For soil applications, this is the basis of elastic deformation of soil particles. Each discrete particle of soil, in contact with another discrete particle of soil, will deform when loaded, depending on the force that is "driving" contact between the two particles. The elastic half space is the volume in which this deformation takes place. The surface area over which this occurs is known as Hertzian contact stress and applies to any elastic material, not just soil.
Soil is a little more complicated because as each particle is loaded, it has two choices....to move into an unoccupied space or deform in contact with another particle. If it deforms, it does so in the "half space" defined by the contact area that increases with deformation until the stress stabilizes. This part if soil movement is recoverable and is known as "elastic deformation or elastic settlement". The first part is re-orientation of the soil grains (compaction or decrease in void ratio), which is generally not recoverable and results in permanent deformation of the soil mass, but not of the individual particles.
Maybe some of our geotechnical colleagues here can expand on this a bit.
Gee, Ron, I learned a new word - Hertzian Contact Stress!! From Poulos and Davis' Tome on Elastic Solutions for Soil and Rock Mechanics -
"The half space analysed in this work (their book) can be described as an elastic body having infinite lateral extent and depth with loads applied to its horizontal plane surface. Being elastic and orthorhombic the material has three mutually perpendicular planes of elastic symmetry. The normals to these planes are assumed to be parallel to the vertical, lateral, and longitudinal directions associated with the load."
I always thought of the "half space" as the elastic body below the loading - with "air" above . . . that's why it wasn't/isn't a "full space" - simplistic yes.
BigH, your last paragraph was very nice and it makes much more easier to understand/remember this concept.
Also, from my school notes, my understanding of "half space" is that it can be defined as the space to the boundaries of a specific soil model in which solutions are not affected, so for simplicity it can be assumed as infinite, but for practical purposes, not necessarily it needs to be infinite.
For example, not sure if it is possible to adjust the extent of the soil model in geotechnical software for calculating settlements, but, if you analyze the settlement for a footing with a "space" of 2B (which B is the width of the footing) you will get larger settlements than if you analyze for a model with a "space" of 1B. However, then, if you analyze for "spaces" of 4B, 5B, 6B, etc, you will see that the settlement will converge to a given value. So, the "half space" in this case may be 5B-6B. That is how I understood "half space".
hi hokie66, your post reminded me that I saw an article in the Geostrata magazine from ASCE some time ago about why for geotechnical engineers soils are not just "dirt"... I will try to locate that article and post it here....
Just to expand on this while it is "fresh" in my head. On the other hand, you may have the "full space" condition that BigH mentioned. This can occur when the load is not applied on the surface of a "half space", rather, the load is applied within the "space" (for example a load acting in a pile which is transferred to the pile tip). If the space in this case is very large, this is no longer a "half space", this will be a "full space" or "infinite space". This is applicable in the analysis for settlement of pile foundations. You can search for "Mindlin's problem". I found this link that may help. Look at page 20.
