Mathematical models

Published on 18 February 2008

There are certain fields where prediction of how a phenomenon will develop is too complex to be treated in terms of traditional calculation methods. This is where mathematical modelling comes in.

Example of stability calculation for a slope (Talren program)

Mathematical model : Set of equations and relations for the representation and study of a complex system.

There are certain fields where prediction of how a phenomenon will develop is too complex to be treated in terms of traditional calculation methods. They may also prove impossible to reproduce under laboratory conditions or to simulate on a test site when it comes to dealing with cost and risk analysis issues.
This is where mathematical modelling comes in, which, when used in tandem with powerful modern computers, allows a wide range of stimulations to be performed under variant input parameters so as to find the optimum solution (safety, cost, sustainability).

Example 1: Stability calculations. Earthworks for a motorway section cut into a hill, for instance, will require confirmation both of the stability of the slope and that it will not cause movement to adjoining ground.
These calculations are extremely complex because allowance must be made for a large number of parameters, such as the site geology, the quality of each ground stratum, the presence of water tables, ground cohesion, the density and geometry of the ground and of the structure etc. Computer programs have been created to allow such calculations to be performed at high speeds.

Example 2: Blasting simulations. Rock cuttings and rock quarries require the use of large quantities of explosives. Initial simulations are indispensable to optimise the yield of the blast, to reduce the vibrations it causes and which might prove a problem, and to improve fragmentation of the rock. For a number of years now there has been CAD support for shot blasting. This is based on seismology tools, and uses mathematical software to model the efficiency of the complex processes that occur in mine shot blasting as well as to simulate their seismic impact on the environment. In this way it is possible to optimise the effect of the interactions between the various shot blasting parameters to achieve the desired results.