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Time-domain soil-structure interaction analysis of nuclear facilities
Nuclear Engineering and Design 298 (2016) 264–270
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Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Time-domain soil-structure interaction analysis of nuclear facilities Justin L. Coleman a,∗ , Chandrakanth Bolisetti a,1 , Andrew S. Whittaker b,2 a b
Idaho National Laboratory, 2525 Fremont Avenue, Idaho Falls, ID 83402, USA University at Buffalo, The State University of New York, North Campus, 212 Ketter Hall, Amherst, NY 14260, USA
a r t i c l e
i n f o
Article history: Received 15 December 2014 Received in revised form 21 August 2015 Accepted 22 August 2015 Available online 21 October 2015
a b s t r a c t The Nuclear Regulatory Commission (NRC) regulation 10 CFR Part 50 Appendix S requires consideration of soil-structure interaction (SSI) in nuclear power plant (NPP) analysis and design. Soil-structure interaction analysis for NPPs is routinely carried out using guidance provided in the ASCE Standard 4-98 titled “Seismic Analysis of Safety-Related Nuclear Structures and Commentary”. This Standard, which is currently under revision, provides guidance on linear seismic soil-structure-interaction (SSI) analysis of nuclear facilities using deterministic and probabilistic methods. A new appendix has been added to the forthcoming edition of ASCE Standard 4 to provide guidance for time-domain, nonlinear SSI (NLSSI) analysis. Nonlinear SSI analysis will be needed to simulate material nonlinearity in soil and/or structure, static and dynamic soil pressure effects on deeply embedded structures, local soil failure at the foundation-soil interface, nonlinear coupling of soil and pore fluid, uplift or sliding of the foundation, nonlinear effects of gaps between the surrounding soil and the embedded structure and seismic isolation systems, none of which can be addressed explicitly at present. Appendix B of ASCE Standard 4 provides general guidance for NLSSI analysis but will not provide a methodology for performing the analysis. This paper provides a description of an NLSSI methodology developed for application to nuclear facilities, including NPPs. This methodology is described as series of sequential steps to produce reasonable results using any time-domain numerical code. These steps require some numerical capabilities, such as nonlinear soil constitutive models, which are also described in the paper. © 2015 Elsevier B.V. All rights reserved.
1. Introduction In the 1960s, the dynamic responses of nuclear power plant (NPP) structures were calculated using analytical calculations of fixed-base structures. Computer programs were developed in the late 1960s that could predict the seismic response of multi-degree of freedom systems. By the late 1970s numerical programs that could consider soil-structure interaction (SSI) problems had been developed. Although these programs performed linear analysis and operated in the frequency domain, they were used with equivalentlinear soil properties to approximate nonlinear response. The System for Analysis of Soil-Structure Interaction (SASSI) (Lysmer et al., 1999) is a frequency-domain code that was first released
∗ Corresponding author. Tel.: +1 208 526 4741. E-mail addresses: [email protected] (J.L. Coleman), [email protected] (C. Bolisetti), [email protected] (A.S. Whittaker). 1 Tel.: +1 208 526 8161. 2 Tel.: +1 716 645 4364. http://dx.doi.org/10.1016/j.nucengdes.2015.08.015 0029-5493/© 2015 Elsevier B.V. All rights reserved.
in 1981 and is still widely used to calculate the dynamic seismic response of nuclear facilities. Current seismic analysis of NPPs, high-hazard nuclear waste facilities, and spent fuel storage systems is carried out using the guidance provided in American Society of Civil Engineers (ASCE) Standard 4 (ASCE, 1998). Soil-structure-interaction (SSI) analysis of these structures is generally performed using frequency-domain codes such as SASSI. These linear analysis codes, when used in accordance with ASCE Standard 4 (ASCE, 1998) and Standard 43 (ASCE, 2005), should generally lead to appropriate NPP designs for low to moderate amplitude earthquake shaking. However, these codes cannot address gapping, sliding and other nonlinear effects that may result from intense earthquake shaking that is expected at many sites of nuclear facilities for design basis and beyond design basis shaking. Nonlinear analysis is required to capture these effects and to generate appropriate in-structure response spectra. In recent years, re-evaluations of seismic hazard at sites of NPPs and other safety-related nuclear structures in the United States have increased earthquake demands. In the aftermath of the Fukushima accident, more attention has been paid to beyonddesign basis earthquakes (BDBE), with shaking often much more
J.L. Coleman et al. / Nuclear Engineering and Design 298 (2016) 264–270 Table 1 Design peak ground acceleration and recorded peak ground acceleration at NPPs.
Design value Recorded value (year) a
KashiwazakiKariwa, Japan
Fukushima Daiichi, Japan
North Anna, USA
0.20 g 0.32 g (2007)
0.26 ga 0.56 g (2011)
0.18 g 0.26 g (2011)
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active faulting. For many sites of nuclear facilities in the Western United States and all sites in the Central and Eastern United States, where such knowledge is (and will be) unavailable, probabilistic seismic hazard assessment, using modern ground motion prediction equations, will form the basis of inputs to soil-structure analysis models for the coming decades.
Design basis updated in 2009 to 0.45 g (The National Diet of Japan, 2012).
