International Journal of Rock Mechanics and Mining Sciences
Technical noteFuzzy genetic programming method for analysis of ground movements due to underground mining
Introduction
The ground surface movements due to underground mining has often resulted in major disasters throughout the world, frequently inflicting heavy losses of life and damage to property. The prediction of ground surface movements is an important problem in rock and soil mechanics in the excavation activities especially the coal and metal mining [1], [2], [3].
Underground mining causes the formation of surface subsidence trough. The prediction of the consequences of mining is an important task for the mine surveying service [4], [5]. The knowledge about the surface activity caused by mining, and the prediction of subsidence enable efficient repairs of the mining damage, and has a positive impact on the economic results of mining. Accurate and reliable prediction can, beside other factors, influence significantly the strategy of the operation of a mine. Due to a large number of parameters influencing the behaviour of the rock above the excavated space, the prediction of mining consequences is a demanding task. It is difficult to determine all the parameters, and it is even more difficult to determine their relative impact [2], [5], [6].
Displacements cause damage in different objects on the surface. Therefore, the aim of mine surveyors at the beginning of the last century was to estimate the impact of underground mining on buildings, transport systems and surface above mines. They started to measure the displacements of points in the mine and on the surface, in order to be able to control the subsidence process and to diminish the damages caused by the excavation. They prescribed procedures of monitoring displacements and developed the methods for the prediction of surface subsidence in individual mines [6], [7], [8], [9], [10], [11]. Several prediction methods have been developed.
The first methods for the prediction of surface subsidence were empirical prediction methods. These methods are based on the correlation of measured data with the geometric parameters of the excavations. As these methods are derived from the measurements in a specific area, they are in direct relation to it, and the results are valid only for the investigated area.
Prediction methods based on influential functions form the second group of prediction methods. The influential function is used to describe the value of the impact of elementary part of the excavation on the formation of subsidence. This group of prediction methods is based on seven assumptions or principles which simplify the calculus and make the methods generally applicable. The principle of using the methods is to select the influential function for each mine and then determine the coefficients in order to ensure that the subsidence curve is similar to the form of the subsidence in nature.
The third group of prediction methods consists of the model prediction methods. Their origin is in mathematical–physical models. The behaviour of roof and the development of subsidence are calculated according to the laws of mechanics. The elastic and plastic models of subsidence belong to this group of prediction methods. When using these models, the problem is usually solved by numerical methods, such as the finite element method, the finite difference method or the boundary element method.
Based on results of the statistical analysis of a large amount of measured data in underground excavation engineering, the fuzzy genetic programming method (FGPM) of ground surface movements is given by using the theory of fuzzy probability measures and genetic programming (GP). And GP approach is proposed to determine the parameter of ground surface movements due to underground mining in this paper.
Section snippets
Mathematical models for analysis of ground movements
It is difficult to calculate the accurate movement of every point in a body of rock because of the complexity of the problem. Instead, various approximate methods have been used for this calculation. In recent years, in mining engineering in particular, theory of fuzzy mathematics has been applied to analyse the problems of ground surface movement due to underground mining [2], [4], [5], [10].
In fact, the movement of each point at a level of overburden can be regarded as a fuzzy event. In other
The GP approach to determine the parameters of ground movements
It is difficult to determine all the engineering parameters of ground movements due to underground mining, and it is even more difficult to determine their relative impacts. The engineering parameters can be determined by the artificial neural network (ANN) method [5], or by GP. In this research, the engineering parameters of ground movements are obtained by using the GP method.
GP is probably the most general approach of evolutionary computation methods [13]. GP can be viewed as an extension of
The process of estimating the displacements
In order to demonstrate the application of the method for the ground surface movements the engineering example of the practical application of the above theoretical results is given. Fig. 3 is a full flow chart with the steps in the method for estimating the movement values.
The flow chart of GP is given in Fig. 4. The training parameters (the parameters of the GP algorithm) are given in Table 1.
Determining subsidence factor
The engineering parameters can be determined by the GP method. Training samples and GP parameters are
Conclusions
In this paper, by applying the concepts of fuzzy probability measures and GP to actual cases of excavation, mining, ground surface movement have been analysed and the corresponding membership function established. And the engineering parameters for the ground surface movements are obtained by using the GP method. The approximate subsidence and horizontal displacement has been calculated and compared with the recorded data obtained from monitoring stations. The comparison shows that the
Acknowledgements
The support of this research work by a key project of science and technology from the Hebei province is gratefully acknowledged (No. 05213706). The project was supported by the research fund of the project of science and technology from the Educational Office of the Hebei Province is gratefully acknowledged (No. 2004308).
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