The Roscoe surface
For any value of the consolidation pressure p(> there will be a corresponding position for A and hence an infinite number of possible planes, drained or undrained, on which stress paths travelling from A to B may lie. A number of planes with their stress paths are shown in Figs 13.1 la (undrained) and 13.1 lb (drained).
If we place the two sets of stress paths together we see that they appear to lie on a threedimensional surface bounded by the critical state line at the top and by the normal consolidation line at the bottom. It can be shown that both sets of stress paths do lie on this surface by the technique of normalisation. If we take the results of a set of undrained and drained compression tests and divide the test q and p' values by their corresponding Pe values the resulting plots tend to lie on a single unique line of the form illustrated in Fig. 13.12. Undrained and drained stress paths plotted in p'qv space therefore lie on the same threedimensional surface. This surface is called the Roscoe surface.
Fig. 13.12 The Roscoe surface. EXAMPLE 13.3
A sample of saturated clay had an initial volume of 86.2 ml and was isotropically consolidated at a cell pressure of 300kN/m2, which assured normal consolidation. During consolidation 6.2 ml of water was expelled into the drainage burette and the void ratio of the sample at this stage was estimated to be 0.893. The sample was then subjected to drained shear and readings of deviator stress and volume change were taken at increments of axial strain with the following results:
Fig. 13.12 The Roscoe surface. EXAMPLE 13.3
A sample of saturated clay had an initial volume of 86.2 ml and was isotropically consolidated at a cell pressure of 300kN/m2, which assured normal consolidation. During consolidation 6.2 ml of water was expelled into the drainage burette and the void ratio of the sample at this stage was estimated to be 0.893. The sample was then subjected to drained shear and readings of deviator stress and volume change were taken at increments of axial strain with the following results:
£a (%) 
a'a  a'r (kN/m2) 
AV (ml) 
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