2. Literature review demanding than design basis earthquake (DBE) shaking. Indeed, shaking more intense than design basis has been recorded at NPP sites in the last decade, as summarized in Table 1. These changes in seismic hazard, and the need to understand soilstructure-interaction for levels of ground shaking greater than those considered, in past years has made clear the need for analysis tools that can capture highly nonlinear soil behavior. Nonlinear SSI (NLSSI) analysis, which can only be performed in the time domain, may be needed to explicitly capture material nonlinearity in the soil, and geometric nonlinearity at the foundation (gapping and sliding) during design basis and beyond-design-basis earthquake shaking. Since nonlinear time-domain analysis is not yet routinely performed in the nuclear industry, a methodology is needed for its implementation. Appendix B in the forthcoming ASCE Standard 4 (ASCE, forthcoming) provides guidance for implementing such a methodology. The primary objectives of this paper are to (1) present a methodology for performing nonlinear SSI (NLSSI) analysis in the time domain, (2) introduce guidance provided in Appendix B of the forthcoming edition of ASCE Standard 4, (3) discuss the circumstances for which nonlinear seismic soil structure interaction (SSI) analysis may be necessary for NPPs and high-hazard nuclear waste facilities, and (4) identify the need for mesh and time-step sensitivity studies. Nonlinear soil-structure interaction analysis will be used for both design and probabilistic risk assessment. A necessary input for such analysis is the wave field at the boundary of the soil-structure numerical model. At this time, and for the foreseeable future, the wave field will be established in a two-step process, namely, (1) probabilistic seismic hazard assessment to generate uniform hazard or scenario spectra for specified mean annual frequencies of exceedance, and (2) selection and scaling of three-component ground motions, consistent with the chosen spectra, to be applied at the boundary of the model. Modern probabilistic seismic hazard assessment involves a formal treatment of uncertainty and variability, and return seismic hazard curves that can be used to generate horizontal and vertical (translational) spectra, from which sets of ground motions can be developed. Techniques and tools are being developed to generate surface free field rotational ground motions (e.g., Basu et al. (2012a,b)) but these have not been integrated into the process described above, nor have strategies been developed to deconvolve them to the boundary of a soil-structure model. Earth scientists are developing numerical methods to propagate seismic waves from an earthquake source to the site of a structure. The Southern California Earthquake Center (www.scec.org) and its research team have made significant progress over the course of the past decade at simulating rupture and the resultant wave fields for large magnitude earthquakes in Southern California [e.g., Taborda and Bielak (2011), Day et al. (2006) and Restrepo et al. (2011)]. These petascale simulations can predict site-specific wave fields, including body and surface waves, at frequencies of 1 Hz and lower. Work continues to drive the threshold frequencies toward 10 Hz and higher to enable simulations of wave fields at frequencies of importance to the nuclear industry. Such simulations could supplement recorded ground motions in support of future probabilistic seismic hazard assessment in those regions where there is detailed knowledge of geologic structure (e.g., the Los Angeles basin) and
Nonlinear SSI analysis can be performed using commercial finite element (FE) programs such as ABAQUS (Dassault Systèmes, 2005), ANSYS (ANSYS Inc., 2013) and LS-DYNA (LSTC, 2013). Although such analysis has been performed for canal locks, bridges and liquid natural gas tanks (Willford et al., 2010), it has yet to be used for nuclear facility applications. A few studies of nonlinear SSI analysis for nuclear facilities have been performed. Xu et al. (2006) compared predictions made using SASSI and LS-DYNA (LSTC, 2013) with a focus on deeply embedded nuclear structures. They found that the results calculated using SASSI and LS-DYNA differed considerably for both linear and nonlinear analyses. Although differences are expected between results of linear and nonlinear analysis, they identified the differences in results of linear SSI analysis to be due to alternate implementations of damping. Anderson et al. (2013) and Coronado et al. (2013) showed that linear SSI analyses of deeply embedded nuclear structures using time-domain and frequency-domain codes produced very similar structural responses: Anderson et al. (2013) compared results of analysis using SAP2000 (Computers and Structures Inc., 2011) and SASSI2010 (Ostadan and Deng, 2011), and Coronado et al. (2013) compared results of analysis using the extended subtraction method in SASSI2010 and ANSYS. In another benchmarking exercise, Spears and Coleman (2014) identified possible shortcomings with the use of both frequency- and time-domain SSI codes. Bolisetti et al. (2014) and Bolisetti and Whittaker (2015) benchmarked time-domain methods in site-response and SSI analyses against the widely-used frequency-domain methods for low and high amplitude shaking across a number of sites, inducing linear and highly nonlinear response, and listed some of the challenges associated with their implementation by design professionals. They performed time-domain SSI analyses using LS-DYNA and frequency-domain SSI analyses using SASSI2000 and benchmarked the Domain Reduction Method (DRM: Bielak et al. (2003)) implemented in LS-DYNA against SASSI2000 for linear analyses. Jeremic et al. (2011) are developing a stand-alone code, ESSI, for nonlinear SSI analysis of nuclear facilities, with funding from the US Nuclear Regulatory Commission. This code is expected to have features of commercial FE codes and includes a version of the DRM.
3. A methodology for time-domain SSI analysis The Idaho National Laboratory (INL) in the US Department of Energy complex, is developing a methodology for NLSSI analysis of nuclear facilities (Spears and Coleman, 2014). This methodology is intended to accommodate those nonlinear behaviors of nuclear facilities considered to meaningfully contribute to seismic risk calculations: (1) nonlinear site response, (2) large-strain soil hysteresis, (3) geometric nonlinearities at the foundation-soil interface, including gapping and sliding, and (4) nonlinear behavior of structures, components and systems. Fig. 1 illustrates the current version of the INL methodology, which has been supported by on-going benchmarking of SSI results using SASSI and LS-DYNA. (Analysis has also been performed with ABAQUS.) Only those commercial FE codes with an ASME NQA-1 (ASME, 2015) pedigree are being used. A generic NPP structure on
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Fig. 1. INL time-domain SSI methodology.
3.1. Building the NLSSI model
Fig. 2. Finite-element NLSSI model of a generic nuclear power plant on a representative soil site.
a representative soil site is used for the benchmarking studies: see Fig. 2. As described in Fig. 1, constructing an NLSSI model requires modeling (1) the soil domain, (2) the foundation and the supported structure, and (3) the interface between the soil and the structure. Procedures for accomplishing these tasks are outlined below. The section numbers in Fig. 1 point to the corresponding sections below. The NLSSI methodology can be implemented using both the so-called direct, method and the DRM. The direct method is capable of simulating vertically propagating waves only. The domain reduction method can accommodate a more complex three-dimensional wave field as input. However, because (1) the proposed methodology is planned for use in the near term, (2) seismic hazard calculations will be performed for translational components of ground motion for the coming decades, (3) not all NQA-1 FE codes implement the DRM at present, the direct method is used for the presentations in the following sections.
3.1.1. Soil domain The soil domain has to be large enough to dissipate the scattered waves from the structure. The soil response at the boundaries of the domain should be virtually identical to the free-field response, which can be calculated by site-response analysis. The ground motion input is applied at the base of the soil domain as either a force input (when an outcrop motion is available) or an acceleration input (when a within profile motion is available) as explained in Section 3.4. An NLSSI model for analysis using the direct method is illustrated in Fig. 3. The first step in building the soil domain model is to gather the site-specific soils data, suitable and sufficient for nonlinear dynamic analysis. Mechanical properties will be established from laboratory tests of soil recovered from bores driven at the site. The properties needed for analysis will be a function of the expected deformation in the soil layers below the nuclear facility. The second step is to mesh the soil domain. The required element size(s) depends on the soil properties, element formulation (e.g., constant strain, fully integrated), integration technique (implicit or explicit) and the desired maximum frequency of analysis. The mesh should be sufficiently fine to transmit seismic motions up to the chosen cut-off frequency and to capture nonlinear soil behavior, especially in the immediate vicinity of the foundation. Jeremic´ et al. (2009) recommend an (constant strain) element size less than the small-strain shear-wave velocity divided by 10 times the cut-off frequency (e.g., 50 Hz), which is equivalent to discretizing the harmonic wave at the cut-off frequency into tenths, noting that wave velocity is equal to the product of wavelength and frequency. However, finer meshes may be required if the earthquake shaking leads to high shear strains and significant softening of the soil. The required element size will vary by layer based on the corresponding shear-wave velocity.
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Fig. 3. Illustration of the soil domain in direct method of NLSSI analysis (Bolisetti and Whittaker, 2015).
