Keywords: seismic risk, storage tanks, dynamic analysis, ground motion, sliding, elephant foot buckling.

The seismic behaviour of steel tanks for oil storage is relevant in the light of industrial risk assessment because collapse of these structures may trigger other catastrophic phenomena, such as fires or explosions due to loss containment. Therefore, seismic assessment should be focussed on leakage-based limit states. Damage suffered by storage tanks under seismic action is generally related to large axial compressive stresses that can induce shell buckling near the base and to large displacements of unanchored structures leading to detachment of piping, liquid. The present paper approaches the analysis of the seismic response of sliding, non-uplifting, unanchored liquid storage tanks subject to three-dimensional ground motion.

Earthquakes represent an external hazard for industrial plants and may trigger accidents, i.e. fire and explosions resulting in injury to people and to near field equipments or constructions, if structural failures result in release of hazardous material. Quantitative Risk Analysis (QRA) [1] provides a guide for the analysis of industrial risk; such an assessment may include the seismic threat if ground motion related malfunctioning (i.e. failure) rates are available for components [2]. From the structural perspective, steel tanks for oil storage are standardized structures both in terms of design and construction [3,4,5]. Review of international standards for the construction points out that design evolved slowly; therefore, a large number of post-earthquake damage observations [6] is available and empirical vulnerability functions have been developed [7]. This is a privileged case with respect to other building-like and non-building-like structures, however empirical fragility typically suffers some shortcomings; for example vulnerability data also contains information about the site effects which may be hard to disaggregate. Therefore, the development of analytical models able to predict the response of the structural components and systems under seismic loading is worth exploring.

The present work is aimed at the discussion of an algorithm able to analyse the three-dimensional response accounting for sliding behaviour of unanchored tanks. It accounts for fluid-structure interaction in a simplified manner, since limitation of the computational effort is a key aspect of seismic reliability evaluations. It takes advantage of several proposals to approximate the seismic dynamics of tanks available in the literature and makes an attempt to extend them in order to include large-displacement limit states. Then, the model and algorithm have been employed for the estimation of seismic demand in terms of base plate-ground relative displacement and shell compressive stress, which represents the engineering demand parameters related to the failure of connection piping and the shell's elephant foot buckling (EFB). The method used is the incremental dynamic analysis which has been originally developed for buildings and recently extended to tanks [8].

The numerical study consisted of: (1) incremental dynamic analysis with one horizontal and the vertical ground acceleration components; (2) analysis with three acceleration components. Each of the two investigations were repeated for a for a range of (filling ratio) and a set of (friction coefficient). For both the analyses the discussed algorithm to solve the equation of motion was implemented in a computer code using the Wilson theta method [9].

The model does not includes the base uplifting, which may affect compressive stress demand, but it may be incorporated in the future. The model has been employed to produce incremental dynamic analysis demand curves for building-like structures. Comparison of the two models has also been carried out, the results show that the uni-directional results may be un-conservative, at least in terms of base-displacement demand for sliding tanks.

1

F.P. Lees, Loss Prevention in the Process Industries, second ed., Butterworth-Heinemann, Oxford, 1996.

2

Fabbrocino G., Iervolino I., Orlando F., Salzano E., "Quantitative Risk Analysis of Oil storage facilities in seismic areas", Journal of Hazardous Materials, (2005), in press. doi:10.1016/j.jhazmat.2005.04.015

3

AWWA D100-96, "Welded Steel Tanks for Water Storage", American Water Works Association, Denver, Colorado, USA, 1996.

4

API 620, "Welded Steel Tanks for Oil Storage", American Petroleum Institute, Washington D.C., USA, 1998.

5

API 650, "Design and Construction of Large, Welded, Low-Pressure Storage Tanks", American Petroleum Institute, Washington D.C., USA, 1998.

6

NIST GCR 97-720, "Reliability and restoration of water supply systems for fire suppression and drinking following earthquakes", National Institute of Standards and Tecnology, Gaithersburg, MD, USA 1997.

7

Salzano E., Iervolino I., Fabbrocino G., "Seismic Risk of Atmospheric Storage Tanks in the Framework of Quantitative Risk Analysis", J. Loss Prevent. Proc., 16, 403-409, 2003. doi:10.1016/S0950-4230(03)00052-4

8

Iervolino I., Fabbrocino G., Manfredi G., "Fragility of Standard Industrial Structures by a Response Surface Based Method", Journal of Earthquake Engineering, 8, 927-946, 2004. doi:10.1142/S1363246904001717

9

Chopra, A.K., Dynamics of Structures, "Theory and applications to earthquake engineering", Prentice Hall.

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