The University of Southampton
Engineering and the Environment

Research project: Modelling the effects of material microstructure

Currently Active: 

Although their effect is largely ignored in the theoretical framework that underpins every-day practice, there are occasions when the microstructural details (e.g. grain size) of a soil or rock come to dominate its mechanical behaviour. Developing theoretical and numerical tools that include the effects of microstructure will lead to more robust predictions of the behaviour of soils and rocks in a broad range of settings.

Project Overview

All geomaterials, from clays to sands and rocks, have microstructure that, depending on the material in question, may be visible to the naked eye (e.g. the grains of a sand) or not (e.g. clay particles.) However, conventional models that are used in everyday practice for predicting the mechanical response of geomaterials generally ignore their microstructure and treat them as amorphous continua.

Ignoring microstructure has the advantage of offering a relatively simple theoretical framework that provides adequate predictions in most cases. It cannot however describe phenomena where microstructure comes to dominate the macroscopic behaviour of the material. For example, the formation of localised deformation bands that is observed under certain conditions cannot be adequately described: the thickness of the bands, and consequently the mechanical response of the modelled slope, borehole or other structure, cannot be predicted. Scale effects are another example: although in practice the strength of a rock as measured in the lab often depends on the size of the specimen used, conventional models will predict the same strength for all geometrically similar specimens.

In lab tests, the thickness of the localisation band and the strength degradation associated with its formation cannot be predicted by conventional models.
Localised deformation in dry sand

Our research has produced a theoretical framework for including microstructure in continuum models of geomaterials, and is currently focussed on the development of appropriate numerical methods for solving engineering problems with such models.


Theoretical framework

We developed “Gradient Elastoplasticity”, a theoretical framework for introducing microstructure in conventional models. This framework assumes that the behaviour of the material depends, among other things, on internal length-scale parameters that we broadly identify with the grain size.
In this context, localised deformation bands and their behaviour are correctly predicted, while scale effects arise naturally. Using this approach we were able to model, in a robust way, such phenomena as:

  • The formation of localised deformation zones in laboratory tests.
  • The development of instabilities in deep boreholes and the resulting formation of “breakouts”.
  • The lower-than-expected strength of pressurised cavities in weak rocks.


Modelling localisation bands (in cyan) in a pressurised rock cavity. The spiral pattern seen is consistent with experimental observations
Modelling localisation bands
Development of numerical methods

Using the popular Finite Element method to solve engineering problems in the above context is challenging. The microstructural assumptions we use in Gradient Elastoplasticity and other theories of the same type change the mathematical structure of the equations we need to solve, making the standard finite elements commonly used in practice inappropriate.

One solution is to use elements that preserve deformation continuity, of which however very few exist. In our work we pursue the development of appropriate elements and have so far been successful in developing:


Modelling a localisation band during a laboratory test. The predicted reorientation of the band quantitatively agrees with empirical evidence
Modelling localisation bands

  • Generic procedures for systematically designing whole classes of such elements for two-dimensional analyses.
  • The first three-dimensional such element ever constructed.
  • Procedures for obtaining approximate solutions with elements that do not preserve deformation continuity.

Our research in this area is ongoing, with particular focus on three-dimensional analyses and the inclusion of pore water.

Associated research themes

Geomechanics and environmental geotechnics

Related research groups

Infrastructure Group


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