SEISMIC STRUCTURE-SOIL-STRUCTURE INTERACTION IN NUCLEAR POWER PLANT STRUCTURES

Soil-structure interaction is integral to the seismic analysis and design of safety-related nuclear structures, but interaction between multiple structures supported on the same soil domain is generally ignored. It is unknown whether structure-soil-structure interaction (SSSI) can lead to significant changes in the response of nuclear structures. The study described in this paper examines the influence of SSSI on the response of a pair of Nuclear Power Plant (NPP) structures by comparing their response with and without a neighboring structure. Both in-plane SSSI (structures aligned parallel to the direction of ground motion) and anti-plane SSSI (structures aligned perpendicular to the direction of ground motion) are considered. The analyses are performed using the industrystandard frequency-domain code, SASSI. Lumped mass models of the Advanced Candu Reactor (ACR) are used for the analyses. Frequency-domain transfer functions are calculated at various locations in the reactors for different separation distance and relative mass of the reactors. Seismic responses are compared to the benchmark case where only one reactor is analyzed. Three pairs of NPP structures are considered: 1) two standard reactors (ACR’s), 2) two heavy reactors with four times the mass of the standard reactor, and 3) a heavy ACR placed next to the standard reactor. Each pair is analyzed considering in-plane and anti-plane arrangements for three values of separation distance. Seismic analysis is performed for one of the cases and the acceleration responses of the reactors are presented for the El Centro ground motion input at the free field. On-going studies are extending the scope of the analysis to other ground motion records and site soil profiles to enable the authors to generalize results and develop recommendations for analysis and design of nuclear structures. INTRODUCTION The phenomenon of soil-structure interaction has been studied extensively, especially for nuclear power plants (NPP’s). Analytical and numerical studies have been performed on individual NPPs installed over soil columns. However interaction between adjacent structures through their common soil domain, termed structure-soilstructure interaction (SSSI) here, has received much less attention. Most safety-related nuclear structures are designed with considerations of soil-structure-interaction (SSI) and SSSI is not considered. It is unknown whether the practice of ignoring SSI is conservative or nonconservative in terms of seismic demands on structures, systems and components. A seminal study by Luco and Contesse [1] on SSSI examined anti-plane interaction between two infinitely long shear walls subjected to vertically incident SH waves of harmonic time-dependence. Wong and Trifunac [2] extended this study to an array of several structures with varying size and stiffness subjected to a shear wave incident at an arbitrary angle. Both of these analytical studies considered the significance of parameters such as separation distance, foundation size, and stiffness of the structures on SSSI. Luco and Contesse [1] identified the factors that determine the degree of interaction between structures as a) relative foundation sizes, b) the distance between the structures, c) the mass of the superstructure relative to the mass of the soil excavated for the foundation, d) mass of the foundation relative to the mass of excavated soil, and e) relative stiffness of the structures and the soil. Parametric analyses were performed and it was concluded that SSSI effects are especially important for smaller and lighter structures situated close to heavier structures. A similar conclusion was drawn by Wong and Trifunac [2]. Both studies noted that the degree of interaction depends mainly on the type of wave interference (constructive or destructive) occurring between the scattered waves from the foundations, which is a function of the spacing and arrangement of the foundations. The primary objective of the study described in this paper is to examine the effects of 1) separation distance, 2) relative mass of reactors, and 3) the frequency of excitation, on the magnitude of SSSI between a pair of nuclear reactors. Numerical parametric analyses are performed to examine and understand the nature of this interaction. Two reactor masses are considered: standard and heavy. Three analysis cases are considered, each with a different pair of nuclear reactors: 1) two standard reactors, 2) two heavy reactors, and 3) a heavy reactor constructed Transactions, SMiRT 21, 6-11 November, 2011, New Delhi, India Div-V: Paper ID# 228 2 near a standard reactor. Each of these cases is analyzed for both in-plane and anti-plane interaction (Figure 1), and multiple values of separation distance are considered. Frequency-dependent transfer functions are sought at important locations in the reactors and are compared with corresponding transfer functions calculated for the same