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Evolution of Seismic Analyses of Unanchored Tanks

Researchers did not realize until 1967 that unanchored tanks need more attention than anchored tanks. Rinne [231] reported that the Prince William Sound, Alaska, earthquake of 1964 caused more extensive damage to oil storage tanks, most of which were unanchored, than to other structures. This damage highlighted the need for a careful analysis of such tanks. Shell buckling near the bottom of unanchored tanks was a phenomenon experienced during this earthquake. In a few tanks, buckling was followed by a total collapse of the tank. For most tanks, uplift occurred typically around the periphery of the tank bottom plate, which was lifted as much as two inches off the supporting foundation, causing yielding and plastic deformations in the plate.

The Balboa Water Treatment Plant was under construction when the 1971 San Fernando earthquake struck. Housner, Jennings and Brady [132] estimated that ground shaking at the plant's site was in the range of 0.3-0.5 g peak acceleration, and reported that there were many tanks affected and damaged by the earthquake. A large steel wash-water tank with a diameter of 100 ft and a height of 30 ft was approximately 1/2 to 3/4 full. After the earthquake, the tank showed signs of having rocked on its foundation. Some anchor bolts failed in tension, and others failed in bond and were pulled up off their anchorage. The pullout varied from 2-14 inches. The upper part of the shell buckled inward due to high stresses that existed in the tank when it was tilting on its toe. Another tank suffered damage in the form of an axisymmetric outward bulge of its shell close to ground level almost all the way around the circumference. The bulge covered a height of approximately 20 inches with an amplitude of about 8 inches.

Figure 1.3: Elephant Foot Buckling

Figure 1.4: Diamond Shape Buckling

In 1982, Niwa and Clough [203] investigated the earthquake response behavior and the buckling mechanism of a tall cylindrical wine storage tank similar to those damaged in the 1980 Livermore earthquake. It was reported that most of damaged tanks were unanchored and completely full of wine. The elephant foot buckling, Figure (1.3), was the most common damage in broad tanks while tall tanks suffered a diamond shaped buckling spreading around the circumference, Figure (1.4). A 9.5 ft diameter by 20 ft high tank was tested under simulated earthquake accelerations up to 0.95g, and buckling patterns similar to those that occurred in the earthquake were observed during tests. The critical buckling stress observed during the development of the diamond-shaped buckle pattern was about 60% of the theoretical buckling stress. This value was considerably higher than that adopted in the API 650 and AWWA D100 Standards. Hence, Niwa and Clough concluded that the critical buckling stress assumed in current standards for the steel tank design might lead to rather conservative estimates of the buckling strength of a free base tank subjected to rocking motions. The actual loading conditions during the uplift response were far different from those provided in static buckling tests of small cylinders under uniform axial compression, on which the current design buckling stress has been based. It was also reported that the uplifting behavior of the bottom plate showed that ignoring the membrane stress mechanism considerably underestimated the uplifting stiffness of the bottom plate, and they recommended further studies of uplifting kinematics of free base tanks.

Hanson [79] discussed the behavior of liquid storage tanks during the 1964 Alaska earthquake. He reported that although considerable damage to such tanks has occurred during the earthquake by tsunamis, earth settlement and subsoil liquefaction, a significant portion of damage resulted from direct structural action of the tank and its contents generated by the earthquake ground shaking. He showed that earthquake forces can cause an uplift of the tank edge, and this uplift increases the possibility of the tank damage and subsequent loss of its contents. By using Housner's model, and assuming a 20% g peak ground acceleration and a lightly damped spectral velocity, he concluded that this ground motion was sufficiently intense to cause a typical tank to uplift and to account for the observed damage. For an uplifted tank, he found that true stresses and the precise progress of failure is very hard to analyze, and that any reasonable estimate of the factor of safety against collapse is difficult to make. However, he recommended that liquid storage tanks should be designed and constructed to resist realistic earthquake forces without significant uplift, or provisions should be made to contain the contents of tank after its collapse.

A brief description of the structural and nonstructural damages of unanchored tanks during the 1979 Imperial Valley earthquake was presented by Haroun [99] in 1983. Observed damages were similar to those produced by past major earthquakes. He reported that buckling of the bottom of tank shells due to excessive compressive stresses, damage to fixed roofs due to liquid sloshing and failure of attached pipes due to their inability to allow for the shell movement, had occurred. He also reported that tall tanks have suffered shell damage. In addition, he investigated the validity of current standards and codes by comparing observed damages with predictions obtained by using existing methods of analysis. Based on an approximate analysis of damage, he concluded that current design codes for seismic analysis of unanchored tanks can lead to a conservative design because of the very low allowable buckling stress. Further evaluations and comparisons between design codes and guidelines were performed by Haroun in different publications such as ([82], [85], [91]).

The 1983 Coalinga earthquake subjected many unanchored oil storage cylindrical tanks to an intense ground shaking. Damages occurred to these tanks were studied by Manos and Clough [173]. Observed damages included elephant foot buckling of the tank wall at the base, joint rupture, top shell buckling, bottom plate rupture, damage to floating roofs and pipe connections, and spilling of oil over the top of many tanks. They estimated peak ground accelerations at various tank sites to range from 0.39g to 0.82g. Based on a correlation of observed damages with the response parameters specified by current codes, Manos and Clough concluded that current U.S. practice underestimates sloshing response of unanchored tanks with floating roofs, and does not adequately address the dynamic uplift mechanism and buckling behavior.

All aforementioned studies showed the need for rigorous analysis of unanchored tanks. Improved methods of analysis need to properly account for the effects of large-amplitude of base uplifting, large-amplitude liquid sloshing, liquid-structure interaction, pre- and post-buckling behavior of the shell, material plasticity and soil-structure interaction. Thus, the problem associated with the seismic behavior of unanchored tanks was cited by the National Research Council [194] as the most challenging problem in fluid-structure systems.

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A. Zeiny