The following is an article by Cyrille Séguineau de Préval, Amélie Ouellet, and Patrick Andrieux, A2GC, Canada which appeared in the Deep Mining 2024 Supplement.

# Use of inelastic continuum models to assess mine seismicity levels

by Cyrille Séguineau de Préval, Amélie Ouellet, and Patrick Andrieux, A2GC, Canada

#### Introduction

Deep mining operations are increasingly challenged by mining-induced seismicity, which can have serious health and safety consequences. Significant mining-induced seismicity can result in extended re-entry times and operational delays, and ground rehabilitation needs in more severe cases. Hence there is a need to better understand and anticipate site-specific mining-induced seismicity.

Despite increasing understanding of rock mass behaviour, it is still unrealistic to ‘predict’ single seismic events or precisely located seismic clusters, in both time and space. However, the global seismic response (i.e. seismic events within a given time range and space range) can be correlated to numerical model outputs, also compiled within a time frame and space frame (Beck et al. 2007; Jarufe et al. 2020).

This article proposes a methodology to anticipate from 3D inelastic continuum modelling results, time periods in the life of mine (LOM) susceptible to generate higher levels of seismicity. This is achieved by processing the numerical results against catalogues of recorded seismic events, hence defining a so-called ‘seismic response index.’

#### Establishment of the seismic response index

The seismic response index, referred to as SRI, is meant to anticipate the level of seismicity to be expected as a given mining sequence unfolds. Correlations are first established between the observed seismicity caused by historical stopes (‘real’ seismic response) and the results of the corresponding numerical simulation steps (‘numerical’ response). Then these correlations are applied to forward simulation results, to estimate future seismic responses. The calibration process is schematised in Figure 1.

#### Definition of the ‘real’ seismic response

Prior to establishing any link between seismicity and numerical LOM simulations, a site- and project-specific definition of the seismicity of interest must be established. It can be seismicity located in the vicinity of a geological structure, or more simply the local and immediate seismicity triggered by the blasts of a given stope. In the current example, a seismic event from the catalogue was considered related to a stope blast, if the event was located within 300 m of the stope centroid and took place within 11.5 hours of the stope blast time.

Following this selection of events, the seismic response is characterised by aggregating some of the seismic source parameters. This example uses, for instance, the maximum local magnitude of all selected events and the total energy released (sum of the energy of all selected events). Note that other source parameters such as the potency, the apparent stress, or the Es:Ep ratio could have been considered.

Figure 2 shows the total released energy and the max ML event magnitude for the calibration stopes (95 stopes) used in the example case. The colour scale represents the number of selected events for every stope blast.

#### Definition of the ‘numerical’ seismic response

Similarly to the ‘real’ seismic response, criteria first needs to be established to define which numerical zones in the model will be considered as affected by the simulation of a given stope extraction. Ideally, these are similar to the criteria used for the ‘real’ seismic response. In this example, numerical zones within 100 m of the stope centroid were considered for the collection of numerical quantities to be used in the regressions.

At every stage of the LOM, simulation various quantities (such as the plastic shear work, the deviatoric stress to strength ratio variations or plastic softening parameters) are summed within 30, 50 and 100 m spheres around the stope centroid over all the selected numerical zones associated with a given stope excavation. Thereby, providing numerical indicators for each excavated stope (its ‘numerical’ seismic response), which can then be used as variables for the regressions.

#### Regressions between the seismic parameters and the numerical indicators

In the example case, 95 past individual stopes were excavated in the numerical model, allowing to derive regressions between the two selected seismic parameters (total energy and max ML) and the identified numerical indicators.

A first linear regression searched for total energy. The regression coefficient of this linear regression was found to be 0.27. Isocurves of the linear regression are shown in Figure 3, together with calibration data points. The visual fit was judged satisfying.

In order to avoid similarities, a logistic regression instead of a linear regression searched for whether the max ML is below or above a 1.5 threshold. The comparison between the max ML class prediction and the real max ML value is shown in Figure 4 for the calibration stopes of the example case.

#### Definition of the seismic response index

The total energy prediction and the probability of having a max ML above 1.5, can be combined to define a single scalar value, the ‘seismic response index’ (SRI). As seen in Figure 5, the clear trend (black line in the figure) between the total energy prediction and the probability of having a max ML above 1.5, defines a reference line on which the data points can be projected. The lowest projected data point is assigned an SRI of 0, and the highest projected data point is assigned an SRI of 1.

Figure 6 compares the SRI (obtained from regressions and represented by the colour scale) and the ‘real’ seismic response (the observed total energy and max ML extracted from the seismic events catalogue). Despite some variability, the fit was found to be satisfying (top right data points mostly red, bottom left data points mostly green).

The variability observed may be explained by underlying assumptions of the numerical model used namely, but not exhaustively, the homogeneity of the rock strength throughout the geomechanical domains, the isotropic behaviour and the absence of explicit discontinuities in the modelled rock mass.

#### Forward simulations

Once regressions between seismic parameters and numerical indicators are established, with a calibrated SRI defined for the historical stopes, this workflow is applied to forward simulations to anticipate future levels of seismicity. As there is an inherent variability in the regressions used, the SRI calculations for stopes should be averaged over time periods or regional clusters. In Figure 7, the SRI was averaged over yearly quarters to provide a seismic response risk profile over the LOM.

This information can be used for mine planning, for instance, where specific seismic protocols could be implemented to mitigate the seismic hazard. Additionally, the spatial distribution of the SRI can be visualised by colouring each stope according to its SRI. This allows regional clusters, which are likely to trigger seismicity, to be readily identified. Here again, this information can be used as a mine planning tool.

#### References

Beck, D, Reusch, F & Arndt, S 2007, ‘Estimating the probabaility of mining-induced seismic events using mine-scale, inelastic numerical models’, in Y Potvin (ed.), Deep Mining 2007: Proceedings of the Fourth International Seminar on Deep and High Stress Mining, Australian Centre for Geomechanics, Perth, pp. 31–41, https://doi.org/10.36487/ACG_repo/711_2

Jarufe, J, Wesseloo, J, Potvin, Y & Dhanér, C 2020, ‘Numerical modelling calculation of probabilistic seismic hazard in cave mining’, in R Castro, F Báez & K Suzuki (eds), MassMin 2020: Proceedings of the Eighth International Conference & Exhibition on Mass Mining, University of Chile, Santiago, pp. 1225–1234, https://doi.org/10.36487/ACG_repo/2063_90

Part of this article is taken from Séguineau de Préval, C, Ouellet, A & Andrieux, P 2024, ‘Use of inelastic continuum models to assess mine seismicity levels’, in P Andrieux & D Cumming-Potvin (eds), Deep Mining 2024: Proceedings of the Tenth International Conference on Deep and High Stress Mining, Australian Centre for Geomechanics, Perth, pp. 1165–1178.