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Re: Differential Settlement

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While I haven't read the geotech report, the 1.7 inches probably does not
take mat stiffness into account.  I.E., if you had two isolated spread
footings with 1500 psf load there is a potential of up to 1.7 inches.  But
to be safe, you need to carefully read the report and call the geotech.
Some times the reports are prepared by a new EIT, and the wording might not
be exactly correct.  I've saved lots of time and construction money in the
past by simply calling and asking for a clarification.

In my opinion, using M=(6EI x defl)/L^2 is probably too conservative.
Moments and forces are (usually) caused by live and dead loads -- not
settlements.  Picture three columns in a line connected by a fairly rigid
mat.  Assume the two end columns are rigidly supported and the soil under
the center column settles 1.7".  The moment in the mat is caused by the
building loads and mat weight forcing the mat down.  If the loads aren't
heavy enough, the mat will simply bridge over the low spot in the soil, and
the moment in the mat will be less than indicated by the formula above.

I've handled this problem in the past by finding the maximum and minimum
subgrade moduli.  Get these from the geotech or by approximating from the
values you have.  With clay soils, I take the maximum bearing pressure
divided the maximum and minimum deflections to get spring stiffnesses.  I've
never done this with dry sand, so the solution may be different.

Model the mat with springs representing the soil.  Run different models with
the weak soil under different groups of columns.  Large groups of columns on
the weak soil will generate higher moments at the transition between the
weaker and stronger soil.  Make sure to check out edge, corner, and
"special" conditions.

Jason Kilgore
Leigh & O'Kane, L.L.C.
(816) 444-3144

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