Absolute-Relative settlements under 10m¦ vs. 100m¦ spread foundation? 2

[drile007]

Is it true, that the absolute settlements under the 100m² are larger than under 10m² spread foundations? I assume that the bearing pressure is equal under both foundations! What about relative settlements? I think they are smaller under 100m² spread foundations. Am I right?

PS: I hope that I use the right words (large-big, small-less than, etc.). I’ll be glad if someone will correct me.

Drile007

 

[fattdad]

If a larger foundation is loaded to the same bearing pressure as a smaller foundation and the soil characteristics are equal for both conditions, the larger foundation will settle more. The "seat of settlement" is greater for the larger footing (i.e., the stress increase with depth is greater). For the case that you are evaluating settlement on the basis of elastic compression, it's easy to visualize that the integril of the stress distrubution will be greater for the larger footing.

Hope this helps.

f-d

¡papá gordo ain’t no madre flaca!

 

[msucog]

exactly. this topic usually generates a big surprise to non-geotech folks when you relate the idea back to large areas of new soil fill. in a sense, you think of the fill as one big footing so the settlement is usually significant over the short term after it's placed.

 

[drile007]

Thanks Fattdad & msucog, but may I continue with real example:

We have a building which total weight is F and we have an option to transfer this weight either on two foundation systems:
A) Number of pad foundation (np=10...number of pad foundation, a=10m² area of one pad foundation)
B) One large raft foundation (nr=1...number of raft foundation, A=100m² area of raft foundation).
If we calculate the stresses under foundations, we see that they are 10 times smaller under the raft than under each pad foundation. OK, that’s clear, but which system will have smaller settlements? Stresses under the raft are 10 times smaller, but as Fattdad said, there is a big influence of stress increase with depth? I think this influence is not of factor 10? How big is it?


Drile007

 

[hokie66]

"OK, that's clear". As mud, maybe.

10 x 10 = 100, same area, same stress, same settlement.

 

[drile007]

10 x 10 = 100, same area, same stress, same settlement.

I'm afraid that's not true. My thought was the same but...
Hope someone will reply to my previous doubt: the influence factor is...

Thanks in advance


Drile007

 

[hokie66]

Would be interested to know what you think is not true about my statement. You said the stress under the raft was 1/10 of that under the footings, but if the total load is the same and the area is the same, the stress is the same.

 

[drile007]

Read the fattdad reply!

 

[hokie66]

Yes, I did, and I agree completely with him, but according to your example, you have just divided the 100 m2 raft under your building (I assume the building has not changed in size) into 10 section of footing each 10m2, so the area is the same. If you meant that a 1000 m2 vs 10 x 10 m2, then I at least understand your question.

 

[drile007]

If I understand fattdad right, there is a big difference between ten 10m² and one 100m² footing. It's different if you put those ten 10m² footings one by one or you separate them far away from each other. If they are closed together each one has impact to his neighbour. And this impact is summing! If they are far away this impact will disappear.
And the consequence is:

The stress increase with depth is greater

Maybe I'm wrong? That's my doubt: the influence is not of factor 10? How big is it?

 

[fattdad]

Given a building of a fixed mass (weight) - let's say 156 tons and it's supported by 10, 10-ft square footings, that results in a bearing stress of 3,000 psf for each footing.

If you then attempt to support that by one 33 ft square footing you'd have the same reaction. Bearing in mind that you'd have a lot of building spilling over the edge of the footing.

Bousinesq would show that the stress distribution immediately below each footing will be 3,000 psf. However, the stress distrubution at depths of 10, 20, 30, 40, and 50 ft will be very different.

If you have similar soil conditions, you will experience more settlement below the larger footing. That's a big IF! More typically, you will have hyperbolic modulus relationships where the elastic modulus will increase with depth. This may all equal out - don't know. Then again, you may have bedrock at the depth of 20 ft. If so, 100 percent of the seat of settlement for the smaller footings will be in the soil zone as opposed to the larger footing.

Unfortunatly, sometimes these answers require calculation and there's no general answer. . . .

Hope this helps.

f-d

¡papá gordo ain’t no madre flaca!

 

[drile007]

Thank you Fattdad...you help me to view this problem from different perspective.

 

[fattdad]

I really need to add a comment to my earlier reply: Much of this really depends on the bay spacing of the structure. You can only consider attenuation of load with depth if there is no overlap of stress from adjacent footings. If the footings are too close together, the seat of settlement is affected by multiple loads.

f-d

¡papá gordo ain’t no madre flaca!

 

[BigH]

Fattdad has explained it okay. Suggest you get a intro soils book and do a few examples - say a single footing of 3m by 3m and determine the stress distribution and then estimate settlement. Then take two 3m by 3m footings and place them 6 m apart and see if there is any overlapping of stress bulbs (use 10% isochrone). Then put the footings 3 m apart and see again, then 1.5 m apart, 0.5 m apart and then touching. See how the pressure bulbs will increase the stresses under a footing due to its neighbour. Then take a single 30m by 30m footing and determine the stress distribution with depth. Compare it to the smaller footing - see how the bigger footing goes significantly deeper. If one has a thoroughly uniform medium to infinitum, you can see how the settlements would compare. Now, though, as fattdad said, what if you have a stronger layer 5 m down - or 10 m or 15 m down. Settlements are affected signficantly for those cases where the pressure bulbs are "cut" by the stronger layer - you will need to go to 2-layer or even 3-layer theories for working out stresses.

The above is "good" for elastic settlements (granular - or immediate settlements of clay) - but, there is also a problem of consolidation settlement - again, you need, even more so, to know the actual stress distribution under your footing (large or small) and also the overconsolidation behaviour of the stratum with depth - to determine settlements in these cases.

There are many variables - and I think that if you sit down one evening and do a few scenarios like indicated above, using a calculator, bousinesque charts, graph paper, engineers scale (hopefully you know what it is) and pencil, you will gain a lot better appreciation of what has been explained above.

 

[drile007]

Thanks (again) guys, but I'm wondering now what are the Pros/Cons between pad and raft foundation (if the soil conditions are uniform and the distances between pad foundations are big):
Pad:
[tab]Pros: absolute settlements are smaller; the stress/capacity ratio is higher; their area is smaller, so they are cheaper
[tab]Cons: relative settlements are bigger (between pads) and the consequence is aditional "load" on the structure
Raft:
[tab]Pros: relative settlements are smaller, so there is no danger for the structure above the foundations
[tab]Cons: absolute settlements are bigger; the stress/capacity ratio is small; they are huge and consequently more expensive
Am I right?