## Consolidation by drainage in two and three dimensions

The majority of settlement analyses are based on the frequently incorrect assumption that the flow of water in the soil is one dimensional, partly for ease of calculation and partly because in most cases knowledge of soil compression values in three dimensions is limited. There are occasions when this assumption can lead to significant errors (as in the case of an anisotropic soil with a horizontal permeability so much greater than its vertical value that the time-settlement relationship is considerably altered) and when dealing with a foundation which is relatively small compared with the thickness of the consolidating layer some form of analysis allowing for lateral drainage becomes necessary. For an isotropic, homogeneous soil the differential equation for three-dimensional consolidation is:

For two dimensions one of the terms in the bracket is dropped.

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