Bearing Capacity Calculator - Meyerhof Approach

In 1963, Meyerhof introduced a solution for determining bearing capacity applicable to shallow foundations irrespective of load inclination. 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.
CalculationInputsFooting Geometry
﻿﻿B
:3.00m​
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﻿﻿D
:5.00m​
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﻿﻿L
:3.00m​
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Soil Properties
﻿﻿γ
:11.00kN/m3​
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﻿﻿α
:10deg​
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﻿﻿ϕ
:35deg​
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﻿﻿c
:20.00kPa​
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Output﻿﻿qu
:4,332kPa​
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Explanation
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The shape factor determines the bearing capacity of circular or rectangular footing. The depth factor accounts for the development of shearing resistance. The inclination factor accounts for the inclination of the footing placement and the angle of load application.
Ultimate Bearing CapacityThe ultimate bearing capacity, qu, is calculated as:
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qu=scNCdcicc′+sqNqdqiqγD+12γBsγNγdγiγ\large{q_u=s_cN_Cd_ci_cc'+s_qN_qd_qi_q\gamma D+\frac{1}{2}\gamma Bs_\gamma N_\gamma d_\gamma i_\gamma}qu​=sc​NC​dc​ic​c′+sq​Nq​dq​iq​γD+21​γBsγ​Nγ​dγ​iγ​
Bearing Capacity
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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')Nc​=(Nq​−1)cot(ϕ′)Nq​=1−sin(ϕ′)1+sin(ϕ′)​eπtan(ϕ′)Nγ​=(Nq​−1)tan(1.4ϕ′)
Shape Factor
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sc=1+0.21+sin⁡(ϕ′)1−sin⁡(ϕ′)(BL)sq=1+0.11+sin⁡(ϕ′)1−sin⁡(ϕ′)(BL)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=1+0.1\frac{1+\sin(\phi')}{1-\sin(\phi')}(\frac{B}{L})\\s_\gamma=1+0.1\frac{1+\sin(\phi')}{1-\sin(\phi')}(\frac{B}{L})sc​=1+0.21−sin(ϕ′)1+sin(ϕ′)​(LB​)sq​=1+0.11−sin(ϕ′)1+sin(ϕ′)​(LB​)sγ​=1+0.11−sin(ϕ′)1+sin(ϕ′)​(LB​)
Depth Factor
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dc=1+0.21+sin⁡(ϕ′)1−sin⁡(ϕ′)(DB)dq=1+0.11+sin⁡(ϕ′)1−sin⁡(ϕ′)(DB)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=1+0.1\sqrt{\frac{1+\sin(\phi')}{1-\sin(\phi')}}(\frac{D}{B})\\d_\gamma=1+0.1\sqrt{\frac{1+\sin(\phi')}{1-\sin(\phi')}}(\frac{D}{B})dc​=1+0.21−sin(ϕ′)1+sin(ϕ′)​​(BD​)dq​=1+0.11−sin(ϕ′)1+sin(ϕ′)​​(BD​)dγ​=1+0.11−sin(ϕ′)1+sin(ϕ′)​​(BD​)
Inclination Factor
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ic=(1−α90o)2iq=(1−αϕ′)2iγ=(1−αϕ′)2i_c=(1-\frac{\alpha}{90^o})^2\\i_q=(1-\frac{\alpha}{\phi'})^2\\i_\gamma=(1-\frac{\alpha}{\phi'})^2ic​=(1−90oα​)2iq​=(1−ϕ′α​)2iγ​=(1−ϕ′α​)2
ReferencesFoundation by Engineering Infinity 
Principles of Geotechnical Engineering 7th Edition by Braja M. Das
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