Just simplify it - Take the height of the soil above the lower wall and apply it as a uniform load offset the tired distance. Use a Boussinesq type analysis.
Or you could try to use the bearing pressure from the top wall as a strip load. However if you are also relying on passive pressure for your top wall then this may throw a wrinkle in the analysis.
THanks to both Hokie66 & RFreund-- Indeed there is a wrinkle. The problem is to determine the amount of passive pressure from the upper wall that is to be applied to the lower wall. We've tried several approaches but all have been rejected by the S.E. revier for the state agency involved. One method we suggested was to draw a line from the top of the lower wall to the top of the upper wall and use the resultant slope to calculate the active pressure. Another was to draw the active and passive wedges and if they do not intersect the upper wall does not load the lower wall. If they do intersect the passive pressure on the lower wall would be proportional to the triangular areas involved. Any thoughts?
You can just take the part of the upper soil mass (and concrete wall) that is above the top of the lower wall as a superimposed load. The lower wall doesn't know the difference between a concrete wall and a vertical, stable, soil block.
I would do as Hokie, yourself and I have said. Take the difference from the top grade of the upper wall and the top grade of the lower wall and treat it as an offset surcharge. Run a boussinesq analysis to find resultant force and location.
Or even more conservative (I would think) is to do as you previously suggested and draw line form top of the lower to the top of the upper wall.
I agree with drawing the active and passive wedges and if they do not intersect then they should not influence each other. This would also put the upper walls bearing pressure behind the failure plane of the lower wall which most research would indicate that the bearing pressure does not influence the lower wall (but I would use a 1:1 to be more conservative).
If the lines do intersect I'm not sure how to apply the passive pressure to the lower wall but I have been very interested in this. I imagine something like this - The passive pressure is due to the weight of the passive soil wedge in front of the upper wall. Therefore the soil inside of both the active and passive wedges cannot be used for passive resistance. The weight of this soil would then need to be applied to the lower wall as a force. But I'm not sure how to distribute it.
The earth pressure(s) from the higher terraces applied to the lower level walls can be approximated as if they were an embankment. Influence diagrams for various geometries were derived by Perloff (1967)and can be found summarized in the "Foundation Engineering Handbook" edited by Winterkorn and Fang. Once you have that load distribution from the upper wall(s) you can apply it to the tier below.
The passive resistance provided by the terrace can be calculated using a Culman curve. Details on how to construct a Culman curve can be found in the "USS Sheet Piling Design Manual".
I'm slightly confused on what you mean by "the passive resistance provided by the terrace" - is this the passive resistance provided by the soil between the upper and lower wall?
Geotech should be able to develop this for you. Elastic solutions of horizontal surcharge loads are available. The real question is if the horizontal passive load and the vertical nearby load affect the soil slope stability wedge if the lower wall ...and thus load. Shoring suite has a method you may want to look at
you should also search the forums at one point I posted another PDF of a stepped wall situation and the load conditions a geotrch developed for me.
Worst case just apply the full passive resistance horizontal load as a partial load behind the lower wall & then add the boussinesq surcharge from the vertical bearing pressure.
Yup, those are it. If you use the civiltech software method you'll have to ask for their technical reference. The other doc with geotech recommendations should be updated for your soil conditions.
here is a link to a good book that has various solutions, including the passive pressure and the soil stress at a distance away.
