Hvoslev surface

This result is similar to drained triaxial tests (namely, CTj = constant, dp = — (l/3)rfa(, dq= — da, dq/dp = 3). As shown in Fig. 6.2d, if an undrained stress path B-B under a consolidation pressure p g intersects with a drained stress path A-A" under a consolidation pressure a point C, the void ratio obtained from the undrained test is the same as the void ratio obtained from the drained test. We can draw these states in a space p, q, e) as illustrated in Fig.6.2f, which shows that the critical state is reached after travelling the surface referred to as the state boundary surface or Roscoe surface in both the undrained and drained tests. The line of failure is known as the critical state line (CSL). It is noted that the projection of CLS in the space p, q, e) onto the space (p, q) is given as = Mp, and the surface formed by CLS and its projection onto q, e) is referred to as Hvoslev surface, which is a failure surface found by Hvoslev in 1937 through a series of direct shear tests conducted on Vienna clay. 

Let us consider the shearing behavior of a heavily over-consolidated clay. We start to make it swell from a point A on the normally consolidated line (NCL) to a point B shown in Fig. 6.3d, e. When we perform an undrained triaxial test, the shear stress q attains the yield point P on the Hvoslev surface (namely the maximum point for the stress ratio rj = q/p ), and moves on the Hvoslev surface to reach the point C on the CSL. On the other hand, if a drained triaxial test is performed from the point B, the shear stress q attains the peak strength Q, then the stress reaches a residual state R through a softening process. Note that in practical experiments a shearing slip surface is commonly observed, and the whole specimen cannot reach the residual state. 

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