PSI - Issue 45

Nhan T. Nguyen et al. / Procedia Structural Integrity 45 (2023) 52–59 Nguyen et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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inside and outside indicates the formation of a localisation band. In the case of confining pressure at 200 MPa, we can see the outside behaviour unloads elastically by going down below the initial yield surface at first, while the inside is under inelastic loading which travels toward negative indicating softening. Although bifurcation occurs at 150 MPa, the inelastic outside setting cannot produce the localisation response. This may be due to the incapability of the breakage model in the low-confining pressure regime where the yield surface cannot shrink back to the critical state line in correspondence to softening behaviour.

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Fig. 4. Model calibration on the macroscopic response using the elastic outside setting with the experimental results: (a) volumetric behaviour and; (b) shear behaviour of Berea sandstone under drained triaxial loading.

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Fig. 5. Demonstration of model behaviour at three different scales in triaxial stress path shearing at 150 MPa and 200 MPa confining pressure with two different settings: (a) the outside zone is forced to be elastic; (b) the outside zone is allowed with the inelastic response.

For the elastic outside case, the outside response holds the elastic slope while the inside behaviour undergoes inelastic softening (Fig. 6a,b and Fig. 7a) which is much closer to the macroscopic response indicating the dominating effect of the localisation zone on the host rock. The inability of the breakage yield surface to shrink following the softening response in a medium-low confining regime can also be observed (Fig. 6c,d) where the three behaviour converges despite the activated bifurcation.

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Fig. 6. Model response at 150 MPa confining pressure at the macroscopic scale and the inside/outside localised zone: (a) elastic outside volumetric response; (b) elastic outside shear response; (c) inelastic outside volumetric response and; (d) inelastic outside shear response. Regarding the inelastic outside case, right after bifurcation, the outside zone unloads elastically with a volumetric response and remains elastic (Fig. 7c) while the shear response exerts a steep drop, which is also parallel to the elastic response (Fig. 7d). Simultaneously, the behaviour inside of the compaction band immediately shows softening indicating localisation is taking effect. Afterwards, localisation also occurs in the outside zone so its response starts to drop with softening (Fig. 7c). The key enhancement for allowing inelastic behaviour outside the localisation band leads to the deactivation and activation of compaction localisation in terms of the first band. In this sense, another compaction band occurs in the zone outside the first one, which is in agreement with the progressive mechanism of the compaction band observed in experiments.