Effect of Size of Footings on Settlement.

Figure 13.3a gives typical load-settlement relationships for footings of different widths on the surface of a homogeneous sand deposit. It can be seen that the ultimate bearing capacities of the footings per unit area increase with the increase in the widths of the footings. However, for a given settlement S, such as 25 mm, the soil pressure is greater for a footing of intermediate width Bb than for a large footing with BC. The pressures corresponding to the three widths intermediate, large and narrow, are indicated by points b, c and a respectively.
The same data is used to plot Fig. 13.3b which shows the pressure per unit area corresponding to a given settlement S1, as a function of the width of the footing. The soil pressure for settlement Sl increases for increasing width of the footing, if the footings are relatively small, reaches a maximum at an intermediate width, and then decreases gradually with increasing width.

Although the relation shown in Fig. 13.3b is generally valid for the behavior of footings on sand, it is influenced by several factors including the relative density of sand, the depth at which the foundation is established, and the position of the water table. Furthermore, the shape of the curve suggests that for narrow footings small variations in the actual pressure, Fig. 13.3a, may lead to large variation in settlement and in some instances to settlements so large that the movement would be considered a bearing capacity failure. On the other hand, a small change in pressure on a wide footing has little influence on settlements as small as S1 , and besides, the value of ql corresponding to S1 is far below that which produces a bearing capacity failure of the wide footing.

For all practical purposes, the actual curve given in Fig. 13.3b can be replaced by an equivalent curve omn where om is the inclined part and mn the horizontal part. The horizontal portion of the curve indicates that the soil pressure corresponding to a settlement S1 is independent of the size of the footing. The inclined portion om indicates the pressure increasing with width for the same given settlement S1 up to the point m on the curve which is the limit for a bearing capacity failure. This means that the footings up to size Bl in Fig. 13. 3b should be checked for bearing capacity failure also while selecting a safe bearing pressure by settlement consideration.

The position of the broken lines omn differs for different sand densities or in other words for different SPT N values. The soil pressure that produces a given settlement Sl on loose sand is obviously smaller than the soil pressure that produces the same settlement on a dense sand. Since N- value increases with density of sand, qs therefore increases with an increase in the value of N.

Figure 13.3 Load-settlement curves for footings of different sizes (Peck et al., 1974)