mat foundation using finite element analysis

[monchie]

Hello,

I'm new to the forum.My question is regarding mat foundation. Normally, we design mat foundation(w/ regular column spacing/grid) using the conventional method(assumed as "rigid", steps to be taken are; finding the resultant force"R" and its center of gravity etc. and its required depth is based on punching shear, and check that the max bearing pressure on corner points are below the allowable bearing pressure).

Now with the advent of finite element methods and instead of soil bearing capacity, subgrade of soil modulus("k") are the necessary input to model the interaction of mat and the soil. I believe that this finite element method is very useful in modelling irregular slab, but to be honest I am having a hard time interpreting the result!The ff. are my questions;

1. How do we get a "feel" for the value of "k"(subgrade modulus). Normally, we are used to soil bearing capacity and we are happy if our structure(ie,3 to 5 story bldg) were sitting on adequate ground(even with our eyes closed, 150 to 200 kPa is sufficient enough).

2. Is there any guidelines on mat foundations being analyzed on finite element analysis?

- How to check the depth of mat foundation?
(How do you know that the assumed depth is right based on the result of finite element analysis?)
- What's the limit for deflection?

I am firmly believe that this forum have numerous members who can address my questions(by the way, I used ROBOT Millenium in Finite Element Analysis).


Regards,

 

[ishvaaag]

I first encountered the modulus of subgrade reaction in 2 books, one by Fructuoso Mañá and another by Albert Fuentes. Mañá was classical in his exposition (even if I knew of him -indirectly, he never was my teacher, such rules of thumb such for edge footings take 1.5 times area of centered, for corner 2.5 times!) and then Fuentes gave a simple rule for k of the soils:

0.5 kgf/cm^3 for bad soils
4 kgf/cm^3 for soils of allowable pressure 2 kgf/cm^2
12 kgf/cm^3 for very good soils.

This venue proved more useful along my practice, taking such values uncorrected (against most recommendations, thar recommend to correct the k values if k30 on 1 ft of side footing), i.e., uncorrected, I have found to give better probabilistic prediction of the behaviour in most soils that once corrected. This point is important because when looking after serviceability on the viewpoint of deflection we are looking for solicitations concomitant with movements actually expected, and not much overconservative predictions of the same; so, recapitulating, no much overconservative prediction of the settlement must be introduced in the serviceability checks, nor by their own interest (influence of deformation in damage) nor through their influence in strength (for overprediction of the settlements would incurr in unbearable structural expense by the standard of the whole of the traditional practice). Just as an example, you may well obtain 2 cm settlement in one way and 20 cm if believing some much conservative prediction of settlement made by some geotechnical people -this I have seen- and anyone can see that imparting the unrealistical settlement to the structure would be some catch 22 for any ordinary building in ordinary soils.

In any case, even if there is some variation in the design from taking one reasonable value or another for k, the variations are not that bigger for a range of k, and it is always a sound practice to take 3 values, central and extremes of k for making your structural design, what normally won't influence much the rebar pattern, except if the extremes differ too much and the layout of the structure is irregular and the loading somewhat impredictable, upon which case even more care needs to be taken.

Some ACI code directs to use differents k values for different parts of the mat, maybe another contributor can identify which (I don't practice here by ACI codes).

It is VERY important to remark that the use of the modulus of subgrade reaction as the dominant method for the design of the response of the foundations will prove one or another time risky and improcedent. Particularly near edges and corners it does not approach well the behaviour, and a foundation on elastic halfspace analysis if well tuned will give better approximation (and contrast); this is made readily these days with the help of ordinary FEM. For worrying cases, particularly clayey etc other considerations need be introduced.

Respect the limits to deformation, there are many published opinions and some code standardization; not bad at it is our Spain's Código Técnico de la Edificación when addressing Foundations that at least risks to set values.

http://www.codigotecnico.org/web/recursos/documentos/dbse/se4/030.html

In general terms, predicted distortions to L/200 between points distant L are surmised to cause controllable and repairable damage (the L/400 for deflection); whereas L/125 distortion (the L/250 of deflection) would be looking to major loss of serviceability and maybe unworthy repairment. But you need to be aware of that fragile masonries with hard mortars may start to show hairline cracks even at L/2000 deflections (L/1000 distortions).

 

[monchie]

Thanks for your informative reply ishvaaag. Correct me if i'm wrong regarding my interpretation to your comments;

1. According to you, it is a good practice to design mat foundation using finite element analysis using ,ie, 3 values for "k". So it means to say that you need to model your mat foundations three times(since you need to input 3 different "k" values).

Also, I know for a fact that there's no direct co-relation between "k" values and soil bearing capacity because they are separate soil properties.But what I don't understand why do we need to use different values of "k"?(Is it tantamount of using 3 different soil bearing capacities?,ie, 150 kPa, 180 kPa & 200 kPa to your mat ?)


2. Also, it seems to me regarding allowable deflections that you favor L/400(is there any guidelines for this?eurocode?).If there's an existing guidelines for this(limiting deflection), that's might as well be the basis for defining the depth of the mat foundation( the thicker the mat the lesser the deflection etc,)

Again, thanks for your input.

 

[ishvaaag]

Respect point 1 certainly using 3 k values, hence 3 k designs is more a convenience of information than a must. It mainly serves you to ensure something significant of the behaviour is not escaping you, normally it won't be the case and maybe we are only talking of some more length of rebar, and not more.

