Mechanical Assessment of the Waste Package Subject to Vibratory Motion Rev 00A, ICN 00 CAL-WIS-AC-000001 October 14, 2004 1. PURPOSE The purpose of this document is to provide an integrated overview of the calculation reports that define the response of the waste package and its internals to vibratory ground motion. The calculation reports for waste package response to vibratory ground motion are identified in Table 1-1. Three key calculation reports describe the potential for mechanical damage to the waste package, fuel assemblies, and cladding from a seismic event. Three supporting documents have also been published to investigate sensitivity of damage to various assumptions for the calculations. While these individual reports present information on a specific aspect of waste package and cladding response, they do not describe the interrelationship between the various calculations and the relationship of this information to the seismic scenario class for Total System Performance Assessment-License Application (TSPA-LA). This report is designed to fill this gap by providing an overview of the waste package structural response calculations. Table 1-1. Major References for Waste Package Damage Calculations Damage Process Calculation Report Key Report for Kinematics and Structural Response of Waste Package: Damage to the waste package from vibratory ground motion Structural Calculations of Waste Package Exposed to Vibratory Ground Motion, 000-00C-WIS0-01400-000-00A (BSC 2004 [DIRS 167083]) Key Report for Damage Caused by Side and End Impacts: Calculation of damaged area caused by end- to-end impacts of adjacent waste packages for a predefined set of impact velocities and impact angles 21-PWR Waste Package Side and End Impacts, 000-00C-DSU0-01000-000-00B (BSC 2003 [DIRS 162293]) Key Report for G-Loads on Fuel Assemblies Caused by End Impacts: Acceleration of the fuel assemblies from end- to-end waste package impacts Maximum Accelerations on the Fuel Assemblies of a 21-PWR Waste Package During End Impacts, 000-00C-DSU0-01100- 000-00A (BSC 2003 [DIRS 162602]) Supporting Documents to These Key Reports: Sensitivity of damaged area caused by end-to- end impacts of adjacent waste packages to mesh refinement 21-PWR Waste Package End Impacts – A Mesh Study, 000-00C-WIS0-02100-000-00A (BSC 2004 [DIRS 170844]) Sensitivity of damaged area to spectral matching and intercomponent variability of ground motion time histories for the 2.44 m/s PGV level Additional Structural Calculations of Waste Package Exposed to Vibratory Ground Motion, 000-00C-WIS0-01700-000-00A (BSC 2004 [DIRS 168385]) Sensitivity of damaged area to interpolation scheme for impact angles between 0-degree and 1-degree Alternative Damaged Area Evaluation for Waste Package Exposed to Vibratory Ground Motion, 000-00C-WIS0-01900-000- 00A (BSC 2004 [DIRS 170843]) Other Reports Not Directly Relevant to the Seismic Abstractions: Sensitivity of damaged area to in-plane mesh refinement for waste package impact on the emplacement pallet Drop of Waste Package on Emplacement Pallet – A Mesh Study, 000-00C-DSU0-002200-000-00A (BSC 2003 [DIRS 165497]) Analysis of spatial distribution of damaged area on the waste package for criticality analyses Spatial Distribution of Damage to Waste Package in Aftermath of Vibratory Ground Motion, 000-00C-WIS0-01100-000-00A (BSC 2003 [DIRS 166247]) Define relative velocity time histories in the vertical direction between the waste package and emplacement pallet during vibratory ground motion Relative Vertical Velocity Between Waste Package and Emplacement Pallet During Vibratory Ground Motion, 000-00C- WIS0-01800-000-00A (BSC 2004 [DIRS 170850]) 21-PWR = 21-Pressurized Water Reactor spent nuclear fuel waste package; PGV = peak ground velocity Of the nine reports listed in Table 1-1, three are not relevant to abstractions for the seismic scenario class and are not discussed further in this document. The general purpose of the remaining 6 design calculations is to determine the response of the waste package and/or its internals to the vibratory ground motion hazard at the proposed geologic repository at Yucca Mountain, Nevada. More specifically, the output data from the structural response of the waste package and its internals are the basis for development of damage abstractions for the seismic scenario class for TSPA-LA, as described in the Seismic Consequence Abstraction model report (BSC 2004 [DIRS 169183]). The results from the structural response calculations also address portions of integrated subissue Integrated Subissue for the Mechanical Disruption of Engineered Barriers, 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 [DIRS 163274]). The purpose of the first two key reports in Table 1-1 is to determine the damaged areas on the waste package from impacts between the waste package and emplacement pallet and from impacts between adjacent waste packages in response to vibratory ground motion. The purpose of the third key report in Table 1-1 is to determine the average and maximum g-loads on the fuel rod assemblies due to impacts between adjacent waste packages. These g-loads define the axial loads on fuel rod cladding, providing the basis for definition of cladding failure during end-to-end impacts of adjacent waste packages. The three supporting documents in Table 1-1 provide supplemental analyses supporting the results and conclusions in the three key reports. The rationale and results from the supplemental analyses are as follows: • It is always necessary to demonstrate that the results from a finite element (FE) analysis are insensitive to the level of mesh refinement. The first supporting document reports on a very detailed mesh refinement study for end-to-end impacts of adjacent waste packages, and demonstrates that the original damaged area calculations in 21-PWR Waste Package Side and End Impacts (BSC 2003 [DIRS 162293]) are almost always conservative. • Structural response calculations were based on the most current ground motions available at the time the analyses were performed. However, two aspects of the ground motions (intercomponent variability and spectral matching) have changed over time, as explained in Section 1.3.4. The second supporting document evaluates the effect of intercomponent variability and spectral matching for the ground motions at the 2.44 m/s peak ground velocity (PGV) level, and again demonstrates that the range of damaged area in the original calculations (BSC 2004 [DIRS 167083]) is conservative. • The damaged area calculations for end-to-end impacts incorporate a simple interpolation scheme on impact velocity and impact angle. Damage at an impact angle of zero degrees is substantially less than damage at an impact angle of 1 degree because the impact load is uniformly distributed around the circumference, rather than concentrated at a point. In practice, a zero degree impact is very unlikely because it requires perfect alignment of waste package centerlines. The third supporting document reanalyzes the damaged areas for end-to-end impacts with an alternate interpolation scheme. This alternate scheme holds damaged area constant at the 1-degree value for impact angles greater than zero degrees and less than 1 degree. This change in interpolation scheme produces only minor changes in total damaged area, in part because multiple impacts at angles greater than 1 degree tend to dominate the total damaged area. The information in the calculation reports in Table 1-1 is not being superseded by this report. Although selected material from the key reports and supporting documents is repeated in this calculation report, the reports listed in Table 1-1 remain the basic references that document the analyses of waste package response to vibratory ground motion. In particular, the attachments to the reports in Table 1-1 are incorporated by reference, and are not repeated in this report. This document is prepared in accordance with the applicable technical work plan: Technical Work Plan For: Regulatory Integration Modeling of Drift Degradation, Waste Package and Drip Shield Vibratory Motion and Seismic Consequences (BSC 2004 [DIRS 171520]), which directs the work identified in work package ARTM05. The technical work plan was prepared in accordance with AP-2.27Q, Planning for Science Activities. Although the underlying reports listed in Table 1-1 use qualified software to perform structural response calculations, no software of any kind has been used in the preparation of this report, so LP-SI.11Q-BSC, Software Management, is not applicable to this report. The 21-Pressurized Water Reactor spent nuclear fuel (SNF) waste package (21-PWR) is classified as a Safety Category item by the Q-List (BSC 2004 [DIRS 168361], page A-4). Therefore, this calculation is subject to the requirements of Quality Assurance Requirements and Description (DOE 2004 [DIRS 171539]). This document is prepared in accordance with AP-3.12Q, Design Calculations and Analyses. 1.1 SCOPE The scope of this report is limited to summarizing the mechanical response of the waste package and its internals to vibratory ground motion during the postclosure period. All results are evaluated for the outer, Alloy 22 shell of the waste package or for the fuel rod assemblies that are internal to the waste package. The damage abstractions for the waste package and cladding are not documented in this report; rather, the results from these design calculations provide the input data that the abstractions are based on. The damage abstractions for the seismic scenario class are developed and documented in the Seismic Consequence Abstraction model report (BSC 2004 [DIRS 169183]). This report does not address the performance of naval SNF during seismic events. The Naval Nuclear Propulsion Program Technical Support Document for the License Application will provide the seismic analysis for naval SNF. 1.2 LIMITATIONS The major limitations of these design calculations are as follows: • The calculations include degradation of the waste package over a 20,000-year time frame, which includes the initial 10,000-year regulatory period (see Assumption 3.12). 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. • Calculations are performed for the 21-Pressurized Water Reactor (21-PWR) waste package type. This type of waste package is the most common package type in the repository, constituting 38 percent of the anticipated inventory by package type (BSC 2004 [DIRS 169472], Table 11). • Structural response calculations for the 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 an engineered backfill, is consistent with the results from drift degradation analyses under nominal repository conditions, and is consistent with rockfall analyses that indicate complete drift collapse does not occur in the lithophysal zones until a peak ground velocity exceeds 2 m/s in most of the lithophysal zones of the repository (BSC 2004 [DIRS 166107], Section 6.4). • The ground motion time histories1 for structural response calculations were created using different approaches for intercomponent variability and for spectral matching. The results from a limited sensitivity study (Section 5.3.7) indicate that the original damage calculations using ground motion time histories for the 2.44 m/s PGV level are conservative. Section 1.3.4 provides a discussion on the methodology for defining the suites of ground motions that are used in the structural response calculations. 1.3 BACKGROUND INFORMATION ON SEISMIC SCENARIO CLASS This section summarizes information about the seismic scenario class that is relevant to the structural response of the waste package and cladding under vibratory ground motion. This information includes: • A description of the components of the engineered barrier system • The anticipated failure mechanisms for these components under seismically-induced loads • The residual stress damage threshold for failure of Alloy 22 from accelerated stress corrosion cracking • The Probabilistic Seismic Hazard Analysis that provides a framework for definition of ground motions at Yucca Mountain • The procedure for developing site-specific ground motions • The hazard levels and terminology that are relevant to these calculations. The focus of this background discussion is on the response of the waste package and cladding to vibratory ground motion; the response of the drip shield to ground motion or to rockfall induced by ground motion and the response of engineered barrier system components to fault displacement is only mentioned in passing. A complete discussion of the technical basis for the seismic scenario class in TSPA-LA can be found in the Seismic Consequence Abstraction model report (BSC 2004 [DIRS 169183]). Figure 1-1 illustrates the major components of the engineered barrier system in a typical emplacement drift. The major engineered barrier system components are the waste package, the drip shield, and the fuel rod cladding (the cladding is not shown in Figure 1-1). These are important components because they provide barriers to the release of radionuclides from the fuel rods into the unsaturated zone. The effectiveness of these barriers is potentially compromised by the direct effects from an earthquake, which include vibratory ground motion, fault displacement, and rockfall induced by ground motion. The effectiveness of these barriers is also potentially compromised by indirect effects after an earthquake, including changes in seepage, temperature, and relative humidity if an emplacement drift collapses completely during a very low probability earthquake. The major engineered barrier system components are free standing structures. The drip shield and the emplacement pallet rest on top of the invert, while the waste package rests on top of the pallet. The invert consists of a framework of mild steel structural components that is filled with ballast from run-of-the-mine tunneling operations. Because the engineered barrier system components are unconstrained, impacts can occur between waste packages, drip shields, emplacement pallets, the invert, and the drift walls in response to significant ground motions. 