 1987, p. 2), and (2) the potential effects of cladding
defects or existing failures are not included in the analysis. These effects increase the inertial
mass or weaken the clad, possibly causing failure at lower g-loads.
Based on Table 17, end-on impacts of adjacent waste packages result in average fuel assembly
accelerations of 85 gs at the lowest impact velocity, and often much greater values for higher
impact velocities. The use of a 600 Hertz cutoff filter increases this minimum value to 113 gs.
Simple fuel rod failure criteria indicate that clad failure occurs between 82 and 252 gs,
depending on the type of fuel rod (Chun et al. 1987, Table 4). In this situation, 100 percent
perforation of the cladding is reasonable when a ground motion event with an annual exceedance
frequency less than or equal to 10-6 per year occurs.
One calculation is available for the structural response of the waste package to a ground motion
with an annual exceedance frequency of 510-4 per year (BSC 2003b, Section 6.3). There is no
damage to the cladding for this ground motion because there is no appreciable motion of the
waste package and no impact between adjacent waste packages. As explained in Assumption 5.1
(see Section 5.1), it is reasonable to expect that there will be no impact between adjacent waste
packages for the 10-4 per year seismic hazard, and therefore no cladding damage for this hazard.
However, the potential exists for more significant displacements and impacts at the 10-5 per year
ground motion level.
The cladding damage for ground motion at the 10-5 per year mean annual exceedance frequency
(or less) is conservatively set to 100 percent. In addition, the cladding damage is assumed to go
to zero at the 510-5 per year ground motion level. This approach is consistent with Assumption
5.1, whereby damage from vibratory ground motion first begins between the 10-4 and 10-5 per
year ground motion levels. In other words, ground motions greater than those at the 10-4 per year
level are required to damage the drip shield. This approach is also consistent with the zero
damage state chosen for the abstraction for damage to the drip shield from rockfall (see Section
6.6.1.4) and from vibratory ground motion (see Section 6.6.3)
In terms of PGV, the abstraction for damage to the cladding is a simple look-up table with a
linear interpolation between the four points in Table 18. The mean annual exceedance
frequencies of 510-5 per year and 10-5 per year have been replaced with the corresponding PGV
values in the emplacement drifts, 0.55 and 1.067 m/s, respectively, based on the scaled hazard
curve for Point B in Table 5.
Table 18. Abstraction for Damage to the Cladding from Vibratory Ground Motion
PGV Value
(m/s)
Damage to Cladding
(%)
0.0 0
0.55 0
1.067 100
20 100
There is no uncertainty in this abstraction because the abstraction represents a conservative,
bounding estimate for cladding response at all values of PGV.
6.8 RESPONSE TO FAULT DISPLACEMENT
In addition to inducing severe ground motion/acceleration as discussed in the previous sections,
seismic events can also result in fault displacements within the emplacement drifts. Fault
displacement could impact key EBS components in two ways:

Separation between adjacent drip shields can allow a pathway for seepage to contact the
waste packages thereby potentially accelerating corrosion-induced waste package failure.

Mechanical damage to the waste packages caused directly by the fault displacement.
Potential faulting within the emplacement drifts that have a reasonable likelihood of slipping
over the 10,000-year regulatory period generally have very small displacements associated with
the faults. With the exception of the Solitario Canyon fault and the Ghost Dance fault, which are
immediately outside the western and eastern boundaries of the emplacement drifts, a fault
displacement of greater than 0.1 cm requires an annual frequency of occurrence of less than 10-5
per year. For such low-probability events, there is significant uncertainty in the expected
magnitude of the fault displacement, and the estimates that have been developed are necessarily
quite conservative. Given the lack of precision in the estimated fault displacement magnitudes at
low probability, a highly detailed calculation of drip shield and waste package response to such
events is not warranted. Thus, the response calculations presented herein are intentionally quite
simplistic and conservative.
For a fault displacement that occurs along an emplacement drift, a sudden discontinuity in the
floor and roof of the tunnel may occur. This would result in one portion of the tunnel being
displaced vertically relative to the adjacent section. Such a discontinuity in the tunnel axis could
cause separation of adjacent drip shields, and if severe enough, could cause shearing of a waste
package at that location. The discussion in this section identifies the conditions under which
these damage mechanisms could occur.
6.8.1 Clearance Between EBS Components and the Drift
To determine the response of the drip shield and waste package to a fault displacement, consider
the layout within the emplacement drift, shown schematically in Figure 14. The tunnel itself is
5500 mm in diameter. Within the tunnel, the steel support beams and associated ballast form a
level invert whose top surface is 806 mm above the lowest part of the tunnel floor. Sitting on
this invert floor is the waste package emplacement pallet, which raises the waste package off the
invert floor. While the actual elevation difference between the invert floor and the bottom of the
waste package varies depending on the specific diameter of the waste package, the exact value is
not important for this analysis. As indicated in the discussion that follows, this elevation
difference is not actually used in the analysis.
The drip shield is also sitting on the invert floor. The drip shield has an external height of
2886 mm (BSC 2003f, Table 1). The internal height of the drip shield, defined as the distance
from the invert floor to the lowest point on the underside of the top of the drip shield, is 2716
mm (BSC 2003f, Table 1). There is then a clearance of 1808 mm between the top of the drip
shield and the tunnel roof. A summary of these parameters, which are independent of waste
package design, along with the source of the values, is provided in Table 19.
Without
Pallet
Drip
Shield
Invert
Clearance If
Rockfall Fills
the Tunnel
Clearance
Rockfall
Emplacement
Waste
Package
Figure 14. Schematic Diagram of EBS Components Illustrating the Clearances for Fault Displacement
Table 19. Emplacement Drift Configuration Dimensions that Are Independent of the Waste Package
Description Value Source
Drift Diameter 5.5 m BSC 2003i, Figure 1
Invert Thickness (maximum) 806 mm BSC 2003i, Figure 2
Drip Shield Height - Exterior 2886 mm BSC 2003f, Table 1
Drip Shield Height - Interior 2716 mm BSC 2003f, Table 1
Clearance Between Top of Drip Shield and Roof of Tunnel 1808 mm Calculated (5500 - 806 - 2886 = 1808)
Table 20 summarizes the exterior dimensions of the various waste package designs (BSC 2003j,
Table 1). The most important parameter for the analyses presented herein is the waste package
diameter, which is seen to vary between 1,318 mm and 2,110 mm. Also shown in Table 20 is
the calculated clearance between the top of the waste package and the underside of the drip
shield in the undisturbed state. This clearance is defined as the interior height of drip shield less
the package diameter. The elevation of the package above the invert is ignored in calculating the
clearance, as explained below. This clearance varies between 606 mm and 1398 mm, depending
on waste package type.
Table 20. Waste Package Dimensions and Clearance Between Drip Shield and Waste Package
Package Type Diameter (mm) Length (mm) Clearance (mm)
44-BWR 1674 5165 1042
24-BWR 1318 5105 1398
21-PWR 1644 5165 1072
12-PWR 1330 5651 1386
Naval-Long 1949 6065 767
Naval-Short 1949 5430 767
5 DHLW/DOE SNF -Short 2110 3590 606
5 DHLW/DOE SNF -Long 2110 5217 606
2-MCO/2-DHLW 1814 5217 902
Source: BSC 2003j, Table 1 for diameter and length
NOTE: Clearance is calculated as the interior height of the drip shield minus waste package diameter.
The clearance between the top of the drip shield and the roof of the tunnel (Table 19) and the
clearance between the top of the waste package and the bottom of the drip shield (Table 20) are
measures of how much fault displacement could occur before the waste packages are potentially
degraded through a shearing mechanism. However, the clearance above the drip shield is only
relevant if tunnel collapse does not occur. Once a tunnel collapses, the space surrounding the
drip shield will be filled with rock fragments (previously called natural backfill) that prevent
free motion of the drip shield in all directions. For those tunnels in the lower lithophysal zone of
the repository, tunnel collapse is calculated to occur for ground motion hazards with an annual
occurrence frequency of 10-6 per year or less (BSC 2003h, Section 6.4.1.1).
The actual response of the EBS components to a fault displacement scenario is complicated. As
a conservative simplification, the fault displacement is analyzed considering:

The fault is perpendicular to the tunnel axis with the displacement being purely vertical

The fault displacement occurs at a discrete point, creating a knife-edge discontinuity.
Vertical faulting is consistent with the faults investigated at the site. As part of the exploratory
studies of the site, the Enhanced Characterization of the Repository Block (ECRB) Cross-Drift
was dug through a representative part of the repository footprint to obtain visual evidence of both
rock stratigraphy and faulting. The results of this investigation (Mongano et al. 1999, pp. 51 to
59) found evidence for four faults along the length of the ECRB Cross-Drift between the two
major north/south faults (Ghost Dance and Solitario Canyon) that bound the location of the
emplacement drifts. One of these was the Sundance fault, the other three are unnamed faults that
showed between one and a few meters of cumulative faulting. In each of these cases, the
measured displacements were characterized as vertical, which is consistent with the assumption
made herein. By treating the faults as perpendicular to the tunnel axis, no credit is taken for
sideways movement of the waste packages that could lessen the degree to which fault
displacement could cause damage.
An actual fault zone has a finite width over which the displacement could occur. However,
based on the observations reported in the investigation of the ECRB Cross-Drift (Mongano et al.
1999, pp. 51 to 59), the width of the fault disturbed zone varied between just under a meter to a
little over 2 meters. Thus, the width of the zone is in all cases less than the length of a typical
waste package. If during a single seismic faulting event, the total displacement were to be
distributed over a sufficiently wide zone, a single waste package could potentially see less than
the total fault displacement, resulting in a decreased likelihood of failure. By treating the
displacement as a sharp discontinuity in the tunnel floor/roof, the likelihood of damage to the
waste package is increased. Thus, the overall treatment is conservative.
A sudden discontinuity in the tunnel floor would tend to raise one end of a drip shield and waste
package. However, the other EBS components, specifically the invert and emplacement pallet,
would also be affected. A significant amount of the invert (ballast) from the elevated portion of
the tunnel is expected to fall into the lower tunnel segment. In addition, the steel supports in the
invert and the emplacement pallet are likely to collapse at the plane of displacement, further
degrading the integrity of the invert.
The exact details of these events are difficult to predict. As a simplification, the approximation
is simply made that the emplacement pallet collapses into the invert on the elevated side of the
fault. No credit is taken for any further shifting of the ballast in the invert. Using this
approximation, the total available free height that the waste package can move through before
contacting the underside of the drip shield can be calculated as the clearance between waste
package and drip shield, without consideration for the elevation of the package above the invert
(see Table 20). In those cases where drift collapse has occurred, the drip shield would be
effectively held in place, so this free height represents the maximum allowable (vertical) fault
displacement before the waste package could be damaged (waste package shearing is assumed at
this point).
In those cases where drift collapse does not occur from the seismic hazard or from gradual
degradation of the drift and host rock, waste package displacement beyond that required for
contact with the underside of the drip shield is possible without damage. Further displacement
would cause the drip shield to lift since there is no tunnel debris to hold it in place. Such lifting
would occur until the drip shield contacts the roof of the drift. Thus, the clearance between the
top of the drip shield and the roof of the drift (1,809 mm; see Table 19) is also available, and the
maximum allowable fault displacement prior to waste package damage is increased by this
amount. These calculated results are summarized in Table 21.
Table 21. Maximum Allowable Displacement Before Waste Package Is Pinned
Package Type
Maximum Allowable Displacement
With Tunnel Collapse (mm)
Maximum Allowable Displacement
Without Tunnel Collapse (mm)
44-BWR 1042 2850
24-BWR 1398 3206
21-PWR 1072 2880
12-PWR 1386 3194
Naval-Long 767 2575
Naval-Short 767 2575
5 DHLW/DOE SNF -Short 606 2414
5 DHLW/DOE SNF -Long 606 2414
2-MCO/2-DHLW 902 2710
NOTES: Maximum allowable displacement with tunnel collapse = clearance in Table 20
Maximum allowable displacement without tunnel collapse = clearance in Table 20 + 1808 mm
MDL-WIS-PA-000003 REV 00 69 of 118 August 2003
The values in Table 21 represent the failure criteria for waste packages and drip shield under
fault displacement. Any fault displacement in excess of these values is conservatively
considered to fail the waste package, the overlying drip shield, and the internal cladding through
direct shearing.
Failure of the drip shields could also occur without direct waste package damage. One
mechanism for this is lifting of one drip shield relative to its neighbor, thereby creating a
pathway for ingress of seepage water onto the waste package. However, drip shield failure
without waste package damage will have low consequence for performance assessment, so it will
be screened out from TSPA-LA based on low consequence and is not considered further herein.
6.8.2 Faults Intersecting Emplacement Drifts
The location, likelihood, and magnitude of potential fault displacements within the emplacement
drift footprint must be analyzed to determine the potential impacts of fault displacement on the
Yucca Mountain repository. Such fault displacements could occur at known faults that intersect
the emplacement drifts (based on surface mapping), or at other locations within the repository.
6.8.2.1 Location of Known Faults
Information on known faults intersecting the emplacement drift is obtained from two sources.
The actual location of known faults relative to the repository location is provided in Figure 7 of
Site Recommendation Subsurface Layout (BSC 2001b). A more detailed mapping of each
emplacement drift tunnel, indicating locations of known fault zones intersecting each tunnel, as
well as whether those locations occur in the lower lithophysal zone, is provided as part of the
output from the multiscale thermo-hydrologic model (DTN: LL030704623122.031,
tspa03.mesh03-150w). From these two sources of information, the known faults that intersect
the drifts, the specific tunnels impacted, and whether the specific location is in the lower
lithophysal zone or not can be determined. This information is summarized in Table 22, where
tunnels are identified by panel number and tunnel number, plus a designation for east or west
when appropriate (see the standard subsurface facilities layout shown in BSC 2003o).
As can be seen from Table 22, there are 19 locations in the lower lithophysal zones where a
known fault intersects an emplacement drift, plus another 11 locations where such an intersection
occurs in the nonlithophysal zones. This information, along with the probability of a fault
displacement of sufficient magnitude to cause waste package failure at these locations, can be
used to determine the likelihood and consequence of waste package failure.
Table 22. Intersections of Known Faults with Emplacement Drifts
Fault Designator
Tunnels in Lower
Lithophysal Zones
Tunnels in
Nonlithophysal Zones
Sundance Fault 1-8 -
1-7 -
1-6 -
Drill Hole Wash Fault 3-2 2-17E
3-1 2-16E
2-10W 2-15E
2-9W 2-14E
2-8W 2-13E
2-7W 2-12E
2-6W 2-11E
2-5W 2-10E
-2-9E
Pagany Wash Fault 2-2W 2-7E
2-1W 2-6E
2-5E -
2-4E -
2-3E -
2-2E -
2-1E -
Sevier Wash Fault 2-2E -
Source: DTN: LL030704623122.031, tspa03.mesh03-150w
6.8.2.2 Faulting Other Than At Known Faults
During a major seismic event, faulting could occur not only coincident with the location of well-
characterized, known faults, but also elsewhere in the repository. In characterizing the potential
magnitude of fault displacement elsewhere in the repository (see Section 6.8.3), rock conditions
ranging from intact rock to the presence of existing small faults with ~2 meters of cumulative
offset are considered. As is discussed in Section 6.8.3, the likelihood of significant fault
displacement (>10 cm) is low, even for 10-8 probability events, except where an existing fault is
located with cumulative displacement of ~2 meters. However, the exact location and number of
such small faults is not known at this time, because they are not readily identified through
surface mapping. Thus, it is necessary to estimate the density of such smaller faults based on
either existing site data or natural analogues.
One means of quantifying the likelihood of such smaller faults is through use of the data
obtained from the characterization of the ECRB Cross-Drift (Mongano et al. 1999, pp. 51 to 59).
The ECRB Cross-Drift extends through the repository footprint near its north/south midpoint and
spans the approximate east/west extent of the repository. Over the length of this tunnel, three
small faults with cumulative displacement of between ~1 and a few meters were identified. If we
assume that this is representative of the density of small faults throughout the repository, one can
make an estimate of the number of such small faults that might intersect the emplacement drifts.
In reviewing the repository layout (BSC 2003o), it can be seen that there are 46 emplacement
drifts that span the entire north to south extent of the repository (designated 2-1W through
2-23W, 1-1 through 1-8, and 5-1 through 5-15). While in several cases these tunnels are much
shorter than the ECRB Cross-Drift, for conservatism it is assumed that there exist three unknown
small faults that intersect the repository footprint along its entire north to south extent. Thus, it is
estimated that there are 138 locations (3 times 46) where small faults intersect the emplacement
drifts.
Since the exact location of these potential faults is unknown, one cannot determine with certainty
whether they would intersect the emplacement drifts in the lower lithophysal zone or not. To
estimate what fraction of these intersections correspond to the lower lithophysal zone, we use the
fact that the estimated fraction of the overall repository in the lithophysal zone is 85 percent
(Section 5.1). This fractional distribution is applied to the 138 small fault intersections to get a
probability-weighted distribution of fault intersections versus rock stratigraphy.

117.3 Small fault intersections with drifts in lower lithophysal zone

20.7 Small fault intersections with drifts other than in lower lithophysal zone.
6.8.3 Fault Displacement Hazards
Magnitudes of fault displacements along two of these known faults (Sundance and Drill Hole
Wash) as a function of probability are obtained from Probabilistic Seismic Hazard Analyses for
Fault Displacement and Vibratory Ground Motion at Yucca Mountain, Nevada (CRWMS M&O
1998; DTN: MO0004MWDRIFM3.002). In Section 8 of that document, the DOE has
developed fault displacement hazard curves for fifteen faulting conditions mapped within the
immediate vicinity of Yucca Mountain. Mean fault displacement curves are used in all the
following analyses. The faulting conditions relevant to this abstraction are as follows:

Site 2 - Solitario Canyon Fault.

Site 3 - Drill Hole Wash Fault.

Site 4 - Ghost Dance Fault.

Site 5 - Sundance Fault.

Site 7 - A generic location within the repository, approximately 100-meters east of the
Solitario Canyon fault. The ground conditions at the generic location include intact rock
(7d), a hypothetical fracture with no cumulative displacement (7c), a hypothetical shear
with 10-cm of offset (7b) and a hypothetical small fault with 2-meter offset (7a).

Site 8 - A generic location within the repository, midway between the Solitario Canyon
fault and the Ghost Dance fault. The ground conditions at the generic location include
intact rock (8d), a hypothetical fracture with no cumulative displacement (8c), a
hypothetical shear with 10-cm of offset (8b) and a hypothetical small fault with 2-meter
offset (8a).
Four named secondary faults intersect the emplacement areas of the repository. These four faults
are the Drill Hole Wash fault, the Sundance fault, the Pagany Wash fault, and the Sevier Wash
fault. It is assumed that displacements on the Pagany Wash and Sevier Wash faults are identical
to those on the Drill Hole Wash fault (see Assumption 5.2).
The generic locations designated Site 7 and Site 8 apply throughout the repository. The
estimated 138 intersections between the emplacement drifts and various small faults (~2 meter
offset) identified in Section 6.8.2.2 correspond to locations 7a and/or 8a.
Table 23 provides the fault displacement values from the mean hazard curves as a function of the
mean annual exceedance frequency (or probability) (DTN: MO0004MWDRIFM3.002). The
first two faults (Solitario Canyon and Ghost Dance) in Table 23 are directly adjacent to the
repository block and are not considered further because no waste packages lie on these faults.
Locations 7 and 8 have essentially the same estimated displacements relative to the accuracy of
the results in Probabilistic Seismic Hazard Analyses for Fault Displacement and Vibratory
Ground Motion at Yucca Mountain, Nevada (CRWMS M&O 1998; DTN:
MO0004MWDRIFM3.002). Thus, the distinction between 7a and 8a for the 138 small fault
intersections described in Section 6.8.2.2 is not relevant.
6.8.4 Consequence for the Waste Packages
A comparison of Table 23 with Table 21 shows that all the waste packages would survive even a
10-8 frequency fault displacement at locations 7a, b, c and 8a, b, c because the maximum
displacement at these sites (9 cm = 90 mm) is always less than the available clearances in
Table 21. However, several of the waste package designs could potentially fail due to fault
displacement for hazards near the 10-8 per year level if they are directly over any of the four
known faults (Drill Hole Wash, Sundance, Pagany Wash, and Sevier Wash) intersecting the
emplacement drifts. Further, the waste packages containing DHLW would potentially fail when
placed over a small displacement fault (designated 7a and 8a). Thus, the likelihood of waste
package failure at a given fault location is a function of the clearance for the specific type of
waste package emplaced there.
Waste package distribution by type is available in the design basis inventory. This inventory is
repeated in Table 24, along with the waste package dimensions. Repository Design Project,
RPD/PA IED Typical Waste Package Components Assembly, 1 of 9 (BSC 2003j), the source
document for the waste package dimensions, does not provide information for the 5 DHLW
Long/1 DOE SNF Short or the 5 DHLW Long Only waste package configurations. This is
because these two configurations use the same waste package as the 5 DHLW Long/1 DOE SNF
Long configuration with different assemblies loaded. Thus, the waste package exterior
dimensions are the same for all three configurations.
Table 23. Fault Displacement from Mean Hazard Curves
Mean Annual Exceedance Frequency (1/yr)
10-4 c 10-5 c 10-6 d 10-7 d 10-8 d
Site Number and Fault Name Displacement (cm)
2 - Solitario Canyon <0.1 32.0 190 500 >1000
4-Ghost Dance <0.1 <0.1 13 58 160
3 - Drill Hole Wash a <0.1 <0.1 17 80 240
5 - Sundance <0.1 <0.1 6 42 ~145
7a - small fault with 2-m offset <0.1 <0.1 2 20 ~75
7b - shear with 10-cm offset <0.1 <0.1 1 6 9
7c - fracture with no displacement <0.1 <0.1 0.1 <1 <1
7d - intact rock b <0.1 <0.1 <0.1 <0.1 <0.1
8a - small fault with 2-m offset <0.1 <0.1 2 20 ~75
8b - shear with 10-cm offset <0.1 <0.1 1 6 9
8c - fracture with no displacement <0.1 <0.1 0.1 <1 <1
8d - intact rock b <0.1 <0.1 <0.1 <0.1 <0.1
DTN: MO0004MWDRIFM3.002
a
NOTES: Also representative of Pagany Wash and Sevier Wash faults.
b Zero displacement at Sites 7d and 8d is documented in DTN:
MO0004MWDRIFM3.002. See also CRWMS M&O 1998, Section 8.2.1.
c
See DTN: MO0004MWDRIFM3.002 for displacement hazards at Sites 3, 5,
7a-c and 8a-c for the 10-4 and 10-5 per year annual exceedance
frequencies. See also CRWMS M&O 1998, Table 8-1 for displacement
hazards at 10-4 and 10-5 annual exceedance frequencies.
d See DTN: MO0004MWDRIFM3.002 for displacement hazards at Sites 3, 5,
7a-c and 8a-c for the 10-6, 10-7, and 10-8 per year annual exceedance
frequencies. See CRWMS M&O 1998, Figures 8-3 and 8-5 for
displacement hazards at Sites 2 and 4 for the 10-6, 10-7, and 10-8 per year
annual exceedance frequencies.
To simplify the analysis, the inventory of waste packages is split into four groups. Waste
packages of similar design (similar waste type) are grouped together, and the maximum diameter
for all included waste packages is conservatively assigned to the group. These groupings are
chosen to facilitate consequence assessment for the waste package groupings in TSPA-LA. The
four groupings are as follows.
 PWR: includes 21-PWR with absorber plates, 21-PWR with control rods, and the
12-PWR Long with absorber plates.
 BWR: includes 44-BWR with absorber plates and 24-BWR with absorber plates.

Naval: includes Naval-Long and Naval-Short.

