retaining wall 9soil is at a decreasing slope0

huangyhg

retaining wall (soil is at a decreasing slope)
i know this post belongs in the soil mechanics forum, to which it has already been posted, i just wanted to stick it in here as well since it seems as though this forum is quite a bit more active than that one.  so here's what i have.
i've done the calcs for a retaining wall (t-shaped cantilever) i will be putting into a firewall (constructed of a clay based material).
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                   |      \
                   |       \
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           ________|____     \

above is a crude drawing of what my finished product will look like.  as you can tell (hopefully) my soil behind the retaining wall is horizontal at the top of the wall for four feet, then starts to slope down to grade at a 1:1.5 slope (firewall & retaining wall are approx. nine feet tall).
question is, i used rankin's theory to find my active resultant force acting on my wall, to me this seems to be quite conservative since i have a decreasing slope directly behind my wall and the theory is generally used for either a horizontal or in most cases an increasing slope behind the wall.  is there another way to go about getting a more accurate number for my resultant pressure on the wall.  the only reason i ask is to me my final design seems mighty conservative, i ended up putting a four foot heel, as well as a 1.5 foot key.
any input would be appreciated.
thanks in advance!
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rull,
same theory applies. draw a slip plane at 45 less half the angle of repose. (plus for passive resistance, minus for active - just check that idea - i haven't any text books about. that's what the (1 +/- tan theta) is all about).
1 - pressure at wall / horizontal surface is zero
2 - go to end of horizontal surface and calculate pressure at (density x height x active pressure coefficient)
3 - go to bottom of decline slope - at intersection of slip plane. pressure here must be zero
4 - anything below this does not impinge on the wall
5 - draw a straight line for the variation of pressure from max to min
the formulae are calculated out in books such as reynolds - concrete design handbook.
an alternative way of looking at it is
1 - look at your horizontal section - calculate pressures
2 - use this as a surcharge on the decline slope
third option
1 - calculate for horizontal soil surface throughout
2 - use decline as equivalent negative pressure
once you understand the geometric basis for rankine's calculations it all comes to the same mathematics in the end.
johnp.rz
an even simpler way of looking at it is to think of soil as hydraulic pressure (equal in all directions). associate the ka factor with the head h. the ka factor converts the vertical component into an equivalent, but reduced horizontal pressure. vola - any slope, up or down, at any point based on the rankine formula (i.e wall friction neglectable).
johnp.rz