Slab on grade cast on compacted soil 4

[fa2070]

Hello,

Let's consider this situation.
I need to design a concrete slab-on-grade for a site with an ML-type soil. (sandy silt). The contractor is going to strip the upper layer of natural soil (1.00m thick) and replace it with sheepfoot-roller compacted structural fill (k > 300pci). The underlying strata are natural soil (-1.00m and beyond).
My question then is,
What modulus of subgrade reaction "k" do I have to use in my calculations to design this slab-on-grade? Should I use the "k" of the underlying natural silt or the "k" of the roller compacted fill (which ultimately will be supporting the slab) ?

Thanks.

 

[Panars]

First, the section you are using in NAVFAC 7.1 is for excavating vertical shafts in ground for tunneling. As you noted, your dimensions for the tank lie on the edge of the graph. I would not recommend using Figure 24 for what is essentially a retaining wall design.

Second, also as you noted concrete tanks cannot tolerate much movement before cracking. To develop full passive pressure can take quite a lot of movement, up to 5 percent of the wall height in some cases. (See NAVFAC 7.2, page 60 for the figure) This would be .19 meters (7.5 inches) for your 3.86 meter high tank wall. I doubt that the tank could withstand this much movement.

NAVFAC 7.2 can be downloaded here:

http://vulcanhammer.net/download/foundations.php

I think your reasoning is correct, but I would recommend that you use concepts related to retaining wall design, rather than the Figure 24 you found. The major question is, how much movement (expansion) of the tank can occur before "failure"? With a circular tank, I would think the answer is not much. Definitely not enough to develop full passive pressure in the backfill.

I would use the at-rest earth pressure, and if this is not enough, then resist the rest of the hydrostatic pressure structurally with the hoop stress.

 

[fattdad]

Wow! Looks complicated. You have a sloping buttress of soil that is counteracting the fluid pressure. Is it water (i.e., 62.4 pcf)? When empty, the earth pressure is determined by at rest conditions, which I would calculate aw 1.5 times the active earth pressure for sloping backfill (from DM 7). I would use full friction between the soil and the wall face, which in this case is your tank with a corregated texture.

Now consider what happens when the product is introduced into the tank: you begin to mobilize passive earth pressure. However, you will never mobilize the full passive earth pressure that's available to you. That's a good think as there could be strain incompatibility. I would guess your sloping at-rest earth pressure would be on the order of 45 to 50 pcf and the fluid content on the order of 60 to 70 pcf. Seems that it would all work out, eh?

Interested in your thoughts, but keep it simple if possible - ha.

f-d

¡papá gordo ain’t no madre flaca!

 

[oneintheeye]

first I would never rely on backfill to 'balance' pressure of tank as a) water test is likely to be carried out before backfill b) you can never I would suggest be 100 % confident that the backfilling will be provide required pressure to outside of walls. think you would be on dangerous ground to rely on backfill. As I said i would never rely on it and if I did and something went wrong, I know i'll be signing my resignation.

 

[fa2070]

Thank you all for having taken the time to read my post and share your thoughts. Very interesting insights.

First, yes, water unit weight = 62.4 pcf = 1,000 Kg/m³

I think things have started to come together now. A few rough edges, though, mostly due to my illiteracy in geotechnics and the complexity of the structure.

For me this subject boils down to understanding how the whole system works so as to develop an abstracted physical model and eventually apply the necessary math to sustain it. Ultimately it will help me to decide whether this construction methodology scales up to be applied in larger tanks or not. This is a geotech problem, not a structural one, I think.
For radii up to 15m (50ft) and depths up to 3m (10ft) there's no need to do any fine-grained analysis or calculations. The system just works.
My boss, however, has the habit of calling me whenever he needs to extend and utilize this same system in bigger tanks, that is, R > 15m or H > 3m. From my experience, I can say that the larger tanks are less tolerant to flaws in the backfill than the smaller ones. I need to understand how this thing works intimately so that I can give him a qualified authoritative answer (and design) instead of an opinionated perception of how I think things work or should be done.

