With the Newmark chart in Fig. 4.8, determine the vertical stress increment at a depth of 5 m in Example 4.4.
As z is 5 m, the distance AB on the chart represents 5 m to the same scale as that to which the foundation must be drawn. Owing to the symmetry only a quarter of the foundation need be considered (Fig. 4.8), the number of influence units enclosed by this quarter being 13.9.
This method is simple but can become very tedious; it is used for peculiarly shaped foundations and can be applied to spoil heaps.
If points of equal vertical pressure are plotted on a cross-section through the foundation, diagrams of the form shown in Figs 4.9a and 4.9b are obtained.
These diagrams are known as bulbs of pressure and constitute another method of determining vertical stresses at points below a foundation that is of regular shape, the bulb of pressure for a square footing being obtainable approximately by assuming that it has the same effect on the soil as a circular footing of the same area.
In the case of a rectangular footing the bulb pressure will vary at cross-sections taken along the length of the foundation, but the vertical stress at points below the centre of such a foundation can still be obtained from the charts in Fig. 4.9 by either (i) assuming that the foundation is a strip footing or (ii) determining a, values for both the strip footing case and the square footing case and combining them by proportioning the length of the two foundations.
From a bulb of pressure one has some idea of the depth of soil affected by a foundation. Significant stress values go down roughly to 2.0 times the width
of the foundation, and Fig. 4.10 illustrates how the results from a plate loading test may give quite misleading results if the proposed foundation is much larger: the soft layer of soil in the diagram is unaffected by the plate loading test but would be considerably stressed by the foundation.
Boreholes in a site investigation should therefore be taken down to a depth at least 1.5 times the width of the proposed foundation or until rock is encountered, whichever is the lesser.
Small foundations will act together as one large foundation (Fig. 4.11) unless the foundations are at a greater distance apart (c/c) than five times their width, which is not usual. Boreholes for a building site investigation should therefore be taken down to a depth of approximately 1.5 times the width of the proposed building.
Plate loading test Proposed foundation u
j ' •■; ' ' \ Soft layer ■'.■:•/■.' .;■':;>; yJS). -|".;:V-\ -
Wims
Fig. 4.10 Illustration of how a plate loading test may give misleading results.
Fig. 4.11 Overlapping of pressure bulbs.
4.7 Shear stresses
In normal foundation design procedure it is essential to check that the shear strength of the soil will not be exceeded. The shear stress developed by loads from foundations of various shapes can be calculated. Jiirgenson obtained solutions for the case of a circular footing and for the case of a strip footing (Fig. 4.12). It may be noted that, in the case of a strip footing, the maximum stress induced in the soil is p/7r, this value occurring at points lying on a semicircle of diameter equal to the foundation width B. Hence the maximum shear stress under the centre of a continuous foundation occurs at a depth of B/2 beneath the centre.
Uniform pressure, P
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