By Félix Darve, Ioannis Vardoulakis
This publication offers the main recents advancements within the modelling of degradations (of thermo-chemo-mechanical starting place) and of bifurcations and instabilities (leading to localized or diffuse failure modes) happening in geomaterials (soils, rocks, concrete). functions (landslides, rockfalls, particles flows, concrete and rock getting old, etc.) are mentioned in detail.
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Extra info for Degradations and Instabilities in Geomaterials
Thus both the loading circles have the same center and the same radius, but they are situated in two orthogonal planes. The qualitative simulation of Kishino's discrete numerical results is presented on Figures 12, 13, 14, 15, and 16. Figures 12 and 13 illustrate the existence of a flow rule in axisymmetric conditions with both the non-linear model and the octo-linear one and with both the loose Hostun sand (Figure 12) and dense Hostun sand (Figure 13). The computation has been performed degree by degree on the stress loading circle, what means that there are 360 points on each figure.
The length of the 'steps' varies and five cases have been considered : 1, 2, 4, 8 and 16 kPa. Two main conclusions can be exhibited from results depicted on Figure 7: 1. when the length of the 'steps' decreases, the response diagrams converge to certain asymptotical behaviour, 2. these converged response curves are not confounded with the responses to the proportional loading, but remain satisfactorily close. It is also interesting to notice that the total length of the rectilinear proportional path and the decomposed paths (even for 'small' lengths of 'steps') are completely different (the ratio of both the lengths is equal to v'2).
0 el'4 Figure 7. Comparison between numerical responses obtained from the incrementally non-linear model in the case of a rectilinear proportional loading (with a constant lateral pressure)- dash lines- and of 'staircase' paths - continuous lines. , 1995). 24 F. Darve and G. Servant 300 paths with sharp ben ds ( p=cst. ) -;;;- (). 0 500 400 -;;;0.. >ll 300 M t> 200 I b • * • ...... 0 • • • • • experience computing: with sharp bends direct Figure 8. Comparison between numerical responses obtained from the incrementally non-linear model in the case of a rectilinear proportional loading (with a constant lateral pressure)- dash lines- and of 'staircase' paths - continuous lines.