The background to numerical models

'How important is it to understand how a numerical analysis programme works in order to use it for design?'. I guess if you asked any engineer this question the answer would always be very. But if we asked if those same engineers understand the analysis programmes that they use for design, we might get the answer no more often than I think we would find comfortable. It's an uncomfortable truth about the industry we work in.

When I ask myself the question why this should be the case I personally can't come up with one answer. One obvious reason would be that so many users are self taught when using analysis programmes. The documentation, especially covering the theory, is often poor and as usual the training of the user is also limited if it actually exists at all. Learning the theory behind a program is often very difficult and can be very mathematical..... but that doesn't mean you have to learn this hard maths to understand how a program works.

To prove this I want to consider a numerical analysis programme called UDEC (ref 1.). This is a very powerful tool, typically used for analysing two dimension rock mechanics problems such as rock slopes or tunnels in rock. The image shows a typical analysis of a tunnel in rock showing how the programme can analyse complex joint patterns in the rock around the excavation. So how does it actually work?

Rather than quoting the extensive manual, going into the finite difference method in detail I am going to give a very quick and dirty explanation of how it solves the problem. The solution method used by UDEC is basically to apply Newton's laws of motion to each block, zone or other structure within the model. From this an acceleration can be determined for each element. By considering very small time steps the gradually movement and straining of each part of the model can be calculated. Once the small movements and strains have been calculated for one time step, the resulting small changes in the contact stresses, stresses within blocks and any other forces on the model can be calculated. These forces can then be applied to the elements within the model and the acceleration and displacement can be calculated for the next time step. The model steps through time slowly until a solution is reached i.e. the out of balance forces within the model tend to zero.

That is all there is to it. It doesn't mean if you know this, you are ready to use the programme in anger. There is a lot more theory to learn, but that theory doesn't have to be mathematical. The problem is that it is finding non-mathematical explanations of the theory is difficult. If we can get more explanations of how things work without being too mathematical I can only see this as being a positive.

If you have any explanations for how things work or find any please post them here so that we can all improve our understanding of the tools we use.

Ref 1 - UDEC (Universal Distinct Element Code), HC Itasca