## Jurgenson Stress 1934

Point load (Boussinesq Theory, 1885)

The simplest case of applied loading has been illustrated in Example 4.2. However, most loads are applied to soil through foundations of finite area so that the stresses induced within the soil directly below a particular foundation are different from those induced within the soil at the same depth but at some radial distance away from the centre of the foundation.

The determination of the stress distributions created by various applied loads has occupied researchers for many years. The basic assumption used in all their analyses is that the soil mass acts as a continuous, homogeneous and elastic medium. The assumption of elasticity obviously introduces errors but it leads to stress values that are of the right order and are suitable for most routine design work.

Some more modern methods of settlement analysis, such as those proposed by Lambe (1964, 1967), necessitate determining the increments of both major and minor principal stresses, but Jurgenson (1934) has prepared stress tables based on the elastic theory that can be very helpful in this and other aspects of stress analysis. A description of many solutions has also been prepared by Poulos and Davis (1974).

In most foundation problems, however, it is only necessary to be acquainted with the increase in vertical stresses (for settlement analysis) and the increase in shear stresses (for shear strength analysis).

Boussinesq (1885) evolved equations that can be used to determine the six stress components that act at a point in a semi-infinite elastic medium due to the action of a vertical point load applied on the horizontal surface of the medium.

His expression for vertical stress is: 3Pz3

where

P = concentrated load r = \/x2 + y2 (see Fig. 4.5). The expression has been simplified to:

where K is an influence factor. Values of K against values of r/z are shown in Fig. 4.5.

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