Alert Doctoral School 2024: Numerical methods in geomechanics

The contributions assembled in the present volume proceed from the lectures of the 2024 ALERT Geomaterials Doctoral School devoted to Numerical methods in geomechanics. The school has been organized and coordinated by Claudio Tamagnini (Università degli Studi di Perugia), Lorenzo Sanavia (Università degli Studi di Padova) and Manuel Pastor (Universidad Politécnica de Madrid). It follows the 1st and the 2nd ALERT Olek Zienkiewicz Course organized at the Universidad Politécnica de Madrid by Manuel Pastor and Claudio Tamagnini in 2009 (Numerical Methods in Geomechanics) and in 2014 (Advanced Numerical Modelling in Geomechanics), respectively. The study and application of rock and soil mechanics require solving mainly nonlinear initial boundary value problems on complex domains, for which the analytical solution is usually unavailable. It also needs to consider the material as a multiphase porous system characterized by coupled multiphysics phenomena. Consequently, only numerical methods can be applied successfully to solve real problems and, because they are approximate methods, need to be thoroughly understood and used carefully and critically. This volume contains eleven chapters presenting the fundamentals that help in understanding numerical methods applied to multiphase porous systems. The volume is divided into five main parts: (i) an introduction to the finite element method for ellipt, parabolic and hyperbolic equations, (ii) the constitutive modelling of geomaterials within the Theory of plasticity and Generalized plasticity, also for rate dependent materials and unsaturated soils, respectively, (iii) the formulation of a mathematical model for non-isothermal multiphase porous materials based on the Hybrid Mixture Theory, which includes, as a particular case, the well-known Biot poromechanical model, (iv) the numerical approaches for the solution of nonlinear problems, the computational plasticity, and the space and time discretization of a multiphase porous media model at large elasto-plastic strains as an example of the application of the previous sections, and (v) the finite element modelling of non-isothermal variably saturated soils under quasi-statics or dynamics conditions. The 2024 ALERT Geomaterials Doctoral School also includes some practical sessions to practice with the numerical solution of some geomechanical problems with the finite element code GeHoMadrid. We believe that this volume may provide to postgraduate students, researchers and practitioners, a valuable introduction and a sound basis for further progress in the challenging field of virtual modelling of coupled and multiphysics phenomena in multiphase porous systems, which extends not only to geomechanics but far beyond. Claudio Tamagnini (Università degli Studi di Perugia) Lorenzo Sanavia (Università degli Studi di Padova) Manuel Pastor (Universidad Politécnica de Madrid)