By Félix Darve, Ioannis Vardoulakis
This e-book provides the main recents advancements within the modelling of degradations (of thermo-chemo-mechanical beginning) and of bifurcations and instabilities (leading to localized or diffuse failure modes) occurring in geomaterials (soils, rocks, concrete). functions (landslides, rockfalls, particles flows, concrete and rock getting older, etc.) are mentioned in detail.
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Extra resources for Degradations and Instabilities in Geomaterials
0 , 40 ~ "' ~ ""' ""~ ' "" 0 ~ ...... 0 ~~~~~-~0~~ ~ ~ ...... ~~~~~-~0~~ ~~ ~~ Figure 13. Flow rule in axisymmetric conditions for dense Hostun sand degenerating response- envelops. Incrementally non-linear model on the left, octo-linear model on the right (q = 2000 kPa, 3 = 500 kPa, j ~ar + 2~a5 = 1 kPa) (Fernandez, 2002) a 0 ....... ,. 2 .. Ct(X 104 1 Figure 14. 3D response-envelops for loose Hostun sand. Octo-linear model (q kPa, a3 = 500 kPa, j ~a? ·::: ..................... -· ···:::, ..
The first path is applied until a given path length is reached: V(flp) 2 + (~q) 2 = 2kPa The results are depicted in Figures 10 and 11 and show that there is not any significant influence of the kind of decomposition on the quantitative responses. _ I I I I II 'I I I I I (Q.. '::! // / ' / p ' I \ #;>(o I \ Figure 9. The considered decomposition of the loading path in the case of an isochoric loading The four chosen lengths are equal to : V(~p) 2 + (~q) 2 = 1, 2, 4, 8 kPa Finally the computation is stopped only because of an artefact : for small levels of stress both the decomposition paths become contractant.
Comparison of experimental and calculated behaviour for Hostun sand in triaxial compression (after Lade, 1989). Immediately after Lade, Venneer ( 1978) and Nova and Wood ( 1979) published two other models for sand. Many other laws, based on the theory of plasticity with hardening, have been proposed since then. As far as virgin soils under monotonic loadings are concerned, however, the proposed modifications were not relevant for our scope, the model structure being the same. Different were instead the constitutive functions proposed.