Institute of Geotechnical Engineering and Construction Management

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Course

Numerical Methods in Geotechnical Engineering
(Numerische Methoden in der Geotechnik)

 

Status: 10.02.2026

 

Lecturer

Dr.-Ing. Hans Stanford

Language

German

Participants

  • Until summer term 2020: students of the master's degree program “Civil Engineering”, 2nd term, part of the mandatory module “Marine Geotechnics and Numerics” (3 ECTS, 3 SWS) for students with specialization in Geotechnical Engineering, and Port Construction and Flood Protection.
  • Since winter term 2020/2021: part of the module “Geotechnical Engineering III” (3 ECTS, 3 SWS) for the following degree program's:

    • BAUMS: specialization in Geotechnical Engineering, Structural engineering, Port Construction and Flood Protection (mandatory),
    • BAUMS: specialization in Water and Traffic (compulsory elective),
    • IWIMS: specialization II Civil Engineering (compulsory elective).

  • Since summer term 2026 (current): part of the mandatory module “Soil Mechanics and Soil Dynamics” (2 ECTS, 2 SWS) for students of the master's degree program “Civil Engineering” with specialization in “Geotechnical Engineering”. For all other students, compulsory elective course.

Location and space of courses

  • Summer term 2026: SD22, seminar room 1.028, Monday 13:15-15:30, start at 13.04.2026 (bus line 42, exit Theodor-Yorck-Straße)

Requirements

  • Successful participation in the courses Mathematics I to III as well as Geotechnical Engineering I (Soil Mechanics) and Geotechnical Engineering s II (Foundation Engineering) in the Bachelor's degree program in Civil and Environmental Engineering. Participation in the “soil mechanics laboratory course” is an advantage.
  • Registration via Stud.IP.

Learning objectives

  • Acquisition of the basics of numerical simulation of physical processes in the soil, taking into account soil-structure interaction:

    • Analysis of the initial situation, including evaluation of the data basis 
    • Formulation of boundary value problems and initial boundary value problems
    • Analytical, symbolic and numerical solution of basic mathematical problems
    • Numerical solution of boundary value problems and initial boundary value problems using the Finite Element Method (FEM)
    • Performance, evaluation, and validation of numerical simulations based on the FEM

  • Independent problem-solving in geotechnical engineering
  • Preparation for project and master's theses
  • Suggestion for self-study

Lecture

  • Soil models and model equations: Conceptual models for soil based on continuum theories (material-independent and material-dependent equations); mathematical models based on continuum theories for soils (elliptical and parabolic partial differential equations, initial conditions, boundary conditions)
  • Numerical mathematics: Differentiation and integration; differential equation including initial value problems, boundary value problems, and initial boundary value problems; algebraic equation including nonlinear equations, linear and nonlinear equation systems
  • Finite Element Method (soil): Deformation analysis (static, drained and undrained, linear and non-linear); groundwater flow analysis (steady-state, transient); Consolidation analysis (quasi-static, coupled and uncoupled); safety and limit analysis for drained and undrained conditions; error analysis
  • Finite Element Method (Soil-Structure Interaction, SSI): Modelling of structures (discretization, material models; modelling of soil-structure contact (contact variables, contact conditions, contact properties, discretization); Soil-structure interaction for selected problems

Exercises

Exercises with own software and application software:

  • Exercises in numerical mathematics: analytical, symbolic and numerical solution of mathematical problems: differentiation and Integration, ordinary and partial differential equations. Algebraic equations including nonlinear equations, linear and nonlinear equation systems by means of the programming language Python and the Python libraries NumPy and SciPy (numerical solution), SymPy (symbolic solution), and Matplotlib (visualization of results). Note, that Python is not part of the exam.
  • Exercises in Finite Element Method (Soil): deformation analysis, groundwater flow analysis, consolidation analysis, safety analysis, and limit analysis based on the FEM and soft software PLAXIS 2D
  • Exercises in Finite Element Method (Soil-Structure Interaction): Solution of (initial) boundary value problems based on the FEM and the software PLAXIS 2D
  • Exercises in Finite Element Method (Visualization): Visualization of results of Finite Element Analysis with focus on geotechnical engineering

Computer course

A computer course with the software PLAXIS 2D is offered in June for active participants of the course, if required. This course includes six exercises that are solved individually under the guidance of the lecturer:

  • One-dimensional compression of a soil column
  • Simulation of a CD triaxial test
  • Groundwater flow in a water basin
  • Stability of a slope
  • Behaviour of an excavation support system (2D)
  • Behaviour of an excavation support system (3D)

Digital offers

  • Learning material via Stud.IP (lecture notes for lecture and exercises, add-ons, material for the computer course)
  • Exercises with the software PLAXIS 2D, OptumG2, and programming with Python including the packages SymPy, NumPy, SciPy, and Matplotlib
  • Computer course in the institute's PC pool with the software PLAXIS

Certificate of achievement (exam)

  • Exam material: The exam covers everything in the lecture and exercise notes, except for sections marked with an asterisk and sections containing Python programs and application software such as PLAXIS 2D, OptumG2, and GGU Stability. 
  • Exam mode:

    • As part of the module “Numerical Methods in Geotechnical Engineering” together with the course “Selected Topics in Soil Mechanics” for students beginning their study before winter term 2014/2015: oral exam (duration: 40 min; weighting of module grade according to ECTS points)
    • As part of the module “Marine Geotechnics and Numerics” from summer term 2015 to summer term 2020: written exam (duration: 60 min; weighting of module grade according to ECTS points; examination aids: lecture notes, possibly the PLAXIS course materials, non-programmable pocket calculator)
    • As part of the module “Geotechnical Engineering III” from winter term 2020/2021 to summer term 2025: written exam (duration 60 min; weighting of module grade according to ECTS points; examination aids: lecture notes, possibly the PLAXIS course materials, non-programmable pocket calculator)
    • As part of the module “Soil Mechanics and Soil Dynamics” since summer term 2026 (current mode): written exam (duration 45 min; weighting of module grade according to ECTS points; examination aids: lecture and exercise notes, possibly the PLAXIS course materials, non-programmable pocket calculator) 

References

  • Textbooks:

    • Wriggers P. (2001): Nichtlineare Finite-Elemente-Methoden. Springer 
    • Wriggers P. (2008): Nonlinear Finite Element Methods. Springer

  • Recommendations:

    • EANG (2013): Empfehlungen des Arbeitskreises "Numerik in der Geotechnik". Ernst & Sohn, Hrsg.: Deutsche Gesellschaft für Geotechnik (DGGT)