1.3.1 Failure Mechanisms Under Seismic Loads Mechanical processes that occur during a seismic event may compromise the functionality of the waste packages and drip shields as barriers to radionuclide release. These mechanical processes include impacts caused directly by vibratory ground motion during an earthquake, impacts caused by rock blocks and rockfall induced by vibratory ground motions, and mechanical loading from fault displacement. Under vibratory ground motions, impacts can occur between adjacent waste packages and between the waste package and its emplacement pallet, the surrounding drip shield, and the invert. Impacts can also occur between the drip shield and the emplacement pallet, the invert, and even the drift wall. Rockfall induced by vibratory ground motions can result in impacts on the drip shield in the postclosure period and impacts on the waste packages in the preclosure period, when drip shields are not yet in place. Rockfall induced by vibratory ground motion in the lithophysal zones may collapse the drifts, resulting in static loads from the mass of rubblized rock surrounding the drip shield. Finally, mechanical loads may be generated by fault displacement within the repository block. In this case, engineered barrier system components may become pinned if fault displacement is greater than the available clearances between components. rce BSC 2004 [DIRS 169183], Figure 6.1-1. RM=Continuous Recording Monitor; CAM=Continuous Air Monitor. -1. Schematic Diagram of the Engineered Barrier System Components in a Typical Emplacement Drift These mechanical processes are associated with a number of potential failure mechanisms for the waste package and cladding under vibratory ground motions: • Peak dynamic loads have the potential to result in immediate puncture or tearing of an engineered barrier system component if the failure criterion is met. A puncture provides a potential pathway for flow into and radionuclide transport out of an engineered barrier system component. • Impact-related dynamic loads may dent a component, resulting in permanent structural deformation with residual stress. High levels of residual tensile stress may lead to local degradation from accelerated corrosion processes. Areas that are breached from corrosion processes provide a potential pathway for flow into and radionuclide transport deformed fuel rods and perforated cladding. Failure of cladding provides a potential pathway for release of radionuclides from fuel rods. metal that requires very high dynamic loads to reach the tearing failure threshold. Additionally, the tearing failure of ductile material is, in general, accompanied by large distortion and significant expenditure of energy. Consequently, a small tear (through-wall macrocrack) is expected to be encompassed by a much larger highly-distorted region that is the preferable site for stress corrosion cracking. Therefore, a small tear is anticipated to be accounted for by the deformed area, which is defined and discussed in the following paragraph. The potential for immediate breach through tensile or shear failure is included in the nonlinear FE calculations supporting the seismic scenario class; however, the computational meshes are genera package drops on the emplacement pallet indicate that the maximum stress intensity2 for the impact velocities observed in the vibratory ground motion calculations is significantly below the ultimate tensile strength (BSC 2003 [DIRS 165497]). In this situation, a localized puncture or tearing is very unlikely from impact processes caused by vibratory ground motions and is not included in the seismic scenario class. On the other hand, the presence of high residual tensile stress has the potential to result in accelerated stress corrosion cracking. This combined m processes caused by vibratory ground motions. The areas that exceed the residual tensile stress threshold are referred to as the damaged area throughout this document. The effective area for flow and transport through the damaged areas will be substantially less than the damaged area because the cross-sectional area of the stress corrosion cracks is much less than the total surface area that exceeds the residual stress threshold (BSC 2004 [DIRS 169183], Section 6.3.5). Application of a residual tensile stress threshold for seismic failures is nonmechanistic in the sense that detailed calculations with accelerated corrosion rates or crack propagation are not used to determine the actual failure time after a seismic event. Rath in initiate accelerated localized corrosion or on of a once nucleated stress corrosion crack could be arrested by an encounter Source: BSC 2004 [DIRS 169183], Figure 6.3-1. Figure 1-2. Permanent Deformation from Plastic Yielding Generates Residual Stress The dynamic loads on fuel rods from end-to-end impacts of adjacent waste packages and from impacts between waste package and pallet (and, to a smaller degree, the drip shield) have the potential to fail the cladding. In the former case, direction of the fuel rods loading is predominantly axial while in the latter is transversal. The primary cladding failure mechanism is perforation due to acceleration (g-loads) in the axial and transversal direction of (BSC 2004 [DIRS 169183], Section 6.5.7). The primary deformation mode of axially loaded fuel rods (end-to-end impact of adjacent waste packages) is buckling and the resulting cladding failure mechanism is the only one considered in this study. The g-loads required to buckle fuel rods are estimated from a simple analytic model based on Euler buckling of a column (Chun et al. 1987 [DIRS 144357]). It is estimated that the cladding fails when the impact accelerations are in the range of 82 g to 252 g for axial impacts (a impacts) (Chun et al. 1987 [DIRS 144357], Table 4). 1.3.2 Residual Stress Damage Threshold for the Waste Package Accelerated stress corrosion cracking from high residual stress is expected to be the most likely cause of failure for the waste package from impact processes under vibratory ground motion. The residual stress thresholds for seismic response are similar to the criteria for initiation of stress corrosion cracking on smooth surfaces of Alloy 22 (BSC 2004 [DIRS 169042], Section 6.2.1), with thresholds defined on page 22). The use of a stress corrosion cracking initiation criterion is appro from mechanical damage exceeds the tensile failure criterion are expected to be severely cold-worked and, hence, potentially subject to enhanced stress corrosion cracking. A residual stress threshold is a conservative failure criterion because detailed corrosion models will have a delay time until failure. A conservative approach is appropriate because it is consistent with other tensile failure criteria (BSC 2004 [DIRS 169042], Section 6.2.1, second paragraph on page 22), because the residual stress failure criterion is transparent, and because it is easily applied to the output from structural response calculations. 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 is based on experimental data and conservatively in lower bound is introduced to evaluate the sensitiv is also consistent with the failure criterion for initiation of stress corrosion cracking in other waste package analyses. 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 corrosion barrier (OCB) of the waste package whose residual stress exceeds 80 percent of the yield strength of Alloy 22 and to determine the elements in the OCB of the waste package whose residual stress exceeds 90 percent of the yield strength of Alloy 22. These elements are then converted into an area susceptible to accelerated stress corrosion cracking at the 80 and 90 percent criteria. The ap 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. 1.3.3 Probabilistic Seismic Hazard Analysis A probabilistic seismic hazard analysis (PSHA) was performed to assess the seismic hazards of vibratory ground motions repository’s long-term performance and to form the basis for deve ) utilization of an extensive geologic and seismologic database developed over a 20 year the Yucca Mountain region; (2) explicit considerati alternative seismic-source, ground-motion, and fault-displacement ls; and (3) use of a formal, structured expert elicitation process to capture the informed community’s views of key inputs to the PS SH methodology for vibratory ground motions has become standard practice for deriving ground motion hazards for design purposes. Less commonly, probabilistic fault ent analyses are conducted to provi nt of differential ground displacement that might occur. Both analyses provide hazard s, which express the probability of exceeding various amounts of ground motion (or fault ent). The probability is usually expressed as a frequency of exceedance per year. The seismic hazard curves represent t magnitudes of the probability of future earthquake occurrence and, given an occurrence, its effect at a site of interest. The basic elements of a PSHA for vibratory ground motions are: a) Identification of seismic sources that contribute to the vibratory ground motion hazard at Yucca Mountain and characterization of their geometry b) Characterization of seismic sources by the recurrence rate of earthquakes of magnitudes and the maximum magnitude c) Attenuation relations that define a specified ground motion parameter (such as PGV) as a function of magnitude, source-to-site distance, local site conditions, and, in some cases, seismic source characteristics d) Integration of the seismic source characterization and ground motion attenuation evaluations, including associated uncertainties, into a seismic hazard curve and associated uncertainty distribution. The PSHA incorporates both variability and uncertainty. Variability, also termed randomness or aleatory variability, is the natural randomness in a process. For discrete variables, the randomness is parameterized by the probability of each possible value. For continuous variables, the randomness is parameterized by the probability density function. An example of variability is the amplitude of ground motion that would occur at a particular location from repeated earthquakes having exactly the same magnitude at exactly the same distance (magnitude 6 at 25 km distance). Variations in ground motion amplitude are expected due to unknowable complexities in earthquake-to-earthquake source properties and in the propagation path. Uncertainty, also termed epistemic uncertainty, is the scientific uncertainty in the model of the process. It is due to limited data and knowledge. The uncertainty is characterized by alternative models. For discrete random variables, the epistemic uncertainty is modeled by alternative probability distributions. For continuous random variables, the uncertainty is modeled by alternative probability density functions. Examples of uncertainty are alternative ground motion attenuation relations that express the amplitude of ground motion at a particular site as a function of dist reducible with additional knowledge and data. Given the input evaluations, the hazard calculation method integrates over all values of the variables and estimates the annual probability of exceedance of any ground-shaking amplitude at the site. The hazard curve quantifies the variability of the earthquake occurrence and ground-shaking attenuation. In addition to the variability of the seismic hazard, however, is uncertainty about the seismotectonic environment of a site. Significant advances in development of methodology to quantify uncertainty in seismic hazard have been made in the past 20 years (Budnitz et al. 1997 [DIRS 103635]). These advances involve the development of alternative interpretations of the seismotectonic environment of a site by multiple exp interprtations are expressed by use o seismic hazard curve is computed. The result of computing the hazard for all pathways is a distribution of hazard curves representing the full variability and uncertainty in the hazard at a site. The seismic scenario class for TSPA-LA uses the mean hazard curves for PGV and for fault displacement. Each mean hazard curve, which is defined as an average of the distribution of hazard curves referred to in the preceding paragraph, typically lies above the 80th percentile of the distrib appropriate for calculations of the mean dose to the reasonably maximally exposed individual, as required to demonstrate acceptable repository performance over 10,000 years (10 CFR 63.303 and 63.311 [DIRS 156605]). However, the use of the mean hazard curves does not propagate the epistemic uncertainty in the distributions of the hazard curves into TSPA. 1.3.4 Site-Specific Ground Motions Site-specific ground hypothetical reference rock outcrop and do not reflect site-specific soil and rock properties at the locations for which the ground motions are needed (e.g., the horizon where the emplacement drifts are located). The PSHA was conducted in this fashion because the site-specific rock and soil properties were not characterized at the time of the PSHA. Thus, further analyses are carried out to modify the PSHA results to reflect the appropriate site-specific conditions for the site of interest. developed for the waste emplacement level. Selection of annual exceedance probabilities is motivated by the requirement to “consider only events that have at least one chance in 10,000 of occurring over 10,000 years” (10 CFR 63.114(d) [DIRS 156605]). To address this requirement, ground motions are developed for annual exceedance probabilities of 10-5, 10-6, and 10-7 per year. Analyses using the developed ground motions form the basis for evaluating repository performance for seismic events with annual exceedance probabilities from-4-8 A detailed site response model provides the basis for development of seismic time histories at the emplacement drifts. Different approaches are used for developing time histories depending on how they will be used (e.g., in design or in evaluating postclosure repository performance). For Yucca Mountain, three approaches have been used to develop time histories: spectral matching, scaling to PGV, and scaling to PGV preceded by spectral conditioning. The spectral-matching approach is used primarily to develop time histories that will be used in design analyses and is not discussed further here. analyses, such as the calculations documented in this report. In addition to determining the consequences of these low-probability ground motions, another goal is to evaluate the variability in the consequences. Because much of the variability in consequences will be driven by random variability in ground motion, the time histories for postclosure analyses are developed to capture and represent that random variability. PGV is selected as the scaling p appropriate for structural damage caused by sliding or impact under earthquake loads (Newmark and Rosenblueth 1971 [DIRS 151246], Section 11.3.5 and Section 11.4). Finally, PGV is also 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. The abstractions in this document therefore use the horizontal PGV as the measure of the amplitude of the ground motion. Alternate measures, such as peak ground acceleration or the spectral acceleration at a given frequency, are anticipated to give similar results. In the PGV-scaling approach, the earthquake recordings are scaled such that the PGV matches the PGV determined in the site-response analysis for a location of interest. The records may be scaled such that both horizontal components match the target horizontal PGV and the vertical component matches the targe maintain the intercomponent variability of the original recordings. Both of these methods have been used at Yucca Mountain. For each annual exceedance probability of interest, 17 sets of time histories are developed. Each set of time histories consists of acceleration, velocity and displacement in each of two horizontal component directions and in the vertical component direction. The site-specific time histories are based on actual recordings of strong ground motion from earthquakes in the western United States and around the worl probability of exceedance. In other words, the recordings used as a basis for the time histories are selected to have a range of magnitudes and distances that corresponds to the magnitudes and distances of earthquakes contributing to the seismic hazard at the given annual exceedance