Prediction of elevation of substantial fluctuation in coal seam floor based on surface spline function and its derivative

With the increasing depth of coal mining, the geological stress and structure becomes more and more complex. The elevation of No.8 coal floor significantly undulates in the studied coal mine. Even though a lot of boreholes have been drilled, it remains difficult to predict the spatial distribution features and it becomes challenging to plan the tunnel for the working face. Consequently, there has been a great loss of production in the coal mine, therefore, it is of great significance to study the prediction method for coal floor elevation of the working face. The surface spline function can be regarded as an infinite flat plate deformation in pure bending. The fluctuation of the coal floor can be considered to be the result of multi-period tectonic stress applied on the coal seam, so, the prediction of elevation of the coal floor with surface spline method is feasible. An advantage of surface spline method is that any order differentiable smooth surface can be obtained without regular known lattice and boundary derivatives. In the paper, the complete expression of surface spline function is derived, which is used to predict the elevation of No.8 coal floor of the coal mine. The results show that the trend of elevation of the coal floor can be extrapolated by known data, and the maximum error is 20 m, the minimum error is 0 m, and the error of 80% of the data is less than 3 m. The general trend of the coal floor has been predicted well. However, local peaks and valleys could not be predicted correctly, therefore, the first and second order derivative are projected to predict the peaks and valleys in the head of the tunneling.