# Shallow foundations on stratified ground

In the context of the evaluation of the bearing capacity of shallow foundations presented so far, it has been assumed that the underlying ground is homogeneous, i.e., the thickness of the soil layer, whose strength data is considered in the preceding expressions, is sufficiently large for the bearing capacity to depend exclusively on that same layer. Taking Figure 6.3 as

Table 6.3 Expressions of the corrective factors for the simplified theoretical solution of the bearing capacity of a shallow foundation.

 Effect 1st term (cohesion) 2nd term (surcharge) 3rd term (weight) Foundation shape (s factors) (see note 1) Load inclination (/ factors) (see note 2) Foundation base inclination (b factors) (see note 3) Ground surface inclination (g factors) (see note 4) Proximity of a firm stratum (f factors)

reference, this means that the sliding surface developed at failure does not extend to a layer other than that immediately underlying the foundation. As already discussed, the maximum depth, d, reached by that surface depends both on the soil friction angle and on the foundation dimensions, and may be estimated with the help of Figure 6.4.

When the bearing capacity depends on more than a single layer, its evaluation requires sound judgement and imagination for adapting the basic solution previously described.

If the contrast in strength between the two (or more) layers involved is not considerable, the computation of the bearing capacity exclusively on the basis of the data from each of them will allow calculation of the limits of an interval, within which lies the actual value of the bearing capacity. If this interval is relatively narrow, then a satisfactory solution has been found. Otherwise, the consideration of the relative importance of the layers in question may allow, in many cases, for the extraction of acceptable practical conclusions, concerning the proximity of the real bearing capacity to the upper or to the lower limit of that interval.

A simpler situation, and a particularly interesting one in practical terms, is when a firm stratum, of significantly higher strength, underlies the loaded soil layer. This problem has been tackled by Mandel and SalenĀ£on (1969, 1972), who, by applying the theory of plasticity, obtained a numerical solution for the (larger than 1.0) corrective factors, fc, fp and fY, for the three terms of the bearing capacity to account for the effect of the lower, rigid boundary of the soil layer. Those factors, included in Table 6.4, are a function of the friction angle of the soil layer and of the ratio between the foundation width, B, and the layer thickness, Dt.