Retaining wall toe design 1

[wrxsti]

I was perusing a particular retaining wall design example

For the design moment for the toe at the stem
if the pressure on the toe creates a larger moment
than the moment in the stem
the max moment for the stem overrides the larger moment for the
toe using the pressure

 

[BAretired]

I can't think of an example of a retaining wall where this is the case.

BA

 

[wrxsti]

A wall entirely comprised of toe?

 

[jayrod12]

Terminology thing then? To me the toe of the retaining wall is the portion which it rotates around, therefore it is on the dredged side. The heel is buried beneath the retained soil.

In that instance, the overburden pressure is always greater than the bearing pressure from below due to statics.

 

[wrxsti]

@jayroad12 for sure

and usually the toe design moment would be less than the stem moment
and you can design for this moment below stem moment

i'm just trying to figure out the reasoning behind not using the greater moment.
and whether to use this procedure for design.

 

[Celt83]

can you post a sketch of the condition you are talking about as well as a screenshot of the example?

My Personal Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer

 

[wrxsti]

here is the example

 

[RPMG]

I feel like something is not quite right, but I'm not going to write a math proof to figure it out. My brain, which like simple rules, says that heel + toe = stem, approximately. Therefore, toe > stem requires heel < 0, so false.

 

[Celt83]

yeah something seems fishy with that example, from a pure statics perspective I'd also expect the moment created by the shear key resistance to be included in the toe design. I'm used to seeing the key directly under the wall stem.

My Personal Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer

 

[BAretired]

Active pressure = 15.71*(1-0.5)/(1+0.5) = 5.24kN/m^2 per m of depth
H = 5.24*(8.5)[sup]2[/sup]*1/2 = 189.3kN per m
M[stem] = 5.24(8.5)[sup]3[/sup]/6 = 536kN-m per m
Mu[stem] = 1.6*536 = 857.6kN-m per m

Mu[toe] at middle of ftg. = [(8.5 + 0.6)/8.5][sup]3[/sup]*857.6 = 1052kN-m per m

So the difference is a result of the thickness of the footing, namely 1200mm.

I see no reason to use the lesser moment for the footing, particularly as we are turning a 90[sup]o[/sup] corner which has its own issues as has been discussed in another thread. I would reinforce the footing for 1052kN-m per m and give careful thought to turning the corner into the wall.

BA

 

[wrxsti]

RPMG i get what youre saying but that sounds like a weird function to be put in
I was thinking among the lines that if the moment is being transferred to the stem
then the stem couldn't accommodate the higher moment
ie. its a balance like you suggest

but its not a warning like toe moment higher than stem redesign
but toe moment need not be higher
like there is some explanation of how that extra moment is redistributed or absorbed somehow

 

[wrxsti]

@BARetired you have a link for that thread?

 

[r13]

Agree with BA.

 

[wrxsti]

@BARetired why use back same active pressure concept with extended half thickness of footing
and not use pressure distribution from P/A +- M/Z to calculate moment in the toe?

 

[BAretired]

@BARetired you have a link for that thread?

wrxsti

not offhand. I'll find it and get back to you. It is a very long thread.

EDIT: Found it! thread507-401855

@BARetired why use back same active pressure concept with extended half thickness of footing
and not use pressure distribution from P/A +- M/Z to calculate moment in the toe?

Same answer either way. Equilibrium demands it!

EDIT #2: Let me re-phrase that. It should be the same answer either way. It not, the toe pressures are incorrect.

BA

 

[jsmith234]

if equilibrium required
wouldnt the stem need to be now reinforced for the higher moment then
active pressure?

 

[BAretired]

if equilibrium required
wouldnt the stem need to be now reinforced for the higher moment then
active pressure?

if equilibrium required? Equilibrium is always required for any structure which is not in motion.

No, the stem need not be reinforced for higher than active pressure. The maximum moment in the stem occurs at the top of the footing, so the stem moment is correct as calculated.

The maximum moment in the footing occurs at the point where a vertical plane through the leftmost contact between wall and footing meets the neutral axis of the footing and decreases toward the toe. The eccentricity of the wall and the end of the footing would decrease the footing moment slightly, but was not included as the wall dimensions are not known.

BA

 

[jsmith234]

wall dimensions also 4ft it seems

 

[RPMG]

What's the width of the footing?

 

[wrxsti]