It also depends on how easily you design the variations. In Spain the more common structural design software, CYPECAD, makes it just with the change of the k, hence it is not much deal to establish the comparison. In fact, with these programs it is common to create a model or more to just design the foundation since the column loads convenient to its design are different on account of allowed live load reductions than for the design of floors, and given the unique reinforcement pattern produced that would affect overconservatively to the design of the mat if a separate model is not made.

Respect the second point take it as what retained over 3 decades perusing the literature I have got about the subject, that I have seen to correlate well with the behaviour in the field. Anyway, what practical at the present moment is to look to the remarks in the applicable code, or if not, find substitute one, and then ensure you are complying. I would say that for any even midrise building I without doubt will include by now an exam of the building on the elastic halfspace, because this is much more informative of the actual pattern of (at least elastic) deformation, and how it is going to affect to neignbouring buildings (in our towns it is still common to make one building attached to the other, with no provision against seismic hammering, here fortunately till now quite uncommon).

Respect basis of what the code says, of course there is, always made in succesive committees perfecting the thing; and in fact eurocodes themselves make a point of it in one of their first volumes.

The code guidelines are also continuously changing, and CTE has taken lately a path of harmonization on the calculation of deflections with other european practice. Previously our standards on steel deflection were more stringent, now less; just to make steel more marketeable, I think.

I refer you to the article

Serviceability Limit States under Wind Load
Lawrence G. Griffis
NSCC Proceedings 1994


that is between the finest info in deflection effects given that I have and from which the following attached table is taken

 

[ishvaaag]

I extract from the

Guide to Implementation of Eurocodes

the attached table. On deflections we are always talking around similar limits, or at least so seems to one that has read more or less what I have. Fortunately with the expansion of computing we are better endowed to check deflections each day and we will be falling less and less in these problems in the coming years.

in the table wtot (deflection from initial center of beam line) is the same than wmax except that wmax deduces any camber when present.

 

[JoshPlumSE]

Monchie -

Question #1: modulus of subgrade reaction:
The best way to get an accurate value for the modulus of subgrade reaction is to get it from a Geotech report. In fact, when you are contracting with a Geotech firm it is a good idea to put that into the written contract. In my experience they tend to hem and haw a bit before giving you the value. Probably because the assumption with the modulus of subgrade reaction is that it is a linear stiffness and soils are always non-linear. But, there are standard ways of measuring it that they can give you.... So, they will eventually give it to you.

Question #2: Guidelines for FEM analysis of Foundations:
There are some references that might be useful. For Foundation design in general, I like Bowles book, "Foundation Analysis and Design". This book actually has some decent values listed for estimating modulus of subgrade reaction as well.

The other reference I tend to use is a ACI report: "336.2$-88 Suggested Analysis and Design Procedures for Combined Footing and Mats".

Shameless Plug:
I actually work for a company that writes a Foundation Analysis and design package (RISAFoundation). So, I would tend to recommend a package like this. It's not explicitly necessary, of course. It's more a matter of saving you time an energy with the model and the results interpretation.

If you're interested at all, you can download a free demo. It's a fully working program. We just restrict you to using a very weak grade of steel and concrete.

http://www.risatech.com/p_risafoundation.html

2. Is there any guidelines on mat foundations being analyzed on finite element analysis? - How to check the depth of mat foundation? (How do you know that the assumed depth is right based on the result of finite element analysis?) - What's the limit for deflection? I am firmly believe that this forum have numerous members who can address my questions(by the way, I used ROBOT Millenium in Finite Element Analysis).

 

[JoshPlumSE]

Ooops.... Please ignore that that paragraph from my post. That was not supposed to be in my response. I just copied a portion of the original post so that I could read it as I typed my response.

Also, the ACI report is actually: 336.2R-88, not 336.2$-88..... I must not be fully functional yet this morning. Where's my coffee?

 

[monchie]

@ishvaag - basically the attached table you sent is for typical rc elements for limiting deflections, I am just wondering if ever that we have a better guidelines regarding deflections of rc beams/mat foundation on elastic foundation/soil.

@joshplum - thanks for your reply. I agree with you that it is the job of the geotechnical engineer to provide the value of "k". But in our prelim. designs , we need to have at least a value of "k"(by our own estimate) to proceed with the initial designs of foundation.

 

[ishvaaag]

You have them as per the standing current code in Spain, CTE, specific for foundations, in the first link I gave:

http://www.codigotecnico.org/web/recursos/documentos/dbse/se4/030.html

See section 2.4.3. Maybe you can translate it to english with google language tools or other. There the restrictions are given as a function of distortion between settled points.

See attached image.

You see the limits are quite stringent, since the generic statement of distortion of L/500 point to point for most common structures is what would be one L/1000 when translated to deflection. This means that the code wants that additively the settlements at foundations have limited impact on what deflection itself in the floors above is causing. Not a moot issue since really many of the times the significant cracks observed in the buildings are originated as much by the dishing action of the building weighing on the soil as the general or local weakness of the structure.

Anyway my giving the other references it is because damage on construction as related to geometrical deformation is irrespective of cause and structural material: the same deformation on the same non-structural parts (that use to be those that show the problems of concern, except maybe structural masonry) will cause akin damage be it steel or concrete structure, caused by lateral or gravity etc.