How numerical modelling can fill the gaps of the empirical method

While the empirical method is widely used for mine design, it has limitations since it relies on practitioners’ experience and observation rather than on scientific theories or analyses. The aim is to predict ground behaviour based on the experiences of past practices. When site condition is out of the range of past experiences, however, an alternative approach is needed since there are little reference data to compare with.

In addition, conventional approaches based on the empirical method are impractical for design questions that involve a complex interaction between such parameters as irregular geometries, anisotropic, inhomogeneous, and non-linear elastic behaviour, due to the large number of simplifications that are required to make the problem determinate.

Numerical modelling can make up for limitations of the empirical method. It enables practitioners to extrapolate the results of empirical analysis with enhanced confidence, explains observed physical behaviours, and evaluation various hypotheses and design options.

Three-dimensional numerical modelling is especially useful since most mine design problems are three-dimensional. For an open pit with curvature, underground excavation, ore geometry, and irregular-shape faults, 3D numerical modelling is definitely the preferable option.

Three-dimensional numerical modelling for slope stability analysis is recommended in the following cases (Lorig and Varona, 2004):

The direction of principal geologic structures does not strike within 20–30° of the strike of the slope;

• The axis of material anisotropy does not strike within 20–30° of the slope;
• The directions of principal stresses are neither parallel nor perpendicular to the slope; or
• The distribution of geo-mechanical units varies along the strike of the slope.
• Figure 1 shows an example of 3D numerical modelling case.

Figure 1 – Open pit geometry with faults in 3D modelling

As numerical modelling technique is getting popular in mining industry, practitioners’ thorough understanding of not only modelling software skills but also mathematics theories behind modelling mechanism as well as ability to interpret modelling results are getting more important. 

Even a very advanced numerical modelling software could produce misleading results if wrong input parameters are used and a practitioner’s lack of understanding could lead to misinterpretation of modelling results.

When using advanced numerical modelling software, the following considerations need to be made in advance:

• Is sufficient knowledge and experience acquired?
• Are there sufficient laboratory test data available for the determination of input parameters?
• Is the laboratory test data including rock mass properties understood thoroughly?

It is also important to calibrate numerical models using field monitoring data. A well-calibrated numerical model is an excellent tool for forward analysis. Figure 2 shows the result of a 3D shaft modelling forward analysis using calibrated rock mass properties (left) and the corresponding as-built geometry (right), and it is evident that the prediction made by the model is quite accurate.

Figure 2 – 3D shaft modelling forward analysis result with calibrated rock mass properties and as-built geometry

Reference

Lorig, L., and Verona, P. 2004. Numerical analysis. In Rock slope engineering Civil and Mining Editated by D.C Wylie, C. W.Mah and E. Hoek. London: Spon Press.

Kyuseok Woo