Load spread under footings

[ashjun]

Hi ya,
A small question that I have been asked.
In routine consolidation analysis, the load spread under a shallow foundation can be taken as varying from 30 to 45 degrees. This is used to compute additional stresses induced within the clay due to the superstructure.

I have been asked why 30 to 45?..I feel this question might have been addressed before (which unfortunately I have been unable to locate).

In relation to the above, does the angle depend upon the type of soil or just the footing? Loose the soil, less is the angle of dispersion of the load?

Would someone also guide me to the relevant literature?

Thanks very much!

 

[cap4000]

This is a popular issue in this forum. Basically depending
on the type of footing and the soils you will get varing distributions. 30 to 45 degrees is a good rule of thumb. Get a hold of any Foundation Engineering Book by either Das, Cernica, or Bowles. You need to look at the pressure distributions isobars that occur under footings. On excavation details I have always seen the following: With crushed stone under the footings the distribution angle is 26.5 degrees + or -. With compacted fill its about 45 degrees. This is just my experience and I cannot explain the technical differences. Not following these basic values may lead to a soil failure, as the bearing pressure will push out the soil sideways. Good Luck.

 

[Focht3]

The pressure bulbs have to do with closed form elastic half-space models originally developed by Boussinesq, and later modified by Westergaard. The 30&[ignore]deg[/ignore]; or 2:1 slope comes from observations made of the Westergaard charts.

The choice of 30&[ignore]deg[/ignore]; or 45&[ignore]deg[/ignore]; depends on what you are trying to solve. If you are looking at stress overlap, then it is common to use the more punitive (i.e. "conservative&quot angle. If you are looking at settlement, though, the answer is usually 30&[ignore]deg[/ignore]; or 2:1 (V:H) slope (which is the same distribution.)



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[BigH]

Focht3 is correct (although I think that 2:1 is 26.5deg which is quoted by cap4000). This is a standard way in uniform soils for estimating the soil pressures - but it gives a "uniform" pressure across the width and Westergaard shows a non-uniform pressure - but difference isn't much. I point out, though, that if you have two layer or multiple layer systems, then there are changes to the simple spread of pressures depending on the modulii values of the various layers. For cap4000 spread through crushed stone, say to a lower sandy or clayey soil, I would think that the spread will be "wider" than his 26.5deg as the crushed stone is likely significantly stiffer. Compacted fill is likely in similar range as underlying soil unless firm or less in cohesive - then the spread could be maintained at 2V:1H. You can check out Polous and Davis Elastic Solutions for Soil and Rock for distributions of multi-layer half-space. If you are in India, Dr. N. Som's book (of Javadpur University) covers the topic quite nicely.

 

[ashjun]

Thanks guys I appreciate all your help.

I am still unclear about one thing:
sands- is it appropriate to use load dispersion of 30 degrees in loose sands and 45 degrees in medium to medium dense sands?
Likewise, in clays how about the affect of void ratio?

Regards

 

[Focht3]

Void ratio doesn't come into play for clays. And the "dispersion angle" chosen will depend on what you are evaluating. If it's settlement of the soil under increased load, I'd use multiple angles (say, 25&[ignore]deg[/ignore];, 30&[ignore]deg[/ignore];, 35&[ignore]deg[/ignore]; 40&[ignore]deg[/ignore];, and 45&[ignore]deg[/ignore] and plot calculated settlement versus assumed dispersion angle. This will also give you a good feel for the sensitivity of the analytical results to your assumptions.

Please share your analytical results with the group -



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[BigH]

Why don't you just use the Bousinesque charts and get the "actual" pressures - not that much harder. The sensitivity analysis is a good idea - I use it on slope stability problems - but haven't done as pressure spread - a lot depends on the layering of the soils, their relative stiffnesses, etc.

 

[ashjun]

Thank you.
Focht3:
This was not a part of any project, but a question in general. Once I come across any similar works, I shall update on this forum.

Yes, estimating the sensitivity of the results due to the angle of load dispersion is a good idea. Will follow on that.

I conclude that there is no "correct" assumption of this dispersion angle and it is mainly dependent on the engineer's judgement or at his fancy.

Regards

 

[Focht3]

And the precedent of prior use...

My "sensitivity analysis" was intended as much as a teaching tool as anything. And by that I mean "self teaching" - if you get conflicting recommendations, run the analyses in a way that helps you see how sensitive the final answer is to a given assumption. Then you can decide whether the worry was worth all the effort -






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