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caisson footings

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I have two general questions regarding 94 UBC caisson footing equations:
     1) I was able to derive the constrained formula for required depth of
        a caisson footing using simple statics, however was not able to exactly
        derive the non-constrained formula.  I have researched several
        texts and have found no method of modeling a laterally loaded
        that yield any similar results.  Does anyone know the general
        used to derive this formula?  I'm sure it has something to do active
        passive pressure or bearing stress reversal, but all the attempts I
        made yield a similar formula with two constants off (one by 50%!)
     2) The code allows for a developed frictional force between the walls of
        a cast in place caisson footing and the soil equal to 1/6 the allowable
        bearing stress (per table).  By using this value I find that the
frictional resistance
        is several times that derived using standard skin friction
equations.  Why is this?
        The maximum the code allows is 250 psf of frictional resistance which
        is way more than you can achieve in any standard soil.  Is this value
        perhaps only allowed for resistance in the downward direction, or can
        it be used to resist uplift as well?
Any help would be greatly appreciated.  So far I am getting widely varied 
opinion on this, and it seems different building departments are interpreting 
these provisions differently.  I have even called ICBO directly and received an
unsure at best response.