probability. By basing the time histories on actual earthquake recordings and choosing records consistent with the seismic hazard, the resulting time histories will exhibit realistic phase characteristics and durations. A variation of the PGV-scaling approach involves spectr modifies the original strong motion records such that their response spectra reflect to a greater degree the site conditions at Yucca Mountain. Conditioning can be done with respect to the PSHA reference rock outcrop conditions or to the waste emplacement level conditions that reflect the site response. Conditioning can be thought of as a weak spectral match. A strong spectral match is not desired in this case because it would tend to reduce the random variability of the original recordings. For the annual exceedance probability of 10-6 per year, two suites of 17 sets of time histories each were developed. The 17 sets of recorded strong ground motion that form part of the basis for the time histories were selected to represent the range of magnitudes and distances consistent with the range indicated by the PSHA. The first suite consists of time histories for which both horizontal components were scaled to the site-specific horizontal variability is therefore not maintained for the first suite. Also, the records used to generate the time histories were not spectrally conditioned prior to scaling. A second suite of time histories for an annual probability of exceedance of 10-6 was developed by first spectrally conditioning the records to weakly match Yucca Mountain site conditions based on the response spectra for the PSHA reference rock outcrop. Specifically, t for the PSHA reference rock outcrop at Yucca Mountain were determined. The western U.S. response spectra are considered typical of the strong motion records forming the basis for Yucca Mountain time histories. These ratios, or transfer functions, were then applied to the response spectrum for each of the strong ground motion records to be used in generating time histories. Finally, the modified response spectra formed targets for weak spectral matches of the original records. Following this conditioning, the records were scaled to the site-specific PGV. In this case, only one horizontal component was scaled to the PGV and the other components were scaled to preserve the intercomponent variability of the original rec Two suites of 17 sets of time histories were also de of 10. For both of these suites, the records forming the basis for the time histories were spectrally conditioned prior to scaling. In one case, they were spectrally conditioned to weakly match the response spectra for the PSHA reference rock outcrop, similar to the approach for the second suite of ground motions for 10-6 annual exceedance probability. In the second case, they were conditioned to the site-specific response spectra for the waste emplacement area. Analyses of waste package structural response used the most current suite of groun were available when the calculations were performed. The waste package structural response calculations for the 10-6 per year ground motions were performed with the first suite of ground motions, wherein the time histories are scaled to the known values of PGV in the horizontal and vertical directions; intercomponent variability was not preserved. The waste package structural response calculations for the 10-7 per year ground motions were again performed with the first suite of ground motions that were spectrally conditioned to the reference rock outcrop and preserved the intercomponent variability of the original records. 1.3.5 Terminology for Ground Motion Level The terminology for the ground motion hazard curves and for the suite of ground hazard curve defines the relationship between the mean estimate of the mean annual frequency of exceedance and the amplitude of the vibratory ground motion, measured by PGV. The mean annual exceedance frequency represents the mean value of the frequency in any year with which one observation to the next. We use the mean of this random number as a measure of how likely an event is over any future year. When the mean annual exceedance frequency of interest is much less than 1, as it is here, the mean annual exceedance frequency and the annual exceedance probability are essentially equal3. This report uses the term exceedance frequency because it is more general, although the annual exceedance frequency and annual exceedance probability are interchangeable for the very infrequent seismic hazards considered in this study. The ground motion hazard curve for this report is based on the mean annual exceedance frequency. The effect of vibratory ground motion on the engineered barrier system components is assessed for a set of ground motions with a given value of the horizontal PGV. of 5.35 m/s. These ground motion sets are often referred to as the 10-6 per year and the 10-7 per year ground motions (respectively) because PGV values of 2.44 m/s and 5.35 m/s correspond to these frequency values on the hazard curve at the emplacement drifts. Unfortunately, this convenient terminology is misleading because a seismic event with a PGV of 2.44 m/s will NOT occur with a frequency of 10-6 per year. The correspondence o-6 a mean annual frequency of 10-6 per year. In other words, the ensemble of sei ns with PGV exceeding 2.44 m/s will occur with a mean frequency of 10-6 pe , the probability of encountering an earthquake with a PGV of exactl tesimally small, and will certainly not occur with a frequency of 10-6 per yea e identified by the appropriate value of PGV because the value 2. METHOD The waste package calculations presented in this overview document were conducted using commercial FE software. The FE method is a numerical technique in common use for analysis of engineering problems in structural dynamics. The method requires discretization of the structure as a number of elements that are interconnected by nodal points (the FE mesh). The governing equations of motion, subject to imposed boundary and initial conditions, are solved to provide the solution of the transient mechanical response of the structure. The boundary and initial conditions imposed on a waste package in this particular case are a result of the constraints supplied by the emplacement drift, adjacent waste packages, drip shield, and pallet; and from the applied dynamic loading conditions. The explicit FE method with the central difference method of time integration was employed in all calculations. Results are given in terms of the transient induced stresses, strains and displacements. Three-dimensional graphical representation of the motion of the waste package as well as the stress and strain states are used to aid in interpretation of the results. The design of the 21-PWR waste package is used for all calculations and is defined in Repository Design, Waste Package, Project 21-PWR Waste Package with Absorber Plates, Sheet 1 of 3, Sheet 2 of 3, and Sheet 3 of 3 (BSC 2001 [DIRS 157812]); exceptions are the gap between the inner vessel (IV) and the OCB, for which a value of 4 mm was used (Plinsky 2001 [DIRS 156800], Section 8.1.8), and the OCB thickness, for which a value of 18 mm was assumed (Assumption 3.12). The sketch in (BSC 2004 [DIRS 167083], Attachment I) provides additional information not included in Repository Design, Waste Package, Project 21-PWR Waste Package with Absorber Plates, Sheet 1 of 3, Sheet 2 of 3, and Sheet 3 of 3 (BSC 2001 [DIRS 157812]). The methods for the calculations in the three key reports identified in Table 1-1 are as follows: • Structural Calculations of Waste Package Exposed to Vibratory Ground Motion (BSC 2004 [DIRS 167083]) The structural response calculations were performed using off-the-shelf versions of commercially available FE programs. The FE mesh was created with the ANSYS V5.6.2 FE code (Software Tracking Number [STN] 10364-5.6.2-01, BSC 2002 [DIRS 159357]). Calculations were then performed with the LS-DYNA V960.1106 (STN 10300-960.1106-00, BSC 2002 ([DIRS 158898]) FE code or performed with the LS-DYNA V970.3858 (STN 10300-970.3858 D SMP-00, BSC 2003 [DIRS 166139]) FE code. All versions of LS-DYNA are simply referred to as LS-DYNA, unless it is necessary to distinguish features of different versions. These calculations also require design information for the emplacement pallet and drip shield. Design of the emplacement pallet (pallet, for brevity, throughout the document) is defined in Emplacement Pallet (BSC 2003 [DIRS 161520]); the sketch in Structural Calculations of Waste Package Exposed to Vibratory Ground Motion (BSC 2004 [DIRS 167083], Attachment II) provides additional information not included in (BSC 2003 [DIRS 161520]) (see also Assumption 3.8). Finally, design of the interlocking drip shield (DS) used in this calculation is provided in D&E / PA/C IED Interlocking Drip Shield and Emplacement Pallet (BSC 2004 [DIRS 169220]). A set of 15 structural response calculations is performed at each of two different ground motion amplitudes: 2.44 m/s PGV and 5.35 m/s PGV level, corresponding to the 10-6 and the 10-7 annual exceedance frequencies, respectively. One calculation is also performed at each of 0.19 m/s and 0.384 m/s PGV levels, corresponding to the 5×10-4 and 1×10-4 annual exceedance frequencies, respectively. Additionally, three simulations are performed using approximate time histories with a 0.992 m/s PGV level, corresponding to an annual exceedance frequency of 10-5 per year. These approximate time histories are created by scaling the three acceleration components for selected 2.44 m/s PGV level time histories, as explained in Section 1.3.5 and in Structural Calculations of Waste Package Exposed to Vibratory Ground Motion (BSC 2004 [DIRS 167083], Attachment XI). Fifteen ground motion time histories are required for the calculations at the 2.44 m/s and 5.35 m/s PGV levels. The fifteen ground motions represent the uncertainty in the seismic sources and in seismic wave propagation through geologic media, as explained in Sections 1.3.3 and 1.3.4. The uncertainty in the ground motions is substantial. For example, at the 5.35 m/s PGV level, the first horizontal velocity component is scaled to always have a PGV of 5.35 m/s. However, the range in PGV values for the second horizontal velocity component is 1.72 m/s to 17.9 m/s, and the range in PGV values for the vertical velocity component is 2.27 m/s to 17.1 m/s (BSC 2004 [DIRS 166107], Appendix X). In fact, the uncertainty in the ground motions is the dominant uncertainty in the damaged areas from the structural response calculations, as shown by the results in Tables 5.3-22 and 5.3-55. • 21-PWR Waste Package Side and End Impacts (BSC 2003 [DIRS 162293]) The structural response calculations were performed using off-the-shelf versions of commercially available FE programs. ANSYS V5.4 (CRWMS M&O 1998 [DIRS 153710]) was used to generate the FE meshes. The calculations were then performed with the commercially available LS-DYNA V950 FE code (CRWMS M&O 2000 [DIRS 149714]) or with the LS-DYNA V960.1106 FE code (BSC 2002 [DIRS 158898]). Ground motion time histories are not required for these calculations. Rather, the range of impact velocities and impact angles observed in the calculations for Structural Calculations of Waste Package Exposed to Vibratory Ground Motion (BSC 2004 [DIRS 167083]) provides the basis for developing a matrix of representative values of the impact velocity and impact angle. This matrix and the damaged areas associated with each representative impact provide a basis for determining damaged areas by interpolation for the multiple waste package-to-waste package impacts in each realization, as summarized in Sections 5.3, 5.3.1, 5.3.2, and 5.3.3 of this report. • Maximum Accelerations on the Fuel Assemblies of a 21-PWR Waste Package During End Impacts (BSC 2003 [DIRS 162602]) The structural response calculations were performed using off-the-shelf versions of commercially available FE programs. ANSYS V5.4 (CRWMS M&O 1998 [DIRS 153710]) was used to generate the FE meshes. The calculations were then performed with the commercially available LS-DYNA V950 FE code (CRWMS M&O 2000 [DIRS 149714]) or with the LS-DYNA V960.1106 FE code (BSC 2002 [DIRS 158898]). Ground motion time histories are not required for these calculations. Rather, the range of impact velocities and impact angles observed in the calculations for Structural Calculations of Waste Package Exposed to Vibratory Ground Motion (BSC 2004 [DIRS 167083]) provides the basis for developing a matrix of representative values of the impact velocity and impact angle. This matrix and the g-loads on the fuel rod assemblies for each representative impact provide a basis for determining cladding failure under the multiple waste package-to-waste package impacts summarized in Sections 5.3.1, 5.3.2, and 5.3.3 of this report. The methods of the calculations in the supporting documentation for the seismic scenario are as follows: • 21-PWR Waste Package End Impacts – A Mesh Study (BSC 2004 [DIRS 170844]) This calculation is a supplemental study of mesh sensitivity for the damaged area from end impacts. This study is based on the general approach and results for end impact calculations documented in 21-PWR Waste Package Side and End Impacts (BSC 2003 [DIRS 162293]), with appropriate changes to the FE mesh. The design of the 21-PWR waste package is used for all calculations and is defined in Repository Design, Waste Package, Project 21-PWR Waste Package with Absorber Plates, Sheet 1 of 3, Sheet 2 of 3, and Sheet 3 of 3 (BSC 2001 [DIRS 157812]); exceptions are the gap between the IV and the OCB, for which a value of 4 mm is used (Plinsky 2001 [DIRS 156800], Section 8.1.8), and the OCB thickness, for which a value of 18 mm is assumed (Assumption 3.12). All material properties are evaluated at 150ºC, which is the base case for structural response in the seismic scenario. Finally, ground motion time histories are not required for these calculations. The structural response calculations were performed using off-the-shelf versions of commercially available FE programs LS-DYNA Version (V) 970.3858 D SMP-00 and LS-DYNA V970.3858 D MMP-00 (BSC 2003 [DIRS 166139] and BSC 2003 [DIRS 166918]). • Additional Structural Calculations of Waste Package Exposed to Vibratory Ground Motion (BSC 2004 [DIRS 168385]) This calculation is a supplemental study of the sensitivity of damaged area to the conditioning of ground motion time histories. This study is based on the general approach and results documented in Structural Calculations of Waste Package Exposed to Vibratory Ground Motion (BSC 2004 [DIRS 167083]), with appropriate changes for the ground motions. Four additional calculations are performed with selected ground motions from the 2.44 m/s PGV level. The original ground motions (BSC 2004 [DIRS 167083]) did not preserve intercomponent variability in the original ground motion recordings and were not spectrally conditioned. The new ground motions (BSC 2004 [DIRS 168385]) preserved intercomponent variability in the original ground motion recordings and were spectrally conditioned for ground motions typical of the western United States. The issues of spectral conditioning and intercomponent variability are