bearing capacity on a larger area

[jimzhang]

I recently ran into problems about calculating the bearing capacity in large areas like a landfill. The Terzaghi theory and all the others are based on footings on a small area (strip, square, etc). What is the appropriate way to calc the bearing capacity for a large area as a whole?

Also, there are only equations calculating the stress distribution in the ground under a load/stress that applies in a small area. How to find the stress distribution under a stress/load that (say evenly) applies to a very large area (like in a landfill)?

 

[fattdad]

For large areal fills you must look at settlement and slope stability. The term "bearing capacity" just doesn't relate to landfills no matter what the regulators require.

Just my opinion.

f-d

¡papá gordo ain’t no madre flaca!

 

[jimzhang]

I guess so. Bearing capacity theory only applied to footings in my opinion.

As to landfill, I am wondering the Settlement calc. If a height of waste (surcharge) is applied, should I assume this load will induce the same stress (unit weight x waste height)in the sugrade (no matter how deep it is)? Because Bousenesq's theory again applies to footings only. That stress may be used for consolidation calc. But How to get immediate settlement in landfill case?

These questions are all about applying load in a very large area, and the current theory seems to be all about footings.

 

[BigH]

Jimzhang - are you a bit out of your depth - you seem to "focu" on footings; yet to me and fatdad, you should be focusing on embankments. (and Bousinesq doesn't really just apply to footings - although that is how it is typically shown. Find Poulos and Davis' book on Elastic Solutions to Soil and Rock Mechanics (Wiley - 1974)for determining stresses beneath an embankment in an elastic medium. You are not quite clear as to whether you are placing "regular" fill onto a landfill or placing landfill. Basically, your fill becomes a wide embankment. Nevertheless, for the most part - except near the edges, you would be correct that the applied stress onto the foundation is the fill (regular type or landfill) density times the height of the fill. As in all elastic solutions - you have problems with determining realistic values of "Young's" Modulus - both for the foundation, landfill and new fill on landfill.
Why don't you google for articles on settlements of and in landfills? There are a number of papers I have seen that address this issue.
Now with landfills, you will also have to deal with long term (secondary) consolidations and also of settlements due to decay.

 

[jimzhang]

Thanks, and that is pretty good discussion. I thought about embankment too, however, it seems like an enlargened strip footing above ground level because it uses the parameter of embankment width to calc.

To make my questions clear, I made a simple problem: Say, an area of 3000ftx3000ft site with orinal soil of clay, (or silt, or sand), now apply a stress (say 10,000 psf)over the site (equal to placing fill on top), what will be way to find out the settlement and bearing capacity? Embankment looks different from this. And why can we ignore bearing capacity like Fattdad said? I think there should be theory to address them. But So far I have no luck to it..

 

[BigH]

Jimzhang - please toss the notion of bearing capacity out the door. IT IS NOT A BEARING CAPACITY PROBLEM. If you must, "worry" about slope stability at the edges of the fill (sort of like a bearing capacity if you wish the dwell on the notion (see Lambe and Whitman for their example of a very large tank on the foundation)). Your main issue would be settlement - a lot depends on the stratigraphy underlying the ground level. How thick are the various layers - where is rock (i.e., hard bottom). Consolidation theory for clay; elastic theory for sand. But question - if the "fill" is landfill, why are you worried about settlement anyway? You'll get more fill into the landfill if the base settles. If the fill is general fill, 10,000 psf is equivalent to some 80 to 100 ft of fill! (and slope stability of the edges would be important!) - sort of unreasonable and so thick that almost any footing you put on the fill will be of be minimally affected, in my view, by settlement of the underlying material. There will be a tendency of the fill to even out the settlements. Might be a bit different if you consider airport runways, though. (hope this is a real problem and not a university assignment!)

 

[jimzhang]

Unfornately, this is not a univ assignment. I have been doing the geotech analysis on a couple of landfills. It includes slope stability, bearing capacity, settlement, veneer stability, piping delfection, etc.....It is straightforward for all but bearing capacity and settlement to me. I sense that bearing capacity should not an issue, but I have to figure out a calc to show that to certain ppl, if you know what I mean. The settlement matters because liner system and piping will be placed on the subgrade/base. Differential settlement due to waste place above might lead to cracking and malfuntion of them. In my cae, the soils at one landfill are silt, clay, and glacial till for the other. The highest waste is about 250ft...Now the settlement calc needs the stress distribution caused by surcharge (landfilled waste) in underlying soil layers. So far, I assumed that the surcharge (waste heightxunit weight) is applied to all layers of soils for consolidation calc. And, As to immediate (elastic) settlemetn, From Foundation Analysis and Design by Bowels, all cohesionless soil and cohesive soil with saturaion <90% will have elastic settlement. If elastic theory used in such a large site, no equations for embankment/footing seems to apply. If using Young's modulus and Poission's ratio, what will be the affecting depth?...I think this is a very commom problem. But due to my lack of experience, I'd like to listen to the seasoned engineers. Thanks, BigH, you have been really a help on this.

 

[fattdad]

pertaining to landfills:

As the fill is applied, there is a change in the stresses in the clay. With this change in stress there is an increase in the undrained shear strength. When looking at large areal fills, the tendency is to do a "gravity turnon" type analysis, which won't work. You really need to look at the incremental addition of load.

Regarding the settlement, you can use Bousinesq to determine the increase of vertical stress with depth. However, as you will quickly realize it takes a great depth to show any real attenuation (i.e., the seat of settlement will go down several thousand feet). Because of this problem, you have to look at the soil modulus as a function of confining stress. The best way to do this is via the hyperbolic model. I would expect several feet of settlement will be realized by the liner system. Now you just have to consider the angular distortion and whether it exceeds the capacity of the liner.

Forget bearing capacity. Now that I said this, I also realize that the regulations are short sighted and written to require that you make some statement on the "bearing capacity". The "best" way to handle that is via slope stability, which is how the fundemental bearing capacity was determined in the first place (in my opinion).

This is truly a settlement/slope stability problem - now you just have to figure out how to repackage it to the regulators as a "bearing capacity" response.

f-d

¡papá gordo ain’t no madre flaca!

 

[BigH]

Package the bearing capacity issue as I indicated as per Lambe and Whitman's example of a large tank (chapter 32 of their book - look especially at Section 32.1) - this would show that common sense does not prevail. I recommend L&W's book to you - it has a lot of points that would be of interest (Lambe and Whitman, Soil Mechanics, Wiley, 1969 (1970 for SI version). Piping should be as flexible as possible. I would think that for the most part (except near the edges) the settlement of piping would be rather uniform from point to point. But at the edges you will need to be able to accomodate the lesser settlements under the edge slope and the central parts. In tank design we usually specify flexible connections of piping to the tanks.