# Bearing capacity for circular foundations (Terzaghi's Theory)

## Description

In geotechnical engineering, bearing capacity is the capacity of soil to support the loads applied to the ground. The bearing capacity of soil is the maximum average contact pressure between the foundation and the soil which should not produce shear failure in the soil. Ultimate bearing capacity is the theoretical maximum pressure which can be supported without failure; allowable bearing capacity is the ultimate bearing capacity divided by a factor of safety. Sometimes, on soft soil sites, large settlements may occur under loaded foundations without actual shear failure occurring; in such cases, the allowable bearing capacity is based on the maximum allowable settlement.

Karl von Terzaghi was the first to present a comprehensive theory for the evaluation of the ultimate bearing capacity of rough shallow foundations. This theory states that a foundation is shallow if its depth is less than or equal to its width. Later investigations, however, have suggested that foundations with a depth, measured from the ground surface, equal to 3 to 4 times their width may be defined as shallow foundations.

Terzaghi developed a method for determining bearing capacity for the general shear failure case in 1943. The equations, which take into account soil cohesion, soil friction, embedment, surcharge, and self-weight.

Related formulas## Variables

q_{ult} | Bearing capacity (dimensionless) |

c | effective cohesion (dimensionless) |

N_{c} | N_c bearing capacity factor (dimensionless) |

σ_{D} | vertical effective stress (dimensionless) |

N_{q} | N_q bearing capacity factor (dimensionless) |

γ | effective unit weight (dimensionless) |

B | width or the diameter of the foundation (dimensionless) |

N_γ | N_gamma bearing capacity factor (dimensionless) |