Valoración de criterios de evaluación para EJB3/JPA

The critical state model, (section 2.3), has been used to interpret the behaviour of sedimentary rocks by a number of authors. Most notable is the large body of work on the deformation of chalk (for example Addis, 1987; Leddra, 1990; Loe et al., 1992; Andersen eta!., 1992; Petley eta!., 1993; Kageson-Loe, 1994; Petley eta!., 1994). In addition, some research has been undertaken into the application of critical state models to remoulded clays (Yassir, 1989), mudrocks (Horseman et a!., 1993) and to sandstones (Taylor and Coop, 1993).

In chapter 1 problems with the use of terminology with respect to the critical state model were outlined. In particular it was noted that whilst a clear failure state can frequently defined for a material, deformation in this state will frequently not precisely fit the definition of 'critical state'. End-state deformation is frequently not at absolutely

constant pore pressure (or volume) and / or stress. However deformation is

frequently defined as at 'critical state'. This is probably mainly due to the existence of linear failure and / or residual strength envelopes, which tend to be termed 'critical state lines'. This section will therefore outline the relevance, and short-comings, of the critical state model to sedimentary materiais.

In broad terms the critical state model describes the behaviour of materials in the 1 - 70 MPa pressure range reasonably well, but some modifications are necessary to account for the particulate nature of sedimentary rocks and for bonding. At lower confining pressures sedimentary rocks generally behave in a manner similar to that of heavily over-consolidated soils, displaying a brittle response to undrained loading (figure 2.4.1). Failure and residual strength tend to define linear envelopes, with the residual envelope frequently being termed the critical state line. Deformation is usually similar to a critical state, but due to the particulate nature of these materials is rarely at absolutely constant pore pressure and / or deviatoric stress. At higher confining pressures the behaviour of sedimentary rocks is similar to that of normally- consolidated soils, displaying ductile failure during undrained shear deformation (figure 2.4.1). Again end-state deformation is rarely at critical state sensu stricto. Between brittle and ductile response there is a poorly-described transitional regime.

o CL 2 (0 CO 0) (/) u * o I o 3.6.7 30.0 25.0 20.0 13.0 3.0 10.0 0.0 Axial strain (%)

Figure 2.4.1 Example of the mechanical behaviour of a sedimentary rock: Graph of

deviatoric stress / axial strain for the undrained shear deformation of Butser Hill chalk (from Leddra, 1990).

A plot of the mechanical behaviour of samples of Butser Hill and Stevn's Klint chalk under undrained shear at different consolidation stresses (from Leddra et al., 1993) is illustrated (figure 2.4.2). Undrained behaviour is dependent upon the magnitude of the initial consolidation stress (po') in a manner that is simile ' to, but not the same as, soils. Samples at the lower consolidation stresses fail in a brittle manner after following a post-yield Hvorslev surface. It can be seen that the peak strength of the sample consolidated to the lowest effective stress fails at a peak strength greater than that predicted by the Hvorslev surface. Therefore at the lowest confining pressures the stress path is able to cross the state boundary surface. Vaughan et al. (1988), Leddra (1990) and Loe et al. (1992) suggest that such behaviour is due to the bonded structure of chalk. The bonds provide chalk with a strength that enables the material to exceed the strength of the equivalent chalk powder. Under low confining pressures failure may be described by Mohr-Coulomb failure criteria. The failure line described at the low confining pressures, when the rock is still bonded, will be equivalent to a Mohr-Coulomb envelope. Once the rock has undergone failure, it will strain weaken to the residual strength envelope. Thus materials that have a bonded structure are able to exceed the strength suggested by the Hvorslev surface.

Beyond yield under compaction, bonded materials behave In a manner similar to that of remoulded soils. Failure is intrinsically ductile in nature, having followed a Roscoe- type surface to the failure envelope.

Figure 2.4.1 also illustrates that end-state deformation is not at a true critical state for many of the samples. For example samples 1 and 4 show sustained strain hardening after yield whilst samples 3, 6 and 7 continued to strain weaken at axial strains of 20%. The only sample that is at a state that is similar to critical state is sample 8, which appears to be at constant deviatoric stress.

Such behaviour is also demonstrated by the chalk illustrated in figure 2.4.2. The shape of the Hvorslev surface is clearly shown. However, even in the ductile regime failure is not described perfectly by the critical state model. If compacted to lower effective stresses, the chalk will remain at constant deviatoric stress after failure, but at higher effective stresses it tends to strain soften. When compacted to higher effective stresses the chalk follows a Roscoe-type surface to failure, but it undergoes strain hardening once the failure line is reached. It is interesting to note that the sample compacted to the highest stress never reaches the linear failure envelope. This is attributed to inaccuracies In the determination of the states of stress

2 “ 1 60.0 90.0 40.0 30J> 20.0 10.0 0.0

Mean effective stress (MPa)

Figure 2.4.2 Example of the mechanical behaviour of a sedimentary rock: Graph of deviatoric stress / mean effective stress for the undrained shear deformation of Butser Hill chalk (from Leddra, 1990).

as the sample strains radially (M. Leddra pers. comm., 1993) and to mechanical breakage of grains causing changes in grain size and pore volume (Petley et al.,

1994). The failure envelope for these materials was labelled as the critical state line despite the lack of a critical state in most samples.

Similar behaviour has been demonstrated for other sedimentary materials, such as cemented carbonate sands. Therefore, natural materials are described reasonably well by the critical state model, except for the following qualifiers.

• Deformation in bonded materials that have not undergone yield may be

characterised by failure at a deviatoric stress greater than that suggested by the Hvorslev Surface. Failure occurs on a Mohr-Coulomb envelope that may have a straight or curved form. The residual strength of the material may lie on the critical & te line of the material;

• Stable state deformation, which is sometimes erroneously described as the

critical state, may not be at constant pore pressure (volume) or deviatoric stress.

2.5 The Mechanical Behaviour of Mudrocks during Undrained