Performance and practice for earthquake resistance ~ _ _ ~ ~ BY IAVEED A. MUNSHl AND WILLIAM C.SHERMAN istorically, reinforced concrete tanks have performed very well against earthquakes. Recent ' reports on the Northridge earthquake of 1994 and the Kobe earthquake of 1995 have given minimal, if any, evidence of damage to these structures. There are various reasons why it is common that many tanks behave elastically during an earthquake, thus are not damaged. The questions then arise: Can there be a simple approach to designing these structures against earthquakes? When do we need to use more elaborate procedures? This article addresses these issues and provides an example of how to apply t h e current design code, ACI 350-01. There are several reasons why these structures escape damage: Concrete tanks are inherently rigid and are often f partially or fully buried in the ground. Because o this, they d o not deform much with respect to the ground. Research' has shown that for buried structures subjected to ground excitation up to 0.3 x acceleration due to gravity 5. nonseismic load combinations control the design. The in-plane shear resistance of the walls is generally adequate to resist seismic loads, with both the concrete and the reinforcement contributing to the structure's strength. Out-of-plane wall deformations are minimal f due to the rigidity o the concrete walls and the structure's boundary conditions: m Concrete tanks have typically been designed using provisions similar to those included in "Code Requirements for Environmental Engineering Concrete Structures (ACI 35Mll) and Commentary (35OR-01):' Those provisions require that concrete tanks minimally crack under static service load f conditions.' Section 21.2.1.6 o ACI 35041 clearly indicates that liquid-tightness should not be f compromised as a result o inelastic action. To achieve this, the load factor used with lateral fluid pressures is increased from 1.4 to 1.7 and an additional environmental durability factor S H' ranging from 1.3 for flexure and shear to 1.65 for direct tension is imposed on static load conditions to reduce the service level stresses and minimize crack widths and leakage. This results in the nonseismic load combinations governing over seismic load combinations in many cases: and I Concrete tanks are designed using low response I modification factors Rr to ensure that the structure is not significantly damaged during an earthquake. The response modification factor reduces the elastic response spectrum to account for the structure's ductility, energydissipating properties, values ranging from and redundancy. Typically, RE, 2 to 3 are used, which are much smaller than those for building structures. PMcncE mind The seismic design of tanks varies from that of f buildings in part due to the sloshing effect o the contained fluid. Furthermore, cracking, which may be permitted in the design of buildings, is avoided in liquid-containing structures to prevent leakage. Methods of seismic analysis of tanks, currently f adopted by a number o industry standards, have evolved from earlier analytical work by Housner;L5 Haroun and Housner," Haroun,i,8Veletsos.Y Vestos and f Shivakuinar."' and others. O these, the best known Is Housner's pioneering work published i n the early 1960s in the Atomic Energy Commission's (now the U.S. Nuclear Regulatory Commission) Technical information Document (TID) 7024." It is interesting to note that while the dynamic modeling of the tank contents (impulsive and convective components) has remained pretty much as developed by Jacobsen and Housner, the modeling of the tank structure has undergone certain modifications and refinements. For example, where Jacobsen and Housner's early models (for example, in TlD7024) were f based on the impulsive component o the liquid being Undiclurbsd water surface -1 , I 1Oscillatin sr, u% water CPO!LJ (a) FLUiD MOTION INTANK (b) DYNAMIC MODEL FOR RIGID WALLTANK on ground. taken horn ACI 350.3'' Fig. I: Dynamic model o liquid-containingtank rigidly supported f lmpuiiive W w e Motion rilh Hlgb Fiqwnry rigidly attached to a rigid tank structure, later studies (including work by Housner) introduced the concept of wall and foundation flexibility. According to this concept, the impulsive component is' still modeled as rigidly attached to the tank shell, but the shell itself is now flexible. This has a significant effect on the response o the overall system to ground motions. f Fig. 2: Frequency idealization OF impulsive and convective motion orthe liquid in a tank subject to earthquake forces indicated previously that use strength-level earthquake forces. The concepts o ACI 350-01 and ACI 350.Mi f have been extended for use with the IBC 2000, UBC 1997, BOCA 1996, and SBC 1997 for the design of liquidcontaining structures. Despite these developments, several issues related to the analysis, design, and detailing o liquid-containing structures remain f unclear and need to be explored in the interest of providing a simple design procedure. RBCPimdevelouments The design o tanks, like building structures, has to f conform to the applicable building codes such as the IBC 2000," UBC 1997," UBC 1994," BOCA 1996.'3and SBC 1997.'* Note that although these codes d o not contain provisions for detailed seismic analysis and design of liquid-containing structures, they allow the use o consensus industry standards. The seismic f design provisions developed by ACl Committee 350, Environmental Engineering Concrete Structures, meets the requirement of being a nationally recognized consensus standard applicable to liquid-containing structures. The committee recently published t h e provisions "Seismic Design of Liquid-Containing Concrete Structures (ACI 350.3-01) and Commentary (ACI 350.3R-01)" that give detailed procedures for determining the loading for the seismic analysis and design of liquid-containing structures.'" Furthermore, Chapter 21 provisions of ACI 350-01 focus on the resistance of liquid-containing structures to seismic loads (much the same way Chapter 21 of ACI 318 does for building structures). f Note that ACI 350-01 includes modified portions o ACI 318-95,1tiwhile ACI 350.341 is compatible with UBC 1994 service-level (allowable stress) earthquake f design methodology. Thus, provisions o ACI 350.3-01 are not presently compatible with iBC 2000, UBC 1997, BOCA 1996, and SBC 1997, all of which use the strength-level earthquake force. Therefore, ACi 350.3-01 in its current form cannot be used directly with the seismic provisions in these building codes. A publication" was recently developed to bridge the gap between ACl 350.3-01 and the model codes AlwrslgAMDDESI61 ounanircmodeling ACI 350.3-01 uses the previously indicated references, particularly the Housner method.:'.5 This method essentially assumes that hydrodynamic effects due to seismic loading can be approximated as the sum of the following two parts: 1. The impulsive part, which represents t h e portion of the liquid that moves in unison with t h e structure in its fundamental mode of vibration: and 2. The convective part, which represents the effect of the sloshing action o the liquid in its fundamental f mode of vibration. Figure I shows the typical schematic of a rectangular tank with inside length L (parallel to the direction of the earthquake force [use the inside diameter D for circular tanks]), inside width B (perpendicular to t h e direction of the earthquake force). and height of liquid H. The equivalent mass of the impulsive component , o the stored liquid f is assumed to be rigidly attached to the structure at height h,, while the equivalent mass of the convective component of the stored liquid W, is attached to the structure by springs of finite stiffness and damping at height h