Numerical and Analytical Methods in Geotechnics

The course focuses on application of the finite element method to solve problems in geotechnics / porous media deformations - flow (of water) and connected problems (consolidation). The course provides an introduction on how to find analytical solutions for failure capacity from plasticity theory (plastic stress fields, basic elements and combinations of these). The course provides the basis for describing material behavior with elasticity and elastoplasticity as a framework (Tresca, Coulomb).

Knowledge:

The candidate must have knowledge of:

• Soil strength expressed by total and effective stresses
• Stress fields based on plasticity theory
• Constitutive relations for soil behavior (stiffness and conductivity)
• Key finite element method (FEM) concepts applied to porous media (soil)
• Soil deformation
• Flow in soil, including coupled problems
• Digital tools and programming languages such as Python for modeling and analysis
• Numerical methods and simulation tools for geotechnical applications

Skills:

The candidate can:

• Calculate the capacity of simple problems based on plasticity theory
• Use Python to implement solutions for simple problems using the finite element method
• Use analytical solutions to verify well-defined numerical analyses
• Develop and apply digital models to simulate soil behavior under various loading conditions
• Utilize relevant libraries and tools for computation and visualization

General competence:

The candidate can:

• Understand the fundamentals of the finite element method for multiphysics problems in porous media (soil)
• Understand the computational process in FEM analyses
• Evaluate and apply digital tools and methods to solve complex geotechnical problems
• Communicate results from numerical analyses clearly and effectively, including through digital visualizations
• Reflect on the quality and reliability of digital models and simulations

Lectures and assignments with supervision.