Mesh sensitivity studies will also be required to confirm the choice of element size and analysis time step. Fig. 4 presents snapshots of a wavelet passing through a sample soil column. The first three models of the soil column are meshed with 25, 10 and 5 linear elements per wavelength of the input wavelet, respectively; the fourth model uses 5 quadratic elements per wavelength of the input wavelet. The figure shows high-frequency noise trailing the wavelet when 5 linear elements per wavelength are used. This noise is removed with 10 or 25 linear elements per wavelength, and for 5 quadratic elements per wavelength, indicating that at least 10 linear finite elements per wavelength should be used in the case to avoid generating artificial high-frequency noise. Implicit solver time step should also be interrogated to avoid spurious high-frequency noise. An interim recommendation is to use a time step that is one-tenth (or less) that of the input time series.
The minimum lateral dimensions of the soil domain will depend on the amplitude of the scattered waves, which will be a function of the mass of the structure, the intensity of shaking, and the inherent energy dissipation (damping) in the soil. In the absence of experience, the dimensions of the soil domain should be chosen by trial and error, with the chosen domain satisfying the following: (1) the response of the soil domain at the edge of the domain is not significantly different from the free-field response calculated from one-dimensional site-response analysis, and (2) the in-structure response does not change significantly with a further increase in the lateral dimensions. The vertical dimension of the soil domain is determined by the depth at which the ground motion is defined. The soil domain should also be sufficiently deep to capture the vertical dynamic stiffness of the foundation. A depth below the foundation of one to two times the largest plan dimension of the basement will generally be sufficient.
Fig. 4. Snapshots of a wavelet passing through a 200 m deep soil profile with a shear wave velocity of 1000 m/s.
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Table 2 Verification and/or benchmarking of NLSSI models. Section of paper
NLSSI modeling step
Parameters to be verified or benchmarked
Verification and/or benchmarking approach
3.1.1
Calibration of site-specific soil material models Building 3D soil model
Constitutive models including energy dissipation (damping) Material model; boundary conditions
Single element models
3.1.2
Calibration of structural constitutive models Building structural model
Constitutive models including energy dissipation (damping) Fixed-base frequencies; structural damping
3.2
Modeling soil-structure interface
3.5
Assembling NLSSI model
3.5
Assembling NLSSI model
Coefficient of friction; lateral force required for uplift Absorbing boundary conditions; size of soil domain Final benchmarking
3.1.1
3.1.2
The lateral boundaries of the soil domain should dissipate the arriving scattered waves. This can be achieved with absorbing boundaries, which have been implemented in commercial FE programs for linear elastic materials. (Absorbing boundaries have not yet been developed for nonlinear materials, to the knowledge of the authors.) A reasonable approach at this time is to build a sufficiently large soil domain such that the scattered waves are dissipated before reaching the boundary, and constrain the boundary nodes to move in pure shear, thus simulating a free-field condition. The pure shear constraint can be achieved by constraining the nodes at the lateral boundaries at the same elevation to move together horizontally and vertically, assuming that the input ground motions consists of vertically propagating waves. 3.1.2. Foundation and superstructure Superstructure models for traditional frequency-domain SSI analysis have utilized lumped masses and linear beam-column elements. These simplified models are numerically efficient and were consistent with the equivalent linear models of the soil domain. For NLSSI analysis, most of the computational effort is spent analyzing the (large) soil domain and so a detailed FE model of the superstructure can be built, utilizing nonlinear shell, solid, and beam-column elements as required. The meshing of the structure should enable resolution of forces and deformations in critical regions, with considerations of element size for explicit analysis such that the critical time step for the structural elements is similar to that for the soil elements. 3.2. Modeling the soil-foundation interface The geometric nonlinearities at the soil-foundation interface of gapping and sliding are expected to play a significant role in the seismic response of many nuclear facilities for shaking in excess of design basis. The soil-foundation interface can be modeled using (1) contact elements that are available in most commercial finite-element codes, (2) nonlinear springs and dashpots connected between the soil and foundation nodes that have zero strength in tension and simulate the necessary frictional behavior in shear, and (3) thin layers of nonlinear hysteretic soil that have zero strength in tension and the necessary peak shear strength to simulate friction. The choice of interface model will depend somewhat on the FE code being used for analysis and the expected amplitude of gapping and sliding. If these nonlinear effects are likely small in terms of altering structural response, they can be simulated using a thin, soft layer between the foundation and the soil domain, with properties chosen to capture the expected frictional response. Contact models can be used if significant gapping and/or sliding are expected but
Comparison with equivalent linear site-response codes for low-amplitude inputs Single element models Modal analysis and comparison of fixed-base responses with other verified codes Analysis of simple models or comparison with closed form solutions NLSSI analyses with increasing soil domain sizes Comparison with equivalent-linear SSI codes for low-amplitude inputs
they may generate spurious high-frequency noise. Regardless of the chosen model, it should be verified as described in Section 3.3. 3.3. Verification of the model Model verification and benchmarking are crucial aspects of any FE analysis. Verification is the process of showing that the implemented numerical solution solves the associated mathematics correctly. Benchmarking involves a comparison of results with other verified solutions or numerical codes. This NLSSI methodology involves verification and/or benchmarking of all components of the numerical model (e.g., soil domain, structure, soil-structure interface) and the fully assembled model. The suggested verification and benchmarking activities are summarized in Table 2 and discussed below. • Calibration of soil models: Constitutive models of soils for NLSSI analysis should be verified and validated. The mechanical properties assigned to elements of a soil layer should be based on project-specific laboratory experiments. Calibration of a constitutive model can be accomplished through analyses of a single element or a small number of elements: typically the eight-node solids used for the soil domain. • Verification of the soil domain model: The model of the soil domain should be verified for material properties and boundary conditions. This task can be performed by comparing the response of the free-field soil domain model (without the structure) with equivalent linear site-response analysis codes at low levels of input ground motion. • Calibration of structural models: Identical to soils, constitutive models of structural components should be verified and validated. Calibration of a component model should be undertaken using single elements and three-dimensional loadings. • Benchmarking of fixed-base structural model: The model of the fixed-base structure should be analyzed and evaluated for (a) static loadings to confirm the expected seismic load paths, and (b) dynamic properties (modal frequencies, modal participation factors, mode shapes, and modal damping ratios). Results could be compared with those from analysis of simpler models used for preliminary design and assessment. • Verification of the soil-foundation interface: The soil-foundation interface should be verified for the desired sliding and gapping behavior through the application of force and/or displacement functions. • Assembling the NLSSI model: The full NLSSI model should be benchmarked after it has been assembled from the soil, structure and interface models. Benchmarking should involve calculations
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laboratories, and curated and archived for use by modelers, engineers, analysts, and researchers. 5. Appendix B of ASCE Standard 4
Fig. 5. Specification of outcrop input for the direct method.
of modal frequencies and modal participation factors, and a comparison of results with analysis of a SASSI-type model of the soil-structure system for low amplitude ground motion inputs for which linear response is anticipated. 3.4. Imposing external loadings Input ground motions corresponding to vertically propagating wavefields are imposed at the base of the soil domain in the direct method. When a within motion [e.g., Bolisetti and Whittaker (2015) and Kwok et al. (2007)] is available, or if the soil or rock below the soil domain can be assumed rigid, the input ground motion can be applied as an acceleration, velocity or displacement history. If outcrop motions are used, the input ground motion is applied as a force history and an absorbing boundary condition is provided at the base. Since an outcrop motion is essentially an incoming wave, which travels upwards to the top of the soil domain and then and reflects back into domain, an absorbing boundary is provided to avoid trapping energy in the soil domain. The process of specifying an outcrop input is illustrated in Fig. 5. Gravity loads are imposed prior to the application of the seismic input. These loads are applied using static or pseudo-static analysis, depending on the FE code being used.
