Assumptions of Boussinesq's equation

Boussinesq's equation for the vertical stress below a point load on the surface is based on these assumptions:

1. The soil mass is a semi-infinite half-space bounded by a horizontal surface.
2. The soil is homogeneous, with the same properties at all points.
3. The soil is isotropic, with the same properties in all directions.
4. The soil is linearly elastic (stress proportional to strain, following Hooke's law).
5. The soil is weightless; the stresses considered are only those due to the applied load.
6. The load acts as a concentrated point load on the surface, vertical, and the soil is initially free of stress.
7. The soil is a continuous medium, and the stress distribution is independent of the elastic constants (the vertical stress does not depend on $E$ or $\nu$).