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Bearing Capacity Calculator - Meyerhof Approach's banner
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Bearing Capacity Calculator - Meyerhof Approach

Verified by the CalcTree engineering team on July 20, 2024

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


Calculation

Assumption

  1. The water table is below the foundation and hence soil properties are undrained
  2. Applicable to shallow foundations only, where
    
  3. Assumes friction angle
    
    , therefore excludes pure clay

Inputs

Footing Geometry



D
:1.50 m​



B
:2.00 m​



L
:5.00 m​



alpha
:12.00 deg​


Soil Properties



phi
:37.00 deg​



c
:40.00 kPa​



gamma
:11.00 kN / m^3​



Output



N_c
:5.3​



N_q
:1.1​



N_g
:0.0​



s_c
:1.08​



s_g
:1.04​



s_q
:1.04​



d_q
:1.08​



d_c
:1.15​



d_g
:1.08​



i_c
:1.00​



i_q
:1.00​



i_g
:0.46​



qu
:282 kPa​


Explanation

In 1963, Meyerhof introduced a solution for determining bearing capacity applicable to shallow foundations. Meyerhof's theory has similarities to Terzaghi's theories, the distinction being that there are additional factors to account for the footing shape, depth and load inclination:
  1. the shape factor determines the bearing capacity of circular or rectangular footing
  2. the depth factor accounts for the development of shearing resistance
  3. the inclination factor accounts for the inclination of the footing placement and the angle of load application.

The ultimate bearing capacity,

is calculated as:

qu=scNcdcicc′+sqNqdqiqγD+12γBsγNγdγiγ\large{q_u=s_cN_c d_ci_cc'+s_qN_qd_qi_q\gamma D+\frac{1}{2}\gamma Bs_\gamma N_\gamma d_\gamma i_\gamma}
Where:
  1. 
    
    is the cohesion of the drained soil
    
    
  2. 
    
    is the unit weight of the soil
    
    
  3. 
    
    is the depth of the footing below ground level
    
    
  4. 
    
    is the width of the footing
    
    
  5. 
    
    ,
    
    and
    
    are the bearing capacity factors, given by:

Nc=(Nq−1)cot⁡(ϕ′)Nq=1+sin⁡(ϕ′)1−sin⁡(ϕ′)eπtan⁡(ϕ′)Nγ=(Nq−1)tan⁡(1.4ϕ′)N_c=(N_q-1)\cot(\phi')\\N_q=\frac{1+\sin(\phi')}{1-\sin(\phi')}e^{\pi \tan(\phi')}\\N_\gamma=(N_q-1)\tan(1.4\phi')
  1. 
    
    and
    
    are the shape factors, given by:

sc=1+0.21+sin⁡(ϕ′)1−sin⁡(ϕ′)(BL)sq=sγ=1+0.11+sin⁡(ϕ′)1−sin⁡(ϕ′)(BL)s_c=1+0.2\frac{1+\sin(\phi')}{1-\sin(\phi')}(\frac{B}{L})\\s_q=s_\gamma=1+0.1\frac{1+\sin(\phi')}{1-\sin(\phi')}(\frac{B}{L})
  1. 
    
    and
    
    are the depth factors, given by:

dc=1+0.21+sin⁡(ϕ′)1−sin⁡(ϕ′)(DB)dq=dγ=1+0.11+sin⁡(ϕ′)1−sin⁡(ϕ′)(DB)d_c=1+0.2\sqrt{\frac{1+\sin(\phi')}{1-\sin(\phi')}}(\frac{D}{B})\\d_q = d_\gamma=1+0.1\sqrt{\frac{1+\sin(\phi')}{1-\sin(\phi')}}(\frac{D}{B})
  1. 
    
    and
    
    are the inclination factors, given by:

ic=iq=(1−α90o)2iγ=(1−αϕ′)2i_c=i_q=(1-\frac{\alpha}{90^o})^2\\i_\gamma=(1-\frac{\alpha}{\phi'})^2

References

  1. Foundation by Engineering Infinity
  2. Principles of Geotechnical Engineering 7th Edition by Braja M. Das

Related Resources

  1. 3D Mohr's Circle
  2. Mohr's Circle for 2D Stresses
  3. Weight to Volume relationships in soils

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