retaining wall with sloped backfill

huangyhg

retaining wall with sloped backfill
i am designing a retaining wall that has a 1:2 sloped backfill.  i have a couple of questions regarding this design.
1.  becasue of the sloped backfill, the pressure that the soil exerts on the wall is not horizontal, but rather is at an angle perpendicular to the backfill.  is that correct?
2.  when calcualting the moment acting on the heel of the footing at the face of the stem, do i include the vertical component of the force described above multiplied by the length of the heel (moment arm)?  this is what i have done to this point.
3.  is this vertical force included in the overturning/stability check?
4.  does anyone have a reference for a good design example for this, possibly from a book or a dot web page?
thanks in advance for your help.

1. not quite so simple - the angle at which the soil pressure resultant acts is a non-linear function of the soil type and slope of backfill. it is necessary to pick the value of the "kv" coefficient from a graph. (i have the book "foundation engineering" by peck, hanson, and thornburn). it is page 425 in that book, that is, the 1974 edition.
2. according to example shown on p.428, the answer is no. you do include the weight of the small wedge of soil include within the backfill slope.
3. according to example shown on p.428, the resultant of the vertical force acts at the edge of heel. its force is included in the vertical force summation, but the moment arm for resisting moment (moment of stability) is zero.
1.  the soil force is parallel to the backfill.  if the backfill is sloped at alpha from the horizontal, the resultant force is alpha from the horizontal.  if the part of the wall facing the back fill is itself sloped then the above is not necessarily true.
2.  you can include the vertical component of the soil force in your calculations for the factored soil pressure.  you should include all forces acting on the heel to find the moment in the heel.  this can be found by applying the factored soil pressure to the footing and designing the heel and toe like little cantilevers with a linearly varying load.  the heel will also have to provide the moment from the stem.  i would take the moments for the heel and toe design from the appropriate location as given by the aci 318 in chapter 15.4.2.
3.  you can include the vertical force for stability.  it may be a good idea not to just for some extra factor of safety.  that's up to your judgment.
4.  das, coduto and bowles are all good references.  
go to my web page (link below). from the "steel sheet piling & h-piles" page download "us steel sheet piling design extracts". page 5 of the download shows the math for the rankine-coulomb approach. krey's method is discussed beginning on page 75.
principles of foundation engineering by das is a good book, and has procedures and examples of how to analyze retaining walls with sloping backfill.
good advice has already been given which i can't improve on.
now 1:2 slope on the backfill? i take it that is 1 vertical for every 2 horizontal - 26.5 degrees. that is steep. what kind of ground is to be retained? how high is the wall? what is the ground slope on the non-retained side?
i've only encountered one wall with this type of slope. we installed ground anchors to hold back the top.
the angle of the resultant is not quite parallel to the slope of the backfill.
starting with zero slope (level backfill), the resultant is of course horizontal. as we increase the slope of the backfill, the resultant vector changes to be nearly parallel to the backfill slope. as the backfill slope further increases, the angle of the resultant vector increases at a decreasing rate (non-linear). as the slope of the backfill becomes large, the resultant vector is much less parallel to it.
this is non-linear, and can be determined from either the geotech report, or determined approximately per soil type, using a chart shown in a reference book as i described in my op.
i'm no expert, but i'll offer some of my thoughts, assuming a cantilevered wall subject to active pressure:
unless the wall/backfill interface is frictionless, there will be a vertical component. that is why there is a reduction in the horizontal component of ka when there is wall friction present. this is shown by table 9.2 in das and in the graphs in annex a of bs8002, code of practice for earth retaining structures.
if the back of wall is frictionless then the pressure exerted must be perpendicular to the wall back face, and not necessarily horizontal. (a frictionless wall might only exist in theory.)
ka will increase if the backfill slopes up. as noted above, there are standard solutions in texts such as by das.
i believe assuming a frictionless wall will always give a conservative answer as ka is higher and resistance to overturning is lower when ignoring the vertical component.
my observation as a structural engineer is that the determination of soil loads is somewhat approximate and will vary depending on which theory is followed. my understanding of it is certainly limited.
brokie,
you raise an interesting question about the use of the vertical component of the active force.  all the above references agree to its use for the stability and sliding calculations.  however, i cannot find it's use in any of the references (i don't have the coduto) for the calculation of the bending moment in the heel.  i have a xeroxed example from an old textbook where it is included in the stability calculations and not in the heel calculations.  i believe this example came from a text by peck, but i'm not sure.  based on that textbook example, i have never included the verticle force in the design of the heel.
sacrebleu,
could you check your peck reference to see if this force is included in an example calculation of the heel design?
sacrebleu-
oops, guess you already answered my question.
commercial software such as enercalc gives you the option to include the vertical component in the stability calculation. since we do design with more precision (hopefully) now with computer design, i actually am leaning more towards including the vertical component in the stability calculation, especially since the sloped backfill induces much more overturning to begin with.