Advanced Mathematical and Computational Geomechanics

Geomechanics is the mechanics of geomaterials, i.e. soils and rocks, and deals with fascinating problems such as settlements, stability of excavations, tunnels and offshore platforms, landslides, earthquakes and liquefaction. This edited book presents recent mathematical and computational tools and models to describe and simulate such problems in geomechanics and geotechnical engineering. It includes a collection of contributions emanating from the three Euroconferences GeoMath ("Mathematical Methods in Geomechanics") that were held between 2000 and 2002 in Innsbruck/Austria and Horto/Greece. TOC:Part I. Material Modelling: On thermodynamic modeling and the role of the second law of thermodynamics in geophysics. Some mathematics for the constitutive modelling of soils. Elasticity in constitutive modeling of soils. Experimental characterization of localized deformation in geomaterials. Discontinuous character of rock masses: some open questions related to rock fracture mechanics and scale effects. Similarity in soil and rock mechanics.- Part II. Modelling of Boundary Value Problems: Numerical predictions and reality. Objective integration and geometric properties of hypoplasticity. Using constitutive models of the rate type in implicit finite-element calculations: error-controlled stress update and consistent tangent operator. Efficient and reliable: nonlocal damage models. Regularized formulations of strain-softening plasticity. Fuzzy data in geotechnical models.