Average degree of consolidation
Instead of thinking in terms of Uz, the degree of consolidation of a particular point at depth z, we think in terms of U, the average state of consolidation throughout the whole layer. The amount of consolidation still to be undergone at a certain time is represented by the area enclosed under the particular isochrone, and the total consolidation is represented by the area of the initial excess pore pressure distribution diagram (Fig. 10.3a). The consolidation achieved at this isochrone is therefore the total consolidation less the area under the curve (shown hatched in Fig. 10.3b). Average degree of consolidation,
The mathematical expression for U is:
A theoretical relationship between U and T can therefore be established and is shown in Fig. 10.4, which also gives the relationship for Uj distributions that are not uniform, m = u;/u2.
Time factor
Time factor
Impermeable
Fig. 10.4 Theoretical consolidation curves.
Impermeable
Fig. 10.4 Theoretical consolidation curves.
10.5 Drainage path length
A consolidating soil layer is usually enclosed having at its top either the foundation or another layer of soil and beneath it either another soil layer or rock. If the materials above and below the layer are pervious, the water under pressure in the layer will travel either upwards or downwards (a concrete foundation is taken as being pervious compared with a clay layer). This case is known as twoway drainage and the drainage path length, i.e. the maximum length that a water particle can travel (Fig. 10.5a) Thickness of layer
If one of the materials is impermeable, water will only travel in one direction the oneway drainage case  and the length of the drainage path = thickness of layer = 2H (Fig. 10.5b).
The curves of Fig. 10.4 refer to cases of oneway drainage (drainage path length = 2H). Owing to the approximations involved the curve for m = 1 is often taken for the other cases with the assumption that Uj is the initial excess pore pressure at the centre of the layer. For cases of twoway drainage the curve for m = 1 should be used and the drainage path length, for the determination of T, is taken as H.
Permeable
Permeable
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