discussed in more detail in Section 1.3.4. The structural response calculations were performed using an off-the-shelf version of commercially available FE program LS-DYNA Version (V) 970.3858 D SMP-00 (BSC 2003 [DIRS 166139]). • Alternative Damaged Area Evaluation for Waste Package Exposed to Vibratory Ground Motion (BSC 2004 [DIRS 170843]) This calculation is a supplemental study of the sensitivity of damaged area to the interpolation scheme for impact angles between zero degrees and one degree. The calculations documented in (BSC 2004 [DIRS 167083]) determine the timing, speed, and impact angle for multiple waste package-to-waste package impacts between adjacent waste packages exposed to ground motion time histories. The calculations documented in (BSC 2003 [DIRS 162293]) define the damaged areas on the waste package that result from individual end impacts at specific values of the impact speed and impact angle. This matrix of values provides a basis for predicting end-to-end damage under the complex kinematics of multiple impacts. The methodology in (BSC 2004 [DIRS 167083]) uses a linear interpolation on impact angle to estimate damaged area. However, ideal zero degree impacts are anticipated to be extremely unlikely because they require perfectly flat contact and because the centerlines of adjacent packages must be perfectly collinear. Since it will be very difficult to achieve the ideal zero degree impact, it may be more reasonable to estimate damage for low angle impacts (i.e., those below 1 degree) with the damaged area for a one-degree impact. In other words, all impact angles greater than zero and less than one degree are assumed to be one degree for purposes of damage estimation. This supplemental study consists entirely of recalculating by hand the damaged areas in (BSC 2004 [DIRS 167083]). No new structural response calculations were performed for this study. It follows that ground motion time histories are not required for this study and no qualified software is required for this study. Damaged area is estimated from the residual stress distribution and a residual stress threshold for accelerated stress corrosion cracking of Alloy 22 in (BSC 2004 [DIRS 167083]) and (BSC 2003 [DIRS 162293]). The residual stress threshold is defined as a fraction of the yield strength of the OCB material, Alloy 22 [SB-575 N06022], at given temperature. Lower and upper thresholds for Alloy 22 are based on 80 percent and 90 percent of the yield strength of Alloy 22 (see discussion in Sections 1.3.1 and 1.3.2). The yield strength and other material properties are generally evaluated at a temperature of 150°C. However, a few simulations use 100ºC (BSC 2003 [DIRS 162293], Tables 9 to 11) or 200°C (BSC 2004 [DIRS 167083], Attachments V and VIII, and BSC 2003 [DIRS 162293], Tables 7 and 8) for sensitivity purposes. The residual stress distribution is evaluated from plots of the residual first principal stress in the OCB of the waste package. These plots are prepared by the postprocessing programs available with LS-DYNA. Analysis of the residual first principal stress in these plots identified those elements wherein the residual tensile stress exceeded the residual stress threshold for accelerated stress corrosion cracking. It is important to acknowledge that this failure criterion is applied in a very conservative manner. Namely if an element on either (inner or outer) surface of the OCB exceeds the residual stress threshold, then the area “fails” (i.e., it is considered damaged by accelerated stress corrosion cracking) regardless of the residual stress distribution across the thickness of the shell. If an element on the outer surface fails, then all elements beneath this element are assumed to fail, even though a compressive stress state may arrest crack propagation through the OCB. INTENTIONALLY LEFT BLANK 3. ASSUMPTIONS The following assumptions are made regarding the FE representations in Structural Calculations of Waste Package Exposed to Vibratory Ground Motion (BSC 2004 [DIRS 167083]) and in Additional Structural Calculations of Waste Package Exposed to Vibratory Ground Motion (BSC 2004 [DIRS 168385]). Assumptions related to calculation of material properties at 100°C, 150°C, and 200°C are not listed here, but can be found in Section 3 of the referenced documents. 3.1 The exact geometry of the waste package internals is simplified for this calculation. The waste package IV (including the IV lids) and its internals, including SNF, are represented by a thick-wall cylinder of 316 stainless steel (SS) with uniform thickness and circular cross section (see Section 5.2). The thickness of this cylinder is determined by the cumulative mass of these components. The rationale for this assumption is that the IV and the SNF affect the results of this calculation predominantly through their total mass and overall dimensions. This assumption is used in Section 5.2.1.2. 3.2 The friction coefficients for metal-to-metal contact and metal-to-rock contact are considered random parameters in this calculation. The range of values for both of these friction coefficients is 0.2 to 0.8. The rationale for this assumption follows: Coefficients of static and sliding friction for various metals and other materials are provided in various handbooks (for example, Avallone and Baumeister 1987 [DIRS 103508], Table 3.2.1, page 3-26). However, the coefficients of friction for the specific materials in this calculation are not defined in this handbook. In addition, the potential for long-term corrosion to modify the sliding friction must also be considered in defining the friction coefficient. In this situation, the appropriate coefficients of friction for the repository components have high uncertainty. It is thus appropriate to pick a distribution of values for the coefficients of friction that encompass a range of materials and a range of mechanical responses from little or no sliding between components to substantial sliding between components. A distribution of values for the friction coefficient between 0.2 and 0.8 will achieve these goals (DTN: MO0301SPASIP27.004. [DIRS 161869], Table I-4). First, this distribution is broad enough to encompass typical values of the dry sliding friction coefficients for a wide variety of metals and other materials (Avallone and Baumeister 1987 [DIRS 103508], Table 3.2.1, page 3-26). The appropriateness of this range is independently confirmed by seismic analyses for spent fuel storage racks (DiGrassi 1992 [DIRS 161539]). This distribution is also broad enough to represent a range of mechanical response for the waste package, pallet, and drip shield. A friction coefficient near 0.2 maximizes sliding of the waste package on the pallet, of the pallet on the invert, and of the drip shield on the invert. Similarly, a friction coefficient near 0.8 minimizes sliding among the various components. This assumption is used in Sections 5.2.1.2, 5.2.2.2.1 and 5.2.3.2.1. 3.3 The variation of functional friction coefficient between the static and dynamic values as a function of relative velocity of the contact surfaces is not available in the literature for the materials used in this calculation (see Section 5.2.1.2). The effect of relative velocity of the contact surfaces is neglected in these calculations by assuming that the functional friction coefficient and the static friction coefficient are both equal to the dynamic friction coefficient. The impact of this assumption on results presented in this document is anticipated to be negligible. The rationale for this conservative assumption is that it provides the bounding set of results by minimizing the friction coefficient within the given FE analysis framework. This assumption is used in Section 5.2.1.2 and corresponds to Mecham 2004 ([DIRS 170673], paragraph 5.2.14.2). 3.4 The FE representation of the drip shield is simplified in this analysis (see Section 5.2 for details), and the density of Titanium Grade 7 (Ti-7) is modified to conserve mass in the simplified representation. The impact of this assumption on results presented in this document is anticipated to be negligible. The rationale for this assumption is that it captures the essential kinematics of freestanding components in the drift while reducing the computer execution time. This assumption is used in Section 5.2.1.2. 3.5 Interactions with neighboring (adjacent) waste packages are represented by using a rigid longitudinal boundary that is attached to the invert. That is, for the purposes of calculating the damaged area on the waste package, the interaction between adjacent waste packages is assumed to be adequately described by a sequence of impacts of the waste package on a rigid wall (BSC 2003 [DIRS 162293]). The rationale for this assumption is that the initial longitudinal distance between adjacent waste packages is only 0.1 m (BSC 2004 [DIRS 168489], Table 1). In the course of the strong vibratory ground motions considered in this study, it is conceivable but very unlikely that the motion of the waste package-pallet assemblies would result in the local pile-up of the assemblies along the drift. In this situation, the impact of the adjacent waste package is represented by an unyielding, reflective boundary that is fixed to the invert. This assumption is used in Section 5.2.1.2. This assumption provides a major simplification for the calculations, but is probably extremely conservative. Low frequency seismic waves have waste lengths that are much longer than the characteristic length scale of the waste package (about 5 meters). In this situation, adjacent waste packages are more likely to move in tandem. It follows that the damage from end-to-end impacts of adjacent waste packages is overestimated by the computational approach. 3.6 The interaction between the waste package and drip shield through lateral or side impacts is not taken into account for the calculation of the total damaged area of the waste package. The impact of this assumption on results presented in this document is anticipated to be negligible. The rationale for this assumption is twofold. First, the waste package is heavier than the drip shield (DS) by a factor of 10 (BSC 2004 [DIRS 167083], Attachments I and III); consequently, an impact between the waste package and drip shield results in the drip shield being pushed around by the waste package without significant deformation of the waste package OCB. Second, the interaction between waste package and drip shield takes place at the trunnion collar sleeves, which is similar to the interaction from end-to-end impacts. Since the end-to-end impacts are much more frequent, and since the waste package is a much stiffer “target” than the drip shield, it is not likely that the side impacts would damage an area that is not already damaged by the end impacts (BSC 2003 [DIRS 162293], Tables 4 through 8, for impact angles). This assumption is used in Sections 5.3.1.3 and 5.3.2.3. 3.7 All interactions between the waste package and the longitudinal boundaries (representing the neighboring waste package) with impact velocity less than 1 m/s are not included in the calculation of damaged area. The impact of this assumption on results presented in this document is negligible. The rationale for this assumption is that the damaged area for an impact velocity of 1 m/s is either zero or negligible compared to higher impact velocities, as presented in Tables 5.3-56 through 5.3-64. This assumption is used in Section 5.3.1.2. 3.8 The longitudinal tubes in the emplacement pallet (Tube 1 in Attachment II of BSC 2004 [DIRS 167083]) are, for the purpose of this calculation, assumed to be made of Alloy 22. This assumption has a significant impact on the calculation results. The rationale for this assumption is that it is impossible to take structural credit for these tubes as long as they are made of 316 SS because of long-term corrosion. Thus, unless this design change is made, the pallet is going to fail due to an unacceptable performance (i.e., it would fail to support the waste package as intended). This assumption is used in Sections 2, 5.1, and 5.2. 3.9 The waste package rests on two “cradles” formed by the opposite ends of the emplacement pallet, and either cradle may damage the OCB of the waste package if the vertical impact velocity is large enough. However, the damaged area of the OCB due to the waste package-pallet interaction is evaluated only on one side of the waste package, in a finely meshed OCB region (see Section 5.2.1.2 for details). The total damaged area due to the waste package-pallet interaction is calculated by assuming that the damaged areas on either end of the waste package are the same (i.e., by multiplying by two the damaged area evaluated on one side). The rationale for this assumption is that the number and intensity of impacts on the two ends should be statistically similar. The rationale for this approach is that the waste package is symmetric, there is no spatial variability of friction coefficients, and the ground motion is uniformly applied to the invert, consequently the number and intensity of impacts on two ends should be similar. Obviously, the damaged areas on the two ends may be somewhat different due to the random nature of the event, but, on average, there should be no reason for a bias or preference. This assumption is used in Section 5.3.1.1 and Section 5.3.2.1. 3.10 The waste package is assumed to be symmetric about its mid-plane. Both waste package ends are represented based on the bottom-end configuration (BSC 2004 [DIRS 167083], Attachment I and BSC 2001 [DIRS 157812]). This simplification has no effect on the results, as obtained in this calculation. The rationale for this assumption is that it simplifies the FE representation, without affecting the calculation results. This assumption is used in Section 5.2.1.2. 3.11 The temperature of the waste package is assumed to be 150°C for temperature-dependent material properties. A temperature of 150°C is appropriate and reasonable for evaluation of material properties at the time of the seismic event. This value (150°C) is conservative for evaluation of material properties during 98.5 percent of the first 10,000 years after repository closure. This result is based on a thermal analysis for an open drift with three infiltration levels and five host-rock units (BSC 2004 [DIRS 169565], Figure 6.3-7 through Figure 6.3-11). The peak waste package temperature ranges from 147.4°C to 177.8°C (BSC 2004 [DIRS 169565], Table 6.3-8). The waste package temperature time histories demonstrate that temperature exceeds 150°C for, at most, the first 150 years after ventilation ceases. In some cases, the temperature never exceeds 150°C for certain infiltration levels and host rock units. Since the time period when temperature exceeds 150°C is never greater than 150 years, it follows that evaluating material properties such as the yield strength at 150°C is conservative for at least 98.5 percent of the 10,000 year regulatory period or 99.25 percent of the first 20,000 years after repository closure. This assumption is used in Sections 5.1 and 5.2.2.1. 