Dynamical Systems-Based Soil Mechanics

The book is a detailed course on a new paradigm in soil mechanics, one solidly based on science (thermodynamics) and findings by Cassagrande’s group at Harvard University. The theory holds that soils when sheared reach a “steady-state” condition, a finding that is exactly in line with the thermodynamics of dissipative systems. From this, the theory is extended to show that soil deformation is the result of a simple friction based Poisson process in which particles move to their final position at random shear strains. The book introduces the reader to this concept, and unpacks it. It aims at both advanced undergraduates, as well as graduate and research students.

Paul?graduated from a five year undergraduate in Civil Engineering at Engineering College, University of Madras, Madras, India in?1983. He then went on to graduate work in soil mechanics/geotechnical engineering at Purdue University, Indiana and after that, at the Massachusetts Institute of Technology, Massachusetts. He finished a Masters in Applied Mathematics at the University of Massachusetts (Lowell) in 2010, and in Fall 2013, obtained his Ph.D.Paul is registered Professional Engineer (PE) in the State of Massachusetts.

"Steady states are ubiquitous in nature and a mathematical framework (loosely called "dynamical systems theory") exists to describe systems with a steady state. The Great Red Spot on Jupiter is an example of a steady state generated by a dynamical system; mathematicians have extensively studied such dynamical systems. In 1971, Steve Poulos at Harvard first described the steady-state condition in soils. Based on this I was able to show that soil shear can be described as a "dynamical system" whose underlying basis is nothing but Poisson process based simple friction. These basic findings (steady-state, dynamical systems, Poisson process based simple friction) mark the advent of a new paradigm for describing soil deformation that is at once both simple and powerful. I call this new paradigm Dynamical Systems Soil Mechanics (DSSM for short). It is the only theory that predicts key relationships observed in the empirical evidence from decades of soil tests, relationships which hitherto, have simply been taken as "given.""