HLW: includes 5 DHLW/1 DOE SNF  Short, 5 DHLW/1 DOE SNF  Long, and all
other HLW designs.
The waste package designs in bold letters are the ones with the largest diameter in the group, and
thus are chosen to represent the diameter for all packages in that group. While the inclusion of
the 12 PWR design with the PWR group, the 24 BWR design with the BWR group, and the
2-MCO/2-DHLW design with the HLW group conservatively accounts for the likelihood of
failure for those waste package designs (by overestimating diameter), the impact of this
approximation is small because in each case the number of such packages is small relative to the
total number of packages in the group.
Table 24. Design Basis Waste Package Dimensions and Inventory
Waste Package Configuration
Waste Package
Length (m)
Waste Package
Diameter (m) Nominal Quantity
21-PWR with Absorber Plates 5.165 1.644 4299
21-PWR with Control Rods 5.165 1.644 95
12-PWR with Absorber Plates - Long 5.651 1.330 163
44-BWR with Absorber Plates 5.165 1.674 2831
24-BWR with Absorber Plates 5.105 1.318 84
5 DHLW Short/1 DOE SNF - Short 3.590 2.110 1147
5 DHLW Long/1 DOE SNF - Long 5.217 2.110 1406
5 DHLW Long/1 DOE SNF - Short 5.217 2.110 31
5 HLW Long Only 5.217 2.110 679
2-MCO/2-HLW 5.217 1.814 149
Naval-Short 5.430 1.949 144
Naval-Long 6.065 1.949 156
Source: BSC 2003j, Table 1 for length and diameter
BSC 2003k, Table 11 for nominal quantity
NOTES: The diameter of DHLW packages and HLW package is taken to be that of the DHLW packages
in Table 20.
The length of the DHLW Short package is taken to be that of the 5 DHLW/DOE SNF - Short
package in Table 20.
The length of the DHLW Long and HLW Long packages is taken to be that of the 5 DHLW/DOE
SNF - Long package in Table 20.
The percentage of the inventory of the waste packages for each group is calculated based on the
total length of that waste package type versus the total length of all emplaced waste packages.
Length is the appropriate parameter here because it more accurately represents the probability
that a waste package will lie on a fault. These results are shown in Table 25. The average length
per package type is shown for information only. It is used to calculate the fraction of waste
packages by waste package type.
Table 25. Parameters for Simplified Groups of Waste Packages
Waste
Package
Group
Average
Waste
Package
Length (m)
Maximum
Waste
Package
Diameter (m)
Waste
Package
Surface Area a
(m2)
Nominal
Quantity(-)
Effective Waste
Package Length
for Group b (m)
Fraction of
Waste Packages
(% of Total
Length)
PWR 5.1824 1.644 31.01 4557 23616 41.9
BWR 5.1633 1.674 31.55 2915 15051 26.7
Naval 5.760 1.949 41.24 300 1728 3.1
HLW 4.670 2.110 37.95 3412 15934 28.3
NOTES: a Surface Area = (p/2)(Dmax)2 + pDmaxLavg.
b Effective Length = (Average Length)  (Nominal Quantity).
Using the maximum waste package diameter in Table 25 and the calculated maximum fault
displacements before the waste package is pinned in Table 21, the following maximum fault
displacement values (to cause waste package damage) are used in the analysis.
Table 26. Maximum Allowable Fault Displacements Before a Waste Package Group Is Pinned
Waste
Package
Group
Maximum Allowable Displacement
With Tunnel Collapse (mm)
Maximum Allowable Displacement
Without Tunnel Collapse (mm)
PWR 1072 2880
BWR 1042 2850
Naval 767 2575
HLW 606 2414
A determination of waste package failure is made by comparing the maximum allowable
displacements in Table 26 with the fault displacement hazard curve in Table 23. As a reminder,
the Solitario Canyon and Ghost Dance faults are not included in this analysis because these faults
lie outside the emplacement areas of the repository.
Consider the case where tunnel collapse has not occurred. As can be seen from Table 26, the
HLW/Naval waste package design is subject to potential failure when the fault displacement
exceeds the maximum allowable displacement of 2,414 mm. However, as can be seen from
Table 23, the maximum fault displacement for any of the faults that intersect the emplacement
drifts is 230 cm = 2,300 mm, which corresponds to a 10-8 fault displacement along the Drill Hole
Wash fault. (The Solitario Canyon fault has larger displacements, but no drifts in the current
repository layout intersect this known fault.) Thus, since the maximum fault displacement is less
than the allowable displacement of 2,414 mm, no damage to EBS components would be
predicted without tunnel collapse. The same conclusion is valid for the other waste package
designs, with even greater margin.
Now consider the case where tunnel collapse has occurred, as is expected in the lower
lithophysal zones for seismic hazards with an annual exceedance frequency of 10-6 or less. First,
it is evident from a comparison of Tables 25 and 22 that all BWR, PWR, and Naval waste
packages will survive a fault displacement event for Sites 7a and 8a, even in the lower
lithophysal zones. The maximum fault displacement in Table 23 for Sites 7 and 8 is 75 cm =
750 mm, slightly less than the allowable fault displacement of 767 mm for the Naval group with
drift collapse in the lower lithophysal units. Again, the same conclusion is valid for the BWR
and PWR waste package designs, with even greater margin.
However, at mean annual exceedance frequencies between 10-7 per year and 10-8 per year, waste
package failure may occur for any of the waste packages placed directly over the four known
secondary faults intersecting the emplacement drifts, as well as for the HLW packaged placed
over faults characterized by location 7a and 8a. In those cases, the fault displacement values in
Table 23 exceed the maximum allowable displacements summarized in Table 26 for the case of
drift collapse.
The probability of a fault displacement event severe enough to cause waste package failure is a
function of both the specific fault (different fault displacements for a given probability) as well
as the specific waste package design (different allowable displacements). (The exceedance
frequency is equal to the exceedance probability for values much less than one per year.) To
determine the probability associated with a fault displacement event severe enough to cause
waste package damage, the fault displacement hazard curves from the Probabilistic Seismic
Hazard Analyses for Fault Displacement and Vibratory Ground Motion at Yucca Mountain,
Nevada (CRWMS M&O 1998; DTN: MO0004MWDRIFM3.002) are used. The relevant
information is provided in file ./displ/tot-haz/s3.frac_mean.gz of the DTN for the Drill Hole
Wash fault, in file ./displ/tot_haz/s5.frac_mean.gz for the Sundance fault, and in files ./displ/tot-
haz/s7a.frac_mean.gz and ./displ/tot-haz/s8a.frac_mean.gz of the DTN for locations 7a and 8a.
These curves show the predicted fault displacement as a function of probability of the event (a
graphical presentation of the results in Table 23). Using the maximum allowable displacements
from Table 26 (for each waste package design), the associated event probabilities are determined
from the hazard curves in DTN: MO0004MWDRIFM3.002. The resulting fault exceedance
probabilities that would cause waste package failure are summarized in Table 27. As previously
stated, the Pagany Wash and Sevier Wash faults are assumed to be represented by the Drill Hole
Wash fault (see Assumption 5.2). Again, these results only apply to the lower lithophysal zone,
which is predicted to collapse from seismic hazards at these annual exceedance frequencies.
Table 27. Fault Exceedance Probabilities That Cause Failure in the Lower Lithophysal Zonea
Fault HLW Naval BWR PWR
Sundance < 510-8 < 4x10-8 < 310-8 < 310-8
Drill Hole Wash < 210-7 < 1x10-7 < 610-8 < 610-8
Pagany Wash < 210-7 < 1x10-7 < 610-8 < 610-8
Sevier Wash < 210-7 < 1x10-7 < 610-8 < 610-8
7a/8a < 2x10-8 N/A N/A N/A
NOTE: a Tunnels in the lithophysal zones are predicted to collapse from ground motions at these mean annual
exceedance frequencies, so the maximum allowable displacement is based on Table 21 with tunnel
collapse.
As expected, the highest probability fault displacement events leading to waste package failure
are associated with the HLW waste packages, which have the largest diameter.
There are three locations where the Sundance fault intersects the emplacement drifts in the lower
lithophysal zone (from Table 22), 16 locations where either the Drill Hole Wash, Pagany Wash,
or Sevier Wash faults intersect the emplacement drifts in the lower lithophysal zone (see Table
22), and 117.3 locations (probability-weighted) where additional small faults intersect the
emplacement drifts in the lower lithophysal zone (Section 6.8.2.2). Combining this information
with the probability of finding a particular waste package group at a given point in the repository
(see Table 25), one can estimate the expected number of each type of waste package found at the
four secondary faults. This result is shown in Table 28. Note that the number of waste packages
is not an integral number because it represents an average expectation of finding a particular
waste package along a particular fault. The Pagany Wash, Sevier Wash and Drill Hole Wash
faults have been combined in Table 28 because they have the same fault displacement hazard
curves.
Table 28. Expected Number of Waste Packages Emplaced on Faults
PWR Group BWR Group Naval Group HLW Group Total
Sundance 1.26 0.80 .09 0.85 3
Drill Hole Wash, etc. 6.71 4.28 .49 4.53 16
7a/8a 49.18 31.34 3.60 33.18 117.3
6.8.5 Damage Abstraction for Fault Displacement
The expected number of waste package failures as a function of annual exceedance frequency
can be calculated by combining the results in Tables 26 and 27. These results are shown in
Table 29. A spreadsheet with the details of this calculation is provided as Attachment VII.
Table 29. Expected Waste Package Failures versus Annual Exceedance Frequency
Annual Exceedance
Probability (1/yr)
Expected Number of Waste Package Failures
PWR BWR Naval HLW Total
> 2  10-7 0 0 0 0 0
1  10-7 to 2  10-7 0 0 0 4.53 4.53
6  10-8 to 1  10-7 0 0 0.49 4.53 5.02
5  10-8 to 6  10-8 6.71 4.28 0.49 4.53 16.00
4  10-8 to 5  10-8 6.71 4.28 0.49 5.37 16.85
3  10-8 to 4  10-8 6.71 4.28 0.58 5.37 16.94
2  10-8 to 3  10-8 7.97 5.08 0.58 5.37 19.00
1  10-8 to 2  10-8 7.97 5.08 0.58 38.56 52.18
NOTE: Total values are based on the spreadsheet in Attachment VII.
Sums of the contributions by waste package type are not exact
because of roundoff.
When a waste package fails by fault displacement, the failed area on the waste package is
determined by sampling a uniform distribution with a lower bound of 0 m2 and an upper bound
equal to the area of the waste package lid, as explained below. The area of the lid for the PWR,
BWR, Naval, and HLW groups is 2.123 m2, 2.201 m2, 2.983 m2 and 3.497 m2, respectively,
based on the maximum waste package diameter in Table 25. The total failed area from a faulting
event is based on the weighted sum of the damage to each type of waste package.
The lower bound is appropriate for annual exceedance probabilities near 10-7 per year because a
waste package that is minimally pinned from fault displacement should only have minor
crimping with a very small damaged area. The upper bound is appropriate for a fault that shears
a waste package near its lid. In this case, the lid welds can fracture, separating the lid from the
package and potentially exposing the entire waste form to seepage and release. The use of a
uniform distribution is appropriate here because reasonable upper and lower bounds can be
defined and because the use of this type of distribution maintains the uncertainty in the damaged
area for this abstraction.
When a waste package fails from fault displacement, the associated drip shield and fuel rod
cladding also fail as barriers to flow and transport. A sheared drip shield will allow all seepage
to pass through it; that is, the failed area is taken as the total surface area of the drip shield so
there is no flux splitting (diversion of seepage) on the drip shield. Similarly, cladding becomes
100 percent perforated in response to a fault displacement that can shear a waste package. These
changes represent conservative, bounding approximations, particularly for annual exceedance
frequencies near 10-7 per year.
6.8.6 An Alternate Conceptual Model For Damage From Fault Displacement
The analysis of waste package failure due to fault displacement presented herein provides a basis
for estimating the number of potentially damage-inducing faults that intersect the emplacement
drifts. This analysis uses the known location of larger faults (e.g., Sundance fault, Ghost Dance
fault, etc.) relative to the planned location of the emplacement drifts, as well as an estimate of the
density of smaller-displacement faults based on the observed fault density along the exploratory
tunnel. The maximum allowable fault displacement before waste package damage is assumed to
occur was shown to vary between 606 mm and 1072 mm depending on waste package design
(Table 26). Using this site-specific information, it is shown that there are 30 locations where
known faults intersected the planned emplacement drifts (Table 22) plus an estimated 138
locations where unmapped faults could intersect the drifts (Section 6.8.2.2) for a total of 168
fault intersections. Of these, there are a maximum of 52.2 locations (probability weighted by
waste package type and location within the repository footprint) that are calculated to cause
waste package damage (Table 29) with an occurrence frequency between 210-7 per year and
10-8 per year.
As an alternate conceptual model, we consider work published in Methodologies for the
Evaluation of Faulting at Yucca Mountain, Nevada (Waiting et al. 2003). This paper presents
an assessment of the consequences of fault displacement at Yucca Mountain based on historical
earthquake activity in the Western United States. Four historic rupture events were considered to
arrive at a median value for fault rupture density (length of faulting per unit area of surface). A
conservative median value of 20 km/km2 was obtained from this analysis of the four events
considered. Using this value, along with a representative angle of 50 degrees between the typical
tunnel orientation and the orientation of the faults and an 80-meter drift spacing, the authors
determined that there would be 191 waste package locations where a fault would intersect an
emplacement drift at Yucca Mountain. This result compares favorably to the 168 fault
intersections calculated in this report.
The specific analog event considered by the authors for purposes of quantification was the Borah
Peak earthquake from 1983. Prior analysis of this event had shown that the maximum
displacement for the Borah Peak earthquake was 2.7 meters, with an average displacement of
approximately 1 meter. Given the fact that the mean annual exceedence probability for 1 meter
of displacement at Yucca Mountain ranges from ~10-6/yr for the Solitario Canyon fault to
~10-8/yr for the Sundance fault, the probability-weighted number of waste package failures is
calculated to be between 1.9110-4 to 1.9110-6. It should be noted that the upper end of this
range applies only to the Solitario Canyon fault. As shown in Section 6.8.2.1, no drifts intersect
the Solitario Canyon fault for the current repository footprint. The largest fault displacement
would be expected to correspond to the Drill Hole Wash fault. The mean annual exceedence
probability for one meter of displacement for this fault is on the order of 10-7/yr. Thus, the
probability-weighted number of waste package failures would be between 1.9110-5 to
1.9110-6.
The results presented herein in Table 29 are not quoted in terms of probability-weighted number
of waste package failures. Thus, a direct comparison with the results of the alternate model is
not possible. However, it is straightforward to recast the Table 29 results in a compatible form.
If for each probability range we consider the number of incremental waste packages that are
calculated to fail, then the product of the annual exceedence probability (using the upper end of
the range) and the number of incremental waste packages calculated to fail represents the
probability-weighted number of waste package failures for that exceedence interval. If we sum
this result for all exceedence probability ranges, one arrives at the equivalent total number of
probability-weighted waste package failures. This is shown in the following calculation:
Exceedence Probability # Incremental WP Failures Probability Weighted WP Failures
210-7 4.53 0.9110-6
110-7 0.49 0.0510-6
610-8 10.98 0.6610-6
510-8 0.85 0.0410-6
410-8 0.09 0.0010-6
310-8 2.06 0.0610-6
210-8 33.18 0.6610-6
Totals 52.18 2.3810-6
So the probability-weighted number of waste package failures for the model in this report is
2.3810-6. This value is within the range of results provided by the alternate conceptual model,
1.9110-5 to 1.9110-6. Thus, the alternate conceptual model based on the use of analog data
provides results that are consistent with the results of the model presented in this report for both
the probability-weighted number of waste package failures and the number of fault intersections
with the emplacement drifts. This provides added confidence in the validity of the results
presented herein.
6.8.7 Final Abstraction for Damage from Fault Displacement
The seismic scenario class for TSPA-LA will use the abstraction described in Section 6.8.5 as
the basis for damage to EBS components from fault displacement.
6.9 POST-SEISMIC CHANGES IN THE LOCAL ENVIRONMENT
A large seismic event, involving both vibratory ground motion and/or fault displacement, can
change the local environment around the emplacement drifts. The most obvious physical change
is that the emplacement drifts in the lithophysal zone are predicted to collapse as a result of the
10-6 per year ground motion level, and by inference at greater ground motion levels. Drift
collapse can alter the shape of the drift and fill it with a natural backfill, resulting in the
following potential process-level changes in and around the engineered barrier system:

Seepage may increase because of the irregular drift shape and because of a loosening of the
fractures around the drift.

Temperature of the drip shield and waste package may increase relative to an unfilled drift
because the backfill provides an insulating blanket on top of the drip shield. General
corrosion may increase because of increased temperature and because of rock and water
contact with the drip shield or waste package.

