By Krzysztof Wilmanski (auth.), Professor Dr. Dimitrios Kolymbas (eds.)
Geomechanics is the mechanics of geomaterials, i.e. soils and rocks, and offers with interesting difficulties comparable to settlements, balance of excavations, tunnels and offshore systems, landslides, earthquakes and liquefaction. This edited ebook offers fresh mathematical and computational instruments and types to explain and simulate such difficulties in Geomechanics and Geotechnical Engineering. It encompasses a choice of contributions emanating from the 3 Euroconferences GeoMath ("Mathematical tools 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
Hence the scalar ﬁeld of porosity is a minimum extension which we have to make for porous materials. It does not seem to make sense to introduce any further volume fractions if there is solely one solid component. g. ) – one on the microscale (say – 10−2 m) and one on the macroscale of big macrocracks and clefts (say – 10m). There may be also the necessity to incorporate some additional parameters describing the geometry of channels such as tortuosity. We do not consider these generalizations in this work even though some of them can be treated by thermodynamic methods.
Berryman, Graeme W. Milton; Exact results for generalized Gassmann’s equations in composite porous media with two constituents, Geophysics, 56, 1950-1960, 1991.  James G. Berryman, David E. Lumley; Inverting Ultrasonic Data on Solid/Fluid Mixtures for Biot-Gassmann Parameters, in: Proc. of the Second Int. Conf. on Mathematical and Numerical Aspects of Wave Propagation, SIAM, 57-68, 1993.  Sebastiano Foti, Carlo G. Lai, Renato Lancellotta; Porosity of FluidSaturated Porous Media from Measured Seismic Wave Velocities, G´eotechnique, 52, 5, 359-373, 2002.
We will consider a free energy in the form g = g1 (σij ) + g2 (αij ) − σij αij , which immediately leads to the result εij = −∂g1 /∂σij + αij , so that the internal variable αij plays the role of the plastic strain, as it simply serves as an additive term to the elastic strain (which is just a function of the stress state) −∂g1 /∂σij . We also obtain χ ¯ij = −∂g2 /∂αij + σij . In the case where g2 = 0, as considered below, the generalised stress χ ¯ij is simply equal to the stress σij . In more general cases Some mathematics for the constitutive modelling of soils 39 σij = ∂g2 /∂αij + χ ¯ij = ρij + χ ¯ij , where ρij = ρij (αij ) is the “back stress” in kinematic hardening, which is a function of the plastic strains.
Advanced Mathematical and Computational Geomechanics by Krzysztof Wilmanski (auth.), Professor Dr. Dimitrios Kolymbas (eds.)