A concentrated load of 400 kN acts on the surface of a soil.
Determine the vertical stress increments at points directly beneath the load to a depth of 10 m.
Solution
For points below the load r = 0 and at all depths r/z = 0, whilst from Fig. 4.5 it is seen that K = 0.48.
This method is only applicable to a point load, which is a rare occurrence in soil mechanics, but the method can be extended by the principle of superposition to cover the case of a foundation exerting a uniform pressure on the soil. A plan of the foundation is prepared and this is then split into a convenient number of geometrical sections. The force due to the uniform pressure acting on a particular section is assumed to be concentrated at the centroid of the section, and the vertical stress increments at the point to be analysed due to all the sections are now obtained. The total vertical stress increment at the point is the summation of these increments.
Uniform rectangular load (Steinbrenner's method, 1934)
If a foundation of length L and width B exerts a uniform pressure, p, on the soil then the vertical stress increment due to the foundation at a depth z below one of the corners is given by the expression:
0Z = pl(j where ICT is an influence factor depending upon the relative dimensions of L, B and z.
I^ can be evaluated by the Boussinesq theory and values of this factor (which depend upon the two coefficients m = B/z and n = L/z) were prepared by Fadum in 1948 (Fig. 4.6).
With the use of this influence factor the determination of the vertical stress increment at a point under a foundation is very much simplified, provided that the foundation can be split into a set of rectangles or squares with corners that meet over the point considered.
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