lateral spread in soft soil overlying stiff soil layer 1

[microseismic]

In general the stress distribution below a footing spreads laterally at a 2V:1H ratio. I know that if the footing was resting on a soft layer of soil overlying a stiffer soil layer that the lateral spread would be greater than the 2V:1H generalization. Can anyone provide some numbers to the amount of lateral spread or can someone recommend a reference where I can read about the topic? Thank you in advance for your help.

 

[oldestguy]

Interesting question.

Why ask about "spreading the spread"? Are you calculating possible settlement? If so, reducing the spread will give you a safer result, so why risk it? What about shear bearing failure in soft stuff? That may control what you are working with.

Also, I'll bet others will question being so sure about that 2 to 1 figure and being so sure about it changing for soft soil.

If I had to guess, I'd say the reverse is true.

 

[fattdad]

I think Bousinesq's equation assumes a Poisson's ratio of 0.5. Westergaard may offer some layering affects. You'd have to go to the source derivations to see how to vary load spread via Poisson's Ratio. By the way, I consider the term "load spread" a simplified approach to the problem and I feel you are working on a complicated problem, which really does warrant the use of either Bousinesq or Westergaard equations. Your bigger issue (if you are working on compression is the proper assignment of soil modulus values.

f-d

¡papá gordo ain’t no madre flaca!

 

[microseismic]

First off thanks to everyone for the advice. This is a great forum that has loads of good advice.

Oldestguy: Sorry,I phrased my question wrong. What I meant to say is that it is generally accepted that the load spreads horizontally from a single edge of a strip footing at a rate of 2V:1H.

Fatdad: I will look into the Westergaard equations to see if they deal with varying layers of soil. I have been using Bousinesq's in the past but it would really be valuable if Westergaard provides this added advantage

What I was looking for is advice on how the combination of soil layers with extreme variations in stiffness affects the stress distribution below the layer. I remember reading a section of a book that describes this effect and seeing drawings depicting how the combination of layers effect the spread of the load. I can not remember the source of the information.

I had hope to provide this information to some of my coworkers who are working on a downdrag problem in soft clay underlain by a layer of sand which is underlain by another layer of soft clay. The neutral axis of the pile is located in the upper layer of soft clay. The pile is tipping in a sand layer. The settlement is calculated for the equivalent footing located at the neutral plan using a Bousinesq stress distribution. There is a lot of settlement predicted in the clay layer underlying the sand layer. I was wondering if the stress distribution would flatten out when it hit the sand layer thus reducing the stress in the underlying soft clay.

Thanks again everyone for taking the time to respond.

 

[ishvaaag]

Maybe the finite element method can be of help here. Make a layered model of the soils, a stack of layers and bore a hole to the proper depth. Extend the model to rock or some unaffected or uncompressible layer. Apply the loads you think will be standing to the cylindrical segments and the bottom. And the info it will give on the restrictions of the hypothesis will be good.

 

[iandig]

Tomlinson discusses a method of analysing foundations on a stiff soil overlying a soft layer, which is similar to what you are talking about, although reversed. (6th edition, page 132, figure 4.2 with associated equations).
He states that for square or circular foundations, the bearing pressure on the soft (lower layer), (q1) is equal to:
q1 = qn (B/(B + d))^2
or for strip footings:
q1 = qn (B / (B + d))
where B is the breadth of the foundation, qn is the bearing pressure from the foundations and d is the thickness of stiff soil(upper layer) below the base of the foundaiton above the soft layer (lower layer). This is based upon a 1:2 or 30º. I have also seen the french method of calculating working paltforms, where they use the angle of internal friction for granular layers to calcuate the corresponding 'footprint' of a loaded area on underlying layers of soil.
This does all seem to be based around a global poissons ratio of 0.5, although accroding to Tomlinson (trying to keep to the same reference here), only undrained clays have a v of 0.5, stiff undrained clays are in the order of 0.1 to 0.2, silt = 0.3, sands = 0.1 to 0.3 and rocks are around 0.2.
On the point of assessing the settlement to a layer which can be deemed to be 'relatively incompressible' Tomlinson also suggests limiting the effect of settlemnt analysis to where the applied vertical pressure reduces to less than 205 of the overburden pressure.

 

[BigH]

Soft over stiffer clays has been covered by many researchers - for bearing capacity - one can view Button (1953) or Srinivansin (1975?). These are noted in several textbooks. For determining the vertical (and other) stresses under a footing with two or more dissimilar materials, one would normally use elastic theory and the best source is Poulos and Davis' Elastic Solutions for Soil and Rock Mechanics. It is now downloadable from the net - I think if you go to Paul Mayne's site you can find it. I don't have th URL on hand at present as I am enjoying Hua Hin.

 

[ishvaaag]

The Poulos and Davis text downloadable as pdf

http://www.ce.ncsu.edu/usucger/PandD/PandD.htm

 

[microseismic]

Thanks for all the valuable information. iandig thanks for the valuable info. I will need some time to digest. Thanks for the link to Poulos and Davis This book is too expensive to purchase ($1000 on Amazon). I tried to give everyone a check for a valuable post but I did not do it in the correct order so it may have not worked properly.

 

[iandig]

Just noticed an important typo in my earlier response, it should be 20% not 205 of the overburden pressure. This works very well when you start looking at large slabs as the zone of inlfuence does reduce from around 3 of the width for a pad to significanlt less than that for larger, rigid slabs

 

[ishvaaag]

I attach 3 pdfs where 4 footings apply 3 kgf/cm2 to one 4 m thick soft sand layer over a gravel layer that is cut to fixity 10m in the gravel layer. The footings apply the loads at -2.5 m. The mesh is quite coarse, and the calculation elastic only. The interface in the boundary betwen layers proves to be a great divisor of behaviour. The soft layer takes the worse part.

 

[ishvaaag]

Just trying Autodesk Algor Simulation.

 

[ishvaaag]

And the third

 

[ishvaaag]

By whatever the reasons the last two pdfs do not open well. May try later again.

 

[ishvaaag]

Let's try again, minimum principal stress

 

[ishvaaag]

It seems was a matter of tildes in the names. Von Mises now