Regarding the typical case where the resultant is within the kern, if the soil bearing pressure diagram is assumed to be linear then the vertical surcharge pressure below the footing is only slightly less on the driving side relative to the resisting side of the key (based on the key width and bearing diagram slope).
I do agree that the soil between the key and the back of the heel could be considered if the driving pressure is drawn at the back of the heel. It would make sense to consider the weight of that soil times the soil friction coefficient to reduce the effective driving force that occurs below the footing on the driving side. If this friction force exceeds the added driving force, the added driving force and soil weight should then be neglected. This method would at least provide a way of estimating the potential driving force on the keyway, and it accounts for a full free-body diagram.
Any others care to comment on this approach?
Bill Sherman
CH2M HILL / DEN
720-286-2792
From: Jake Watson [mailto:jake.watson1@gmail.com]
Sent: Monday, July 16, 2007 12:57 PM
To: seaint@seaint.org
Subject: Re: Retaining Wall with Key
If the retaining wall resultant force is in the middle third (kern), then the full footing is loaded in compression. What is the horizontal active+surcharge load below the footing? Remember that the soil above the footing is resting on the footing. Effectively, that soil weight is supported by the soil under the tow, not the heel. So your equivalent fluid pressure (EFP) below the heel is lower than behind the heel. This is really hard to explain without a drawing.....
The more extreme case is where the resultant is outside the kern. In this case, the EFP under the heel has very little surchage from above because there is no soil compression (the footing uplifts and picks up the heel soil).
If you draw your free-body behind the footing for both case you are correct. I think the piece you may be missing is the at rest / passive resistance of the soil between the key and back of the heel.
I wrote this quickly so it probably isn't very clear but I hope it helps a little.
Jake Watson, S.E.
Salt Lake City, UT
On 7/16/07, William.Sherman@ch2m.com < William.Sherman@ch2m.com> 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.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.)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.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!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!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.BillWilliam Sherman - CH2M HILL / DenverStructural Technology Discipline Leader (TeD)Engineering Design Group - Civil / Federal Engineering (EDG-CFE)720.286.2792