3.12 The thickness of the waste package OCB is reduced by 2 mm to represent degradation of the package from general corrosion. The rationale for this assumption is that the thickness reduction of 2 mm over the period of 10,000 years to 20,000 years corresponds to very high rates of general corrosion. For example, the median general corrosion rate is 51.8 nanometers per year at 150°C (BSC 2004 [DIRS 169984], Section 8.1). This rate leads to a maximum thickness loss of 0.518 mm after 10,000 years or 1.036 mm after 20,000 years. Similarly, the maximum rate of general corrosion is 256 nanometers per year, based on the 99.99th percentile corrosion rate at 150°C (BSC 2004 [DIRS 169984], Section 8.1). This rate leads to a maximum thickness loss of 2.56 mm after 10,000 years or 5.12 mm after 20,000 years. Both rates have a very conservative bias because (1) waste package temperature is significantly less than 150°C during 98.5 percent of the first 10,000 years after repository closure (see discussion for Assumption 3.11), and (2) the maximum corrosion rate is based on the 99.99th percentile. Given the conservative biases in these estimates, a thickness reduction of 2 mm is a reasonable representation of degradation of the waste package OCB during the 10,000 year regulatory period or during the first 20,000 years after repository closure. This assumption is used in Sections 5.2.1.2, 5.2.2.2.1, 5.2.3.2.1, 5.2.4.2 and 5.2.5.2. The calculations documented in 21-PWR Waste Package Side and End Impacts (BSC 2003 [DIRS 162293]), in Maximum Accelerations on the Fuel Assemblies of a 21-PWR Waste Package During End Impacts (BSC 2003 [DIRS 162602]), and in 21-PWR Waste Package End Impacts – A Mesh Study (BSC 2004 [DIRS 170844]) use assumptions 3.3 and 3.12, plus the following additional assumptions: 3.13 The exact geometry of the 21-PWR fuel assemblies is simplified for the purpose of this calculation in such a way that its total mass is assumed to be distributed within a bar of square cross section with uniform mass density. The rationale for this assumption is to simplify the FE representation while providing a set of bounding results. This assumption is used in Section 5.2.2.2.1, 5.2.3.2.1 and corresponds to Mecham (2004 [DIRS 170673], paragraph 5.2.9.1). 3.14 The material used to represent the fuel assemblies is 304 SS. The rationale for this assumption is that the end fittings are made of 304 SS (Punatar 2001 [DIRS 155635], Section 2.1, page 2-4) and they are the parts that will come in contact with other components. This assumption is used in Sections 5.1, 5.2.2.2.1, 5.2.3.2.1 and 5.2.4.2 and corresponds to Mecham (2004 [DIRS 170673], paragraph 5.2.9.2). 3.15 The following design parameters are assumed for the 21-PWR SNF assemblies to be loaded into a 21-PWR waste package: mass = 773.4 kg, width = 216.9 mm, and length = 4407 mm. The rationale for this assumption is that these parameters correspond to the B&W (Babcock & Wilcox) 15x15 fuel assembly, which is the heaviest 21-PWR fuel assembly available (BSC 2004 [DIRS 170803], Table 3-3). The mass of the B&W fuel assembly has been increased by 25 lbs (11.4 kg) to account for variations in fuel assembly mass. It should be noted that South Texas 21-PWR fuel assemblies will not be disposed in the 21-PWR waste package, and are therefore excluded from this assumption. This assumption is used in Section 5.2.2.2 and corresponds to Mecham (2004 [DIRS 170673], paragraph 5.2.9.5). 3.16 The target surface is assumed to be unyielding (i.e. elastic), and A 36 carbon steel (CS) is used to represent it in the FE analysis. The rationale for this assumption was that this material has a high modulus of elasticity compared to concrete and it is known that the use of an unyielding surface with high modulus of elasticity would ensure conservative results in terms of residual stresses in the waste package. This assumption is used in Section 5.1, 5.2.1.2, 5.2.2.2.1, 5.2.3.2.1, and 5.2.4.1 and corresponds to Mecham (2004 [DIRS 170673], paragraph 5.2.8.1). 3.17 It is assumed that the dynamic (sliding) friction coefficient is 0.5 for all contacts because the friction coefficients for the materials in this calculation are not available in the literature. The rationale for this assumption is that this friction coefficient represents a typical value for most metal-on-metal contacts (Avallone and Baumeister 1987 [DIRS 103508], Table 3.2.1, pp. 3-26). This assumption is used in Section 5.2.2.2.1 and 5.2.3.2.1. The hand calculations documented in Alternate Damaged Area Evaluation for Waste Package Exposed to Vibratory Ground Motion (BSC 2004 [DIRS 170843]) require one additional assumption: 3.18 All impact angles between the waste package and the longitudinal boundary greater than zero and less than one degree are assumed to be one degree for the purpose of the damaged area calculation. The results from the single end impact calculations for the waste package (see Tables 5.3-56 and 5.3-57 in this report) demonstrate that the damaged area for a zero degree impact is substantially less than that for a one degree impact at the same impact speed. In this situation, a simple linear interpolation of damaged area values between zero and one degree may not be conservative. That is, the damaged area for a 0.2 degree impact may be more similar to the damaged area for a one degree impact because the load is not spread perfectly uniformly on the trunnion collar sleeve, as occurs for a zero degree impact. Resetting impact angles that are greater than zero and less than one degree to one degree is conservative because damage is greater for the one-degree impact angle at a given impact velocity. The rationale for this approach is that it provides the bounding set of results. This assumption is used in Section 5.3.8.3. 4. USE OF COMPUTER SOFTWARE Although the underlying reports listed in Table 1-1 and summarized in Section 2 use qualified software, no software has been used in the preparation of this report. For the reader’s convenience, the software codes and versions used in the underlying reports are summarized in Table 4-1. The operating systems, CPU numbers, input files, and output files for all calculations are provided in the reports listed in Table 1-1, but are not repeated here. Table 4-1. Software for Structural Response Calculations Code Name Version Use Documentation ANSYS V5.6.2 Mesh generation BSC 2002 [DIRS 159357] ANSYS V5.4 Mesh generation CRWMS M&O 1998 [DIRS 153710] TrueGrid V2.1.5 Mesh generation N/A – Exempt Software LS-DYNA V950 Structural response CRWMS M&O 2000 [DIRS 149714] LS-DYNA V960.1106 Structural response BSC 2002 [DIRS 158898] LS-DYNA V970.3858 D SMP-00 Structural response BSC 2003 [DIRS 166139] LS-DYNA V970.3858 D MMP-00 Structural response BSC 2003 [DIRS 166918] LSPOST V2.0 Post-processing of computational results N/A – Exempt Software LS-PREPOST V1.0 Post-processing of computational results N/A – Exempt Software INTENTIONALLY LEFT BLANK 5. CALCULATION Throughout Section 5, ground motions are identified by the appropriate value of PGV because the value of PGV provides a unique and unambiguous identifier for each set of ground motions, even when multiple hazard curves have been developed for a site. Often, the original source information is given in annual exceedance frequency, which is then converted to PGV for use in this text. For the reader’s convenience, the following list repeats the correspondence identified in Section 1.3.5: • PGV of 0.19 m/s corresponds to the 5x10-4 per year exceedance frequency. • PGV of 0.384 m/s corresponds to the 10-4 per year exceedance frequency. • PGV of 1.05 m/s corresponds to the 10-5 per year exceedance frequency. • PGV of 2.44 m/s corresponds to the 10-6 per year exceedance frequency. • PGV of 5.35 m/s corresponds to the 10-7 per year exceedance frequency. 5.1 MATERIAL PROPERTIES Material properties at room temperature and at elevated temperatures are defined in the individual design calculations listed in Table 1-1. Details of the assumptions for and the calculation of the material properties at 100°C, 150°C and 200°C are provided in the individual design calculations, and will not be repeated here because no calculations are performed in this document. The following summary identifies the major materials for the waste package structural response calculations: • SB-575 N06022 (Alloy 22) (OCB of waste package, OCB lids, upper and lower trunnion collar sleeves, IV support ring, and pallet (see Assumption 3.8)) • SA-240 S31600 (316 SS) (IV, IV lids, shear ring, and shell interface ring) • SA-240 S30400 (304 SS) (21-PWR fuel assemblies, see Assumption 3.14) • SA-516 K02700 (A 516 Grade 70 Carbon Steel [CS]) (basket guides and stiffeners, fuel basket plates and tubes) • SA-36 K02600 (A 36 Carbon Steel) (unyielding surface for the side and end impact calculations; see Assumption 3.16) • SB-265 R52400 (Titanium Grade 7 [Ti-7]) (drip shield plates) • TSw2 Rock (the drift walls). Table 5.1-1 lists typical material properties of these materials at 150°C. Table 5.1-1. Typical Material Properties at 150°C Alloy 22a 316 SSa 304 SSb 516 CSb A 36 CSb Ti-7a TSw2a Density (kg/m3) 8690 7980 N/A 7850 7860 N/A 2370 Modulus of elasticity (GPa) 199 186 186 195 203 101 33.0 Poisson’s ratio (-) 0.278 0.298 0.29 0.3 0.3 0.32 0.21 Yield strength (MPa) 310 161 154 232 N/A N/A N/A Tangent modulus (GPa)c 1.77 1.94 1.69 3.08 N/A N/A N/A a BSC 2004 [DIRS 167083], Sections 5.1, 5.1.1, and 5.3. b BSC 2004 [DIRS 170844], Section 5.1.1 and Table 3 in Section 5.1.3. c Tangent (hardening) modulus defines the slope of the stress-strain curve in the hardening (plastic) region. TSw2 = Topopah Spring welded-lithophysal poor tuff 5.2 FE REPRESENTATIONS 5.2.1 FE Representation for Structural Calculations of Waste Package Exposed to Vibratory Ground Motion 5.2.1.1 Objective and Methodology The objective of this calculation is to determine the residual stress distribution in the OCB of a waste package under vibratory ground motion, and to estimate the area of the waste package OCB for which the residual first principal stress exceeds the residual stress threshold. This area is called the “damaged area” in this document. 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 (BSC 2004 [DIRS 167083], Section 6.1). A similar set of calculations is also performed for a PGV of 5.35 m/s (BSC 2004 [DIRS 167083], Section 6.2). These values for PGV correspond to the peak of the first horizontal velocity component, which is always in a horizontal plane and perpendicular to the longitudinal direction for the structural response calculations (the longitudinal direction runs along the centerline of the drift). The stochastic (uncertain) input parameters for the 15 simulations are 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 2004 [DIRS 169999], Section 6.4) for each PGV level. The sampled values of these stochastic parameters are listed in Table 5.2-1, with the friction coefficients rounded to two significant figures. Each FE simulation is performed in three steps. The first step calculates the transient vibratory motion and impacts. The goal of this step is to compute the deformation of the waste package during the dynamic impacts between package and emplacement pallet. During this computational phase the three components of ground-motion acceleration time history are simultaneously applied to all invert nodes. The stochastic (uncertain) input parameters for 15 simulations corresponding to the 2.44 m/s PGV level and for 15 simulations corresponding to the 5.35 m/s PGV level are listed in Table 5.2-1 (DTN: MO0301SPASIP27.004 [DIRS 161869], Table I-4). No system damping or contact damping is applied during the transient vibratory simulations. This admittedly conservative approach is used in order to prevent unwanted influence of damping on the rigid-body motion of unanchored structures. Table 5.2-1. Values of Randomly Sampled Input Parameters for Each Realization Realization Number Ground Motion Number Friction Coefficient (-) Metal to metal Metal to rock 1 7 0.80 0.34 2 16 0.33 0.49 3 4 0.50 0.62 4 8 0.60 0.22 5 11 0.20 0.24 6 1 0.27 0.69 7 2 0.71 0.60 8 13 0.56 0.54 9 10 0.55 0.36 10 9 0.36 0.41 11 5 0.42 0.67 12 6 0.65 0.73 13 12 0.75 0.31 14 14 0.29 0.45 15 3 0.46 0.78 Source: BSC 2004 [DIRS 167083], Table 6.1-1. The second step of the simulation is the post-vibratory relaxation. The goal of this step is to obtain steady-state results (i.e., residual stresses) at the end of the ground motion. During this computational phase, the motion of the invert nodes is fixed in all three directions, and the only load applied to freestanding objects is the acceleration of gravity. In addition, system damping is applied globally (to all objects) to accelerate the convergence to steady-state results (see Section 5.2.1.4 for details). The specified duration of this post-vibratory relaxation part of simulation is such to allow for the steady-state stresses to establish; most of the time duration of 0.5 s suffices. The third step of the analysis is comparison of the first principal residual stress with the residual stress threshold for accelerated corrosion cracking of Alloy 22. The goal of this step is to determine the “damaged areas” wherein the first principal stress exceeds the residual tensile stress threshold for Alloy 22. If an element on the surface of the waste package OCB exceeds this threshold, then its area is included in the total damaged area, independent of the stress state through the thickness of the waste package OCB. This is a conservative approach because it ignores the potential for a compressive stress profile through the thickness of the OCB to arrest crack propagation. 