Most soil samples tested in the triaxial apparatus are isotropically consolidated, i.e. consolidated under an all-round hydrostatic pressure, before the commencement of the shearing part of the test. It is appreciated that other forms of consolidation are possible, e.g. K0 consolidation, but these forms will not be considered here.
The form of the compression curve for an isotropically consolidated clay is shown in Fig. 13.1a. It should be noted that the plot is in the form of a v-p', plot the vertical axis being 0: v and the horizontal axis 0: p'. The v-lnp' plot is shown in Fig. 13.1b and from this diagram we see that, if we are prepared to ignore the slight differences between the expansion and the recompression curves, the semi-log plot of the isotropic consolidation curve for most clays can be assumed to be made up from a set of straight lines and to have the idealised form of Fig. 13.1c.
Any point on the line ABC represents normal consolidation whereas a point on the line BD, or indeed any point below ABC, represents over-consolidation. As line DB represents the idealised condition that the expansion and recompression curves coincide, it is probably best to give it a new name and it is therefore usually called the swelling line.
If the maximum previous pressure on a swelling line is pi„ and the pressure at D, a point on the swelling line, is p' then we can say that the degree of overconsolidation represented by point D is Rp = pin/p'. (Note the use of the subscript p- in Rp to indicate isotropic consolidation.)
Figure 13.2 is a close-up of Fig. 13.1c. In the diagram let the slope of AC, the normal isotropic consolidation line, be -A, and the slope of the swelling line, DB, be — k. N = the specific volume of a soil normally consolidated at lnp' value of 0.0. This gives lnp' = 0. Then the equation of line AC is:
A swelling line, such as BD can lie anywhere beneath the line AC as its position is dependent upon the value of the maximum pressure on the line, pm, which determines the position of B.
Let vK — the specific volume of an overconsolidated soil at p' = unity (i.e. 1.0kN/m2). Then the equation of line DB is:
A, N and k are measured values and must be found from appropriate tests.
Note The normal consolidation line, AC, is often referred to as the A line, i.e. the lambda line and the swelling line BD is often called the k line, i.e. the kappa line.
13.4.1 Equivalent isotropic consolidation pressure, p'e
Consider a particular specific volume, v. Then the value of consolidation pressure which corresponds to v on the normal isotropic consolidation curve is known as the equivalent consolidation pressure and is given the symbol In Fig. 13.2 the point P represents a soil with a specific volume, v, and an existing effective consolidation pressure p'x. The procedure for determining p£ is illustrated in the diagram. Note that as P is below AB, it represents a state of overconsolidation.
For a normally consolidated clay, subjected to an undrained triaxial test, Pe = a[ but with drained tests p|. will vary (see Example 13.3).
13.4.2 Comparison between isotropic and one-dimensional consolidation
If a sample of clay is subjected to one-dimensional consolidation in an oedometer and another sample of the clay subjected to isotropic consolidation in a triaxial cell then the idealised forms of the v-ln p' plots for the tests will be more or less as illustrated in Fig. 13.3.
The values of the slopes of the two normal consolidation lines are very close and, for all practical purposes, can both be assumed to be equal to —A. Similarly the slopes of the swellling lines can both be taken as equal to —k.
Note that the values of lnp' for the one-dimensional test are taken as equal to In a' where a' = the normal stress acting on the oedometer sample.
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