Science and Technology of Nuclear Installations

Volume 2015 (2015), Article ID 840507, 8 pages

http://dx.doi.org/10.1155/2015/840507

## AP1000 Shield Building Dynamic Response for Different Water Levels of PCCWST Subjected to Seismic Loading considering FSI

Beijing Key Laboratory of Passive Nuclear Safety Technology, North China Electric Power University, Beijing 102206, China

Received 8 October 2014; Accepted 12 January 2015

Academic Editor: Alejandro Clausse

Copyright © 2015 Daogang Lu et al. 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

Huge water storage tank on the top of many buildings may affect the safety of the structure caused by fluid-structure interaction (FSI) under the earthquake. AP1000 passive containment cooling system water storage tank (PCCWST) placed at the top of shield building is a key component to ensure the safety of nuclear facilities. Under seismic loading, water will impact the wall of PCCWST, which may pose a threat to the integrity of the shield building. In the present study, an FE model of AP1000 shield building is built for the modal and transient seismic analysis considering the FSI. Six different water levels in PCCWST were discussed by comparing the modal frequency, seismic acceleration response, and von Mises stress distribution. The results show the maximum von Mises stress emerges at the joint of shield building roof and water around the air inlet. However, the maximum von Mises stress is below the yield strength of reinforced concrete. The results may provide a reference for design of the AP1000 and CAP1400 in the future.

#### 1. Introduction

The passive containment cooling system water storage tank is key equipment which should remain operational after earthquakes to ensure the passive safety of the AP1000. As the quality of PCCWST is approximately 3000 ton. The presence of water in water tank might have an important influence on the dynamic behavior of the shield building and can affect the safety of the shield building under seismic loading from an earthquake with long-period component [1].

As for conventional assessment of nuclear equipment, the response spectrum focuses on the short-period seismic component because there is little equipment with fundamental period above 5 s [2]. However, for PCCWST, the sloshing frequency is beyond that value. Therefore, it is necessary to investigate the dynamic behavior of the elevated water tank under long-period earthquake considering FSI phenomenon especially the water sloshing.

Fluid-structure interaction of elevated tank has been studied numerically and experimentally by many researchers. Livaoğlu and Doğangün [3] presented a review of simplified seismic design procedures for elevated tanks and the applicability of general-purpose structural analyses programs to fluid-structure-soil interaction problems for these kinds of tanks. It turned out that the distributed added mass with the sloshing mass is more appropriate than the lumped mass assumptions for finite element modelling. Moslemi et al. [4] adopted the finite element (FE) technique to investigate the seismic response of liquid filled tanks considering the effect of tank wall flexibility and sloshing of the water free surface. El Damatty conducted a small scaled liquid filled conical tank model to study the elevated water tank. He found a very good agreement between the experiment and analytical model for the fundamental sloshing frequency. Masoudi et al. [5] discuss the failure mechanism of elevated concrete tanks with shaft and frame staging (supporting system) along with seismic behavior of these construction types.

The AP1000 shield building has also been studied by researchers recently. Lee et al. [6] and [1] investigated the influence of elevation and shapes of air inlets on AP1000 shield building by FEM. The simulation result indicated that an optimal parametric design for air intake must be implemented around the middle of the shield building, with 16 circular or oval shaped air intake.

The PCCWST is the water source of cooling water which guarantees the 72 hours safety without operator actions. However, with the water draining to cool down the inner steel containment, the change of huge water volume may influence the dynamic behavior of shield building under seismic loading. In current study, a finite element model of AP1000 shield building was established and the different water levels were discussed for both modal and transient analysis. The FEM results may also provide a reference for design of the AP1000 and CAP1400 in the future.

#### 2. Theory of Fluid-Structure Interaction

For a structural system, the governing equation derived from finite element formulation can be obtained as follows: where , , and are mass, damping, and stiffness matrix for structure and is the displacement vector. is the total force applied by other systems. However, for fluid-structure interaction problem, the FSI can be expressed by coupling the governing equation of the structure and fluid at the interface. The interface force caused by the fluid pressure at the interface is transferred to the structure. So the of equation can be extended to where is the integration of fluid pressure on the fluid-structure interface and is the external force excluding . The fluid pressure field can be derived from the following equation assuming the fluid as incompressible and inviscid: where is the fluid sound speed and is the time. The detailed formula deduction can refer to the work by Choi et al. [7]. The final matrix equation involves nonsymmetric and stiffness matrix. The eigenvalues of the coupled problem can be obtained with unsymmetrical algorithm for modal analysis by ANSYS.

For FEM transient analysis, the Newmark algorithm is an effective way of solving the structural response. In Newmark’s algorithm, Rayleigh damping is adopted for defining the damping denoted as where and are the mass and stiffness proportional Rayleigh damping coefficient, respectively. The , , and are damping ratio, the first and second undamped natural frequency of the structure. According to the AP1000 DCD [8], the damping ratio 7% is adopted. In materials science and engineering the von Mises yield criterion is used to predict yielding of materials. A material is said to start yielding when its von Mises stress reaches a critical value known as the yield strength. In this paper, the yield strength of reinforced concrete 27.6 MPa is used according to the AP1000 DCD.

#### 3. Structural Assessment of AP1000 PCCWST by FEM Model

##### 3.1. AP1000 PCS

The main part of the structure for shield building includes shield building wall with 16 rectangular cooling air intakes, the shield building roof, PCCWST, and water shown as Figure 1. The uniform reinforced concrete model is adopted to simulate shield building. The material properties and geometric conditions are shown in Tables 1 and 2. In this paper, six different water levels (Table 3) corresponding to the 100%, 80%, 60%, 40%, 20%, and 0% of operational water volume are analyzed to figure out the structure assessment of water level decreasing owing to the water draining in accident scenario. Both modal analysis and transient analysis are carried out for six different water levels.