Skip to main content

ES96V - Finite Element Methods for Tunnelling

Module Leader: Dr Alan Bloodworth

BTS Champion: Dr Andrew Mar, Morgan Sindall Underground Professional Services

(15 Credits)

This module is one of a set of core modules for the MSc course in Tunnelling and Underground Space.


Aims :

Finite element methods are widely used to determine the structural integrity of underground openings and their support systems. The first half of the module aims at introducing the fundamental principles of the mathematical modelling for statics and dynamics analyses. In the second half of the module the students will be taught how to use the method in practice and to critically assess and evaluate the results. The module aims to provide an introduction to the use of commercial FEM software commonly used in underground design.

Learning Outcomes: At completion, students will be able to:
  • Identify the significance and importance of finite element methods to the professional tunnel design engineer.
  • Utilise a theoretical understanding of the fundamentals of finite element methods for small displacement linear elastic analysis (statics) to solve a problem.
  • Recognise when to use a non-linear finite element method.
  • Solve problems using commercial FE software (Abaqus & Plaxis).
  • Demonstrate how to develop good models and how to interpret the numerical results in design

Syllabus :

  • History of Finite Element (FE) methods and the place of computational methods in structural analysis.
  • Small displacement linear elasticity (equilibrium, compatibility, stress-strain relationships, boundary conditions).
  • Integral formulation for static analysis by the implicit FE method.
  • Displacement functions and formulation of element stiffness and load characteristics (bar, membrane, flexure, and plate bending).
  • Shape functions and the isoparametric element formulation, introduction to curved surfaces.
  • Requirements for FE displacement fields.
  • Methods to solve the matrix equations for the discretised structure.
  • Introduction to the non-linear finite element method.
  • Introduction to the explicit FE method.
  • Practical aspects (e.g. mesh design, constitutive modelling, boundary conditions) for the FE modelling and simulation of real components.
  • Application of commercial FE software (Abaqus) in engineering design.

Illustrative Bibliography:

J T Mottram, and C T Shaw, Using finite elements in mechanical design, McGraw-Hill, Maidenhead, 1996 . T353.M6
R D Cook, Finite element modeling for stress analysis, Wiley, New York, 1995. QC137.C6
R D Cook, D S Malkus and M E Plesha, Concepts and applications of FE analysis, John Wiley, New York, 1989. QC137.C6
Adams, V., and Askenazi, A., Building better products with Finite element analysis, OnWord Press, Santa Fe, (1999). QC 137.A3
P. Jacob, and L. Goulding, An explicit finite element primer, NAFEMS, 2002.


A 15 CATS module: Assignment (70%), In-class Test (30%)