Glass dissolution rate and some radionuclide solubility limits will increase with increasing
temperature.
A change in the seepage flux into the emplacement drifts in the lithophysal zones is being
incorporated into the seismic abstractions for TSPA-LA. The seepage into the emplacement
drifts in the lithophysal zones will be determined in analogy with ambient seepage by using the
seepage table for degraded drifts as provided in DTN: LB0307SEEPDRCL.002. This table is
invoked after a seismic hazard occurs, provided the hazard is large enough to collapse the drifts.
The seepage fluxes provided in this table are considered conservative but not unrealistic. If a
more realistic model for seepage after drift collapse becomes available through Abstraction of
Drift Seepage (BSC 2003q) or through related work, then this new information should be
incorporated into TSPA-LA.
For TSPA-LA, all ground motions with mean annual exceedance frequency of 10-4 per year or
less will be considered large enough to collapse the drifts. This threshold for change is
consistent with the fact that tunnels in the lithophysal zone do not collapse for the 5  10-4 per
year ground motion, except for very minor damage at the lowest level of compressive strength
(BSC 2003h, Section 6.4.1.1).
There is no change in the seepage flux into the emplacement drifts in the nonlithophysal zones.
The seepage abstraction already includes an enhancement factor for limited collapse of the
emplacement drifts, and this enhancement factor is deemed adequate because the rockfall
calculations show only limited collapse of the emplacement drifts in the nonlithophysal zones
A second seepage-related change can occur for seismic hazards that occur during the rewetting
period. The flux splitting algorithm for the waste package and drip shield is unchanged from that
for the nominal scenario class, with one exception. If the seismic hazard occurs at a time when
the conditions for the existence of accelerated localized corrosion of Alloy 22 are satisfied, then
all seepage that enters the drip shield will flow into the waste package without any flux splitting.
This is a reasonable change because enhanced localized corrosion on the waste package will
generate corroded areas directly beneath the seeps through the drip shield. Once these corroded
areas penetrate the outer and inner shells of the waste package, the seeps will fall directly onto
the waste package internals, without diversion by the surface of the waste package.
The presence of rubble about the drip shield after drift collapse could cause changes in the
thermal environment in the EBS if a seismic event occurs relatively soon after repository closure,
while the waste package and drip shield are at elevated temperatures. However, the irregular and
coarse nature of the rubble is expected to allow sufficient convective heat transfer that the
temperature histories calculated for the nominal scenario class may reasonably be used to
approximate conditions following a seismic event during the thermal period. Because potential
changes in temperature due to the presence of rubble are not expected to be significant, the
possible associated changes in temperature-dependent solubility and corrosion rate have not been
included in TSPA-LA.
6.10 SEISMIC SCENARIO CLASS
The impact of seismic hazards on repository performance is being represented in a separate
scenario, called the seismic scenario, for TSPA-LA. The rationale for defining a separate
scenario is based on several key observations:
 Seismic events with annual frequencies down to 10-8 per year must be considered by
TSPA-LA.
10 CFR 63.114, Requirements for Performance Assessment, states that:
Any performance assessment used to demonstrate compliance with
63.113 must: . . . (d) Consider only events that have at least one
chance in 10,000 of occurring over 10,000 years.
Very large seismic hazards (i.e., ground motions and/or fault displacements) with annual
probability of occurrence down to 10-8 per year must be considered by TSPA-LA, even
though their probability is very low during the 10,000-year regulatory period.
 The nominal scenario class cannot determine the impact of low probability seismic
events in a computationally efficient manner. A separate scenario for seismic hazards
is desirable.
Events with very small annual probabilities of occurrence cannot be represented in the
nominal scenario class in a computationally efficient fashion. Accurate representation of
events with annual probability of occurrence down to 10-8 per year would require millions
of realizations in the nominal scenario class, which is not computationally feasible. The
alternative is to define a separate scenario for seismic hazards that determines dose in a
probability-weighted manner, as explained below.
 The mean dose time history is the main parameter for compliance determinations.
Radionuclide release limits for the repository are expressed in terms of the mean of the
distribution of projected doses to the reasonably maximally exposed individual, per 10 CFR
63.303 and 63.311. Calculation of releases from the seismic scenario class must generate
mean dose for consistency with the nominal scenario class.
 Damage from seismic events is expressed as a failed area on the surfaces of the drip
shield, the waste package, and the cladding.
The damage from seismic events is expressed as a failed area for advective flow on the
surfaces of the drip shield, the waste package, and the cladding. These failed areas are a
function of the amplitude of the seismic event. For example, the amplitude of a ground
motion is defined through the horizontal PGV. The individual damage abstractions for the
waste package, the drip shield, and the cladding are based on the results from structural
response calculations and rockfall calculations, as discussed in Sections 6.5 through 6.9.
The seismic scenario class is based on a single seismic hazard that occurs at a randomly chosen
time in each realization of the TSPA-LA. That is, the conditional probability of a seismic event
is 1 for each realization. The damage from this single event is based on the damage abstractions
for the drip shield, the waste package and the cladding. The damaged areas on the EBS
components define pathways for flow and transport through the EBS. The seepage flux for the
emplacement drifts in the lithophysal zones changes after a seismic hazard occurs, and there is
no flux splitting on the waste package if the seismic event occurs when conditions for
accelerated localized corrosion are satisfied. Once radionuclides are released from the EBS,
flow and transport in the unsaturated zone and the saturated zone are based on the same models
and algorithms as for the nominal scenario class. Biosphere calculations and parameters for the
seismic scenario class are also unchanged from the nominal scenario class.
Each realization of the seismic scenario class determines an annual dose time history for a single
seismic hazard with mean annual exceedance frequency .i. These dose time histories do not
represent the mean dose, as called for in 10 CFR 63.303, because a single hazard always occurs
in each realization. A mean dose time history is calculated using a probability-weighted sum and
average of all the realizations for the seismic scenario class. The weighting factor for each
realization corrects for the expected number of seismic events in each realization and for the
logarithmic sampling of the hazard curve for PGV.
6.10.1 Computational Approach
The mean dose for the seismic scenario class is calculated using a two-step approach: (1) in the
first step, TSPA-LA generates a set of R realizations that have robust sampling of all levels of
seismic hazards with the potential to generate releases from the EBS, and (2) in the second step,
the mean or expected dose time history is calculated using a weighted sum and average of the
dose time histories from the R realizations evaluated during the first step. Additional postprocessing
can present results as cumulative distribution functions, as complementary
cumulative distribution functions, or can evaluate the variability of the dose time histories, if
necessary.
The mathematical basis for calculating the mean dose as a weighted sum and average of the
individual dose time histories is presented in Attachment VIII. The following discussion
explains how these two steps are implemented in a Monte Carlo computational procedure.
6.10.1.1 Description of the First Step
The first step generates R realizations of future performance with the TSPA-LA model for the
seismic scenario class for all seismic hazards. This suite of R realizations represents the
epistemic and aleatory uncertainty in the TSPA-LA model for the seismic scenario class.
Epistemic uncertainty is captured by all those stochastic parameters that represent the lack of
knowledge uncertainty in various processes. Aleatory uncertainty is captured by the stochastic
parameters that represent the randomness of processes, such as the uncertainty in the timing and
amplitude of seismic hazards.
The TSPA-LA model for the seismic scenario class is very similar to the TSPA-LA model for
the nominal scenario class, with two major exceptions: (1) failed areas on the drip shield, waste
package or cladding are determined by sampling stochastic parameters in abstractions for
damage to EBS components, rather than by the waste package degradation (WAPDEG) model
for corrosion processes; and (2) a single seismic event occurs at a random time during each
realization. The output from each these R realizations is a time history of dose to the reasonably
maximally exposed individual.
For each realization, the annual exceedance frequency of the seismic hazard, .i, and the time of
occurrence of the seismic hazard, Ti, are determined by a Monte Carlo process that samples
appropriate distributions for these parameters. (Each realization has a single seismic hazard that
occurs at a randomly selected time during the calculation.) The type of distribution for .i
and Ti
are determined as follows.
The sampling for the annual exceedance frequency uses a logarithmic, rather than a linear, scale
to ensure robust sampling throughout all frequency ranges. More specifically, .i
is determined
by sampling a log-uniform distribution with lower bound .min and upper bound .max. The bounds
must be chosen to encompass all seismic exceedance frequencies with the potential to release
significant radionuclides from the EBS. Typical values of .max and .min for the seismic scenario
class are 10-4 per year and 10-8 per year, respectively, because this range spans the response of
the system, from no damage at 10-4 per year (see Assumption 5.1) to the regulatory limit at 10-8
per year.
The time of the seismic event, ti, is determined by sampling a log-uniform distribution between
Tmin and Tmax. Typical values of Tmax will be 10,000 years, the regulatory period, or 20,000 years.
As noted in Section 1.2, the 20,000-year duration for the seismic analyses is designed to
demonstrate that repository performance remains robust well after the 10,000-year regulatory
period. The value for Tmin will be determined through sensitivity studies with the TSPA-LA
model.
Once the value of the annual exceedance frequency (.i) is determined for the ith realization, the
corresponding values of the peak ground velocity (PGVi) is calculated. The relationship between
PGV and . is called a hazard curve, and is site- and location-specific. The mean hazard curve
for the Yucca Mountain site at Point A, a reference rock outcrop at the repository elevation, is
defined in Probabilistic Seismic Hazard Analyses for Fault Displacement and Vibratory Ground
Motion at Yucca Mountain, Nevada (CRWMS M&O 1998; DTN: MO03061E9PSHA1.000, file
h_vel_extended.frac_mean), based on the results of an expert elicitation.
The TSPA-LA requires a mean hazard curve at Point B, corresponding to the emplacement
drifts. The derivation of the PGV hazard curve at Point B is explained in Section 6.4, with the
calculations documented in Attachment I. Figure 3 in Section 6.4 illustrates the scaled hazard
curve for Point B. The PGV hazard curve at Point B provides the basis for determing the value
of PGVi for the ith realization. Once the value for PGVi is known, the distributions for the failed
areas on the waste package, drip shield, and cladding are sampled. For example, the damaged
area on the waste package is represented as a uniform distribution whose upper bound is a
function of the value of PGV for the ith realization. Once the value of PGVi is known, the upper
bound is calculated and the uniform distribution sampled to determine the damaged area on the
waste package for this realization. This approach explicitly includes the variability from the
structural response calculations in the TSPA-LA model by sampling this distribution.
Damage from fault displacement occurs simultaneously with damage from vibratory ground
motion. The value of .i
determines the number of damaged waste packages by type, based on
the abstraction in Table 28. The damaged area from fault displacement is determined by
sampling a distribution with a lower bound of 0 and an upper bound based on the lid area for
each type of waste package.
Simultaneous damage from fault displacement and vibratory ground motion is a reasonable
approach for the seismic scenario class. Damage from fault displacement only occurs for the
largest seismic hazards, with an annual exceedance frequency of 2  10-7 per year or less (see
Table 28). Such a large seismic hazard is always accompanied by vibratory ground motion, so
fault displacement and ground motion are not considered independent processes for TSPA-LA.
It is reasonable to expect that 50 to 100 realizations in each decade (i.e., from 10-5 to 10-6) of the
hazard curve are sufficient to provide robust sampling for this scenario. If the hazard spans three
decades (such as 10-5 to 10-8 per year), then the simulation requires 150 to 300 realizations. In
practice, the variability of the mean dose is used to determine an adequate number of
realizations. In this approach, a comparison of TSPA-LA calculations with 300 and
500 realizations is used as a test to determine when the mean dose has converged within
acceptable limits.
6.10.1.2 Description of the Second Step
Each of the R realizations generates a time history of dose to the reasonably maximally exposed
individual, conditional upon the occurrence of a single seismic event. However, compliance is
based upon the mean of the distribution of projected doses of DOE's performance assessments
which project the performance of the Yucca Mountain disposal system for 10,000 years after
disposal, as noted in 10 CFR 63.303.
The mean annual dose is calculated using a weighted sum and average of the R realizations
performed during the first step. The weighting factors for each realization are derived in
Attachment VIII. The weighting factors for each realization correct for the number of expected
seismic events in each realization and for the log-uniform distributions for the annual frequency
of occurrence and for the sampling on time. The mean dose, as derived in Section 2 of
Attachment VIII, is given by Equation VIII.2.12 as:
R
max
D(t ) = 1 ln.... ...
ln
...
Tmax ...
. t . Di { t | PGV , t } , (Eq. 10)
iiR ..min .. Tmin . i= 1
ii
where
{
t D|PGV , t i } is the dose at time t for the ith realization, which has a seismic event of
ii
magnitude PGVi occurring at time ti
D(t ) is the mean dose for the scenario at time t
R is the number of realizations in the scenario
.max is the maximum value for the occurrence frequency
.min is the minimum value for the occurrence frequency
Tmax is the maximum time (duration) of the scenario
Tmin is the minimum time in the log-uniform sampling for the event time
6.10.2 Computational Algorithm
The first step in the computational algorithm for the seismic scenario class, as described in
Section 6.10.1.1, generates R realizations of future performance with the TSPA-LA model. The
computational algorithm has been split into 12 simple operations to document the procedure for
this scenario class. The first nine operations define the constant parameters, the stochastic
parameters, and the formulas that represent the epistemic and aleatory uncertainty for the TSPALA
model. Each realization of the TSPA-LA model is based on a single sampling of the
stochastic parameters from the first nine operations. Repeated samplings of the stochastic
parameters generate a full suite of R realizations of the TSPA-LA model. The second step in the
computational algorithm (see Section 6.10.1.2) evaluates the mean dose from these
R realizations, using the formula and parameters defined in the tenth operation.
The modifications for post-seismic event response are summarized in Operations 11 and 12.
While these operations are part of the TSPA-LA model calculations in the first step, the
parameter values are defined by reference rather than by analysis in this model report. These
modifications are listed last in the procedure to emphasize this difference.
A list of the 12 operations in the computational procedure is indicated below. The parameters
for the computational procedure are listed in Table 30.
1.
Determine the mean annual exceedance frequency, .i, for the ith realization.
The value of . is sampled from a log-uniform distribution between .min and .max. A log-
uniform distribution ensures robust sampling in each decade of the distribution. The values
of .min, .max, and .i
are represented by the parameters LAMBDA_MIN, LAMBDA_MAX,
and LAMBDA, respectively, in Table 30.
2.
Determine the corresponding value of PGVi through the hazard curve, . = . (PGV).
The value of PGVi is determined by a table lookup, using the scaled PGV hazard curve for
Point B. The scaled hazard curve is calculated in Attachment I and tabulated in Table I-1.
The interpolation between points in this table is based on a linear interpolation using the
value of log(.) at individual points. This is referred to as a log-linear interpolation scheme
in Table 30. The value of PGVi is the parameter PGV in Table 30.
3.
Determine the fraction of failed waste package surface area due to vibratory ground motion
for each realization.
The percent of failed waste package area is a random variable with distribution parameters
that are functions of PGVi. This damage abstraction is defined by a uniform distribution
with a lower bound of 0 percent failed area and an upper bound that is a linear function of
PGVi. The fraction of failed surface area is applied to all packages in the repository (i.e.,
there is no spatial variability).
- The upper bound of the uniform distribution is defined by:
MAX(0.0, 0.436  PGVi - 0.305) (Eq. 11)
in units of % damage. The value of this function is represented in Table 30 by the
parameter WP_DAMAGE_MAX.
-The lower bound of the uniform distribution is 0 percent. This value is represented by
the parameter WP_DAMAGE_MIN in Table 30.
-The sampled value of the uniform distribution (for each realization) is denoted as
WP_DAMAGE%.
- The fraction of failed surface area is denoted as WP_DAMAGE and calculated as:
WP_DAMAGE = WP_DAMAGE%/100 (Eq. 12)
This failed area allows advective flow and advective and diffusive transport from the
waste package, per Assumption 5.3.
4. Determine the fraction of failed drip shield surface area due to vibratory ground motion for
each realization. This damage abstraction is defined by a uniform distribution with a lower
bound of 0 percent failed area and an upper bound that is a linear function of PGVi. The
fraction of failed surface area is applied to all drip shields in the repository (i.e., there is no
spatial variability).
-The upper bound of the uniform distribution, DS_DAMAGE_MAX, is a function of
PGV and defined in Table 15 with a linear interpolation between the points.
-The lower bound of the uniform distribution, DS_DAMAGE_MIN, is a function of
PGV and defined in Table 16 with a linear interpolation/extrapolation between the
points.
- The sampled value of the uniform distribution is denoted as DS_DAMAGE%_GM.
- The fraction of failed surface area is denoted as DS_DAMAGE_GM and calculated as:
DS_DAMAGE_GM = (DS_DAMAGE%_GM)/100 (Eq. 13)
5. Determine the fraction of failed drip shield surface area due to rockfall in the
nonlithophysal zones for each realization. The probability of no drip shield damage from
rockfall follows a simple power law. The non-zero damage to the drip shield from rockfall
is represented as a log-triangular distribution, with minimum 0.001 percent and maximum
100 percent; the value of the mode follows a simple power law in PGV. The fraction of
failed surface area is applied to all drip shields in the nonlithophysal zones of the repository
(i.e., there is no spatial variability within the nonlithophysal zones).
- The log-triangular distribution is denoted by DS_DAMAGE_LOGTRI in Table 30.
-The upper bound of the log-triangular distribution, is 100 percent. The lower bound of
the log-triangular distribution is 0.001 percent. The mode of the log-triangular
distribution is denoted by DS_MODE and is given by:
DS_MODE = 0.00204  (PGV)3.7767 (Eq. 14)
-The probability of zero damage is represented by DS_NODAMAGE and is given by:
DS_NODAMAGE = MIN(1.0, 0.601  (PGV)-0.735) (Eq. 15)
-The sampling algorithm draws a random number between 0 and 1, denoted by
RANDOM in Table 30. If the random number is less than DS_NODAMAGE then
there is no damage from rockfall for this realization (DS_DAMAGE%_RF = 0). If the
random number is greater than or equal to DS_NODAMAGE, then the log-triangular
distribution is sampled to determine the damage to the drip shield from rockfall for this
realization. That is, DS_DAMAGE%_RF = DS_DAMAGE_LOGTRI, as shown in
Table 30.
- The fraction of failed surface area is denoted as DS_DAMAGE_RF and calculated as:
DS_DAMAGE_RF = (DS_DAMAGE%_RF)/100 (Eq. 16)
6. Determine the total fraction of drip shield damage due to vibratory ground motion and
rockfall in each waste package group.
-In the nonlithophysal zone, the fraction of total damage is given by the sum of
DS_DAMAGE_GM and DS_DAMAGE_RF, with an upper limit of 1.0:
DS_DAMAGE_TOTAL_NONLITH = MIN(1.0, DS_DAMAGE_GM
+ DS_DAMAGE_RF).
(Eq. 17)
The fraction of total damage in the nonlithophysal zone is applied to all drip shields in
this zone (i.e., there is no spatial variability within the nonlithophysal zone).
-In the lithophysal zone, the fraction of total damage is given by DS_DAMAGE_GM:
DS_DAMAGE_TOTAL_LITH = DS_DAMAGE_GM (Eq. 18)
The lithophysal zone does not include the contribution from rockfall because the
lithophysal is expected to shatter into small fragments that cannot produce significant
damage to the drip shield. The fraction of total damage in the lithophysal zone is
applied to all drip shields in the lithophysal zone (i.e., there is no spatial variability
within the lithophysal zone).
-Waste package groups for TSPA-LA may include packages in both the lithophysal and
nonlithophysal zones. If this is the case, an appropriately weighted average should be
used to determine the damage to all packages in each group. The calculation of this
weighted average is not shown in Table 30.
- The total failed area on the drip shield allows advective flow, per Assumption 5.3.
7. Cladding does not fail if the mean annual exceedance frequency of the seismic hazard is
510-5 per year or greater (see Assumption 5.1). Cladding experiences complete failure
(i.e., 100 percent of the cladding is perforated) at the time of the seismic event if the annual
exceedance frequency is less than or equal to 10-5 per year. The abstraction for cladding
failure is defined in Table 18 with a linear interpolation for the percent damage to the
cladding between the appropriate values of PGV. In other words, cladding damage is
(1) always zero for PGV values less than 0.55 m/s (corresponding to annual exceedance
frequencies greater than 510-5 per year), (2) always 100 percent for PGV values greater
than 1.067 m/s (corresponding to annual exceedance frequencies less than 10-5 per year),
and (3) based on a linear interpolation on PGV for values between 0.55 m/s, with 0 percent
damage, and 1.067 m/s, with 100 percent damage.
This parameter is denoted by CLAD_DAMAGE in Table 30. There is no uncertainty is
this damage abstraction because it is a bounding estimate for cladding failure. The percent
of failed cladding is applied to all fuel assemblies in the repository (i.e., there is no spatial
variability).
8. Determine the percent failed area on the waste package due to fault displacement. The
expected number of waste packages that fail, as a function of annual exceedance
probability, is defined in Table 29.
-The expected number of waste packages that fail from fault displacement is a very
small fraction of the total packages in the repository because very few waste packages
are located on secondary faults. In addition, these failures only occur for a small
fraction of the realizations in the seismic scenario class because there are no failures
from fault displacement for an annual frequency of occurrence greater than 210-7 per
year. In this situation, a special waste package group, such as the juvenile failure
group, should be used to represent the failures from fault displacement.
-When a waste package fails by fault displacement, the failed area on each waste
package is determined by sampling a uniform distribution with a lower bound of 0 m2
and an upper bound equal to the area of the waste package lid. These sampled
distributions are denoted by FAILED_AREA_PWR, FAILED_AREA_BWR,
FAILED_AREA_NAVAL, and FAILED_AREA_HLW in Table 30.
-The area of the lid for the PWR, BWR, Naval, and HLW groups is 2.123 m2, 2.201 m2,
2.983 m2, and 3.497 m2, respectively, based on the maximum waste package diameter
in Table 25. These areas are denoted as LID_AREA_PWR, LID_AREA_BWR,
LID_AREA_NAVAL, and LID_AREA_HLW in Table 30.
- The surface area of a package in the PWR, BWR, Naval, and HLW groups is 31.01 m2,
31.55 m2, 41.24 m2, and 37.95 m2, respectively. The values of the surface areas are
based on the average waste package lengths and maximum waste package diameters for
each of the four groups, as listed in Table 25. These areas are denoted as
SURF_AREA_PWR, SURF_AREA_BWR, SURF_AREA_NAVAL, and
SURF_AREA_HLW in Table 30.
-The fraction of failed area for the PWR waste package type is calculated as:
FRACTION_FAILED_PWR = LID_AREA_PWR/SURF_AREA_PWR (Eq. 19)
with similar equations for the BWR, Naval, and HLW waste package types. This failed
area allows advective flow and advective and diffusive transport, per Assumption 5.3.
-The expected number of package failures for the three waste package types are denoted
by NO_PWR_FAILURES, NO_BWR_FAILURES, NO_NAVAL_FAILURES, and
NO_HLW_FAILURES in Table 30.
-The damage to drip shields from a fault displacement with annual exceedance
probability less than 2 10-7 per year is taken to be 100 percent. The number of
impacted drip shields is identical to the total number of waste packages that will be
damaged by the fault displacement.
-Cladding that is impacted by a fault displacement with annual exceedance probability
less than 2 10-7 will be 100 percent perforated. The impacted cladding is associated
with the fuel assemblies in the number of waste packages that are damaged by the fault
displacement.
9.
Determine the time of the seismic event for each realization.
The time of the event, EVENT_TIME, is determined by sampling a log-uniform
distribution with a lower bound denoted by TIME_MIN and an upper bound denoted by
TIME_MAX in Table 30. A typical value of TIME_MAX is 10,000 or 20,000 years.
Appropriate values for TIME_MIN will be determined through sensitivity studies with the
TSPA-LA model.
10.
Calculate the mean dose for all realizations, i = 1, 2, , R.
The weighting factor for each realization corrects for the expected number of seismic
events in each realization and for the log-uniform sampling for the exceedance frequency,
.i. The appropriate formula for calculating the mean or expected dose with uniform
sampling for the event time and log-uniform sampling for the annual exceedance
frequency, .i, is:
R
max
D(t ) = 1 ln.... ...
ln
...
Tmax ...
. ti. D { t | PGV , t } ,
iR ..min .. Tmin . i= 1
ii i
R
1
=. WEIGHTED DOSE _ iR 1
= Mean(WEIGHTED DOSE _ )
i
where D(t ) is the expected (mean) dose, Di{t|ti,PGVi} is the dose from the ith realization
with a seismic hazard of amplitude PGVi occurring at time ti, and R is the total number of
realizations. The term ti.i
is denoted by EVENT_WEIGHT in Table 30. The term
ln...
Tmax ...
ln
.....
max ..
is represented as the parameter SAMPLE_WEIGHT in Table 30. The
. Tmin . ..min .
term WEIGHTED_DOSE is the product of EVENT_WEIGHT, SAMPLE_WEIGHT, and
the DOSE at any given time.
11. Modify the seepage in the lithophysal zones after the seismic event.
The seepage into the emplacement drifts in the lithophysal zones is determined by the
seepage table for degraded drifts provided in DTN: LB0307SEEPDRCL.002. This table is
invoked after a seismic hazard occurs, provided the hazard is large enough to collapse the
drifts. If a more realistic model for seepage after drift collapse becomes available through
Abstraction of Drift Seepage (BSC 2003q) or through related work, then this new
information should be incorporated into TSPA-LA.
For TSPA-LA, all ground motions with mean annual exceedance frequency of 10-4 per year
or less (equivalent to a PGV greater than 0.388 m/s) are large enough to collapse the drifts
in the lithophysal zones. There is no change in the seepage flux into nonlithophysal zones
because complete collapse of the drifts is not predicted for this type of host rock.
12. Modify the flux into the waste package after the seismic event if accelerated localized
corrosion can occur.
The flux splitting algorithm for the waste package and drip shield is identical to that for the
nominal scenario, with one exception. If the seismic hazard occurs at a time when the
conditions for the existence of accelerated localized corrosion of Alloy 22 are satisfied,
then all seepage that passes through the drip shield flows into the waste package without
any flux splitting.
Table 30. Definition of Parameters for the Seismic Scenario Class
Parameter Name Description, Units, and Type Definition
EVENT_TIME Distribution for the time when the
seismic event occurs in this
realization
Units: {yr}
Type: Distribution sampled once per
realization
Log-Uniform Distribution:
Minimum Value: TIME_MIN
Maximum Value: TIME_MAX
TIME_MAX Duration of the seismic scenario class
Units: {yr}
Type: Data
Typical values are 10,000 years or 20,000
years.
TIME_MIN Minimum value of the log-uniform
distribution for event time
Units: {yr}
Type: Data
The appropriate value for TIME_MIN will be
determined by sensitivity studies with the
TSPA-LA model.
LAMBDA Distribution of annual exceedance
frequency for the seismic scenario
class
Units: {1/yr}
Type: Distribution sampled once per
realization
Log-Uniform Distribution:
Minimum Value: LAMBDA_MIN
Maximum Value: LAMBDA_MAX
LAMBDA_MIN Minimum annual exceedance
frequency
Units: {1/yr}
Type: Data
110-8 per year
LAMBDA_MAX Maximum annual exceedance
frequency
Units: {1/yr}
Type: Data
110-4 per year
PGV Hazard curve for horizontal PGV as a
function of LAMBDA
Units: {m/s}
Type: 1D table, function of LAMBDA
1D table lookup as a function of the value of
LAMBDA for this realization. Use log-linear
interpolation between . values:
. (1/yr) PGV (m/s)
6.26  10-4 0.159
2.78  10-4 0.239
9.30  10-5 0.398
1.84  10-5 0.796
3.07  10-6 1.59
2.28  10-7 3.98
8.15  10-8 5.57
2.60  10-8 7.96
6.56  10-9 11.9
WP_DAMAGE Fraction of failed surface area on the
waste package
Units: {-}
Type: Function
WP_DAMAGE%/100
WP_DAMAGE% Distribution of percent failed area on
the waste package
Units: {%}
Type: Distribution sampled once per
realization
Uniform Distribution:
Minimum Value: WP_DAMAGE_MIN
Maximum Value: WP_DAMAGE_MAX
Table 30. Definition of Parameters for the Seismic Scenario Class (Continued)
Parameter Name Description, Units, and Type Definition
WP_DAMAGE_MAX Maximum value of percent failed area
on the waste package for this
realization
Units: {%}
Type: Function of PGV
MAX(0.0, 0.436*(PGV)  0.305)
WP_DAMAGE_MIN Minimum value of percent failed area
on the waste package for this
realization.
Units: {%}
Type: Constant
0%
DS_DAMAGE_GM Fraction of failed surface area on the
drip shield from ground motion
Units: {-}
Type: Function
DS_DAMAGE%_GM/100
DS_DAMAGE%_GM Distribution of percent failed area on
the drip shield from vibratory ground
motion
Units: {%}
Type: Distribution sampled once per
realization
Uniform Distribution:
Minimum Value: DS_DAMAGE_MIN
Maximum Value: DS_DAMAGE_MAX
DS_DAMAGE_MAX Maximum value of percent failed area
on the drip shield from ground motion
for this realization
Units: {%}
Type: Table Look-up as function of
PGV with linear interpolation between
points
1D table lookup as a function of the value of
PGV for this realization.
PGV (m/s) Damage (%)
0 0
0.55 0
2.44 2.68
5.35 50
20 50
DS_DAMAGE_MIN Minimum value of percent failed area
on the drip shield from ground motion
for this realization.
Units: {%}
Type: Table Look-up as a function of
PGV, with linear interpolation
between points & linear extrapolation
for PGV > 5.35 m/s.
1D table lookup as a function of the value of
PGV for this realization.
PGV (m/s) Damage (%)
0 0
2.44 0
5.35 10%
DS_NODAMAGE Probability of no damage to the drip
shield from rockfall in the
nonlithophysal zones of the
repository.
Units: {-}
Type: Function of PGV
MIN(1.0, 0.601(PGV)-0.735)
RANDOM Random number between 0 and 1 for
determining if rockfall damages the
drip shield.
Units: {-}
Type: Distribution sampled once per
realization
Uniform distribution:
Minimum Value: 0
Maximum Value: 1
Table 30. Definition of Parameters for the Seismic Scenario Class (Continued)
Parameter Name Description, Units, and Type Definition
DS_DAMAGE_LOGTRI Log-triangular distribution defining the
percent failed area on the drip shield
due to rockfall in the nonlithophysal
zone. This distribution is used for the
non-zero damage cases.
Units: {%}
Type: Distribution sampled once per
realization
Log-triangular distribution in PGV
Minimum Value: 0.001%
Maximum Value: 100%
Mode: DS_MODE (function of PGV)
DS_MODE Mode of the percent failed area of the
drip shield due to rockfall in the
nonlithophysal zones.
Units: {%}
Type: Function of PGV
(0.00204)(PGV)3.7767
DS_DAMAGE%_RF Percent failed area on the drip shield
from rockfall in the nonlithophysal
zones
Units: {%}
Type: If-Then-Else Logical Operator
If(RANDOM<DS_NODAMAGE)
Then DS_DAMAGE%_RF = 0,
Else DS_DAMAGE%_RF =
DS_DAMAGE_LOGTRI
DS_DAMAGE_RF Fraction of failed surface area on the
drip shield from rockfall in the
nonlithophysal zones
DS_DAMAGE%_RF/100
Units: {-}
Type: Function
DS_DAMAGE_TOTAL_
NONLITH
Total fraction of failed surface area on
the drip shield in the nonlithophysal
MIN(1.0, DS_DAMAGE_RF +
DS_DAMAGE_GM)
zones
Units: {-}
Type: Function
DS_DAMAGE_TOTAL_
LITH
Total fraction of failed surface area on
the drip shield in the lithophysal
zones
DS_DAMAGE_GM
Units: {-}
Type: Function
CLAD_DAMAGE Percent perforated cladding from
vibratory ground motion
Units: {%}
Type: Table look-up as function of
PGV
1D table lookup as a function of the value of
PGV for this realization.
PGV {m/s} Damage {%}
0 0
0.55 0
1.067 100
20 100
LID_AREA_PWR Lid area of the PWR waste package
group for fault displacement
Units: {m2}
Type: Data
2.123 m2
LID_AREA_BWR Lid area of the BWR waste package
group for fault displacement
Units: {m2}
Type: Data
2.201 m2
Table 30. Definition of Parameters for the Seismic Scenario Class (Continued)
Parameter Name Description, Units, and Type Definition
LID_AREA_NAVAL Lid area of the Naval waste package
group for fault displacement
Units: {m2}
Type: Data
2.983 m2
LID_AREA_HLW Lid area of the HLW waste package
group for fault displacement
Units: {m2}
Type: Data
3.497 m2
FAILED_AREA_PWR Distribution of failed area on the PWR
waste package group for fault
displacement
Units: {m2}
Type: Distribution sampled once per
realization
Uniform Distribution:
Minimum Value: 0.0
Maximum Value: LID_AREA_PWR
FAILED_AREA_BWR Distribution of failed area on the BWR
waste package group for fault
displacement
Units: {m2}
Type: Distribution sampled once per
realization
Uniform Distribution:
Minimum Value: 0.0
Maximum Value: LID_AREA_BWR
FAILED_AREA_NAVAL Distribution of failed area on the
Naval waste package group for fault
displacement
Units: {m2}
Type: Distribution sampled once per
realization
Uniform Distribution:
Minimum Value: 0.0
Maximum Value: LID_AREA_NAVAL
FAILED_AREA_HLW Distribution of failed area on the HLW
waste package group for fault
displacement
Units: {m2}
Type: Distribution sampled once per
realization
Uniform Distribution:
Minimum Value: 0.0
Maximum Value: LID_AREA_HLW
SURF_AREA_PWR Surface area for a waste package in
the PWR group for fault displacement
Units: {m2}
Type: Data
31.01 m2
SURF_AREA_BWR Surface area for a waste package in
the BWR group for fault displacement
Units: {m2}
Type: Data
31.55 m2
SURF_AREA_NAVAL Surface area for a waste package in
the Naval group for fault
displacement
Units: {m2}
Type: Data
41.24 m2
SURF_AREA_HLW Surface area for a waste package in
the HLW group for fault displacement
Units: {m2}
Type: Data
37.95 m2
Table 30. Definition of Parameters for the Seismic Scenario Class (Continued)
Parameter Name Description, Units, and Type Definition
FRACTION_FAILED_A
REA_PWR
Fraction of failed surface area on
PWR waste package group from fault
displacement
FAILED_AREA_PWR/SURF_AREA_PWR
Units: {-}
Type: Function
FRACTION_FAILED_A
REA_BWR
Fraction of failed surface area on
BWR waste package group from fault
displacement
FAILED_AREA_BWR/SURF_AREA_BWR
Units: {-}
Type: Function
FRACTION_FAILED_A
REA_NAVAL
Fraction of failed surface area on
Naval waste package group from fault
displacement
FAILED_AREA_NAVAL/SURF_AREA_NAVAL
Units: {-}
Type: Function
FRACTION_FAILED_A
REA_HLW
Fraction of failed surface area on
HLW waste package group from fault
displacement
FAILED_AREA_HLW/SURF_AREA_HLW
Units: {-}
Type: Function
NO_PWR_FAILURES Number of failed PWR waste
packages from fault displacement
Units: {-}
Type: Step function of annual
exceedance frequency, .
1D table lookup as a function of the value of .
for this realization.
. (1/yr) # Failures (-)
> 210-7 0
110-7 to 210-7 0
610-8 to 110-7 0
510-8 to 610-8 6.71
410-8 to 510-8 6.71
310-8 to 410-8 6.71
210-8 to 310-8 7.97
110-8 to 210-8 7.97
NO_BWR_FAILURES Number of failed BWR waste
packages from fault displacement
Units: {-}
Type: Step function of annual
exceedance frequency, .
1D table lookup as a function of the value of .
for this realization.
. (1/yr) # Failures (-)
> 210-7 0
110-7 to 210-7 0
610-8 to 110-7 0
510-8 to 610-8 4.28
410-8 to 510-8 4.28
310-8 to 410-8 4.28
210-8 to 310-8 5.08
110-8 to 210-8 5.08
Table 30. Definition of Parameters for the Seismic Scenario Class (Continued)
Parameter Name Description, Units, and Type Definition
NO_NAVAL_FAILURES Number of failed Naval waste
packages from fault displacement
Units: {-}
Type: Step function of annual
exceedance frequency, .
1D table lookup as a function of the value of .
for this realization.
. (1/yr) # Failures (-)
> 210-7 0
110-7 to 210-7 0
610-8 to 110-7 0.49
510-8 to 610-8 0.49
410-8 to 510-8 0.49
310-8 to 410-8 0.58
210-8 to 310-8 0.58
110-8 to 210-8 0.58
NO_HLW_FAILURES Number of failed HLW packages from
fault displacement
Units: {-}
Type: Step function of annual
exceedance frequency, .
1D table lookup as a function of the value of .
for this realization.
. (1/yr) # Failures (-)
> 210-7 0
110-7 to 210-7 4.53
610-8 to 110-7 4.53
510-8 to 610-8 4.53
410-8 to 510-8 5.37
310-8 to 410-8 5.37
210-8 to 310-8 5.37
110-8 to 210-8 38.56
EVENT_WEIGHT Expected number of events in this
realization
Units: {-}
Type: Function
LAMBDA  EVENT_TIME
SAMPLE_WEIGHT Correction for sampling of log-uniform
distributions for time of the event and
for annual exceedance frequency
Units: {-}
Type: Function
LN(TIME_MAX/TIME_MIN) 
LN(LAMBDA_MAX/LAMBDA_MIN)
WEIGHTED_DOSE The probability-weighted dose for this
realization
Units: {mrem/yr}
Type: Function
EVENT_WEIGHT  SAMPLE_WEIGHT 
DOSE,
where DOSE is the time dependent
(unweighted) dose for this realization.
6.10.3 Limitations
There are five important limitations for the seismic scenario class for TSPA-LA: the duration of
the calculations, the possibility of rockfall in the drifts before the seismic event, and coupling of
seepage and thermal conditions with rockfall, the range of validity of the model abstraction for
waste package damage, and the potential for rockfall to damage the waste package.
The seismic scenario class for TSPA-LA is designed for a duration of 20,000 years, twice the
length of the established regulatory period of interest. This design limitation arises from two
factors. The first factor relates to the parameters for the structural response calculations, namely
structural thicknesses and mechanical properties for the drip shield and waste package. The
thicknesses of the drip shield and waste package have been reduced to (conservatively) represent
the potential degradation of these structures by general corrosion over the first 10,000 years to
20,000 years after repository closure. The mechanical properties of Alloy 22 and of Titanium
Grade 7 have been evaluated at an elevated temperature that provides conservative values for
over 97 percent of the 10,000-year regulatory period for the high temperature operating model
and for 100 percent of the time for the low temperature operating mode. This approach is highly
conservative from a risk assessment viewpoint because it is conservative for almost all the
realizations in the TSPA-LA. The definition of structural thickness and material properties
should be reevaluated and new abstractions developed if the duration of the seismic scenario
class is extended beyond 20,000 years.
The second factor for the design limitation related to the duration of the seismic scenario class is
that coupled effects from multiple seismic events are not considered because seismic hazards
with the potential to have a significant impact on engineered barriers are anticipated to occur
very rarely during the 20,000-year period. This is a reasonable approach for events which occur
with an annual frequency of 10-5 per year or less over a 10,000 year or 20,000 year period. This
is also a reasonable approach for annual exceedance frequencies between 10-4 and 10-5 per year if
the corresponding ground motions and fault displacements produce negligible damage to EBS
components (as is true for these abstractions).
The second limitation is related to the condition of the drifts at the time of the seismic event.
Structural response calculations for the drip shield and waste package do not include any initial
backfill around the drip shield at the time of the seismic event. This representation is consistent
with the present design that does not include engineered backfill but may become invalid if long-
term fatigue of the tuff rock causes drift degradation and substantial collapse before the seismic
hazard occurs.
If natural backfill is present, the kinematics of the waste package and drip shield will be altered,
leading to changes in the impacts between and associated failed areas on both EBS components.
For the waste package, there may be less damage from end-to-end impacts if the fixed drip shield
restricts the motion of the waste package. However, damage may increase from side-on impacts
in comparison to the no backfill case. The change in damage area for the drip shieldmay be
substantial because the damage from impact of large blocks of rock ejected from the
nonlithophysal zone will be mitigated.
The third limitation relates to the potential for a tunnel collapse caused by a seismic event to alter
the temperature of the EBS components because of the presence of natural backfill. The
presence of rubble about the drip shield after drift collapse could cause changes in the thermal
environment in the EBS if a seismic event occurs relatively soon after repository closure, while
the waste package and drip shield are at elevated temperatures. However, the irregular and
coarse nature of the rubble is expected to allow sufficient convective heat transfer that the
temperature histories calculated for the nominal scenario class may reasonably be used to
approximate conditions following a seismic event during the thermal period. Because potential
changes in temperature due to the presence of rubble are not expected to be significant, the
possible associated changes in temperature-dependent solubility and corrosion rate have not been
included in TSPA-LA.
The fourth limitation relates to the range of validity for the waste package damage abstraction.
The abstraction for damage to the waste package from ground motions is based on data that
cover a range of PGV of 1 m/s to 6 m/s and have a maximum damage of less than 2 percent of
the surface area of the waste package; there is no spatial variability in this damage abstraction.
This is a reasonable approach if sensitivity studies for the TSPA-LA calculations indicate that the
maximum risk occurs within this range of PGV values.
A fifth limitation relates to waste package damage from rockfall. Damage to the waste package
from rockfall is not included in the abstraction for the waste package. This is a reasonable
approach for intact EBS components because an intact drip shield can deflect large rock blocks
away from the waste package. However, if separation of drip shields occurs for very high
amplitude ground motions and if natural backfill is not present, the shields will no longer protect
the waste packages from rockfall during a second seismic event. Multiple hazards occur with a
very low probability, as noted previously, so this is a reasonable approach for TSPA-LA.
6.11 DISCUSSION OF YUCCA MOUNTAIN REVIEW PLAN ACCEPTANCE
CRITERIA
The acceptance criteria that are relevant to requirement PRD-002/T-015 (Canori and Leitner
2003, Section 3.4) for the seismic abstractions are found in Section 2.2.1.3.2.3 of Yucca
Mountain Review Plan, Final Report (NRC 2003). The manner in which the seismic
consequence abstractions meet the five acceptance criteria are summarized in the following
bulletized list. More detailed discussions of issues related to uncertainty in input parameters, to
the propagation of uncertainty into TSPA, and to model uncertainty (alternate conceptual
models) are provided in the following sections.
The features of the seismic consequence abstractions that meet these five general acceptance
criteria are identified in the following list, along with the subcriteria that are relevant to each
feature.
 Acceptance Criterion 1: System Description and Model Integration Are Adequate
-The abstractions for damaged areas on the waste package, drip shield, and cladding are
based on a statistically robust sampling of uncertain parameters, including the ground
motion time histories, rock fracture patterns, and friction coefficients. The abstractions
are based on calculations that use consistent assumptions and consistent material
properties. (Subcriteria (1), (3), and (4))
-All results are based on the mean hazard curves for ground motion and fault
displacement. (Subcriteria (1), (3) and (4))
-Degradation of the drip shield and waste package is addressed for the first 10,000 to
20,000 years after repository closure. (Subcriteria (1), (3), and (4))
-Material properties for structural response calculations are based on a temperature of
150C, resulting in conservative values for 97 percent of the first 10,000 years after
closure for the high temperature operating mode. This choice is even more
conservative over the first 20,000 years after repository closure. (Subcriteria (1), (3),
and (4))
-Drip shield damage from rockfall induced by vibratory ground motion in the
lithophysal and nonlithophysal zones is included in the abstractions. Rockfall is
analyzed with state-of-the-art computer codes that are used for other drift degradation
calculations. (Subcriterion (1) and (3))
-The seismic-related FEPs in Table 4 are directly considered in these abstractions.
Damage to EBS components from ground motion, rockfall, drift collapse, and shear due
to fault displacement have been considered in the abstractions for the seismic scenario
class or in the structural response calculations that support the abstractions. (Subcriteria
(1) and (5))
-The description of rockfall and structural response are based on state-of-the-art
computer codes using nonlinear constitutive relations that describe material yield and
failure. These computer codes are also used for the design of other repository
structures and components. (Subcriterion (3))
-The residual stress threshold for failure of Alloy 22 is also used as the threshold for
initiation of stress corrosion cracking in the representation of corrosion processes on the
waste package. (Subcriterion (3))
 Acceptance Criterion 2: Data Are Sufficient For Model Justification
-The residual stress failure criteria are based on experimental data for Alloy 22 and for
Titanium Grade 7 (BSC 2003l, Section 6.2.1). (Subcriteria (1) and (3))
-The constitutive models for Alloy 22 and for Titanium Grade 7 are based on material
properties in the published literature. (Subcriteria (1), (3), and (4))
-Hazard curves are based on the results of an expert elicitation (CRWMS M&O 1998;
DTN: MO0004MWDRIFM3.002). (Subcriteria (1))
 Acceptance Criterion 3: Data Uncertainty Is Characterized And Propagated Through The
Model Abstraction
-Rockfall models and structural response calculations use parameter values and
parameter ranges that are defensible and account for variabilities in rock properties and
fracture patterns and uncertainties in ground motion time histories and friction
coefficients. (Subcriteria (1), (2), and (3))
-A major uncertainty in the response of the lithophysal zone is the rock compressive
strength. This parameter is sampled from 5 levels for the rockfall calculations.
(Subcriteria (1) and (3))
-A major uncertainty in the response of the nonlithophysal zone is the fracture geometry
and fracture properties. These uncertainties are represented by the use of numerous
synthetic joint fracture patterns that are generated in a statistically sound manner and
incorporated into the rockfall calculations for the nonlithophysal zones. (Subcriteria (2)
and (3))
-Material properties for structural response calculations are based on a temperature of
150C, which is conservative over 97 percent of the time for the first 10,000 years after
closure. This choice is even more conservative for the first 20,000 years after
repository closure. (Subcriteria (1) and (3))
-Thicknesses of the waste package outer shell and drip shield plates have been reduced
by 2-mm to conservatively account for general corrosion over the first 10,000 years to
20,000 years after closure. (Subcriterion (3))
-Uncertainty and variability in damaged areas of the waste package and drip shield are
represented in the abstractions as a sampled distribution. This uncertainty is directly
incorporated into the abstractions for TSPA-LA.
 Acceptance Criterion 4: Model Uncertainty Is Characterized and Propagated Through The
Model Abstraction
-Grid convergence studies and alternate finite element representations have been
evaluated for the rockfall models and for the structural response calculations.
Calculations have been performed with the most appropriate numerical representations,
so this particular source of model uncertainty is not propagated through the damage
abstractions for TSPA-LA. (Subcriteria (2) and (3))
-Alternative modeling approaches have been evaluated for the conceptual and
computational models of lithophysal and nonlithophysal rock. (Subcriteria (2) and (3))
-Alternate distributions have been considered in abstracting the damage results for the
waste package and drip shield into model abstractions. (Subcriterion (3))
 Acceptance Criterion 5: Model Abstraction Output Is Supported By Objective
Comparisons
-Objective comparisons between the calculated damage to EBS components and the
corresponding abstractions for TSPA-LA are described in Table 31. (Subcriteria (1),
(2), and (3))
Table 31. Comparison of Seismic Abstractions with Objective Evidence for Review Criteria
Abstraction Objective Comparison
Damage to Waste Package from Ground Motion The abstraction for damage to the waste package is
based on a uniform distribution. Figures 6 and 7
compare the upper bound of this uniform distribution with
the calculated damage from ground motions with a PGV
of 1.067 m/s, 2.44 m/s, and 5.35 m/s. The lower bound
of this distribution is zero. Figures 6 and 7 demonstrate
that the calculated damage to the waste package is
bounded by the upper and lower bounds of this uniform
distribution, providing objective evidence of its adequacy.
An independent technical review has also been
performed for this damage abstraction to provide
increased confidence in the model abstraction.
Damage to Drip Shield from Rockfall Figures 10 and 11 compare the calculated damage from
rockfall induced by ground motions for PGVs of 2.44 and
5.35 m/s with the damage abstraction based on a log-
triangular distribution. These figures demonstrate that
the log-triangular distribution provides a reasonable fit to
the calculated damage at these two PGV levels. Figure
12 compares the mode of this log-triangular distribution
as a function of PGV, demonstrating that it is a
reasonable fit to the value of the mode over a range of
PGV from 0.55 m/s to 5.35 m/s. Collectively, these three
figures provide objective evidence that the abstraction is
an accurate representation of the computational results.
An independent technical review has also been
performed for this damage abstraction to provide
increased confidence in the model abstraction.
Damage to Drip Shield from Ground Motion The abstraction for damage to the drip shield from
ground motion is based on a uniform distribution. The
upper limit of this uniform distribution provides an upper
bound for the calculated damage from ground motions
with a PGV of 0.55 m/s, 2.44 m/s, and 5.35 m/s,
providing objective evidence of its adequacy.
Damage to Cladding from Ground Motion The abstraction for damage to the cladding assumes that
100 percent of the cladding perforates after a ground
motion with PGV of 1.067 m/s or larger occurs. This
scientific analysis is based on a conservative, bounding
approach that can be verified through the checking
process for model reports.
Damage to Waste Package and Drip Shield from
Fault Displacement
The abstraction for damage to the waste package and
drip shield from fault displacement is based on the
hazard curves for displacement of secondary faults in the
repository block and available clearances for EBS
components. The analysis of fault displacement
demonstrates that there is only damage from fault
displacement with a 2  10-7 per year annual exceedance
frequency, or less (see Table 29). In this situation,
damage from fault displacement is a very low probability
occurrence. In addition, a maximum of 53 packages is
affected by fault displacement (see Table 29). In this
situation, it is appropriate to verify this scientific analysis
through the normal checking process for model reports.
6.11.1 Treatment of Parameter Uncertainty
Data uncertainty is explicitly included in the seismic abstractions for TSPA-LA. Uncertainty has
been directly represented through the use of sampled input parameters for the structural response
calculations for the drip shield and waste package under vibratory ground motions, and in the
rockfall analyses. The uncertainty in these input parameters and its propagation into TSPA-LA
is discussed in the next three sections, followed by a discussion of model uncertainty (i.e.,
alternate conceptual models).
6.11.1.1 Uncertainty in Input Parameters for Structural Response
The structural response calculations for the waste package response and drip shield under
vibratory ground motions include three major sources of uncertainty: (1) the ground motion time
histories, (2) the metal-to-metal friction coefficient, and (3) the metal-to-rock friction coefficient:

Fifteen sets of three-component ground motion time histories are used to represent the
uncertainty in the seismic hazard at a given annual exceedance frequency (i.e., 10-6 per year
or 10-7 per year). Although these fifteen ground motions are scaled to have the same
horizontal PGV, the PGA and the duration of the time histories span a wide range of
response. For example, the PGA for the first horizontal ground motion component at the
10-6 per year hazard level ranges from about 1.5 g to 7 g.

