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Bearing Capacity of Soil Equation and Calculator
Soil Bearing Capacity Equation and Calculator
Related: Bearing Capacity of Soils Analysis Document
Preview Soil Bearing Capacity Calculator
The approximate ultimate bearing capacity under a long footing at the surface of a soil is given by Prandtl's equation:
Where:
q_{u} = Ultimate bearing capacity of soil, lb/ft^{2} (kg/m^{2})
c = Soil cohesion, lb/ft^{2} (kg/m^{2})
Φ = Angle of internal friction, degree
γ_{dry} = Unit weight of dry soil, lb/ft3 (kg/m3)
b = Width of footing, ft (m)
d = Depth of footing below surface, ft (m)
e = 2.718....
K_{p} = Coefficient of passive pressure
For footings below the surface, the ultimate bearing capacity of the soil may be modified by the factor 1 + Cd/b
The coefficient is about 2 for cohesionless soils and about 0.3 for cohesive soils. The increase in bearing capacity with depth for cohesive soils is often neglected.
Rankine Earth Pressure Coefficients
φ (deg) 
Rankine Ka 
Rankine Kp 
28 
.361 
2.77 
30 
.333 
3.00 
32 
.307 
3.26 
The Coulomb active and passive earth pressure coefficient is derived from a more complicated expression that depends on the angle of the back of the wall, the soilwall friction value and the angle of backfill. Although this expression is not shown, these values are readily obtained in textbook tables or by programmed computers and calculators. The Table shown below some examples of the Coulomb active and passive earth pressure coefficient for the specific case of a vertical back of wall angle and horizontal backfill surface. The Tables illustrate increasing soilwall friction angles (δ).
Coulomb Active Pressure Coefficient
φ (deg) 
δ (deg) 

0 
5 
10 
15 
20 

28 
.3610 
.3448 
.3330 
.3251 
.3203 
30 
.3333 
.3189 
.3085 
.3014 
.2973 
32 
.3073 
.2945 
.2853 
.2791 
.2755 
Coulomb Passive Pressure Coefficient
φ (deg) 
δ (deg) 

0 
5 
10 
15 
20 

30 
3.000 
3.506 
4.143 
4.977 
6.105 
35 
3.690 
4.390 
5.310 
6.854 
8.324 
Contributed by: Prashant Kien University of Montreal Pune, India