Foundation Rigidity and Settlement

[NBRY1]

Is it reasonable to use rigidity factors? I would like to hear back from engineering community on this.
Some texts say they can be used if the site is well understood; but most engineers ignore for conservatism.
I haven't seen anything stating they should not be used.

 

[ATSE]

Quoting "... it seems logical to reduce the calculated settlement..."
Yes, you do this far more accurately with FEA, not with a crude coefficient method. but if you insist, Fellenius is not a bad source at all.
If your null hypothesis is to use a analysis method that 95% of structural engineers don't use, I'm not sure why you came to this forum.

A good reference for those interested in this subject: "Subgrade Modulus - Revisted" published in Structure magazine in 2014. Aristorenas and Gomez. Quick easy read.

 

[NBRY1]

I would love to see this approach as compared with reducing the center settlement of a rigid foundation by 15%.
My guess is that they are probably very similar; and trying to split hairs is not warranted for small spread ftg. evaluations.
…...certainly for a flexible mat, this approach seems reasonable.

Regards,

 

[BWCSA]

These rigidity factors in literature (Bowles, Das, Coduto) all seem to be derived from elastic half-space theory, often simplified to one number for practical application on a range of foundation shapes. They are calculated as the ratio between :
• I_flexible = The (Influence factor for the) center settlement of an infinitely flexible foundation under a uniformly distributed loading (e.g. terrain load) on an elastic half-space, and
• I_rigid = The (Influence factor for the) settlement of an infinitely rigid foundation symmetrically loaded with the same total load on an elastic half-space (uniformly distributed or otherwise, doesn't matter because of the infinite rigidity).

rigidity factor = s_rigid / s_flexible (= I_rigid / I_flexible) for a square foundation:
• Center point: 0.79
• Corner point: 1.58
• Midpoint of a side: 1.157

rigidity factor for a circular foundation:
• Center point: π/4=0.785

rigidity factor for a rectangular foundation:
• Center point: 0.79 to 0.84 for a L/B range of 1 to 10

Some takeaways from the values above:
• 0.85 is a safe value to take into account the effect of (perfect) rigidity on center settlement for the variety of foundation shapes mentioned above
• By stiffening the foundation the max settlement in the center reduces but settlement in points away from the center increases. "Average" settlement (however you would like to define average) under a rigid foundation and a flexible foundation are more or less the same. So in my view it's better to say that by stiffening the foundation the settlement is "redistributed under the foundation slab" rather than "reduced".
• These ratios are for flexible and rigid foundation slabs under the same load, self-weight included. If a lot of weight/plate thickness is added to stiffen the foundation as to make it "perfectly rigid" one might end up with more settlement at the center.

I am trying to determine if the use of rigidity factors for reducing the settlement of a rigid foundation (where settlement was estimated at its center assuming the foundation was perfectly flexible) is appropriate.

Depends on how you want to use it to "reduce" settlement in your calculation procedure.

Do you want to slap it on a calculated value of the settlement as a 15% reduction factor --> that's a big no no in my book. Real soil masses (even unlayered ones) don't deform like an elastic half-space, so proper settlement models like Terzaghi's (or variants of it), Bjerrum's, isotaches … aren't linear elastic either. Directly applying this rigidity factor (that does come from elastic theory, as explained above) to calculated settlement values from these models will lead to scaling errors.

However, in every settlement calculation procedure there is the prior step of estimating the stress increases in each soil layer through a stress distribution model. Here we do typically rely (for lack of better alternatives) on elastic models (Bousinesq, Westergaard, Frölich) and it is perfectly reasonable and justifiable to take into account how the relative stiffness of the foundation influences the contact pressure distribution under the foundation and the subsequent stress distribution in the layers below, either through simple means like stiffness factors or through more refined means.

 

[BWCSA]

The use of rigidity factors seems to be similar to the use of a characteristic point as described in 'Basics of Foundation Design'; by Fellenius. The concept seems appropriate and not overly conservative

Saying there is a characteristic point is just another way of expressing that St-Venant's principle applies in an elastic half-space:

The value of the stress increase in a certain point z below the foundation is dependent on the distribution of the contact pressure directly under the foundation (rigidity / relative stiffness of the foundation influences this distribution) ONLY if point z is above the characteristic point. Further down below this characteristic point, the value of the stress increase in a point z is always the same for the same value of loading increase no matter how it is distributed on the surface of the elastic half-space (within the foundation area).

How this relates to rigidity factors:

If you have weak soil layers (those that will cause the bulk of the settlement) situated in the zone between the underside of the foundation and the characteristic point, then taking into account aspects that influence the contact pressure distribution like the foundation's relative stiffness (through rigidity factors or other means) is useful.

If your weak soil layers are situated in the zone between the characteristic point and the point where stress increases become negligible (where settlement calcs are typically cut-off), then trying to determine the contact pressure distribution and differentiating between rigid and flexible foundations is pretty useless, just use the uniformly loaded perfectly flexible foundation (r=1) as your calculation model.