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# Re: Factor of Safety against Uplift

• To: <seaint(--nospam--at)seaint.org>
• Subject: Re: Factor of Safety against Uplift
• From: "John MacLean" <john_maclean(--nospam--at)pomeroy.ca>
• Date: Tue, 13 Nov 2001 13:27:34 -0800

```Paul Martin wrote:

<I am sure you realize that allowable stress design had been used for many
years, so your question about how can one possibly design reinforcing in the
toe of a retaining wall footing can be answered by looking in a text book.>

Well you could figure out the soil pressure distribution under the specified
(allowable stress) loads and may be you wind up with a trapezoidal pressure
distribution under the footing with the highest pressure under the toe and
the lowest pressure under the heel. Then when you want to design your
concrete section using the ACI code you could apply a 1.7 load factor to the
trapezoidal soil pressure and then use that factored pressure to design the
toe for moment and shear. Unless you're designing concrete by the allowable
stress method.

The problem with this is that just factoring the soil pressure is overly
simplistic. If your retaining wall is to be in equilibrium under the applied
factored loads, you would have to factor the lateral soil pressure and the
structure dead load by the same 1.7 factor. This might make sense for the
lateral soil pressure but it would be very unconservative to assume that the
with stability.

In the LRFD method the trapezoidal soil pressure will likely be more of a
triangle concentrated out at the toe. Virtually the whole dead weight of the
structure will be resisted by soil pressure on the toe and maybe even out at
the end of the toe. This will greatly increase the moment and shear in the
toe of the footing. Don't know how you can model this using allowable stress
design.

<When factored loads are used to determine soil pressure, it seems that
there should be a limiting value ... a value higher than that for
serviceability. For this to work, that value is going to have to be more
than 1.5 times greater. I have not seen such a value, but I haven't
requested a limiting value from a geotech engineer either.>

That's a good point. The geotechnicals seem to be way behind on
accommodating LRFD. Typically I just factor up my allowable soil pressure by
the live load factor (1.5 here in Canada) and use that. I get into trouble
with the retaining wall design above because the toe pressures can become
extremely high as you start to get a lot of uplift along the bottom of the
footing. In the extreme case you could have the soil reaction out at the
very tip of the toe of the footing and the soil pressures would
theoretically go to infinity. Naturally this won't happen. You would get
some sort of localized failure as the toe of the footing pressed into the
ground. It seems to me that the factored resistance of the soil out at the
toe should be much higher than it is for a general footing governed by
settlement. I generally let the pressure go up to 3 or 4 times allowable
without much worry. And I often use a rectangular "stress block" similar to
concrete instead of a triangular distribution to reduce the calculated
pressure. But I don't have any real justification for that.

Nels Roselund wrote:

<Our seismic codes may still be conservative on this issue because we don't
compare the structural system's overturning response
period with its flexural response period -- for simplicity we arbitrarily
require static stability based on unfactored service loads.>

Your points on seismic design are interesting. The usual argument for
allowable stress is that it's simple. Which is true and is a valuable point.
The codes these days seem to be getting way too complex. But in this case I
believe it is also unconservative. I haven't found too many other places in
design where LRFD makes a huge difference but it does seem to in this area.
At least in my mind. On the other hand there haven't been too many failures
of retaining walls overturning.

John MacLean

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