This cue card is based on chapt. 4 sect. 6 of Foundation Analysis and Design (5th ed) by Jospeh E. Bowles. To understand it, the user should have the book. Permission to quote from the book has been granted. Comments or questions concerning the cue card should be directed to the developer, Helmut Schmidhofer, on 02 4862 1295 (international replace leading 0 with 61) or email engcomp@gmail.com.

There is currently no method of obtaining the ultimate bearing capacity of a foundation other than an estimate. Keep this statement in mind when using the formulas.

Enter your custom values at lines marked ****, then process all lines. The word "process" means to select (highlight) the relevant text and click the spinning globe in the Engineers' Compendium window. To work with the cue card, you need MATHSERV, which you may download here.

STEP 1: The given values are taken from example 4-5:

**** footing width in m, B = 1.8
**** footing length in m, L = 1.8
**** overburden depth in m, D = 1.8
**** applied vertical load in kN, V = 1800
**** moment L-direction (about X-axis) in kNm, MX = 450
**** moment B-direction (about Y-axis) in kNm, MY = 360
**** internal friction in degrees, PHID = 36
**** cohesion in kPa, C = 20
**** soil weight in kN/m3 (water table at 6.1 m), GAMMA = 18

STEP 2: Some basic values and tests. Process all lines:

offset L-direction in m, EL = MX/V := 0.25
offset B-direction in m, EB = MY/V := 0.2
TEST1 = EL <= L/6 := 1
TEST2 = EB <= B/6 := 1
TEST3 = (4*EL + .4) <= L := 1
TEST4 = (4*EB + .4) <= B := 1

STEP 3: All tests must be TRUE (1). If not, modify input before proceeding. If all true, process the next two lines:

effective width in m, BD = B - 2*EB := 1.4
effective length in m, LD = L - 2*EL := 1.3

Hansen's and Meyerhof's bearing capacity equations are illustrated. See also hansen-vesic.doc and bowles4-3.doc respectively, for these methods.

STEP 1: Process the next ten lines:

overburden pressure in kPa, QBAR = D*GAMMA := 32.4
45 degrees in radians, A45 = 45*_pi/180 := 0.7854
internal friction in radians, PHI = PHID*_pi/180 := 0.6283
passive pressure coefficient, KP = (tan(A45+PHI/2))^2 := 3.8518
Coefficient NQ = round(exp(_pi*tan(PHI))*KP) := 38
Coefficient NG = round(1.5*(NQ-1)*tan(PHI)) := 40
Coefficient NC = round((NQ-1)/tan(PHI)) := 51
shape factor (cohesion) SC = 1 + NQ*BD/(NC*LD) := 1.8024
shape factor (overburden) SQ = 1 + BD/LD*sin(PHI) := 1.633
shape factor (gamma), SG = max(.6, 1-.4*BD/LD) := 0.6

NOTE: error in book (BD and LD transposed), the incorrect values are used here to check the remainder of the example.
NB: DO NOT PROCESS THE NEXT 3 LINES MARKED * WHEN USING YOUR VALUES!

* SC = 1.69
* SQ = 1.55
* SG = .62

if D/B <= 1 then
  K = D/B
else
  K = atn(D/B)
end if

STEP 3: Process the next five lines:

depth factor (cohesion), DC = 1 + .4*K := 1.4
depth factor (overburden), DQ = 1 + 2*tan(PHI)*(1-sin(PHI))^2*K := 1.2469
depth factor (gamma), DG = 1.0
ultimate in kPa, QULT = C*NC*SC*DC+QBAR*NQ*SQ*DQ+.5*GAMMA*BD*NG*SG*DG := 5105.3525
safety factor, SF = QULT*BD*LD/V := 5.1621