reactors constructed alone. The seismic response for the 1940 El Centro ground motion is calculated for one of these cases and compared to the case where there is only one reactor. Results for more parametric analyses and responses for other ground motions will be reported in Bolisetti [3]. NUMERICAL MODELING The equivalent-linear frequency-domain program, SASSI [4] is used for the numerical SSI analyses. In this program, the soil medium is represented by a semi-infinite halfspace composed of horizontal layers, and the structure is modeled using finite elements. The ground motion is specified at one of the layer interfaces as a combination of S-, Pand surface wave fields. In this study a vertically propagating SV-wave field is specified, which induces displacements in the X direction (Figure 1). The interaction forces on the foundation are calculated using the substructuring method [5] and the forces in the structure are then calculated using finite element analysis. The substructure subtraction method [5], which is a type of substructuring, is used for the analyses described here. a. In-plane SSSI arrangement b. Anti-plane SSSI arrangement Figure 1: In-plane and anti-plane SSSI models of the reactor pairs separated at 45m on center (shaking in X direction) A lumped-mass stick model of the ACR-700 (Advanced Candu Reactor) reactor building [6] is adopted in this study (Figure 1). The model, which was initially developed by Huang et al. [7], for studies of seismic isolation of nuclear structures, enables calculation of macro-level deformation and force demands on structure floor acceleration response spectra at important locations in the reactor building. This dynamic model accounts for the mass and stiffness characteristics of the structure, and major equipment in the building, and has the same key dynamic properties as the complete three-dimensional building. Huang et al. [7] provide details on the development of the simplified numerical model. The superstructure consists of three sticks, two for the internal structure and one for the containment. These sticks are joined at the concrete mat foundation. The actual containment vessel is a steel-lined, 1.2m thick, 59.5m tall, vertical cylinder and a 1.0m thick hemispherical dome. The horizontal cross-section of the containment wall is an annulus with an inner diameter of 39.5m and an outer diameter of 41.9m. Three-dimensional beam elements are used to model the containment stick using equivalent section properties for the beams, and masses are lumped at 12 nodes along the height. The internal structure of the reactor building consists of reinforced concrete shear walls and floor slabs that support the equipment and systems of the power plant. Its numerical model is approximately Transactions, SMiRT 21, 6-11 November, 2011, New Delhi, India Div-V: Paper ID# 228 3 symmetric about two vertical planes, and consists of masses lumped at 16 nodes. The reactor building is supported on a circular reinforced concrete foundation with a thickness of 2.5m, and a radius (r) of 20.95m. For the SASSI analyses described here, the foundation is shallowly embedded, and its thickness is reduced to 2m to make the foundation lighter and magnify interaction effects. Analysis case 1 uses the standard reactor building described above. The heavy version of the same reactor building used in analysis cases 2 and 3 is created by increasing the mass of the foundation and superstructure of the standard reactor building by a factor of four, and keeping the geometry of the structure unchanged. The heavy model is herein referred to as the modified reactor building. A 31m deep linear elastic soil domain with an S-wave velocity of 600 m/s and P-wave velocity of 1200 m/s is considered for the analysis. The soil profile is modeled in SASSI using 14 horizontal layers overlying bedrock, with control ground motion specified on the topmost layer in the free field. Preliminary linear elastic ground response analysis in SASSI indicated that the soil column has a natural frequency of 5 Hz. Separate analysis of the two reactor buildings embedded in the soil column described above was performed using SASSI. The computed natural frequencies are summarized in Table 1. For reference, the natural frequencies of the containment vessel and internal structure of the standard reactor installed on a fixed (rigid) base are 4.5 Hz and 6.7 Hz, respectively. A damping ratio of 0.05 is used for the superstructure and soil in all subsequent analyses. Table 1: Translational and rocking frequencies (Hz) of the reactor buildings considered in this study Standard reactor building Modified reactor building Containment Internal Structure Containment Internal Structure f fix 1 (translational mode) 4.5 6.7 2.2 3.4 f fix 2 (translational mode) 14.2 14.8 7.1 7.3 fSSI 1 (rocking mode) 2.6 2.6 1.2 1.2 NUMERICAL ANALYSIS Frequency dependent transfer functions with respect to the input ground motion at the free field are calculated at two locations in the reactor building