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Re: FOS for overturning

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Let's first define overturning about what point, and what are the
conditions....

Ideally, we check for overturning about the lower right hand corner (Case 1
only first), call it point "O", assuming that the soil is rigid and non
yielding. If we apply enough lateral load to tilt it sideways, the footing
will rotate about point "O". We assume that this rotaton point is pinned and
restrained from moving laterally both sides and vertically downward only. 

>From basic statics, for equilibrium, summation of overtuning moment about a
point equals zero.. The lateral external force will cause a clockwise
overturning moment about point "O". The ftg dead wt will cause a
counterclockwise resisting moment about point "O"(forget about the 2/3 dl
factor for now). The external uplift force is more com0plicated to analyze. If
the resultant sum of the vertical forces(dl + uplift) is downward,  we include
the uplift force in our calculation for clockwise overturning about point "O".
This is because point "O" is restrained from moving downwards(see assumption
above). Do not consider for now the lateral soil bearing pressure resisting
the oveturning.

If the uplift force is greater than the dead wt. of the ftg, then the system
is unstable since we assume that point "O" is not restrained vertically
upwards.(which is close to reality). The footing will continue to move move
upward  until the downward force becomes greater than or equal to the upward
force. As the ftg lift up above the soil, there is no lateral restraint
anymore so the ftg slides sideways.

So, the contribution of the uplift force(it does not matter where it is
applied) on overturning about point "O"(considering  point "O"'s vertical and
lateral restraint conditions) depends on it's magitude compared to the
downward force. 

However, if point "O" is restrained from moving vertically upward also(by some
kind of connection at the edge of the footing to the rigid foundation) then,
the uplift force will always be considered in overturning, no matter
what(until the upward ftg restraint is exceeded).

This is just the theoretical analysis. In practice, we need to use our
judgement in defining the actual point of overturning(for a soft soil, the
footing may not actually rotate about point "O"), the actual vertical and
lateral restraint at the overturning point and the contributions of other
materials on the stability of the system(lateral soil bearing capacity, soil
friction at the sides of the ftg, dl of slab above soil, etc).

Just my theoretical opinion.

Ernie Natividad