Appendix B of the forthcoming edition of ASCE Standard 4 will provide non-mandatory guidance for performing three dimensional nonlinear SSI analysis. The guidance notes that the numerical modeling of the nonlinear response of a nuclear facility should consider the following: material nonlinearity, hysteretic behavior (in soil and/or structure), uplift and/or sliding of the foundation, static and dynamic soil pressure effects on deeply embedded structures, local soil failure at the soil-foundation interface, and nonlinear behavior of seismic isolators where included. NLSSI can be used to provide element forces and deformations for superstructure component checking and in-structure response spectra, or foundation input motions, which is the first step in a multistep analysis of a seismically isolated nuclear structure. The appendix does not alter other guidance on the use of three soil columns [best estimate (BE), lower bound (LB), upper bound (UB)] for SSI analysis or peak smoothing and broadening of in-structure response spectra. The appendix provides summary information on the development of finite element meshes, ground motion inputs, nonlinear constitutive models, analysis results and interpretation, and verification and validation. 6. Closing remarks This paper presents a NLSSI methodology for application to nuclear facilities for both design and beyond-design basis ground motions. The methodology assumes vertically propagating waves and accommodates the effects of nonlinear soil behavior and geometric nonlinearities at the soil-foundation interface, such as gapping and sliding. The framework presented here is constructed around verification and validation of constitutive models and numerical tools and emphasizes calibration and benchmarking, all of which are necessary for the analysis, design and risk assessment of nuclear facilities in the United States. 7. Related research and development on NLSSI
3.5. Assembling the NLSSI model After building and verifying the individual components of the NLSSI model they are assembled to construct the numerical model for analysis. The loads are then applied and benchmarking analyses are performed, as described in Section 3.3. 4. Validation of the NLSSI methodology Developing confidence in accurate numerical predictions of the seismic response of nuclear facilities relies heavily on verification and validation (V+V). Verification and validation procedures are the primary means of assessing accuracy in modeling and computational simulations. Verification provides evidence that the mathematical models are solved correctly and involves comparing the numerical results with known closed-form solutions. Validation provides evidence that the correct model is solved and typically involves comparisons with experimental data (Oberkampf and Trucano, 2008). There are three nonlinear behaviors in a nonlinear SSI problem that should be independently validated: soil nonlinearity, structural nonlinearity, and contact interface nonlinearities (sliding and/or separation). Information is available for validating soil, concrete, and contact models (FIB, 2008) but much more is needed, as described below. The data need to be collected in accredited
Spears and Coleman (2014) developed, verified and benchmarked the methodology presented in this paper by comparing NLSSI results to those calculated using SASSI for multiple levels of input ground motion. They considered a representative site in the western United States for this study and are extending the methodology for a site and seismic hazard representative of the central and eastern United States. Other activities under way at INL related to NLSSI analysis include (a) efficient modeling of soilstructure interfaces that do not generate spurious, high frequency noise, (b) verification and validation of site response and SSI codes in the frequency and time domains using the geotechnical laminar box at the University at Buffalo, (c) verification and validation of algorithms for gapping and sliding using the six-degree-of-freedom earthquake simulators at the University at Buffalo, and (d) integration of NLSSI tools into an advanced seismic probabilistic risk assessment framework under development at INL for Department of Energy. Future work will include (a) streamlining NLSSI analysis using commercial FE codes with an NQA-1 pedigree by identifying practical issues with their use and working with code developers to resolve them, (b) automating the model building process, (c) extending the NLSSI methodology to deeply embedded reactors that directly experience shaking around most their perimeter, and (d) accommodating inclined body waves and surface waves.
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Acknowledgments The development of this NLSSI methodology was made possible by funding from the U.S. Department of Energy’s National Nuclear Security Administration and Nuclear Safety Research and Development, and TerraPower, LLC. The authors gratefully acknowledge this financial support but note that the opinions expressed in this paper are those of the authors and not necessarily the Department of Energy or TerraPower. References Anderson, L.M., Elkhoraibi, T., Ostadan, F., 2013. Validation of SASSI2010 solution methods through independent verification using SAP2000 for deeply embedded structures with large footprints. In: 22nd International Conference in Structural Mechanics in Reactor Technology – SMiRT 22, August 2013, San Francisco, California. ANSYS Inc., 2013. Computer Program: ANSYS 13.0. ANSYS Inc., Canonsburg, Pennsylvania. American Society of Civil Engineers (ASCE), 1998. Seismic analysis of safety-related nuclear structures and commentary. In: ASCE 4-98, Reston, Virginia. American Society of Civil Engineers (ASCE), 2005. Seismic design criteria for structures, systems and components for nuclear facilities. In: ASCE 43-05, Reston, Virginia. American Society of Civil Engineers (ASCE), 2015. Seismic analysis of safety-related nuclear structures and commentary. In: ASCE 4-14, Reston, Virginia (forthcoming). American Society of Mechanical Engineers (ASME), 2015. Quality assurance requirements for nuclear facility applications. In: ASME NQA-1, New York, NY. Basu, D., Whittaker, A.S., Constantinou, M.C., 2012a. On estimating rotational components of earthquake ground motion using data from a single recording station. J. Eng. Mech. 138 (9), 1141–1156. Basu, D., Whittaker, A.S., Constantinou, M.C., 2012b. Extracting rotational components of earthquake ground motion using data recorded at multiple stations. Earthq. Eng. Struct. Dyn. 42 (3), 451–468. Bielak, J., Loukakis, K., Hisada, Y., Yoshimura, C., 2003. Domain reduction method for three-dimensional earthquake modeling in localized regions. Part-I: Theory. Bull. Seismol. Soc. Am. 93 (2), 817–824. Bolisetti, C., Whittaker, A.S., Mason, H.B., Almufti, I., Willford, M., 2014. Equivalent linear and nonlinear site response analysis for design and risk assessment of safety-related nuclear structures. Nucl. Eng. Des. 275, 107–121, http://dx.doi. org/10.1016/j.nucengdes.2014.04.033. Bolisetti, C., Whittaker, A.S., 2015. Site Response, Soil-structure Interaction and Structure-soil-structure Interaction for Performance Assessment of Buildings and Nuclear Structures. Multidisciplinary Center for Earthquake Engineering Research (MCEER), University at Buffalo, The State University of New York, Buffalo, NY. Computers and Structures Inc., 2011. Computer Program: SAP2000 – Structural Analysis Program, Version 11.0.0. Computers and Structures, Inc., Berkeley, California.
