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Vesic Model The data below provide the Vesic dimensionless bearing capacity and correction factors required for general soil bearing capacity Equation .

Bearing Capacity Factors

Φ	Nc - Cohesion	NY - Wedge	Nq - Surcharge
0	5.14	0.0 or if b >0 -2sin(b)	1.0
>0	(Nq-1)COT(Φ)	2(Nq+1)TAN(Φ)	NΦeπTAN(Φ)

Correction Factors Correction factors are given by the following and are individually calculated as shown below
Cohesion: Z_c = Z_cs Z_ci Z_cd
Wedge: Z_Y = Z_Ys Z_Yi Z_Yd
Surcharge: Z_q = Z_qs Z_qi Z_qd



Foundation
Shape with Eccentricity

Φ	Zcs - Cohesion	ZYs - Wedge	Zqs - Surcharge
0	Strip - 1.0 .2+B'/W'	1.0	1.0
>0	1+NqB'/NcW'	Strip - 1.0 1 - 0.4+B'/W'	strip - 1.0 1+ B'/W' Tan(Φ)

Inclined Loading

Φ	Zci - Cohesion	ZYi - Wedge	Zqi - Surcharge
0	(1- mT/(AecaNc)/2	[1 - T/(Q+AecbCot()]m+1	[1 - T/(Q+AecbCot(Φ)]m
>0	Zqi - [1 - Zqi /Nq - 1]	[1 - T/(Q+AecbCot(Φ)]m+1	[1 - T/(Q+AecbCot(Φ)]m

Foundation Depth

Φ	Zcd - Cohesion	ZYd - Wedge	Zqd - Surcharge
0	1+0.4k	1.0	1.0
>0	1+0.4k	1.0	1+ 2Tan(Φ) (1 - sin(Φ))2k

Foundation on Slope b

Φ	ZcB - Cohesion	ZYB-Wedge	ZqB-Surcharge
Φ=0	1 - b/147.3	[1.0 - TAN(b)]2	[1.0 - TAN(b)]2
Φ>0	ZqB - (1 - ZqB/147.3)	[1.0 - TAN(b)]2	[1.0 - TAN(b)]2

Tilted Foundation delta

Φ	Zcdelta - Cohesion	ZYdelta-Wedge	Zqdelta-Surcharge
Φ=0	1 - delta/147	(1 - 0.017delta Tan(Φ))2	(1 - 0.017delta Tan(Φ))2
Φ>0	Zqdelta - ( 1 - Zqdelta/147.3)	(1 - 0.017delta Tan(Φ))2	(1 - 0.017delta Tan(Φ))2

Notes:
Eccentricity and Inclined Loading Factors are not to be used simultaniously
Factors not used are equal to 1.0
Φ = Angle of internal friction angle in degrees
N_Φ = TAN²(45 + Φ/2)
B' = effective width of foundation - B - 2e_B in feet
W' = effective lateral width of foundation - W - 2e_W in feet
B = Foundation width in feet
W = foundation lateral width in feet
D = foundation depth in feet
Q = vertical load on foundation - qBW in kips
q = bearing pressure on foundations in ksf
T = horizontal load on foundation - positive - right in kips
R = resultant load on foundation (Q² + T²)^0.5 in kips
Θ = Angle of Resultant load with vertical axis - COS ^-1(Q/R) in degrees
e_B = eccentricity parrallel with B - MB/Q
e_W = eccentricity parrallel with W - MW/Q
MB = Moment parrallel with B - ft-kip
MW = Moment parrallel with W - ft-kip
Φ_a = Friction angle between base and soil in degrees
c_a = Adhesion of soil to base in ksf
c = soil cohesion or undrained shear strength
delta = base tilt from horizontal - upward positive - degrees
b = slpe of ground from base - downward positive - in degrees
k = D/B if D/B <=1 - or TAN^-1(D/B) if D/B > 1 - in radians
A_e = Effective area of foundation - B'W' - in ft²
m = 2 + R_BW/1+R_BW'
R_BW = B/W if T is parallel to B
R_BW = W/B if T is parallel to W


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