Rev 1 of this report provides corrections and clarifications in response to reviewer comments arising during a project review meeting held June 7-8, 2007.

The work reported in this document was performed in support of a project entitled ''Double-Shell Tank (DST) Integrity Project - DST Thermal and Seismic Analyses''. The overall scope of the project is to complete an up-to-date comprehensive analysis of record of the DST System at Hanford. The work described herein was performed in support of the seismic analysis of the DSTs. The thermal and operating loads analysis of the DSTs is documented in Rinker et al. (2004). The work herein was motivated by review comments from a Project Review Meeting held on March 20-21, 2006. One of the recommendations from that meeting was that the effects of the interaction between the tank liquid and the roof be further studied (Rinker, Deibler, Johnson, Karri, Pilli, Abatt, Carpenter, and Hendrix - Appendix E of RPP-RPT-28968, Rev. 1). The reviewers recommended that solutions be obtained for seismic excitation of flat roof tanks containing liquid with varying headspace between the top of the liquid and the tank roof. It was recommended that the solutions be compared with simple, approximate procedures described in BNL (1995) and Malhotra (2005). This report documents the results of the requested studies and compares the predictions of Dytran simulations to the approximate procedures in BNL (1995) and Malhotra (2005) for flat roof tanks. The four cases analyzed all employed a rigid circular cylindrical flat top tank with a radius of 450 in. and a height of 500 in. The initial liquid levels in the tank were 460,480,490, and 500 in. For the given tank geometry and the selected seismic input, the maximum unconstrained slosh height of the liquid is slightly greater than 25 in. Thus, the initial liquid level of 460 in. represents an effectively roofless tank, the two intermediate liquid levels lead to intermittent interaction between the liquid and tank roof, and the 500 in. liquid level represents a completely full tank with no sloshing. Although this work was performed in support of the seismic analysis of the Hanford DSTs, the tank models in this study are for an idealized flat top configuration. Moreover, the liquid levels used in the present models are for study purposes only and are independent of the actual operating levels of the DSTs. The response parameters that are evaluated in this study are the total hydrodynamic reaction forces, the peak convective hydrodynamic forces, the fundamental convective frequencies, the liquid pressures, and peak slosh heights. The results show that the Dytran solutions agree well with the known solutions for the roofless tank and completely full tank. At the two intermediate liquid levels, there are some significant differences between the Dytran results and the approximate estimates. The results show that the estimates of peak hydrodynamic reaction forces appearing in BNL (1995) and Malhotra (2005) are reasonable and generally conservative relative to the Dytran solutions. At the 460 and 480 in. liquid levels, Dytran underestimates the convective component of the reaction force compared to the estimated in BNL (1995) and Malhotra (2005), but the convective component of the reaction force is small relative to the total reaction force. At the 490 in. liquid levels, the peak convective reaction force is more than twice as large as predicted by the approximate methods in BNL (1995) and Malhotra (2005). All three methods give similar answers for the fundamental convective frequency at the 460 and 480 in. liquid levels, but the Dytran solution indicates a significant increase in the apparent convective frequency at the 490 in. liquid level that is caused by the interaction with the roof. The peak wall pressures in the tank at the two intermediate liquid levels are essentially the same as for a roofless tank in the lower two-thirds of the tank wall, but diverge from that solution in the upper third of the tank wall. The estimates of peak wall pressures appearing in BNL (1995) are quite conservative lower in the tank, but may underestimate the peak wall pressures closer to the tank roof. Finally, the peak roof pressures predicted by Dytran at the 480 and 490 in. liquid levels are approximately twice as large as those predicted using the methodology of Appendix D of BNL (1995) and are ten to twenty times higher than predicted using the simple hydrostatic approach in Malhotra (2005).

Revision 0A of this document contains new Appendices C and D. Appendix C contains a re-analysis of the rigid and flexible tanks at the 460 in. liquid level and was motivated by recommendations from a Project Review held on March 20-21, 2006 (Rinker et al Appendix E of RPP-RPT-28968 Rev 1). Appendix D contains the benchmark solutions in support of the analyses in Appendix C.

