## Foundation – Stability Analysis

The maximum load that can be sustained by shallow foundation elements due to the bearing capacity is a function of the cohesion and friction angle of bearing soils as well as the width B and shape of the foundation. The net bearing capacity per unit area, q_{u}, of a long footing is expressed as:

where

(alpha)_{f}= 1.0 for strip footings and 1.3 for circular and square footings

c_{u}= Un-drained shear strength of soil

_{(sigma) }_{vo} = effective vertical shear stress in soil at level of bottom of footing

(beta)_{f} = 0.5 for strip footings, 0.4 for square footings, and 0.6 for circular footings

gamma =unit weight of soil

B=width of footing for square and rectangular footings and radius of footing for circular footings

N_{c}, N_{q}, N=bearing-capacity factors, functions of angle of internal friction (phi)