intersecting foundation beams

[Mccoy]

Hi all, a more relevant topic after the snow olympics:
This foundation model (beams make up a grid with loads on nodal points spaced usually about 5-6 meters apart) is used in the 95% of cases in the seismic area where I work for shallow foundations.
But it creates calculation problems which have been grating me for some time.
Strucuralists will verify the foundation to (immediate) settlements by a Winkler model. Yet regulations require a bearing capacity verification which, as far as I know, does not exists in literature for this model. To say nothing of consolidation settlements in clays.
Treat it as a continuos beam? Mmmmm, far from realistic, costraints are many, degrees of freedom few, even at the angles. Treat it as a continuos slab? May be if rigid enough? but I have doubts that the soil underneath, for such spacing between beams, may behave as a single element and create single failure surfaces instead of many of them underneath each single beam.
Even usual settlements models will fail because of the nodal constraints, may be FEM? But this would be a costly choice and impossible to follow in practice because of lack of collaboration with the structuralist (the no-meddling philosophy).
I read Poulos and Davis used some codes based on intersecting strip model, but there you necessarily have to input structural data (such as beams inertia).
I wonder if, in your opinion, there is a classic geotechnical model better suited to the intersecting beams prob, and what you would do if asked to verify bearing capacity + settlement of such a foundation, and if there is some dedicated code (aside from winkler-based), where you can enter, from example, assumed and "typical" structural data (I can get "training" by structural engineers) and have a reasonable output which you can feed to the structuralist.
Sometimes I wonder if such a foundation may ever fail by soil rupture.

 

[Mccoy]

An insight which occurred to me after starting this thread: I can only think of the collapse of such a foundation as a whole, similar to a continuos slab. How can single beams reach the large values of movement necessary to collapse if they are so strictly constrained?

As to settlements, analysis based on single beams may still be valid, with a condition:

total beam settlement = (immediate + consolidation) beam settlements <= allowable maximum settlement (due to beams constraint).

The settlement calculated by the usual means would be an upper bound value (max value).

If we see the foundation as a whole, usual total settlements analysis would still stand true, reasonably assuming lack of constaints because continuos beams are settling themselves (assuming soil lateral homogeneity).

I would be very interested in hearing your opinions about the above reasonings

 

[VAD]

Mccoy:

For the problem cited experience and judgement are perhaps the only approach to providing answers. Assumptions have to be made and these are based on what one considers best fits the existing conditions. For bearing capacity one can use the concept that the nodal loads are distribted uniformly over the area of the foundation and the allowable soil bearing capacity should not be exceeded by the pressure/stress imposed of the foundation.

If loads are treated as localized and there are overstressed locations then differential immediate settlement results but this can be offset by the fact that the foundation is rigidly tied together. Here the beam stiffness etc comes into the equation. Treatment here invokes structural principles - moment distribution etc.

Increased stiffness would result in smaller deflections etc. Design of beams is also often based on upward pressure of soil on the member

The other aspect is the differential settlement caused by consolidation. If this is excessive The tolerable maximum permisssible deflection of the structure has to be addressed. This often dictates the choice of foundation type. Reinforecment and size of connecting beams are dictated by the need to prevent their structural failure. Plastic collapsevia hinges are assumed for upper bound.

This is a complex topic and in my opinion requires the geotech and structural engineer to work together. However, structural engineers more than often undertake the structure design and use models that are based on elatic principles generally. If this is the case then as a geotech only the magnitude of the consolidation settlement issue and providing the safe bearing capacity are all that the structural engineer wishes. The upperbound approach you have stated for settlement would be the only desirable.

There are few references you may wish to review if you consider in undertaking the foundation design -geotec and structural. These are:

Foundation Analysis by RF Scott

Soil Mechanics and Foundations by J.V Parcher and R.F Means.

Design and construction of Foundations by Manning,G.P

Just as a parting thought as I have mentioned in other threads, complete design of foundations by the geotechnical engineer is what I consider the ultimate. Unfortunately, this is hardly ever broached in the geotechnical program in Universities. The structural engineer (not all), on the other hand, often lacks the basic geotech knowledge but relies on computer programs to provide the answers.

Very often you would find that you are asked for specific information. It would be a great day when a truly Foundation Engineering course can be established and when both structural and geotechnical profs can collaborate in teachning what we have to face in the real world. I once asked this question during graduate work and was told that there was not sufficient time in University for this and you can learn that outside. Yeah right.

In closing, I think your thought process is sound and that it is not far different from the approach taken by others.

 

[Mccoy]

VAD,
it really occurred many times to me to buy some specific software and do the foundation grid analysis myself, after some appropriate training.
Alas, here in Italy, as apparently everywhere else, the separation between geotech and structural is strong.
I could only do such a thing where the structuralist is a friend of mine, and free of charge!

 

[BigH]

Mccoy - this sounds like a grillage foundation to me. If you look in Tomlinson's Foundation book - he talks about closely spaced foundations and intersection pressure bulbs. That is how I would go about settlement - if the grillages are closely spaced, draw them up and determine the stress distribution in the layer due to a single grillage and adjacent ones. If the spacing is 'far' apart, the settlement would be controlled by the single footing settlement. As for bearing capacity - the grillages do act as a mat so I would, at first glance, look at the whole as a single rigid mat/footing. May not be 'elegant' but I am of the opinion that this is a reasonable approach. A friend of mine was involved with a project near Philadelphia where they found 'voids' in the rock and had to assume the loss of an 'intersecting node' in their structural analysis - beam over a void.