5.2.1.2 FE Representation As seen in Figure 5.2-1, it represents the components of the three-dimensional FE representation for the vibratory ground-motion simulations. Figure 5.2-2 presents a cut-away view (portions of various parts are removed to offer a more revealing outlook) showing details of the waste package and emplacement pallet. As shown in these figures, the FE representation consists of the waste package mounted on its emplacement pallet, the surrounding drip shield, the invert surface, and the lateral and longitudinal boundaries. The longitudinal boundary represents the neighboring waste package/pallet assembly (Assumption 3.5), while the lateral boundary represents the drift walls. The FE representation is developed in ANSYS V5.6.2, based on the dimensions provided in the Emplacement Pallet report (BSC 2003 [DIRS 161520]), the Repository Design, Waste Package, Project 21-PWR Waste Package with Absorber Plates, Sheet 1 of 3, Sheet 2 of 3, and Sheet 3 of 3 report (BSC 2001 [DIRS 157812]), and the Structural Calculations of Waste Package Exposed to Vibratory Ground Motion report (BSC 2004 [DIRS 167083], Attachments I, II, and III). The FE representations are then used in LS-DYNA V960.1106 and LS-DYNA V970.3858 to perform a transient analysis of the waste package exposed to vibratory ground motion. The average waste package skirt-to-skirt spacing is 0.1 meters in the high temperature operating mode (BSC [DIRS 168489], Table 1). Thus, the distance between the waste package (specifically, the trunnion collar sleeve [i.e., the skirt]) and the longitudinal boundary (representing the neighboring package and emplacement pallet) is 0.1 meters. Three components of the acceleration time history are simultaneously applied on the platform representing the top surface of the invert for each ground motion. The same acceleration time history is applied to all platform nodes simultaneously, resulting in zero deformation of the invert. The invert surface is represented in LS-DYNA as an elastic material. The externally applied momentum from the ground motion is transferred to all freestanding (unanchored) objects solely by friction and impact. The lateral and longitudinal boundaries move synchronously with the platform and are rigid. In effect, these boundaries act like rigid members that are fixed to the platform. Both ends of the waste package are represented as the bottom-end configuration (Assumption 3.10) (BSC 2004 [DIRS 167083], Attachment I and BSC 2001 [DIRS 157812]). The details of the waste package top end, such as the extended OCB lid and closure lid, are not explicitly represented and their mass is taken into account by increasing the thickness of the OCB lid. The thickness of the waste package OCB is reduced by 2 mm (from 20 mm to 18 mm; see Assumption 3.12) to represent degradation of the OCB over a 10,000 year to 20,000 year period. It needs to be emphasized that this is not a rigorous evaluation of shell thickness due to corrosion or potential corrosion-acceleration effects. Rather, a thickness reduction of 2 mm is a reasonable conservatism within the stated objective of this calculation. The waste package OCB, the trunnion collar sleeve, and the boundary walls are represented by 8-node solid (brick) elements. The constant-stress 8-node solid element (Livermore Software Technology Corporation 2003 [DIRS 166841], p. 26.30) with one-point Gaussian quadrature (Hallquist 1998 [DIRS 155373], Section 3) is used for all vibratory ground motion calculations. The part of the OCB that can come in contact with the pallet (see Figures 5.2-3 and 5.2-7; also identified by regions F and C in Fig. 5.2-4) is the most important area for these calculations. The FE representation for this region of the OCB is finely meshed on one side of the waste package (region F in Figure 5.2-4), with four layers of brick elements across the OCB thickness and a relatively dense in-plane mesh. The corresponding OCB region on the other side (region C in Figure 5.2-4) is more coarsely meshed with only two layers of brick elements across the thickness (see Figures 5.2-3 and 5.2-4). These two parts of the waste package OCB are represented as elastoplastic, with linear kinematic hardening. Time = 0 Source: BSC 2004 [DIRS 167083], Figure 1. Figure 5.2-1. Initial Configuration for Waste Package Vibratory Simulations for Ground Motions at the 2.44 m/s PGV Level Time = 0 Source: BSC 2004 [DIRS 167083], Figure 2. Figure 5.2-2. Cut-Away View of Initial Configuration for Waste Package Vibratory Simulations Time = 0 Source: BSC 2004 [DIRS 167083], Figure 3. Figure 5.2-3. The Emplacement Pallet and Two Regions on the Outer Surface of the Waste Package That Can Come in Contact with the Pallet All damage resulting from the waste package-pallet interaction during the vibratory ground motion reported in this document are based on the part of the OCB designated by region F in Figure 5.2-4. The part of the OCB designated by region C (Figure 5.2-4), although coarsely meshed compared to region F, is still relatively finely meshed compared to the remaining part of the OCB (regions P and R in Figure 5.2-4) in order to ensure proper waste package-pallet interaction and the resulting rigid-body motions. The main purpose of the coarsely zoned parts of the mesh, designed P and R in Figure 5.2-4, is to provide appropriate boundary conditions for the more finely zoned F and C parts of the mesh. The main difference between parts of the OCB designated as P and R is that P is represented as elastoplastic (linear kinematic hardening) while R is rigid. The waste package components (excluding IV and IV lids) represented as rigid bodies are presented in Figures 5.2-5 and 5.2-7b. Region F is especially important for the vibratory ground motion calculations because the stress state and damaged area are evaluated only for this region on the cylindrical surface of the waste package OCB. The two regions of the OCB that can contact the pallet, F and C, are connected to the remaining part of the OCB (P and R) by tied-interface contacts (Hallquist 1998 [DIRS 155373], Section 23.9; and Livermore Software Technology Corporation 2001 [DIRS 159166], page 6.29). Source: BSC 2004 [DIRS 167083], Figure 4. Figure 5.2-4. Side View of OCB of Waste Package, Showing Variations in FE Grid The waste package IV and its lid, pallet, and drip shield are represented by shell elements. Shell elements provide an adequate representation of these components because their dominant mode of deformation is bending. Additionally, this analysis is focused on the waste package OCB, so the stress states in the IV, pallet, and drip shield are of secondary importance. The IV and IV lids, and drip shield are represented as rigid bodies (BSC 2004 [DIRS 167083], Attachment VI) in order to reduce the computer execution time while preserving all the features relevant for the solution. The shell element used for representation of the pallet is fully-integrated 4-node shell element with Gauss integration and three integration points through the shell thickness (Livermore Software Technology Corporation 2003 [DIRS 166841], p. 26.22). The pallet is represented as elastoplastic but it is very coarsely meshed for the calculations at the 2.44 m/s PGV level (see Fig. 5.2-6). The coarse mesh of the pallet, necessitated by computer-execution-time considerations, results in an artificial increase of the pallet stiffness. In other words, the pallet is not as flexible as in reality and some of the cushioning effect of the pallet on the waste package is lost. The ultimate consequences of the coarse pallet mesh are an increase in the relative motion between the waste package and pallet, and an increase in deformation and residual stress in the OCB. Both of these effects are conservative for this analysis. Nonetheless, the pallet mesh has been refined (see Fig. 5.2-6b) for the calculations for the 5.35 m/s PGV level to prevent excessive relative motion and ensure more realistic results. This change is motivated by the much higher intensity of the ground motion at the 5.35 m/s PGV level in comparison to the 2.44 m/s level. (b) NOTE: IV and IV lids excluded. Figure 5.2-5. Parts of the Waste Package Rep (a) Source: BSC 2004 [DIRS 167083], Figure 6. NOTE: (a) 2.44 m/s PGV calculations, (b) 5.35 m/s PGV calculations. Figure 5.2-6. Front View of Pallet Mesh The internal structure of the 21-PWR waste package is simplified by representing the IV and all waste package internals, including the fuel assemblies, as a thick-wall cylinder of circular cross section and uniform density (Assumption 3.1). The outside diameter of the IV is kept unchanged. The thickness of the IV is determined by using the material properties (including density) of 316 SS, and matching the total mass of the IV and internals as presen [DIRS 167083], Attachment I). The benefit of this approach is a reduction in the computer execution time while preserving all features of the problem relevant to the structural response. The FE representation of the 21-PWR waste package maximizes the loose-fit gap between the IV and OCB to 4 mm (Plinski 2001 [DIRS 156800], Section 8.1.8). Consequently, the IV is free to move within the OCB. This maximized gap provides a conservatively bounding set of results, as demonstrated in 21-PWR Waste Package Side and End Impacts (BSC 2003 [DIRS 162293], Attachment II). The drip shield has a simplified FE representation (Assumption 3.4). The drip shield is represented as a rigid shell structure following the contour of the actual drip shield presented in Structural Calculations of Waste Package Exposed to Vibratory Ground Motion (BSC 2004 [DIRS 167083], Attachment III). All of the structural details of the drip shield are ignored. The drip shield is assumed to be made completely of Ti-7 and the density of Ti-7 is modified to match the total mass of the drip shield. These simplifications make it possible to capture the essential kinematics of freestanding components in the drift, while reducing the computer execution time. The impact of these simplifications in representation of the drip shield on the computational results presented in this document is anticipated to be negligible. T and metal-to-rock contacts. In other words, the friction coefficients vary from r (a) (b) Source: BSC 2004 [DIRS 167083], Figure 7. NOTE: (a) Extended finely-meshed OCB region; (b) Rigid parts. Figure 5.2-7. Modifications in FE Represen The functional friction coefficient used by LS-DYNA is defined in terms of static and dynamic friction coefficients, and relative velocity of the surfaces in contact (Livermore Software Technology Corporation. 2001 [DIRS 159166], page 6.9). The effect of relative velocity between contact surfaces is represented by a fitting parameter, called the exponential decay coefficient. However, this parameter cannot be defined for these calculations because the variation of static and dynamic friction coefficients are not available for Alloy 22 and Ti-7. In this situation, the effect dynamiciction coefficient. This approach maxim framework (Assumption 3.3). The friction coefficient affects the onset of sliding and dissipation components as a function of the ground msity. However, the importance of friction is anticipated to dim n level because the engineered barrier system components begin to slide almost diately for high-amplitude ground motions. esh of the FE representation was appropriately generated and refined in the contact regions ding to standard engineering practice. Thus, the accuracy and representativeness of the this calculation are deemed acceptable (BSC 2004 [DIRS 167083], Attac gh IX for discussion of results). The uncertainties are taken into account by random ling (from appropriate probability distributions) of the calculation inputs that are inherently ncertain) an and friction coefficients). 5.2.1.3 Ground-Motion Time History Cutoff The structural response calculations for the waste package are computationally intense because: (1) The FE representation is quite detailed (Section 5.2.1.2) (2) The calculations are highly nonlinear, with large deformation plasticity, friction, and impacts (3) The computational time step is quite small to ensure numerical stability of the conditionally-stable explicit FE method (typically one microsecond or less) (4) The ground motion duration is quite long, typically 30 to 40 seconds, relative to the time ste Given these factors, it is attractive to reduce the duration of the calculations by considering only that portion of the ground-motion time history that causes changes in the damaged area. For the ground motions at the 2.44 m/s PGV level, the computational duration is usually restricted to the 5 percent to 95 percent levels of ground motion energy, where energy is based on all three components of the ground motion. Measured by Arias Intensity - energy delivered to structures. For a definition, see Kremer (1996 [DIRS 103337], Section 3.3.4). For brevity, the minimum time corresponding to the 5 percent level of the ground motion energy is called the “5 %-time”, and the maximum time corresponding to the 95 percent level of the ground motion energy is called the “95 % time”. All simulations for ground motions at the 5.35 m/s PGV level are performed from the 5 percent-time to the 90 percent level of the ground motion energy, referred to as the “90 %-time”. Thus, the starting times for the 2.44 m/s and 5.35 m/s PGV level coincide with the 5 percent-time, while the ending time for the 5.35 m/s PGV level has been reduced to the 90 percent-time. able 5.2-2 presents the characteristic times for the 2.44 m/s PGV level calculations (BSC 2004 e and end timulations e f the und t ns (denotedhe FE as FE Starrt timehe 9 -time, 95 percent-timme and F ime for mo equal to t 5 perce y sub ng th e r ons, the starting tim t-tim omp per on ( ble 5. Simi e FE e ha ied 5 tim few amin nsit dam toff ning volu f dam ter 1 , Att nt V n the hand tion , an ot Ex bra roun tion (BS 2004 S 16 Tab d ar ome hara Simul or 2.4 V Gr Dura 5%- ime Staime 95%- Time Time to 95 Motion Number T (s) T (s) (s) 2 0.58 0.41 8.13 8.41 7.6 8.0 7 3 1.7 1.5 5.04 5.00 3.4 3.5 15 4 1.3 1.1 15.0 13.9 13.7 12.8 3 5 2.0 2.0 10.3 10.3 8.3 8.3 11 6 2.3 2.3 9.96 11.2 7.7 8.9 12 7 4.0 4.0 11.6 12.9 7.6 8.9 1 8 1.1 1.1 5.99 6.80 4.9 5.7 4 9 0.79 11 2.1 2.1 10.3 10.3 8.2 8.2 5 1.4 1.4 13.6 12.9 7.2 3.8 1.85 7.2 3.8 21.5 11.8 15.4 15.1 18.2 14.3 10.9 9.0 04 7083 5.2.1.1 se haracteristic tim 44 m erce el of in t ulatio 0 per nt V le V ine th toff time-historyu. Characteristic Times and Duration of Simulations for the 5 GroundMotion E Star Time n of Simula Time ealization (s) (s) (s) 1 0.85 5.21 4.36 6 2 0.41 6.05 5.47 7 3 1.5 3.64 1.94 15 4 1.1 10.2 8.90 3 5 2.0 7.46 6 2.3 9.20 6.90 12 7 4.0 11.1 7.10 1 8 1.1 5.12 4.02 4 9 0.6 6.98 6.19 10 10 1.6 7.66 6.06 9 Table 5.2-3. Characteristic Times and Duration of Simulations for the 5 Percent-90 Percent Energy Range at the 2.44 m/s PGV Ground Motion Level (Continued) GroundMotion Number FE Start Time (s) 90% Time(s) Duration of Simulation to 90% Time (s) Realization Number 11 2.1 8.30 6.20 5 12 1.4 12.2 10.8 13 13 1.85 12.7 10.8 8 14 7.2 19.8 12.6 14 16 3.8 9.57 5.77 2 ource: BSC 2004 [DIRS 167083], Table 5.2.1.2. s the charac 2.1.2). Tons times e 5.2-4n t r the 5.35 m/s PGV lerc 90 percent4 presen ts the 5 petimes. Fi nt time, y, Tabl on arac tim tio C 20 IRS .1.2) case, as discussed e pre in t th ig digits. T e mo erence between 2.44 ns he l run to ] S 1 , A nt V d it riate mulation 5.35 m/s PG arac 90% ratio latio GroundTime 5% to 95% Motion Number 5%-Time (s) 2 0.80 5.8 5.0 5.0 7 3 1.75 3.45 1.7 1.7 15 4 1.5 11.8 10.3 10.3 3 5 1.7 9.3 7.6 7.6 11 6 2.4 8 1.2 5.1 3.9 3.9 4 9 0.70 6.7 6.0 6.0 15.2 13.3 13.3 8 21.0 15.7 15.7 14 16 3.4 9.0 5.6 5.6 2 Source: BSC 2004 [DIRS 167083], Table 5.2.1.3. 5.2.1.4 System Damping In order to obtain steady-state results (i.e., residual stresses) in a reasonable time, it is necessary to apply damping during the second post-vibratory relaxation step of the computational process. The system damping is strictly a numerical technique for accelerating convergence to the steady-state stress state after the transient simulation is completed. elements and nodes of the FE grid. As discussed in Hallquist (1998 [DIRS 1553 sradsradDC70035022min=·=·=., where srad350562min˜··=p. is the minimum non-zero frequency of the waste package OCB (BSC 2004 [DIRS 167083], Attachment X [Modal Analysis/wpp6Bmod.out, line #6517]). Since the engineered barrier system components are unanchored in these calculations, the damping constant is reduced to sradDC200= to avoid over-damping the system. Furthermore, the parametric study of various damping constants presented in 21-PWR Waste Package Side and End Impacts (BSC 2003 [DIRS 16 choice. The system is obviously not over-damped, and a steady state is reached in reasonable time (BSC 2003 [DIRS 162293], Figure 4, page 21). 