张仲杰, 陈振南, 刘江斌,等.基于改进Knothe时间函数的地表动态移动变形预测模型研究[J].河南理工大学学报（自然科学版）,2024,43(6):82-89.

ZHANG Z J, CHEN Z N, LIU J B, et al.Study on the prediction model of the surface dynamic movement and deformation based on improved Knothe time function[J].Journal of Henan Polytechnic University(Natural Science) ,2024,43(6):82-89.

基于改进Knothe时间函数的地表动态移动变形预测模型研究

张仲杰1, 陈振南2,3, 刘江斌1, 马子韬1, 闫伟涛3, 陈俊杰3

1.国家能源集团 宁夏煤业有限责任公司，宁夏 灵武  750411；2.哈密市伊吾县自然资源局，新疆 哈密  839304；3.河南理工大学 测绘与国土信息工程学院，河南 焦作  454000

摘要: 目的 为进一步探究地表动态移动变形特征，加深认识矿山开采沉陷基本规律，更好地服务于矿山安全绿色生产，  方法 针对原Knothe时间函数模型表达地表下沉及其速度变化规律的缺陷，基于矿山开采过程中地表下沉盆地动态形成机理，分析时间函数参数c对地表下沉量、下沉速度和下沉加速度影响规律；以地表下沉速度达到最大值时刻，将地表动态移动变形分为两个阶段，进一步改进Knothe时间函数模型，在此基础上，建立地表动态下沉、倾斜、曲率移动变形预测模型，并以某矿2201开采工作面为例，进行地表动态移动变形预测和精度分析。  结果 结果表明：改进后的Knothe时间函数形态与矿山开采沉陷地表动态移动变形一致，可以较好地描述采动地表“稳定→变化→稳定”全过程动态演化特征；参数c是该函数模型的重要参数，与覆岩力学性质、开采条件和开采速度等地质采矿条件有关，对描述地表动态移动变形量较敏感，随着参数c增大，地表下沉量和下沉速度显著增大；运用改进的Knothe地表动态移动变形预测模型计算，得到的地表下沉量误差为厘米级精度，倾斜值误差在5 mm/m以内，曲率误差在0.7 mm/m²以内，其相对误差均在6.0%以内，预测结果与实测结果较吻合。  结论 提出的预测模型具有一定可靠性与实用性，可较准确分析地表动态移动变形全过程的规律，从而为“三下”采煤及保护煤柱留设提供参考。

关键词:开采沉陷;Knothe时间函数;动态预测模型;地表移动变形

doi:10.16186/j.cnki.1673-9787.2022120036

基金项目:国家自然科学基金河南省联合基金重点资助项目（U21A20108）；国家自然科学基金资助项目（42207534）；河南省自然科学基金资助项目（242300421363）

收稿日期:2022/12/15

修回日期:2023/03/01

出版日期:2024-09-24

Study on the prediction model of the surface dynamic movement and deformation based on improved Knothe time function

ZHANG Zhongjie1, CHEN Zhennan2,3, LIU Jiangbin1, MA Zitao1, YAN Weitao3, CHEN Junjie3

1.Ningxia Coal Industry Co.，Ltd.，State Energy Group，Lingwu  750411，Ningxia，China；2.Yiwu County Natural Resources Bureau of Hami City，Hami  839304，Xinjiang，China；3.School of Surveying and Land Information Engineering，Henan Polytechnic University，Jiaozuo  454000，Henan，China

Abstract: Objectives In order to further explore the dynamic movement and deformation characteristics of the surface，and to deepen the understanding of the basic law of mining subsidence so as to better serve the safety and green production of mines，  Methods in view of the defect of the original Knothe time function model to express the law of the surface subsidence and its velocity change，based on the dynamic formation mechanism of the surface subsidence basin during mining，the influence law of time function parameter c on the surface subsidence，subsidence velocity and subsidence acceleration was analyzed theoretically.When the subsidence velocity reached the maximum，the dynamic movement and deformation of the surface were divided into two stages，and the Knothe time function model was further improved.On this basis，the prediction models of dynamic subsidence，inclination and curvature movement and deformation of the surface were established.Taking 2201 mining face of a mine as an example，the prediction and accuracy of movement and deformation were analyzed.  Results The results showed that，the shape of the improved Knothe time function was consistent with the dynamic movement and deformation of the surface in mining subsidence，it could better describe the whole process of “stability→change→stability” dynamic evolution of mining surface.The time function parameter c was an important parameter of the function model，which was related to geological mining conditions such as overburden mechanical properties，mining conditions and mining speed，and it was sensitive to describe dynamic surface movement and deformation，the subsidence value and subsidence velocity increased sharply with the increase of parameter c.By using the improved Knothe time function prediction model，the error of the predicted surface subsidence value was centimeter-level accuracy，the error of the tilt value was within 5 mm/m，the error of the curvature was within 0.7 mm/m²，and the relative error was within 6.0%.The predicted results were in good agreement with the measured results.  Conclusions The prediction model had certain reliability and practicability，the law of the whole process of dynamic movement and deformation of the surface could be analyzed more accurately，and reference could be provided for mining under “three body” and coal pillar protection.

Key words:mining subsidence;Knothe time function;dynamic prediction model;surface movement and deformation