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Re: passive pressure for retaining wall

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As Stan Johnson pointed out, "I would think that a few limitations should be 
looked at" before calculating passive pressure using the methods in the 
example in REINFORCED MASONRY ENGINEERING HANDBOOK BY James Amrhein - I also 
suggest that most designs using a keyway to develop passive pressure are based 
on an invalid free body diagram.   
 
Regarding limitations of Amrhein's method, in my opinion Amrhein presents one 
such limitation on sliding resistance in the "Alternate Design of Shear Key" 
shown just after his special method being discussed (presented on page 256 of 
the fourth edition).  Again as Stan pointed out, "His approach does seem to 
have some logic to it.  Essentially he is saying that the pressure from the 
footing above is providing a confinement pressure for the soil".  It may be 
true that the soil immediately behind the keyway has enhanced passive 
resistance due to confinement pressure, but the overall wall does not have 
such confinement beyond the toe of the footing - thus the "Alternate Design of 
Shear Key" which considers passive pressure at the toe (without confinement 
pressure) should actually be viewed as a "limitation" of passive resistance 
for the overall wall, rather than as an "alternate" design.   
 
It should also be noted that Amrhein's examples do not include a factor of 
safety against sliding (typically 1.5).   
 
The "alternate" design method presented by Amrhein is basically the method I 
typically use to analyze sliding resistance with a keyway - with at least one 
essential correction.  Since the passive pressure is considered to the bottom 
of the keyway, the active pressure must also be extended to the bottom of the 
keyway.  Although most design examples I've seen for sliding resistance with a 
keyway do not address this added active pressure, a proper free body diagram 
would include the soil pressure on both sides of the keyway.  Consider for a 
moment if the entire footing were thickened 1 ft rather than just a keyway 
extended down 1 ft - there would be no question that the active pressure 
diagram should be extended to the bottom of the footing in an opposing 
direction to the resisting passive pressure.  The fact that only a portion of 
the footing is extended down as a keyway should not alter this load effect.  
(Can anyone explain why this added force is neglected in many design 
examples??)  And this is a significant effect - for example, with a 10 ft high 
retaining wall with 2 feet of passive soil resistance, the active soil 
pressure at the top of the keyway with 40 pcf EFP would be 400 plf - the same 
as the passive soil pressure at this point using 200 pcf EFP.  Thus the active 
and passive soil pressures would approximately balance, eliminating the 
benefit of the keyway in developing passive soil resistance.  Thus I rarely 
use keyways since they are not very effective in increasing passive soil 
resistance.   
 
The main benefit a keyway seems to provide is that the sliding plane is moved 
from the concrete-soil interface to a plane within the soil.  Per Amrhein's 
example, a higher coefficient of friction may possibly be used at this 
location, although geotechnical recommendations rarely address this improved 
sliding coefficient below the base.  Additionally, I would include the weight 
of the soil wedge mobilized between the face of the keyway and the toe of the 
footing in the vertical force used to determine frictional sliding resistance. 
 Thus a keyway may provide enhanced sliding resistance due to added frictional 
resistance rather than due to any gain in passive resistance.   
 
Regarding the value used for passive soil pressure, it is generally recognized 
that greater wall movement is required to develop full passive pressure.  
Since I typically don't want much movement in the walls I design, I use a 
conservative value of passive pressure which can be developed with little wall 
movement.  For example, I would use a lateral passive coefficient of 1.00 for 
sand in lieu of 3.00 (see Figure 1 in Chapter 3 of NAVFAC DM-7.2).  This 
further limits any gain in passive pressure from keyways.