CE394M: Advanced analysis in geotechnical engineering

Krishna Kumar, Assistant Professor, UT Austin

Jupyter Notebook

Jupyter notebooks in support of the lecture course CE 394M 'Advanced analysis in geotechnical engineering'.

Course outline

1. Introduction to numerical modeling in geomechanics (2 lectures)
    * Role of numerical modeling in geotechnical engineering
    * Matrix analysis of structures

2. Finite Element method (11 lectures)
    * Finite Element formulation (strong and weak forms)
    * Shape functions
    * Element matrices, assembly and application of boundary conditions
    * Two-dimensional problems
    * Isoparametric elements (quadrilateral, triangle)
    * Numerical integration
    * Error estimations
    * Time-dependent problems
    * Application of Finite Element methods to geomechanics
    * An introduction to PLAXIS

3. Constitutive modeling of soils (20 lectures)
    * Introduction to tensors and continuum mechanics
    * Soil behaviour (stresses and strains)
    * Stress paths
3.1 Linear elasticity
    * Theory
    * Isotropic/anisotropic
    * Plane stress/plane strain/axisymmetry
3.2 Linear elastic-perfectly plastic
    * Theory
    * Yield functions and failure criteria
    * Drucker-Prager and Mohr-Coulomb
3.3 Non-Linear, stress-dependent elastic hyperbolic model
    * Theory
    * Developing model parameters from laboratory data
3.4 Critical state soil mechanics and Cam-Clay
    * Hardening laws
    * Critical state soil mechanics
    * Cam-Clay and modified Cam-Clay models

4. Seepage (6 lectures)
    * Darcy’s law in one and two dimensions
    * Laplace’s equation for flow
    * Using the finite element method to solve Laplace’s equation

5. Other numerical methods (4 lectures)
    * Finite Difference
    * Material Point Method
    * Discrete Element Method