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Bearing Capacity

 

Ultimate Bearing Capacity formula
\( q_u \;=\; ( c \cdot N_c) + (\gamma \cdot D_f \cdot N_q) + (0.5 \cdot \gamma \cdot W_f \cdot N_{\gamma}) \)
Symbol English Metric
\( q_u \) = Ultimate Bearing Capacity \(lbf\;/\;in^2\)  \(Pa\)
\( c \) = Cohesion (Internal Molecular Attraction) \(lbf\;/\;in^2\)  \(Pa\)
\( N_c \) = Shape Factor \(dimensionless\) \(dimensionless\)
\( D_f \) = Foundation Depth \(ft\) \(m\) 
\( N_q \) = Depth Factor \(dimensionless\) \(dimensionless\)
\( \gamma \) (Greek symbol gamma) = Unit Weight of Soil \(lbf\) \(N\)
\( W_f \) = Foundation Width \(ft\) \(m\)
\( N_{\gamma} \) = Inclination Factor \(dimensionless\) \(dimensionless\)

Bearing capacity is the maximum load that a soil or rock mass can support without undergoing excessive settlement, shear failure, or other detrimental deformations.  It is a crucial consideration in geotechnical engineering and foundation design, as it determines the safe load carrying capacity of the ground upon which structures are built.

Bearing Capacity Types

  • Ultimate Bearing Capacity  (\(q_u\))  -  This is the maximum load per unit area that the soil can support without failure.  It is often determined through laboratory tests or field tests and is used as a design parameter in foundation engineering.
  • Allowable Bearing Capacity (Safe Bearing Capacity)  (\(q_a\))  -  It is the maximum load per unit area that is deemed safe for the soil without causing excessive settlement or shear failure.  It is typically a fraction of the ultimate bearing capacity and is used in design calculations to ensure the stability and safety of foundations.
  • Net Bearing Capacity  (\(q_n\))  -  This refers to the effective bearing capacity of the soil after considering factors such as the weight of the footing or foundation and the influence of groundwater.

Allowable Bearing Capacity formula
\( q_a \;=\;  \dfrac{ q_u }{ FS }\)
Symbol English Metric
\( q_a \) = Allowable Bearing Capacity \(lbf\;/\;in^2\)  \(Pa\)
\( q_u \) = Ultimate Bearing Capacity \(lbf\;/\;in^2\)  \(Pa\)
\( FS \) = Factor of Safety \(dimensionless\) \(dimensionless\)

The determination of bearing capacity involves various factors, including soil type, density, moisture content, loading conditions, and the geometry of the foundation or footing.  Engineers use methods such as plate load tests, standard penetration tests, cone penetration tests, and empirical correlations to estimate bearing capacity and ensure that foundations are designed to safely support the intended loads without causing settlement or instability issues.

Key Points about Bearing Capacity

Bearing capacity factors are coefficients used in the calculation of the ultimate bearing capacity of soil.  These factors are applied to various soil parameters and geometrical factors to estimate the maximum load that a foundation or footing can safely support without causing failure or excessive settlement.  The bearing capacity factors are typically denoted by symbols and represent the influence of different factors on the bearing capacity of the soil.

Shape Factor  (\(N_c\))  -  This factor accounts for the shape of the foundation.  It depends on the shape of the footing and the depth at which the foundation is located.  For example, for a square footing, the shape factor is different than for a circular or strip footing.
Depth Factor  (\(N_q\))  -  This factor considers the depth of the foundation relative to the ground surface.  It takes into account the influence of the depth on the bearing capacity of the soil.  It is typically higher for shallow foundations and decreases with increasing depth.
Inclination Factor  (\(N_{\gamma}\))  -  This factor accounts for the inclination of the failure plane with respect to the horizontal.  It is relevant for sloping ground conditions where the failure plane may not be vertical.
Soil Friction Coefficient  (\(tan(\theta)\;\))  -  The angle of internal friction (\(tan(\theta)\;\)) of the soil is a crucial parameter in bearing capacity calculations.  It represents the resistance of the soil to shear deformation.  A higher value of (\(tan(\theta)\;\))  indicates a stronger soil, resulting in higher bearing capacity.
Overburden Pressure Factor  (\(\gamma\))  -  This factor considers the effect of the weight of the soil above the failure plane on the bearing capacity.  It depends on the unit weight of the soil and the depth of the foundation.

These factors are typically used in bearing capacity equations, such as Terzaghi's bearing capacity equation or Meyerhof's bearing capacity equation, to estimate the ultimate bearing capacity of the soil and ensure the safe design of foundations.  The values of these factors depend on soil properties, foundation geometry, and loading conditions and are determined through empirical correlations, laboratory tests, or field test.

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