Meyerhof Bearing Capacity Calculator
Foundation Engineering: Determine ultimate and allowable bearing capacity ($q_{ult}$, $q_{all}$) for shallow footings using the Meyerhof general bearing capacity theory.
Footing Geometry & Embedment
Soil Shear Strength & Groundwater
Ultimate & Allowable Bearing Capacities
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Meyerhof General Bearing Capacity Theory (1963)
Meyerhof's bearing capacity formulation is the premier classical model for shallow footings, accounting for soil cohesion, surcharge embedment, self-weight, and structural load geometry.
1. General 3-Term Formula
The ultimate bearing capacity $q_{ult}$ is given by:
q_ult = c' · N_c · s_c · d_c · i_c + q' · N_q · s_q · d_q · i_q + 0.5 · γ · B · N_γ · s_γ · d_γ · i_γ
2. Bearing Capacity Factors
N_q = e^(π · tan φ') · tan²(45° + φ'/2) N_c = (N_q - 1) · cot φ' N_γ = (N_q - 1) · tan(1.4 · φ')
Frequently Asked Questions
How does Meyerhof's theory differ from Terzaghi's bearing capacity equation?
Terzaghi assumed the shear failure surfaces terminate at the foundation base level and treated the soil above as an equivalent surcharge ($q = \gamma D_f$) with no shear strength. Meyerhof (1963) extended the failure surfaces through the overburden soil up to the ground surface, introducing rigorous shape ($s$), depth ($d$), and load inclination ($i$) factors that yield more realistic bearing capacities for deep and inclined footings.
Why does load inclination drastically reduce bearing capacity?
Horizontal or inclined loads induce shearing stresses along the footing base that accelerate plastic yielding in the active wedge. Meyerhof's inclination factor $i_\gamma = (1 - \theta/\phi')^2$ diminishes rapidly as horizontal shear angle $\theta$ approaches the internal friction angle $\phi'$, severely cutting allowable pressure.
What factor of safety is typically used for shallow foundations?
A factor of safety of $FS = 3.0$ is standard in geotechnical engineering practice for shallow spread footings under dead and live load combinations. For transient loads (wind or seismic combinations), $FS = 2.0$ or $2.25$ is frequently accepted in modern building codes (IBC/Eurocode 7).