Metodología de diseño

The concept of a pre-consolidation pressure was introduced in section 2.3, and is defined as the stress at which the gradient of the void ratio / mean effective stress curve changes (figure 2.6.1). At the pre-consolidation pressure, the behaviour of the rock changes from elastic to elasto-plastic. Hysteresis in the unloading / re loading loop can sometimes be observed, but this is generally sufficiently small as to be negligible (Atkinson and Bransby, 1978). Such changes in behavioural style can also be seen in compression experiments, and occur in all sedimentary rocks (Yassir, 1988; Leddra, 1990; Kageson-Loe, 1994; for example).

Legend

VR

VR Void Ratio

Mean effective stress Yield point

Figure 2.6.1 The change in slope of the compaction curve representing the pre­

The yield envelope for a remoulded soil may be determined by stress path testing. Identical samples are tested along different stress paths in the low (0 MPa to 1 MPa) environment. The yield point for each sample may be determined, and thus a locus of yield points deduced, representing the yield envelope. Thus 7or any stress path the yield point, representing the boundary between elastic and elasto-plastic behaviour, may be deduced (Muir-Wood, 1990). Such plots have been produced for soils in the low pressure environment by Wong and Mitchell, (1975) for example.

Studies of the yield behaviour of chalk in the high pressure regime have been undertaken (e.g. Leddra, 1990; Kageson-Loe et al., 1993). Yield in this case is a different process to that described for the low pressures. Yield in the high pressure regime generally describes the breakdown of cement bonds in a material as opposed to the change in behaviour from normally to over-consolidated. Loe et al. (1992) examined the yielding behaviour of chalk by testing identical samples along stress paths with different k-ratios (the k-ratio is the ratio between lateral and vertical stress; Loe et al., 1992). Figure 2.6.2 illustrates the stress paths derived from that study, with the yield envelope included. Of note is the shape of the yield envelope which has a complex form and, most notably, yields at higher mean effective stresses if an isotropic stress path is followed than if the sample is tested along a uniaxial stress path. This is in contradiction of the results of Elliot and Brown (1985), who suggested that for sedimentary materials the magnitude of stresses at yield were...stress path independent'.

The yield behaviour of an artificially bonded material deformed under uniaxial strain conditions (from Vaughan etal, 1988; redrawn by Leddra, 1990) is illustrated (figure 2.6.3). Vaughan et al (1988) suggest that yield is a more complex process than the simple breakdown of cement bonds described by Loe et al. (1992). The sample is seen to have two yield points during compaction. Yield is thus seen as a double process, representing different failure mechanisms.

The first yield is the point at which some of the bonds begin to fail. Up to this point, the bonds are able to sustain the applied stresses and there is no reduction in void ratio. Thereafter the bond strength of the sample (i.e. the stress that a sample can sustain without loss of void ratio) decreases as applied stress, the so-called bond stress of Vaughan et al. (1988), increases (Kageson-Loe et al., 1994). The second yield represents the point at which decreasing bond strength becomes equal to the

50 200 1 8 0 40 1 6 0 S 30 1 4 0 GO liJ 1 0 0 8 0 10 %"0 5-0 50 40 20 " ^ 30

MEAN EFFECTIVE STRESS (MPa)

Figure 2.6.2 Axial strain contours (in %) for the stress path testing of Loe ef al

1st yield

2nd yield 140-

p - 9 -

O edom eter test from

V maximum initial void ratio

,0-8- 0 7 2nd yield \ 1 s t yield 0-6 8 0 0 6 0 0 200 4 0 0 0 P ^ (kP a)

Figure 2.6.3 Plot of the yield behaviour of an artificially bonded material deformed under unaxial strain conditions compared to that of a similar unbonded sample (Vaughan et al, 1988; redrawn by Leddra, 1990)

decreases and thus the bond stress must also decrease. The sample will thereafter behave in a destructured manner, and the stress-strain curve will tend towards the compression curve for a remoulded material.

Vaughan et at. (1988) emphasise that first and second yield do not represent complete destruction of bond strength, and verify this with examination of the tensile strength of samples that have yielded. Vaughan ef a/. (1988) describe the shear behaviour of samples that have undergone first and second yield. Samples that have remained within first yield show full strength under undrained shear. However, a sample that has exceeded the first yield point has incurred some irreversible loss of strength and may not reach the ultimate strength otherwise expected. Yield beyond the second point induces substantial damage to the bond structure of the sample and large strains accumulate before failure.

In addition to the double yield in compaction described by Vaughan ef a/. (1988), all undisturbed materials, whether in the brittle or the ductile regime, show an initial elastic response to undrained deformation (figure 2.6.4). This deformation is termed phase I in section 2.4. This suggests that in the early phase of loading the deformation is dominantly elastic. This supports the assertion of Vaughan ef ai

(1988) that first' and 'second' yield do not represent the point at which breakdown of all of the bonds within the sample occurs. Yield in compaction must be viewed as the progressive breakdown of the bonds within the material and should not be seen as an instantaneous event, or one which occurs throughout the sample. Yield envelopes should be viewed as the point at which bond breakage is initiated rather then the point at which all bonds fall. The yield in shear represents the point at which inter­ particulate shearing is mobilised in the sample.

1

Axial Strain (%l

2.7 Summary

In chapter 2, the main mechanical properties of mudrocks in the geologically-relevant 1 - 70 MPa stress range have been described. The compaction of mudrocks has been outlined and the behaviour of these materials under shear stresses detailed. It has been shown that at low confining pressures, shales behave in a brittle manner when subjected to shear stresses. A few studies (most notably Ibanez and Kronenberg, 1993) have suggested that at higher pressures behaviour of undisturbed mudrocks will be ductile in the same manner as remoulded mudrocks and other sedimentary materials. The results of Bishop et al. (1965) and Ibanez and Kronenberg (1993) suggest that as the deformation mechanism in mudrocks changes from brittle to ductile the gradient of the failure envelope will also change.