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These equations are for shallow footings, where D <= B
The spreadsheet is based on Chapter 4-3 of Foundation Analysis and Design, Ed. 5 by Joseph E. Bowles (permission granted).
The equations are:
q-ult = c*Nc*s-c + q-bar*Nq + 0.5*gamma*B*Ngam*s-gam
where:
c = soil cohesion in kPa
Nc = cohesion multiplier = (Nq - 1)*cot(PHI)
s-c = shape factor for cohesion
q-bar = overburden pressure in kPa = gamma*D where D = depth to base in m
Nq = overburden multiplier = a^2/(2*cos^2(45+PHI/2))
where a = e^((0.75*PI - PHI/2)*tan(PHI)) and
PHI = angle of internal friction in radians (entered in degrees)
gamma = unit weight of soil in kN/m3
B = least lateral base dimension in m
Ngam = wedge weight multiplier = (tan(PHI)/2)*(Kpy/cos^2(PHI) - 1)
where Kpy is taken from Table 4-2 as follows:
PHI 0 5 10 15 20 25 30 35 40 45
Kpy 10.8 12.2 14.7 18.6 25.0 35.0 52.0 82.0 141.0 298.0
s-gam = shape factor for soil wedge.
Input values are obtained from tests of soil samples.
You should do at least one calculation manually, for two reasons:
1. to check the spreadsheet so you can have confidence in its results; and
2. to appreciate how much time the spreadsheet saves.
Please support the ongoing maintenance of this site.
For just $9.70 I shall send you the Excel spreadsheet
so you can satisfy yourself that the program uses the equations correctly.
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