The metal-to-metal friction coefficient between the waste package and emplacement pallet
varies from 0.2 to 0.8. The friction coefficient affects the onset of sliding and dissipation
of energy for the EBS components as a function of the amplitude of the ground motion.
However, the importance of friction is anticipated to diminish with increasing ground
motion level because the EBS components begin to slide almost immediately for high
amplitude ground motions.

The metal-to-rock friction coefficient between the emplacement pallet and the invert or
between the drip shield and the invert varies from 0.2 to 0.8. Again, the friction coefficient
affects the onset of sliding and dissipation of energy for the unanchored EBS components
as a function of the amplitude of the ground motion. However, the importance of friction is
anticipated to diminish with increasing amplitude of the ground motions.
The selection of friction coefficients as major sources of uncertainty, in addition to the ground
motions, is based on engineering judgment. Variability in ground motions is often the most
significant uncertainty in structural response calculations for nuclear plant components.
Variability of friction coefficients may be important if damage varies significantly with the
relative motions or impacts between adjacent structures.
The variations of these uncertain input parameters are simultaneously included in the fifteen
structural response calculations at each seismic hazard level. This is accomplished by a Monte
Carlo procedure that ensures robust sampling of the uncertain parameters over their full ranges.
The Monte Carlo procedure and the sampled values of the three uncertain input parameters are
described and documented in Sampling of Stochastic Input Parameters for Rockfall and
Structural Response Calculations Under Vibratory Ground Motion (BSC 2003r).
The results from the structural response calculations are postprocessed to determine the damaged
areas on the drip shield or waste package. The seismic damage abstractions for the waste
package and drip shield make use of a residual stress threshold as a failure criterion. If the
residual stress from mechanical damage exceeds the stress threshold for the barrier, then the
affected area(s) are considered to have failed as a barrier to flow and transport. The residual
stress threshold for the waste package is based on a uniform distribution between 80 and
90 percent of the yield strength for Alloy 22 (see Section 6.2). Postprocessing of the output from
waste package calculations has determined the damaged areas corresponding to both 80 and
90 percent of the yield strength of Alloy 22 (BSC 2003b, Tables 6.4.1-2 and 6.4.2-2). The
residual stress threshold for titanium is (very) conservatively set to a constant value of 50 percent
of the yield strength of Titanium Grade 7, so no uncertainty is propagated into TSPA-LA for
damaged area on the drip shield from vibratory ground motion.
6.11.1.2 Uncertainty in Input Parameters for Rockfall Calculations
All rockfall calculations include the ground motion time histories as a major source of
uncertainty. Fifteen ground motions again represent the uncertainty in the seismic hazard at each
annual exceedance frequency. In the lithophysal units, the rock compressive strength is an
uncertain input parameter that is represented as five discrete levels of rock strength, ranging from
low (5 MPa) to high (30 MPa). In the nonlithophysal units, the synthetic fracture pattern is an
uncertain input parameter. The synthetic fracture pattern is a representation of the fracture
system geometry in three dimensions. Approximately 70 synthetic fracture patterns are used in
the rockfall calculations for the nonlithophysal units. The variations in these uncertain
parameters are simultaneously included in the rockfall analyses at each seismic hazard level
(BSC 2003r).
The stochastic input parameters for the rockfall calculations are based on engineering judgment.
For example, the rock compressive strength is a key parameter for tunnel failure in a continuum
material, while the fracture geometry is a key parameter for identifying the size and location of
rock blocks that can be ejected from the walls of a tunnel. Fracture properties can also be
important in the nonlithophysal units, but are conservatively represented rather than being
incorporated into the stochastic sampling scheme.
The results from the rockfall calculations are not direct inputs to TSPA-LA. Rockfall
calculations for lithophysal units predict drift collapse at seismic hazard levels of 10-6 and 10-7
per year; however, the strong seismic waves are predicted to shatter the lithophysal rock into
small fragments that cannot fail the drip shield or waste package as a flow barrier.
Rockfall calculations for the nonlithophysal units predict a wide range of block sizes and
velocities that can be ejected from the tunnel walls and impact the drip shield. More specifically,
each rockfall calculation for the nonlithophysal unit predicts a complex, time-dependent
sequence of rock blocks that impact the drip shield at varying locations and velocities. These
impacts can cause damage if the block has enough mass and kinetic energy.
Numerous rockfall calculations are performed for the nonlithophysal zone, so it is impractical
from a computational viewpoint to perform a structural response calculation for each time-
dependent sequence of rock blocks. Instead, structural response calculations are performed for a
single block impacting the drip shield over a range of block sizes/velocities and impact points. A
range of six block kinetic energies and three impact points (crown, corner, and side) span the
range of response observed for the 10-6 and 10-7 per year seismic hazards. The damaged areas
for these 18 cases provide a basis for determining the total damage from a time-dependent
sequence of rock blocks by interpolation and summation of damaged areas for the individual
impacts.
This approach (interpolation and summation) preserves the variability in the damaged areas of
the drip shield due to the uncertainties in the quantity and velocity of rock blocks striking the
drip shield.
6.11.1.3 Propagation of Uncertainty into Abstractions for TSPA-LA
The calculations of damaged areas on the waste package and drip shield due to vibratory ground
motions and rockfall induced by vibratory ground motions exhibit substantial variability induced
by the uncertainties in seismic ground motions and other input parameters. This variability has
been directly represented in TSPA-LA by defining stochastic parameters that are sampled during
each realization of the seismic scenario class. For example:

For a given value of PGV, damage to the waste package from vibratory ground motion is
represented as a uniform distribution that is sampled for each realization of the seismic
scenario class. The lower bound of this distribution is zero damage for all values of PGV.
The upper bound of this distribution is a linear function of PGV. This function represents
the maximum damage with a 95 percent confidence limit, based on the damage results for
the 10-6 and 10-7 per year hazard levels. The upper range of this uniform distribution is
illustrated in Figures 6, 7, and 8.

The uncertainty in the residual stress threshold for Alloy 22 has not been propagated into
the abstraction for TSPA-LA. The damage states for the waste package are based on an
average of the damage areas using the 80 and 90 percent Alloy 22 failure criteria. This is
an accurate representation for the mean damage area due to the variability in the uniformly
distributed residual stress threshold. This approach is reasonable because the variability in
damaged area due to the uncertainty in failure criterion is approximately a factor of 2,
while the variability in damaged area due to the ground motions at a given value of PGV is
more than an order of magnitude (see Tables 6 and 7). In this situation, it is reasonable to
ignore the variability in damaged area due to failure criterion because the variability from
ground motions is the dominant effect on uncertainty.

For a given value of PGV, damage to the drip shield from vibratory ground motion is
represented as a uniform distribution for annual exceedance frequencies less than 10-6 per
year. This distribution is sampled for each realization of the seismic scenario class. The
lower bound of this distribution is zero damage. The upper bound of this distribution is a
linear function of PGV that rises from zero damage to 50 percent damage between 10-6 and
10-7 per year, and then remains constant at 50 percent below 10-7 per year.

Damage to the drip shield from rock blocks in the nonlithophysal units depends on two
distributions that are sampled in each realization. The first distribution determines the
probability of no damage at a given level of PGV (see Figure 13). If damage occurs, its
value is determined by sampling a log-triangular distribution whose mode is a function of
PGV (see Figure 12).
The abstraction for cladding does not propagate uncertainty into TSPA-LA because it is based on
a simplified response that is bounded with two damage states: zero damage or 100 percent
damage.
6.11.2 Treatment of Model Uncertainty (Alternate Conceptual Models)
The seismic consequence abstractions have considered alternate conceptual models, primarily
through different representations of the mean damage and the distribution of damage about the
mean.
In Section 6.3, the maximum damage to the waste package is represented as a linear function of
PGV. This is equivalent to a linear function for the mean because damage is represented as a
uniform distribution from zero to its maximum value. This linear function is consistent with
Assumption 5.1 because it results in zero damage at the 210-5 per year hazard level or for
greater values of the exceedance frequency. An alternate formulation is to represent the mean
damage as a power law function of PGV. However, this alternate formulation has been
eliminated because it results in substantially greater damage than calculated for the 10-5 per year
ground motions, while the linear function is an excellent fit to the damage data at this ground
motion level.
The distribution of damaged areas on the waste package has been analyzed for the 10-7 and 10-6
per year ground motion levels. At the 10-7 per year level, the damage values can be represented
by either a normal distribution or a uniform distribution. At the 10-6 per year level, the damage
becomes bimodal. These points can be represented with a normal distribution that is truncated at
a small, nonzero damage value, or again with a uniform distribution. The uniform distribution is
selected for the abstraction for several reasons. First, it is conservative relative to a normal
distribution for high values of damage because it will be sampled uniformly across its range,
rather than being skewed towards sampling around the mean. Second, the normal distribution at
10-6 produces negative damage values because its mean and standard deviation are
approximately equal. Extrapolating this behavior to lower ground motions, say at the 10-5 per
year level, is highly uncertain without additional calculations. Third, a uniform distribution is a
reasonable representation for the computational results for damage.
The damage to the drip shield from rockfall is based on similar considerations. The damage to
the drip shield at 10-6 per year and 10-7 per year ground motion levels (remember that the rockfall
is induced by the ground motions) follows a bimodal pattern for the zero and non-zero damage
points. The probability of zero damage is represented as a linear function of PGV. The non-zero
damage to the drip shield is represented as a log-triangular distribution with a mode that is a
linear function of PGV. A single distribution did not produce a reasonable match to all the
damage values at the two ground motion levels. The log-triangular distribution provides a
simple representation of the computational results for damage.
6.12 VERIFICATION OF SCIENTIFIC ANALYSES FOR CLADDING AND FOR
FAULT DISPLACEMENT
The abstractions for cladding damage from vibratory ground motions and for the EBS damage
from fault displacement are stochastic distributions whose parameters are a function of the
amplitude or the exceedance frequency of the ground motion. These abstractions are considered
scientific analyses because they are based on standard statistical techniques that bound the
component response, rather than the results from detailed engineering calculations or other
scientific analyses. Since these abstractions are not models, they are not validated per
AP-SIII.10Q, Models. However, the abstractions still require verification, defined as providing
objective evidence that the abstractions are an accurate representation of the variability and
uncertainty in damage to the EBS components.
 Damage to Cladding from Vibratory Ground Motion
The abstraction for damage to the cladding assumes that 100 percent of the cladding
perforates after a ground motion with PGV of 1.067 m/s or larger occurs. This is a
conservative, bounding approach that does not require further verification.
 Damage to EBS Components from Fault Displacement
The abstraction for damage to the waste package and drip shield from fault displacement is
based on the mean hazard curves for displacement of secondary faults in the repository
block and on the available clearances between EBS components. The analysis of damage
from fault displacement demonstrates that there is no damage from faulting until an annual
exceedance frequence less than 210-7 per year is reached. In other words, only the largest
fault displacements can damage the EBS components.
Once damage can occur, the failed area on the waste package is defined as a uniform
distribution with a lower bound of 0 and an upper bound given by the lid area. The lower
bound represents a situation with minor crimping of the waste package; the upper bound
represents a situation in which the welds fail and the lid completely separates from the
waste package. These damage states are intended to be bounding conditions because there
is high uncertainty in the state of the drift, the invert, and the EBS components after a
major fault displacement.
The failed area on the drip shield is assumed to be 100 percent for a fault displacement that
damages the waste package. This total damage state is clearly a bounding condition
because some fault displacements produce minimal crimping between the waste package
and drip shield. Similarly, the cladding is assumed to be 100 percent perforated for a fault
displacement that damages the waste package.
The damage abstraction for fault displacement has been compared to an alternate
conceptual model proposed by (Waiting et al. 2003). There is reasonable agreement
between the damage abstraction in this report and the alternate conceptual model,
considering that the alternate model is based on historical data for fault displacement in the
western United States and that the damage abstraction is based on hazard curves specific to
Yucca Mountain. For example, the number of fault intersections predicted by the damage
abstraction is 168, versus 191 for the alternate conceptual model. Similarly, the probability
weighted number of waste package failures is predicted to be 2.410-6 for the damage
abstraction, within the range of 1.910-6 to 1.910-5 for the alternate conceptual model.
This agreement provides added confidence in the damage abstraction for fault
displacement.
7. VALIDATION
The abstractions for waste package response to vibratory ground motions and for drip shield
response to vibratory ground motions and rockfall are stochastic distributions whose parameters
(i.e., the upper and lower bounds for a uniform distribution or the mode and bounds of a log-
triangular distribution) are a function of the amplitude of the ground motion. These distributions,
also called damage abstractions, are based on information from detailed structural response
calculations and from rockfall calculations. These distributions are model abstractions because
they represent this detailed computational information in a simplified manner for TSPA-LA.
The underlying information for the model abstractions are created by models that have been
validated under SP-SIII.10Q and by engineering calculations with software qualified under
AP-SI.1Q. The status of the engineering calculations for structural response, of the rockfall
models and analyses, and of the failure criteria are discussed next, followed by a discussion of
the validation of the individual model abstractions.
Structural calculations for the response of large engineered components (e.g., waste package,
drip shield, or cladding) due to impact and vibration is a well-established technology. The
deformation of these types of structures can be evaluated with standard, commercially available
finite-element programs. As a result, there is high confidence in the results from the
computational process because of the extensive testing of commercial software on a wide variety
of problems, including impact calculations. In addition, each computational study is based on a
mesh refinement analysis and other supporting calculations that provide additional confidence in
the results. No changes to the finite-element software are needed for these calculations. These
engineering codes have been qualified for their intended use under AP-SI.1Q and the engineering
calculations are performed under AP-3.12Q.
The results from the engineering calculations are considered appropriate for their intended use
for several reasons. First, the calculations are based on standard, commercially available
software that has demonstrated the capability to accurately analyze impact processes. Second,
the finite-element representation of EBS components is designed (via mesh refinement studies)
to accurately represent the potential damage from the impact processes. And lastly, the ground
motions for the calculations are based on state-of-the-art techniques for representing seismic
phenomena.
The seismic failure criteria for Alloy 22 and Titanium Grade 7 have been selected in a
conservative manner. The failure criteria are based on considerations of accelerated corrosion
due to residual stress, rather than the ultimate tensile stress of Alloy 22 or Titanium Grade 7. In
fact, none of the structures reached ultimate tensile failure in any of the structural calculations.
The rationale for selection of the residual stress thresholds for failure is documented in
Section 6.3, based on information in Stress Corrosion Cracking of the Drip Shield, the Waste
Package Outer Barrier, and the Stainless Steel Structural Material (BSC 2003l, Section 6.2.1).
The conservative approach to defining the residual stress thresholds for failure provides ample
safety margin, helping to enhance confidence in the seismic failure criteria. The failure criteria
are considered appropriate for their intended use because they are a conservative interpretation of
the experimental data for the corrosion of Alloy 22 and Titanium Grade 7 under conditions
relevant to Yucca Mountain.
The rockfall calculations are also performed with commercially available software, although it is
necessary to modify the software for computational efficiency, for the representation of fractures
with short or intermittent trace lengths, and for constitutive models for tuff. Because of these
modifications, the rock mechanics codes are qualified and the models validated for their intended
application to lithophysal and nonlithophysal tuffs. This model validation is documented in
Section 7 of Drift Degradation Analysis (BSC 2003h).
The model abstractions for waste package response to vibratory ground motions and for drip
shield response to vibratory ground motions and rockfall are simple numerical fits to the percent
failed surface area as a function of PGV. The fits involve selecting the most appropriate
distribution to represent the variability of damage as a function of PGV. The appropriate
distributions and functional fits have been developed and documented in Microsoft Excel
spreadsheets. The numerical values in these spreadsheets have been verified during the checking
process for this model report. These spreadsheets are found in Attachments II, IV, and V of this
report, as well as electronically on a CD-ROM. Details of the validation process for the model
abstractions are as follows:
 Abstraction for Damage to the Waste Package from Ground Motion
The abstraction for damage to the waste package is based on a uniform distribution. The
selection of a uniform distribution is justified by the comparisons shown in Figures 4 and 5
of Section 6.5.1.3. Figure 6 (also in Section 6.5.1.3) compares the upper bound of this
uniform distribution with the calculated damage from ground motions with PGVs of 1.067
m/s, 2.44 m/s, and 5.35 m/s. The lower bound of this distribution is zero. Figure 8
provides an alternate upper bound, based on a lognormal distribution. The discussion in
Section 6.5.3 and Attachments II and III explains how the calculated damage to the waste
package is bounded by the upper and lower limits of the uniform distribution, providing
objective evidence of its adequacy.
The model abstraction for damage to the waste package from vibratory ground motion has
been validated through an independent technical review. This review is documented in
Attachment III. The recommendations of the review have been incorporated into the waste
package abstraction, as discussed in Section 6.5.4.
 Abstraction for Damage to the Drip Shield from Rockfall
Figures 9 and 10 in Section 6.6.1.3 compare the calculated damage from rockfall for PGVs
of 2.44 and 5.35 m/s with the damage abstraction based on a log-triangular distribution.
These figures demonstrate that the log-triangular distribution provides a reasonable fit to
the calculated damage at these two PGV levels. Figure 12 in Section 6.6.1.4 compares the
mode of this log-triangular distribution as a function of PGV, demonstrating that it is a
reasonable fit to the value of the mode over a range of PGV from 0.55 m/s to 5.35 m/s.
Collectively, these three figures provide objective evidence that the abstraction is an
accurate representation of the underlying data.
The model abstraction for damage to the drip shield from rockfall has been validated
through an independent technical review. This review is documented in Attachment V.
The recommendations of the review confirmed the model abstraction, as discussed in
Section 6.6.1.6.
 Abstraction for Damage to the Drip Shield from Direct Ground Motion
The abstraction for damage to the drip shield from ground motion is based on a uniform
distribution. Section 6.6.3 defines the upper bound of this uniform distribution with the
calculated damage from ground motions with a PGV of 0.55 m/s, 2.44 m/s, and 5.35 m/s.
The lower bound of this distribution is zero. The calculated damage to the drip shield is
bounded by the upper and lower bounds of this uniform distribution for a PGV value of
2.44 m/s. The 50 percent upper bound at a PGV of 5.35 is based on the maximum
estimate, as explained in Section 6.6.3. In this situation, there is again objective evidence
of the adequacy of the abstraction, based on the fact that the calculated damage is bounded
by the upper and lower limits of the uniform distribution.
The technical approach for this model abstraction is identical to that for the other model
abstractions for seismic damage. Namely, a simple distribution is fit to the available
information for structural damage. However, this model abstraction is unique in the sense
that damaged areas are only available for a PGV of 2.44 m/s. In particular, the damaged
area at a PGV of 5.35 m/s is conservatively bounded by 50 percent, while the damaged area
at a PGV of 0.55 m/s is set to 0, based on Assumption 5.1. The technical approach here is
consistent with the methodology confirmed by the independent technical review for the
other two model abstractions, although this model abstraction is essentially a bounding
analysis for the low probability, high amplitude seismic events. In this situation, the model
abstraction is considered validated because it is based on a methodology that is identical to
that confirmed by the independent technical review and because it is a bounding
representation of the damage for low probability seismic events.
8. CONCLUSIONS
The purpose of this work is to develop abstractions for the response of EBS components to
seismic hazards at a geologic repository at Yucca Mountain, Nevada, and to define the
methodology for using these abstractions in a seismic scenario class for the TSPA-LA. The
seismic hazards are vibratory ground motion, fault displacement, and rockfall due to ground
motion. The EBS components are the drip shield, the waste package, and the fuel cladding. The
following abstractions for seismically induced damage have been developed:

Damage to the waste package from vibratory ground motions

Damage to the drip shield from vibratory ground motions

Damage to the drip shield from rockfall induced by vibratory ground motions in the
nonlithophysal zones

