Computational Geomechanics

By Prof. Shantanu Patra | IIT Bhubaneswar

Learners enrolled: 141

ABOUT THE COURSE:

The course aims to bridge the gap between theoretical geomechanics and its applications in real-life geotechnical engineering problems. Using appropriate constitutive relations, you will learn to formulate mathematical models, e.g., ordinary and partial differential equations (ODE and PDEs) and eigenvalue problems. You will also be exposed to numerical techniques such as finite difference method (FDM) and finite element method (FEM) to solve problems related to slope stability, the behavior of earth retaining structures, shallow and deep foundations, consolidation settlement and seepage analysis. You will develop the skill to write your own code using Python/MATLAB/Excel VBA. You will also be exposed to computational tools (open-source or having free academic license) like LimitState GEO and OpenSees to solve various geotechnical problems. We will share assignment problems each week and conduct a pen-and-paper exam at the end of the course. This course will enhance your understanding of the fundamentals of geomechanics and will impart the necessary numerical skills to tackle complex geomechanics problems. The course will be equally beneficial if you are a student preparing for competitive exams or a design practitioner.

INTENDED AUDIENCE: UG and PG students. Research Scholars and Practicing Engineers can also take this course.

PREREQUISITES: Exposure to Soil Mechanics, Numerical Methods and basic programming

INDUSTRY SUPPORT: Most design companies working in Geotechnical Engineering like L&T, TCE, Reliance Infra, AFCONS, HCC, Keller, Golder Associates, etc.

Summary

Course Status :	Upcoming
Course Type :	Elective
Language for course content :	English
Duration :	12 weeks
Category :	Civil Engineering
Credit Points :	3
Level :	Undergraduate/Postgraduate
Start Date :	21 Jul 2025
End Date :	10 Oct 2025
Enrollment Ends :	28 Jul 2025
Exam Registration Ends :	15 Aug 2025
Exam Date :	02 Nov 2025 IST
NCrF Level	4.5 — 8.0

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1: Introduction to course, Physical laws and governing equations, Numerical modelling and Numerical error, Convergence and stability, Introduction to constitutive law, Winkler soil model, plane stress, plane strain and axi-symmetry problems

Week 2: Finite difference methods (FDM): Numerical differentiation and order of error, Application of FDM to solve Eigen value problem, Computer Implementation and Case studies: buckling of piles, wave propagation through soil, natural frequency of pile foundation

Week 3: Application of FDM to solve Boundary Value Problem,: axially loaded pile and pullout of reinforcement, beam on elastic foundation (BEM): formulation, boundary conditions and solution using FDM

Week 4: Computer implementation of FDM for Beam on elastic problems: shallow foundation and railway track, laterally loaded pile and Sheet pile wall

Week 5: Application of FDM to solve Partial Differential Equations: Parabolic and Elliptic Equations, Explicit, and Implicit scheme, Computer implementation and case studies: Consolidation and Seepage analysis

Week 6: Finite element method: General steps in FEM; Approaches in FEM-Method of weighted residual, Variational principle; determination of stiffness matrix and element equation for 1D Bar element, 1D steady-state flow

Week 7: Interpolation functions: one dimension elements, two-dimensional elements, Lagrangian form in natural and Cartesian coordinate system, Isoparametric elements, two dimensional serendipity elements, Local and Global coordinate system

Week 8: Direct Approach, Principle of Virtual Work, System of springs and bar element, Computer Implementation

Week 9: Energy approach: principal of minimum potential energy, Derivation of Stiffness Matrix for bar element, Truss, Local and Global Element Equations, transformation matrix, and Computer Implementation

Week 10: Beam element - Derivation of Stiffness Matrix, Local and Global Element Equations, Computer Implementation

Week 11: Finite element method of 2D element, Plane stress, plane strain and axi-symmetry, formulation of stiffness matrix and element equation for 2D element: CST and Isoparameteric element

Week 12: Treatment of loads: Numerical Integration, Finite Element Solution of Partial Differential Equations, Case study: Flow through porous media, 2D beam problem and Computer Implementation

Books and references

Ghaboussi, J. (1979). Numerical methods in geotechnical engineering. Edited by CS Desai and JT Christian. McGraw‐Hill Book Company, 1977. No. of Pages: 783
Davis, R. O., & Selvadurai, A. P. (2005). Plasticity and geomechanics. Cambridge university press.
Zienkiewicz, O. C., Chan, A., Pastor, M., Schrefler, B., & Shiomi, T. (1999). Computational soil dynamics with special reference to earthquake engineering.
Potts and Zdravkonics (1999) Finite element analysis in geotechnical engineering: Part-I Theory & part-II Applications, Thomas Telford Publishers.
Canale, Raymond P., and Steven C. Chapra. Numerical methods for engineers. Mcgraw-hill New York, NY 10121, 2010.
Jones, G. (1997). Analysis of beams on elastic foundations: using finite difference theory. Thomas Telford.
Verruijt, A. (1995). Computational geomechanics (Vol. 7). Springer Science & Business Media.
Desai, C. S., & Gioda, G. (Eds.). (2014). Numerical methods and constitutive modelling in geomechanics (Vol. 311). Springer.
Desai, C. S., & Zaman, M. (2013). Advanced geotechnical engineering: Soil-structure interaction using computer and material models. CRC Press.
Logan, D. L. (2011). A first course in the finite element method. Cengage Learning, USA
Bull, J. W. (2003). Numerical analysis and modelling in geomechanics. CRC Press.
Chan, A. H., Pastor, M., Schrefler, B. A., Shiomi, T., & Zienkiewicz, O. C. (2022). Computational geomechanics: theory and applications. John Wiley & Sons.
Aydan, Ö. (2021). Continuum and computational mechanics for geomechanical engineers. CRC Press.
Wood, D. M. (2017). Geotechnical modelling. CRC press.
Reddy, J. N. (2005). An introduction to the finite element method (Vol. 3). New York: McGraw-Hill.
Liu, G. R., & Quek, S. S. (2013). The finite element method: a practical course. Butterworth-Heinemann.
Rahman, M. S., & Ulker, M. C. (2018). Modeling and computing for geotechnical engineering: an introduction. CRC Press

Instructor bio

Prof. Shantanu Patra

IIT Bhubaneswar

Dr. Shantanu Patra is presently an Associate Professor in the School of Infrastructure (Civil Engineering) at Indian Institute of Technology Bhubaneswar. Dr. Patra did his Masters and PhD from IIT Delhi and postdoctoral research at University of Dundee, United Kingdom. With extensive research and teaching experience in geotechnical engineering, Dr. Patra has published numerous papers in reputed journals, national and international conferences. Dr. Patra specializes in Physical and Numerical Modelling, geosynthetics and its application, and soil-structure interaction problems. Dr. Patra awarded with several sponsored projects (ECR grant from SERB, SPARC project from Ministry of Education; and CRG grant from SERB). Besides, Dr Patra have undertaken more than twenty five consultancy project. Dr. Patra is teaching and supervising PhD, MTech and BTech thesis for the last ten years. Dr Patra is known for his student-centric teaching approach and his ability to simplify complex concepts. Dr. Patra is dedicated to provide a comprehensive and engaging learning experience in the field of Geotechnical Engineering.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.

The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).

Date and Time of Exams: November 02, 2025 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.

Registration url: Announcements will be made when the registration form is open for registrations.

The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.

Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

Please note that assignments encompass all types (including quizzes, programming tasks, and essay submissions) available in the specific week.

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Kharagpur .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

SWAYAM Helpline / Support