The influence of complex topography on the stress of underlying coal strata
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摘要: 为了掌握地表的山体和山体间的沟谷区域等复杂地形地貌对下伏煤岩层应力的影响规律，本文通过理论分析构建了山体下煤岩层垂直应力计算模型，并以禾草沟煤矿50205工作面为背景，研究了复杂地形地貌对下伏煤岩层荷载作用特征及应力传递规律。结果表明：山体荷载对浅部煤层具有较明显的应力影响，在水平方向上影响明显范围与山体坡度呈负相关性，影响范围系数与山体坡度成正相关性，山体对下伏煤层垂直应力影响特征可分为初始影响、剧烈增长影响和缓慢增长影响3个阶段；沟谷区域下伏煤岩层垂直应力叠加数值呈现随深度变化先增大后减小的特征，且当两山体相邻间距大于山体底面宽度1.25倍时，应力叠加效应很小，可忽略不计；随着相邻山体间距逐渐增大，沟谷区域下伏煤岩层形成一个应力叠加不明显的倒三角区域。Abstract: To master the influence law of complex landform such as the surface mountain and the valley area between the mountains on the underlying coal rock stress, this study constructed a calculation model of the vertical stress of the coal strata under the mountain through theoretical analysis.Taking the 50205 working face of Hecaogou coal mine as example for analysis, This paper studied the complex landform on the underlying coal rock load characteristics and stress transfer law.Results show that: mountain load has significant stress effect on shallow coal seam.In the horizontal direction, the influence range is negatively correlated with the mountain slope, and the coefficient of influence range is positively related to the mountain slope.The effect of mountain on the vertical stress of the underlying coal seam can be divided into three stages: initial effect, intense growth effect and slow growth effect.The vertical stress superposition value of the underlying coal strata in the gully region firstly increases and then decreases with the change of depth.Moreover, when the distance between two adjacent mountains increases to more than.1.25 times of the width of the mountain bottom, the effect of stress superposition is very small and can be ignored.As the distance between adjacent mountains gradually increases, an inverted triangle area with insignificant stress superposition is formed in the coal strata under the gully area.
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图 1 山体荷载作用下基础内应力扩散示意图
Figure 1. Schematic diagram of foundation internal stress diffusion under mountain load
图 2 集中荷载P作用在半平面体的边界上
Figure 2. Concentrated load P is on the boundary of the semi-plane body
图 4 不同深度水平截面上的垂直应力曲线
Figure 4. Vertical stress curves on horizontal cross sections at different depths
图 5 山体荷载在弹性基础内的垂直应力σZ曲线
Figure 5. Vertical stress σZ curve of mountain load in elastic foundation
图 6 相邻山体不同间距垂直应力叠加影响曲线
Figure 6. Influence curve of vertical stress superimposed with different spacing of gully
图 7 50205工作面井上下局部对照
Figure 7. Local comparison of upper and lower wells in 50205 working face
图 8 50205工作面5号煤层赋存深度曲线
Figure 8. Curve of occurrence depth of No.5 coal seam in 50205 working face
图 10 不同山体荷载下煤岩层垂直应力等值线
Figure 10. Vertical stress isoline map of coal strata under mountain load
图 11 山体不同坡度下煤岩层垂直应力等值线
Figure 11. Vertical stress isolines of coal strata under different slopes of mountain
图 12 30°山体荷载下煤岩层垂直应力等值线
Figure 12. Vertical stress isoline map of coal strata under 30° mountain load
图 13 山体不同坡度时垂直应力影响明显范围
Figure 13. Range of significant influence of vertical stress in different slopes of mountains
图 14 上坡段山体荷载下垂直应力曲线
Figure 14. Vertical stress curve of the uphill section under mountain load
图 15 相邻山体不同间距时5号煤层垂直应力等值线
Figure 15. Vertical stress contour map of No.5 coal seam with different spacing of adjacent mountains
图 16 相邻山体不同间距时5号煤层垂直应力曲线
Figure 16. Vertical stress curve of No.5 coal seam with different spacing of adjacent mountain
表 1 相邻山体不同间距沟谷中央下伏煤岩层垂直应力叠加值
Table 1. Vertical stress superposition values of the coal strata under the central gullies at different intervals of adjacent mountains
间距/m 埋深/m 0 1B 2B 3B 4B 5B 6B 7B 8B 9B 10B 11B 0 0.20P 0.56P 0.60P 0.52P 0.45P 0.39P 0.35P 0.32P 0.30P 0.28P 0.25P 0.21P 1B — 0.20P 0.40P 0.41P 0.39P 0.37P 0.35P 0.32P 0.29P 0.26P 0.24P 0.20P 2B — — 0.31P 0.35P 0.34P 0.33P 0.31P 0.30P 0.28P 0.26P 0.23P 0.20P 3B — — — 0.28P 0.30P 0.31P 0.28P 0.26P 0.24P 0.22P 0.20P — 4B — — — 0.20P 0.23P 0.26P 0.25P 0.24P 0.22P 0.20P — — 5B — — — — — 0.20P 0.21P 0.20P — — — — 注：“—”表示沟谷中央下伏煤岩层垂直应力叠加值小于0.2P，可忽略不计。 
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表 2 山体和山体下基部模型尺寸
Table 2. Model dimensions of mountain and base under mountain
m 山体高度 山体模型尺寸 基部模型尺寸 长 宽 高 长 宽 高 50 200 200 50 2 000 200 400 100 400 200 100 3 000 200 600 150 600 200 150 3 000 200 800
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表 3 煤岩物理力学参数
Table 3. Physical and mechanical parameters of coal and rock
煤岩名称 容重/(kg·m-3) 抗拉强度/MPa 抗压强度/MPa 弹性模量/MPa 泊松比/μ 内聚力/MPa 内摩擦角/(°) 泥岩 2 570 1.89 20.29 10 190 0.29 1.97 31 中粒砂岩 2 282 1.70 42.96 24 617 0.23 4.53 34 细粒砂岩 2 320 1.60 50.94 33 482 0.21 4.21 32 粉砂岩 2 462 1.86 31.16 22 365 0.26 4.6 32 油页岩 2 371 1.70 37.36 17 033 0.25 3.98 30 泥质粉砂岩 2 370 2.1 32.20 24 967 0.27 3.98 30 5号煤层 1 321 0.61 15.92 4 900 0.28 1.96 30
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表 4 不同山体高度下煤岩层不同埋深时垂直应力值
Table 4. Vertical stress values of coal strata at different mountain heights and different buried depths
煤岩层埋深/m 50 m 100 m 150 m N/MPa Y/MPa S N/MPa Y/MPa S N/MPa Y/MPa S 1B 1.19 1.84 1.55 2.38 3.83 1.61 3.46 5.53 1.60 2B 2.38 2.88 1.21 4.71 5.78 1.22 6.98 8.46 1.21 3B 3.51 3.85 1.10 7.06 7.83 1.11 10.38 11.44 1.10 4B 4.71 5.02 1.06 9.37 10.01 1.07 13.85 14.75 1.06 5B 5.93 6.19 1.04 11.72 12.24 1.04 17.33 18.07 1.03 6B 7.06 7.27 1.03 13.90 14.34 1.03 — — — 注：N表示煤岩层未受山体影响垂直应力值；Y表示煤岩层受山体影响下最大垂直应力值；S表示沟谷区域煤岩层垂直应力影响系数，S=Y/N。
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