Soil Pressure under Isolated footings
Allowable Soil Pressure
The plan area of a footing base slab is selected so as to limit the maximum soil bearing pressure induced below the footing to within a safe limit. This safe limit to the soil pressure is determined using the principles of soil mechanics. The main considerations in determining the allowable soil pressure, as well as fixing the depth of foundation, are
(i) that the soil does not fail under the applied loads.
(ii) that the settlements, both overall and differential, are within the limits permissible for the structure. The safety factor, used in soil mechanics, lies in the range 2 – 6, and depends on the type of soil, and related uncertainties and approximations.
It should be noted that the value of the safe soil bearing capacity (‘allowable soil pressure’), qa, given to the structural designer by the geotechnical consultant, is applicable for service load conditions, as qa includes the factor of safety. Another point to be noted is that the prescribed allowable soil pressure qa at a given depth is generally the gross pressure, which includes the pressure due to the existing overburden (soil up to the founding depth), and not the net pressure (in excess of the existing overburden pressure). Hence, the total load to be considered in calculating the maximum soil pressure q (≤ qa) must include the weight of the footing itself and that of the backfill. Often, in preliminary calculations these weights are accounted for approximately as 10 – 15 percent of the axial load on the column; however, this assumption should be verified subsequently.
Distribution of Base Pressure
The distribution of the soil reaction acting at the base of the footing depends on the rigidity of the footing as well as the properties of the soil. The distribution of soil pressure is generally non-uniform. However, for convenience, a linear distribution of soil pressure is assumed in normal design practice.
Concentrically Loaded Footings
Thus, in a symmetrically loaded footing, where the resultant vertical (service) load P ΔP (where P is the load from the column and ΔP the weight of footing plus backfill) passes through the centroid of the footing, the soil pressure is assumed to be uniformly distributed, and its magnitude q is given by
where A is the base area of the footing.
Assumed uniform base pressure distribution under concentric loading Limiting q to the allowable soil pressure qa will give the minimum required area of footing:
Eccentrically Loaded Footings
The load P acting on a footing may act eccentrically with respect to the centroid of the footing base. This eccentricity e may result from one or more of the following effects:
• the column transmitting a moment M in addition to the vertical load ;
• the column carrying a vertical load offset with respect to the centroid of the footing;
• the column (or pedestal) transmitting a lateral force located above the foundation level, in addition to the vertical load.
For the purpose of determining the base pressures under eccentric loading, the footing is assumed to be rigid and the contact pressure distribution to be linear. The magnitude of the pressure distribution is determined from considerations of simple static equilibrium. Essentially this means that the centre of pressure (through which the resultant soil reaction R acts) must be collinear with the resultant line of action of the eccentrically applied load P ΔP, with R = P ΔP.
For preliminary calculations, ΔP, the weight of footing plus backfill, may be taken as 10–15 percent of P.
It is seen that the entire contact area of the footing is subject to a (nonuniform) pressure which varies linearly from qmin to qmax. These pressures are easily obtained by superposing the separate effects due to the direct load (P ΔP) and the bending moment M = (P ΔP) e:
with area A = BL and section modulus Z = BL2/6, where L is the length of the footing in the direction of the eccentricity e, and B the width of the footing. Accordingly,