Damage to the cladding from end-to-end impacts of adjacent waste packages

Damage to the waste package, drip shield and cladding from fault displacement.
The recommended implementation of these abstractions and their associated input parameters for
TSPA-LA is defined in Section 6.10.2 and Table 30. This computational algorithm can also be
referenced through DTN: MO0308SPACALSS.002.
Damage to the drip shield from rockfall in the lithophysal zones is not abstracted for TSPA-LA
because the lithophysal zone is expected to shatter into small fragments that cannot produce
failed areas on the drip shield.
The seismic scenario class is designed to efficiently determine the mean dose for seismic events
with annual frequencies down to 10-8 per year. The seismic scenario class is based on a single
seismic hazard occurring at a randomly chosen time in each realization of the TSPA-LA. That
is, the conditional probability of a seismic event is 1 for each realization. The damage from this
single event is based on the abstractions for the drip shield, the waste package and the cladding.
The damaged areas on the EBS components define pathways for flow and transport through the
EBS. Once radionuclides are released from the EBS, flow and transport in the unsaturated zone
and the saturated zone are based on the same models and algorithms as for the nominal scenario
class. Biosphere calculations and parameters for the seismic scenario class are also unchanged
from the nominal scenario class.
Each realization of the seismic scenario class will determine an annual dose time history for a
single seismic hazard with mean annual exceedance frequency .i. These dose time histories do
not represent the mean dose, as called for in 10 CFR 63.303, because a single hazard always
occurs in each realization. However, a mean dose time history can be calculated using a
probability-weighted sum and average of all the realizations for the seismic scenario class. The
weighting factor for each realization corrects for the expected number of seismic events in each
realization and for the logarithmic sampling of the hazard curve for PGV and of the time of the
seismic event.
9. INPUTS AND REFERENCES
9.1 DOCUMENTS CITED
Brocoum, S. 2001. Transmittal of Report Addressing Key Technical Issues (KTI) Structural
Deformation and Seismicity (SDS). Letter from S. Brocoum (DOE/YMSCO) to C.W. Reamer
(NRC), October 25, 2001, OL&RC:TCG-0140, with enclosure. ACC: MOL.20020304.0297;
MOL.20030714.0094.
BSC (Bechtel SAIC Company) 2001a. FY 01 Supplemental Science and Performance Analyses,
Volume 1: Scientific Bases and Analyses. TDR-MGR-MD-000007 REV 00 ICN 01. Las
Vegas, Nevada: Bechtel SAIC Company. ACC: MOL.20010801.0404; MOL.20010712.0062;
MOL.20010815.0001.
BSC 2001b. Site Recommendation Subsurface Layout. ANL-SFS-MG-000001 REV 00 ICN 02.
Las Vegas, Nevada: Bechtel SAIC Company. ACC: MOL.20010411.0131.
BSC 2002. The Enhanced Plan for Features, Events, and Processes (FEPs) at Yucca Mountain.
TDR-WIS-PA-000005 REV 00. Las Vegas, Nevada: Bechtel SAIC Company. ACC:
MOL.20020417.0385.
BSC 2003a. Technical Work Plan for: Engineered Barrier System Department Modeling and
Testing FY03 Work Activities. TWP-MGR-MD-000015 REV 03. Las Vegas, Nevada: Bechtel
SAIC Company. ACC: DOC.20030225.0001.
BSC 2003b. Structural Calculations of Waste Package Exposed to Vibratory Ground Motion.
000-00C-EBS0-00300-000-00B. Las Vegas, Nevada: Bechtel SAIC Company. ACC:
ENG.20030520.0003.
BSC 2003c. Repository Design Project, RDP/PA IED Typical Waste Package Components
Assembly (5). 800-IED-WIS0-00205-000-00A. Las Vegas, Nevada: Bechtel SAIC Company.
ACC: ENG.20030707.0001.
BSC 2003d. Maximum Accelerations on the Fuel Assemblies of a 21-PWR Waste Package
During End Impacts. 000-00C-DSU0-01100-000-00A. Las Vegas, Nevada: Bechtel SAIC
Company. ACC: ENG.20030327.0002.
BSC 2003e. Repository Design Project, RDP/PA IED Typical Waste Package Components
Assembly (4). 800-IED-WIS0-00204-000-00A. Las Vegas, Nevada: Bechtel SAIC Company.
ACC: ENG.20030702.0004.
BSC 2003f. Repository Design Project, Repository/PA IED Interlocking Drip Shield and
Emplacement Pallet. 800-IED-WIS0-00401-000-00A. Las Vegas, Nevada: Bechtel SAIC
Company. ACC: ENG.20030730.0004.
BSC 2003g. Drip Shield Structural Response to Rock Fall. 000-00C-TED0-00500-000-00A.
Las Vegas, Nevada: Bechtel SAIC Company. ACC: ENG.20030327.0001.
BSC 2003h. Drift Degradation Analysis. ANL-EBS-MD-000027 REV 02. Las Vegas, Nevada:
Bechtel SAIC Company. ACC: DOC.20030709.0003.
BSC 2003i. Repository Design Project, Repository/PA IED Emplacement Drift Committed
Materials (2). 800-IED-WIS0-00302-000-00A. Las Vegas, Nevada: Bechtel SAIC Company.
ACC: ENG.20030627.0004.
BSC 2003j. Repository Design Project, RPD/PA IED Typical Waste Package Components
Assembly 1 of 9. 800-IED-WIS0-00201-000-00A. Las Vegas, Nevada: Bechtel SAIC
Company. ACC: ENG.20030702.0001.
BSC 2003k. Repository Design Project, RPD/PA IED Typical Waste Package Components
Assembly (2). 800-IED-WIS0-00202-000-00A. Las Vegas, Nevada: Bechtel SAIC Company.
ACC: ENG.20030702.0002.
BSC 2003l. Stress Corrosion Cracking of the Drip Shield, the Waste Package Outer Barrier,
and the Stainless Steel Structural Material. ANL-EBS-MD-000005 REV 01. Las Vegas,
Nevada: Bechtel SAIC Company. ACC: DOC.20030717.0001.
BSC 2003m. Repository Design Project, RDP/PA IED Typical Waste Package Components
Assembly (8). 800-IED-WIS0-00208-000-00A. Las Vegas, Nevada: Bechtel SAIC Company.
ACC: ENG.20030707.0004.
BSC 2003n. Repository Design Project, RDP/PA IED Typical Waste Package Components
Assembly (7). 800-IED-WIS0-00207-000-00A. Las Vegas, Nevada: Bechtel SAIC Company.
ACC: ENG.20030707.0003.
BSC 2003o. Repository Design Project, Repository/PA IED Subsurface Facilities. 800-IED-
WIS0-00101-000-00Ad. Las Vegas, Nevada: Bechtel SAIC Company. ACC:
MOL.20030730.0337. TBV-5310
BSC 2003p. Structural Calculations of Drip Shield Exposed to Vibratory Ground Motion. 000-
00C-PEC0-00100-000-00A. Las Vegas, Nevada: Bechtel SAIC Company. ACC:
ENG.20030618.0009.
BSC 2003q. Abstraction of Drift Seepage. MDL-NBS-HS-000019 REV 00C. Las Vegas,
Nevada: Bechtel SAIC Company. ACC: MOL.20030728.0198. TBV-5280
BSC 2003r. Sampling of Stochastic Input Parameters for Rockfall and Structural Response
Calculations Under Vibratory Ground Motion. ANL-EBS-PA-000009 REV00. Las Vegas,
Nevada: Bechtel SAIC Company. ACC: DOC.20030707.0003.
BSC 2003s. Drip Shield Statically Loaded by Backfill and Loose Rock Mass. 000-00C-TED0-
00300-000-00A. Las Vegas, Nevada: Bechtel SAIC Company. ACC: ENG.20030224.0004.
Canori, G.F. and Leitner, M.M. 2003. Project Requirements Document. TER-MGR-MD-
000001 REV 01. Las Vegas, Nevada: Bechtel SAIC Company. ACC: DOC.20030404.0003.
Chun, R.; Witte, M.; and Schwartz, M. 1987. Dynamic Impact Effects on Spent Fuel Assemblies.
UCID-21246. Livermore, California: Lawrence Livermore National Laboratory. ACC:
HQX.19881020.0031.
CRWMS M&O (Civilian Radioactive Waste Management System Management and Operating
Contractor) 1998. Probabilistic Seismic Hazard Analyses for Fault Displacement and Vibratory
Ground Motion at Yucca Mountain, Nevada. Milestone SP32IM3, September 23, 1998. Three
volumes. Las Vegas, Nevada: CRWMS M&O. ACC: MOL.19981207.0393.
CRWMS M&O 2000a. Characterize Framework for Seismicity and Structural Deformation at
Yucca Mountain, Nevada. ANL-CRW-GS-000003 REV 00. Las Vegas, Nevada: CRWMS
M&O. ACC: MOL.20000510.0175.
CRWMS M&O 2000b. Features, Events, and Processes: Disruptive Events. ANL-WIS-MD-
000005 REV 00 ICN 1. Las Vegas, Nevada: CRWMS M&O. ACC: MOL.20001218.0007.
CRWMS M&O 2000c. Total System Performance Assessment for the Site Recommendation.
TDR-WIS-PA-000001 REV 00 ICN 01. Las Vegas, Nevada: CRWMS M&O. ACC:
MOL.20001220.0045.
DOE 2002. Yucca Mountain Science and Engineering Report. DOE/RW-0539, Rev. 1.
Washington, D.C.: U.S. Department of Energy, Office of Civilian Radioactive Waste
Management. ACC: MOL.20020404.0042. [155943]
DOE 2002. Yucca Mountain Site Suitability Evaluation. DOE/RW-0549. Washington, D.C.:
U.S. Department of Energy, Office of Civilian Radioactive Waste Management. ACC:
MOL.20020404.0043. [156958]
Freeze, G.A.; Brodsky, N.S.; Swift, P.N 2001. The Development of Information Catalogued in
REV00 of the YMP FEP Database. TDR-WIS-MD-000003 REV 00 ICN 01. Las Vegas,
Nevada: Bechtel SAIC Company. ACC: MOL.20010301.0237.
Gardner, D. 2000. Meeting Summary, NRC/DOC Technical Exchange on Structural
Deformation and Seismicity KTI, October 11-12, 2000. E-mail from D. Gardner to C. Hanlon,
October 13, 2002, with attachment. ACC: MOL.20001102.0041; MOL.20001102.0042.
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Helton, J.C. 1997. Uncertainty and Sensitivity Analysis in the Presence of Stochastic and
Subjective Uncertainty. Journal of Statistical Computation and Simulation, 57, (1-4), 3-76.
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Helton, J.C. and Davis, F.J. 2000. Sampling-Based Methods for Uncertainty and Sensitivity
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Chapter 4.2 of Seismotectonic Framework and Characterization of Faulting at Yucca Mountain,
Nevada. Whitney, J.W., ed. Milestone 3GSH100M. Denver, Colorado: U.S. Geological
Survey. TIC: 237980. ACC: MOL.19970129.0041.
Mongano, G.S.; Singleton, W.L.; Moyer, T.C.; Beason, S.C.; Eatman, G.L.W.; Albin, A.L.; and
Lung, R.C. 1999. Geology of the ECRB Cross Drift - Exploratory Studies Facility, Yucca
Mountain Project, Yucca Mountain, Nevada. Deliverable SPG42GM3. Denver, Colorado: U.S.
Geological Survey. ACC: MOL.20000324.0614.
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Engineering and Engineering Mechanics Series. Englewood Cliffs, New Jersey: Prentice-Hall.
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NRC (U.S. Nuclear Regulatory Commission) 2003. Yucca Mountain Review Plan, Final Report.
NUREG-1804, Rev. 2. Washington, D.C.: U.S. Nuclear Regulatory Commission, Office of
Nuclear Material Safety and Safeguards. TIC: 254568.
Pat-Cornell, M.E. 1996. Uncertainties in Risk Analysis: Six Levels of Treatment.
Reliability Engineering and System Safety, 54, 95-111. New York, New York: Elsevier. TIC:
245961. [107499]
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Uniform Distribution. Journal of Statistic Education. Alexandria, Virginia: American
Statistical Association. Accessed April 7, 2003. TIC: 254033.
http://www.amstat.org/publications/jse/v6n3/rossman.html
Rubinstein, R.Y. 1981. Simulation and the Monte Carlo Method. New York, New York: John
Wiley & Sons. TIC: 254563. [163476]
Sanders, T.L.; Seager, K.D.; Rashid, Y.R.; Barrett, P.R.; Malinauskas, A.P.; Einziger, R.E.;
Jordan, H.; Duffey, T.A.; Sutherland, S.H.; and Reardon, P.C. 1992. A Method for Determining
the Spent-Fuel Contribution to Transport Cask Containment Requirements. SAND90-2406.
Albuquerque, New Mexico: Sandia National Laboratories. ACC: MOV.19960802.0116.
Waiting, D.J.; Stamatakos, J.A.; Ferrill, D.A.; Sims, D.W.; Morris, A.P.; Justus, P.S.; and
Ibrahim, A.K. 2003. Methodologies for the Evaluation of Faulting at Yucca Mountain,
Nevada. Proceedings of the 10th International High-Level Radioactive Waste Management
Conference (IHLRWM), March 30-April 2, 2003, Las Vegas, Nevada. Pages 377-387. La
Grange Park, Illinois: American Nuclear Society. TIC: 254559.
9.2 CODES, STANDARDS, REGULATIONS, AND PROCEDURES
10 CFR Part 63. Energy: Disposal of High-Level Radioactive Wastes in a Geologic Repository
at Yucca Mountain, Nevada. Readily available.
AP-2.14Q, Rev. 2, ICN 2. Review of Technical Products and Data. Washington, D.C.: U.S.
Department of Energy, Office of Civilian Radioactive Waste Management. ACC:
DOC.20030206.0001.
AP-2.22Q, Rev. 0, ICN 1. Classification Criteria and Maintenance of the Monitored Geologic
Repository Q-List. Washington, D.C.: U.S. Department of Energy, Office of Civilian
Radioactive Waste Management. ACC: DOC.20030422.0009.
AP-2.27Q, Rev. 1, ICN 1. Planning for Science Activities. Washington, D.C.: U.S. Department
of Energy, Office of Civilian Radioactive Waste Management. ACC: DOC.20030724.0001.
AP-3.12Q, Rev. 2, ICN 0. Design Calculations and Analyses. Washington, D.C.: U.S.
Department of Energy, Office of Civilian Radioactive Waste Management.
ACC: DOC.20030403.0003.
AP-3.15Q, Rev. 4, ICN 2. Managing Technical Product Inputs. Washington, D.C.: U.S.
Department of Energy, Office of Civilian Radioactive Waste Management. ACC:
DOC.20030627.0002.
AP-SI.1Q, Rev. 5, ICN 1. Software Management. Washington, D.C.: U.S. Department of
Energy, Office of Civilian Radioactive Waste Management. ACC: DOC.20030708.0001.
AP-SIII.10Q, Rev. 1, ICN 2. Models. Washington, D.C.: U.S. Department of Energy, Office of
Civilian Radioactive Waste Management. ACC: DOC.20030627.0003.
AP-SV.1Q, Rev. 0, ICN 3. Control of the Electronic Management of Information. Washington,
D.C.: U.S. Department of Energy, Office of Civilian Radioactive Waste Management. ACC:
MOL.20020917.0133.
9.3 SOURCE DATA, LISTED BY DATA TRACKING NUMBER
MO0004MWDRIFM3.002. Results of the Yucca Mountain Probabilistic Seismic Hazard
Analysis (PSHA). Submittal date: 04/14/2000.
MO0210PGVPB107.000. Design Peak Ground Velocity for the Repository Level (Point B) at
10-7 Annual Exceedance Probability. Submittal date: 10/17/2002.
MO0301MWD3DE27.003. Results from 3DEC Nonlithophysal Rockfall Analyses with 10-7
Ground Motion Level. Submittal date: 01/23/2003.
MO0303DPGVB106.002. Design Peak Ground Velocity for the Repository Level (Point B) at
10-6 Annual Exceedance Probability. Submittal date: 03/10/2003.
MO0305MWDNLRKF.001. Results from 3DEC Nonlithophysal Rockfall Analyses with 10-6
Ground Motion Level. Submittal date: 05/27/2003.
MO03061E9PSHA1.000. Spectral Acceleration and Velocity Hazard Curves Extended to 1E-9
Based on the Results of the PSHA for Yucca Mountain. Submittal date: 06/09/2003.
LB0307SEEPDRCL.002. Seepage Into Collapsed Drift: Data Summary. Submittal Date:
07/21/2003.
LL030704623122.031. NUFT Input File Data Development to support LA Multi-Scale
Analyses. Submittal Date: 07/23/2003.
TBV-5106: Assumption 5.1  MDL-WIS-PA-000003 REV 00  No damage from ground
motions hazards with exceedance frequencies greater than 10-4 per year.
9.4 PRODUCT OUTPUT, LISTED BY DATA TRACKING NUMBER
MO0305SPASFEGM.000. Scaling Factor for Estimating the 10-5 Per Year Ground Motions.
MO0308SPACALSS.002. Computational Algorithm of the Seismic Scenario for TSPA.
Submittal Date: 08/13/2003.
10. ATTACHMENTS
Attachment Title
I Spreadsheet for Point B Hazard Curve (8 pages)
II Spreadsheet for Waste Package Damage Abstraction (10 pages)
III Review Comments on Response Surface for Waste Package Damage from
Vibratory Ground Motion, by R. P. Kennedy (12 pages)
IV Spreadsheet for Drip Shield Damage Abstraction from Rockfall (6 pages)
V Review Comments on Response Surface for Drip Shield Damage from Rockfall
In Nonlithophysal Zone, by R. P. Kennedy (6 pages)
VI Review Comments on Response Surface for Drip Shield Damage from Vibratory
Ground Motion, by R. P. Kennedy (6 pages)
VII Spreadsheet for Fault Displacement Damage Abstraction (8 pages)
VIII Representation of Aleatory and Epistemic Uncertainty in the Calculation of
Expected Dose from Seismic Events at the Proposed Yucca Mountain Facility for
the Disposal of High-Level Waste, by J. C. Helton (18 pages)
Electronic copies of Attachments I, II, IV, and VII are available on CD-ROM.
ATTACHMENT I
SPREADSHEET FOR POINT B HAZARD CURVE
List of Inputs
DTN: MO0004MWDRIFM3.002. Results of the Yucca Mountain Probabilistic Seismic Hazard
Analysis (PSHA). Submittal date: 04/14/2000.
DTN: MO0303DPGVB106.002. Design Peak Ground Velocity for the Repository Level (Point
B) at 10-6 Annual Exceedance Probability. Submittal date: 03/10/2003.
DTN: MO0210PGVPB107.000. Design Peak Ground Velocity for the Repository Level (Point
B) at 10-7 Annual Exceedance Probability. Submittal date: 10/17/2002.
Relevant Formulas
The PGV hazard curve at Point A is defined by the points (PGVPoint A,i, .Point A,i) for i = 1, 2, , n,
where PGV is the peak ground velocity and . is the annual exceedance frequency. The scaled
hazard curve for point B is defined by the following formulas:
PGV
Po int B,i = a(PGVPo int A,i )
.
Po int B,i =.Po int A,i , (Eq. I-1)
for i = 1, 2, , n. Note that the values of the exceedance frequency remain unchanged in
Equation 1, and can be denoted more simply as .i. The quantity a is a constant, 0.7736, that
minimizes the error with the known PGV values at Point B for the 10-6 per year and 10-7 per year
annual exceedance frequencies. The value of a is determined by trial and error, using the
spreadsheet to calculate the error with the known values at Point B for varying values of a.
The values of PGV between the n points defined by Equation 1 are calculated with a log-linear
interpolation scheme. For a given value of . such that .k < . <.k+1, the interpolation is given by:
,,
PGV = PGVPo int k B +
PGVPo int k B +1 - PGVPo int k B (log(.) - log(. )) (Eq. I-2), log(. ) - log(. ) k
k +1 k
Output Information
Table I-1 defines the points for the scaled PGV hazard curve at Point B.
Table I-1. Scaled Points for the PGV Hazard Curve at Point B
Scaled PGV At Point B Annual Exceedance
(cm/s) Frequency (1/yr)
15.9 6.26  10-4
23.9 2.78  10-4
39.8 9.30  10-5
79.6 1.84  10-5
159 3.07  10-6
398 2.28  10-7
557 8.15  10-8
796 2.60  10-8
1190 6.56  10-9
The interpolated values of PGV for various values of the annual exceedance frequency are given
in Table I-2. Note that the errors of the scaled hazard curve with the known values at Point B for
the 10-6 per year and 10-7 per year annual exceedance frequencies are +7.5 percent and
-1.7 percent, respectively.
Table I-2. Interpolated Values on the Scaled PGV Hazard Curve for Point B
Annual Exceedance Frequency
(1/yr)
Interpolated PGV at Point B
(cm/s)
Comments
5  10-4 18.1
10-4 38.8
5  10-5 55.0
10-5 106.7
10-6 262.4 Error of +7.5% relative to the
exact value of 244 cm/s
10-7 525.8 Error of 1.7% relative to the
exact value of 535 cm/s
1  10-8 1073
Finally, the ratio of the PGV values at Point B for annual exceedance frequencies of 10-5 per year
to 10-6 per year is given by:
at PGV 10-5
= 7.106 cm / s = .4066.0 (Eq. I-3)
at PGV 10-6 4.262 cm / s
This ratio has been used to generate approximate ground motions for the 10-5 per year hazard
level. It is available as a product output in DTN: MO0305SPASFEGM.000.
The spreadsheet defining the values in Tables I-1 and I-2 follows.
DEFINE THE MEAN HORIZONTAL PGV HAZARD CURVE AT POINT B
(THE EMPLACEMENT DRIFTS) AND USE THIS CURVE TO ESTIMATE
THE HORIZONTAL PGV VALUES AT ANNUAL EXCEEDANCE FREQUENCIES
BETWEEN 5E-04 PER YEAR AND 1E-08 PER YEAR.
This calculation estimates the mean hazard curve for horizontal PGV at Point B (the
emplacement drifts), based on the mean hazard curve for PGV at Point A, a reference
rock outcrop at the repository elevation, and the known PGV values at Point B for
the 10-6 per year and 10-7 per year annual exceedance probabilities. More specifically,
the two known PGV values at point B are the basis for defining a scaling factor
that minimizes the least squares differences with respect to these two points.
This approach preserves the shape of the Point A hazard curve.
The scaling factor, 0.7963, minimizes the sum of the squared errors, based on a
least squares analysis. The small magnitude of the errors, +8% and -2%,
between the scaled Point A hazard curve and the known Point B values confirms
that this is a reasonable approach.
PGV values at Point B for various annual exceedance probabilities are calculated using a
log-linear interpolation for the annual exceedance frequency between the scaled points
defining the new hazard curve for Point B.
Input Data for the mean horizontal PGV hazard curve at Point A:
DTN: MO03061E9PSHA1.000.
PGV values are in cm/sec.
Input Data for mean horizontal PGV values at Point B:
Horizontal PGV value at Point B for the 10-6 mean annual exceedance probability, 2.44 m/s,
is from DTN: MO0303DPGVB106.002.
Horizontal PGV value at Point B for the 10-7 mean annual exceedance probability, 5.35 m/s,
is from DTN: MO0210PGVPB107.000.
First, define the PGV value at Point A for the annual exceedance frequency of 1e-06,
based on a log-linear interpolation scheme.
Annual Point A Interpolated
Exceedance Horizontal Value At
Frequency PGV Point A
(1/yr) (cm/sec)
3.07E-06 2.00E+02 3.30E+02
2.28E-07 5.00E+02
Second, define the PGV value at Point A for the annual exceedance frequency of 1e-07,
based on a log-linear interpolation scheme.
Annual Point A Interpolated
Exceedance Horizontal Value At
Frequency PGV Point A
(1/yr) (cm/sec)
2.28E-07 5.00E+02 6.60E+02
8.15E-08 7.00E+02
Third, use the Excel equation solver to find the value of the Scale Factor that minimizes
the sum of the square of the residuals with the known values at Point B.
Scale Factor 0.796294795
Known Scaled Value
Annual Point A for
Exceedance Horizontal Horizontal
Frequency PGV PGV
(1/yr)
Known
Point B Square
Horizontal of the Percent
PGV Residuals Error
(cm/sec)
(cm/sec)
(cm/sec)
(cm2/sec2)
(%)
1.00E-06 3.30E+02 2.62E+02 2.44E+02 339.1 7.55%
1.00E-07 6.60E+02 5.26E+02 5.35E+02 84.5 -1.72%
Sum: 423.6
Define the New Points for the Scaled PGV Hazard Curve at Point B:
PGV Scaling Factor 0.7963
Point A Scaled Annual
Horizontal Horiz. PGV Exceedance
PGV for Point B Frequency
(cm/sec) (cm/sec) (1/yr)
1.00E+01 7.96E+00 2.19E-03
2.00E+01 1.59E+01 6.26E-04
3.00E+01 2.39E+01 2.78E-04
5.00E+01 3.98E+01 9.30E-05
1.00E+02 7.96E+01 1.84E-05
2.00E+02 1.59E+02 3.07E-06
5.00E+02 3.98E+02 2.28E-07
7.00E+02 5.57E+02 8.15E-08
1.00E+03 7.96E+02 2.60E-08
1.50E+03 1.19E+03 6.56E-09
10
Interpolation for horizontal PGV values at Point B at 510-04, 10-04, 510-05,
-05, 10-06, 10-07, and 10-08 per year. The interpolation is linear in the log(.),
where . is the annual exceedance probability.
Points on the Point B Curve
Value of Bracketing This Value
Annual Annual Scaled % Error With
Known
Exceedance Exceedance Horizontal PGV Interpolated
Value of
Values
Frequency
(1/yr)
Frequency
(1/yr)
for Point B
(cm/sec)
PGV
(cm/sec)
At Point B for
10-6 and 10-7
5.00E-04 6.26E-04 1.59E+01 18.1
2.78E-04 2.39E+01
1.00E-04 2.78E-04 2.39E+01 38.8
9.30E-05 3.98E+01
5.00E-05 9.30E-05 3.98E+01 55.0
1.84E-05 7.96E+01
1.00E-05 1.84E-05 7.96E+01 106.70
3.07E-06 1.59E+02
1.00E-06 3.07E-06 1.59E+02 262.42 7.55%
2.28E-07 3.98E+02
1.00E-07 2.28E-07 3.98E+02 525.8 -1.72%
8.15E-08 5.57E+02
1.00E-08 2.60E-08 7.96E+02 1073
6.56E-09 1.19E+03
Ratio of PGV at 10-5 to PGV at 10-6: 0.4066
0 1000 1500
/)
/y
iilii1.00E-08
1.00E-07
1.00E-06
1.00E-05
1.00E-04
500
Horizontal PGV (cmsecAnnual Exceedance Frequency (1Pont A Hazard Curve
Scaled Hazard Curve for Pont B
Known Vaues at Pont B
Calculaton in Attachment I
Figure I-1. Scaled Hazard Curve for Point B
INTENTIONALLY LEFT BLANK
ATTACHMENT II
SPREADSHEET FOR WASTE PACKAGE DAMAGE ABSTRACTION
This spreadsheet contains the calculations that produce the
waste package damage abstraction described in Section 6.5.1.
The following worksheets are included:
(1)
results_80% YS
(2)
results_90% YS
(3)
fit_80%_90%_vs_Uniform_Dist
(4)
fit_80%_90%_Upper_Bound
The inputs, outputs, and formulas used in each worksheet are described below.
(1) results_80% YS
This worksheet is a copy of the results presented in Tables 6 and 7 (see column
labeled Cumulative Damaged area expressed as % of total area) for the damaged
areas from vibratory ground motion for 80% of yield strength (YS) failure threshold.
Minimum, maximum, mean, and standard deviation of the damaged areas are
calculated for the results.
The PGV values are from DTN: MO0303DPGVB106.002 and
DTN: MO0210PGVPB107.000. The damaged areas are from BSC 2003b
Table 6.1.4-2; BSC 2003c, Table 16.
(2) results_90% YS
This worksheet is a copy of the results presented in Tables 6 and 7 (see column
labeled Cumulative Damaged area expressed as % of total area) for the damaged
areas from vibratory ground motion for 90% of yield strength (YS) failure threshold.
Minimum, maximum, mean, and standard deviation of the damaged areas are
calculated for the results.
The PGV values are from DTN: MO0303DPGVB106.002 and
DTN: MO0210PGVPB107.000. The damaged areas are from BSC 2003b,
Table 6.2.4-2; BSC 2003c, Table 17.
3) Avg_80%_90%_vs_Uniform_Dist
In this worksheet, the cumulative % damage area is computed as the average
of the 80% YS and 90% YS results given in worksheets (1) and (2).
These average values are shown in column B.
The average values are then sorted in ascending order in column C.
The cumulative probability is computed for each point in column D.
Finally, the points are compared with a least squares fit to a straight line
determined by Excel's fitting routine for PGV of 2.44 m/s and for the PGV of 5.35 m/s.
The equation of the straight line and the r^2 value for the fit is also shown.
(4) Avg_80%_90%_Upper_Bound
In this worksheet, the cumulative % damage area is computed as the average
of the 80% YS and 90% YS results given in worksheets (1) and (2).
These average values are shown in columns B and D.
Then, the 95% upper confidence limit associated with this value is computed
Using 95% UCL = (a)(-1/(n-1))  max{observed value}
where a = 0.05 is the level of significance and UCL = upper confidence limit.
This is shown in Row 26 for PGV of 2.44 m/s and 5.35 m/s.
These formulas are by Rossman et al. (1998).
Also shown in this worksheet are three graphs of percent failed area versus PGV.
The magenta squares and diamonds are the computed % cumulative damage.
The red squares are the Bayesian 95% UCL in Row 26 of this worksheet.
Three graphs then present (1) comparison of the Bayesian upper bound with the
damaged areas for PGV of 2.44 m/s and 5.35 m/s, (2) a comparison of the upper
bound with the results for PGV of 2.44 m/s, 5.35 m/s, and 1.067 m/s, and
(3) a comparison of the upper bound for the lognormal distribution,
derived in Attachment III, with the upper bound for the uniform distribution.
(1) results_80% YS
Cum. %
Damage Cum. % Damage
at 1E-06 1/yr
for 80% of PGV
at 1E-07 1/yr
for 80% of
PGV (m/s) Yield (m/s) Yield
2.44 0.092% 5.35 1.280%
2.44 0.060% 5.35 1.840%
2.44 0.710% 5.35 0.820%
2.44 0.530% 5.35 0.960%
2.44 0.530% 5.35 1.670%
2.44 0.640% 5.35 1.280%
2.44 0.460% 5.35 1.490%
2.44 0.430% 5.35 0.140%
2.44 0.050% 5.35 1.740%
2.44 0.300% 5.35 1.060%
2.44 0.270% 5.35 0.570%
2.44 0.110% 5.35 0.530%
2.44 0.057% 5.35 0.099%
2.44 0.099% 5.35 1.030%
min 0.050% 0.099%
max 0.710% 1.840%
mean 0.310% 1.036%
stnd, dev. 0.237% 0.560%
confidence 95% 95%
alphaupper conf
limit
5%
0.894%
5%
2.317%
Ref: Rossman et al.
1998
(2) results_90% YS
Cum. % Cum. %
Damage Damage
at 1E-06 1/yr
for 90% of PGV
at 1E-07 1/yr
for 90% of
PGV (m/s) Yield (m/s) Yield
2.44 0.046% 5.35 0.920%
2.44 0.032% 5.35 0.890%
2.44 0.290% 5.35 0.530%
2.44 0.240% 5.35 0.530%
2.44 0.230% 5.35 0.600%
2.44 0.230% 5.35 0.600%
2.44 0.200% 5.35 0.740%
2.44 0.220% 5.35 0.074%
2.44 0.025% 5.35 1.030%
2.44 0.130% 5.35 0.390%
2.44 0.130% 5.35 0.300%
2.44 0.057% 5.35 0.250%
2.44 0.026% 5.35 0.071%
2.44 0.043% 5.35 0.500%
min 0.025% 0.071%
max 0.290% 1.030%
mean 0.136% 0.530%
stnd, dev. 0.097% 0.298%
confidence 95% 95%
alphaupper conf
limit
5%
0.365%
5%
1.297%
Ref: Rossman et al.
1998
(3) Avg_80%_90%_vs_Uniform_Dist
Cum. %
Damage
PGV (m/s)
at 1E-06 1/yr
for AverageYS
Sorted %
Damage
Cumulative
Probability
()
2.44 0.069% 0.038% 0.036
2.44 0.046% 0.042% 0.107
2.44 0.500% 0.046% 0.179
2.44 0.385% 0.069% 0.250
2.44 0.380% 0.071% 0.321
2.44 0.435% 0.084% 0.393
2.44 0.330% 0.200% 0.464
2.44 0.325% 0.215% 0.536
2.44 0.038% 0.325% 0.607
2.44 0.215% 0.330% 0.679
2.44 0.200% 0.380% 0.750
2.44 0.084% 0.385% 0.821
2.44 0.042% 0.435% 0.893
2.44 0.071% 0.500% 0.964
Cum. %
Damage
PGV (m/s)
at 1E-07 1/yr
for Average
YS
Sorted %
Damage
Cumulative
Probability
()
5.35 1.100% 0.085% 0.036
5.35 1.365% 0.107% 0.107
5.35 0.675% 0.390% 0.179
5.35 0.745% 0.435% 0.250
5.35 1.135% 0.675% 0.321
5.35 0.940% 0.725% 0.393
5.35 1.115% 0.745% 0.464
5.35 0.107% 0.765% 0.536
5.35 1.385% 0.940% 0.607
5.35 0.725% 1.100% 0.679
5.35 0.435% 1.115% 0.750
5.35 0.390% 1.135% 0.821
5.35 0.085% 1.365% 0.893
5.35 0.765% 1.385% 0.964
yR2liili)
iiilli i
= 174.65x + 0.111
= 0.946
0.0
0.2
0.4
0.6
0.8
1.0
0.0% 0.1% 0.2% 0.3% 0.4% 0.5% 0.6%
% Damaged Area on Waste Package
Cumuatve Probabty (Data
CDF for Unform Distrbuton
Cacuatonn Attachment II
Figure II-1. Comparison of Damage Results for 10-6 per Year Ground Motions with a Uniform Distribution
R2
(-)
iiilli iy = 69.959x -0.048
= 0.9685
0.0
0.2
0.4
0.6
0.8
1.0
0.0% 0.2% 0.4% 0.6% 0.8% 1.0% 1.2% 1.4% 1.6%
% Damaged Area on Waste Package
Cumulative ProbabilityData
CDF for Unform Distrbuton
Cacuatonn Attachment II
Figure II-2. Comparison of Damage Results for 10-7 per Year Ground Motions with a Uniform Distribution
MDL-WIS-PA-000003 REV 00 II-6 of II-10 August 2003
(4) Avg_80%_90%_Upper_BoundCum. % Cum. % Cum. %
Damage Damage Damage
at 1E-06 1/yr at 1E-07 1/yr at 1E-05 1/yr
PGV (m/s) for Average PGV (m/s) for Average PGV (m/s) for Average
2.44 0.069% 5.35 1.100% 1.067 0.0105%
2.44 0.046% 5.35 1.365% 1.067 0.0000%
2.44 0.500% 5.35 0.675% 1.067 0.0255%
2.44 0.385% 5.35 0.745%
2.44 0.380% 5.35 1.135%
2.44 0.435% 5.35 0.940%
2.44 0.330% 5.35 1.115%
2.44 0.325% 5.35 0.107%
2.44 0.038% 5.35 1.385%
2.44 0.215% 5.35 0.725%
2.44 0.200% 5.35 0.435%
2.44 0.084% 5.35 0.390%
2.44 0.042% 5.35 0.085%
2.44 0.071% 5.35
Minimum 0.038%
Maximum 0.500%
Mean 0.223%
Standard
Deviation 0.166%
0.765%
0.085% 0.000%
1.385% 0.026%
0.783% 0.012%
0.420% 0.013%
Calculation of Bayesian Maximum:
Confidence 95% 95% 95%
Alpha 5%5% 5%
Upper Conf Limit 0.630% 1.744% 1.067 0.114%
Ref: Rossman et al. 1998
Plot the Straight Line Through the Bayesian Maxima:
Upper
PGV (m/s) Limit (%)
2.44 0.63%
5.35 1.74% Plot the Linear Fit:
Slope 0.003829389 PGV Damage
y-intercept -0.00305 0.7959322 0
x-intercept 0.795932203 8 0.02758718
Plot Maximum of Lognormal Distribution (Attachment III, Eq. III-9):
PGV Damage
0.7
0.0002%
7.6
3.01%
3.0%
Percent of Failed Area Per WP (-)
2.5%
2.0%
1.5%
1.0%
0.5%
0.0%
1e-6 ground motion level
1e-7 ground motion level
upper bound values
Linear Fit to Upper Bound
0 24 68
Peak Ground Velocity (PGV) (m/s)
Calculation in Attachment II
Figure II-3. Linear Fit to Bayesian Upper Bound of Damage Distribution
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
0 2 4 6 8
) (m/s)
l(-)
il
il
lues
iil
iPeak Ground Velocity (PGVPercent of Faied Area Per WP
1e-6 ground moton leve1e-7 ground moton leveupper bound vaLinear Ft to Upper Bound
1e-5 ground moton leveCalculaton in Attachment II
Figure II-4. Comparison of Linear Fit to Bayesian Upper Bound of Damage Distribution with the Damage
Results for the 10-5 per Year Ground Motions
Figure II-5. Comparison of Upper Bounds Based on a Lognormal Distribution (Blue Curve) with the
Bayesian Upper Bound
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
0 2 4 6 8
) (m/s)
i(-)
ion ll
ion ll
Liiion ll
iPeak Ground Velocity (PGVPercent of Faled Area Per WP
1e-6 ground moteve1e-7 ground moteveupper bound values
near Ft to Upper Bound
1e-5 ground moteveUpper Bound - Lognormal Dist.
Calculaton in Attachment II
INTENTIONALLY LEFT BLANK
ATTACHMENT III
REVIEW COMMENTS ON RESPONSE SURFACE FOR WASTE PACKAGE DAMAGE
FROM VIBRATORY GROUND MOTION
by R. P. Kennedy
Review Comments on Response Surface
for Waste Package Damage from Vibratory
Ground Motion1
R.P. KennedyJune 2003
III.1. Introduction
This report presents my review comments on the response surface for waste package
damage from vibratory ground motion developed and presented in Section 6.5.1 of Ref. III.1.
Damage is defined in terms of the percentage of damaged area D. The response surface
defines the exceedance probability EP that the defined percentage of damaged area D might be
exceeded as a function of the peak ground velocity PGV,
III.1.1 Symbols and Units Used Herein
D = Percentage of damaged area (%)
DUB = Upper bound on D (%) as a function of PGV
D80 = Value of D obtained using 80% yield criteria
D90 = Value of D obtained using 90% yield criteria
EP = Exceedance Probability (%)
NEP = Non-Exceedance Probability (%)
PGV = Peak ground velocity (m/sec)
U = Uniform damage surface defined by Eqns. (III-1) and (III-2)
LN = Lognormal damage surface defined by Eqn. (III-9)
III.1.2 Response Surface Recommended in Ref. III.1
Ref. III.1 defines an upper bound DUB (%) on D as a function of PGV (m/sec) by:
DUB = 0.383(PGV)  0.305 (III-1)
At any given PGV, Ref. III.1 assumes the percentage of damaged area D(%) is uniformly
distributed between zero and DUB. Thus, the exceedance probability EP(%) for any specified D
conditional on the given PGV is defined by:
...
1
DUB
D
.
..
(%)100 (III-2)
EP
=
-
1 Section numbers, table numbers, equation numbers, and reference numbers have been changed by adding a III
to distinguish this attachment from the main body of the text. No other changes have been made to the content of
this independent review, beyond these editorial changes.
MDL-WIS-PA-000003 REV 00 III-2 of III-12 August 2003
Representation of the damage response surface by Eqns. (III-1) and (III-2) is attractive
because it is very easy to use. However, several conservatisms and unconservatisms are
embedded into the development of the damage surface represented by Eqns. (III-1) and (III-2).
It is not intuitively obvious whether Eqns. (III-1) and (III-2) provide an adequate representation
of the damage surface. It is also questionable as to how far this damage surface can be
extrapolated beyond the limited data base. Over what range of PGV values and what range of D
values is it reasonable to express the damage surface by Eqn. (III-1) and (III-2)?
The damage surface defined by Eqns. (III-1) and (III-2) will be called herein the
Uniform damage surface and will be represented in the attached tables by the symbol U.
III.1.3 Scope of Review
Starting with the same data base defined in Tables 6 and 7 of Ref. III.1, I have developed
in Section III.2 a more complex description of the damage surface. This more complex damage
surface attempts to correct the unconservatisms and conservatisms described subsequently
associated with the U damage surface. This more complex damage surface is defined by
lognormally distributed exceedance probabilities EP as a function of both D and PGV, and will
be called herein the Lognormal damage surface and will be represented in the attached tables
by the symbol LN.
Exceedance probability EP results computed using this LN damage surface will be
compared with those computed for the U damage surface. Recommendations concerning both
the LN and U damage surface representations are presented in Section III.3.
III.1.4 Data Base Used to Develop Damage Surface Representations
Nonlinear time history analyses were performed for the following two ground motion
levels:
PGV = 2.44 m/sec
(III-3)
PGV = 5.35 m/sec
The results are reported in Tables 6 and 7 of Ref. III.1. A total of 14 analyses for PGV = 2.44
m/sec are summarized in Table 6 of Ref. III.1. A total of 14 analyses for PGV = 5.35 m/sec are
summarized in Table 7 of Ref. III.1. Two damage thresholds are used to compute the percentage
of damaged area D for each analytical simulation. These two damage thresholds are:
1.) Damage occurs where the residual stress exceed 80% of yield (called 80% yield
criteria)
2.) Damage occurs where the residual stress exceeds 90% of yield (called 90% yield
criteria)
It is outside of my expertise to comment on these damage threshold criteria. Furthermore, I have
