settlement beneath a column footing

[fattdad]

Consider an 8-by-8 column footing designed for 2,000 psf and a clay layer 5 to 20 ft below the footing. Run stress distribution beneath the center, edge and corner. Complete the settlement calculations for each stress distribution. You'll get three different results.

Here's my stress distribution (5, 10, 15 and 20 ft in psf):
below the corner: 440, 292, 184, 120
below the edge: 710, 373, 211, 131
below the center: 1170, 482, 243, 143

Knowing that the foundation can't deform to the calculated settlement profile, what is your approach to evaluating the foundation settlement? It's clearly conservative to design for the center stress distribution only. What if Pp-Po is 900 psf, would you really get virgin consolidation beneath the center only (I would doubt it)?

Here I am with my gray hair thinking of a half-dozen ways I could handle this, but would like to hear from others. . .

f-d



¡papá gordo ain’t no madre flaca!

 

[moe333]

I have always taken the center stress condition for a column footing. I typically would only look at edge and corner stress for slabs or mats that are more flexible. But technically, I guess you could take some weighted average of the three for the column, maybe 80/10/10 for center/corner/edge. As you say, if you are in the area of Pp, it could make a difference, so I would tend to be conservative in that case and use center stress. What about overlapping stresses from adjacent footings/floor slab loading?

 

[fattdad]

I've already accounted for industrial floor loads and for the purpose of this discussion, let's ignore it. I usually also take the center stress and run the numbers. But, I also know that this is conservative.

If we consider the footing to be rigid, the "actual" settlement cannot be what is calculated from the center stresses, as the tendency for this settlement to be realized would result in stress re-distribution toward the edge/corner. At some point the soil-structure interaction would normalize to one amount of settlement.

I would tend to agree that some weighted average would be appropropriate, but would be interested in knowing if someone uses this in practice and if it was a calculated method. I would tend to think that 80/10/10 would be a conservative approach, based on "feel". Is there something more refined?

Here is one thought - just attenuate the stresses at 1/2:1. This simplified approach does accomplish one goal, it makes the entire stress below the footing (i.e., within the 1/2:1 envelope) uniform. As a result you'd avoid some varying computation of settlement below the otherwise ridid footing.

f-d

¡papá gordo ain’t no madre flaca!

 

[BigH]

Tomlinson: "In the calculation of consolidation settlement we are concerned wiht the pressure distribution for a contact pressure which has a reasonable safety factor against shear failure of the soil. Also, it is impracticable to obtain complete rigidity in a normal foundation structure. Consequently the contact pressure distribution is intermediate between that of rigid and flexible foundations, and for all practicable purposes it is regarded as satisfactory to assume a uniform pressure distribution beneath the loaded area." If you do have a fully rigid footing, he goes on to say that the immediate settlement of a rigid foundation divided by immediate settlement at centre of flexible foundation = 0.8 approximately.

 

[oldestguy]

As approximate as the whole business is in estimating settlements, I have used a very simple method and never had any difficulty with being either too conservative or liberal in comparing to actual measured settlements (which by the way was seldom done in my jobs in the past). This apparently is the 1/2:1 method fattdad uses.

I take the width of the footing and add to it the depth to the given layer center as the dimensions of a square or rectangle which area is divided into the column load.

When structural engineers or others need to compute stresses at different depths below footings, I have given them this method and they thrive on it due to simplicity. It's not the 60 degree thing, but close. This would be for a case of a less compressible layer over a weaker one where some limiting maximum stress on the weak layer controls what the footing design pressure might be at the higher elevation.

My comps for the subject case came out at: 757, 395,242 and 163

For a commonly used settlement computation method on a simple computer program, I even covert rectangular footings into an equivalent area of a square footing. It usually is sufficiently in the "ball park" to be useful.

Then comes what do you do for a single pedestal water tower on a doughnut shaped footing. An equivalent square footing as plus and an interior square footing for minus numbers has been used for a rough idea for calculating average total settlement. But that does not help the structural guy wanting to know what happens with strong wind and the resulting increased edge pressures. We've generally been quite conservative with design pressure recommendations due to this factor.

What is done by others for this doughnut case?

 

[fattdad]

thanks BigH and oldestguy. Regarding the 1/2:1 stress distribution and the donut foundation, I kind of like the negative pressure approach, but don't quite see the need to make an equivalent rectangle. You can use 1/2:1 for the diameters, I'd think.

f-d

¡papá gordo ain’t no madre flaca!

 

[BigH]

Stresses are typically based on elastic theory - if you read Harr's book, there is a whole different ballgame out here using particulate theory. Too, there are so many variations of how to compute settlement. Years ago, in Ground Engineering Magazine, there was a paper that presented the 12 to 15 methods of settlement computations for sand. Pretty well written paper - when Ground Engineering was more practical - the author's conclusion - carry out three or so different means of computing the settlement that you are comfortable with and take the average for a "reasoned" estimate. Don't think things have changed that much given that AASHTO wants settlements to be computed by Hough method (I know, OldestGuy, you like the method - I'd like to see the original paper in that none of my books (some 20 of them) talk about Hough) and the Hough method is from the 1950s. Nothing wrong with that, though, but AASHTO seems to neglect the work of Burbidge and Burland which was pretty extensive.

 

[aeoliantexan]

I have used the 1/2 to 1 truncated pyramid for stress calculation and called it the average. I also use a chart that shows the average Boussinesq stress at various depths beneath round, square, and rectangular footings. It is credited to Fry and Calhoun.

Obviously, if the footing is rigid, there has to be a lot of stress transfer to the corners and edges to make it all settle equally. The bending stress in the footing must be greater than that calculated for a uniform contact stress. I have never understood why this is not recognized in the structural design of footings. I suspect that it may become an issue for large footings when the settlement is large. I once saw an 8-foot wide cantilever at the edge of a mat foundation for a grain elevator that sheared off, and concluded that the soil pressures under the cantilever were two to three times the average.