## Hvorslev Surface

The normalised plot is shown in Fig. 13.13. Overconsolidated clays

We have established that the stress paths of normally consolidated clays lie on the Roscoe surface and, in order to complete the picture, we must determine whether the stress paths of overconsolidated clays also lie on this surface or whether they have a unique surface of their own.

Fig. 13.13 Example 13.3.

Figure 13.14 shows a series of normalised stress paths of undrained shear obtained from tests carried out on overconsolidated clays. As expected, with Rp = 1.0 the stress path lies on the Roscoe surface (as the soil is normally consolidated). For lightly overconsolidated clays, i.e. for Rp values up to about 2.5, the stress paths rise upwards, more or less vertically in the initial loading stage, towards the Roscoe surface but, before reaching it, they bend slightly and gradually make their ways to the critical state line where failure occurs.

The stress paths for the more heavily overconsolidated clays initially rise up more or less vertically and then incline inwards during the final loading stages to become tangential to a common straight line as they make their way towards the critical state line. This straight line is a boundary known as the Hvorslev surface.

### 13.9 The overall state boundary

The Roscoe surface has the property that any stress state outside it cannot exist in a soil. It is a boundary between possible stress states and impossible

Fig. 13.14 Undrained stress paths of overconsolidated clay.

stress states and is therefore usually referred to as a state boundary. The Hvorslev surface is a similar state boundary and links up with the Roscoe surface at the critical state line (point B in Fig. 13.15). The Hvorslev surface cannot extend to the q/p£ axis because of the line of no tension, OC, which rises from the origin at a slope of 1:3.

Note If we assume that soil cannot carry tension then tension failure must occur if ever a'a is less than o\. Now the lowest possible value of q is 0 which means that the tension failure boundary must pass through the origin. The highest possible value for q will occur when a'T = 0 and q therefore equals <r'a. At this stage p' = cra/3 which means that q/p' = 3.

Hence, if we select some value for p'/p'e, say x, then = p'/x and q/Pe = 3x. The unified plot of the complete state boundary, in q/Pe-p'/Pe space is shown in Fig. 13.15a and in p'-q-v space in Fig. 13.15b.

### Wet and dry regions

If we examine Fig. 13.15 we see that the state boundary surface for normally consolidated soils is further from the origin than the critical state line. In this region, any soil travelling along a drained stress path from A to B suffers a gradual reduction in specific volume, meaning that the water content at the end of the test must be less than it was immediately before the shearing stage. We can say therefore that soils in this region, when subjected to drained shear, have an initial state that is wetter than the critical state.

Heavily overconsolidated clays have initial consolidation points A on the other side of the critical state line and if these soils are subjected to drained shear they will expand as they approach failure conditions with a corresponding increase in water content. Such soils have an initial state that is drier than the critical state.

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