not reviewed any of the nonlinear analyses from which the percentage of damaged area D
reported in Tables 6 and 7 of Ref. III.1 were obtained.
The results presented in Tables 6 and 7 of Ref. III.1 are tabulated herein in Tables III-1
and III-2 in which these results are ordered in the order of increasing percentage of damaged area
D. Also shown in Tables III-1 and III-2 is the non-exceedance probability NEP corresponding to
each of these ordered results as computed from:
n - 5.0
NEP = (%)100(III-4)
N
where N is the total number of trials and n is the ordered trial number. The results shown in
Tables III-1 and III-2 are the basis for both the U damage surface developed in Ref. III.1 and the
LN damage surface presented herein in Section III.2.
Ref. III.1 has assumed a uniform distribution of D between a lower bound value D90
based on the 90% yield criteria to an upper bound value D80 based on the 80% yield criteria.
This assumption seems reasonable and will be made herein as well.
III.1.5 Comments on Development of U Damage Surface
As noted earlier, several conservatisms and unconservatisms are embedded into the
development of the U damage surface developed in Ref. III.1. These conservatisms and
unconservatisms will be briefly discussed in the subsections of this section.
III.1.5.1 Establishment of Upper Bound DUB
Ref. III.1 developed a mean estimate of D for each of the trials from:
D =
D90 + D80 (III-5)
2
which is the appropriate equation for the mean D for a uniform distribution. However, Ref.
III.1 ignored the scatter of D about D . On average:
D80  2 D90 (III-6)
This scatter of D about D should be considered when establishing DUB. Since it was not
considered DUB was unconservatively established.
Secondly, DUB was established at the 95% upper confidence limit for the upper bound on
D . This upper bound DUB cuts off the uniform distribution at the 5% EP, and assumes 0% EP
beyond DUB. In most seismic risk evaluations, the fragility curve or damage surface between
about 1% EP and 5% EP significantly contributes to the mean computed annual risk when the
fragility curve or damage surface is convolved with the hazard curve.
For both of the above reasons, DUB has been unconservatively established. For example,
Ref. III.1 has established the following values of DUB.
PGV
DUB
(m/sec
(%)
2.44
0.630
5.35
1.744
Two of the 14 results reported in Table III-1 exceed DUB = 0.630% for the 80% yield criteria
case. Similarly two of the 14 results reported in Table III-2 are either at or exceed DUB = 1.744%
for the 80% yield criteria case.
III.1.5.2 Use of Uniform Distribution From Zero to DUB
For the U damage surface, Eqn. (III-2) is used to establish EP for any D corresponding to
a specified PGV. This uniform distribution is very conservative for the distribution shown in
Table III-1 for PGV = 2.44 m/sec. The trial results are not uniformly distributed, but are heavily
skewed to low D. The distribution shown in Table III-2 for PGV = 5.35 m/sec is more nearly
uniform and can be reasonably approximated by a uniform distribution.
III.1.5.3 Linear Variation of D With PGV
Eqns. (III-1) and (III-2) assume that DUB and D for any specified EP vary linear with
PGV. My experience with sliding and impact problems is that the sliding displacements and
impact velocities vary with PGV to a power greater than unity. If my past experience proves
correct for the current problem, then this linear variation of DUB and D with PGV may be
increasingly unconservative for PGV values greater than 5.35 m/sec. Conversely, some
conservatism may be introduced for PGV values between 2.44 m/sec and 5.35 m/sec. I am
concerned about the extrapolation of Eqn. (III-1) beyond the range of PGV between about 1.5
m/sec and 6.0 m/sec.
The most important region of a fragility curve or damage surface is typically between EP
values of 1% to 50%. Because of their shapes, either a lognormally distributed or normally
distributed fragility curve or damage surface will result in EP increasing faster than linear with
PGV over this important range. Therefore, these distributions can generally be extrapolated
further beyond the range of available data points. My preference is for the lognormal
distribution because within my experience, a lot of nonlinear computed fragility results
reasonably fit this distribution. However, even this distribution should not be extrapolated too
far. Extrapolation beyond the range of 1.5 m/sec to 8.0 m/sec is suspect even using a lognormal
distribution.
III.2. Development of Improved Damage Surface Estimation
III.2.1 Approach to Account for Variability of D between D80 and D90
Assuming D varies uniformly between D80 and D90, the cumulative NEP for various D
values can be estimated by the following procedure from the trial results presented in Tables III1
and III-2 for PGV = 2.44 m/sec and 5.35 m/sec, respectively. First determine the NEPTH for
the highest trial in Tables III-1 or III-2 for which D80 is less than the specified D. Next,
determine all of the trials for which D is between D90 and D80. For each of these trials find the
percentage associated with being less than D assuming a uniform distribution. Then, the NEP
associated with the specified D is given by:
%100
NEP = NEPTH +
N
.
.
...
DD80
-
-
DD9090 .
...
(III-7)
where N is the total number of trials, and the summation is performed only for the trials where D
is between D90 and D80. Lastly, the exceedance probability EP is given by:
EP = 100% - NEP (III-8)
The NEP or EP for D values less than the lowest D90 or greater than the highest D80 in
Table III-1 for PGV = 2.44 m/sec or Table III-2 for PGV = 5.35 cannot be estimated by the
above procedure. There are insufficient numbers of trials to cover these D values. The NEP for
D below the lowest D90 is less than the lowest NEP in the tables, and the NEP for D higher than
the highest D80 is greater than the highest NEP in the tables. Values of NEP for D in these
regions are estimated by judgment.
Table III-3A presents the estimated EP values obtained for various D from the data in
Tables III-1 and III-2 using the above procedure. Table III-3A becomes the data base for
establishing the damage surface.
III.2.2 Improved Approximation of Damage Surface
A lognormally distributed approximation of the damage surface was fit by trial and error
to the exceedance probability EP data shown in Table III-3A. The following lognormal
distribution was found to provide a good fit to Table III-3A:
Lognormal Distribution Parameters
Median : PGV50 = (5.7 m/sec)D0.5
Log. Std. Dev.:  = 0.28D-0.5 = 0.8 (III-9)
Truncation Point: EP = 1 %
A practical problem associated with the use of the lognormal distribution is that it will
predict small EP values even at very low PGV values. For sliding and impact problems, the
extreme lower tail of the lognormal distribution should not be used because damage wont occur
for low PGV values. A practical solution to this problem is to truncate the lognormal
distribution at an EP of about 1.0%. Below this level EP should be taken as zero. Nonlinear
analyses performed for lower PGV levels would enable this truncation point to be better defined.
However, the above recommendation has proven to be adequate for all risk assessments of which
I am aware that have included sliding and impact fragilities.
Table III-3B show the EP predicted by the lognormal LN damage surface defined by the
parameters in Eqn. (III-9). Good agreement exists between Table III-3B and Table III-3A except
for the D = 0.03% and PGV = 2.44 m/sec case. The agreement for this case could be improved
by use of a more complex equation for the logarithmic standard deviation . However, this
improvement was considered to be unnecessary because the computed risk is insensitive to EP
when EP exceeds about 70%. Therefore, even for D = 0.03% and PGV = 2.44 m/sec, the fit is
more than adequate.
III.2.3 Comparison of Uniform U Damage Surface With Table 3A
Table III-3C shows the EP predicted by the uniform U damage surface used in Ref. III.1
for the same cases shown in Table III-3A. The agreement is not as good as that obtained from
the LN damage surface approximation.
For PGV = 5.35 m/sec, the U damage surface provides a good approximation to the Table
III-3A results except for D greater than about 1.67% where the U damage surface estimate of EP
becomes seriously unconservative. This unconservatism could have significant unconservative
consequences for estimating the annual probability of exceeding higher values of D.
For PGV = 2.44 m/sec, the U damage surface approximation significantly overestimates
EP for D between 0.06% and 0.56%. However, a more significant issue is that the U damage
surface significantly underestimates EP for D greater than 0.60%.
This unconservatism at higher D values can be easily corrected by changing Eqn. (III-1)
to slightly increase DUB. The unconservatism shown when comparing Table III-3C with Table
III-3A is eliminated when:
DUB = 0.436(PGV)  0.305 (III-10)
is used instead of Eqn. (III-1). The resulting DUB values become:
PGV
DUB
(%)
(m/sec
2.44
0.759
5.35
2.028
These DUB values lie at about the EP = 1% level based upon the data presented in Table III-3A.
They also adequately exceed the highest D80 values shown in Tables III-1 and III-2.
MDL-WIS-PA-000003 REV 00 III-7 of III-12 August 2003
II.2.4 Extension of Damage Surface to Other PGV Values
Nonlinear analyses have only been performed for PGV of 2.44 m/sec and 5.35 m/sec.
However, it is necessary to extend the candidate damage surfaces over as broad a range of PGV
values and D values as is credible. Table III-4 extends the estimated damage surface over the
range of PGV from 1.5 m/sec to 8.0 m/sec, and D from 0.03% to 2.0%. This range is the
maximum range over which I believe it is credible to extend the nonlinear results summarized in
Tables III-1 and III-2.
Table III-4 shows the exceedance probabilities EP predicted by both the uniform U
damage surface proposed in Ref. III.1 and the lognormal LN damage surface proposed in Section
2.2. Over the majority of the damage surface region covered by Table III-4, the U damage
surface approximation provides a conservatively biased estimate of EP. In my judgment, the
amount of conservative bias is not sufficient to seriously over predict the annual probability of
exceeding any specified D when this damage surface is convolved with a seismic hazard curve.
However, there are a few regions where the U damage surface is significantly
unconservative. These regions are identified by a dash __ under the U predicted values. These
under prediction regions could have an important unconservative effect on predicted annual
probability of exceeding a specified D because they all occur at low EP values within the range
that generally significantly influences the annual probability of exceedance. These underlined
under predictions of EP should be eliminated by the following suggestions.
First, the U damage surface proposed in Ref. III.1 should not be extended to PGV values
greater than about 6.0 m/sec. Extension to higher PGV values is likely to become seriously
unconservative for the reason discussed in Section 1.5.3.
Secondly, the upper bound DUB should be defined by Eqn. (III-10) instead of Eqn. (III-1).
This change will resolve the issues discussed in Section 1.5.1.
III.3. Recommendations
III.3.1 Recommendations Concerning LN Damage Surface Representation
The LN damage surface representation defined by Eqn. (III-9) is judged to provide an
good description of the damage surface over the entire range of PGV and D values covered by
Table III-4. This range covers:
1.5m/sec = PGV = 8.0 m/sec
0.03% = D = 2.0% (III-11)
Extension of this LN damage surface representation beyond the range of Eqn. (III-11) becomes
questionable unless additional nonlinear analyses are performed.
An additional 15 nonlinear analyses conducted at a PGV of approximately 1.0 m/sec
should be sufficient to enable a modified LN damage surface to be extended down to about 0.5
m/sec for D = 0.03% and larger. However if percent damage areas less than 0.03% are also
required, it will be necessary to perform nonlinear analyses at two PGV levels below 2.44 m/sec.
The existing nonlinear analysis results are not helpful in defining the important region of the
damage surface from EP = 1% to 70% for D less than 0.03%.
It is unlikely that the damage surface needs to be extended beyond PGV of 8.0 m/sec
because such a high PGV is not very credible at least in my judgment. However, it might be
necessary to define the damage surface for percent damage area D greater than 2%. Nonlinear
analyses would have to be conducted at a ground motion significantly above PGV of 5.35 m/sec
to enable the damage surface to be extended above D = 2.0%. Ideally, the PGV for these
additional analyses should be selected so that the nonlinear simulations produced D in the range
of 1.5% to 10% if D needs to be extended beyond 2%.
III.3.2 Recommendations Concerning U Damage Surface Representation
The primary advantage of the U damage surface representation presented in Ref. III.1 is
the ease with which it can be used. With one correction, this U damage surface representation is
judged to provide a more than adequate representation of the damage surface over the following
range:
1.5m/sec = PGV = 6.0 m/sec
0.03% = D = 2.0% (III-12)
The one recommended correction is that DUB used in Eqn. (III-2) should be computed by Eqn.
(III-10) as opposed to Eqn. (III-1) recommended in Ref. III.1.
It is very questionable whether a linear equation such as either Eqn. (III-1) or (III-10) can
be extended to cover a range of PGV values larger than about a factor of four. Therefore if the
PGV range defined in Eqn. (III-12) must be extended, it is questionable whether the
simplification of the U damage surface representation format can be maintained over a broader
PGV range.
References
III.1 Seismic Consequences Abstraction Report, Draft, Rev00C, June 2003
Table III-1: Percentage Damaged Area D
Obtained From Nonlinear Analyses for
PGV = 2.44 m/sec
NEP (%)
D(%)
80% Yield 90% Yield
Criteria Criteria
3.57 .050 .025
10.71 .057 .026
17.86 .060 .032
25.0 .092 .043
32.14 .099 .046
39.29 .11 .057
46.43 .27 .13
53.57 .30 .13
60.71 .43 .20
67.86 .46 .22
75.0 .53 .23
82.14 .53 .23
89.29 .64 .24
96.43 .71 .29
Table III-2: Percentage Damaged Area D
Obtained From Nonlinear Analyses for
PGV = 5.35 m/sec
NEP (%)
D(%)
80% Yield 90% Yield
Criteria Criteria
3.57 .099 .071
10.71 .14 .074
17.86 .53 .25
25.0 .57 .30
32.14 .82 .39
39.29 .96 .50
46.43 1.03 .53
53.57 1.06 .53
60.71 1.28 .60
67.86 1.28 .60
75.0 1.49 .74
82.14 1.67 .89
89.29 1.74 .92
96.43 1.84 1.03
Table III-3: Exceedance Probabilities EP for
Various Damage Area Percentages D and
Peak Ground Velocities PGV
Table III-3A: Nonlinear Data Results From Tables III-1 and III-2
PGV D(%)
(m/sec) .03 .06 .12 .25 .50 .75 1.00 1.25 1.5 1.75 2.0
2.44
5.35
97.6
X
77.4
98.5
60.7
91.5
46.0
89.3
11.1
75.8
1.5
55.8
X
35.1
X
19.8
X
10.2
X
4.4
X
2.0
Table III-3B: Lognormal LN Damage Surface Approximation
PGV D(%)
(m/sec) .03 .06 .12 .25 .50 .75 1.00 1.25 1.5 1.75 2.0
2.44
5.35
87.1
98.3
75.7
95.3
60.4
89.4
39.1
87.0
10.2
76.3
1.5
59.8
0
41.0
0
24.2
0
12.9
0
5.2
0
1.9
Table III-3C: Uniform U Damage Surface Approximation
PGV D(%)
(m/sec) .03 .06 .12 .25 .50 .75 1.00 1.25 1.5 1.75 2.0
2.44
5.35
95.2
98.3
90.5
96.6
80.9
93.1
60.3
85.7
20.6
71.3
0
57.0
0
42.7
0
28.3
0
14.0
0
0
0
0
Table III-4: Exceedance Probability EP Extended Over
A Wide Range of PGV
PGV Damage Area Percent DP(%)
(m/sec) .03 .06 .12 .25 .5 .75 1.0 1.25 1.5 1.75 2.0
1.5 LN
U
69.9
88.9
53.6
77.7
36.6
55.5
12.6
7.2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2.0 LN
U
81.1
93.5
67.3
87.0
50.6
74.0
26.4
45.8
3.8
0
0
0
0
0
0
0
0
0
0
0
0
0
3.0 LN
U
91.7
96.4
83.0
92.9
69.9
85.8
53.6
70.4
22.8
40.8
6.2
11.1
1.1
0
0
0
0
0
0
0
0
0
4.0 LN
U
95.9
97.6
90.6
95.1
81.1
90.2
72.8
79.6
49.2
59.3
25.8
38.9
10.3
18.5
3.1
0
0
0
0
0
0
0
5.0 LN
U
97.9
98.1
94.5
96.3
87.7
92.6
84.2
84.5
70.7
68.9
51.6
53.4
32.0
37.9
16.6
22.4
7.4
6.8
2.6
0
0
0
6.0 LN
U
98.8
98.5
96.6
97.0
91.8
94.0
90.8
87.5
84.2
74.9
72.7
62.4
57.3
49.8
40.5
37.3
25.4
24.7
14.0
12.2
6.8
0
7.0 LN
U
99.3
98.7
97.8
97.5
94.3
95.0
94.6
89.5
91.8
79.0
86.0
68.4
76.8
57.9
64.6
47.4
50.5
36.9
36.3
26.4
23.8
15.8
8.0 LN
U
99.6
98.9
98.5
97.8
96.0
95.7
96.0
90.9
95.8
81.9
93.2
72.8
88.7
63.8
81.8
54.7
72.4
45.6
61.0
36.6
48.5
27.5
ATTACHMENT IV
SPREADSHEET FOR DRIP SHIELD DAMAGE ABSTRACTION FROM ROCKFALL
This spreadsheet contains the calculations that produce the drip shield damage
abstraction for rock blocks in the nonlithophysal zones, as described in
Section 6.6.1 of this report.
This spreadsheet is not reproduced here because it is very complex, with
large tables and many graphics. This Attachment summarizes the contents
of the 15 worksheets in the spreadsheet, including sources of input information
and the outputs from the calculations. The reader is referred to the electronic file
on CD-ROM to view the details of the calculations.
The following worksheets are included:
(1)
rockfall 1e-7
(2)
block information 1e-7
(3)
rockfall 1e-6
(4)
block information 1e-6
(5)
selected blocks
(6)
Impact information
(7)
intermediate pivot calculation
(8)
impact information by case
(9)
1e-7 CDF fit
(10)
1e-7 CDF chart
(11)
1e-6 CDF fit
(12)
1e-6 CDF chart
(13)
statistics
(14)
mode_PGV
(15)
frac_no_fail PGV
The inputs, outputs, and formulas used in each worksheet are described below.
(1)
rockfall 1e-7
This worksheet is a copy of the results presented in DTN: MO0301MWD3DE27.003
and shows the overall amount of rockfall on a case by case basis for each combination
of ground motion time history and synthetic fracture pattern.
No new calculations have been done.
(2) block information 1e-7
This worksheet is a copy of the results presented in DTN: MO0301MWD3DE27.003
and shows the details of rockfall on a case by case basis for each combination
of ground motion time history and synthetic fracture pattern.
No new calculations have been done.
(3) rockfall 1e-6
This worksheet is a copy of the results presented in DTN: MO0305MWDNLRKF.001.
and shows the overall amount of rockfall on a case by case basis for each combination
of ground motion time history and synthetic fracture pattern.
No new calculations have been done.
(4) block information 1e-6
This worksheet is a copy of the results presented in DTN: MO0305MWDNLRKF.001.
and shows the details of rockfall on a case by case basis for each combination
of ground motion time history and synthetic fracture pattern.
No new calculations have been done.
(5) selected blocks
Here, the blocks selected for detailed structural response calculations and the results
of these calculations are presented. The first two columns are a summary of Table 10
in this report, and the last 3 columns are a summary of Table 11 in this report.
The only calculations is shown in Column 3, where the natural logarithm of
column 2 is calculated. The Figure IV-1 shows the coordinate system
for the finite-element grid. Note the rockfall angles.
(6) impact information
In this worksheet, the block information for the 1e-6 and 1e-7 cases are combined for
convenience. Then, the information from "selected blocks" worksheet is used to
calculate the damage due to rockfall for all other cases by log-linear interpolation.
Figure IV-2 shows the angle sectors used to assign each impact angle to one of the classes
given in the "selected blocks" worksheet.
Note that the spreadsheet coordinate system origin (Figure IV-2, see below) is at
the vertical and horizontal center of the dripshield, whereas the finite element grid
coordinate system origin (Figure IV-1) is at the horizontal center and bottom of the
dripshield. Bins are created around the three discrete rockfall angles by bisection.
The angles that define the bins are shown in Figure IV-2. Column O shows the class
assignments based on each impact angle. In column P, the patch area is log-linear
interpolated for the given kinetic energy level (column N) and the angle information (column O)
from the six points given in the "selected blocks" worksheet.
In column Q, the number of rockfall events with damage for each case is computed
by simple summation.
(7) intermediate pivot calculation
In this worksheet, the pivot table feature of Excel is used to sum the total damaged
patch area for all events for a given case (column AV).
(8) impact information by case
This worksheet presents the total damaged patch area on a case by case basis for both
the 1e-6 per year and 1e-7 per year hazard levels. Column C shows the damaged patch
area in m^2 (same as column AV in previous worksheet). This is converted into a
percentage of the total area in Column D by dividing by 38.2667 m^2, which is
the surface area of the drip shield (BSC 2003g, Section 5.5.1).
Also, summary statistics for the failed area calculations are calculated using the
mean, median, standard deviation, min and max functions of Excel.
These statistics are also reported in Table 12 of the main text.
(9) 1e-7 CDF fit
This worksheet fits a triangular CDF to the logairthm of the percent failed patch area.
Column A contains the patch area for the 1e-7 per year hazard level case. Column B
contains the logarithm of Column A. Column C contains the fitted CDF.
Column D contains the actual CDF, and column E is the difference between columns
C and D. The triangular distribution is assigned a minimum value of -3 (i.e., minimum
percent failed patch area is 0.001%) and a maximum value of 2 (i.e., maximum percent failed
patch area is 100%). The mode is unknown and estimated by minimizing the squares
of column E using the "Solver" tool in excel. These calculations are shown in the block
shaded in yellow.
Here - Actual CDF = rank / (n+1),
where rank = rank of observation in ascending order and n = number of observations.
Also, the f_no_fail is the fraction of cases with no failure, computed by counting the
number of cases with zero failed patch area, and dividing by the number of observations.
(10) 1e-7 CDF chart
This worksheet compares the actual CDF to the fitted CDF. It is the source
for Figure 10 in the main text.
(11) 1e-6 CDF fit
This worksheet fits a triangular CDF to the logairthm of the percent failed patch area.
Column A contains the patch area for the 1e-6 per year hazard level case. The methodology
is the same as that used in the worksheet "1e-7 CDF fit".
(12) 1e-6 CDF chart
This worksheet compares the actual CDF to the fitted CDF. It is the source
for Figure 9 in the main text.
(13) statistics
This worksheet summarizes the statistics of the fits for the 1e-7 and 1e-6 cases.
The information is taken from the worksheets "1e-7 CDF fit" and "1e-6 CDF fit".
Also included are the assumed damage for the 5e-5 per year hazard level case,
as discussed in Section 6.6.1.4.
(14) mode_PGV
This worksheet shows a graph of the mode of percent failed area versus PGV using
information from the previous worksheet. Also shown is the power-law fit to the damage
using the "add trendline" option of Excel.
(15) mode_PGV
This worksheet shows a graph of the fraction of undamaged cases versus PGV using
information from the previous worksheet. Also shown is the power-law fit to the damage
using the "add trendline" option of Excel.
40
60
Vertical Corner
Drip Shield
Side-Wall
Figure IV-1. Coordinate System for the Finite-Element Grid
13.5
63.1
Side-Wall
Corner Vertical
Figure IV-2. Spreadsheet Coordinate System
INTENTIONALLY LEFT BLANK
ATTACHMENT V
REVIEW COMMENTS ON RESPONSE SURFACE FOR DRIP SHIELD DAMAGE
FROM ROCKFALL IN NONLITHOPHYSAL ZONE
by R. P. Kennedy
Review Comments on Response Surface
for Drip Shield Damage from Rockfall in
Nonlithophysal Zone2
R.P. KennedyJuly 2003
V.1. Introduction
This report presents my review comments on the response surface for drip shield damage
from rockfall in nonlithophysal zone developed and presented in Section 6.6.1 of Ref. V.1.
Damage is defined in terms of the percentage of damaged area D. The response surface
defines the exceedance probability EP that the defined percentage of damaged area D might be
exceeded as a function of the peak ground velocity PGV,
V.1.1
Symbols and Units Used Herein
V.1.2
Response Surface Recommended in Ref. V.1
Ref. V.1 recommends that the non-exceedance probability NEP0 (%) for no damage be
computed as a function of PGV(m/sec) by:
NEP0 = 60.1%(PGV)-0.735 (V-1a)
Thus, the exceedance probability EP0 for no damage is:
EP0 = 100% - NEP0 (V-1b)
D = Percentage of damaged area (%)
DM = Mode of D (%)
EP = Exceedance Probability (%)
EP0 = Zero damage exceedance probability (%)
EPD = Damage area exceedance probability conditional on damage occurring (%)
NEP = Non-Exceedance Probability (%)
NEP0 = Zero damage non-exceedance probability (%)
NEPD = Damage area non-exceedance probability conditional on damage occurring
(%)
PGV = Peak ground velocity (m/sec)
Given the condition that damage occurs, Ref. V.1 recommends that the mode (most
likely) percentage of damaged area DM be computed from:
2 Section numbers, table numbers, equation numbers, and reference numbers have been changed by adding a V to
distinguish this attachment from the main body of the text. No other changes have been made to the content of this
independent review, beyond these editorial changes.
DM = 0.0088%(PGV)3.7767 (V-2)
Furthermore, Ref. V.1 recommends that a log-triangular distribution be used to define the
conditional probability density function (PDF) on the percentage of damaged area D given the
condition that damage occurs. This PDF is zero at -3 (D = 0.001%) and at +2(D = 100%) and is
maximum at DM. Thus defining:
YM = Log (DM) (V-3a)
Y = Log (D) (V-3b)
the conditional exceedance probability EPD and non-exceedance probability NEPD for any
percentage of damaged area D are given by:
-3 < Y = YM
2
(
Y %20 + 3)NEPD =
YM + 3 (V-4a)
EPD = %100 - NEPD
2> Y = YM
2
(
2 %20 - Y)EPD =
2 - YM (V-4b)
NEPD = %100 - EPD
Lastly, the exceedance probability EP for any given damage area percentage D at a
specified PGV is given by:
EP = (EP0)(EPD) (V-5)
V.2.
Review Comment
V.2.1
Comment on Drip Shield Damage Criteria
Ref. V.1 assumes that the drip shield is damaged over any areas where the computed
residual stress due to rockfall impact exceeds 50% of yield. Considering the large uncertainty on
what residual stress level might ultimately lead to damage, I dont believe that a single
deterministic percentage of yield residual stress value should be used to define the damage area.
Instead, uncertainty bounds and a distribution function between these bounds should be
estimated for the residual stress associated with damage. Based on the discussion in Ref. V.1,
the deterministic 50% of yield criteria appears to be very conservative.
V.2.2 Comment on Ref. V.1 Damage Surface Equations
The Ref. V.1 damage surface equations (summarized herein in Section 1.2) were based
on nonlinear time history analyses for rockfalls associated with the following two ground motion
levels:
PGV = 2.44 m/sec (V-6)
PGV = 5.35 m/sec
The results are summarized in Worksheets (9) and (11) of the Excel Spreadsheet defined in
Attachment IV of Ref. V.1. These results are ordered from lowest to highest percentage of
damaged area D.
I have three comments on the development of the damage surface equations given in Ref.
V.1.
First, I believe that it would be preferable for the NEP and EP for each of the ordered trial
result tabulated in Worksheets (9) and (11) be computed from:
n - 5.0
NEP =(%) 100 (V-7)
N
EP = % 100 - NEP
where N is the total number of trials (60 in worksheet (9) for PGV = 5.35 m/sec, and 51 in
Worksheet (11) for PGV = 2.44 m/sec) and n is the ordered trial number.
Secondly, although Ref. V.1 does compare the conditional NEPD computed by Eqn. (V4)
versus the tabulated data, no overall comparison is made for EP computed from Eqn. (V-5)
versus the Worksheet data. Therefore, it is difficult for the reviewer to judge the overall
adequacy of the Ref. V.1 damage surface even at PGV of 2.44 m/sec and 5.35 m/sec. In order to
rectify this deficiency, I have compared the data base results (Da) with Ref. V.1 with the
predicted (Pr) EP for various D in Table V-1. I recommend that Ref. V.1 should contain a table
similar to Table V-1.
Third, even thought the Ref. V.1 damage surface equation was developed only from
multiple analyses at PGV of 2.44 m/sec and 5.35 m/sec, no PGV bounds are placed on the
proposed damage surface.
I make some recommendations in Section V.3 concerning the Ref. V.1 damage surface
for drip shield damage from rockfall in nonlithophysal zone.
V.3. Recommendations
For PGV = 2.44 m/sec, Table V-1 shows good agreement with the data for the Ref. V.1
predicted damage surface for all D from zero to 30%. For PGV = 5.35 m/sec, the agreement is
also good up to D of about 1.5%. Above D of about 1.5%, the predicted damage surface
becomes very conservative. This over prediction of EP occurs within a potentially important
region (EP between 1% and 50%) of the damage surface. It could lead to significant
overestimation of the annual probability of exceeding higher D percentages. So long as this
potential conservatism is acceptable, I consider the Ref. V.1 damage surface to be more than
adequate within the following range of PGV values.
Data is only available to define the damage surface at PGV values of 2.44 m/sec and 5.35
m/sec. Without data at other PGV values, I judge that it is highly suspect to extend the predicted
damage surface beyond the range of:
1.5 m/sec = PGV = 6.0 m/sec (V-8)
References
V.1. Seismic Consequences Abstraction Report, Rev00E, Draft, July 2003
Table V-1: Exceedance Probabilities EP for
Various Damage Area Percentages D and
Peak Ground Velocities PGV
PGV Damage Area Percent DP(%)
(m/sec) 0 0.01 0.03 0.10 .30 1.0 3.0 10.0 30.0
2.44 Da
Pr
75.5
68.8
69.9
63.1
53.9
56.3
45.9
45.9
41.1
33.8
20.4
21.2
10.9
12.3
7.0
5.3
1.2
1.5
5.35 Da
Pr
80.8
82.5
79.3
78.0
68.3
72.7
65.8
64.8
64.8
55.1
48.0
42.3
17.2
28.5
7.5
12.6
2.3
3.5
Da = Data
Pr = Predicted
INTENTIONALLY LEFT BLANK
ATTACHMENT VI
REVIEW COMMENTS ON RESPONSE SURFACE FOR DRIP SHIELD DAMAGE
FROM VIBRATORY GROUND MOTION
by R. P. Kennedy
Review Comments on Response Surface
for Drip Shield Damage from Vibratory
Ground Motion3
R.P. KennedyJuly 2003
VI.1. Introduction
This report presents my review comments on the response surface for drip shield damage
from vibratory ground motion developed and presented in Section 6.6.3 of Ref. VI.1.
Damage is defined in terms of the percentage of damaged area D. The response surface
defines the exceedance probability EP that the defined percentage of damaged area D might be
exceeded as a function of the peak ground velocity PGV.
VI.1.1 Symbols and Units Used Herein
D = Percentage of damaged area (%)
DUB = Upper bound on D (%) as a function of PGV
EP = Exceedance Probability (%)
NEP = Non-Exceedance Probability (%)
PGV = Peak ground velocity (m/sec)
U = Uniform damage surface defined by Eqns. (VI-1) and (VI-2)
LN = Lognormal damage surface defined by Eqn. (VI-4)
VI.1.2 Response Surface Recommended in Ref. VI.1
Ref. VI.1 defines an upper bound DUB (%) on D as a function of PGV (m/sec) by:
PGV Value DUB
(m/s) %
0.0 0
0.55 0
2.44 2.68
5.35 50
20 50
(VI-1)
At any given PGV, Ref. VI.1 assumes the percentage of damaged area D(%) is uniformly
distributed between zero and DUB. Thus, the exceedance probability EP(%) for any specified D
conditional on the given PGV is defined by:
3 Section numbers, table numbers, equation numbers, and reference numbers have been changed by adding a VI
to distinguish this attachment from the main body of the text. No other changes have been made to the content of
this independent review, beyond these editorial changes.
EP
1
...
=
D
.
-
(%)100(VI-2)
DUB
..
The damage surface defined by Eqns. (VI-1) and (VI-2) will be called herein the
Uniform damage surface and will be represented in the attached tables by the symbol U. In the
following sections, I will present my review comments on this at each of the PGV values
tabulated in Eqn. (VI-1).
VI.2 Damage Surface At PGV=2.44m/sec
VI.2.1 Comment on Drip Shield Damage Criteria Used At PGV=2.44m/sec
Ref. VI.1 assumes that the drip shield is damaged over any areas where the computed
residual stress due to rockfall impact exceeds 50% of yield. Considering the large uncertainty on
what residual stress level might ultimately lead to damage, I dont believe that a single
deterministic percentage of yield residual stress value should be used to define the damage area.
Instead, uncertainty bounds and a distribution function between these bounds should be
estimated for the residual stress associated with damage. Based on the discussion in Ref. VI.1,
the deterministic 50% of yield criteria appears to be very conservative.
VI.2.2 Comment on Uniform Damage Surface Equations At PGV = 2.44 m/sec
The percentage damage area D was computed in 14 simulations performed using
PGV=2.44m/sec ground motion records. The results are presented in Table 14 of Ref. VI-1.
These results are shown herein in Table VI-1 ordered from the lowest to highest D. Also shown
in Tables VI-1 is the non-exceedance probability NEP corresponding to each of these ordered
results as computed from:
NEP
=
n
-
5.0
(%)100(VI-3)
N
where N is the total number of trials and n is the ordered trial number.
Table VI-2 compares these data results with percent damage areas predicted from the
Uniform distribution U at PGV=2.44m/sec. It can be seen that the Uniform distribution defined
in Ref. VI.1 is very conservative for percent damage areas D from about 0.50 percent and higher.
It could lead to significant overestimation of the annual probability of exceeding D percentages
greater than 0.50 percent.
A much better fit at PGV=2.44m/sec is provided by the following lognormal distribution:
Lognormal LN
Median: D50 = 0.55% (VI-4)
Log. Std. Dev.:  = 0.85
Table VI-2 also shows the damage area percentage predicted by this Lognormal distribution LN.
This Lognormal distribution predicts the simulation results well, although it also tends to
overpredict the exceedance probability EP for D greater than about 1.25 percent. However, this
overprediction is much less than for the U distribution.
If the conservatism of the Uniform distribution U is unacceptable, one should consider
using the Lognormal distribution at PGV=2.44m/sec.
VI.3 Damage Surface At PGV=5.35m/sec and Higher
Five simulations were performed for ground motions with PGV=5.35m/sec. Ref.-VI.1
reports that large plastic deformations of the drip shield and separation between drip shields on
the order of 10 to 25 percent of the length of the drip shield occurred in each of the simulations.
This limited data is not a very adequate basis for estimating the exceedance probability
EP for various percent damage areas D at PGV =5.35m/sec. All that one can really say is that D
will be large.
The upper bound DUB=50 percent in Table 15 of Ref. VI-1 is probably reasonable at
PGV=5.35m/sec. However, a Uniform distribution, with a lower bound of zero is not reasonable
in my opinion. Considering increased corrosion rates due to high residual stresses as well as drip
shield separation, I would expect a lower bound on a Uniform distribution should be in excess of
10 percent at PGV=5.35m/sec. A more detailed review of the results of the five simulations
might allow this lower bound to be better established.
Considering both increased corrosion rates and drip shield separations, I would expect
both the upper bound and lower bound on a Uniform distribution for D to further increase as