5.2.2 FE Representation for 21-PWR Waste Package Side and End Impacts 5.2.2.1 Objectives and Methodology The objective of these calculations is to determine the damage to a 21-PWR waste package from end-to-end impacts of adjacent waste packages and from side-on impacts of a waste package. These structural response calculations are based on a relatively detailed FE mesh to determine damaged areas more accurately than is possible in Structural Calculations of Waste Package Exposed to Vibratory Ground Moti process because the long duration of ground motions and the complexity of the FE representation in Structural Calculations of Waste Package Exposed to Vibratory Ground Motion (BSC 2004 [DIRS 167083]) precludes such a detailed analysis. These calculations represent a parametric study of waste package impact as a function of six values of the impact velocity and up to four values of the impact angle (see Figures 5.2-8 and 5.2-9 below). The end-to-end impact calculations are performed with vertical rigid walls at 0.1 m spacing from the ends of the waste package. This b as a FE structure. The use of a rigid, unyielding sur reduces the computational mesh by a factor of two and also provides a conservative representation of the damaged area. The damaged area with an unyielding surface will generally damaged area with an adjacent waste package because the unyielding surface aximizing impact stresses and deformation of the waste pack M after reposd re fo e T F Initial velocity Source: BSC 2003 [DIRS 162293], Figure 2. Figure 5.2-8. Initial Position of the Waste Package for the End Impacts For side impacts: Initial velocity is 1 m/s, 2 m/s, 4 m/s, 6 m/s, 10 m/s, and 20 m/s; Initial angle between the axis of the waste package and the horizontal (a in Figure 5.2-9) is 0 degrees, 1 degree, and 8 degrees. Source: BSC 2003 [DIRS 162293], Figure 3. Figure 5.2-9. Initial Position of the Waste Package for the Side Impacts a a Initial velocity The selected impact velocity range from 1 m/s to 20 m/s and impact angle range from 0 to 8 degrees were anticipated to be sufficiently wide to encompass all velocities and angles encountered during simulations of the vibratory ground motion. The appropriateness of this selection was confirmed by the results of the vibratory ground motion simulations (Tables 5.3-2 through 5.3-15 and Tables 5.3-24 through 5.3-38). 5.2.2.2.1 Description of FE Representation There are ten different variations of the FE mesh (BSC 2003 [DIRS 162293], Table III-1 for a complete list) for an essentially same FE representation. The different meshes are used for the purpose of computational economy. Following a standard engineering practice, the mesh of the OCB is refined in the region where significant deformations and residual stresses are expected (i.e., “region of interest”). The remaining part of the mesh is coarser to reduce the simulation running time. The extent of the region of interest depends on the and angle of impact). For example, B and C (BSC 2003 [DIRS 162293], he reater damaged area extension due to the greater impact velocity. The initial tion for 5-degree end impact of the 21-PWR waste package is illustrated in imensional FE representation of the waste package was developed in ANSYS V5.4 dimensions provided in 21-PWR Waste Package Side and End Impacts (BSC 2003 2293], Attachment I). The waste package O nt Livermore Software Technology Corporation 2003 [DIRS 166841], p. 26.30) with Gaussian quadrature (Hallquist 1998 [DIRS 155373], Section 3) was used for all end impact calculations. As indicated by Figure 5.2-11 ckage was simplified in several ways: The 21-PWR fuel assemblies were reduced to bars of square cross section of uniform mass density, and assumed to be constructed of 304 SS (Assumptions 3.13 and 3.14). The geometric dimensions of the fuel assemblies were modified to keep the value of the gap between the fuel assemblies and the nearest element consistent with the gap defined using the elements found in 21-PWR Waste Package Side and End Impacts (BSC 2003 [DIRS 162293], Attachment I). The mass density of the fuel assemblies was mo acts (BSC 2003 [DIRS 162293], 4. The fuel basket tubes were not represented in the FE mesh for end impacts. 5. The thickness of the OCB was reduced by 2 mm on its outer surface (see Assumption 3.12). The target surface was conservatively assumed to be unyielding (Assumption 3.16), and its density was rounded up to 8000 kg/m3. A static and dynamic friction coefficient of 0.5 was taken into account between all parts (Assumption 3.2 and Assumption 3.17). The value of 0.5 is an average value for the range of friction coefficient, 0.2 to 0.8, de ctural response calculation an unyielding surface, so frictional forces should have a very minor effect in determining damaged area on the waste package. 5.2.2.2.2 Gap Between the IV and OCB As shown in Repository Design, Waste Package, Project 21-PWR Waste Package with Absorber Plates, Sheet 1 of 3, Sheet 2 of 3, and Sheet 3 of 3 (BSC 2001 [DIRS 157812], Section B-B’), a tight fit between the IV and the OCB is indicated. However, Plinski (2001 [DIRS 156800], Section 8.1.8) describes the fit between the two shells as “loose”. In order to determine which v between the IV and the OCB. 5.2.2.2.3 esh Refinement Study Source: BSC 2004 [DIRS 170844], Figure 1. 5- Source: BSC 2004 [DIRS 170844], Figure 2. End Impact 5.2.2.2.4 System Damping Source: BSC 2003 [DIRS 162293], Figure 4. NOTE: Time in seconds. Figure 5.2-12. Variation of Maximum First Principal Stress with Time for Different Values of the Damping Coefficient 5.2.2.2.5 Post-Processing An element where the residual first principal stress is above the residual stress threshold is called a damaged element. If an element has its first principa to as an undamaged element. In order to determine the damage, the results obtained in the last time step of each simulation are post-processed with LS-POST V2 as follows: the undamaged elements of the OCB are “blanked out” (dark blue color in Figure 5.2-13). The damage on the OCB outer surface is estimated by calculating the area of each damaged element’s face that coincides with the OCB Since the number of damaged elements can be very large, the area of neighboring elements is calculated as the area of a rectangle containing these elements. However, if the damaged elements do not form a perfect rectangle, outside elements can be accounted for as shown in Figure 5.2-13 (count these 2 elements/do not count these 2 elements). O c the junction is taken into account. For examis taken into account to avoi T( F t 10,000 years and 99.25 percent of th for impact velocities of 1 m/s and 4 m/s are also performed with material evaluate the sensitivity of fuel assembly accelerations at temperature. The initial conditions for the calculations are an initial velocity of 0.5 m/s, 1 = 1º in Figure 5.2-15). Additional calculations at multiple impact angles were not because the g-loads from these initial analyses were generally sufficient to fail most if ore limited set of analyses provided sufficient data velping the damage abstraction for the fuel rod cladding. C 2003 [DIRS 162293], Figure 2. Figure 5.2-15. Initial Position of the Waste Package for the End Impacts FE Representation Description of FE Representation mmetry, three-dimensional FE representation of the waste package was developed in 5.4 using the dimensions provided in Maximum Accelerations on the Fuel Assemblies WR Waste Package During End Impacts (BSC 2003 [DIRS 162602], Attachment I). e package OCB and lids, IV and lids, trunnion sleeves, and fuel assemblies were d by solid (brick) elements. The constant-stress 8-node solid element e Software Technology Corporation 2003 [DIRS 166841], p. 26.30) w The FE msh is illustrated in Figure 5.2-16. a Figure 5.2-16. Standard Mesh for Determination of Fuel Assembly Accelerations The internal structure of the waste package was simplified in several ways: 1. The 21-PWR fuel assemblies were reduced to bars of square cross section of uniform mass density, and assumed to be constructed o e Package During End Impacts (BSC kg/m of 0.5 was taken dynamic friction coefficie(Assumption 3.2 and Assum the average value of the distribution (0.2 to 0.8) used in Structural Calculations of bottom lid of the IV) to verify that the results are not mesh sensitive. The variation in volume of a representative element and the variation in acceleration of the fuel assemblies are compared in Maximum Accelerations on the Fuel Assemblies of a 21-PWR Waste Package During End Impacts (BSC 2003 [DIRS 162602], Attachment III), based on the method described in Mecham (2004 [DIRS 170673], Section 6.2.3). The accuracy and mesh representativeness are deemed acceptable for this calculation because the criterion in Mecham (2004 [DIRS 170673], Section 6.2.3) is met. 5.2.3.2.4 Output Period Computational results are saved at a user-defined output period. This output period is small enough to accurately capture the maximum values of acceleration. An output period of one nanosecond ensures stable values for the maximum acceleration, as demonstrated in Maximum Accelerations on the Fuel Assemblies of a 21-PWR Waste Package During End Impacts (BSC 2003 [DIRS 162602], Attachment IV). This output period is used for all results 5.2.4.1 Methodology pact ca calculations that were previously performed with a coarser mesh, as identified in Section 5.2.2.1 for end impacts. Furthermore, the selected calculations are representative of the contribution to damaged area from various impact velocities encountered during the simulations for a waste package exposed to vibratory ground motion, identified in Tabl mesh-refinement study in 21-PWR Waste Package Side and End Impacts (BSC increased mesh density (see Fi (a) the base mesh (BSC 2003 [DIRS 162293]) (b) the ed mes 844], Figu Ten FE meshes were used in the or end-impacts rerun during this study, each FE mesh is refined by using the base mesh in 21-PWR Waste Package Side and End Impacts (BSC 2003 [DIRS 162293]) as a starting point. It would be tedious and unnecessary to discuss all details of mesh refinement for each case. Instead, the general approach to mesh-refinement is explained using the FE mesh for a 0 degree impact. Figure 5.2-17 shows a detail of the base and refined FE meshes. As indicated by Figure 5.2-17, the number of the solid element layers in key regions of the OCB and its bottom lid is increased from four to eight. Such a significant increase is necessary because the damaged area is entirely contained within the OCB-lid junction for this i impacts with more extended damage area (as in BSC 2004 [DIRS 170844], Figure I-4). The mesh refinement of the OCB surface is schematically illustrated by Figure 5.2-18. The red polygons superimposed on the base mesh outline the element contours of the refined mesh at the OCB surface. Source: BSC 2004 [DIRS 170844], Figure 3. Figure 5.2-18. Schematic Illustration of Mesh Refinement of OCB Surface for Ideal (0 degree) E ts - A ME mesh Study (BS av 2004 [DIR 21 170844], Tables 2, 3, 22 ot fil ttachm 5.2.5 FE Representation for Additional Structural Calculations of Waste Package Exposed to Vibratory Ground Motion PGV level. The original ground motions for the 2.44 m The new ground motions for these calculations spectrally condition the ground motions for the western United States and preserve intercomponent variability in the ground motion recordings. The changes between the two ground motion sets for the longitudinal (along the tunnel, denoted as H2) and vertical (denoted as V) components of PGV are summarized in Table 5.2 motion time histories presented in Structural Calculations of Waste Package Exposed to Vibratory Ground Motion (BSC 2004 [DIRS 167083], Section 5.2.1) and Additional Structural Calculations of Waste Package Exposed to Vibratory Ground Motion (BSC 2004 [DIRS 168385], Table 5.1), respectively. Four realizations were selected to maximize the potential damage and maximize the changes in the H2 or V components of PGV. Note that the H1 component of PGV does not change between the two sets of ground motions because it is always scaled t e characterizd by the largest total damaged areas (in the descending order) at the 2.44 m alization 6 ents. Th the hig realizati n the V comped area with significan capture the poten changes from the ea and large ch in individual co 4 n characterized est da th d change b on 1 (realizatio repre V in both th itudinal and ve 00 16 Table 5-1). otion mo V the d dec 3 tion 15) is char y a d Tab Ch PGV Between Grou n Set 2) PGV Vertical (V) PGV Change Old Newm/s 2.97 m/ 4 2.43 m/s 2.60 m/s +7% 8 2.44 m/s 4.02 m/s +65% 5.2.5.2 FE Representation The three-dimensional FE representation for these supplemental calculations is discussed in detail in Section 5.2.1.2. The only difference in the FE representation between these supplemental calculations and the representation in Section 5.2.1.2 is that the supplemental calculations are performed without any rigid elements in the waste package OCB. The potential effects of rigid elements in the FE representation of the OCB were analyzed in detail in Structural Calculations of Waste Package Exposed to Vibratory Ground Motion (BSC 2004 [DIRS 167083], Attachment VI), and it was demonstrated that this simplification had only a minor effect on the calculated damaged areas. A ground motion time history cutoff is applied to the supplemental calculations, similar to that for the original calculations (Section 5.2.1.3). The 2.44 m/s PGV level, the computational duration for the supplemental calculations is restricted to the 5 percent to 95 percent levels of ground motion energy, where energy is based on all three components of the ground motion. The times corresponding to the 5 percent and 95 percent energy levels are defined in Additional Structural Calculations of Waste Package Exposed to Vibratory Ground Motion (BSC 2004 [DIRS 168385]) and summarized in Table 5.2-6. The effect of the time history cutoff on the results for the 2.44 m/s PGV level was demonstrated to be negligible in Structural Calculations of Waste starting (5 percent) time from the ending (95 percent) time. 5.3 RESULTS Sections 5.3.1 through 5.3.3 present the results for damaged area on the waste package from vibratory ground motion, based on the calculations documented in Structural Calculations of Waste Package Exposed to Vibratory Ground Motion (BSC 2004 [DIRS 167083]). Section the calculations documented in 21-PWR Waste Package Side and End Impacts (BSC 2003 [DIRS 162293]). Section 5.3.5 presents the results for maximum acceleration of fuel rod assemblies due to end impacts, based on the calculations documented in Maximum Accelerations on the Fuel Assemblies of a 21-PWR Waste Package During End Impacts (BSC 2003 [DIRS 162602]). A series of additional studies aimed at examining sensitivity of damage estimates to mesh refinement, alternative ground motions representation and methodology for damage estimates of end impacts are given in Sections 5.3.6 to 5.3.8. The stress time histories, residual stress distribution plots, impact parameters, and damaged areas presented in this section have been obtain Table 5.2-6. Duration and Characteristic Times Corresponding to 5 Percent - 95 Percent Energy Range Ground Motion 5%- Time (s) 95%- Time Duration of Simulation 1 2 5 Ground Realization Number Motion Number 80% Yield Strength 90% Yield Strength 9 10 9 12 6 0.0039; 0.014% 0; 0 13 12 14 14 0.010; 0.035% 0.0043; 0.015% 15 3 0.0078; 0.028% 0.0015; 0.0053% Source: BSC 2004 [DIRS 167083], Table 6.1.1-1. 