Passive pressure, by definition, implies a mobilizing action on the soil mass. Concrete in general, and these walls in particular, admit very small positive strains (and their corresponding tension stresses). As a result, I think it is rare that the associated displacement -in the form of an increase in radius- can trigger mobilization of the soil mass. This, plus the sub-optimal steel/concrete ratio used in the standard walls makes me think that the analysis of these tanks must be done within the at-rest + compaction pressures domain (emphasis on compaction) as the soil never becomes aware of anything pushing into it. If it weren't like that, by the time the radial swelling derived from the hydrostatic pressure becomes significant, the wall will have cracked severely. I have verified that this is not the case when the backfill is properly executed. In such cases, the uncracked state of the thin walls is a strong indication of the pro-active role of the sloping backfill, such that:

[ul square]
[li]when the tank is empty, the circular concrete shell is fully compressed (this configures the most severe condition during the tank's lifetime).[/li]
[li]when the tank is filled, the circular concrete shell either has a residual compression or, at most, a very very small tension.[/li]
[/ul]

That, however, is very difficult to prove and even harder to guarantee in practice, especially in the context of larger tanks (R > 15m or H > 3m). Besides height, radius and support conditions, which are the well known factors driving the tension derived from hoop force & bending moments, and consequently the compression that the soil buttress will be "expected" to provide, there are so many construction unknowns such as soil types, moisture content, slope steepness, contractors, equipment, labor, etc. that makes it difficult to accurately predict how much residual compression the walls will have at the full/empty conditions.
Add to that the compaction techniques. Each contractor seems to have its own sui generis way of doing compaction. E.g. How each lift is effectively compacted by the rubber-tyre rollers and rammers makes a difference. Is it carried out from the wall outwards or viceversa?. It's not the same. Neither are the resulting pressures on the wall. And that's just one out of many variables.
Then we have rain. How sensitive is the backfill's performance to a heavy rain? Yet another potential headache.

It might seem that I've almost aggressively put the backfill buttress under the magnifying glass here. It is so because of its fundamental role in the stability of the whole system. Like I said above, it's a geotech problem after all. The standard thin concrete wall panels act as a mere liner. They contribute very little stiffness to the whole picture, so to say. (See the photo of a severely damaged tank in my previous post in which the backfill on the upper 4 ft of the wall is missing). In most "normal" projects involving tanks the approach is quite the opposite. The design of the wall (concrete + steel areas) is the primary focus and is designed based on a myriad of other variables. Backfill being just one of them. Its effect is conservatively guesstimated and that's it. Here, I have to demonstrate that with ordinary wall panels + a sloping backfill a safe, durable and stable large tank (R > 15m or H > 3m) is possible.
Codes as well as specialized literature from ACI, PCI (Precast Prestressed Concrete Institute) and PCA (Portland Cement Association) set the basis for tank design. Most notably, they introduce a sanitary coefficient (1.65) and a load factor (1.7). They also make it clear that the effect of backfill should not be taken into account when it is beneficial in counteracting fluid pressure. The rationale, as it has been said, is that leak tests must be done before applying the backfill. Imagine if I had the freedom to design according to those guidelines...things would be much easier (I and my license would be thankful).

Now, to shape things and tie loose ends:

I would guess your sloping at-rest earth pressure would be on the order of 45 to 50 pcf...

If we assume the soil's equivalent fluid weight = 50 pcf = 802 Kg/m³, then, does it mean that it will handle 80% of the hydrostatic pressure ? If so, the reinforcement will have to deal with the remaining 20%, won't it? I've done the calculations and the steel area needed to deal with 20% of the hydrostatic pressure is higher than the actual steel that's been used in these precast panels for decades. This sort of confirms my previous speculation in the sense that there must be a larger external pressure from the backfill acting on the wall. Maybe if we add the compaction surcharge to these 50 pcf we could fully compensate the hydrostatic pressure and even get some precious residual compression, right ?

Steel wouldn't be the problem eventually. I could embed bigger bars in the ribs of the panel and deal with the difference.
However, considering there cannot be any tension in the walls for the reasons exposed earlier, and despite all the soil-related uncertainties (also mentioned above) the common denominator is that most tanks in service today -even those with sub-optimal reinforcement- perform well and don't leak. Granted! those tanks are short, R < 15m or H < 3m.

What I'd like, as I said above, is to outline a reliable model that validates all these things. And most importantly it should protect me from liability in case things go wrong. And yes, I've seen a few projects, most notably those involving large rectangular tanks, gone totally wrong after a heavy rain caught them empty. Apparently the soil's Liquid Limit went overboard and so did the horizontal pressures...needless to say, collapse followed. Although I wasn't involved in any of them, they really raised awareness that these things are not to be taken lightly. As tanks approach R = 15m or H = 3m there begins to be a faint line that divides a fully functional structure from a collapsible one. If the wall panels are all the same, then success or failure depends exclusively on the characteristics of backfill and how it is carried out.

