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Author: ccg 2001-07-03

I have two questions,

1)anybody knows that the derivation of Boussinesq's equation on the change of stress at any point beneath the level of applied load. What puzzle me is that normally the state of stress should be related to the strain of soil being stressed. what is the assumption behind this equation.

2) The stress distribution of shallow foundation differs from clayey to sandy formation and as well for the flexible to rigid raft. Why the maximum settlement occurs at the centre of foundation for flexible raft in clay while for sand, it occurs at edge. What is the truely machanisme behind these two behaviours ?


have a nice day
ccg
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Follow-up:
Author: Tom Sklucki 2001-07-13

To ccg (singapore) and nj (turkey)

With a flexible foundation, the bearing pressure is uniform over the base of the foundation. On a linearly elastic elastic material (which we use to model clay over a relatively short time span) there is more settlement under the centre of the foundation because we superimpose the effects of the contact on the ground of each part of the foundation (in the model by summing a set of point loads, i.e. integrating Boussinesq equation). Put simplistically, the stress at a point beneath the centre of the foundation has contributions from more elements of the foundation than the stress at a point beneath the edge of the foundation so the point beneath the centre settles more.

In practice, with a granular material (sand) as opposed to a continuum (clay) the stress-strain behaviour of the material is much more strongly influenced by the three dimensional state of stress. In simple terms the soil under the centre of the foundation is more 'confined' and therefore 'stiffer' than the soil under the edges of the foundation. Thus we get more settlement at the edges. You do still get the same 'confining' effect with the continuum - strain is calculated using Poisson's Ratio as well as Elastic Modulus - but in this case the effect is relatively small and does not noticeably change the shape of the settlement profile.

With a rigid foundation on a linearly elastic material the settlement at all points under the foundation is the same. As the foundation presses into the soil, the edges of the foundation must, because of the rigidity of the foundation, settle by the same amount as the centre.

With the continuum (clay), points under the centre of the foundation settle more than points ubder the edge of the foundation because they have contributions of stress from more elements of the foundation. Thus, as the rigid foundation sinks into the soil, bearing pressure rises at the edges to enforce the requirement for uniform settlement and remains relatively high when the foundation reaches equilibrium.

With the granular soil, which is much more strongly influenced by the three dimensional state of stress, the soil under the centre has a much 'stiffer' response than soil under the edges of the foundation. In this case, as the foundation sinks into the soil a higher bearing pressure will develop under the centre of the foundation than under the edges, in order to cause the same deformation (settlement) of the soil.


Sorry if the explanation is a bit long, but I couldn't think of a way to make it shorter. regards Tom