5.3.1.2 Interaction Between Waste Package and Longitudinal Boundary This section presents the damaged area of the waste package OCB resulting from waste package-waste package interaction due to end-to-end impacts in the longitudinal direction. The damage is package simulations under vibratory ground motion. In other words, the current simulations define the kinematics of the impacts, while the damage from each impact is calculated using the impact it is o ined deen ectly f longit the pinal bou . tprocessorary (repr The impa trun collar s ) node time pac The impact angle prese age espect longit ev re on the trunnion collar rees corresponds to simultaneous contact age fromeometrica individual imargum nts. I two imp their lo less ofts take pl cation. The approach is e sufficie ge ex e a ten impa peed a the ct a e (see Tabl s 5.3-56, 5 tion to ide fy th ons is i ated in on is defined with 12 discrete values (i.e uidistantly distributed in the clockwise direction (see the red numbers in Figure 5.3-1) F” and emphasiz ” sidehat only ss behi wing th F3 in th ly meshed (re designator side vie closer to . Note th entio 12 co pon C12 corresp s to C11 ing t the im f the ste pac ge O the i t locati arked desi ted as 2.” of 1 gments arb The ropriateness of this choice wa more d of imp cations hat need had arisen during post-processing, then it w 5.0× 167 Figure lock” C vent ed f luation act Loc C F C6 count as one-half of the corresponding value, since the damage caused by impact at locatio en into acco NC”) omp ce it is c letely overlapp mete d cor ond am for both the lower and pact ameter d D ed A or Realizati 1 at the 2. Damag Area Impact Location Time (s) Speed(m/s) Angle (degree) 80% YieldStrength F 8 6.025 1.3 1.0 0.0089 0.0046 C 10 4.750 1.0 1.5 0.0031X0.5 0.0017X0.5 Impact Par 4 [DIRS 16eter 708d Dam Table 6. ged Area 2 0.006 r Realizat 2 at the 2 Dama Area (m 2) acttio ime (s) eed/s) gleree % Yieldtrength 0% YieldStrength anF 0 S0 0 8 092X0.5 .0047X0. 9 0.0127 0.0065 otal .017 0.0089 ource: BSC 2004 [DIRS 167083], Table 6.1.2-2. Table 5.3-4. End-Impact Parameters and Damaged Area for Realization 3 at the 2.44 m/s PGV Level Damaged Area (m2) Impact Location Time (s) Speed(m/s) Angle (degree) 80% Yield Strength 90% Yield Strength Table 5.3-5. End-Impact Parameters and Damaged Area for Realization 4 at the 2.44 m/s PGV Level ImpactLocation Time(s) Speed(m/s) Angle(degree) Damaged Area (m2) 80% Yield Strength 90% Yield Strength F 3 2.400 1.9 1.0 0.0202 0.0103 F 9 2.775 2.5 4.1 0.0307 0.0162 C 9 2.650 2.6 2.9 .0354 N 0166 NC C 9 2.700 3.5 4.0 0.0650 0.0343 Tota l 0.12 0.061 ource C 2004 [DIRS 16 ], Tab 1.2-4. pact ameter d D ed A r Realization 5 at the 2.44 m/s PG age d Dam Area Sp % Yie 0% Yie Location (s) (m/s) (degree) Strength F 2 0.425 1.6 1.2 0.0142 NC 0.0073 NC F 2 2.025 2.0 1.7 0.0201 NC 0.0102 NC F 3 F 3 3.0 2.5 6 NC 0.0275 NC 8 NC 0.0036 NC 0.0137 NC 0.0947 0.0070 NC0.0385 3 0089 NC 0.0046 N 9 0.0064 0.0034 9 0022 NC 0.0013 N .0014 0.0007 C 3 0.800 1.2 1.7 0.0064X C 4 C 9 2.325 2.4 4.7 0.0262 0.0145 urce: BS 2004 [D S 1670 , Table 6 2 0.001 2-5. Table 5.3-7. End-Impact Parameters and Damaged Area for Realization 6 at the 2.44 m/s PGV Level Impact Location Time (s) Speed(m/s) Angle (degree) Damaged Area (m2) 80% Yield Strength 90% Yield Strength F 4 1.950 2.5 1.4 0.0344 0.0140 F 4 2.600 2.4 0.5 0186 NC .0090 NC F 8 1.525 1.9 1.0 0.0202X0.5 0.0103X0.5 F 9 1.100 2.4 1.5 0.0315 0.0134 F 9 3.025 1.9 1.6 0.0187 NC 0.0095 NC C 9 3.125 4.0 2.7 0.0692 0.0300 C 9 2.750 2.9 0.9 0418 NC .0152 NC Total 0.15 0.063 Source: BSC 2004 [DIRS 167083], Table 6.1.2-6. Table 5.3-8. End-Impact Parameters and Damaged Area for Realization 7 at the 2.44 m/s PGV Level Impact Location Time (s) Speed(m/s) Angle (degree) Damaged Area (m2) 80% Yield Strength 90% Yield Strength F 2 2.350 1.4 0.4 0.0043 0.0022 F 9 3.700 2.7 0.5 0.0243 0.0116 F 10 2.925 2.1 2.5 0209 NC .0103 NC C 3.150 2.2 0 0.0024 0.0024 C 3 4.150 1.2 0.8 0056 NC .0029 NC 0.0538 0.0265 C 8 2.775 2.4 3.0 0.029 Total 0.11 0.057 Source: BSC 2004 [DIRS 167083], Table 6.1.2-7. eginning f the ically, ccelera e ton time for realizationl veloc e initiaistory. Consequently, the v ity com torie e not spe d, and t esults f tab umma ng r (Ta 5.3-18, 24, and peedm/s) ngle degree) 80% Yield Strength 0.0059 027 NC .0016 N C 8 1.375 1.4 2.6 0.0086 0.0045 C 9 1.925 1.7 4.2 0.0098X0.5 0.0051X0.5 2004 [DIR 0.12 , Table 6.1.2-9. eae ers amaged Area fo maged Area (m2) pa e dAngle ation ) (degree) gth Strengt 3 25 2.7 50 0.3 NC 0.0020 N 75 3.8 T 14 0.0071 urce: 04 67083], Table 6 act P ers maged Area f Impact Time SpeedAngle 80% Y Table 5.3-9. End-Impact Parameters and Damaged Area for Realization 9 at the 2.44 m/s PGV Level ime s) Damaged Area (m2) 90% Yield Strength 3 0.0116 F 5 2.625 1.7 2.7 0.0129 0.006 F 8 1.575 2.8 4.5 0.0408 0.0226 F 9 2.250 1.6 5.0 0.0072 NC 0.0038 NC F 9 2.325 1.1 4.1 0.0021 NC 0.0013 NC F Source: BSC Dr ct lization 10 at th ield 90% Yie 41 0.0022 4 0.0049 lization 11 at th amaged Area (m2) Table 5.3-12. End-Impact Parameters and Damaged Area for Realization 12 at the 2.44 m/s PGV Level Damaged Area (m2) Impact Time SpeedAngle 80% Yield 90% Yield F 3 6.400 1.1 0.7 0.0036 0.0019 F 8 5.950 3.0 0.4 0.0264 0.0138 F 9 3.575 1.1 0.8 0.0041 NC 0.0022 NC C 3 1.025 2.2 0.5 0.0148 0.0073 C 4 5.825 2.2 0.2 0.0074X0.5 0.0044X0.5 C 4 6.175 1.0 1.7 0.0030 NC 0.0017 NC C 9 3.775 2.3 0.8 0.0246 0.0109 Total 0.073 0.036 5.3-13. End-Impact Parameters and Damaged Area for Realization 13 at the 2.44 m/s PGV Level Damaged Area (m2) Impact Location Time (s) Speed(m/s) Angle (degree) 80% Yield Strength 90% Yield Strength F 4 2.300 1.9 0.6 0.0121 0.0062 C 3 2.025 1.2 2.450 2.0 C 3 7.625 1.1 0.9 0.0047 NC Total 0.032 0.016 Source: BSC 2004 [DIRS 167083], Table 6.1.2-13. Table 5.3-14. End-Impact Parameters and Damaged Area for Realization 14 at the 2.44 m/s PGV Level Damaged Area (m2) Impact Location Time (s) Speed(m/s) Angle (degree) 80% Yield Strength 90% Yield Strength F 2 2.775 1.4 0.2 0.0022 0.0011 F 3 3.925 1.0 0.6 0.0020 0.0011 C 10 4.450 1.2 0.2 0.0014 0.0007 Total 0.0056 0.0029 Source: BSC 2004 [DIRS 167083], Table 6.1.2-14. -15. End-Impact Parameters and Damaged Area for Realization 15 at the 2.44 m/s PG amage(m2) Ti peed gle ield ation (s) (m/s) (degree) Strength Total 0.020 0.010 aged as for ea thro 3-15. izati 16. Damaged Area from End Impacts (Waste Package-Waste Package Interaction) at Dam Area G ; % o B a M 80% Y treng Yie 0.02 82% 0.012; 0.04 0.01 60% .008 0.1 7% 0.08 4 8 0.12; 0.43% 0.06 5 11 0.15; 0.53% 0.066; 0.23% 6 1 0.15; 0.53% 0.063; 0.22% 10 0.10. .39% .43% 0.0570.062; 0.01 50% 1 5 0.074; 0.26% 0.03 14 14 0.0056; 0.020% 0.0029; 0.010% BSC 2004 16708 able 6.1 . Although an attempt has been made to prevent excessive technique described above, the results are still conservative. This conservatism is an unavoidable consequence of the FE representation. Two sources of conservatism need to be mentioned here: • The damaged area from the waste package impacting the longitudinal boundary (representing the neighboring waste package) is calculated based on the end impacts on the surface that is not only unyielding but also completely constrained (BSC 2003 [DIRS 162 transferred into deformation energy is not only distributed between the two colliding waste packages but is also smaller than predicted because of elastic rebound during the impact. The damage accumulation technique is unable to represent relaxation of residua belo eg that thre s, the damaged area is not a mubsequent impacts relieve the stres t can decrease if s of the OCB that excee ed the residual stress th s from a previous shold at time t1 can be old follow g a “favor le” impact time t2 (w re t2 > t1). oates of the dam ognize these e area. cts of current represe n lead ast and D hield ee nte et n the waste aste pac packag e., trunnion collar sleeve s) and the drip shield ations 4age and t , 1 rip . In all ot er realization s there wa no impact events for round motio ns at the 2.4 m/s PGV anpact speeds in this range do not contribu ract zed by r vely impact speete significan s, mostly betly to the to tween 1 m/ tal damaged area even and 2 m/s. (BSC 2003 pacts DIRS 1 3], Tabl ge st ckage, istent w ssumption 3 .6. Moreov er, the drip shield was pact energy was not, after th e impact withed entirely into defor the waste p ackage. Conmation energy but sequently, Table 5.3-17. Lateral-Impact Parameters for Realization 4 at the 2.44 m/s PGV Level Speed Angle Location (s) F 3 2.700 m/s) (degree) 2.9 3.0 urce: BSC 04 [DIRS 16708 3], Table 6.1 -1. 3-18 or Realization 7 at the m/s PGV Lev el Impact Location Tim(s) Speed (m/s) Angle degree) C 3 2.800 1.2 3.4 083], Table 6.1. t t or Realization 9 a m/s PGV el Impact Location (s) (m/s) (degree) F 3 1.575 2.1 4.4 F 3 2.225 2.0 4.8 F 3 2.300 1.2 4.4 F 9 2.600 4.1 0.2 Source: BSC 2004 [DIRS 167083], Table 6.1.3-3. Table 5.3-20. Lateral-Impact Parameters for Realization 11 at the 2.44 m/s P Impact Location Time (s) Speed (m/s) Angle (degree) C 9 2.500 1.8 4.8 Table 5.3-21. Lateral-Impact Parameters for Realization 15 at the 2.44 m/s PGV Level Impact Location Time (s) Speed (m/s) Angle (degree) F 3 1.125 1.2 1.0 Source: BSC 2004 [DIRS 167083], Table 6.1.3-5. .4 Summary of Results at the 2.44 m/s PGV Level ed in Taated by t 22. The results in Tab tribution nd impact e package-waste packag e interaction. As a -waste pack pacts, as discussed at the end le u ctly in the elopment of ag ent mbly (BSC 200 [DIRS 169990 tory Ground Motio e 2.44 maged Area on th Waste Package W Inte WP to WP raction dCumulati (m ) (m2; % of tot rea) on 80% Yield 90% Yield 80% Yield Strength Strength Strength Stre0.0029; 10% 0.0014; 0.0050% 0.023; 0.082% 0.012; 0.043% 0.026; 0.090; 0.017; 0 0 0.060% 0.032% 0.060% 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 0.060% 0 0.11; 0.39% 0.057; 0.20% 0.13; 0.40.0035; 0; 0.012% 0 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% Table 5.3-22. Damaged Area from Vibratory Ground Motion at the 2.44 m/s PGV Level (Continued) (m2; % of total OSd area) (m2; % of total OSd area) (m2; % of total OSd area) Ground 0 0.01 0 .0043; 0.032; 0.10.005 Strength 6; 1% 0.0570.002 0.032; 0.10.016 0.0350.007 % 8; 015% 0015; 0.00.0 0.010.01 0.050.02 0.028 % 0053% 0.0 0.03 0.09 Me luec, e 0.310% 0.136 Sta Deviatio 0.23 Mi Valuecc 0.05 Ma Value 0.71 S 16e pre ], Table le. R tion 8 are no resented bec ation. rmed w 15 grou otio bere 3, …, 14 . Seven ere inlow y develosubs from if an h 15 sets re select t ostclosu titutionsponen found proprian plotte It exhibits anomalously low values at high frequencie for all computational suites at 2.44 m/s PGV level and at 5.35 m/s PGV level because of its anomalous response spectrum. acent and 9 total mean d areercentula yield stmean d nd impacts is 0.27gth, respeage for the lated in Appendixrcent and 0. 8 pevely. These o residual 130 pues represens threshold m G nd M ons e 5.3 PGV L at t .35 m more i than t (g 81 m/ a he a16 rati gravity ile the tely oxim g at the 2.44 aximum peak ground acceleration is appr167083]). As a consequence of the high-intensity Table 5.3-23. Damaged Area from Waste Package-Pallet Interaction at the 5.35 m/s PGV Level RealizatNumbe M tion ber 80% Stren ged Area ld 90 Yield ength 1 0.20 1% 0. ; 0.60% 3 0.096; 0.34 % 0.29% 4 0.12 0.34% 5 0.093 3% 0.0 1; 0.25% 6 0.046 6% 0.0 4; 0.085% 7 0.038; 0.13 % 0 0.099% 8 0.095 4% 0.0 8; 0.24% 9 0052 18% 0.0 5; 0.012% 1 0.16 7% 0. 4; 0.50% 1 0016 057% 0; 0 1 0.062 2% 0.0 1; 0.15% 13 % 0 0.064% 14 .020; 71% 0.0 ; 0.057% 1 0045 16% 0; 0 ource C 2004 [DIRS 16 ], Tab 1-1. OTE: uracy o dam area to the Waste kage-p is do l (see discus on in BSC 4 [DIRS 7083 ion 6 ilabl r real tion This lization i one of fo rme ith the rep ntati or the 2.4 m/s PGV d se cuss in Section .2.1.2). U eshe gion ast kag CB for rea ization 2 ( 7083 igure II-2). The calcu lated dam ble racy a the s are t included Table 5.3- ts th amage area pacts in th longitudin , 5.3 and 0), bas n the s ual en o-end acts ulate y these wa e package tion. other rds, curre imulation define the each ed us imp tive angle as interpolating parameters in individual impacts in T he end-impact parameters and corresponding damaged areas (calculated for both the lower and Impact P ameter and Da ged Are or Realizati 1 at the 5. Dam rea pact Time eed gle 80% Yield 90% Yield ation (s) /s) gree Strength Strength 3 0.0176 0.0090 F 7 0.0085 0.0044 8 0013 NC .0010 NC 8 0.0047 0.0025 9 0.0021 0.0013 2 0.1005 0.0556 3 0183 NC .0093 NC .0158 0.0080 C 10 4.525 1.2 6.6 0.00 Total 0.16 0.086 Damage Area pact Time eed gle % Yield 0% Yield ation (s) /s) gree Strength Strength 2 040X0.5 .0022X0. 3 0.0202 0.0103 9 0.0044 0.0022 12 0.0052 0.0027 C 1 0.0022 0.0011 C 3 0.0054 0.0028 7 0.0089 0.0046 To 0.048 0.025 rce: 2004 [D 167 able 2-2. Table 5.3-26. End-Impact Parameters and Damaged Area for Realization 3 at the 5.35 m/s PGV Level Impact Locat Tim(s Speed(m/s) Angle (degree) Damaged Area 2 80% Yield Strength 0% Yield trength 1.22 1.3 1.7 0.0082 NC .0042 NC 2.65 2.4 1.4 0.0317 .0133 5.60 3.4 1.3 0.0584 0.0196 0.92 1.7 2.2 0140 NC 071 NC 2.90 3.7 2.5 0.0688 NC .0288 NC 3.10 4.0 3.6 0.0809 0.0404 6.60 1.5 0.3 0.0038 NC .0019 NC 8.45 1.7 1.4 0.0156 NC .0080 NC F 9 1.70 2.2 1.7 0.0257X0.5 .0118X0.5 F 9 4.72 2.2 0.2 0074 NC 044 NC 9.00 1.1 5.0 0.0026 NC .0016 NC F 3.97 2.3 3.2 0.0255 0.0125 F 10.27 3.1 0.0121 NC .0062 NC 1.87 2.7 0.8 0338 NC 135 NC 0.37 2.5 2.8 0.0325 0.0151 3.82 2.5 0.4 0.0176 NC .0064 NC 177 N 90 NC C 4 6.750 1.7 5.2 C 5 6.075 1.5 0.6 0.0076 NC 0.0039 NC C 6 6.950 1.3 1.9 0.0079 NC 0.0041 NC C 7 C 8 7.300 1.525 1.0 1.8 4.8 1.4 NC 0.0025 NC 0095 NC 031 NC 049 NC 017 NC C 8 5.425 .4 C 9.825 .5 0105 NC 054 NC C 4.125 .4 0299 NC 137 NC C 1 2.150 .3 0079 NC 0041 NC C 1 3.200 .2 0261 NC 119 NC C 1 4.100 .1 06 NC 98 NC C 1 2.225 .2 0060 NC 031 NC C 1 3.000 .8 0715 293 C 1 5.900 .2 0038 NC 021 NC C 6.150 .8 T Sourc C 2004 167 able -3. Table 5.3-27.End-Impact Parameters and Damaged Area for Realization 4 at the 5.35 m/s PGV Level Location F 3 (s) (m/s) gree) 2.5 (m2) 90% trength .0478 rength .0207 F 2.875 .5 0105 054 F 6 2.925 .6 0109 NC 056 NC F 7 3.000 .4 95 NC 49 NC 266 20 F 12 3.325 1.2 7.0 C 2 1.250 1.2 0.4 0.0028 0.0015 C 5 2.475 1.9 4.6 0.0110 0.0057 C 1.15 1.3 al 0.2 2 NC 0.0045 N8X0.5 0.0026X 0.0018 0.11 0.0009 0.050 So SC 200 Tab arame nd D ed A or Realizati 5 at the 5.3 Dama rea Im Tim Spee ngle (m80% Yield 90% Yield Loc (s) (m/s egre Strength Strength 3.67 1.8 0 0 0 1.92 2.0 4.1 0.0134 0.0069 4.85 1.4 1.6 0100 NC 0052 NC 1.30 2.7 0.9 0.0369 0.0141 2.700 1.8 1.7 0.0167 NC .0085 NC F 6 5.00 1.2 0.4 0.0028 NC .0015 NC F 7 3.42 1.4 2.6 0.0086 0.0045 F 0.35 2.1 1.6 0.0232 0.0111 F 5.90 1.3 3.0 0067X0.5 035X0.5 C 2 0.52 1.6 1.3 0.0140 0.0072 5.37 1.7 0.1 0.0016X0.5 .0008X0.5 0.82 1.2 0.7 0.0049 NC .0026 NC 3.95 1.2 1.0 0.0071X0.5 .0037X0.5 3.00 1.9 2.4 0.0166 0.0085 1.65 3.4 0.8 0.0498 0.0180 2.30 1.5 1.3 0.0122 NC .0063 NC C 11 6.22 1.3 2.0 0.0078 0.0041 C 12 0.10 1.4 0.2 0.0022 0.0011 C 12 3.12 1.4 0.2 0.0022 NC .0011 NC l 0.18 0.080 Sou SC 200 , Tabl .2-5. Table 5.3-29. nd-Impact Parameters and Damaged Area for R