Bearing Capacity equatinos - accounting for fill 1

[GeoCanuck]

Hi,

I'm hoping some of you can help untangle some confusion on bearing capacity. An ongoing argument in our office says the depth of fill should be conservatively discounted in determining ultimate bearing capacity, by setting the gamma*Df term as zero. However no one can say why, or quote a source.

Let's assume we're using a general BC equation (from Canadian Foundation Engineering Manual Ed.4):

qu = cuNcSc + qsNqSq + 1/2*gamma*B*Ngamma*Sgamma

The S-terms are shape factors for strip or rectangular footings. If I understand correctly, the CuNc term is shear resistance along the log-spiral shear surface, qsNq term is the resistance to upwards displacement of the volume within the log-spiral surface due to surcharge above the footing depth, and the 1/2*gamma*B*Ngamma term is the wedge below footing. I assume the wedge below footing is unaffected by the fill, so if correct, have no questions about the 1/2*gamma*B*Ngamma term.

My argument against discounting the gamma*Df term is that the surcharge provided by the depth of fill helps to resist failure along the log-spiral surface extending outside the footing area. Therefore I believe the gamma*Df term can be kept as non-zero.

Also, various textbook diagrams show the footing installed below final grade, with either (i) the log-spiral failure surface (cuNc term) extending to the ground surface (i.e. through the fill in this case, which also contributes to surcharge); or (ii) extending out only as far as to match the bearing depth elevation, and discounting shear within the fill. In Terzaghi's equation, where Nc=(Nq-1)*cot(phi), does the Nc value account for shear within the material above the footing, or does tihs really make much difference? If the fill depth should be discounted, then why?

Does Cu or Nc change depending on whether the material is new fill or native material that's been in place for several thousand years? The only way I can see a difference being made is with fine grained soils, where effective stress takes time to develop under the fill surcharge, increasing Cu. However for coarse grained soils, increases in effective stress should develop quickly after fill placement, so the fill can only help - correct??

Other issues are:
- what influence does fill depth have on gross vs. net ultimate bearing capacity? (i.e. fill adds to gamma*Df term providing resistance to upwards displacement of failure volume, yet reduces the amount of "additional" structural load that can be placed on the bearing surface - confusing!)
- serviceability may be affected by ongoing consolidation settlements if fill is relatively new, reducing the serviceability limit state

Cheers!

 

[motorbiketocrank]

First, I'd say that I typically would not be using all 3 terms together (i.e. for a soil governed by cohesion I'd be using only the first term with Nc and for a soil governed by particle friction I'd be using the second 2 terms with Nq and Ngamma).

I'm interpreting you question on "fill" as basically whether one should consider the "depth of footing" when determining bearing capacity (i.e. whether the second term of the equation should be used in granular soils).

It would be typical to include this second term when analyzing bearing capacity in granular soils. This term isn't calculating friction on a portion of the shear plane above the bearing elevation........instead it's considering that the weight of the soils above the footing elevation increases the normal stress between particles along the log-spiral failure surface below the bearing elevation. So in most cases including this term is appropriate (i.e. the weight of soil above the bearing level is there and it helps). There might be rare cases where it wouldn't apply (for example, say you had an open field, constructed the footings, added all building load, and only then placed fill around the building to finished grade......in this case it wouldn't be appropriate to include the fill surcharge load because there is a period of time where the footings are fully loaded and the fill is not there helping to resist failure.)