 

[fndn]

The following link and the associated website discusses this topic:

http://geotechnic.ucsd.edu/se243/

It feels good to join this distinguished group of geotechs!

 

[Mccoy]

fndn,
thanks for the link. Is it the "flexible beam on elastic foundation?"

I may have missed some URLs because my browser didn't find a required plugin.

I elaborated further on the subject.
BigH, I couldn't find it in the Tomlinson, I have the 1st edition, only reinforced slab in there.
So far I reached the following conclusions:
1) the grillage may be verified as single beams or equivalent footings, only, for that a few assumptions must verify: infinitely rigid beams, hence uniform loading, perfectly homogeneous subsoil, homogeneous distribution of seismic stresses. In this pretty unlikely event, there will be no constraints at nodal points since the beams all move down together in failure.
2) the grillage may be verified as a single slab, only arching is not likely with the usual 4 to 5 meters distance between beams axes. Usually verifying as a continuos mat tends to satisfy limit states much more easily, except possibly when deeper compressible layers exist, or when foundation lays at the edge of a slope (small-width beams are not influenced by sloping, whereas large-width mat is).
3) the most conservative case of course is number 1) above, but I would calculate the mat model as well if unfavourable soil conditions at depth or adjacent slopes exist.
4) Settlements are better veryfied as BigH suggests. There usually is no overlap but for the smallest stress surfaces, far away from foundation base.
5) I wonder if there are any small-scale experiments of grillage failure illustrated in the literature.
6) The only lab tests I know about involved parallel beams, and results obtained by two independent studies did not agree.

BigH, is your "preferred" e-mail still the same, or should I answer to the latest address?

 

[BigH]

My bigfoot address is always good - the four letter one starting with 'i' is also good. I have Tomlinson's 6th or 7th - I'll find it and send. I suppose you could model the grillage by turning it over and thinking of it as a stiffened slab - but a question is why, when it is pretty obvious do you need to 'verify' bearing capacity when, under limiting settlements, it is 90% ALWAYS settlement that governs the bearing pressures that can be used. Seems like a bureaucratic obligation of little to no real use.

 

[Mccoy]

Seems like a bureaucratic obligation of little to no real use.

Actually, both American LRFD and European LSD stress the bearing capacity aspect, even if we all know that, as far as shallow foundations go, settlements tend to govern the calcs.
The justification to such apparently questionable overrating of bearing capacity is that plastic failure entails catastrophic collapse with casualties, fatalities and substantial economic damage, whereas failure of serviceability (excessive settlement) entails usually mere economic damage, not overly serious.
And, on top of that, in seismic conditions load inclination due to base shear severely impairs the bearing capacity.

Howard, I'll appreciate your sending the relevant Tomlinson pages, this topic is of immediate practical interest to me and to Italian colleagues.

 

[BigH]

Aye they (probably) do. And do they stress isolated foundation bearing capacity - or do they ask for/require adjacent footing bearing capacity to be included. I can see where you have adjacent footings where each will impact the "zone" of interest - acting as surcharge on part of the passive outer parts - yet I have not seen any formulations taking into account aspects of "partial" surcharge - it is assumed "D" = surcharge and it is uniform. ??

 

[fndn]

Mccoy;

Yes, I should have mentioned in the last post, there is pdf file on "beams on elastic foundations". This is my train of thought; In the geotechnical aspects-If the footings have length to width ratio of less than 5, I normally treat it as continuous footing and then check for bearing, settlement and stress overlaps. For settlement, I take the footing with the largest LL/DL ratio and use that computed allowable bearing for all the other footings. If L/B ratio is between 1 and 5, I treat is a rectangular shaped footing and do the same clacs.

Rarely are we asked to do the structural design-if so I use"Structural Concrete Text" by N.M. Hassoun. I have the 2nd edition which came with a downloadable small files so that by entering the footing dimensions and structural strengths, I get a quick output. In your case, If the loadings are at the intersections, I would approach it as a strap footing and if loadings are like a wall footing design it as a "grade beam".

 

[Mccoy]

Sorry I'm answering after 10 days.



BigH,
No, regulations do not include effect of adjacent foundations nor similar surcharge situations (lean concrete layers, and so on). Sure, this is another factor in grids. Potential failure surfaces under inner beam members have that additional surcharge/resistance to cope with. That's one more point in favour of block failure, two more points actually since you also point out that failure must be non-rotational, given the constraints.

Only reference by Eurocodes to grid foundations is that sliding analysis must be done assuming an "equivalent footing". That's all.

Thanks for the Tomlinson references, as a matter of fact a grillage is defined by him as a foundation structure reinforced by steel girders in a double level configuration.

The Kurian material is also interesting, He mentions about studies (small scale models?) by which the coverage threshold for rigid/slab behaviour and grid behaviour is defined at 75%. But He focuses on the structural, rather than the geotechnical aspect.

Your story was great reading, how about the Irian Jaya South-North highway I heard Indonesian goverment was planning?

I remember a single Indonesian word, the one a woman in the guest house I was staying pronounced when I gave her most of the durian (tropical fruit) I was eating (I stopped after 2 morsels).
"Enak!" delicious! the locals love durian, the westerners maybe need some more time to get the habit to it.

fndn,
thanks for the link, some good presentations on piles p-y curves as well and more.