M & D Professional Services, Inc. (M & D) is under subcontract to Pacific Northwest National Laboratories (PNNL) to perform seismic analysis of the Hanford Site Double-Shell Tanks (DSTs) in support of a project entitled ''Double-Shell Tank (DSV Integrity Project-DST Thermal and Seismic Analyses)''. The overall scope of the project is to complete an up-to-date comprehensive analysis of record of the DST System at Hanford in support of Tri-Party Agreement Milestone M-48-14. The work described herein was performed in support of the seismic analysis of the DSTs. The thermal and operating loads analysis of the DSTs is documented in Rinker et al. (2004). The overall seismic analysis of the DSTs is being performed with the general-purpose finite element code ANSYS'. The global model used for the seismic analysis of the DSTs includes the DST structure, the contained waste, and the surrounding soil. The seismic analysis of the DSTs must address the fluid-structure interaction behavior and sloshing response of the primary tank and contained liquid. ANSYS has demonstrated capabilities for structural analysis, but has more limited capabilities for fluid-structure interaction analysis. The purpose of this study is to demonstrate the capabilities and investigate the limitations of the finite element code MSC. Dytranz for performing a dynamic fluid-structure interaction analysis of the primary tank and contained waste. To this end, the Dytran solutions are benchmarked against theoretical solutions appearing in BNL 1995, when such theoretical solutions exist. When theoretical solutions were not available, comparisons were made to theoretical solutions to similar problems, and to the results from ANSYS simulations. Both rigid tank and flexible tank configurations were analyzed with Dytran. The response parameters of interest that are evaluated in this study are the total hydrodynamic reaction forces, the impulsive and convective mode frequencies, the waste pressures, and slosh heights. To a limited extent, primary tank stresses are also reported. The capabilities and limitations of ANSYS for performing a fluid-structure interaction analysis of the primary tank and contained waste were explored in a parallel investigation and documented in a companion report (Carpenter and Abatt [2006]). The results of this study were used in conjunction with the results of the global ANSYS analysis reported in Carpenter et al. (2006) and the parallel ANSYS fluid-structure interaction analysis to help determine if a more refined sub-model of the primary tank is necessary to capture the important fluid-structure interaction effects in the tank and if so, how to best utilize a refined sub-model of the primary tank. The results of this study demonstrate that Dytran has the capability to perform fluid-structure interaction analysis of a primary tank subjected to seismic loading. With the exception of some isolated peak pressures and to a lesser extent peak stresses, the results agreed very well with theoretical solutions. The benchmarking study documented in Carpenter and Abatt (2006) showed that the ANSYS model used in that study captured much of the fluid-structure interaction (FSI) behavior, but did have limitations for predicting the convective response of the waste. While Dytran appears to have stronger capabilities for the analysis of the FSI behavior in the primary tank, it is more practical to use ANSYS for the global evaluation of the tank. Thus, Dytran served the purpose of helping to identify limitations in the ANSYS FSI analysis so that those limitations can be addressed in the structural evaluation of the primary tank.

This report (Rev 1) incorporates corrections and clarifications regarding the interpretation of solutions in BNL (1995) per reviewer comments from a June 7-8, 2007 review meeting. The review comments affect Appendixes C and D of this report - the body of the report is unchanged.

M & D Professional Services, Inc. (M & D) is under subcontract to Pacific Northwest National Laboratories (PNNL) to perform seismic analysis of the Hanford Site Double-Shell Tanks (DSTs) in support of a project entitled ''Double-Shell Tank DSV Integrity Project-DST Thermal and Seismic Analyses''. The overall scope of the project is to complete an up-to-date comprehensive analysis of record of the DST System at Hanford in support of Tri-Party Agreement Milestone M-48-14. The thermal and operating loads analysis of the DSTs is documented in Rinker et al. (2004). The work statement provided to M & D (PNNL 2003) required that the seismic analysis of the DST assess the impacts of potentially non-conservative assumptions in previous analyses and account for the additional soil mass due to the as-found soil density increase, the effects of material degradation, additional thermal profiles applied to the full structure including the soil-structure response with the footings, the non-rigid (low frequency) response of the tank roof, the asymmetric seismic-induced soil loading, the structural discontinuity between the concrete tank wall and the support footing and the sloshing of the tank waste. The seismic analysis considers the interaction of the tank with the surrounding soil, and the effects of the primary tank contents. The DST and the surrounding soil are modeled as a system of finite elements. The depth and width of the soil incorporated into the analysis model are sufficient to obtain appropriately accurate analytical results. The analyses required to support the work statement differ from previous analysis of the DSTs in that the soil-structure interaction (SSI) model includes several (nonlinear) contact surfaces in the tank structure, and the contained waste must be modeled explicitly in order to capture the fluid-structure interaction behavior between the primary tank and contained waste. Soil-structure interaction analyses are traditionally solved in the frequency domain, but frequency domain analysis is limited to systems with linear responses. The nonlinear character of the coupled SSI model and tank structural model requires that the seismic analysis be solved in the time domain. However, time domain SSI analysis is somewhat nontraditional and requires that the appropriate methodology be developed and demonstrated. Moreover, the analysis of seismically induced fluid-structure interaction between the explicitly modeled waste and the primary tank must be benchmarked against known solutions to simpler problems before being applied to the more complex analysis of the DSTs. The objective of this investigation is to establish the methodology necessary to perform the required SSI analysis of the DSTs in the time domain. Specifically, the analysis establishes the capabilities and limitations of the time domain codes ANSYS and Dytran for performing seismic SSI analysis of the DSTs. The benchmarking of the codes Dytran and ANSYS for performing seismically induced fluid-structure interaction (FSI) between the contained waste and the DST primary tank are documented in Abatt (2006) and Carpenter and Abatt (2006), respectively. The results of those two studies show that both codes have the capability to analyze the fluid-structure interaction behavior of the primary tank and contained waste. As expected, Dytran appears to have more robust capabilities for FSI analysis. The ANSYS model used in that study captures much of the FSI behavior, but does have some limitations for predicting the convective response of the waste and possibly the response of the waste in the knuckle region of the primary tank. While Dytran appears to have somewhat stronger capabilities for the analysis of the FSI behavior in the primary tank, it is more practical for the overall analysis to use ANSYS. Thus, Dytran served the purpose of helping to identify limitations in the ANSYS FSI analysis so that those limitations can be addressed in the structural evaluation of the primary tank. The limitations of ANSYS for predicting the details of the convective (sloshing) response of the waste are not considered critical due to the large structural margins that exist in the upper portion of the primary tank. However, the analysis of the waste response in the upper portion of the primary tank and the lower knuckle of the primary tank will be supplemented by a more refined ANSYS sub-model to aid in the structural evaluation. The results of all three investigations are used to support the detailed seismic analysis of the DTSs that is reported in Carpenter et al. (2006). The results of the more detailed seismic analysis will be used to provide seismic demands that will be combined with non-seismic demands from the thermal and operating loads analysis (Rinker et al. 2004) to determine the structural integrity of the DSTs.

