Bill,
The simple part of the answer is, yes, apply active pressure to the wall from top of wall to bottom of key. Statics is still statics. After that, it gets more complicated.
It's been a long time since I've used EM 1110, but it does give very long heels. Philosophically, the Corps is designing flood walls, not retaining walls. They're on river banks in crappy soils with full hydrostatic load and full buoyant uplift, based on a river elevation that (thanks to global warming and increased urbanization and resulting faster runoff) may be too low. They often have a sheetpile cutoff wall to preclude piping failure under the wall. (Go ahead and try to think your way through the passive resistance of that sheet pile in your load and resistance tallies. We usually ignore it.) The cost of the wall, which is probably double that of a "civilian" wall retaining earth behind the local big-box, is utterly insignificant in comparison to what it's protecting, which in my own personal experience was half of downtown St. Paul. These people don't screw around; they want to KNOW that their wall is not going to go wrong.
Back to the more academic side. What a lot of engineers don't quite understand is that it takes a lot of movement to fully mobilize the passive resistance value of soil. The number I've read is an order of magnitude greater movement than that which produces the active pressure wedge. In other words, you've got to almost fail the wall in order to really mobilize significant passive pressure. Having processed that idea, I never use passive pressure in my wall designs anymore; I use at-rest pressure. This takes zero movement to mobilize; it's there as soon as they compact the fill in front of your wall. Needless to say, this causes my footings to be longer, which hurts my feelings less and less as time passes. I take what I can get from at-rest pressure resistance, and make up the rest with friction (and adhesion in clays) along the bottom of the footing.
Obviously, you can't have at-rest pressures simultaneously on the front and back faces; if the back faace fill is 2 inches higher than the front face fill, the wall falls down. Use active pressure on the back face. And think about the possibility of hydrostatic pressure adding to this.
In truth, I've come to think that what a key is really good for is to give a place to increase the embedment and distribution length for the main back-face wall reinforcing. This is what I use to locate the key if I choose to use one; the front face of the key thus ends up 6 or 7 inches in front of the back face of the wall.
The historic factor of safety against sliding is 1.5. In the equations using 0.6DL, the 0.6 is basically 1/1.5; don't take them together. Calculating a factor of safety is not particularly well defined. Basically, you've got active pressure, resisting pressure, and friction. Some people subtract resisting pressure from active; some people add it to friction. I do the latter.
Another piece of information is that a lot of wall failures are shear failures at the base of the wall (i.e. concrete failure, not soil-interface failure). The Corps puts a 45 degree bar through the construction joist at the base of the wall, starting in the footing and ending in a 45 degree bend at the front face of wall. These go with every or every other vertical bar. I've always thought this was a good system, and it's not that big a deal to place, but most contractors look at me like I'm nuts.
One other tickler: I've seen a lot of structures (unreinforced basement walls, mostly) that may have the strength and inherent stability to resist perhaps 20% of the loads I'm talking about. They stand there for years with no distress. Hydrostatic forces are extremely well defined and they will exert exactly what you calculate; soil lateral forces are extremely variable and in some cases (such as clays in a drying condition) may literally adhere to a wall and help hold it up. So, when a contractor or an owner huffs and cites his vast positive experience with walls half of what you've just handed them, politely blow them off.
The best text I've found for retaining wall design is Bowles, "Foundation Analysis and Design." I have the 5th Edition, but the 4th is good too. I don't know what the current edition is, but look at that chapter before you buy it because he often doesn't bother to repeat information from one edition to the next, so it's good to have several.
HTH,
Mike Hemstad
MBJ
Minneapolis, Minnesota
Bill Sherman wrote:
I have been searching for a rational load analysis of a retaining wall
with a key into the supporting soil for years, but I have not found a
satisfactory solution yet. Hoping someone on this list can offer
something to help resolve this issue.=20
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Many references on foundation design indicate that a keyway extended
below a retaining wall into the soil will enhance the sliding stability
by engaging more passive pressure for resistance. But they do not
explicitly address the soil pressure on the driving side of the keyway.
This is often interpreted to mean that only the passive pressure is
considered at the keyway. What happened to "free-body diagrams"? What
is the basis to neglect loads on the driving side of the keyway? (Many
software programs use this questionable assumption for retaining wall
design with keyways.)=20
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If significant movement of the wall is permissible and loads are
transient, it might be argued that the keyway moves away from the soil
and leaves a gap. But for sustained loads, the gap is likely to fill in
over time and re-establish a driving soil pressure on the keyway. Also,
for a centrally located keyway, there is a vertical surcharge force on
the soil due to bearing pressure from the wall base that may push the
soil against the keyway.=20
=20
Load diagrams in EM 1110-2-2502, Retaining and Flood Walls, by the
USACE, do show the driving side soil pressure to be extended to the
bottom of the keyway (i.e., a true fee-body diagram with applied loads).
This is the approach I generally use - but it makes the heel on some
retaining walls rather long!=20
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If minimal movement is desirable and at-rest soil pressures are used on
the driving side, it is possible for the at-rest pressures on the keyway
to exceed the passive pressures on the keyway (due to higher soil depth
on the driving side). This implies that the keyway makes the wall less
stable! =20
=20
Thus, I have concluded that using a full driving side soil pressure on
the keyway may be excessively conservative, but that no driving side
soil pressure is overly unconservative. I'm looking for a rational
method that falls somewhere between these two extremes. =20
=20
=20
Bill=20
William Sherman - CH2M HILL / Denver=20
Structural Technology Discipline Leader (TeD)=20
Engineering Design Group - Civil / Federal Engineering (EDG-CFE)=20
william.sherman@ch2m.com
720.286.2792=20
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