Krishna Kumar, Assistant Professor, UT Austin
Jupyter notebooks in support of the lecture course CE 394M 'Advanced analysis in geotechnical engineering'.
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