There isn't anything terribly new on this subject. The methodology in AWWA
and API tank design standards is basically that developed by George Housner
back in the 1950's and published in papers by him and subsequently as part
of "TID-7024 Nuclear Reactors and Earthquakes," which I think you can get
from NTIS. I have an old copy of this that was donated to me by another
engineer, and there were some corrections to some of Housner's formulas
which may not be in the published version. A couple of Housner's original
papers on this subject are included in a collection of his works published
Housner's methodology assumes the tank is rigid, and subsequent papers have
suggested that it may be unconservative for taller steel reservoirs where
there is some interaction and amplification of force due to the flexibility
of the structure. There are also some papers out there that have a little
bit to say about soil-structure interaction.
If you can get to a decent engineering library, there are a number of good
papers in the literature, generally ASCE journals, on the subject of seismic
effects in tanks. Names I have stumbled across include Haroun, Veletsos,
Young, Clough, and Wozniak. Haroun was a student of Housner's and still does
a little research in this area. You should also look at the AWWA standards
for prestressed concrete tanks, D-110 and D-115, which address a few issues
not mentioned in D-100, like adjustments for base isolation.
The fundamental physics for tank seismic effects is expressed in the
Navier-Stokes equations of fluid dynamics, higher order partial differential
equations which are essentially impossible to solve. There are only a couple
of published solutions for very simple vessel shapes and harmonic motion.
Housner made some simplifying assumptions about the physics and used some
alternate energy methods to come up with solutions for ground level circular
and rectangular tanks under simple harmonic motion with certain damping
assumptions. The resulting "simple" equations are still full of hyperbolic
functions. Resulting pressures and forces are supposed to be accurate in a
range of about 5 percent or so, and model tests have supported this.
Considering the vagaries of real earthquakes, however, I even wonder about
AWWA standards have used Housner's approach to develop simpler formulas for
base shear and overturning moment, but don't include formulas for wall
pressures, so you still have to resort to TID-7024 to figure out the
variation of wall pressure with water elevation. Sloshing wave formulas are
all based on first mode effects, and it is important that you provide
adequate freeboard to keep the wave from contacting the roof (something I
have a hard time convincing my clients of--all they see is wasted storage
I have recently been involved in a project where we used computational fluid
dynamics modeling, sort of a liquid version of finite elements, to see how
the liquid behaved when subjected to forcing functions of various
frequencies. Typically, the freeboard concern has usually been directed
toward preventing uplift and failure of the roof to wall connection. The
thing we discovered from the CFD analysis was that a water pressure spike is
also transmitted to the walls and bottom of the tank if the wave can contact
the roof. Also, in certain cases, you can get higher mode waves.
The other thing CFD impressed on me is that a long period earthquake is not
your friend when it comes to large tanks. Unlike the natural period of the
tank structure, which is very low, the natural period of the fluid can be
fairly high. As you approach the natural frequency of the fluid, the
sloshing wave and seismic loads can get out of hand in a hurry.
From: Frank Griffin [mailto:fsg(--nospam--at)freese.com]
Sent: Tuesday, January 30, 2001 5:59 PM
Subject: "Sloshing Effects"
Can someone guide me to any reference materials pertaining to seismic
effects of liquids in storage tanks? UBC '97 makes mention of, "inertial
effects of the contained fluid." IBC 2000 (which is the code in effect for
my project) makes mention of, "sloshing period of the stored liquid," and
states that, "The tank shall be designed to resist the effects of sloshing."
Furthermore, AWWA D100-96 states, "The design of ground-supported
flat-bottom tanks recognizes the reduction in seismic load due to the
sloshing of the contained liquid. This design procedure is referred to as
the effective mass method." There are some references in the Appendix, but
nothing more recent than 1984.
Thanks in advance for any help you can provide.
Ft. Worth, Texas