Topics on Structures and Geotechnics


The purpose of the geotechnical module is to provide generalist training in the geotechnical aspects of underground works to students. To this end, several topics related to the influence of the properties of excavated massifs in the design and sizing of underground projects are studied.
In the 2nd module the main concepts of the theory of plasticity are introduced. Details about the computational implementation of elasto-plastic models are also addressed.

General characterization





Responsible teacher

Mário Jorge Vicente da Silva


Weekly - 8

Total - 60

Teaching language



Available soon


Borja, R.I.; Plasticity - Modeling & Computation, Springer 2013

Simo, J. & Hughes, T.; Computational inelasticity, Springer, 1998

Teaching method

The several subjects will be presented and discussed in both types
of lectures. The several concepts, principles and methods will be
presented at the theoretical classes. The students will then apply
the concepts to simple problems.

At the laboratory classes, the students will finish the problems
started at the lectures. Several applications will then be solved
using the computational tools at hand.

Outside the classes the students are encouraged to study the given
bibliography in order to mature and consolidate the acquired

Evaluation method


Subject matter

Module I:

  1. Introduction to the problem of underground works
  2. Deformation process around underground cavities
  3. Geological prospecting and geomechanical characterization of the massif
  4. Dimensioning of underground works

Module II:

1. Elastoplastic problem in one dimension

  • Yield function
  • Flow rule
  • Isotropic and Kinematic Hardening
  • Implementation algorithms
  • Energy and Plastic dissipation
 2. Elastoplasticity for planar problems
  • Yield functions, J2 yield criterion
  • Perfect plasticity
  • Linear hardening model
  • Non-associative plasticity
  • Tangent elasto-plastic constitutive relation
  • Maximum plastic dissipation
  • Return mapping algorithm
  • Computational elasto-plasticity (implicit and explicit methods)


Programs where the course is taught: