Retaining Wall - Location for taking Moments (Key on resisting side)

[CWEngineer]

I am trying to clarify the location to take the moments about when performing the overturing analysis for a retaining wall. For Case A), B), and C) in the attached document the moments are taken about the point at the bottom/right of the toe . But for Case C) not sure where would I take the moments about (a, b or c). I am thinking b, but want some confirmation.

Thanks

 

[Signious]

I don't have too much to add for this; but I'm excited to see what people have to say.

Would it not be prudent to take the moments about all cases & take the worst result? At least until you get a better personal feel at where the wall will overturn under different conditions.

 

[Ron]

Your locations assume the bearing soils will not move nor deflect during overturning. That is not the case. Be sure to consider cases where you are increasing the bearing pressure on part of the foundation area while decreasing it on the opposite side.

 

[BAretired]

Your sketches do not show reactive forces acting on the foundation. Presumably there will be horizontal shear along the contact surface between the underside of concrete and soil as well as passive pressure on the vertical faces which push against the soil. When these forces are included, it shouldn't matter whether you select point a, b or c.

BA

 

[precast78]

I just recently finished an excel spreadsheet. I personally did the sum of moment at the toe instead of the key. This way it is easier to do the formulas when you want key or no key. I also believe if you have a key, some of your friction coefficient will be higher because it is soil to soil. The question is.. how do you determine the % going to soil on soil vs soil to concrete?

 

[canwesteng]

BA is correct, it doesn't matter where you take moments from. Just include all the forces acting on the structure for it to be in equilibrium. Note that in case A the horizontal shear will act through the point you have picked and therefore generates no moment about that point.

 

[darthsoilsguy2]

hmm.. i try to avoid keys for constructability.... but if i did, i would exclude it from the wall height for active soil like you have showed in diagrams B, C, and D. Then I would rotate it around points shown A, B, D, and point b on diagram C. i would essentially pretend the key doesn't exist except for lateral sliding comps. might get same results, but just saying how i would approach it since you asked. i'm not a fan of having the active triangle not sharing common elevation with the point of rotation.

 

[KootK]

The location about which moments are taken is irrelevant for a system in equilibrium. However, the location selected will affect the calculated factor of safety and thus the final design.

I've yet to see any rational guidance with respect to where moments should be summed in order to determine FOS. So I'll propose my own:

1) pick an arbitrary/convenient location to sum moments.
2) uniformly scale back all of the forces that resist overturning until FOS=1.
3) 1 / scale factor = FOS.

I think that this procedure will yield a factor of safety independent of the location chosen for summing moments.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[canwesteng]

Multiply the earth pressure that would cause overturning by the desired factor of safety, then take moments anywhere. Or is this not correct?

 

[KootK]

It sounds as correct as anything else frankly. It wouldn't produce a location independent FOS however.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[CWEngineer]

I din't show all forces in this example, because I just wanted to illustrate that the location in which the moments are taken about is important, since there will be a different moment arm for the active force, for the the three scenarios in Case C.

From previous discussion with others, it was my understanding that you always take the moment for overturning about the point the retaining wall is rotating about. But I have not been able to locate this in a reference. This methodolgy agrees with Cases A, B and D.

I am planning to use the passive resistance to the bottom of the key, to help me out for sliding. Hence, that is why I am also extending the active force to the bottom of the key.

Appreciate your feedback, in the best approach to handle this particular problem.

Thanks!

 

[precast78]

If you extend the active pressure all the way down to the bottom of the keyway, you will realize that adding keyway will not do anything for taller walls.