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Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Time-domain soil-structure interaction analysis of nuclear facilities Justin L. Coleman a,∗ , Chandrakanth Bolisetti a,1 , Andrew S. Whittaker b,2 a b
Idaho National Laboratory, 2525 Fremont Avenue, Idaho Falls, ID 83402, USA University at Buffalo, The State University of New York, North Campus, 212 Ketter Hall, Amherst, NY 14260, USA
a r t i c l e
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Article history: Received 15 December 2014 Received in revised form 21 August 2015 Accepted 22 August 2015 Available online 21 October 2015
a b s t r a c t The Nuclear Regulatory Commission (NRC) regulation 10 CFR Part 50 Appendix S requires consideration of soil-structure interaction (SSI) in nuclear power plant (NPP) analysis and design. Soil-structure interaction analysis for NPPs is routinely carried out using guidance provided in the ASCE Standard 4-98 titled “Seismic Analysis of Safety-Related Nuclear Structures and Commentary”. This Standard, which is currently under revision, provides guidance on linear seismic soil-structure-interaction (SSI) analysis of nuclear facilities using deterministic and probabilistic methods. A new appendix has been added to the forthcoming edition of ASCE Standard 4 to provide guidance for time-domain, nonlinear SSI (NLSSI) analysis. Nonlinear SSI analysis will be needed to simulate material nonlinearity in soil and/or structure, static and dynamic soil pressure effects on deeply embedded structures, local soil failure at the foundation-soil interface, nonlinear coupling of soil and pore fluid, uplift or sliding of the foundation, nonlinear effects of gaps between the surrounding soil and the embedded structure and seismic isolation systems, none of which can be addressed explicitly at present. Appendix B of ASCE Standard 4 provides general guidance for NLSSI analysis but will not provide a methodology for performing the analysis. This paper provides a description of an NLSSI methodology developed for application to nuclear facilities, including NPPs. This methodology is described as series of sequential steps to produce reasonable results using any time-domain numerical code. These steps require some numerical capabilities, such as nonlinear soil constitutive models, which are also described in the paper. © 2015 Elsevier B.V. All rights reserved.
1. Introduction In the 1960s, the dynamic responses of nuclear power plant (NPP) structures were calculated using analytical calculations of fixed-base structures. Computer programs were developed in the late 1960s that could predict the seismic response of multi-degree of freedom systems. By the late 1970s numerical programs that could consider soil-structure interaction (SSI) problems had been developed. Although these programs performed linear analysis and operated in the frequency domain, they were used with equivalentlinear soil properties to approximate nonlinear response. The System for Analysis of Soil-Structure Interaction (SASSI) (Lysmer et al., 1999) is a frequency-domain code that was first released
∗ Corresponding author. Tel.: +1 208 526 4741. E-mail addresses: [email protected] (J.L. Coleman), [email protected] (C. Bolisetti), [email protected] (A.S. Whittaker). 1 Tel.: +1 208 526 8161. 2 Tel.: +1 716 645 4364. http://dx.doi.org/10.1016/j.nucengdes.2015.08.015 0029-5493/© 2015 Elsevier B.V. All rights reserved.
in 1981 and is still widely used to calculate the dynamic seismic response of nuclear facilities. Current seismic analysis of NPPs, high-hazard nuclear waste facilities, and spent fuel storage systems is carried out using the guidance provided in American Society of Civil Engineers (ASCE) Standard 4 (ASCE, 1998). Soil-structure-interaction (SSI) analysis of these structures is generally performed using frequency-domain codes such as SASSI. These linear analysis codes, when used in accordance with ASCE Standard 4 (ASCE, 1998) and Standard 43 (ASCE, 2005), should generally lead to appropriate NPP designs for low to moderate amplitude earthquake shaking. However, these codes cannot address gapping, sliding and other nonlinear effects that may result from intense earthquake shaking that is expected at many sites of nuclear facilities for design basis and beyond design basis shaking. Nonlinear analysis is required to capture these effects and to generate appropriate in-structure response spectra. In recent years, re-evaluations of seismic hazard at sites of NPPs and other safety-related nuclear structures in the United States have increased earthquake demands. In the aftermath of the Fukushima accident, more attention has been paid to beyonddesign basis earthquakes (BDBE), with shaking often much more
J.L. Coleman et al. / Nuclear Engineering and Design 298 (2016) 264–270 Table 1 Design peak ground acceleration and recorded peak ground acceleration at NPPs.
Design value Recorded value (year) a
KashiwazakiKariwa, Japan
Fukushima Daiichi, Japan
North Anna, USA
0.20 g 0.32 g (2007)
0.26 ga 0.56 g (2011)
0.18 g 0.26 g (2011)
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active faulting. For many sites of nuclear facilities in the Western United States and all sites in the Central and Eastern United States, where such knowledge is (and will be) unavailable, probabilistic seismic hazard assessment, using modern ground motion prediction equations, will form the basis of inputs to soil-structure analysis models for the coming decades.
Design basis updated in 2009 to 0.45 g (The National Diet of Japan, 2012).