M & D Professional Services, Inc. (M & D) is under subcontract to Pacific Northwest National Laboratories (PNNL) to perform seismic analysis of the Hanford Site Double-Shell Tanks (DSTs) in support of a project entitled ''Double-Shell Tank (DSV Integrity Project-DST Thermal and Seismic Analyses)''. The overall scope of the project is to complete an up-to-date comprehensive analysis of record of the DST System at Hanford in support of Tri-Party Agreement Milestone M-48-14. The work described herein was performed in support of the seismic analysis of the DSTs. The thermal and operating loads analysis of the DSTs is documented in Rinker et al. (2004). The overall seismic analysis of the DSTs is being performed with the general-purpose finite element code ANSYS. The overall model used for the seismic analysis of the DSTs includes the DST structure, the contained waste, and the surrounding soil. The seismic analysis of the DSTs must address the fluid-structure interaction behavior and sloshing response of the primary tank and contained liquid. ANSYS has demonstrated capabilities for structural analysis, but the capabilities and limitations of ANSYS to perform fluid-structure interaction are less well understood. The purpose of this study is to demonstrate the capabilities and investigate the limitations of ANSYS for performing a fluid-structure interaction analysis of the primary tank and contained waste. To this end, the ANSYS solutions are benchmarked against theoretical solutions appearing in BNL 1995, when such theoretical solutions exist. When theoretical solutions were not available, comparisons were made to theoretical solutions of similar problems and to the results from Dytran simulations. The capabilities and limitations of the finite element code Dytran for performing a fluid-structure interaction analysis of the primary tank and contained waste were explored in a parallel investigation (Abatt 2006). In conjunction with the results of the global ANSYS analysis reported in Carpenter et al. (2006), the results of the two investigations will be compared to help determine if a more refined sub-model of the primary tank is necessary to capture the important fluid-structure interaction effects in the tank and if so, how to best utilize a refined sub-model of the primary tank. Both rigid tank and flexible tank configurations were analyzed with ANSYS. The response parameters of interest are total hydrodynamic reaction forces, impulsive and convective mode frequencies, waste pressures, and slosh heights. To a limited extent: tank stresses are also reported. The results of this study demonstrate that the ANSYS model has the capability to adequately predict global responses such as frequencies and overall reaction forces. Thus, the model is suitable for predicting the global response of the tank and contained waste. On the other hand, while the ANSYS model is capable of adequately predicting waste pressures and primary tank stresses in a large portion of the waste tank, the model does not accurately capture the convective behavior of the waste near the free surface, nor did the model give accurate predictions of slosh heights. Based on the ability of the ANSYS benchmark model to accurately predict frequencies and global reaction forces and on the results presented in Abatt, et al. (2006), the global ANSYS model described in Carpenter et al. (2006) is sufficient for the seismic evaluation of all tank components except for local areas of the primary tank. Due to the limitations of the ANSYS model in predicting the convective response of the waste, the evaluation of primary tank stresses near the waste free surface should be supplemented by results from an ANSYS sub-model of the primary tank that incorporates pressures from theoretical solutions or from Dytran solutions. However, the primary tank is expected to have low demand to capacity ratios in the upper wall. Moreover, due to the less than desired mesh resolution in the primary tank knuckle of the global ANSYS model, the evaluation of the primary tank stresses in the lower knuckle should be supplemented by results from a more refined ANSYS sub-model of the primary tank that incorporates pressures from theoretical solutions or from Dytran solutions.