Bearing Capacity Equations - Which to use?

One of the readers of this blog recently posted a very good question that led me to dig deeper. The question is, "The 6 minute solutions uses a different equation for circular foundations than the DAS book. Can you reconcile these two equations?

DAS: 1.3cNc + qNq + 0.3yBNy
6 min: (1.2)cNc + qNq + 0.5yBNy(0.7)

Is it something that will allow me to get the correct answer on the test or are they different enough that the solutions could be similar and I would have to decide between to very close sol'ns?"

What do we do?

For PE Exam, lets just stick to what CERM recommends. The problem with this is the fact that shape factors also depend on the type of soil (See Table 4-1, 4-3, 4-5a of Bowles, 5th Ed.) apart from the geometry of the foundation. So Table 36.4 and 36.5 in CERM (11th Ed.) is not clear in that way and it is my opinion that those tables are provided for an approximate solution. So although I recommend using CERM for the PE exam, I would also recommend you to look for other methods (field or theoretical) for calculating bearing capacity in your work.

Lets look at the shape factors proposed by several scientists:

Terzaghi

For Strip Round Square

Sc 1.0 1.3 1.3

Sy 1.0 0.6 0.8

Meyerhof

Sc = 1 + 0.2(Kp)(B/L) for any phi

Sq = Sy = 1 + 0.1(Kp)(B/L) for phi > 10 degrees

Sq = Sy = 1 for phi = 0

Vesic

Sq = 1 + (B/L)tan(phi)

Sc = 1 + (Nq/Nc)(B/L)

Sy = 1 - 0.4(B/L)

If you use all these equations and evaluate bearing capacity, you'll notice a small difference in the answer.

Now, as far as the equations on Das and Six Minute Solutions are concerned:

DAS: 1.3cNc + qNq + 0.3yBNy
6 min: (1.2)cNc + qNq + 0.5yBNy(0.7) = 1.2cNc +qNq + 0.35yBNy

Now, lets take an example: y = 120 pcf, B = 3.0 feet, phi = 30 degrees, Df = 3 feet; c = 500 psf

DAS: 1.3cNc + qNq + 0.3yBNy = 1.3(500 psf)(37.2) + (120 pcf)(3 ft.)(22.5) + (0.3)(120 pcf)(3 ft.)(19.7) = 34407.6 psf
6 min: (1.2)cNc + qNq + 0.35yBNy = (1.2)(500 psf)(37.2) + (120 pcf)(3 ft.)(22.5) + (0.35)(120 pcf)(3 ft.)(19.7) = 32902.2 psf

For practical purposes, both the answers are the same because we are going to apply a very high factor of safety anyway. If I were you, I'd choose the more conservative one.

It is my understanding that the Terzaghi's equation gives the most conservative answer.

Over the period of years, several scientists and engineers have suggested various factors, i.e. shape, depth, inclination, and the bearing capacity factors. There is no significant advantage of one method over another. If you want to dig deeper, I would suggest Foundation Analysis and Design by J.E. Bowles.