2. Literature review demanding than design basis earthquake (DBE) shaking. Indeed, shaking more intense than design basis has been recorded at NPP sites in the last decade, as summarized in Table 1. These changes in seismic hazard, and the need to understand soilstructure-interaction for levels of ground shaking greater than those considered, in past years has made clear the need for analysis tools that can capture highly nonlinear soil behavior. Nonlinear SSI (NLSSI) analysis, which can only be performed in the time domain, may be needed to explicitly capture material nonlinearity in the soil, and geometric nonlinearity at the foundation (gapping and sliding) during design basis and beyond-design-basis earthquake shaking. Since nonlinear time-domain analysis is not yet routinely performed in the nuclear industry, a methodology is needed for its implementation. Appendix B in the forthcoming ASCE Standard 4 (ASCE, forthcoming) provides guidance for implementing such a methodology. The primary objectives of this paper are to (1) present a methodology for performing nonlinear SSI (NLSSI) analysis in the time domain, (2) introduce guidance provided in Appendix B of the forthcoming edition of ASCE Standard 4, (3) discuss the circumstances for which nonlinear seismic soil structure interaction (SSI) analysis may be necessary for NPPs and high-hazard nuclear waste facilities, and (4) identify the need for mesh and time-step sensitivity studies. Nonlinear soil-structure interaction analysis will be used for both design and probabilistic risk assessment. A necessary input for such analysis is the wave field at the boundary of the soil-structure numerical model. At this time, and for the foreseeable future, the wave field will be established in a two-step process, namely, (1) probabilistic seismic hazard assessment to generate uniform hazard or scenario spectra for specified mean annual frequencies of exceedance, and (2) selection and scaling of three-component ground motions, consistent with the chosen spectra, to be applied at the boundary of the model. Modern probabilistic seismic hazard assessment involves a formal treatment of uncertainty and variability, and return seismic hazard curves that can be used to generate horizontal and vertical (translational) spectra, from which sets of ground motions can be developed. Techniques and tools are being developed to generate surface free field rotational ground motions (e.g., Basu et al. (2012a,b)) but these have not been integrated into the process described above, nor have strategies been developed to deconvolve them to the boundary of a soil-structure model. Earth scientists are developing numerical methods to propagate seismic waves from an earthquake source to the site of a structure. The Southern California Earthquake Center (www.scec.org) and its research team have made significant progress over the course of the past decade at simulating rupture and the resultant wave fields for large magnitude earthquakes in Southern California [e.g., Taborda and Bielak (2011), Day et al. (2006) and Restrepo et al. (2011)]. These petascale simulations can predict site-specific wave fields, including body and surface waves, at frequencies of 1 Hz and lower. Work continues to drive the threshold frequencies toward 10 Hz and higher to enable simulations of wave fields at frequencies of importance to the nuclear industry. Such simulations could supplement recorded ground motions in support of future probabilistic seismic hazard assessment in those regions where there is detailed knowledge of geologic structure (e.g., the Los Angeles basin) and
Nonlinear SSI analysis can be performed using commercial finite element (FE) programs such as ABAQUS (Dassault Systèmes, 2005), ANSYS (ANSYS Inc., 2013) and LS-DYNA (LSTC, 2013). Although such analysis has been performed for canal locks, bridges and liquid natural gas tanks (Willford et al., 2010), it has yet to be used for nuclear facility applications. A few studies of nonlinear SSI analysis for nuclear facilities have been performed. Xu et al. (2006) compared predictions made using SASSI and LS-DYNA (LSTC, 2013) with a focus on deeply embedded nuclear structures. They found that the results calculated using SASSI and LS-DYNA differed considerably for both linear and nonlinear analyses. Although differences are expected between results of linear and nonlinear analysis, they identified the differences in results of linear SSI analysis to be due to alternate implementations of damping. Anderson et al. (2013) and Coronado et al. (2013) showed that linear SSI analyses of deeply embedded nuclear structures using time-domain and frequency-domain codes produced very similar structural responses: Anderson et al. (2013) compared results of analysis using SAP2000 (Computers and Structures Inc., 2011) and SASSI2010 (Ostadan and Deng, 2011), and Coronado et al. (2013) compared results of analysis using the extended subtraction method in SASSI2010 and ANSYS. In another benchmarking exercise, Spears and Coleman (2014) identified possible shortcomings with the use of both frequency- and time-domain SSI codes. Bolisetti et al. (2014) and Bolisetti and Whittaker (2015) benchmarked time-domain methods in site-response and SSI analyses against the widely-used frequency-domain methods for low and high amplitude shaking across a number of sites, inducing linear and highly nonlinear response, and listed some of the challenges associated with their implementation by design professionals. They performed time-domain SSI analyses using LS-DYNA and frequency-domain SSI analyses using SASSI2000 and benchmarked the Domain Reduction Method (DRM: Bielak et al. (2003)) implemented in LS-DYNA against SASSI2000 for linear analyses. Jeremic et al. (2011) are developing a stand-alone code, ESSI, for nonlinear SSI analysis of nuclear facilities, with funding from the US Nuclear Regulatory Commission. This code is expected to have features of commercial FE codes and includes a version of the DRM.
3. A methodology for time-domain SSI analysis The Idaho National Laboratory (INL) in the US Department of Energy complex, is developing a methodology for NLSSI analysis of nuclear facilities (Spears and Coleman, 2014). This methodology is intended to accommodate those nonlinear behaviors of nuclear facilities considered to meaningfully contribute to seismic risk calculations: (1) nonlinear site response, (2) large-strain soil hysteresis, (3) geometric nonlinearities at the foundation-soil interface, including gapping and sliding, and (4) nonlinear behavior of structures, components and systems. Fig. 1 illustrates the current version of the INL methodology, which has been supported by on-going benchmarking of SSI results using SASSI and LS-DYNA. (Analysis has also been performed with ABAQUS.) Only those commercial FE codes with an ASME NQA-1 (ASME, 2015) pedigree are being used. A generic NPP structure on
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Fig. 1. INL time-domain SSI methodology.
3.1. Building the NLSSI model
Fig. 2. Finite-element NLSSI model of a generic nuclear power plant on a representative soil site.
a representative soil site is used for the benchmarking studies: see Fig. 2. As described in Fig. 1, constructing an NLSSI model requires modeling (1) the soil domain, (2) the foundation and the supported structure, and (3) the interface between the soil and the structure. Procedures for accomplishing these tasks are outlined below. The section numbers in Fig. 1 point to the corresponding sections below. The NLSSI methodology can be implemented using both the so-called direct, method and the DRM. The direct method is capable of simulating vertically propagating waves only. The domain reduction method can accommodate a more complex three-dimensional wave field as input. However, because (1) the proposed methodology is planned for use in the near term, (2) seismic hazard calculations will be performed for translational components of ground motion for the coming decades, (3) not all NQA-1 FE codes implement the DRM at present, the direct method is used for the presentations in the following sections.
3.1.1. Soil domain The soil domain has to be large enough to dissipate the scattered waves from the structure. The soil response at the boundaries of the domain should be virtually identical to the free-field response, which can be calculated by site-response analysis. The ground motion input is applied at the base of the soil domain as either a force input (when an outcrop motion is available) or an acceleration input (when a within profile motion is available) as explained in Section 3.4. An NLSSI model for analysis using the direct method is illustrated in Fig. 3. The first step in building the soil domain model is to gather the site-specific soils data, suitable and sufficient for nonlinear dynamic analysis. Mechanical properties will be established from laboratory tests of soil recovered from bores driven at the site. The properties needed for analysis will be a function of the expected deformation in the soil layers below the nuclear facility. The second step is to mesh the soil domain. The required element size(s) depends on the soil properties, element formulation (e.g., constant strain, fully integrated), integration technique (implicit or explicit) and the desired maximum frequency of analysis. The mesh should be sufficiently fine to transmit seismic motions up to the chosen cut-off frequency and to capture nonlinear soil behavior, especially in the immediate vicinity of the foundation. Jeremic´ et al. (2009) recommend an (constant strain) element size less than the small-strain shear-wave velocity divided by 10 times the cut-off frequency (e.g., 50 Hz), which is equivalent to discretizing the harmonic wave at the cut-off frequency into tenths, noting that wave velocity is equal to the product of wavelength and frequency. However, finer meshes may be required if the earthquake shaking leads to high shear strains and significant softening of the soil. The required element size will vary by layer based on the corresponding shear-wave velocity.
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Fig. 3. Illustration of the soil domain in direct method of NLSSI analysis (Bolisetti and Whittaker, 2015).
