Course10510569159 lectures
Computational Geomechanics
Prof. Shantanu Patra · IIT Bhubaneshwar
About
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
Lectures
Week 1
- Lecture 1: Mathematical Modeling and Governing Equation
- Lecture 2: Solution of governing equation and computer implementation
- Lecture 3: Estimation of Numerical Error and error propagation
- Lecture 4: Numerical Stability and round -off errors
- Lecture 5: Number representation and Computational Limits
Week 2
- Lecture 06: Numerical differentiation
- Lecture 07: Higher order numerical differentiation and Eigen Value problem
- Lecture 08: Buckling of column and Numerical solution
- Lecture 09: Smallest Eigen value and Roots of characteristic equation
- Lecture 10: Higher Order Numerical Differentiation and Elgen Value Problem
Week 3
- Lecture 11: Buckling of column and Numerical solution
- Lecture 12: Smallest Eigen value and Roots of characteristic equation
- Lecture 13: Roots of characteristic equation- Bracketing method
- Lecture 14: Roots of characteristic equation- Open method
- Lecture 15: Roots of characteristic polynomial
Week 4
- Lecture 16: Initial value vs Boundary value problem
- Lecture 17: RK Method and Multi-Step Method
- Lecture 18: System of equations, stiffness and multi-Step Method (Contd.)
- Lecture 19: System of equations, stiffness and multi-Step Method (Contd.)
- Lecture 20: System of equations, stiffness and multi-Step Method (Contd.)
Week 5
- Lecture 21: Solutions of Simultaneous linear algebraic equations (continued…)
- Lecture 22: Application of FDM - Axially loaded pile
- Lecture 23: BEM for laterally loaded semi-infinite pile
- Lecture 24: BEM for laterally loaded pile (Contd…)
- Lecture 25: Buckling of piles
Week 6
- Lecture 26: FDM Application - infinite beam subjected to a point load
- Lecture 27: FDM Application - infinite beam subjected to a concentrated moment
- Lecture 28: FDM for laterally loaded pile
- Lecture 29: FDM for laterally loaded pile and buckling of column
- Lecture 30: FDM for buckling of column and BEM (contd.)
Week 7
- Lecture 31: Finite Difference Method And Laplace Equation
- Lecture 32: Finite Difference Method And Laplace Equation (Contd.)
- Lecture 33: Finite Difference Method And Laplace Equation (Contd.)
- Lecture 34: Finite Difference Method And Parabolic nequation - Explicit Method
- Lecture 35: Parabolic nequation - Explicit and Implicit Method
Week 8
- Lecture 36 : Parabolic equation- Explicit and Implicit Method
- Lecture 37: Parabolic equation- 1-D Consolidation problem
- Lecture 38: FDM for 2D seepage problem
- Lecture 39: FDM for Mat Foundation
- Lecture 40: Approximate methods of solution
Week 9
- Lecture 41: Constitutive Models for geomechanics
- Lecture 42: Approximate methods for Beam on elastic foundation problem
- Lecture 43: Introduction to Finite Element Method
- Lecture 44: Formulation of Stiffness matrix -direct approach
- Lecture 45: Application of Direct stiffness Methods for 1D Spring element
Week 10
- Lecture 46: Stiffness Matrix Using Shape Functions and Truss Element
- Lecture 47: Truss analysis
- Lecture 48: Flow through porous medium
- Lecture 49: Variational method for flow through porous medium
- Lecture 50: Variational method for 1D consolidation and bar element
Week 11
- Lecture 51: Strain energy method for bar element (contd..)
- Lecture 52: Formulation of stiffness matrix for beam element
- Lecture 53: Formulation of stiffness matrix for beam element (Contd..)
- Lecture 54: Analysis of beam
Week 12
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IIT Bhubaneshwar
- Department
- Civil Engineering
- Teacher
- Prof. Shantanu Patra
- Level
- Undergraduate
- Language
- English
- Subjects
- Engineering
- Source
- NPTEL
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Kharagpur.
- Who can watch
- NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed
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