Wall with unbalanced soil 1

[DTS419]

Considering the attached sketch, how would you apply the soil forces to this wall? In other words, how does the soil on the right respond to the soil on the left...how much can the resultant of the soil on the left be reduced by the soil on the right?

 

[Greenalleycat]

With the slab being a specified resisting element I am again echoing Jayrod
The differential movement required to mobilise slab resistance (no movement) vs the soil (lots of movement) means that the soil is contributing absolutely nothing in my books
I would be designing for a moment couple between the slab tie in compression and the footing at the base wanting to kick back laterally

If you want to avoid excavation behind the wall then I would suggest putting at least a nominal cantilever footing on the front side
This can give your wall reliable stability in the temporary cases (during construction or should the slab be removed for any reason)
Once the slab is installed and the wall backfilled then it will give you a decent area of footing to take out the kickback reaction

 

[DTS419]

The point of rotation is the slab. If you ignore the resisting soil under the slab, then the reaction at the top of wall becomes too conservative.

 

[Greenalleycat]

Well your sketch doesn't even make sense, you've shown soil acting back against the driving force...but if your point of rotation is the slab then the soil reaction you've shown (the small triangle) is a destablilising moment so it makes it worse
In your case, the portion of the triangle on the left side below the slab level is actually a stabilising force, so you could get fancy and try to calibrate this to balance the driving force of the soil above.
But why are you doing that anyway? Surely the excavation depth should be limited to top of slab - required footing depth?

 

[Celt83]

Assuming it has to be as shown in your sketch and the slab is capable of resisting the reaction, then I would use at-rest pressure with the 0.6 ASD load factor for H resisting the primary variable load effect.

Secondary to the above:
1. Why does the wall extend so far below the slab, this is just adding more soil pressure?
2. Why is there no foundation at the base of the wall?
3. How do you envision the slab resisting the horizontal reaction, what is the load path you envision? Is there an isolation joint between the wall and slab that violates your load path assumption?

 

[DTS419]

Green, it’s basic statics. The larger soil load on left causes the wall to rotate about the slab and so there is a top of wall reaction as the top of wall wants to rotate to the left. If we include the soil on right, this causes a counter rotation that reduces the TOW reaction. The system is statically determinate with supports and so stability is not the concern.

Celt, the wall extends down so far for frost. There is a simple footing under it and not shown in my sketch. I could pin to it if I had to, but I’m trying to get it to work without that. Agreed, this condition increases the soil load unfavorably.

Again, this post was borne more out of a question of how opposing unbalanced soils
behave from a geotech perspective rather than a nuts and bolts review of every project detail. There are still a lot of details to work through pending the soil loading is properly accounted for.

 

[Greenalleycat]

Soil above slab on LHS is the driving force causing rotation about the slab into the basement
As the wall is extended deeper below slab on the LHS then the soil pressure below the slab height on the LHS stabilises the rotation about the slab.
However, the deeper the wall goes, the greater the contribution of the soil on the RHS below your basement slab that is generating a driving moment - this also forces the top of the wall into the room
The slab dead weight and surcharge from live loads etc would need to factor into this too
A bit of a headache but all reasonably easily modelled in a spreadsheet to see which way your resultant at the top of the wall acts
In theory, you could calibrate the depth of the wall to cause this to be perfectly stable about the slab point

Hopefully we agree on the statics bit

Your Factor of Safety would be provided by having the wall extend deeper on the LHS which would eventually cause the wall to lean out of the basement rather than in
This seems to be your question - how reliable is it that the wall leaning left can be resisted by the soil?
I think the answer to this is: not very
The reasoning being that at-rest or active pressures (driving forces) from your soil require no/little movement to mobilise
Passive pressure at the top of the wall as a resisting force requires significant movement to mobilise - or so I've always been taught
I think there is a displacement incompatibility here that just won't work

The system that I would design, if you have a net outwards reaction at the top of the wall, is to have the slab in permanent tension and design the wall as a propped cantilever
I would not rely on any passive pressure on the LHS above slab height due to a) displacement compatibility concerns b) to allow for the soil to be excavated later in case of waterproofing works etc
I would factor in the active soil pressure on the RHS below the slab as a small measure of economy as this will reduce your top of wall movement, as you've said
I would check with/without this though as a sanity check and see whether the potential small savings are worth any compromise I'm making

Hopefully I've understood/answered your questions properly this time

Food for thought: how is stability provided in the construction case for this wall?
Is a temporary cantilever footing needed?

 

[DTS419]

Green, still not sure I follow you on the rotation. The resultants of both triangles are below the slab. The LHS resultant rotates the top of wall (pin-connected to framing) out of the room. The resultant on RHS under slab causes the TOW to rotate into the room. Ignoring any soil parameters for the moment and just considering that the triangle on the LHS is bigger, my overall resultant is (LHS - RHS) causes the TOW to go left out of room.

 

[Greenalleycat]

We’re broadly saying the same thing

A difference between you and me here is that I don’t actually know where the centroid of the triangle is on the left hand side - that’s a function of of the depth of the wall below the slab height, and I lack that information but you presumably have it

If the centroid is above the slab then you have two destabalising moments and the top of the wall comes into the room
If the centroid is below the slab then, as you said, they will oppose and, at some point, you end up with the top of the wall going out of the room instead of in

 

[DTS419]

Ha, I guess I should have given you the dimensions.

So to boil all this down, would you agree that a conservative starting point (since I don't have a geotech report) would be to look at both soils as at-rest with 0.6 reduction on the RHS? I will assume something like 120 pcf unit weight and a Ko = 0.5. If that works, then probably not much else to worry about. If it doesn't work out, then I need to either get better soil data, consider active on LHS, etc.

 

[Greenalleycat]

I can't speak to the soil properties as I don't speak Americanese!
Ko of 0.5 seems reasonable though
It feels like one of those situations that you'll either be in the right ballpark or it immediately won't work and you know you need to try something else

I would give a fair bit of attention to the potential deflection at the top of the wall
You want a very rigid wall IMO to prevent moment that could affect the structure above (tilting wall, cladding damage) or damage to the waterproofing on your underground portion of wall