Shock and Vibration

Volume 2016 (2016), Article ID 6127895, 15 pages

http://dx.doi.org/10.1155/2016/6127895

## Seismic Soil-Structure Interaction Analysis of Isolated Nuclear Power Plants in Frequency Domain

College of Civil Engineering, Tongji University, Shanghai 200092, China

Received 25 July 2016; Revised 15 October 2016; Accepted 26 October 2016

Academic Editor: Georges Kouroussis

Copyright © 2016 Zhiguang Zhou and Xiaodong Wei. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

One important aspect of applying seismic isolation to Nuclear Power Plants (NPPs) is that the complex interactions of flexible soil, flexible isolators, and stiff structures require careful investigation. In this paper, a NPP model was used to investigate the effects of SSI and the effects of changing soil and isolator properties on seismic response of an isolated NPP. The following aspects are considered in the study: horizontal excitation and vertical excitation; linear and equivalent-linear models of the isolators; scaling of the shear modulus of the soil profile model; and scaling of the horizontal equivalent stiffness of the isolators. It was found that Pseudospectral Acceleration (PSA) in the nuclear structure at the frequencies near the natural frequency of the structure increase with elevation, and the difference between the in-structure response spectral acceleration with and without SSI effects is concentrated at the frequencies near the natural frequencies of the superstructure. It is also found that the linear SSI analysis underestimates the in-structure response of the nuclear structures compared to the equivalent-linear SSI analyses, and the soil profile properties directly affect the effectiveness of the isolation system.

#### 1. Introduction

Seismic isolation has been used effectively in a number of critical applications to protect important civil infrastructure [1] and seismically isolated structures have performed as expected in major earthquakes in Japan, the US, and elsewhere [2, 3]. As a result, there is active interest in using seismic isolation in developing new seismically resilient NPPs and related facilities [4–9].

Seismic design of isolated buildings is often performed assuming a rigid base and, consequently, the effect of SSI is ignored. This is considered reasonable by some investigators who show that although SSI has some influence on response of the structures this influence is much smaller on an isolated structure than on a nonisolated structure [10, 11]. Other studies argue that seismic design based on the rigid base assumption is not always safe. For example, Song and Ding [12] carried out a finite element study of an isolated 9-story shear wall building. They assumed the soil was elastic but discovered that while the SSI had only modest effect on the story drifts, the isolator displacement could be somewhat bigger or smaller than predicted for a rigid base isolated building depending on the characteristics of input motion. Spyrakos et al. [13] considered a class model based on a two degree of freedom lumped mass system (representing the isolated structure) supported on a two degree of freedom system representing an elastic and deformable half-space. A parametric study was undertaken and it was concluded that the effective period and effective damping of the isolated system will shift especially for softer soils and stiff/squat structural systems that have low mass compared to a representative volume of soil interacting with the structure. The seismically isolated Christchurch Women’s Hospital was shaken by a series of earthquakes in 2010 and 2011. It was noted that the displacement of the isolation system was only 2–5 cm, which is smaller than expected for this building [14]. The investigators suggest that incorporating SSI effects can help explain this phenomenon. Mahmoud et al. [15] compared responses of isolated buildings with and without SSI under different ground motions and concluded that SSI may considerably influence the stiff superstructure response and may only slightly influence the response of more flexible structures. Overall, these analyses suggest that this topic is in its infancy and that additional research and development is needed.

SSI has long been a concern in the design of NPPs subjected to earthquakes [2, 16]. Politopoulos et al. [17] and Zhou et al. [16] demonstrated that SSI may amplify the nonisolated modes’ response and thus it must not be overlooked. Sayed et al. [18] demonstrated that a base isolated NPP model considering pile foundation showed higher responses than the corresponding rigidly fixed base isolated NPP model under short-period inputs, while they are less under the long-period ground motions. A special concern has been raised about the effect of SSI on the effectiveness of an isolation system. This concern arises due to the tendency of SSI to significantly lower the predominant frequencies of the excitations felt by the heavy NPP structure (and thereby reducing the effectiveness of isolation), but also because the significantly lower frequency of an isolated NPP might invalidate some previous observations regarding the effect of SSI on NPPs. Most current isolation systems are not effective in the vertical direction, so response of the plant in the vertical direction will heavily depend on SSI effects. Moreover, some isolation systems (e.g., elastomeric) have frequencies in the vertical direction which are in the frequency range of interest to structural elements and components.

Frequency domain methods have been used extensively in the past for SSI analyses of NPPs [19–22]. In this study, SASSI [23, 24] was used to study the effects of SSI and the effects of changing soil and isolator properties on seismic response of an isolated NPP.

#### 2. Equations of Motion

The basic methods of analysis adopted by the computer program SASSI2000 are called the flexible volume and the subtraction methods. These methods are formulated in the frequency domain using the complex response method and the finite element technique [23, 24]. In the flexible volume method used in this study, the total soil-structure system shown in Figure 1(a) is partitioned into two substructure systems as shown in Figures 1(b) and 1(c). The flexible volume method assumes that the structure consists of the superstructure plus the foundation minus the excavated soil. The equations of motion for the total system shown in Figure 1(a) can be written in the following matrix form:Subscripts , , and are used to refer to degrees of freedom associated with the nodes on the superstructure, basement, and excavated soil, respectively. is the complex Fourier coefficients of the modal displacement solution. is a frequency-dependent matrix representing the dynamic stiffness of the foundation at the interaction nodes and is called the impedance matrix. Moreover, and are the net forces at the superstructure and foundation nodes, respectively, with and denoting the amplitudes of the external forces at those nodes. is a complex frequency-dependent dynamic stiffness matrix:where and are the total mass and stiffness matrices, respectively.