Reliability of numerical modelling predictions

The accuracy of all predictions made using numerical modelling is strictly limited by the natural variability of geologic materials. In this paper, an attempt is made to quantify this accuracy through the straightforward application of probability and statistics. It is shown how the contributions from variability of the input parameters and also errors introduced by the modelling procedure can be combined into a single representative coefficient of variation C_p. This parameter is a characteristic that quantifies how well the entire modelling procedure is performing. It includes contributions from the variability of the pre-mining stress and rock mass strength, material heterogeneity and also errors introduced by the modelling procedure (e.g. elastic versus inelastic), and represent the uncertainty one has in predictive capability.In the paper, a lower limit for C_p of 30% is estimated for use with the conventional empirical approach (i.e. measurement of pre-mining in situ stress state, laboratory testing, and subsequent strength degradation to rock mass scale). Realistic values are most likely higher than this since some contributions have not been included and others are not known with any certainty. Various methods to reduce the magnitude of this parameter are then investigated. It is shown how this parameter can be evaluated by back-analysis of field observations. An example is detailed where a series of pillar failures are back analysed to calculate a site-specific value of 10%. This allows predictions to be made with greatly improved confidence and accuracy, and demonstrates why the back-analysis approach is so appealing. The paper presents a rational means for improving on existing empirical procedures for design of underground excavations.