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"Caisson Footings"

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The "flagpole formula" (nonconstrained) of 1994 UBC 1806.7.2.1, 1997 UBC
1806.8.2.1 or 1991 UBC 2907(g)2, has its origin in an equation derived for
the Outdoor Advertising Association of America (OAAA) by Purdue CE Prof
Rutledge in 1940 (following his 1939 research with Terzaghi at Harvard),
which used Terzaghi's parabolic distributions of resistance by lateral
bearing (reversal from resistance ahead of the pier to resistance behind
the pier at two-thirds of the depth).  ICBO adopted a similar equation, the
present equation, for inclusion at 1964 UBC 2806(f)1 but the equation uses
rectangular resistance distributions (with reversal also at two-third
embedment depth) and other simplifications for general application to
foundations other than free standing poles.

The modified UBC version, adopted by ICBO after field and laboratory
verification tests at Notre Dame in 1948, gives conservative results
because of the rectangular approximation of parabolic distribution coupled
with the conservative tabular values for allowable lateral bearing; if the
one-third increase in allowable stress for short-term loading is added to
the tabular bearing values, the results (depending on the validity of a
subjective estimation of allowable lateral resistance that may be
permanently attributed to the ground) are still conservative.  

All other factors being equal (knowledgeable determination of ground
characteristics, proper modeling of loads [soil, surcharge, hydrostatic],
verification of proper construction), the main problems with blindly using
the nonconstrained formula that are not addressed in the UBC are (1) the
reduction in available lateral and subjacent support due to a sloped ground
surface or disturbance ahead of the structure may be drastic, (2) the
stresses in an embedded member are usually calculated at the ground surface
where maximum moment is thought to occur but logic and the Rutledge model
show maximum moment occurs at one-third the depth of embedment, and (3)
shape factors have to be used carefully; the diagonal distance (1.4 x
diameter) factor for a rectangular pier has been proven sound but the
one-half inch acceptable movement (2.0 x diameter) factor, often given
routinely in geotechnical reports, should only be used for non-restrained
structures (such as isolated retaining walls, where rotation is not only
acceptable but is necessary to maintain active soil pressures that are much
less than those that approach at-rest or passive).

The UBC equation for nonconstrained embedment has been unsuccessfully
challenged in the past, most notably after the suggested revisions to the
1991 UBC (ICBO Building Standards, Nov-Dec 1992, Items 269 & 270), but the
formula has endured due to a good performance record and because nothing
better has been developed.  

*   Lawrence B. Karp          Siesta Valley Ridge     510 254-1111   *
*   Geotechnical Engineer     Orinda, CA  94563       Fax 254-2825   *