Notes on Numerical Modeling in Geomechanics

This book provides an introduction to numerical analysis in geomechanics, focusing on the finite element method and other solution methods. It is intended for advanced undergraduate and beginning graduate study of the mechanics of porous,jointed rocks and soils.

Format: Paperback / softback
Length: 278 pages
Publication date: 21 March 2022
Publisher: Taylor & Francis Ltd

This comprehensive book serves as an introduction to numerical analysis in geomechanics, specifically tailored for advanced undergraduate and early graduate students studying the mechanics of porous, jointed rocks and soils. While a basic understanding of stress, strain, and related concepts is assumed, the book includes an appendix that provides a review of the fundamentals of solid mechanics, encompassing physical laws, kinematics, and material laws. The focus of the text is primarily on the popular finite element method, although brief explanations of the boundary element method, the distinct element method (also known as the discrete element method), and discontinuous deformation analysis are also included. It is noteworthy that familiarity with a computer programming language such as Fortran, C++, or Python is not mandatory for reading this book, although programming excerpts in Fortran are presented at the end of certain chapters.

The book adopts an intuitive approach to interpolation over triangular elements, thereby avoiding the complexity often associated with energy minimization via a calculus of variations approach commonly found in reference books on the finite element method. This approach facilitates a clear understanding of the fundamentals. The presentation then proceeds to discuss the principle of virtual work, utilizing the well-known divergence theorem, to attain element equilibrium and subsequently global equilibrium, both expressed as stiffness equations linking force to displacement. Various solution methods for the finite element approach, including elimination and iteration methods, are explored in detail.

The book also delves into the topic of hydro-mechanical coupling, highlighting its significance in geomechanics. Furthermore, the finite element method is extended to accommodate fluid flow within porous geological media, enabling the analysis of complex fluid-structure interactions. Representative example problems are provided throughout the text to illustrate key concepts and facilitate a better grasp of the material. An appendix offers additional problems for a 15-week course of study, accompanied by solutions in another appendix.

In summary, this book offers a thorough and accessible introduction to numerical analysis in geomechanics, catering to students with a background in mechanics and a desire to explore the computational aspects of porous, jointed rocks and soils. Its comprehensive coverage, intuitive explanations, and practical examples make it an invaluable resource for advancing knowledge in this field.

Dimension: 246 x 174 (mm)
ISBN-13: 9780367762872