采空区地表动态沉降预测是当前开采沉陷领域研究重点解决的问题之一，对沉陷灾害的预防和控制具有重要的作用。针对目前采空区地表沉降预测模型存在的问题，通过对煤矿开采引起地表沉陷变形规律的系统分析，认为采空区地表沉降是一个先加速后减速的S型沉降过程，大致可分为初始沉降、剧烈沉降和衰退沉降3个阶段。总结得出理想的采空区地表沉陷预测模型应具有能较好拟合地表沉降时间关系的沉降曲线，沉降速度和加速度应符合地表沉陷物理过程的基本特征。将用于描述增长信息随时间变化的Usher数学模型引入到采空区地表动态沉降预测中。通过对模型结构及其相关参数的深入分析，认为Logistic模型、Gompertz模型、Knothe模型、Mitscherlich Brody模型和Von Bertalanffy模型均是Usher模型的特例，Usher模型符合理想沉陷预测模型的基本要求，可较好地模拟采空区地表动态沉降过程，其参数可采用遗传算法进行求解。在上述研究基础上，将Usher模型与沉陷稳定后沉陷盆地走向或倾向主断面上的剖面函数相结合，构建了整个沉陷盆地内任意点、任意时刻的沉降量计算模型。研究结果证明，Usher时间函数模型比双参数Knothe模型、正态时间函数模型、Logistic和Gompertz等模型具有更强的适应性、更高的拟合精度和更好的预测效果，可为开采沉陷预测提供一定的借鉴和参考。

The surface dynamic subsidence prediction of the goaf is one of the key problems in the field of mining subsidence，which plays an important role in the prevention and control of the subsidence disaster. In view of the problems existing in the prediction model of surface subsidence in goaf at present，through analyzing the law of surface subsidence and deformation caused by coal mining systematically，it is considered that the surface subsidence in goaf is a S shaped subsidence process with accelerating first and decelerating after，which can be roughly divided into three stages:initial subsidence，severe subsidence and declining subsidence. It is concluded that the ideal prediction model of surface subsidence in goaf should have a curve which can better fit the time relationship of surface subsidence，and the subsidence speed and acceleration should conform to the basic characteristics of the surface subsidence physical process. The Usher mathematical model，which is used to describe the change of growth information with time，is introduced into the surface dynamic subsidence prediction of the goaf. Through the in-depth analysis of the model structure and related parameters，it is considered that the Logistic model，Gompertz model，Knother model，Mitscherlich Brody model and Von Bertalanffy model are all special cases of the Usher model. Usher model，whose parameters can be solved by genetic algorithm，accords with the basic requirements of the ideal subsidence prediction model，and can better simulate the surface dynamic subsidence process of the goaf. On the basis of the above research，the Usher model is combined with the section function on the main section of the strike or dip of the subsidence basin after the stable subsidence，and the settlement calculation model at any point and at any time in the whole subsidence basin is constructed. The results show that Usher time function model，which can provide some reference for mining subsidence prediction，has stronger adaptability，higher fitting accuracy and better prediction effect than Knoth model，normal time function model，Logistic model and Gompertz model.

0 引言

1 采空区地表沉降规律分析

2 地表单点动态沉降预测的Usher模型

   2.1 模型建立与通用性

   2.2 模型参数分析

   2.3 模型参数的确定

   2.4 模型的适用性分析

3 地表沉降的动态过程模型

4 工程实例分析

5 结论