Sloped dredge line vs. Kp

[VQ]

I infrequently analyze/design anchored sheet pile retaining walls with sloped dredge lines in front of the retaining wall. Based on the “recommendations” of senior engineers within the company, a wall is idealized with a horizontal dredge line. The determination of the horizontal dredge line is that elevation that provides a bench in front of the retaining wall that is approximately equal to the height of wall (top of wall to top of dredge line at wall interface.)

Is it proper or within the limits of the Coulomb’s passive earth pressure equation to enter a negative value for an inclined backfill (slope downward from the horizontal) and get a “valid” Kp value? All texts that I’ve seen use the equation with a positive backfill angle (slope upward from the horizontal.) Does anyone have a solid reference that discusses this specific use of Coulomb’s eq. so that I can use as a point of discussion with the senior engineers?

Maybe this is the best way to look at a retaining wall with a sloped dredge line? What do others do?
Thanks - VQ

 

[PEinc]

Well, I guess no one wants to answer this one so I'll try.

Check out NAVFAC'a Design Manual 7.2, Foundations and Earth Structures, page 7.2-64, Figure 3. The figure shows passive earth pressure coefficients for both positive and negative slope angles in front of the wall. A negative angle is below horizontal and reduces the coefficient. A positive angle is above horizontal and increases the passive coefficient. Search the internet for NAVFAC's downloadable Design Manual DM-7.

Soils books give examples with the ground surface rising behind the structure which is being pushed backwards. Therefore, the angle in the example is positive. However, you can use a negative angle in the Coulomb equations if the ground surface slopes downward. The only limitation I know of is that the slope angle must be less than the friction angle of the soil or elde the equations won't work properly. Theoretically, the slope would be unstable if the slope is steeper than the friction angle. This is a common design problem when we know that, in most cases, a 1.5H:1V (33.7 degrees)slope is stable (at least in the short term). It's fairly common to see sheeting walls designed with friction angles less than 33.7 degrees while the contractor has an OSHA approved 1.5:1 slope behind the wall. When this happens, the wall designer has to open his bag of tricks to get an earth pressure coefficient.

 

[VQ]

PEinc, thanks for taking the time to respond and for the reference. - VQ