WORLD FOR CIVIL

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 con ventionally expressed as:

q_u=?_fc_uN_c+?_voN_q+?_f?BN_?

where
?_f= 1.0 for strip footings and 1.3 for circular and square footings

c_u= undrained shear strength of soil

?_vo= effective vertical shear stress in soil at level of bottom of footing

?_f= 0.5 for strip footings, 0.4 for square foot- ings, and 0.6 for circular footings

?=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

For undrained (rapid) loading of cohesive soils, ?=0
thus equation reduced to

q_u= N ‘_c c_u

where
N’_c=?_fN_c

For drained (slow) loading of cohesive

soils,? and c_u are defined in terms of effective friction angle ?’ and effective stress c_u.

Assumptions done in lieu of equation

1) The equation is based on an infinitely long strip footing

2) The soils to be homogeneous throughout the stressed zone,

The value of correction factors can be had from the table below
Correction Factor

Shape of Foundation	Nc	Nq	Ny
Rectangle	1+(B/L)(Nq/Nc)	1+(B/L)tanΦ	1-0.4(B/L)
Circle and Square	1+(Nq/Nc)	1+tanΦ	0.60

Eccentric loading
Eccentric loading have a significant impact on selection of the bearing value for foundation design. The footing is assumed to be rigid and the bearing pressure is assumed to vary linearly .

Points to ponder
For the case where only a portion of the footing is bearing, the maximum pressure may be approximated by trial and error.
For all cases of sustained eccentric loading, the maximum (edge) pressures should not exceed the shear strength of the soil and also the factor of safety should be at least 1.5 (preferably 2.0) against overturning.