PGV is increased above 5.35m/sec. I have no idea as to how one might estimate this further
increase. However, the percent damage areas at PGV=5.35m/sec for the drip shield might be
sufficiently high that further increases in D may not have much impact on the overall risk
assessment. The primary conclusion is that the drip shields are likely to be severely damaged at
a PGV=5.35m/sec or higher.
VI.4 Damage Surface At PGV=0.55m/sec
Ref. VI.1 assumes no damage occurs to the drip shield at a PGV of 0.55m/sec. This
assumption should be validated by performing a few simulations using PGV=0.55g ground
motion.
References
VI.I Seismic Consequences Abstraction Report, Draft, Rev00E, July 2003
Table VI-1: Percentage Damaged Area D
Obtained From Nonlinear Analyses for
PGV = 2.44 m/sec
NEP(%)
3.57
10.71
17.86
25.0
32.14
39.29
46.43
53.57
60.71
67.86
75.0
82.14
89.29
96.43
D(%)
0.12
0.14
0.26
0.26
0.27
0.30
0.50
0.65
0.67
0.98
1.12
1.19
1.25
2.13
Table VI-2: Exceedance Probabilities EP for
Various Damage Area Percentages D at
PGV=2.44m/sec
D%
0.12 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
Data 96.4 82.7 53.6 37.4 31.1 10.7 8.7 6.7 4.6
Uniform U 95.5 90.7 81.3 72.0 62.7 53.4 44.0 34.7 25.4
Lognormal LN 96.3 82.3 54.5 35.8 24.1 16.7 11.9 8.6 6.4
INTENTIONALLY LEFT BLANK
ATTACHMENT VII
SPREADSHEET FOR FAULT DISPLACEMENT DAMAGE ABSTRACTION
Assessment of Waste Package Failure Due To Fault Displacement
This spreadsheet summarizes the supporting calculations for Section 6.8 of this report.
Table VII-1. - Drip Shield Clearance Calculation (all units in mm) (basis for Table 19)
Drift diameter (Dd)
Invert thickness (Ti)
Drip Shield Height - Exterior (Hdse)
Drip Shield Height - Interior (Hdsi)
Clearance above Drip Shield (Hdsc)
Source or Formula
5500 BSC 2003i
806 BSC 2003i
2886 BSC 2003f
2716 BSC 2003f
1808 = Dd - Hdse - Ti
Table VII-2. Waste Package to Drip Shield Clearance (basis for Table 20)
(all units in mm - WP dimensions from BSC 2003j, Table 1)
Package Diameter Length Clearance
44-BWR 1674 5165 1042
24-BWR 1318 5105 1398
21-PWR 1644 5165 1072
12-PWR 1330 5651 1386
Naval-Long 1949 6065 767
Naval-Short 1949 5430 767
5DHLW/DOE SNF --Short 2110 3590 606
5DHLW/DOE SNF --Long 2110 5217 606
2-MCO/2-DHLW 1814 5217 902
The formula for calculating the clearance is given by Hdsi - Diameter
Table VII-3. Maximum Allowable Fault Displacement (in mm) (basis for Table 21)
Two values are provided - with and without drift collapse. In both cases,
the behavior of the invert and pallet is approximated by treating the emplacement
pallet as collapsed into the invert. No further collapse of the invert is accounted for.
With drift collapse, maximum allowable displacement = Hdsi - Diameter
Without drift collapse, maximum allowable displacement = Hdsi - Diameter + Hdsc
where Hdsc equals 1808-mm (see Table VII-2).
Package
44-BWR
24-BWR
21-PWR
12-PWR
Naval-Long
Naval-Short
5DHLW/DOE SNF Short
5DHLW/DOE SNF Long
2-MCO/2-DHLW
with collapse w/o collapse
1042 2850
1398 3206
1072 2880
1386 3194
767 2575
767 2575
606 2414
606 2414
902 2710
Table VII-4. Fault Displacement For Mean Hazard Curves (in cm) (basis for Table 23)
Based on Probabilistic Seismic Hazard Analyses (PSHA) (CRWMS M&O 1998
DTN: MO0004MWDRIFM3.002).
The values for the 1st two probabilities are from Table 8-1 of the cited reference.
The values for the latter three probabilities are obtained from interpolation within
DTN MO0004MWDRIFM3.002 and in Figures 8-2 through 8-14 for the appropriate fault.
Mean Annual Exceedance Probability (-)
Fault 1.00E-04 1.00E-05 1.00E-06 1.00E-07 1.00E-08
1 - Bow Ridge <0.1 7.8 72 220 600
2 - Solitario Canyon
(60 m offset) <0.1 32.0 190 500 >1000
3 - Drill Hole Wash <0.1 <0.1 17 80 240
4- Ghost Dance <0.1 <0.1 13 58 160
5 - Sundance <0.1 <0.1 6 42 ~145
6 - Unnamed <0.1 <0.1 13 70 210
7a <0.1 <0.1 2 20 ~75
7b <0.1 <0.1 1 6 9
7c <0.1 <0.1 0.1 <1 <1
7d <0.1 <0.1 <0.1 <0.1 <0.1
8a <0.1 <0.1 2 20 ~75
8b <0.1 <0.1 1 6 9
8c <0.1 <0.1 0.1 <1 <1
8d <0.1 <0.1 <0.1 <0.1 <0.1
9 <0.1 0.1 11 70 200
Table VII-5. Intersections of Known Faults With Emplacement Drifts (basis for Table 22)
Output from the Multi-scale TH model (DTN: LL030704623122.031, tspa03.mesh03-150w)
provides information on location of fault zones within each emplacement drift tunnel along with
whether that location is within the lower lithophysal zone or not. To correlate this information
to the specific fault in question, the location coordinates must be compared to a map of the
geologic fault locations (e.g., BSC 2003o). The results of this comparison are
summarized below. For each fault, the specific tunnels impacted in the lower lithophysal and
other zones are listed.
Abandoned Wash Fault (comes off Ghost Dance fault)
- Only intersects drifts 5-15 through 5-27, which are in the contingency area
Sundance Fault
lower lith other
1-8 none
1-7
1-6
Drill Hole Wash Fault
lower lith other
3-2 2-17E
3-1 2-16E
2-10W 2-15E
2-9W 2-14E
2-8W 2-13E
2-7W 2-12E
2-6W 2-11E
2-5W 2-10E
2-9E
Pagany Wash Fault
lower lith other
2-2W 2-7E
2-1W 2-6E
2-5E
2-4E
2-3E
2-2E
2-1E
Sevier Wash Fault
lower lith
2-2E
Table VII-6. Design Basis Waste Package Dimensions and Inventory (basis for Table 24)
(dimensions repeated from Table VII-2; waste package inventory from BSC 2003k, Table 11)
WP Configuration WP Length
(m)
WP
Diameter
(m)
Nominal
Quantity
21 PWR with APs 5.165 1.644 4299
21 PWR with CRs 5.165 1.644 95
12 PWR AP Long 5.651 1.330 163
44 BWR with APs 5.165 1.674 2831
24 BWR with APs 5.105 1.318 84
5 DHLW Short/1
DOE SNF Short
3.590 2.110 1147
5 DHLW Long/1
DOE SNF Long
5.217 2.110 1406
5 DHLW Long/1
DOE SNF Short
5.217 2.110 31
5 HLW Long Only 5.217 2.110 679
2-MCO/2-DHLW 5.217 1.814 149
Naval-Short 5.430 1.949 144
Naval-Long 6.065 1.949 156
NOTES: The diameter of DHLW packages and HLW package is taken to be that of the DHLW packages
in Table VII-2. The length of the DHLW Short package is taken to be that of the 5 DHLW/DOE
SNF - Short package in Table VII-2. The length of the DHLW Long and HLW Long packages is
taken to be that of the 5 DHLW/DOE SNF - Long package in Table VII-2.
AP = absorber plate; CR = control rod
Table VII-7. Simplified Groups of Waste Packages (basis for Table 25)
Average Total
WP
Configuration Length (m) Length (m) # packages %
PWR 5.1824 23616.123 4557 41.9%
BWR 5.1633 15050.935 2915 26.7%
Naval 5.760 1728.06 300 3.1%
HLW 4.670 15934.235 3412 28.3%
Total 56329.353 11184 100.0%
Total Length is given by package length times number of packages, summed over each package
type in the group.
Average length is given by Total length / Total number of packages in group.
% = Total length for that group / Total length for all groups.
The PWR group includes the 21 PWR AP, 21 PWR CR, and 12 PWR AP Long packages.
The BWR group includes the 44 BWR AP and the 24 BWR AP packages.
The Naval group includes the Naval-Short and Naval-Long packages.
The HLW group includes all packages containing HLW.
Table VII-8. Fault Exceedance Probabilities That Cause Failure in the Lower Lithophysal Zone
(basis for Table 27)
Using Figures 8-2 through 8-14 of the PSHA, along with the maximum allowable fault displacements
for each simplified waste package group as summarized in Table VII-3, one can
determine the fault displacement event probability required to cause failure for each waste package type.
This is done as follows:
-
the allowable fault displacement is given by the value from Table VII-3 (w/ drift collapse)
-
using Figures 8-4 (Drill Hole Wash), 8-6 (Sundance), and 8-8 (site 7a) the probability associated with
that magnitude of fault displacement is determined from the mean hazard curve
-
this is done for each waste package group
-
note that relative to the accuracy of these figures, the BWR and PWR groups are
shown with the same probability
-
The Drill Hole Wash results apply to Pagany Wash and Sevier Wash.
Fault HLW Naval BWR PWR
Sundance < 510-8 < 410-8 < 310-8 < 310-8
Drill Hole Wash < 210-7 < 110-7 < 610-8 < 610-8
Pagany Wash < 210-7 < 110-7 < 610-8 < 610-8
Sevier Wash < 210-7 < 110-7 < 610-8 < 610-8
7a/8a < 210-8 N/A N/A N/A
Table VII-9. Expected Number of Waste Packages Emplaced on Faults In
Lower Lithophysal Zone (basis for Table 28)
Table VII-5 can be used to determine the total number of waste packages impacted by each fault
in the lower lith (based on number of fault intersections with each tunnel). The results of Table VII-7
can then be used to calculate the expected number of waste packages of each type
(simplified grouping) that would be on a fault. These results are summarized below.
Total PWR BWR Naval HLW
Sundance 3 1.26 0.80 .09 0.85
Drill Hole, etc. 16 6.71 4.28 .49 4.53
7a/8a 117.3 49.18 31.34 3.60 33.18
Table VII-10. Expected Waste Packages Failures Versus Mean Annual Exceedance
Probability (basis for Table 29)
The results of Table VII-8 and Table VII-9 can now be combined to provide the expected number
of packages failed versus probability.
Annual Exceed.
Probability (1/yr)
Expected Number of Waste Package Failures
PWR BWR Naval HLW Total
> 210-7 0 0 0 0 0
110-7 to 210-7 0 0 0 4.53 4.53
610-8 to 110-7 0 0 0.49 4.53 5.02
510-8 to 610-8 6.71 4.28 0.49 4.53 16.00
410-8 to 510-8 6.71 4.28 0.49 5.37 16.85
310-8 to 410-8 6.71 4.28 0.58 5.37 16.94
210-8 to 310-8 7.97 5.08 0.58 5.37 19.00
110-8 to 210-8 7.97 5.08 0.58 38.56 52.18
INTENTIONALLY LEFT BLANK
ATTACHMENT VIII
REPRESENTATION OF ALEATORY AND EPISTEMIC UNCERTAINTY IN THE
CALCULATION OF EXPECTED DOSE FROM SEISMIC EVENTS AT THE
PROPOSED YUCCA MOUNTAIN FACILITY FOR THE DISPOSAL OF HIGH LEVEL
RADIOACTIVE WASTE
BY J. C. HELTON
Representation of Aleatory and Epistemic Uncertainty in theCalculation of Expected Dose from Seismic Events at theProposed Yucca Mountain Facility for the Disposal of HighLevel Radioactive Waste
J. C. Helton
Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1804 USA
and
Department 6849, MS 0779
Sandia National Laboratories
Albuquerque, NM 87185-0779 USA
VIII.1 INTRODUCTION
The following presentation provides a conceptual description of the calculation of expected doses (mrem/yr) to
reasonably maximally exposed individuals (RMEIs) that result from potential seismic events at the proposed Yucca
Mountain (YM) facility for the disposal of high-level radioactive waste.1, 2 A conceptual and representational
distinction is made between the effects and implications of aleatory and epistemic uncertainty in the assessment of
the effects of seismic events at the YM facility, with aleatory uncertainty arising from the many possible seismic
events that could occur over a time period of interest (e.g., 0 to 10,000 yr) and epistemic uncertainty arising from a
lack of knowledge with respect to quantities used in the characterization of aleatory uncertainty or in the calculation
of doses given the occurrence of a seismic event.3-6 Due to the low likelihood of seismic events at the YM facility,
traditional, integration-based importance sampling is introduced as a means to facilitate the computational
determination of expected doses (Ref.7, Section 4.3.1).
The presentation is organized as follows. Initially, the calculation of expected doses that result from aleatory
uncertainty in the occurrence and properties of seismic events is considered (Sect. VIII.2). Such doses are defined by
an integral over possible seismic events, and importance sampling is introduced as a means to accelerate the
convergence of numerical approximations to this integral. Then, the calculation of expected doses that result from
both aleatory uncertainty and epistemic uncertainty is considered (Sect. VIII.3). These doses are defined by a
double integral, with one integral over the possible seismic events that could occur and the other integral over
imprecisely known analysis inputs. Thus, one integral relates to aleatory uncertainty, and the other integral relates
to epistemic uncertainty. Two different, sampling-based strategies for the numerical evaluation of the double
integral that defines expected dose from aleatory and epistemic uncertainty are described, and the prior use of these
strategies in the determination of expected dose from igneous events at the YM facility is indicated. Finally, the
presentation ends with a discussion of the representation of expected doses when synergisms between multiple
seismic events are possible (Sect. VIII.4).
This presentation is very formal, with expected doses being defined by integrals over various spaces related to
aleatory and epistemic uncertainty. However, it is important to recognize that every integral and every quantity used
in association with an integral in this presentation is an entity that must be defined, dealt with, and numerically
evaluated in the actual computational implementation of a performance assessment for the YM facility. The formal
representations given here can be used as a starting point in documentation that clearly connects the overall structure
of analyses of expected doses from seismic events at the YM facility with descriptions that provide the necessary
finer detail required for the complete and unambiguous specification of the individual parts of such an analysis. In
particular, documentation can be written that provides two-way mapping (i.e., from general to specific and also from
specific to general) between the overall structure of an analysis and detailed descriptions of specific parts of that
analysis.
For example, dose to the RMEI at time t from a seismic event at time t with a peak ground velocity of v appears
simply as a function D(t| t, v) in the integrals that define expected dose in this presentation. This usage clearly
indicates how the dose D(t| t, v) to the RMEI enters into the calculation of expected dose but tells nothing about how
this dose is actually calculated. In a complete documentation of the analysis, a formal description of the overall
analysis would provide a forward reference to where D(t| t, v) was defined, and the location at which D(t| t, v) was
defined would provide a backward reference to the description of the overall analysis that clearly indicated the use
of D(t| t, v) in the calculation of expected dose and other summary quantities of interest. Further, complete analysis
documentation would also describe the numerical procedures used to estimate both D(t| t, v) and the integrals
involving D(t| t,v) that determine expected dose. In this way, the interested individual would be provided with a
road map to the complete analysis that clearly tied general structure, specific detail, and numerical procedures
together.
VIII.2 EXPECTED DOSE FROM ALEATORY UNCERTAINTY
The development of results in this section and the next section (Sect. VIII.3) relating to expected doses from
seismic events at the YM facility is based on the following three assumptions: (i) dose to the RMEI at time t (yr)
from a seismic event occurring prior to t depends only on the time of occurrence t (yr) and peak ground velocity
(PGV) v (m/s) at the waste drifts associated with that seismic event (see Assumption 5.4), (ii) the occurrence of a
seismic event has no effect on the dose to the RMEI that derives from any subsequent seismic event, and (iii) the
occurrence of seismic events follows a Poisson process (see Assumption 5.5) characterized by a function .A(v)
(1/yr) of PGV v (Fig. VIII-1), where .A(v) is the annual exceedance frequency for a PGV of size v and
n
probA ..t, . A (). = {..
. A ().t .
n
v .
n
v .
! exp .-. A ().t .
.
v .
}.
(VIII.2.1)
is the probability that exactly n seismic events with a PGV exceeding v occur over a time interval of length .t (yr)
(Ref. 8, pp. 172-173). The synergisms between multiple seismic events are considered in Section VIII.4, so it is not
included as formal assumption in Section 5 of the main body of this report.
With respect to notation, this presentation will use a subscript A to designate quantities that relate primarily to
aleatory uncertainty and, beginning in Sect. VIII.3, a subscript E to designate quantities that relate primarily to
epistemic uncertainty. For notational convenience, it is also assumed that
,
D (t t v ) = dose (mrem/yr) to the RMEI at time t from a seismic event at time t with a PGV of v (VIII.2.2)
and that D(t| t, v) = 0 mrem/yr for t < t. In the computational implementation of an actual analysis for the YM
facility, the function D(t| t, v) would be a complex model implemented through the linked operation of several
computer programs. However, the functional representation in Eq. (VIII.2.2) is all that is needed for the present
discussion.
Fig. VIII-1. Representation of aleatory uncertainty in PGV at disposal drifts induced by seismic events, with (i) [v,
.A(v)] representing a point on the exceedance frequency curve, where v is a PGV from the abscissa and
-1
.A(v) is the corresponding exceedance frequency on the ordinate, and (ii) [ .A (.),.] represending the
same point on the exceedance frequency curve, where . is the exceedance frequency from the ordinate
-1
and .A (.) is the corresponding PGV on the abscissa.
The Poisson process characterized by .A(v) results in an uncountably infinite number of possible dose curves [t,
D(t| t, v)], with one curve resulting for each possible occurrence time, PGV pair [t, v] (Fig. VIII-2). One way to
summarize these dose curves is by calculating an expected dose at each time t. Given the preceding assumptions,
the expected dose EA[D(t| t, v)] to the RMEI at time t from seismic events is given by
vMAX
t, v).=
t D (t
t, v)..
- . A ()
dv
dv ..dvdt (VIII.2.3)
EA ..D (t
..tMIN .vMIN
t.MAX
t, .-1 ())d dt (VIII.2.4)
.
A .
=.tMIN ..MIN
D (t
where (i) [tMIN, tMAX] defines the time interval under consideration (e.g., tMIN = 0 yr, tMAX = 10,000 yr) and
tMIN < t=tMAX, (ii) [vMIN, vMAX] and [.MIN, .MAX] define the ranges of PGVs and exceedance frequencies for
PGVs, respectively, with .A(vMIN) = .MAX and .A(vMAX) = .MIN (e.g., vMIN = 0.388 m/s, vMAX = 10.73 m/s,
84
.MIN = 10- yr-1, .MAX = 10- yr-1), (iii) the double integral in Eq. (VIII.2.3) is defined by the limit of the
approximating sums
nTM nPGV
t, v)....D (t
ti , vj )..A (vj -1 )-.A (vj )..ti
EA ..
D (t
.
. .
i=1 j=1
nTM nPGV
vj A .
=..D (t
ti , vj )..
-
.A ()-. (vj -1 ).. . ti (VIII.2.5)
..vj .
vj
i=1 j=1
. .
nTM nPG
...D (t
ti , vj ).-. A ()
.dv
dv .. . ti
. vj
i=1 j=1
with tMIN = t0 < t1 < < tnTM = t, vMIN = v0 < v1 < < vnPGV = vMAX, .ti = ti  ti1, and .vj = vj  vj1, and (iv)
the double integral in Eq. (VIII.2.4) follows from a change of variables in the integral involving PGV in Eq.
(VIII.2.3). The validity of the integral representations for EA[D(t| t, v)] in Eqs. (VIII.2.3) and (VIII.2.4) depends on
either assumption (ii) indicated in the first paragraph of this section being true or .MAX (t tMIN) being
sufficiently small to render the likelihood of two or more seismic events over the time interval [tMIN, t]
inconsequential (see Eq. (VIII.2.1)).
Fig. VIII-2. Possible time-dependent dose curves [t, D(t| t, v)] (see Eq. (VIII.2.2)) to RMEI due to seismic events
of different PGVs occurring at different times (note: due to the delays associated with groundwater
transport, nonzero doses commence at a time subsequent to the occurrence of the initiating seismic
events) and associated mean dose curve (t, EA[D(t| t, v)]) (see Eqs. (VIII.2.3)  (VIII.2.5)).
As shown in Eqs. (VIII.2.3) and (VIII.2.4), expected dose EA[D(t| t, v)] is defined by double integrals involving
time and PGV (i.e., Eq. (VIII.2.3)) or time and exceedance frequency .(i.e., Eq. (VIII.2.4)). Thus, in concept,
techniques for the numerical evaluation of integrals (e.g., appropriate forms of Simpsons rule or the trapezoidal
rule) could be used to estimate EA[D(t| t, v)]. An alternative approach to the estimation of EA[D(t| t, v)] is to use a
Monte Carlo procedure for the evaluation of the integrals in Eqs. (VIII.2.3) and (VIII.2.4) (Ref. 7, Sect. 4.2.2), with
this alternative approach currently favored for use in performance assessment (PA) for the YM facility.
The integral in Eq. (VIII.2.4) is used for illustration; analogous procedures can be applied to the integral in Eq.
(VIII.2.3). Specifically, the representation for EA[D(t| t, v)] in Eq. (VIII.2.4) can be reformulated as
t, v).=
tMAX .MAX
t, .-1 ())d.dt (VIII.2.6)
EA ..
D (t
A .
..tMIN ..MIN
D (t
t, -1 ..
tMAX .MAX .
(.
.(.
=
. D (t.A ())..IMP ()tIMP t )d dt (VIII.2.7)
.
.
tMIN ..MIN ..IMP ()tIMP t ).
.
..
ti
-1
nIMP . D (t
.i
.
i=1 .
.
,
i
.A ()
(
)
i
.
.
nIMP (VIII.2.8)
. ...
.IMP ()tIMP t ).
..
where (i) Eq. (VIII.2.6) is an immediate reformulation of Eq. (VIII.2.4) based on the convention that D(t| t, v) = 0
mrem/yr for t< t and is introduced so that the importance sampling procedure described in Eqs. (VIII.2.7) and
(VIII.2.8) can sample on [tMIN, tMAX] rather than on [tMIN, t], (ii) Eq. (VIII.2.7) is the standard important
sampling transformation used in the Monte Carlo evaluation of an integral with .IMP(.) and tIMP(t) positive
valued density functions defined on [.MIN, .MAX] and [tMIN, tMAX] (Ref. 7, Sect. 4.3.1), and (iii) Eq. (VIII.2.8) is
the importance sampling approximation to the integral defining EA[D(t| t, v)], and hence to EA[D(t| t, v)], obtained
with a random or Latin hypercube sample [ti, .i], i = 1, 2, , nIMP, generated from [tMIN, tMAX] [.MIN, .MAX]
in consistency with the definitions of the density functions tIMP(t) and .IMP(.).9, 10 It is important to recognize
that the distributions used in importance sampling have nothing to do with the treatment of uncertainty; they are
simply numerical devices used to accelerate the convergence of Monte Carlo integration procedures and have no
effect on the value of the integral being evaluated.
As examples, .IMP(.) and tIMP(t) are often assumed to correspond to uniform or loguniform distributions.
Specifically, uniform and loguniform importance sampling distributions for . result in .IMP(.) being defined by
.1 (.MAX -. MIN ) for .MIN =.=. MAX
(VIII.2.9)
.IMPu ()=.
.
.0 otherwise
and
.1 ..ln (.MAX
.MIN ). for .MIN =.=. MAX
(VIII.2.10)
..
.
.IMPlu ()=.
.
.0 otherwise,
.
respectively. The density functions tIMPu(t) and tIMPlu(t) are defined analogously for uniform and loguniform
sampling, respectively, on [tMIN, tMAX].
For uniform sampling on [.MIN, .MAX] and [tMIN, tMAX] in consistency with the density functions .IMPu(.)
and tIMPu(t), the approximation to EA[D(t| t, v)] in Eq. (VIII.2.8) becomes
nIMP
t, v)..
..
(.MAX -. MIN )(tMAX -tMIN ).
, .A ()). (VIII.2.11)
EA ..
D (t
ti
-1 .i
.
. nIMP ..D (t
.i=1
For loguniform sampling on [.MIN, .MAX] and [tMIN, tMAX] in consistency with the density functions .IMPlu(.)
and tIMPlu(t), the approximation to EA[D(t| t, v)] in Eq. (VIII.2.8) becomes
nIMP
t, v)..
..
ln (.MAX
.MIN ln tMAX tMIN )
..
.tiiD (t
)(
ti , .-
A
1 ()). (VIII.2.12)
EA ..
D (t
.i
.
. nIMP
.
.i=1
Other definitions for .IMP(.) and tIMP(t) result in analogous approximations to EA[D(t| t, v)].
The development of EA[D(t| t, v)] ends with a reminder that EA[D(t| t, v)] does not correspond to an actual dose
received by the RMEI. Rather, EA[D(t| t, v)] is the expected (i.e., average) value of the infinitely many possible
doses that the RMEI could receive at time t from the infinitely many possible seismic events that could (but
probably will not) occur before time t. In particular, EA[D(t| t, v)] is the result of reducing all these possible doses
and their associated likelihood to a single number through the integration processes described in Eqs. (VIII.2.3)
and (VIII.2.4).
The character and likelihood of the actual doses that the RMEI could receive is preserved when the results of
the analysis are presented as a distribution rather than as an expected value (Fig. VIII-3). Exactly the same
information is used in the development of distributions for dose and expected values for dose; the only difference is
in the details of the processing of this information. For example, the complementary cumulative distribution
function (CCDF) for dose to the RMEI at time t is defined by
vMAX
probA .D (t
t, v)>D.=
t
t v )..-. A ()
, ..dv
dv ..dvdt (VIII.2.13)
.
..tMIN .vMIN
dD ..D (t
t.MAX
A ...
t, .-1 ()).d dt , (VIII.2.14)
=.tMIN ..MIN
dD .
.
.D (t
.
where probA[D(t| t, v) > D] is the probability that the RMEI will receive a dose at time t (i.e., D(t| t, v)) that
exceeds a dose of size D and the indicator function dD is defined by
.1ifD (t
,
.
t v ).=.
t v )>D
(VIII.2.15)
dD ..
D (t
, .
.0otherwise.
.
Except for the indicator function dD, the integrals defining EA[D(t| t, v)] in Eqs. (VIII.2.3) and (VIII.2.4) and the
integrals defining probA[D(t| t, v) > D] in Eqs. (VIII.2.13) and (VIII.2.14) are the same. Thus, the same evaluations
of D(t| t, v) that are used to estimate EA[D(t| t, v)] can also be used to estimate probA[D(t| t, v) > D]. In particular,
the expected dose associated with the distribution defined by the CCDF in Fig. VIII-3 is the quantity EA[D(t| t, v)]
defined in Eqs. (VIII.2.3)  (VIII.2.4); thus, the expected dose curve (t, EA[D(t| t, v)]) in Fig. VIII-2 is a summary of
the result of reducing distributions of the form shown in Fig. VIII-3 to expected values.
Fig. VIII-3. Illustration of complementary cumulative distribution function (CCDF) of dose (mrem/yr) to RMEI at
time t (yr) i.e., a plot of (D, probA[D(t| t, v) > D]).
As noted earlier, the integral representations for EA[D(t| t, v)] in Eqs. (VIII.2.3) and (VIII.2.4) are only valid if
either (i) the occurrence of a seismic event has no effect on the dose to the RMEI that derives from any subsequent
seismic event or (ii) .MAX (t  tMIN) is sufficiently small to render the likelihood of two or more seismic events
over the time interval [tMIN, t] inconsequential. A stronger restriction is required for the validity of the integral
representations of probA[D(t| t, v) > D] in Eqs. (VIII.2.13) and (VIII.2.14). In particular, these representations are
valid only if (ii) above is satisfied. This constraint is necessary because the indicator function dD in Eqs. (VIII.2.13)
and (VIII.2.14) is applied to the dose resulting from a single seismic event and thus the additive effects of two or
more seismic events occurring before time t is not incorporated into probA [D(t| t, v) > D]. The appropriate
formalism for the incorporation of the synergisms that could possibly exist in the determination of dose subsequent
to multiple seismic events is discussed in a later section (Sect. VIII.4).
VIII.3 ALEATORY AND EPISTEMIC UNCERTAINTY
The preceding section (Sect. VIII.2) introduces the calculation of expected dose EA[D(t| t, v)] at time t from
seismic events to the RMEI. The indicated expectation is over events that can occur in the future. As indicated in
the Introduction (Sect. VIII.1), uncertainty with respect to what can occur in the future is referred to as aleatory
uncertainty, and in the example of the preceding section, its probabilistic nature was characterized by the function
.A(v). Specifically, aleatory uncertainty arises from the many possible seismic events that could occur over a time
period of interest (e.g., 0 to 10,000 yr). If only aleatory uncertainty was present and D(t| t, v) and .A(v) were known
with complete certainty, then the expected dose EA[D(t| t, v)] would derive solely from aleatory uncertainty and
could be calculated with complete certainty.
Unfortunately, quantities such as D(t| t, v) and .A(v) can never be known with complete certainty in a PA as
complex as the one that must be carried out for the YM facility. As a result, there is significant state of knowledge
uncertainty with respect to how D(t| t, v) and .A(v) should be defined (Fig. VIII-4). This type of uncertainty is
referred to as epistemic uncertainty to distinguish it from the previously introduced concept of aleatory uncertainty.
Specifically, epistemic uncertainty arises from a lack of knowledge with respect to quantities used in the
characterization of aleatory uncertainty or in the calculation of doses or other effects given the occurrence of a
seismic event.
Fig. VIII-4. Illustration of multiple exceedance frequency curves .A(v) resulting from epistemic uncertainty in
PGV at disposal drifts induced by seismic events.
The notation introduced in the previous section (Sect. VIII.2) for D(t| t, v) and .A(v) can be expanded to
explicitly display a dependence on imprecisely known quantities. Specifically, D(t| t, v) and .A(v) can be
represented by D(t| t, v, eD) and .A(v |eA), where
eD = ..
eD1, eD2, K, eD nD . (VIII.3.1)
, .
is a vector of imprecisely known variables required in the determination of D(t| t, v), and
e A = ..eA1, eA2, K, eA nA . (VIII.3.2)
, .
is a vector of imprecisely known variables required in the definition of .A(v). The fundamental idea is that the
analysis has been developed to the point that it is believed that the elements of eA and eD should have fixed values
and that appropriate analysis results would be obtained if these fixed values were known. Unfortunately, the
appropriate values for these quantities are not known with certainty, and so there is epistemic uncertainty with
respect to what their values should be. The elements of eA and eD can be interpreted generally enough to include
imprecisely known functions and designators for alternative models. For notational convenience,
e =[e , eD ]=[ee
,
12, K, enE ] (VIII.3.3)
A
can be used to represent the vector of all imprecisely known variables.
Inclusion of a dependence on e = [eA, eD] results in the representations for EA[D(t| t, v)] in Eqs. (VIII.2.3) and
(VIII.2.4) having the form
vMAX
t,, e).=
t D (t
v
t,, eD )..
-. (v
v dA
dv ..dvdt (VIII.3.4)
e A )
EA ..
D (t
.. tMIN .vMIN
t.MAX
t, .-1 (.
.
e A ), eD )d dt . (VIII.3.5
A
=.tMIN ..MIN
D (t
The preceding notation emphasizes that the possible values for e = [eA, eD] result in different possible values for
.A(v |eA), D(t| t, v, eD) and thus EA[D(t| t, v, e)]. As eD only affects the calculation of dose and eA only affects the
distributions that characterize aleatory uncertainty in t and v, EA[D(t| t, v, eD) | eA] or EA[D(t| t, v) | eA, eD] are
probably more conceptually correct notational representations for expected dose from aleatory uncertainty than
EA[D(t| t, v, e)]; however, for notational simplicity, the use of EA[D(t| t, v, e)] to represent this dose will be
retained. Fortunately, the integrals in Eqs. (VIII.3.4) and (VIII.3.5) remove all ambiguity with respect to exactly
what is represented by EA[D(t| t, v, e)].
Analyses for the YM facility, like most large PAs, use probability to characterize epistemic uncertainty.
Specifically, distributions
D1, D2, , DnE (VIII.3.6)
are specified for the elements of e, where Dk is the distribution assigned to ek. Correlations and other restrictions
involving pairs or larger groups of variables are also possible. These distributions and any associated restrictions
provide a numerical quantification of what is known about individual variables and also the necessary starting
structure to propagate this knowledge through the overall analysis. For notational convenience, the set of all
possible values for e associated with the distributions in Eq. (VIII.3.6) will be represented by the set E (i.e., E is the
sample space or universal set associated with epistemic uncertainty) and the corresponding density function defined
on E will be represented by dE(e)).
Each element e of E gives rise to a value for the expected dose EA[D(t| t, v, e)] indicated in Eqs. (VIII.3.4) and
(VIII.3.5) (Fig. VIII-5). One way of describing the (epistemic) uncertainty in EA[D(t| t, v, e)] is to determine and
present the range of values for EA[D(t| t, v, e)] that results from all possible values of e contained in E. This is the
simplest of all approaches to uncertainty analysis and is typically referred to as interval analysis.
Fig. VIII-5. Illustration of expected dose curves to RMEI resulting from epistemic uncertainty (i.e., plots of (t,
EA[D(t| t, v, e]) for 0 =t=10,000 yr and different values of e; see Eqs. (VIII.3.4)  (VIII.3.5)).
The specification of the distributions in Eq. (VIII.3.6) provides the necessary information to carry out more
sophisticated uncertainty assessments than simple interval analysis. More specifically, the distributions in Eq.
(VIII.3.6) provide the basis for calculating both the expected value and the distribution of EA[D(t| t, v, e)] that arise
from possible values for e (Fig. VIII-6). In particular, the expected value EE(EA[D(t| t, v, e)]) of EA[D(t| t, v, e)]
over epistemic uncertainty is given by
EE (EA .D (t
,, e)..
)=.E EA ..
D (t
t v
t, v, e).d ()dE (VIII.3.7)
. E e
.
tMAX vMAX
. D (t
,, eD )..
-. (v
t v dA
e A )dv ..
dvdt ..
.dE ()dE (VIII.3.8)
e
E ..
=..tMIN .vMIN
tMAX .MAX
.
t, .-1
e A ), eD )dvdt .dE ()dE , (VIII.3.9)
A (.
E ..
. e
=..tMIN ..MIN
D (t
.
where E and dE(e) are defined in conjunction with Eq. (VIII.3.6) and dE corresponds to an increment of volume
from E.
Fig. VIII-6. Illustration of expected and selected quantile curves for distribution of expected (over aleatory
uncertainty) dose curves resulting from epistemic uncertainty (i.e., the indicated expected and quantile
curves derive from the epistemic uncertainty in e and result from integration over the set E of possible
values for e).
Similarly, the epistemic (i.e., degree of belief) probability probE(EA[D(t| t, v, e)] > E) of exceeding an expected
dose to the RMEI of size E is given by
probE (EA .D (t
t,, e).>E )=.E dE (EA ..
D (t
v . t v . E e
,, e).)d ()dE (VIII.3.10)
.
tMAX vMAX
,, eD )..
-. (v
t v dA
dv ..
dvdt
...
dE ()dE (VIII.3.11)
ee A )
=.E dE
...
.tMIN .vMIN
D (t
tMAX .MAX
.
t, .-1
e
e A ), eD )dvdt . ()dE , (VIII.3.12)
A (.
.dE
=.E dE ..
.tMIN ..MIN
D (t
.
where the indicator function dE is defined by
.1ifEA .D (t
t, v, e).>E
(VIII.3.13)
..
.
dE (EA .D (t
t,, e)..)=.
v
.
.0otherwise
.
and plays the same role as the indicator function dD in Eqs. (VIII.2.13) and (VIII.2.14). The qth quantile (e.g., 0.1,
0.5, 0.9) for EA[D(t| t, v, e)] is obtained by solving the equation
qprobE (EA .D (t
=
t v
,, e)..
>E ) (VIII.3.14)
.
for E (see Fig. VIII-6).
Two computational strategies for the estimation of EE(EA[D(t| t, v, e)]) are presented. The first strategy
involves first approximating the integral over E and then approximating the integrals that define EA[D(t| t, v, e)].
The second strategy involves treating EE(EA[D(t| t, v, e)]) as being defined by a single integral over the high
dimensional space AE defined by
AE =[tMIN tMAX ]. MIN , .MAX ]E
, [
t
={ae : ae =[t, ., e], tMIN = = tMAX , .MIN =.=. MAX , e .E} (VIII.3.15)
and then approximating this integral without drawing a distinction between the parts that derive from aleatory
uncertainty and the parts that derive from epistemic uncertainty.
In Strategy 1, a random or Latin hypercube sample
ek =[e , e ]=..
e1k , e2k , K, enE k ..
, k =1, 2, K, nS , (VIII.3.16)
Ak Dk ,
is generated from E in consistency with the distributions indicated in Eq. (VIII.3.6). Then, EE(EA[D(t| t, v, e)]) is
approximated by
nS
EE (EA .D (t
t v .
,, e).)..EA .D (t
, .
t v , ek ).
nS
. (VIII.3.17)
.
.
k =1
To complete the approximation of EE(EA[D(t| t, v, e)]), approximations E A [D(t| t, v, ek)] to EA[D(t| t, v, ek)] for k
= 1, 2, , nS must be developed. Possibilities for the determination of E A [D(t| t, v, ek)] include (i) use of the
importance sampling procedures indicated in conjunction with Eqs. (VIII.2.6)  (VIII.2.12) and (ii) development of
computationally efficient procedures that depend on specific properties of the problem under consideration. Once
the approximations E A [D(t| t, v, ek)] to EA[D(t| t, v, ek)] are determined,
nS

