Table of contents  
Introduction 
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The extent of the elastic layer below the surface loadings may be any one of the following:
The loads at the surface may act on flexible or rigid footings. The stress conditions in the elastic layer below vary according to the rigidity of the footings and the thickness of the elastic layer. All the external loads considered in this book are vertical loads only as the vertical loads are of practical importance for computing settlements of foundations.
Figure 6.1 shows a load Q acting at a point 0 on the surface of a semiinfinite solid. A semiinfinite solid is the one bounded on one side by a horizontal surface, here the surface of the earth, and infinite in all the other directions. The problem of determining stresses at any point P at a depth z as a result of a surface point laod was solved by Boussinesq (1885) on the following assumptions.
The soil is said to be isotropic if there are identical elastic properties throughout the mass and in every direction through any point of it. The soil is said to be homogeneous if there are identical elastic properties at every point of the mass in identical directions.
The expression obtained by Boussinesq for computing vertical stress σ_{z} at point P (Fig. 6.1) due to a point load Q is
(6.1)
where, r = the horizontal distance between an arbitrary point P below the surface and the vertical axis through the point load Q.
z = the vertical depth of the point P from the surface.
I_{B} Boussines q stres s coefficien t = (6.1a)
The values of the Boussinesq coefficient l_{B} can be determined for a number of values of r/z. The variation of I_{B} with r/z in a graphical form is given in Fig. 6.2. It can be seen from this figure
that I_{B} has a maximum value of 0.48 at r/z = 0, i.e., indicating thereby that the stress is a maximum below the point load.
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