Syllabus

Module I: Introduction to Numerical Methods and Properties of Tensors (4 hours)
Introduction to Numerical Methods, Classification of Problems in Geotechnical Engineering, Index Notations, Transformation Rules, Properties of Tensors

Module II: Analysis of Stress and Strain (8 hours)
Traction vector, Stress components at an arbitrary plane, Principal stresses and Invariants, Hydrostatic Stress and Stress Deviator Tensor, Octahedral Stresses, Relative Displacement Vector, Strain and Rotation tensor, Principal strains and invariants, Strain Deviator Tensor, Octahedral Strains, Strain Displacement Relationships, and Equations of Strain Compatibility.

Module III: Constitutive Models for Soils - Elastic and Elasto-Plastic Models (8 hours)
Formulation of general equilibrium equations, Principle of Virtual Work, Generalized theory of elasticity, Lame’s Constants, Plane stress and Plane strain problem, Non-Linear Elastic Stress-Strain relations, Elastic Limit and Yield Function, Criterion for Loading and Unloading, Plastic Potential and Flow Rule, Von-Misces, Tresca, and Mohr-Coulomb Yield Functions, Loading Surface and Hardening Rules, Druckers’s Stability Postulate, Drucker-Prager Model, Cam Clay models, and Modified Cam Clay models.

Module IV: Finite Difference Method and its Applications (8 hours)
Introduction to boundary value and initial value problems in geomechanics, classification of ordinary and partial differential equations, Introduction to the Finite Difference Method, Solution of Ordinary Differential Equations, Parabolic Partial Differentiation Equations (Terzaghi’s consolidation theory), Hyperbolic Partial Differentiation Equations, and Elliptic Partial Differentiation Equations (Steady state seepage flow), Stability and Accuracy of Numerical Methods.

Module V: Finite Element Method (6 hours)
Finite Element Method: Introduction to the Finite Element Method, Weak form and weighted residual methods, Different types of elements, Interpolation and Appropriate shape functions, Classical methods for developing shape functions, Isoparametric Elements, Non-linear and incremental solution procedures, and applications to settlement, slope stability, and coupled stress–seepage behaviour.

At the end of the course, students are expected to develop a fundamental understanding of continuum mechanics and constitutive modelling.

At the end of the course, students are expected to be proficient in classical numerical methods used for geotechnical problem-solving.

At the end of the course, students are expected to understand the role of precision, errors, and tolerances in scientific computing and their impact on solutions.

At the end of the course, students are expected to apply numerical methods to real-world geotechnical engineering problems through programming and computational simulations using a major commercial finite element software.

After completion of the course, students will be able to:
CO1: Understand the Fundamentals of the Tensor Algebra and Index Notation.
CO2: Understand the fundamentals about the Traction vector, Realtive Displacement Vector, Stress and Strain tensor for 2D and 3D elasticity problems.
CO3: Understand the fundamentals of Generalized Theory of Elasticity, Plasticity Theory, and Failure theories for engineering analysis and design in geotechnical engineering.
CO4: Apply the Finite Difference Method to solve selected geotechnical engineering problems and evaluate the accuracy of the solutions.
CO5: Develop a foundational understanding of the Finite Element Method to solve selected geotechnical engineering problems and evaluate the accuracy of the solutions.

W. F. Chen, and D.J. Chen, Plasticity for structural engineers, Springer - Verlag

David M. Potts, and Lidija Zdravkovic, Finite Element Analysis in Geotechnical Engineering: Theory, Thomas Telford

Britto, A.M and Gunn, M.J, Critical State Soil Mechanics Via Finite Elements, Ellis Horwood Publishers, Chichester, England

Bathe, K.J., Finite Element Procedures in Engineering Analysis, Prentice Hall, Prentice-Hall of India Pvt. Ltd., New Delhi