Prediction of progressive surface subsidence above longwall coal mining using a time function

摘要

Based on the Knothe time function, the prediction of progressive subsidence has been demonstrated, and the factor of proportionality, C, describing the influence of geological and mining conditions on the deformation process in time has been determined when there is no measured material in practice. The prediction of progressive subsidence for the 1176E working face, Qianjiaying Coal Mine, indicates that this method is effective and easy to apply for analysis in practice. The differential subsidence characteristics, such as progressive slope, progressive curvature and horizontal strain can also be calculated similarly. Although we found that the tangent of major influence angle is constant, in fact this is different from the traditional Chinese researchers' standpoint.However, determining the real distribution of a time function is not an easy problem in theory and the imperfections of Knothe time function still occur. In order to determine Knothe time function's character, we make an assumption that the variable t has values in the range from zero to + infinity. Results of the analysis demonstrate that in this model the time function increases from a minimal value equal to zero to a maximal value limited by the horizontal asymptote. The first derivative is a decreasing function, and its maximum occurs for a time t = 0. The second derivative is a function increasing from a minimal value to zero. It must be noted that the subsidence rate initially increases from a value equal to zero (for t = 0) to a maximal value, and then it decreases to zero (for t = + infinity) in real conditions. The second derivative, which represents the subsidence acceleration, increases from a value equal to zero (for t = 0) to a maximal value, then it decreases to a minimal value less than zero, and then it increases asymptotically to zero. That is to say, we cannot simulate the subsidence rate and acceleration using the Knothe time function. Thus, further aspects now need to be investigated and remain to be solved in the future.