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# Bearing Capacity using N Value

## Bearing Capacity using N Value

(OP)
I have been practicing for my PE exam and came across a problem which is throwing me off. The problem is to determine the allowable bearing capacity of a mat foundation 40ft x 80 ft with soil unit wt 120lb/ft^3 located 8ft below ground surface with SPT of the soil being 18. Sounds simple, so I use the N value to get the friction angle (~32°) and then go on to get the Terzaghi's bearing capacity factors for that and compute the bearing capacity turns out be 19.74 Te/ft^2 after applying a FOS of 2. The answer however turned out to be 2.49 Te/ft^2. The author (lindberg) used the formula for a FOS of 2 qa = 0.22*Cn*N, where Cn is the depth correction factor (~0.69). This was very puzzling because of the difference of magnitude. I was hoping somebody with more experience can explain why?
The 2nd part of my question comes after doing more research I realized that most of the bearing capacity equations based on N Value for such as Terzhaghi and Peck (as given in Boweles) qa = 0.720(N-3)*(B+1/2B)^2
or Meyerhof qa = N/4(B+1/B)^2*Kd (where Kd = 1+ 0.33D/B) are very counter-intuitive. It almost appears that the bearing capacity is reducing with width of the foundation. I am assuming this is because of stress concentration near the center leading to greater settlement and thereby a lower bearing capacity, Can somebody please confirm if this is correct?

### RE: Bearing Capacity using N Value

The CPT And Pressumeter are much prefered for bearing Capacity Determination on soils.

### RE: Bearing Capacity using N Value

Unfortunately, N values for a "foundation" (a floating slab) is over stretching any formula. Besides, those formulas usually deal with a possible rupture failure, when for the large slab settlement controls. An exception to this might be a grain elevator failure by rupture. Let's hope no question writer is so ignorant as to pose such a question on an exam.

### RE: Bearing Capacity using N Value

With respect to a larger B value decreasing the bearing capacity per square foot, consider that a narrower footing distributes the pressure over a proportionally larger area than does a very wide footing. For a simplified explanation: A 4' wide footing might possibly engage about 8' of soil width (maybe an extra 2' per each side of the footing). Whereas a 20' wide footing might spread the load out over 24' (the same extra 2' per each side). The percentage increase in ultimate and allowable bearing pressure due to this distribution would be greater for a narrower footing. So, the narrower the footing, the greater the percentage of load distribution. This B-width phenomenon may be somewhat like having decreasing soil arching for increasing span width. The wider you go, the less effective the distribution. That is just how I interpret the decreasing bearing capacity due to increasing footing width. These are not exact numbers and I don't want to be arguing about their accuracy. Think concept.

### RE: Bearing Capacity using N Value

See attached. It explains the solution of your problem. Basically, the depth correction factor is considered at a depth of Df+B, where B is the width of the mat.

Also, for your second question, I think that the answer is related to the above: depth corrections are smaller for deeper locations BUT this is considered for sands where you have the same "soil resistance/penetration value" (i.e. SPT N-values) thru the entire depth of consideration. For example, the soil's shear strength parameters (in case of sands, friction angles) are different for the same N-value at say 5 meters and 10 meters (phi @ 5 meters > phi @ 10 meters for the same N-value). I will post later a chart which this can visualized.

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