EE (EA .D (t
v .
t,, e).). .EA .D (t
,, ek ).
t v .
nS
(VIII.3.18)
.
.
k =1
provides the final approximation to EE(EA[D(t| t, v, e)]).
With Strategy 1, the same numerical results used to estimate EE(EA[D(t| t, v, e)]) can also be used to estimate
probE(EA[D(t| t, v, e)] > E). Specifically,
nS

probE (EA .D (t
v .
t,, e
nS
, (VIII.3.19)
t,, e). > E )=.dE (E .D (t
A .
vk )..
)
k =1
where the indicator function dE is defined in Eq. (VIII.3.13). Strategy 1 also provides the mapping

.
t, v, e ).), k =1, 2, K, nS , (VIII.3.20)
(ek , EA .D (t
k .
.
between uncertain analysis inputs (i.e., the ek) and analysis results (i.e., the E A [D(t| t, v, ek)]) that can be explored
with a variety of sensitivity analysis procedures to determine the effects of individual uncertain analysis inputs on
expected dose.11
In Strategy 2, a random or Latin hypercube sample
K
aek =[tk , . , e , eDk ]=.tk , . , e , e ,, enE k ..
, k =1, 2,, nS , (VIII.3.21)
k Ak . k 1k 2k K ,
is generated from AE (see Eq. (VIII.3.14)) in consistency with whatever sampling distributions are assigned to t and
. (see Eqs. (VIII.2.6)  (VIII.2.12)) and also in consistency with the distributions indicated in Eq. (VIII.3.6) for the
elements of e = [eA, eD]. Then, EE(EA[D(t| t, v, e)]) as represented in Eq. (VIII.3.9) is approximated by
.
nS .D (t
tk , .-1 (.k
A
.
EE (EA .D (t
v .
k
e Ak
(
), eDk )
..
. nS , (VIII.3.22)
.
t,, e).)... .IMP (. )tIMP tk )
k =1 .
..
where .IMP(.) and tIMP(t) are the sampling distributions for . and t (see Eqs. (VIII.2.9)  (VIII.2.12)). In
particular,
nS
t,, e).).
.(.MAX -. MIN )(tMAX -tMIN ).
-1
EE (EA .D (t
tk , .A (.k e Ak ), eDk ),
v . ..
nS ..D (t
.
(VIII.3.23)
if .IMP(.) and tIMP(t) correspond to uniform distributions on [.MIN, .MAX] and [tMIN, tMAX] (see Eqs.
.k =1
(VIII.2.9) and (VIII.2.11)), and
nS
t,, e).).
.ln (.MAX
.MIN )ln tMAX tMIN )
..
.tk .kD (t
(
tk , .-1
EE (EA .D (t
v
A (.k. ..
nS .k =1
.
e Ak ), eDk )
(VIII.3.24)
if .IMP(.) and tIMP(t) correspond to loguniform distributions on [.MIN, .MAX] and [tMIN, tMAX] (see Eqs.
(VIII.2.10) and (VIII.2.12)). Analogous approximations also hold for EE(EA[D(t| t, v, e)]) as represented in Eq.
(VIII.3.8).
With Strategy 2, it is not possible to estimate the expected doses EA[D(t| t, v, e)] to the RMEI for different
-1
values of e. This inability results from the concurrent variation of the aleatory variables tk and vk = .A (.k |eAk)
and the epistemic variables e1k, e2k, , enE,k associated with ek = [eAk, eDk] in the determination of the doses
D (t
tk , .-1 (.k
e Ak ), eDk ), k =1, 2, K, nS , (VIII.3.25)
A
to the RMEI that are calculated for each sample element aek (see Eq. (VIII.3.21)) in Strategy 2. Specifically,
because dose to the RMEI is known for only one pair [tk, vk] of time, PGV values for each vector ek = [eAk, eDk] of
epistemic variable values, it is not possible to estimate the integral over time and PGV that defines the expected dose
EA[D(t| t, v, ek)] associated with ek. As a result, Strategy 2 does not provide a basis to estimate the uncertainty in
expected dose EA[D(t| t, v, e)] to the RMEI as defined by probE(EA[D(t| t, v, e)] > E) in Eqs. (VIII.3.10) 
(VIII.3.12).
Strategy 2 does allow an estimate of the uncertainty in the dose to the RMEI due to both aleatory and epistemic
uncertainty. In particular, this uncertainty is characterized by the probability
probEA .D (t
,, e )>D.=
tMAX vMAX
t v D
t, v, e )..-. (v
e A )dv .dE ()dvdt dE (VIII.3.26)
D .. dA
.
. e
. ..tMIN .vMIN
dD ..
D (t
E
tMAX .MAX
t, .-1
. e
e A ), eD ).dE ()dvdt dE (VIII.3.27)
A (.
E
=..tMIN ..MIN
dD
...
D (t
.
tk , .-1 ..
nS .dD
.D (t
A (.k
e Ak ), eDk )..
. nS ,
.
.
.
(VIII.3.28)
...
.
.IMP (. )tIMP tk )
k =1 . k (.
..
where (i) the indicator function dD is defined in Eq. (VIII.2.15), (ii) the density functions .IMP(.) and tIMP(t) are
the same as indicated in conjunction with Eqs. (VIII.2.6  VIII.2.12), and (iii) the sample elements aek = [tk, .k, eAk,
eDk], k = 1, 2, , nS, correspond to the sample in Eq. (VIII.3.21). The preceding probability defines the CCDF for
dose to the RMEI (i.e., D(t| t, v, eD)) that derives from both aleatory and epistemic uncertainty and is very different
from the probability probE(EA[D(t| t, v, e)] > E) defined in Eqs. (VIII.3.10)  (VIII.3.12), which defines the CCDF
for expected dose to the RMEI (i.e., EA[D(t| t, v, e)]) that derives from epistemic uncertainty.
Strategy 2 provides the following mapping from analysis inputs to analysis results:
.aek , D (t
tk , vk , eDk )..
, k =1, 2, K, nS , (VIII.3.29)
.
where vk = .-
A
1(.k | eAk). Like the mapping in Eq. (VIII.3.20) associated with Strategy 1, this mapping can be
explored with a variety of sensitivity analysis procedures12. However, the interpretation of any results obtained in
such a sensitivity analysis would be very different from the interpretation of results obtained from a sensitivity
analysis of the mapping in Eq. (VIII.3.20) for two reasons. First, the mapping in Eq. (VIII.3.20) obtained with
Strategy 1 involves expected dose to the RMEI (i.e., EA[D(t| t, v, e)]) while the mapping in Eq. (VIII.3.29) obtained
with Strategy 2 involves dose to the RMEI (i.e., D(t| t, v, e)). Hence, the dependent variables under study are not
the same. Second, the mapping obtained with Strategy 1 involves only epistemic uncertainty while the mapping
obtained with Strategy 2 involves both epistemic uncertainty and aleatory uncertainty. Thus, the uncertainty spaces
being sampled from (i.e., E and AE) are fundamentally different.
If implemented correctly and with sufficiently large sample sizes to assure convergence, both strategies will
produce the same value for the expected dose EE(EA[D(t| t, v, e)]). Strategy 1 has the advantage that it permits
uncertainty and sensitivity studies of the effects of epistemic uncertainty on the expected dose to the RMEI (i.e.,
EA[D(t| t, v, e)]); such studies are not possible with Strategy 2. Strategy 2 has the advantage that it is likely to be
more computationally efficient (i.e., require fewer evaluations of D(t| t, v, e)) in the determination of EE(EA[D(t| t,
v, e)]) than Strategy 1.
Both computational strategies are used in the determination of expected dose to the RMEI from igneous events
at the YM facility. In particular, the expected dose EE(EA[D(t| t, v, e)]) from the eruptive component of igneous
events is calculated with Strategy 1, and the expected dose EE(EA[D(t| t, v, e)]) from the groundwater release
component of igneous events is calculated with Strategy 2. Thus, when viewed at a sufficiently high-level, the
calculation of expected doses EE(EA[D(t| t, v, e)]) from seismic events, the eruptive component of igneous events,
and the groundwater component of igneous events is conceptually the same, although the uncertain variables, the
representation of aleatory uncertainty, and the dose models are at least partially different for these three cases.
VIII.4 EXPECTED DOSE FROM ALEATORY AND EPISTEMIC UNCERTAINTY
INCLUDING SYNERGISMS
The computational procedures for the calculation of expected doses presented in the two preceding sections
(Sects. VIII.2, VIII.3) are predicated on the assumption that the occurrence of a seismic event has no effect on doses
that derive from any subsequent seismic event. Further, the computational procedures presented for the
determination of distributions of doses do not include the possibility of multiple seismic events occurring before a
given time. This section briefly presents the formal representations for expected dose and distribution of expected
dose that includes the possibility of synergisms between multiple seismic events on dose subsequent to these events.
For this representation, the occurrence of multiple seismic events between tMIN and tMAX is assumed to be
possible. The properties of a sequence of seismic event occurring between tMIN and tMAX is represented by a
vector
a =[a1, a2, K, anO ] , (VIII.4.1)
where
ai = ..
ai1, ai2, K, ai nP . (VIII.4.2)
, .
is the vector of properties (e.g., time of occurrence, PGV, extent of rock fall, ) that, in essence, defines the ith
seismic event occurring between tMIN and tMAX. If time of occurrence and PGV are the only two defining
characteristics of a seismic event, then ai would be defined by
,
ai =[tvi] , (VIII.4.3)
i
where ti and vi are the time of occurrence and PGV associated with the ith seismic event, and a would be defined by
a =[ai1, ai2, K, anO ]
=[tv
,, t2, v2, K, t , vnO ].
(VIII.4.4)
11 nO
For completeness, a0 can be used to represent the degenerate vector (i.e., the vector with no components) that
corresponds to no seismic events occurring between tMIN and tMAX. Then, the set A containing a0 and all possible
vectors a of the form indicated in Eq. (VIII.4.1) corresponds to the universe (i.e., sample space) of all possible
sequences of seismic events that could occur over the time interval [tMIN, tMAX].
Aleatory uncertainty with respect to the potential occurrence of the sequences of seismic events represented by
the elements of A is characterized by a probability distribution defined on A. For notational convenience, this
distribution is represented by its density function dA(a), where the probability probA(U ) of a subset U of A is
given by
probA (U )=.U dA (a)dA . (VIII.4.5)
For example, if the elements of A are of the form indicated in Eq. (VIII.4.4), then dA(a) could derive from a
function .A (v) of the form considered in the two preceding sections (Sects. VIII.2, VIII.3).
The expected dose EA[D(t|a)] to the RMEI at time t would then be defined by
a).= D (t
a)d (a)dA , (VIII.4.6)
EA ..
D (t
A
..A
where
D (t
a)=dose (mrem/yr) to the RMEI at time t from the sequence of seismic events represented by a. (VIII.4.7)
The representation for D(t|a) allows the potential for synergistic interactions involving two or more seismic events.
Similarly, the probability probA[D(t|a) > D] that the dose to the RMEI at time t will exceed a dose of size D is
given by
probA .D (t
a )>D..
=.A dD ..
D (t
(a)dA, (VIII.4.8)
. a)..
dA
where
a)..=.
.
.1if D (t
a)>D
(VIII.4.9)
dD ..D (t
.0otherwise.
.
Unlike the representation for probA[D(t| t, v)] in Eqs. (VIII.2.13) and (VIII.2.14), in which a = [t, v] corresponds to
a single seismic event and D(t| t, v) corresponds to the dose from this single event, the preceding representation for
probA[D(t|a) > D] incorporates the possibility that a corresponds to multiple seismic events and that D(t|a) is
affected by some form of interaction (i.e., synergism) involving these events.
As before, epistemic uncertainty is assumed to exist in the elements of a vector e = [eA, eD] of the form defined
in Eq. (VIII.3.3) with (i) this uncertainty characterized by probability distributions D1, D2, , DnE for the elements
of e as indicated in Eq. (VIII.3.6), (ii) the set of all possible values for e constituting a set E, and (iii) the
distributions D1, D2, , DnE giving rise to a density function dE(e) defined on E. With the introduction of
epistemic uncertainty in the elements of e, dose D(t|a, eD) to the RMEI is a function of eD, and expected dose
EA[D(t|a, e)] to the RMEI arising from aleatory uncertainty is a function of both eA and eD. In particular, the
density function dA(a|eA) and also possibly the sample space A(eA) associated with aleatory uncertainty can change
as a function of eA. As a result, expected dose EA[D(t|a, e)] arising from aleatory uncertainty now has the form
eA )dA , (VIII.4.10)
,
ae)..
=.A(eA )D (t
,
ae D )dA (a
EA ..
D (t
and the expected value EE(EA[D(t|a, e)]) of EA[D(t|a, e)] over epistemic uncertainty has the form
EE (EA .D (t
ae).)= .D (t
, .
,
ae).d ()dE (VIII.4.11)
. E e
.
. EEA .
.
= EA(eA )D (t
,
aeD )dA (a
eA )dA ..
d ()dE . (VIII.4.12)
.
E e
..
.
.
The preceding results are analogous to those in Eqs. (VIII.3.4) and (VIII.3.5) and Eqs. (VIII.3.7)  (VIII.3.9) with a
more general dependence on the properties of the seismic events under consideration now incorporated into the
representation of dose and expected dose.
The probability probE(EA[D(t|a, e)] > E) that an expected dose of size E will be exceeded is now given by
probE (EA .D (t
, .ae).>E )=.EdE (E .D (t
,
ae ).)d ()dE (VIII.4.13)
A .
. E e
.
.
=.EdE ..A(eA )D (t
,
aeD )dA (a
eA )dA .
.
d ()dE , (VIII.4.14)
E e
.
.
where
ae)..
)=
...
1ifEA .D (t
, .
.
dE (EA .D (t
,
ae).>E
(VIII.4.15)
.
.0otherwise.
.
The preceding result is analogous to the results in Eqs. (VIII.3.10)  (VIII.3.12) except, as already explained, a more
general dependence of dose on the properties of seismic events is allowed.
Computational Strategies 1 and 2 described in the preceding section (Sect. VIII.3) for the evaluation of expected
dose EE(EA[D(t|a, e)]) with a= [t, v] can also be applied to the evaluation of expected dose with the more complex
forms introduced in this section for a and the dose that derives from a. The procedures are conceptually the same
for both cases and will not be repeated here. However, the same caveats as presented at the end of Sect. VIII.3 still
apply. Further, if the probabilistic structure of the set A is complicated, the actual construction of iterated integrals
and associated density functions for integration over A can be a difficult task.
VIII.5 REFERENCES
1.
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0539-1, Rev. 1. Las Vegas, NV: U.S. Department of Energy. [155943]
2.
U.S. DOE (U.S. Department of Energy). 2002. Yucca Mountain Site Suitability Evaluation, DOE/RW-0549.
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3.
Kaplan, S. and B.J. Garrick. 1981. "On the Quantitative Definition of Risk," Risk Analysis. Vol. 1, no. 1, pp.
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4.
Helton, J.C. 1994. "Treatment of Uncertainty in Performance Assessments for Complex Systems," Risk
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5.
Pat-Cornell, M.E. 1996. "Uncertainties in Risk Analysis: Six Levels of Treatment," Reliability Engineering
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6.
Helton, J.C. 1997. "Uncertainty and Sensitivity Analysis in the Presence of Stochastic and Subjective
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7.
Rubinstein, R.Y. 1981. Simulation and the Monte Carlo Method. New York: John Wiley & Sons. [163476]
8.
Hahn, G.J. and S.S. Shapiro. 1967. Statistical Models in Engineering. New York: John Wiley & Sons.
[146529]
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McKay, M.D., R.J. Beckman, and W.J. Conover. 1979. "A Comparison of Three Methods for Selecting
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Helton, J.C. and F.J. Davis. 2002. Latin Hypercube Sampling and the Propagation of Uncertainty in Analyses
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Helton, J.C. and F.J. Davis. 2000. Sampling-Based Methods for Uncertainty and Sensitivity Analysis,
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