Soil Dynamics


Robert V. Whitman, Ricardo Dobry and Mladen Vucetic


adapted as

Course Lecture Notes RPI CIVL 6540

“Dynamic Response of Soil and Soil-Foundation Systems”

Prof. Ricardo Dobry

December 2022

Please send any correction or suggestion related to the Notes to Prof. Mourad Zeghal at


History and Explanation


These Notes correspond to the course on Dynamic Response of Soil and Soil-Foundation Systems, taught at Rensselaer Polytechnic Institute (RPI) in Troy, New York, USA, by Prof. Ricardo Dobry.  Professor Dobry taught the course at RPI in the Spring semester, most years since his arrival in 1977 until his retirement in 2020, that is a period of more than 40 years. It was addressed mostly to geotechnical and structural Master and PhD students. The course was originally Soil Dynamics, with the name later changed to Dynamic Response of Soil and Soil-Foundation Systems (DRSSFS).


Since the beginning, a main teaching tool in the course was the available chapters of a comprehensive textbook in preparation on “Soil Dynamics.” This book had been started by Prof. Robert V. Whitman at MIT in the 1960s and continued later as a collaborative effort involving Profs. Ricardo Dobry (RPI) and Mladen Vucetic (UCLA), who became co-authors. However, when Professor Whitman sadly died in 2012, this ambitious book had not yet been finalized, and Profs. Dobry and Vucetic have since retired. It should be added that a number of the written chapters were used over the years by Profs. Whitman, Dobry and Vucetic in their teaching, and they were also distributed to other Instructors in the U.S. and abroad at their request to use in similar soil dynamics courses.


The Lecture Notes consist of the 14 Modules, as listed below. These Modules were mostly developed by modifying the chapters of the “Soil Dynamics” textbook, and adapting them the way the material was actually used by Dobry in his teaching of the DRSSFS course at RPI in the decade 2010-2020, before his retirement. Some material of the “Soil Dynamics” book was not used while new material was added, depending on the needs of the course. The fourteen Modules include 119 solved numerical examples with detailed solutions, and 92 numerical problems with only final answers. The figures are professionally drafted. A List of References is also provided as a separate document.


A main objective of these Notes, completed by Dobry in 2019-2022, is to provide help to future Instructors at RPI who may be teaching this or a similar course. An additional objective is to make the material available free of charge to other professionals that may find it useful, including instructors of similar courses as well as researchers and engineers. The work was requested by the faculty of the Geotechnical Engineering Group and by the Head of the Dept. of Civil and Environmental Engineering at  RPI, and Dobry was pleased to do it. Since Prof. Dobry’s retirement, Prof. Mourad Zeghal has recently taught the course at RPI using the Notes and is in charge of the material including possible future modifications. A number of colleagues and many students have provided feedback and useful contributions to the Notes – both over the years and more recently – and these contributions are gratefully acknowledged. Special thanks are due to Prof. Zeghal who has contributed significantly to the Notes in multiple respects.


A summary of the organization of both the course and the Notes is provided in Section 1.4 of  Module 1.



Module                Subject

  1                                Introduction

  2                                Introduction to the Modeling of Soil During Cyclic Loading

  3                                Wave Velocities, Moduli and Damping at Very Small Strains

  4                                Shear Modulus and Damping at Larger Strains

  5                                Single-Degree-of-Freedom Systems

  6                                Two-Degree-of-Freedom Systems and Modal Analysis

  7                                Traveling One-Dimensional Wave Propagation

  8                                Reflection and Transmission of 1D Waves and Boundary Value Problems

  9                                Two- and Three-Dimensional Wave Propagation

10                                Seismic Response of Earth Embankments

11                                Introduction to the Dynamic Response of Foundations

12                                Dynamic Response of Shallow Foundations

13                                Dynamic Response of Deep Foundations

14                                Seismic Response of Pile Foundations, Buried Structures and Buried Pipes

                                    Appendix A

                                    Appendix B

                                    List of References