Prediction of mining-induced surface subsidence and ground movements at a Canadian diamond mine using an elastoplastic finite element model

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Abstract

A full three dimensional elastoplastic finite element model of Diavik Diamond Mine is developed to predict surface-induced ground movement due to underground blasthole stoping activities. A mesh convergence study has been conducted to reach to an optimum meshing scenario when further mesh refinements produce a negligible change in the results. This way the calculation cost and time has been managed successfully. Furthermore, sequences of the excavation/backfilling in the model are defined according to the mine production plan; however, some simplifications in the shape of the stopes have been made. Consequently, the developed finite element model simulates the complete stress-strain path through the entire excavation and backfilling simulation steps in full three dimensional space. The model is calibrated using two extensometers installed on the back of two secondary undercut drifts in one of the Kimberlite pipes. The results of the calibrated model are validated using pit surface prism monitoring system data. The average relative error between the measured data and FE model predictions is 7.95%. It is shown that the numerical predictions of the mining-induced surface subsidence, due to the blasthole stoping mining method, matched well with the Gaussian distribution. A significant increase, approximately by 44%, to the amount of the induced settlements on the surface occurred as the mining activities reaches near surface ground levels. Finally, the comparison between the predicted results of the finite element model and monitoring data showed that the predictive capacity of the numerical model is a valuable tool for stability and design analysis of underground mines.

Introduction

Subsidence is the downward settlement of the ground surface. Mining-induced surface subsidence is a phenomenon that occurs due to the underground extraction of an orebody. Open pit and underground mining operations cause stress redistribution; consequently, this causes some induced displacements on the ground surface.

According to the elasticity theory, any excavation at any depth and extend can cause movement on the ground surface. This means that all underground mining methods can cause surface subsidence. According to Pariseau,1 the most common reasons of surface subsidence are: (i) redistribution of the stresses due to mining activities, and (ii) de-watering of the ground during mining activities which cause lowering of the groundwater tables.

Prediction of the surface subsidence profile and its magnitude is a critical task for rock mechanics engineers, and it is crucial for planning underground mining operations. A comprehensive review of the methods to determine mining-induced surface subsidence is given by Brady and Brown.2 Several empirical, numerical, observational, graphical, profile function, influence function and physical methods to predict subsidence parameters have been developed by various researchers.3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14

Overall, methods for prediction of mining-induced surface subsidence can be classified into four main categories: (i) empirical methods, (ii) analytical methods, (iii) numerical methods, and (iv) hybrid methods. Empirical methods (i.e. profile functions, influence functions, graphical methods) are based on the back analysis of field data; for instance, Woo et al.15 developed a comprehensive database of block cave mining and mining-induced surface subsidence to guide empirical relationships between caving depth and its impact on surface movements. Consequently, empirical methods can be used only where a large database of measured field data is available. Analytical methods are based on applying mathematical solutions derived from first principles to predict how the rock mass will behave when an excavation is made within it16; for example using elasticity theory, Salamon17 derived analytical solution to calculate displacements and stresses induced on the surface due to longwall mining in coal. Numerical methods can be used to model elastoplastic, non-linear, and post-yield behavior of rock mass and include the effects of in-situ stresses and geological features on the mining-induced surface subsidence. The current approach is to use the hybrid methods, which is the combination of the analytical or numerical methods with back analysis of field data.

To meet the objective of this paper, finite element method (FEM) is used for numerical analysis due to its recognition as a tool to solve rock mechanics and geomechanical problems. It has the ability to deal with material heterogeneity, non-linearity, complex-boundary conditions, in-situ stresses and gravity.

To predict the induced surface subsidence due to underground mining activity at Diavik Diamond Mine, a fully three-dimensional elastoplastic finite element (FE) model was established. The initial results of the model were calibrated using two underground calibration points. Finally, the calibrated model was used to predict the induced settlement profile for the surface of the N9290 bench located in the A154 pit at Diavik Mine. Results of the developed FE model were verified by comparing the outputs of the constructed FE model with available pit monitoring data.

Section snippets

Diavik Diamond Mine

Diavik Diamond Mine is located on a 20-km2 island in Lac de Gras, approximately 300 km northeast of Yellowknife, Northwest Territories.19 Diavik reserves are contained in four diamond-bearing Kimberlite pipes named A154 North, A154 South, A418 and A21. The host rock is granite. All four pipes were located under the waters of Lac de Gras. To enable open pit mining, first the water was removed, and dikes were constructed to drain the water and prepare the surface for open pit mining. In 2002, the

Model geometry

A full three dimensional (3D) finite element analysis model of the mine, as shown in Fig. 2, is constructed using Abaqus.20 Two simple representative geometries of the open pits, A154 and A148, are included in the model. The analysis domain dimensions are 2.2 km by 2.2 km and maximum depth of the model is 800 m. The domain dimensions are sufficient to eliminate the influence of the boundaries on the model. On the vertical boundary of the model, horizontal restraints (on both X and Y directions)

Calibration of the FE model

The developed FE model was calibrated using two extensometers installed on the back of N9175-118 and N9175-148 secondary undercut drifts. To calibrate the model, the preliminary results of the FE model were compared with the results of the underground monitoring data points. Fig. 9a illustrates the data from the multi-point vibrating wire inline extensometers installed at N9175-118 secondary undercut drift. Data are available from October 07, 2013 (the day it was installed) to the September 17,

Results and discussion

The objective of this paper was to develop a realistic numerical model which can be used as a prediction tool to estimate mining-induced surface subsidence. In the following sections, the results of the calibrated numerical model are presented, and the results are validated using available pit monitoring data.

Conclusions

In this paper, a full 3D elastoplastic FE model of Diavik Diamond Mine was constructed. The main objective of the paper was to predict the mining-induced surface subsidence and induced settlements due to underground mining activities in the A154 North Kimberlite pipe.

In order to obtain reliable results, the developed FE model was calibrated with two extensometers installed on the back of two secondary undercut drifts located at the A154 North Kimberlite pipe at mining level N9175. The results

Acknowledgements

This study was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under Collaborative Research and Development (CRD) Grant. Supports from Diavik Diamond Mine Inc. are gratefully acknowledged (Grant No. RES0017514).

Jan Romanowski, the superintendent of mine technical services at Diavik Diamond underground mine is specially acknowledged for his support and technical inputs throughout this research. Also the authors would like to thank Amir Karami, the senior

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