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Bearing Capacity Calculator - Terzaghi's banner
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Bearing Capacity Calculator - Terzaghi

Verified by the CalcTree engineering team on July 20, 2024

This calculator computes the ultimate bearing capacity of a shallow foundation using Terzaghi's approach.
Symbols used in this calculator


Calculation

Assumptions

Terzaghi's bearing capacity equations are based on the following assumptions:
  1. Width of the foundation is equal or greater than its depth (i.e. B > D)
  2. No sliding between foundation and soil
  3. Soil beneath the foundation is a homogenous, semi-infinite mass
  1. No applied moments. Applied load is compressive and is vertically applied to the foundation centroid

Inputs

Water Table Cases



Case
:I​



Footing Geometry



Footing shape
:Strip​



B
:3.0 m​



Df
:3.0 m​



D
:1.0 m​


Soil Properties



γ
:{"mathjs":"Unit","value":20,"unit":"kN / m3","fixPrefix":false}​



γsat
:19.00 kN / m3​



ϕ
:{"mathjs":"Unit","value":29.999999999999996,"unit":"deg","fixPrefix":false}​



c
:{"mathjs":"Unit","value":30,"unit":"kPa","fixPrefix":false}​



Outputs



FoS
:2​


Factors based on footing shape

Outputs based on water table

General Shear Failure



Nc
:37.16​



Nq
:22.46​



Nγ
:19.13​



General - qu
:2483kPa​



General - qu(net)
:1242kPa​



Local Shear Failure



Nc'
:18.99​



Nq'
:8.31​



Nγ'
:4.39​



Local - qu
:849kPa​



Local - qu(net)
:425kPa​


Explanation

In 1943, Karl Terzaghi expanded on Prantl's 1921 study on the penetration of hard bodies on softer materials, the plastic failure theory. Terzaghi used this theory to determine the bearing capacity of soils for shallow strip footing.
According to Terzaghi, a foundation is considered shallow if the footing depth,

is less than or equal to its width,

. Additionally, he assumed that a uniform surcharge,

can replace the weight of soil above the base of the footing.
Terzaghi's equation consists of three components:
  1. the cohesion of the soil edge
  2. the surcharge
  3. the friction along the soil edge
Combining these three together, gives the general equation for the ultimate bearing capacity,

as:

qu=KccNc+KqqNq+Kγγc BNγ q_u = K_ccN_c +K_qqN_q + {K_\gamma}{\gamma_c\ }BN_{\gamma}
Where:
  1. 
    
    is the cohesion of the soil
    
    
  2. 
    
    is the weight of the soil
    
    depending on case I, II or III
  3. 
    
    is the depth of the footing below ground level
    
    
  4. 
    
    is the width of the footing
    
    
  5. 
    
    ,
    
    and
    
    are the bearing capacity factors; for soil cohesion, overburden pressure and unit weight of soil, respectively. They are tabulated in Table 16.1 and 16.2 of Principles of Geotechnical Engineering 7th Edition by Braja M. Das.
  6. 
    
    are constants and depend on the footing shape
  7. 
    
    is the overburden pressure, that is, the effective stress
    
    )


General and Local Shear Failure

For general and local shear failure, the ultimate bearing capacity is dependent on the footing shape:
  1. Strip footing:
    
    
  1. Square footing:
    
    
  1. Circular footing:
    
    
General shear failure

Additionally, for local shear failure, it is assumed that the soil cohesion is reduced to

and the soil friction is changed to

. The latter modification, results in modified bearing capacity factors

and

.
And so the ultimate bearing capacity for local shear failure is adjusted to:

qu=KccˉNc′+KqqNq′+Kγγc BNγ′ q_u = K_c\bar{c}N_c' +K_qqN_q' + {K_\gamma}{\gamma_c\ }BN_{\gamma}'
Local shear failure


Effect of Water Table on

and



The equations above assume the groundwater table depth,

is much greater than the footing width B. However, in other cases wherein the water table is near or above the footing, the subsoil becomes saturated and the unit weight of the submerged soil is reduced, resulting in a decrease in the soil's ultimate bearing capacity.


Case 1: Water table is above the footing base

The overburden pressure,

that appears in the second term of the bearing capacity equation is given by:

 q = γ(Df−D) + γ′D\ q\ =\ \gamma(D_f-D)\ +\ \gamma'D
Where

is the effective unit weight of the soil.
Additionally,

in the third term of the bearing capacity equations is equal to

, that is:

qu=KccNc+KqqNq+Kγγ′ BNγq_u = K_ccN_c +K_qqN_q + {K_\gamma}{\gamma'\ }BN_{\gamma}

Case 2: Water table is at the footing base

The overburden pressure,

that appears in the second term of the bearing capacity equation is given by:

q = γ Dfq\ =\ \gamma\ D_f
Additionally,

in the third term of the bearing capacity equations is equal to

, that is:

qu=KccNc+KqqNq+Kγγ′ BNγq_u = K_ccN_c +K_qqN_q + {K_\gamma}{\gamma'\ }BN_{\gamma}
Where

is the effective unit weight of the soil.


Case 3: Water table is below the footing base

The overburden pressure,

that appears in the second term of the bearing capacity equation is given by:

q = γ Dfq\ =\ \gamma\ D_f
Additionally,

in the third term of the bearing capacity equations should be replaced by

, that is:

qu=KccNc+KqqNq+Kγγavg BNγq_u = K_ccN_c +K_qqN_q + {K_\gamma}{\gamma_{avg}\ }BN_{\gamma}
Where

is taken as:

For D≤B:  γavg =1B[γ D + γ′(B−D)]For D > B:     γavg=γ\text{For\ D}\leq\text{B:\ }\ \gamma_{avg}\ =\dfrac{1}{B}[\gamma\ D\ +\ \gamma'(B-D)]\\\text{For\ D\ >\ B:\ }\ \ \ \ \gamma_{avg}=\gamma


Allowable Bearing Capacity

A factor of safety (FoS) is incorporated into the footing design, which reduces the ultimate bearing capacity. FoS generally varies anywhere from 1.5 ~ 3, depending on the uncertainty in soil properties. The allowable bearing capacity is calculated as:

qallowable =quFoSq_{\text{allowable}}\ =\dfrac{q_u}{\text{FoS}}

References

  1. Foundations of Geotechnical Engineering by DIT Gillesania
  2. Principles of Geotechnical Engineering 7th Edition by Braja M. Das

Related Resources

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  3. Weight to Volume relationships in soils
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