By Krzysztof Wilmanski (auth.), Professor Dr. Dimitrios Kolymbas (eds.)
Geomechanics is the mechanics of geomaterials, i.e. soils and rocks, and offers with attention-grabbing difficulties corresponding to settlements, balance of excavations, tunnels and offshore structures, landslides, earthquakes and liquefaction. This edited booklet provides contemporary mathematical and computational instruments and versions to explain and simulate such difficulties in Geomechanics and Geotechnical Engineering. It contains a number of contributions emanating from the 3 Euroconferences GeoMath ("Mathematical equipment in Geomechanics") that have been held among 2000 and 2002 in Innsbruck/Austria and Horto/Greece.
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Additional resources for Advanced Mathematical and Computational Geomechanics
We assume that the constitutive relations on the microscopic level are of the form pSR = pSR 0 − Ks where ρSR = t SR ρSR 0 − ρt , ρSR 0 R pF R = pF − Kf 0 R R ρF − ρF 0 t , R ρF 0 (80) MS is the true mass density of the skeleton (comp. section 3), VS MF denotes the true mass density of the ﬂuid, Ks is the so-called bulk VF modulus of the solid material composing the porous frame (compressibility modulus of grains), and Kf is the bulk (real) modulus of the ﬂuid. The index zero refers to the initial state.
FS – deformation gradient of the skeleton, 5. x ´α , α = 1, . . , A – velocity ﬁelds of ﬂuid components, 6. T - absolute temperature of the skeleton, 7. n – porosity (the volume fraction of voids). e. ﬁelds 1. , do not require any special justiﬁcation. It should be solely stressed that the multiple velocity ﬁeld x ´S , x ´α means that we include the diﬀusion in the system which is the main diﬀerence between this model and a model of composite materials. However, a single temperature requires already some explanation.
A more detailed introduction to the subject is given by Rockafellar (1970). No attempt is made to provide rigorous, comprehensive deﬁnitions here, and for a fuller treatment reference should be made to the above texts. Although it is currently used by only a minority of those studying plasticity, it seems likely that in time convex analysis will be come the standard paradigm for plasticity theory. In the following C is a subset in a normed vector space V , usually with the dimension of Rn , but possibly inﬁnite dimensional.