3.4 Stresses in the soil due to a strip pressure

Stresses applied on the soil surface e.g., from a footing of “infinite” length can be modelled as an infinitely long (strip) pressure acting on the surface of a homogeneous elastic half-space (Figure 3.7a). As plane-strain symmetry conditions apply, additional stresses due to the application of the pressure q_ext can be calculated as:

(3.10) [latex]\Delta {\sigma _z} = \dfrac{{{q_{ext}}}}{\pi }\left[ {\alpha + {\rm{sin}}\alpha \cos \left( {\alpha + 2\beta } \right)} \right][/latex]

(3.11) [latex]\Delta {\sigma _x} = \dfrac{{{q_{ext}}}}{\pi }\left[ {\alpha - \sin \alpha \cos \left( {\alpha + 2\beta } \right)} \right][/latex]

(3.12) [latex]\Delta {\tau _{zx}} = \dfrac{{{q_{ext}}}}{\pi }\left[ {\sin \alpha \sin \left( {\alpha + 2\beta } \right)} \right][/latex]

Τhe stress increment components and angles α and β are defined in Figure 3.6a. Angles α and β must be input in Eqs. 3.10 to 3.12 in radians, not in degrees, and may attain negative values too, as shown in Figure 3.7b.