Mesh sensitivity studies will also be required to confirm the choice of element size and analysis time step. Fig. 4 presents snapshots of a wavelet passing through a sample soil column. The first three models of the soil column are meshed with 25, 10 and 5 linear elements per wavelength of the input wavelet, respectively; the fourth model uses 5 quadratic elements per wavelength of the input wavelet. The figure shows high-frequency noise trailing the wavelet when 5 linear elements per wavelength are used. This noise is removed with 10 or 25 linear elements per wavelength, and for 5 quadratic elements per wavelength, indicating that at least 10 linear finite elements per wavelength should be used in the case to avoid generating artificial high-frequency noise. Implicit solver time step should also be interrogated to avoid spurious high-frequency noise. An interim recommendation is to use a time step that is one-tenth (or less) that of the input time series.
The minimum lateral dimensions of the soil domain will depend on the amplitude of the scattered waves, which will be a function of the mass of the structure, the intensity of shaking, and the inherent energy dissipation (damping) in the soil. In the absence of experience, the dimensions of the soil domain should be chosen by trial and error, with the chosen domain satisfying the following: (1) the response of the soil domain at the edge of the domain is not significantly different from the free-field response calculated from one-dimensional site-response analysis, and (2) the in-structure response does not change significantly with a further increase in the lateral dimensions. The vertical dimension of the soil domain is determined by the depth at which the ground motion is defined. The soil domain should also be sufficiently deep to capture the vertical dynamic stiffness of the foundation. A depth below the foundation of one to two times the largest plan dimension of the basement will generally be sufficient.
Fig. 4. Snapshots of a wavelet passing through a 200 m deep soil profile with a shear wave velocity of 1000 m/s.
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Table 2 Verification and/or benchmarking of NLSSI models. Section of paper
NLSSI modeling step
Parameters to be verified or benchmarked
Verification and/or benchmarking approach
3.1.1
Calibration of site-specific soil material models Building 3D soil model
Constitutive models including energy dissipation (damping) Material model; boundary conditions
Single element models
3.1.2
Calibration of structural constitutive models Building structural model
Constitutive models including energy dissipation (damping) Fixed-base frequencies; structural damping
3.2
Modeling soil-structure interface
3.5
Assembling NLSSI model
3.5
Assembling NLSSI model
Coefficient of friction; lateral force required for uplift Absorbing boundary conditions; size of soil domain Final benchmarking
3.1.1
3.1.2
The lateral boundaries of the soil domain should dissipate the arriving scattered waves. This can be achieved with absorbing boundaries, which have been implemented in commercial FE programs for linear elastic materials. (Absorbing boundaries have not yet been developed for nonlinear materials, to the knowledge of the authors.) A reasonable approach at this time is to build a sufficiently large soil domain such that the scattered waves are dissipated before reaching the boundary, and constrain the boundary nodes to move in pure shear, thus simulating a free-field condition. The pure shear constraint can be achieved by constraining the nodes at the lateral boundaries at the same elevation to move together horizontally and vertically, assuming that the input ground motions consists of vertically propagating waves. 3.1.2. Foundation and superstructure Superstructure models for traditional frequency-domain SSI analysis have utilized lumped masses and linear beam-column elements. These simplified models are numerically efficient and were consistent with the equivalent linear models of the soil domain. For NLSSI analysis, most of the computational effort is spent analyzing the (large) soil domain and so a detailed FE model of the superstructure can be built, utilizing nonlinear shell, solid, and beam-column elements as required. The meshing of the structure should enable resolution of forces and deformations in critical regions, with considerations of element size for explicit analysis such that the critical time step for the structural elements is similar to that for the soil elements. 3.2. Modeling the soil-foundation interface The geometric nonlinearities at the soil-foundation interface of gapping and sliding are expected to play a significant role in the seismic response of many nuclear facilities for shaking in excess of design basis. The soil-foundation interface can be modeled using (1) contact elements that are available in most commercial finite-element codes, (2) nonlinear springs and dashpots connected between the soil and foundation nodes that have zero strength in tension and simulate the necessary frictional behavior in shear, and (3) thin layers of nonlinear hysteretic soil that have zero strength in tension and the necessary peak shear strength to simulate friction. The choice of interface model will depend somewhat on the FE code being used for analysis and the expected amplitude of gapping and sliding. If these nonlinear effects are likely small in terms of altering structural response, they can be simulated using a thin, soft layer between the foundation and the soil domain, with properties chosen to capture the expected frictional response. Contact models can be used if significant gapping and/or sliding are expected but
Comparison with equivalent linear site-response codes for low-amplitude inputs Single element models Modal analysis and comparison of fixed-base responses with other verified codes Analysis of simple models or comparison with closed form solutions NLSSI analyses with increasing soil domain sizes Comparison with equivalent-linear SSI codes for low-amplitude inputs
they may generate spurious high-frequency noise. Regardless of the chosen model, it should be verified as described in Section 3.3. 3.3. Verification of the model Model verification and benchmarking are crucial aspects of any FE analysis. Verification is the process of showing that the implemented numerical solution solves the associated mathematics correctly. Benchmarking involves a comparison of results with other verified solutions or numerical codes. This NLSSI methodology involves verification and/or benchmarking of all components of the numerical model (e.g., soil domain, structure, soil-structure interface) and the fully assembled model. The suggested verification and benchmarking activities are summarized in Table 2 and discussed below. • Calibration of soil models: Constitutive models of soils for NLSSI analysis should be verified and validated. The mechanical properties assigned to elements of a soil layer should be based on project-specific laboratory experiments. Calibration of a constitutive model can be accomplished through analyses of a single element or a small number of elements: typically the eight-node solids used for the soil domain. • Verification of the soil domain model: The model of the soil domain should be verified for material properties and boundary conditions. This task can be performed by comparing the response of the free-field soil domain model (without the structure) with equivalent linear site-response analysis codes at low levels of input ground motion. • Calibration of structural models: Identical to soils, constitutive models of structural components should be verified and validated. Calibration of a component model should be undertaken using single elements and three-dimensional loadings. • Benchmarking of fixed-base structural model: The model of the fixed-base structure should be analyzed and evaluated for (a) static loadings to confirm the expected seismic load paths, and (b) dynamic properties (modal frequencies, modal participation factors, mode shapes, and modal damping ratios). Results could be compared with those from analysis of simpler models used for preliminary design and assessment. • Verification of the soil-foundation interface: The soil-foundation interface should be verified for the desired sliding and gapping behavior through the application of force and/or displacement functions. • Assembling the NLSSI model: The full NLSSI model should be benchmarked after it has been assembled from the soil, structure and interface models. Benchmarking should involve calculations
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laboratories, and curated and archived for use by modelers, engineers, analysts, and researchers. 5. Appendix B of ASCE Standard 4
Fig. 5. Specification of outcrop input for the direct method.
of modal frequencies and modal participation factors, and a comparison of results with analysis of a SASSI-type model of the soil-structure system for low amplitude ground motion inputs for which linear response is anticipated. 3.4. Imposing external loadings Input ground motions corresponding to vertically propagating wavefields are imposed at the base of the soil domain in the direct method. When a within motion [e.g., Bolisetti and Whittaker (2015) and Kwok et al. (2007)] is available, or if the soil or rock below the soil domain can be assumed rigid, the input ground motion can be applied as an acceleration, velocity or displacement history. If outcrop motions are used, the input ground motion is applied as a force history and an absorbing boundary condition is provided at the base. Since an outcrop motion is essentially an incoming wave, which travels upwards to the top of the soil domain and then and reflects back into domain, an absorbing boundary is provided to avoid trapping energy in the soil domain. The process of specifying an outcrop input is illustrated in Fig. 5. Gravity loads are imposed prior to the application of the seismic input. These loads are applied using static or pseudo-static analysis, depending on the FE code being used.
