Institut für Geotechnik und Baubetrieb

Menu

Course

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

 

Status: 13.04.2026

 

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: part of the mandatory module “Numerical Methods, 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 13:30-15:00, start at 13.04.2026 (bus line 42, exit Theodor-Yorck-Straße)

Requirements

Sucessfull participation of the following courses is required to have a proper background for the course:

  • Mathematics I to III (differentiation, integration, linear algebra, and ordinary differential equations)
  • Soil Mechanics by Prof. Jürgen Grabe (principle of effective stress, Darcy's law, one-dimensional consolidation theory etc.) 
  • Geotechnical Engineering by Prof. Jürgen Grabe (soil-structure interaction, shallow foundations, pile foundations, soil anchors, retaining walls)
  • Soil mechanics laboratory course by Prof. Jürgen Grabe/Göta Bürkner (participation is an advantage, index tests, oedometer and triaxial testing)
  • Finite Element Method by Prof. Bastian Oesterle (partial differential equation, weak form of pde, Galerkin method, discretization, stiffness matrix, load vector, types of finite elements, matrix form of FEM)

A registration under Stud.IP is required to participate. 

Learning objectives

  • Acquisition of the basics of computational geomechanics including the soil-structure interaction:

    • Analysis of situations in soil mechanics and geotechnical engineering as a first step towards computational geomechanics
    • Formulation of boundary value problems (bvp) and initial boundary value problems (ibvp)
    • (Analytical solution, symbolic and numerical solution of basic mathematical problems byed on Python; beginning with summer term 2026 this is no longer part of curriculum and exams)
    • 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 (beginning with summer term 2026 this is no longer part of curriculum and exams)
  • 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. (Beginning with summer term 2026 this is no longer part of curriculum and exams.)
  • Exercises in Finite Element Method (Soil): deformation analysis, steady-state  groundwater flow analysis, uncoupled consolidation analysis, safety analysis based on  FEM and software PLAXIS 2D
  • Exercises in Finite Element Method (Soil-Structure Interaction): Solution of (initial) boundary value problems based on the FEM and software PLAXIS 2D
  • Exercises in Finite Element Method (Visualization): Visualization of results of Finite Element Analysis with focus on geotechnical engineering

Computer course (mandatory)

A computer course with the software PLAXIS 2D is offered in June for active participants of the course, if desired. This course includes six exercises that are solved individually under the guidance of the lecturer: one-dimensional compression of a soil layer, simulation of a CD triaxial test, groundwater flow in a water basin, stability of a slope, deformation behaviour of an excavation support system (2D and 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, and programming with Python including the packages SymPy (symbolic solution of mathematical problems), NumPy and SciPy (numerical solution of mathematical problems, and Matplotlib (visualization of results)
  • Computer course in the institute's PC pool with the software PLAXIS (if desired)

Certificate of achievement (exam)

  • Exam material: The exam material depends on the course content for the current semester and will be determined at the end of the semester together with the participants. Here some hints for summer term 2026:

    • Sections in the lecture notes marked with an asterisk, are not part of exams; futher section can be marked like this during the semester
    • The chapter "Numerical mathematics" is not part of exams anymore beginning with summer term 2026 (note, that older exams include tasks in this field)
    • Software including the programming language Python and Python libraries, as well as apps like the FEM-codes PLAXIS 2D and OptumG2 plus the LEM-codes GGU stability and Free Slope Stability Analysis are not part of exams

  • Exam mode:

    • As part of the ongoing module “Numerical Methods, Soil Mechanics, and Soil Dynamics” since summer term 2026: written exam (duration 45 min; weighting of module grade according to ECTS points; examination aids: lecture notes, PLAXIS course materials, non-programmable pocket calculator) 
    • Participants of former courses may had a 60" exam:

      • 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)
      • 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)
      • 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)

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)