Preface

Chapter 7 **The Grading Entropy-Based Criteria for Structural Stability of**

János Lőrincz, Emöke Maria Imre and Vijay Pal Singh

**Granular Materials and Filters 161**

**VI** Contents

Granular materials are a broad category of materials of interest in civil engineering, chemi‐ cal engineering, physics, chemistry, and pharmacy. In engineering, great advances took place recently by the introduction, both, of experimental and computational methods. X-Ray tomography revealing the grain material structure and the distinct element computational method are two of them. The granular materials may behave as fluids or solids or both. The grain size may span from microscopic to macroscopic scale. From the wet sand effect, Rey‐ nolds inspired in 1885 the notion of granular universe introducing the term "dilatancy." In his Rede Lecture in Cambridge (1902) entitled *On an Inversion of Ideas as to the Structure of Universe,* he presented an explanation of the cause of electromagnetism giving a physical explanation of the equations linking electricity with magnetism. Later on, Lorentz gave the relativistic explanation of the electromagnetic waves. In 1930, Casagrande introduced the concept of critical void ratio to explain the liquefaction phenomenon. Donald Taylor in 1948 used the concept of dilatancy to explain the friction as a result of the interlocking of grains. Later on (1960s), Cambridge soil mechanics group (Roscoe, Schofield, Wroth, etc.) intro‐ duced the models of Cam-Clay and Granta-Gravel to explain the plastic behavior of soil. On the other hand, researchers from mathematics and physics like Bak, Tan, and Wisenfeld (1987, 1988) used the sand pile as a representative model of complex systems. Many re‐ searchers continue developing the concept of self-organized criticality to explain physical phenomena like earthquakes, landslides, and avalanches.

This volume presents basic notions and fundamental properties of granular materials cov‐ ering a wide spectrum of granular material mechanics. In this collection of chapters, granu‐ lar dynamics, granular flow from dilute to jammed states, dynamics of granular gas in microgravity, particle jetting induced by impulsive loadings, particle migration phenom‐ ena in embankment dams, and the grading entropy-based criteria of granular materials and filters are presented.

> **Dr. Michael Sakellariou** Professor Emeritus, National Technical University of Athens, Athens, Greece

**Section 1**

**Introductory Chapter**
