A 4.5 m square foundation exerts a uniform pressure of 200kN/m2 on a soil. Determine (i) the vertical stress increments due to the foundation load to a depth of 10 m below its centre and (ii) the vertical stress increment at a point 3 m below the foundation and 4 m from its centre along one of the axes of symmetry.
(i) The square foundation can be divided into four squares whose corners meet at the centre O (Fig. 4.7a).
0.163 0.652 130
0.074 0.296 59
(ii) This example illustrates how the method can be used for points outside the foundation area (Fig. 4.7b). The foundation is assumed to extend to the point K (Fig. 4.7c) and is now split into two rectangles, AEKH and HKFD. For both rectangles:
From Fig. 4.6, Ia = 0.176, therefore crz = 0.176 x 2 x 200 = 70.4 kN/m2. The effect of rectangles BEGK and KGCF must now be subtracted. For both rectangles:
From Fig. 4.6, la = 0.122 (strictly speaking m is 0.58 and n is 0.75, but m and n are interchangeable in Fig. 4.6). Hence:
Therefore the vertical stress increment due to the foundation
Circular foundations can also be solved by Steinbrenner's method, and according to Jtirgenson (1934) the stress effects from such a foundation may be found approximately by assuming that it is the same as for a square foundation of the same area.
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