buttressing a retaining wall

[Jean G]

I am designing repairs for a 6 ft tall stone retaining wall about 120 feet long that is pitching over. The plan is to stabilize with a series of masonry buttresses. Normally I size buttresses based on their mass to resist overturning moment. Wondering if I can reduce their size by designing them as cantilevered concrete beams (each tied into a spread footing.)

 

[hardbutmild]

Masonry buttresses as in reinforced masonry or unreinforced masonry?
You still need to avoid overturning obviously. How do you plan on tying the buttress to the footing?

 

[Jean G]

If I design the buttress as a cantilevered beam I would go with reinforced concrete. I would design the beam to resist the overturning moment. Then tie it into the footing. The footing would be designed to resist the overturning moment and sized as needed for soil stress.

 

[SWComposites]

How far apart will these buttresses be? What keeps the stone wall from collapsing between the buttresses?

 

[KootK]

How far apart will these buttresses be? What keeps the stone wall from collapsing between the buttresses?

That would be my concern as well. The modified system would require the stone wall to span horizontally. And perhaps it can. I could see that being a challenge to prove however.

 

[Jean G]

Yes, I considered that. The buttresses would be 3 ft wide and 15 ft O.C., so 12 feet of wall between each one.
The wall is mortared, not dry stone. Currently it is relatively plumb at each end, then, as viewed at the top along the length of wall, it is bowing out to a maximum point at mid span, not unlike an overstressed beam. No evidence of cracks indicating discontinuity along its length.

Viewing the conditions, and based on my experience with these walls (I specialize in forensics and repairs of stone and brick structures), I am exercising engineering judgment. These walls, at least where I live, typically move monolithically.

Back to my question about designing the buttress as a reinforced concrete beam….

 

[KootK]

Back to my question about designing the buttress as a reinforced concrete beam….

It's not much of a question. If you design it as a beam, it can be a beam. No problem.

 

[hardbutmild]

I could see that being a challenge to prove however.

I don't see it as a huge challenge, but again US approach is very different I think. You could consider a hidden horizontal arc inside the wall. This arc would have three hinges - one at each buttress and one in the middle. Usually I'd consider it to have a thickness of 1/10 of the wall thickness (this is a provision from Eurocode). At that point it's quite easy to get the forces in the arc and at the buttress.

 

[KootK]

I don't see it as a huge challenge, but again US approach is very different I think.

What you've outlined sounds just like what I had in mind when I described it as a "challenge to prove".

Masonry arching is marvelous when:

a) You've got ample thrust resistance everywhere (no end span).

b) You've got enough arch depth that you can keep everything in compression always and not rely on tensile or shear stresses (L/10 is not that in my book).

c) You've got enough load symmetry that you can keep everything in compression always an not have to consider arch buckling (not plausible with soil load in my book).

You are correct, however, in that, in the global pantheon of structural engineers, we North Americans tend to have relatively less comfort with stone work. That is certainly true of me. My comfort level has also been tainted by my having been involved in some rubble foundation work that got a workman seriously and permanently injured.

I acquired that book "The Stone Skeleton" precisely to help me liberalize myself on unreinforced masonry. It's not come to much I'm afraid.

 

[hardbutmild]

a) You've got ample thrust resistance everywhere (no end span).

If there are concrete piers at the end of the wall, why couldn't it resist lateral loads and provide siffness? Concrete should be significantly stiffer (probably around 20 times) than stone masonry.

b) You've got enough arch depth that you can keep everything in compression always and not rely on tensile or shear stresses (L/10 is not that in my book).

Everything in compression seems too strict for an arch that supports lateral loads, or any URM element. This would mean that no cracks are allowed to form, most books I've read on URM seem to rely on plastic failure mechanism, i.e. finding an arch that "fits" inside the wall, this is very different than everything being in compression.
For example, let's look at a simple wall under vertical load with some out of plane eccentricity. If you want everything to be in compression you need to limit the total eccentricity to t/6. If you allow the stress block to be 10 % of the wall thickness you get an allowable eccentricity of 0,45*t - that is 2,7 times more! Of course, you get a lower axial capacity, but that is usually quite high for standard dimensions.
This arch action is not that high, you get relatively low capacities, but still... it's not zero. Additionally it does span in the opposite direction as well which helps a bit.
What would happen if instead of a 20" stone wall that is cracked you had a 2" thick stone arch that is fully in compression? If you can make sure that this arch is fully in compression that is lower than strength, what is the problem?

c) You've got enough load symmetry that you can keep everything in compression always an not have to consider arch buckling (not plausible with soil load in my book).

How do you consider this non symmetry? Since we're talking about a horizontal arch it should a a horizontal non symmetry. You could still fit an arch of t/10 in there, the ultimate load will be lower depending on the level of symmetry. That is why you do calculations. I have never seen soil non symmetry in a horizontal plane though.

Don't get me wrong, I would also rather have reinforcement in my elements that can resist tension, but if 80 % of buildings in your city (and country... and continent) are over 100 years old with URM basements and they survived without damage a few significant earthquakes you just can't afford to say that it's not good if there is a rational model for it.
Sure, it seems wise to design URM in a way that it is not very close to failure, so I'd deffinitely space the buttresses closer together rather than far apart.
I quite like The Stone Skeleton, "Guastavino vaulting" also seems like an interesting read, I think he did some vaults in the US.