# BEARING CAPACITY OF SOILS

### General Bearing Capacity Theory

Extensive research work and numerous methods proposed by researchers including Meyerhof (1963), DeBeer (1970), Hansen (1970), Vesic (1973, 1975), and Hanna and Meyerhof (1981) led to the formulation of general bearing capacity theory. Originally proposed by Meyerhof (1963), the general bearing capacity theory takes into consideration factors such as rectangular footings, inclined loads, shear resistance due to the soil above the footing etc. which were not considered in Terzaghi's bearing capacity theory.

The ultimate bearing capacity is expressed as per the following equation;

$q u l t = c ' N c F c s F c d F c i + q N q F q s F q d F q i + 1 2 γ B N γ F γ s F γ d F γ i$

where:
c'=effective cohesion of the soil beneath the foundation,
𝛾=unit weight of the homogeneous soil,
B= width of foundation (or diameter in the case of circular foundation),
q=effective stress at the bottom of the foundation (due to the soil above the foundation and surcharge (if any) at the ground surface).
If no surcharge is present at the ground surface, then:
$q = γ D f$ where:
Df=embedment depth of foundation,
𝛾=unit weight of the homogeneous soil,

Bearing Capacity Factors:
The bearing capacity factors, Nc, Nq, and N𝛾 , are expressed as per the following equations; $N q = tan 2 ( 45 + ϕ ' 2 ) e π tan ϕ '$ $N γ = 2 ( N q + 1 ) tan ϕ '$ Shape Factors:
To account for the broad range of footing shapes, the following shape factors were proposed by DeBeer (1970):
$F c s = 1 + ( B L ) ( N q N c )$ $F q s = 1 + ( B L ) tan ϕ '$ $F γ s = 1 − 0.4 ( B L )$ Depth Factors:
Depth factors that take into account the contribution of foundation embedment to the bearing capacity. Hansen (1970) proposed the following equations for the depth factors:
$F γ d = 1$ Load Inclination Factors:
Load inclination factors that take into account the reduction of bearing capacity due to inclined loads. Meyerhof (1963) proposed the following equations for the load inclination factors: $F c i = F q i = ( 1 − β ° 90 ° ) 2$ $F γ i = ( 1 − β ° ϕ ' ) 2$ where:
φ' = Effective internal frictional angle of the foundation soil,
β = Inclination of the load (Q) on the foundation with respect to the vertical.

Ground Water Table above Footing Level
Ground Water Table below Footing Level
Ground Water Table below Footing Level (Dw-Df>B)

General Bearing Capacity - Inputs

Bearing Capacity of Soils - Results

INPUTS:

Effective Cohesion of soil beneath the foundation (c'), KN/m2:

Effective Internal Friction Angle of the foundation soil (Φ'):

Unit Weight of the homogenous soil (γ) KN/m3

Saturated Unit Weight of soil (γsat) KN/m3

Inclination of Load on the Foundation with respect to Vertical (β)

Width/Diameter of Foundation (B), m:

Length of Foundation (L), m:

Depth of Foundation (Df), m:

Depth to Water Table (Dw), m:

OUTPUT:

Bearing Capacity Factors:

Nc:

Nq:

Nγ:

Ultimate Bearing Capacity:

Effective Stress, KN/m2:

Ultimate Bearing Capacity, KN/m2:

REPORT SECTION

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