I'm totally aware that although the stability of these tanks is acceptable (R < 15m or H < 3m), their safety coefficient is 1.00 at best. They have no strength reserve. Period. Even more, they're very sensitive to many imponderable soil-related things and as such I don't want to be held responsible for a concept I didn't even conceive.

I think, generally speaking, what might be happening here is that I have a pressure diagram like this:

(Taken from Fig. 14, page 117 of the .PDF I found here.)

-OR-

From page 8.47 of document ufc_3_220_01n.pdf downloadable from here we've got this diagram:

From the first graph, I see Z_c / h_c = K_A²

Now, here are my doubts:
[COLOR=blue yellow]How can I guarantee that the Hydrostatic pressure + the pressure from the sloping backfill + the compaction surcharge will always remain < 0 ?[/color]

Additionally, will I use [COLOR=blue yellow]K_A[/color] or [COLOR=blue yellow]K₀[/color] ?
Throughout the thread we agreed to employ K₀ and now we have Ingold giving precedence to K_A over K₀. [COLOR=blue yellow]So, do I still stick with K₀ ?[/color]
I understand that the difference between K_A and K₀ lies in how much rotation the wall can tolerate, right?. [COLOR=blue yellow]But, how am I supposed to know beforehand the value of the rotation ?[/color]

For example, the parameter needed to enter Figure 1 from NAVFAC 7.2 (page 7.2-60) is the horizontal displacement Y.

Remember from my previous post that the full height is achieved by stacking two cylinders:

Then, with the last picture in mind, [COLOR=blue yellow]where do I measure the horizontal displacement 'Y' so that I can use it in Figure 1? Is it the largest 'Y' from span AB, for example ?

And why not use Rankine's formula instead of Figure 1?[/color]
(OK, Rankine's assumptions of a flat, frictionless wall are not satisfied here)

P_{horiz. Active} = P_vert. . 1
Tan²(45º + [&phi;]/2)

In this case:
[&phi;] = 35º
[&#947;] = 1,900 Kg/m³ = 119 pcf
Z = 3.86 m = 12.66 ft

Then, P_{horiz. Active} = 1,987 Kg/m² = 407 psf
So P₀ = 1.5 x 407 psf = [COLOR=white magenta]610 psf[/color] [&larr;] remember this

Re-calculating with an at-rest earth pressure of 50 pcf:
P₀ = 50 pcf x 12.66 ft = [COLOR=white magenta]633 psf[/color] [&asymp;] [COLOR=white magenta]610 psf[/color]

[COLOR=blue yellow]So, what's the difference between Rankine's K_A and the K_A from Terzaghi's graph ?
What would be the value of Ingold's [&sigma;]'_hm (or [&sigma;]_HC for that matter) considering pneumatic rollers and rammers are employed for compaction?

And what about the value of D_c?[/color]

Lastly, all of this is from my intuition and thought. Maybe I am completely wrong and instead of having the backfill a pro-active role, the wall's behavior resembles a slab resting on an elastic foundation, and the soil has a mere re-active role, like I suggested in my previous post.

Or perhaps I should go for a Finite Element package. But, what use would the FEM be when I'm not fully understanding how the whole thing works in the first place?

And finally, given the risks involved, [COLOR=blue yellow]what would you do if you were in my shoes? Would you go ahead and apply this system in larger tanks (R > 15m, H > 3m) or would you stop here and stay under the pseudo-safe umbrella of tanks with R [&le;] 15m, H [&le;] 3m ?[/color] A sincere answer, based on experience, will be highly appreciated.

Thanks for reading !

 

[fattdad]

Whatever happened to the "keep it simple" request? I would consider compaction surcharge as a design stress that's transient. I would not consider it for the long-term performance of the structure.

I'm not a structural engineer and don't want to even try to give you advice on the use of reinforcing steel and to what extent you need the rebar to take-up stresses that the soil can't provide.

You need a safety factor greater than 1.

f-d

¡papá gordo ain’t no madre flaca!

 

[oneintheeye]

right i design water retaining tanks etc. on I would say a weekly to bi weekly basis. Never ever rely on the backfill soil to 'reduce' the hoop tension or moments in the tank wall from the fluid pressure. Two cases 1) tank full no backfill 2) tank empty backfill. Youve just said that is what the code says! UK code same and clear. DONT RELY ON BACKFILL, TELL YOUR BOSS!

 

[oneintheeye]

you also state precast panels cannot resist the forces, why? I have seen elevated precast tanks i.e. no backfill. Why use precast if they are not suitable for your size of tank? I'm sorry i can't emphasize enough how ridicolous relying on backfill to conteract forces from the full tank seems to me.

