Improved Knothe surface dynamic subsidence prediction model and its parameter analysis
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摘要: 针对传统Knothe时间模型描述地表动态沉降过程中的不足，在Knothe时间模型基础上考虑了上覆地层非线性力学特征，建立改进Knothe时间模型，理论分析表明改进后时间模型符合地表单点沉降、沉降速度和沉降加速度变化规律；结合现场实测数据和双介质法，给出改进Knothe时间模型参数计算表达式。采用兴隆庄煤矿4326工作面、三道沟煤矿35101工作面和阳泉二矿8403综采工作面开采地表沉降监测数据，对传统Knothe时间模型和改进Knothe时间模型精度进行对比分析。结果表明：改进时间模型能够更真实地反映地表随开采时间的动态变化过程，预测值和实测值的平均相对标准偏差仅为3.22%，远低于Knothe时间模型的15.72%，验证了改进时间模型的精确性和可靠性；地表动态沉降过程受煤层回采速度v、松散层厚度Hs、基岩层厚度Hj、松散层充分采动角φs和基岩充分采动角φj影响，且影响敏感度依次为：Hj，v，Hs，φj，φs。研究可为煤层开采地表动态沉陷预测提供一定的借鉴和参考。
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关键词:
- 地表沉降 /
- Knothe时间模型 /
- 动态预测 /
- 沉降速度 /
- 敏感性
Abstract: In view of the shortcomings of the traditional Knothe time model in describing the process of surface dynamic subsidence, based on the Knothe time model, considering the nonlinear mechanical characteristics of the overlying strata, an improved Knothe time model is established. The theoretical analysis shows that the improved time model conforms to the variation laws of surface single point subsidence, subsidence velocity and subsidence acceleration. Based on the field measured data and the two-medium method, the expression for parameters of the improved Knothe time model is given. Based on the surface subsidence monitoring data of 4326 working face of Xinglongzhuang Coal Mine, 35101 working face of Sandaogou Coal Mine and 8403 fully mechanized working face of Yangquan No. 2 Coal Mine, the accuracies of the traditional Knothe time model and the improved Knothe time model are compared and analyzed. The results show that the improved time model can more truly reflect the dynamic change process of the surface with the mining time. The average relative standard deviation between the predicted and measured values is only 3.22%, which is far lower than 15.72% of the Knothe time model, which verifies the accuracy and reliability of the improved time model. The process of surface dynamic subsidence is affected by the mining speed v of coal seam, the thickness Hs of loose layer, the thickness Hj of bedrock layer and the full mining angle of loose layer φi and the full mining angle of bedrock φj, and the impact sensitivity is in the order of Hj, v, Hs, φj and φi. The results may provide some reference for the prediction of surface subsidence in coal seam mining.-
Keywords:
- surface subsidence /
- Knothe time model /
- dynamic prediction /
- subsidence velocity /
- susceptibility
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图 1 改进模型地表沉降、沉降速度及沉降加速度曲线
Figure 1. Curves of surface subsidence, subsidence velocity and subsidence acceleration by improved model
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图 3 拟合结果与兴隆庄煤矿实测结果对比
Figure 3. Comparison between fitting results and measured results of Xinglongzhuang Coal Mine
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图 4 拟合结果与三道沟煤矿实测结果对比
Figure 4. Comparison between fitting results and measured results of Sandaogou Coal Mine
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图 5 拟合结果与阳泉二矿实测结果对比
Figure 5. Comparison between fitting results and measured results of Yangquan No. 2 Coal Mine
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图 7 回采速度对地表沉降速度的影响
Figure 7. Influences of mining speed on velocity of surface subsidence
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图 8 松散层厚度对地表沉降的影响
Figure 8. Influences of thickness of loose layer on surface subsidence
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图 9 松散层厚度对地表沉降速度的影响
Figure 9. Influences of thickness of loose layer on velocity of surface subsidence
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图 10 基岩层厚度对地表沉降的影响
Figure 10. Influences of thickness of bedrock layer on surface subsidence
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图 11 基岩层厚度对地表沉降速度的影响
Figure 11. Influences of thickness of bedrock layer on velocity of surface subsidence
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图 12 松散层充分采动角对地表沉降的影响
Figure 12. Influences of full mining angle of loose layer on surface subsidence
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图 13 松散层充分采动角对地表沉降速度的影响
Figure 13. Influences of full mining angle of loose layer on velocity of surface subsidence
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图 14 基岩充分采动角对地表沉降的影响
Figure 14. Influences of full mining angle of bedrock layer on surface subsidence
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图 15 基岩充分采动角对地表沉降速度的影响
Figure 15. Influences of full mining angle of bedrock layer on velocity of surface subsidence
表 1 改进模型沉降、沉降速度和沉降加速度变化
Table 1 Change of subsidence, subsidence velocity and subsidence acceleration of improved model
参数 时间 t1 (t1，t2) t2 (t2，t3) t3 W(t) 0 增大 增大 增大 W0 V(t) 0 加速 最大 减速 0 a(t) 0 > 0 0 < 0 0 
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表 2 3个矿区工作面开采参数
Table 2 Mining parameters of working faces in three mining areas
序号 工作面 平均采深/m 松散层厚度/m 基岩层厚度/m 最大沉降量/m 开采速度/(m·d-1) 煤层厚度/m 1 兴隆庄矿4326 517 198 319 5.475 3.80 8.6 2 三道沟煤矿35101 135 70 65 1.673 3.50 2.0 3 阳泉二矿8403 300 10 290 3.231 3.20 6.5
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表 3 预测结果精度分析
Table 3 Accuracy analysis of predicted results
煤矿名称 改进Knothe时间模型 Knothe时间模型 标准差/m 相对标准偏差/% 标准差/m 相对标准偏差/% 兴隆庄煤矿 0.105 1.92 0.836 15.26 三道沟煤矿 0.065 3.88 0.323 19.32 阳泉二矿 0.126 3.86 0.708 12.57 平均值 0.098 3.22 0.622 15.72
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表 4 主要因素对地表动态沉降影响的敏感性
Table 4 Sensitivity of main factors to influence of surface dynamic subsidence
影响
因素变化范围 与达到最大沉降的时间关系 影响幅度/% 与达到最大沉降速度的时间关系 影响幅度/% 与最大沉降速度关系 影响幅度/% v 2~6 m/d 负相关 65.96 负相关 68.00 正相关 194.44 Hs 200~600 m 正相关 29.27 正相关 27.27 负相关 20.00 Hj 200~600 m 正相关 173.17 正相关 177.27 负相关 65.00 φs 82~86° 负相关 15.69 负相关 14.81 正相关 15.15 φj 53~61° 负相关 22.64 负相关 21.43 负相关 25.00
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