动态预计为煤炭开采过程中工作面上方的建构筑物保护提供依据，时间函数作为动态预计的核心尤为重要。传统时间函数研究对象为单点，对开采过程中时间参数随位置变化规律研究不足。基于正态分布时间函数具有较好的时空完备性，通过引入超前影响距L1和最大下沉速度滞后距L2，在优化后的正态时间函数基础上建立了与位置x有关的时间函数模型并给出了参数开始移动时间tp和移动持续时间tc的计算公式。结合某工作面走向点实测数据，运用最小二乘拟合法探究了形态参数c随位置x的变化规律，并选取不同地质条件下的工作面验证规律可靠性。研究结果表明：形态参数c在模型范围内分为两段，第1段表现为减函数，第2段为稳定值，分界点为超前影响距与充分采动距之和。拟合参数代入模型后，将观测点预测值与实测值比较，预测相对中误差保持在5%~9%;在较软弱地质条件下的另一工作面，预测相对中误差保持在1%~5%范围内。与传统的Knothe时间函数、双参数Knothe时间函数、Logistic函数相比，正态时间函数单点精度优于或等于它们，但模型整体精度稳定，精度能够满足实际预测需要。通过处理工作面实测数据，将预测值与实测值对比，其相对中误差在合理范围内，证实了模型的可靠性。因此正态分布时间函数模型可为矿区地表沉陷精确动态预计服务。

The dynamic prediction provides a basis for the protection of the structures above the working face in the process of coal mining.As the core of dynamic prediction,time function is particularly important.The research object of the traditional time function is a single point,so it is insufficient to study the variation of time parameter with position in the mining process.Based on the spatio-temporal completeness of the normal distribution time function,the introduction of the advancing influence distance (L1) and the lag distance of the maximum subsidence velocity (L2),a time function model related to position (x) is established based on the optimized normal time function.The calculation formulas of the parameters starting time (tp) and moving duration time (tc) are given.Based on the measured data of strike point in the working face,the least square fitting method is used to explore the variation law of shape parameters (c) with position (x) and the working faces under different geological conditions are selected to verify the reliability of the law.The results show that the morphological parameters (c) are divided into two sections within the range of the model,the first section is a subtraction function,the second section is a stable value.The dividing point is the sum of the advancing influence distance and the full mining distance.After the fitting parameters are substituted into the model,the mean square error is kept between 5%-9% when the predicted value of the observation points is compared with the measured value.In the other working face under the weaker geological conditions,the mean square error of prediction is kept within the range of 1%-5%.Compared with the traditional Knothe time function,two-parameter Knothe time function and Logistic function,the single point accuracy of the normal time function is better than or equal to them.The overall accuracy of the model is stable and the accuracy can meet the actual prediction needs.By processing the measured data of the working face and comparing the predicted value with the measured value,the mean square error is within a reasonable range,which proves the reliability of the model.Therefore,the normal distribution time function model can serve for the accurate dynamic prediction of mining surface subsidence.

1 正态时间函数模型的建立

   1.1 正态分布时间函数

   1.2 与位置有关的正态时间函数模型构建

2 形态系数c的规律探究

   2.1 c值求解过程及结果

   2.2 精度评定

3 实例验证

4 结论