 

[oneintheeye]

oh and also the 'worst case' will not be empty tank and backfill as you state as the tank wall will act like a big compression ring and if you try crushing a ring you'll see it is very strong. Can post a equation for compression resistance of circular tank wall on tuesday when I get back to work, but mostly I don't even bother checking it except in exceptional circumstances.

 

[fa2070]

Hello,

Thanks again for taking the time to read and respond to my posts.
First of all let me say that I agree with both of you.

@fattdad:
There's very little I can do to keep things simple. I didn't invent this system. It's been in use for 6 decades for small tanks. My bosses want me to embrace, extend and apply it in larger-capacity reservoirs. However I won't do it blindly. The system simply doesn't scale. My calculations and gut feeling point in that direction. I already explained it to them a few times, in a very diplomatic way. I also suggested the development of a post-tensioned tank, an age-old technique that's proven highly successful. That way backfill won't be a concern anymore. However, they're not fully convinced yet despite the overwhelming number of post-tensioned tanks in service today.
Your insights, fattdad, have been invaluable to me.


@herewegothen

DONT RELY ON BACKFILL, TELL YOUR BOSS!

I tried, believe me, I tried.

you also state precast panels cannot resist the forces, why? I have seen elevated precast tanks i.e. no backfill. Why use precast if they are not suitable for your size of tank? I'm sorry i can't emphasize enough how ridicolous relying on backfill to conteract forces from the full tank seems to me.

All the elevated tanks I've seen are small (R < 5 ft.), and so are the hoop forces. They're are a [&fnof;]_unction(pressure, radius). Not a big deal in elevated tanks, like I said. Bigger tanks are a different beast. Let's do this quick exercise:
For R = 15 mts. (50 ft.), and, say, Height = 4 mts. (13 ft.), how do you put the steel bars needed to resist the hoop tension in a concrete section that's 4 in. in the thickest part ?. No sanitary coefficient (1.65) or load factor (1.7). No backfill either. Just the real service load. I see no way of fitting the required steel bars in this concrete section.

And yes, relying on backfill is not very wise, but... that what's there is !!

oh and also the 'worst case' will not be empty tank and backfill as you state as the tank wall will act like a big compression ring and if you try crushing a ring you'll see it is very strong. Can post a equation for compression resistance of circular tank wall on tuesday when I get back to work, but mostly I don't even bother checking it except in exceptional circumstances.

Yes, I'll really appreciate if you post the equation for compression resistance of a circular wall. I don't know, but I guess it must be directly proportional to the height of the wall and inversely proportional to the radius. You know, as the radius grows, the wall pretty much starts behaving like a "flat" slab and the cooperative "shape factor" diminishes.

Thanks !!

 

[oneintheeye]

here the equation i was speaking (or typing) about. Concrete compressive stress = External pressure at depth H * diameter of tank, divided by 2[wall thickness+(modular ratio -1)* area of steel]. sorry in the way i've displayed equation I hope its clear. Not sure how this relates to codes as its from an old book based on permisisable stress design but the theory should hold up for you to prove that the tank is adequate.

On your sketch and question on steel I would say that your wall isn't thick enough for the application. As a starting point I take 100mm thickness for each 1m height and refine downwards from there (should get thinner). I understand that the ACI over with you specifies tanks over 10ft (3m ish) should have minimum 12 in thickness. If you increase your area for 4m deep tank you should comfortably get reinfocement in. Say 300mm thick, max ring tension (for fixed base) say 109kn ish, you would be on minimum steel to control cracking. Bear in mind these are very rushed knocked out figures and conservatively on allowable stress of < 130n/mm2 to keep cracking <0.2mm rather than direct crack width checking and is based on UK code! You will need to factor the load accordingly for strength checks but keep to unfactored for crack control checks. I have design book here given various tables and quite basic but useful guide, it s called Circular Concrete tanks without prestressing and I believe is from portland cement association. Address is in Illinois, Phone 708/966-6200 which means nothing to me as I'm not from US.

I am curious as to how your bosses can justify using backfill if your codes states against it?

 

[oneintheeye]

how you get on with this after? you could possibly design as a vertical ribbed slab as an alternative if for some reason you need to use the ribbed profile. doone this before on square tanks undet certain conditions I.e. no fixity at corners. not sure if it could be adapted for circular. I only used this when I was desperate for space not sure it should be used as 'standard'.