Appendix B of the forthcoming edition of ASCE Standard 4 will provide non-mandatory guidance for performing three dimensional nonlinear SSI analysis. The guidance notes that the numerical modeling of the nonlinear response of a nuclear facility should consider the following: material nonlinearity, hysteretic behavior (in soil and/or structure), uplift and/or sliding of the foundation, static and dynamic soil pressure effects on deeply embedded structures, local soil failure at the soil-foundation interface, and nonlinear behavior of seismic isolators where included. NLSSI can be used to provide element forces and deformations for superstructure component checking and in-structure response spectra, or foundation input motions, which is the first step in a multistep analysis of a seismically isolated nuclear structure. The appendix does not alter other guidance on the use of three soil columns [best estimate (BE), lower bound (LB), upper bound (UB)] for SSI analysis or peak smoothing and broadening of in-structure response spectra. The appendix provides summary information on the development of finite element meshes, ground motion inputs, nonlinear constitutive models, analysis results and interpretation, and verification and validation. 6. Closing remarks This paper presents a NLSSI methodology for application to nuclear facilities for both design and beyond-design basis ground motions. The methodology assumes vertically propagating waves and accommodates the effects of nonlinear soil behavior and geometric nonlinearities at the soil-foundation interface, such as gapping and sliding. The framework presented here is constructed around verification and validation of constitutive models and numerical tools and emphasizes calibration and benchmarking, all of which are necessary for the analysis, design and risk assessment of nuclear facilities in the United States. 7. Related research and development on NLSSI
3.5. Assembling the NLSSI model After building and verifying the individual components of the NLSSI model they are assembled to construct the numerical model for analysis. The loads are then applied and benchmarking analyses are performed, as described in Section 3.3. 4. Validation of the NLSSI methodology Developing confidence in accurate numerical predictions of the seismic response of nuclear facilities relies heavily on verification and validation (V+V). Verification and validation procedures are the primary means of assessing accuracy in modeling and computational simulations. Verification provides evidence that the mathematical models are solved correctly and involves comparing the numerical results with known closed-form solutions. Validation provides evidence that the correct model is solved and typically involves comparisons with experimental data (Oberkampf and Trucano, 2008). There are three nonlinear behaviors in a nonlinear SSI problem that should be independently validated: soil nonlinearity, structural nonlinearity, and contact interface nonlinearities (sliding and/or separation). Information is available for validating soil, concrete, and contact models (FIB, 2008) but much more is needed, as described below. The data need to be collected in accredited
Spears and Coleman (2014) developed, verified and benchmarked the methodology presented in this paper by comparing NLSSI results to those calculated using SASSI for multiple levels of input ground motion. They considered a representative site in the western United States for this study and are extending the methodology for a site and seismic hazard representative of the central and eastern United States. Other activities under way at INL related to NLSSI analysis include (a) efficient modeling of soilstructure interfaces that do not generate spurious, high frequency noise, (b) verification and validation of site response and SSI codes in the frequency and time domains using the geotechnical laminar box at the University at Buffalo, (c) verification and validation of algorithms for gapping and sliding using the six-degree-of-freedom earthquake simulators at the University at Buffalo, and (d) integration of NLSSI tools into an advanced seismic probabilistic risk assessment framework under development at INL for Department of Energy. Future work will include (a) streamlining NLSSI analysis using commercial FE codes with an NQA-1 pedigree by identifying practical issues with their use and working with code developers to resolve them, (b) automating the model building process, (c) extending the NLSSI methodology to deeply embedded reactors that directly experience shaking around most their perimeter, and (d) accommodating inclined body waves and surface waves.
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Acknowledgments The development of this NLSSI methodology was made possible by funding from the U.S. Department of Energy’s National Nuclear Security Administration and Nuclear Safety Research and Development, and TerraPower, LLC. The authors gratefully acknowledge this financial support but note that the opinions expressed in this paper are those of the authors and not necessarily the Department of Energy or TerraPower. References Anderson, L.M., Elkhoraibi, T., Ostadan, F., 2013. Validation of SASSI2010 solution methods through independent verification using SAP2000 for deeply embedded structures with large footprints. In: 22nd International Conference in Structural Mechanics in Reactor Technology – SMiRT 22, August 2013, San Francisco, California. ANSYS Inc., 2013. Computer Program: ANSYS 13.0. ANSYS Inc., Canonsburg, Pennsylvania. American Society of Civil Engineers (ASCE), 1998. Seismic analysis of safety-related nuclear structures and commentary. In: ASCE 4-98, Reston, Virginia. American Society of Civil Engineers (ASCE), 2005. Seismic design criteria for structures, systems and components for nuclear facilities. In: ASCE 43-05, Reston, Virginia. American Society of Civil Engineers (ASCE), 2015. Seismic analysis of safety-related nuclear structures and commentary. In: ASCE 4-14, Reston, Virginia (forthcoming). American Society of Mechanical Engineers (ASME), 2015. Quality assurance requirements for nuclear facility applications. In: ASME NQA-1, New York, NY. Basu, D., Whittaker, A.S., Constantinou, M.C., 2012a. On estimating rotational components of earthquake ground motion using data from a single recording station. J. Eng. Mech. 138 (9), 1141–1156. Basu, D., Whittaker, A.S., Constantinou, M.C., 2012b. Extracting rotational components of earthquake ground motion using data recorded at multiple stations. Earthq. Eng. Struct. Dyn. 42 (3), 451–468. Bielak, J., Loukakis, K., Hisada, Y., Yoshimura, C., 2003. Domain reduction method for three-dimensional earthquake modeling in localized regions. Part-I: Theory. Bull. Seismol. Soc. Am. 93 (2), 817–824. Bolisetti, C., Whittaker, A.S., Mason, H.B., Almufti, I., Willford, M., 2014. Equivalent linear and nonlinear site response analysis for design and risk assessment of safety-related nuclear structures. Nucl. Eng. Des. 275, 107–121, http://dx.doi. org/10.1016/j.nucengdes.2014.04.033. Bolisetti, C., Whittaker, A.S., 2015. Site Response, Soil-structure Interaction and Structure-soil-structure Interaction for Performance Assessment of Buildings and Nuclear Structures. Multidisciplinary Center for Earthquake Engineering Research (MCEER), University at Buffalo, The State University of New York, Buffalo, NY. Computers and Structures Inc., 2011. Computer Program: SAP2000 – Structural Analysis Program, Version 11.0.0. Computers and Structures, Inc., Berkeley, California.
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