This method uses the actual base dimensions B and L and applies reduction factors to account for the moments. Process the next 19 lines:

overburden pressure in kPa, QBAR = D*GAMMA := 32.4
45 degrees in radians, A45 = 45*_pi/180 := 0.7854
internal friction in radians, PHI = PHID*_pi/180 := 0.6283
passive pressure coefficient, KP = (tan(A45+PHI/2))^2 := 3.8518
Coefficient NQ = round(exp(_pi*tan(PHI))*KP) := 38
Coefficient NC = round((NQ-1)/tan(PHI)) := 51
Coefficient NG = round((NQ-1)*tan(1.4*PHI)) := 45
shape factor (cohesion) SC = 1 + .2*KP*B/L := 1.7704
shape factor (overburden) SQ = 1 + .1*KP*B/L := 1.3852
shape factor (gamma), SG = SQ := 1.3852
depth factor (cohesion), DC = 1 + .2*sqrt(KP)*D/B := 1.3925
depth factor (overburden), DQ = 1 + .1*sqrt(KP)*D/B := 1.1963
depth factor (gamma), DG = DQ := 1.1963
ultimate in kPa, QULT = C*NC*SC*DC+QBAR*NQ*SQ*DQ+.5*GAMMA*B*NG*SG*DG := 5762.7152
reduction B-direction, REB = 1 - sqrt(EB/B) := 0.6667
reduction L-direction, REL = 1 - sqrt(EL/L) := 0.6273
after reduction and safety factor of 3, QA = QULT*REB*REL/3 := 803.3507
actual pressure on full area, in kPa, QF = V/(B*L) := 555.5556
ditto, on effective area, in kPa, QE = V/(BD*LD) := 989.011

The book recommends to increase the footing size to 2.4 m x 2.4 m, based on 500 kPa applied to effective area.

STEP 1: The given values are taken from example 4-6. Enter your values and process all lines:

**** footing width in m, B = 0.5
**** footing length in m, L = 2.0
**** overburden depth in m, D = 0.5
**** ultimate vertical load in kN, V = 1060
**** ultimate load L-direction in kN, HL = 382
**** ultimate load B-direction in kN, HB = 0
**** cohesion in kPa, C = 0
**** soil weight in kN/m3 (saturated), GAMMA = 9.43
**** undrained tri-axial friction in degrees, PHIU = 43
internal friction in degrees, PHID = floor(min(1.1*PHIU, 1.5*PHIU-17)) := 47
internal friction in radians, PHI = PHID*_pi/180 := 0.8203
45 degrees in radians, A45 = 45*_pi/180 := 0.7854
overburden in kPa, QBAR = D*GAMMA := 4.715
effective area in m2 (no moments), AF = B*L := 1.
passive pressure coefficient, KP = (tan(A45+PHI/2))^2 := 6.4447
Coefficient NQ = round(exp(_pi*tan(PHI))*KP) := 187
Coefficient NC = round((NQ-1)/tan(PHI)) := 173

2 (a) Hansen's method - process all lines:

This result is much higher than the load test of 1060 kPa.

2 (b) Vesic's method - (cohesion C = 0), process all lines:

Coefficient NG = 2*(NQ+1)*tan(PHI) := 403.2106
exponent M = (2+L/B)/(1+L/B) := 1.2
incl. factor (overburden), IQ = (1 - HL/(V+AF*CA/tan(PHI)))^M := 0.5849
incl. factor (gamma), IG = (1 - HL/(V+AF*CA/tan(PHI)))^(M+1) := 0.3741
shape factor (overburden), SQ = 1 + B/L*tan(PHI) := 1.2681
shape factor (gamma), SG = max(.6, 1-.4*B/L) := 0.9
depth factor (overburden), DQ = 1 + 2*tan(PHI)*(1-sin(PHI))^2*K := 1.1548
depth factor (gamma), DG = 1.0
ult. in kPa, QULT = QBAR*NQ*SQ*DQ*IQ+.5*GAMMA*B*NG*SG*DG*IG := 1075.3197

This result is very close to the test result. However, settlement considerations will override strength considerations.