赵春苏, 陈俊杰, 闫伟涛,等.倾斜不规则工作面开采沉陷预计模型的构建与实现[J].河南理工大学学报（自然科学版）,2026,45(2):204-212.

ZHAO C S, CHEN J J, YAN W T,et al.Construction and implementation of a subsidence prediction model for inclined irregular working face mining[J].Journal of Henan Polytechnic University(Natural Science) ,2026,45(2):204-212.

倾斜不规则工作面开采沉陷预计模型的构建与实现

赵春苏1, 陈俊杰1, 闫伟涛1,2

1.河南理工大学 测绘与国土信息工程学院，河南 焦作  454003；2.煤炭安全生产与清洁高效利用省部共建协同创新中心，河南 焦作  454003

摘要: 目的 为提升复杂开采条件下地表移动变形预计精度，准确预测倾斜不规则工作面开采引起的地表移动与变形。  方法 基于采深变化的单元影响函数，提出倾斜煤层任意开采单元采深计算方法，并构建适用于倾斜不规则工作面的沉陷预计模型。该模型利用格林公式将沉陷面积分转化为边界线积分，推导了相应的线积分预计公式，并给出数值求解方法。在此基础上，开发了一体化预计程序，实现了从参数输入、积分区间确定到线积分求解的全流程计算，能够输出地表下沉、倾斜、曲率、水平移动和水平变形等预计结果的可视化，评价分析工作面采动损害的等级，并结合实际矿区倾斜工作面开采实例，对所构建的预计模型进行验证与分析。  结果 结果表明，提出的倾斜不规则工作面开采移动变形预计模型和一体化程序，能够有效解决复杂开采条件下地表沉陷的精确预测计算和采动损害等级划分，预计结果符合开采沉陷基本规律，预计下沉的相对误差小于10%，满足工程预计的精度要求。  结论 预计模型具有可靠性和实用性，预计精度高，可为倾斜不规则工作面矿山开采优化设计和地表损害精准评估与防护对策制定提供理论依据和技术支撑。

关键词:开采沉陷预计;不规则工作面;倾斜煤层;概率积分法;格林公式

doi:10.16186/j.cnki.1673-9787.2025070033

基金项目:国家自然科学基金资助项目（U21A20108，42207534）；河南省自然科学基金资助项目（242300421363）；河南理工大学杰出青年基金项目（J2024-4）

收稿日期:2025/07/26

修回日期:2025/10/29

出版日期:2026/01/28

Construction and implementation of a subsidence prediction model for inclined irregular working face mining

Zhao Chunsu1, Chen Junjie1, Yan Weitao1,2

1.School of Surveying and Land Information Engineering， Henan Polytechnic University， Jiaozuo  454003， Henan， China；2.Collaborative Innovation Center of Coal Work Safety and Clean High Efficiency Utilization， Jiaozuo  454003， Henan， China

Abstract: Objectives The prediction accuracy of surface movement and deformation under complex mining conditions is to be improved， and the surface movement and deformation induced by inclined irregular working face mining is to be accurately predicted. Methods Based on a unit influence function that considers variations in mining depth， a calculation method for the mining depth of arbitrary units in inclined coal seams was proposed， and a subsidence prediction model suitable for inclined irregular working faces was established. The model applies Green’s theorem to convert subsidence area integrals into boundary line integrals， derives the corresponding line integral prediction formula， and provides a numerical solution method. On this basis， an integrated prediction program was developed, achieving full-process computation from parameter input and determination of integration intervals to line integral solutions. The program enables visualization of prediction results， including surface subsidence， tilt， curvature， horizontal movement， and horizontal deformation, and further evaluates and analyzes the mining-induced damage levels. The proposed model was validated and analyzed through case studies of inclined working faces in actual mining areas.  Results The results show that the proposed prediction model and integrated program can effectively address the accurate prediction of surface subsidence and classification of mining-induced damage under complex mining conditions. The prediction results conform to the fundamental laws of mining subsidence， with a relative error in subsidence prediction of less than 10%， thereby meeting engineering accuracy requirements. Conclusions The proposed model is reliable and practical， with high prediction accuracy， and can provide a theoretical basis and technical support for the mining design optimization， precise surface damage assessment and protection strategies in inclined irregular working face mining.

Key words: mining subsidence prediction; irregular working face; inclined coal seam; probability integration method; Green’s formula