Silicon Dale

Models, Models,... (2) dynamic

Last month we looked at some of the types of geometric model used for static modelling of geology. This month I shall be discussing some of the more dynamic types of model, and whether any of these may be useful for ore deposit modelling.

Finite element nets

For modelling of mechanical properties of structures, finite element analysis has become the conventional nuemrical tool. The object to be modelled - be it a bridge, a building, or an unstable hillside, is discretised by defining a series of points which are linked by a network of lines. These lines usually form a triangular (in the two-dimensional case) or tetrahedral (three dimensional) net. Mechanical (and other) properties are assigned to the links - compressive and tensile strengths, for example - and the behaviour of the structure under applied stresses is determined by a series of computations, using simple Newtonian physics, around each node.

Although this method is very powerful in modelling the behaviour of homogeneous bodies, and has found application in geotechnical engineering, it does not lend itself to modelling local variations in bulk properties, as the discretisation into point nodes and the linear connections between nodes is unsuitable for representation of volume-related properties.

Finite difference grids

Although finite diffeence models share many features with finite element models - including many similarities in the numerical solutions - they have a fundamentally different structure. Normally space is discretised using grids or blocks. This allows volumetric properties to be modelled properly. Finite difference models have been used not only for mechanical modelling, but also - more importantly in geology, for modelling of fluid flows within permeable media.

It should be noted that, as in finite element modelling forces are computed at each node, so in finite difference modelling mass transfer (or forces, or any other properties) are computed across block boundaries (edges in 2D or faces in 3D). It is therefore essential to use a model structure which allows efficient storage and handling of adjacency information. For this reason, simple block models are used rather than the more complex partial- or sub-block models used to represent detail in static geological modelling. In order to look in detail at a particular region, therefore, it is quite common to use grid spacings which vary over entire rows or columns rather than have the added complication of handling adjacency data for sub- blocks.

In finite difference modelling packages used in geology, such as ITASCA's ‘FLAC', it is possible to model deformation of the blocks by storing the actual spatial coordinates separately from the predefined topological grid structure. This allows the development of a very powerful model which can simultaneously represent deformation (in non-homogeneous geology) and flow of fluids through the modelled region. Nevertheless there remain problems. For example, the deformations possible are necessarily continuous - the grid topology cannot be broken - and so faulting cannot easily be included. It is possible only to include pre-existing faults in the model setup.

Particle models

A radically new approach to geological modelling has been made possible in recent years by the development of particle flow codes (PFCs). In this type of model, discretisation takes the form of a large number of ‘particles' of assumed spherical form. These particles can if desired be envisaged as space-filling - even though real spheres must leave some spaces however closely packed they might be. The model ‘particles' are deemed to interact with each other depending on their separation distance and a set of definable physical properties and rules. To that extent they may seem to be similar to finite element nodes. However, PFCs allow particles to move relative to one another, and the sets of nearest neighbours will change as they move so that the net of links between them must be defined dynamically. The size of a ‘particle' has no relationship with the size of real atoms or molecules but can be defined simply as a computationally convenient and geologically meaningful size, in the same way as a block in a conventional orebody modelling system.

The flexibility of the PFC model means that it can be used to model discontinuities as well as continuous phenomena - and it has been used, for example, to simulate crack propagation in solids under stress. It is possible, because of the freedom to define interactions between particles, also to model chemical behaviours such as metasomatism or weathering.

PFCs are currently being used in geomechanical and geodynamic modelling by a number of groups. Possibly the most experienced of these is a team led by Dr Alison Ord at the CSIRO Geomechanics Laboratory at Nedlands, Western Australia, where particle flow codes have been in use since 1996. The method is being developed by CSIRO as a tool in large-scale geodynamic modelling for predictive mineral discovery.

However, there seems to be a clear opportunity for the application of this most powerful new technology to revolutionise the modelling of ore deposits and to allow the integration of the conventional grade model with rock mechanics and hydrogeological models.

Stephen Henley
Matlock, England
steve@silicondale.co.uk
www.SiliconDale.com

Copyright © 2001 Stephen Henley
Models, Models,... 2. Dynamic: Earth Science Computer Applications, v.16, no.5, p.1-2