支护力作用下双向不等压采场围岩应力和位移解析解

doi:10.12068/j.issn.1005-3026.2024.12.011

摘要/Abstract

摘要：

地下倾斜矩形采场的稳定性与顶板应力及位移的分布密切相关，而目前关于矩形开挖围岩应力及位移的解析方法应用于大宽高比倾斜矩形采场时误差较大，且并未考虑采场倾角和支护力的影响.本文基于复变函数理论，提出了大宽高比倾斜矩形采场的映射函数表达式，推导了采场在双向不等压应力和支护力作用下围岩应力和位移解析解，分析了采场倾角、宽高比和支护力对顶板应力和位移分布的影响.结果表明：解析解与FLAC模拟解的偏差小于5%；随着采场倾角的增大，顶板的应力和位移非对称分布趋势加剧，卸压程度和位移量逐渐降低；随着采场宽高比的增大，顶板卸压程度和位移量逐渐增大；采场支护体施加的支护力能够改善采场围岩的应力环境，降低顶板的下沉量.

关键词: 倾斜矩形采场, 宽高比, 复变函数理论, 应力和位移, 支护力

Abstract:

The stability of inclined rectangular stope is closely related to the stress and displacement distribution of stope roof in underground mines. However， the current theoretical method for stress and displacement of surrounding rock in rectangular excavation has a significant error when applied to inclined rectangular stopes with large width‑height ratio， and the influence of excavation dip angle and supporting stress is not considered. Based on the complex function theory， this paper puts forward the mapping function expression of inclined rectangular stope with large width‑height ratio， and derives the analytical solution of stress and displacement of surrounding rock in stope under bidirectional unequal pressure and supporting stress. Besides， the influence of stope dip angle， width‑height ratio and supporting stress on stress and displacement distribution of stope roof is analyzed. The results show that the deviation between analytical solution and FLAC simulation solution is less than 5%. In addition， the asymmetric distribution trend of stress and displacement around stope roof intensifies as the stope dip angle increases， and the degree of pressure relief and vertical displacement gradually decreases. With the increase of stope width‑height ratio， the pressure relief degree and the displacement of stope roof gradually increase. The supporting stress exerted by supporting bodies can improve the stress environment of surrounding rock and reduce the roof subsidence.

Key words: inclined rectangular stope, width?height ratio, complex variable theory, stress and displacement, supporting stress

中图分类号:

TD 355

熊志朋, 李元辉, 李坤蒙, 肖贵轩. 支护力作用下双向不等压采场围岩应力和位移解析解[J]. 东北大学学报（自然科学版）, 2024, 45(12): 1759-1768.

Zhi-peng XIONG, Yuan-hui LI, Kun-meng LI, Gui-xuan XIAO. Analytical Solution of Surrounding Rock Stress and Displacement in Bidirectional Unequal Pressure Stope Under Supporting Stress[J]. Journal of Northeastern University(Natural Science), 2024, 45(12): 1759-1768.

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链接本文: https://xuebao.neu.edu.cn/natural/CN/10.12068/j.issn.1005-3026.2024.12.011

https://xuebao.neu.edu.cn/natural/CN/Y2024/V45/I12/1759

图/表 11

图1 支护力作用下倾斜矩形采场力学模型（a）—边界应力和支护力组合条件；（b）—仅边界应力条件；（c）—仅支护力条件.

Fig.1 Mechanical model of inclined rectangular stope under supporting stress

图2 支护力作用下倾斜采场围岩应力和位移计算流程

Fig.2 Calculation flow of stress and displacement of surrounding rock in inclined stope under supporting force

图3 倾斜矩形采场的保角变换

Fig.3 Conformal transformation of the inclined rectangular stope

表1 不同宽高比条件下映射函数系数

Table 1 The transformation function coefficients with different width‑height ratios

m	ε	R	c₁	c₃	c₅	c₇	c₉
4∶1	0.890	5.689	0.561 5	-0.114 1	-0.038 4	-0.007 0	0.004 2
5∶1	0.879	6.751	0.629 3	-0.100 7	-0.038 0	-0.010 6	0.001 2
6∶1	0.871	7.799	0.678 9	-0.089 9	-0.036 6	-0.012 6	-0.001 1
7∶1	0.866	8.837	0.716 7	-0.081 0	-0.034 9	-0.013 6	-0.002 9
8∶1	0.862	9.867	0.746 6	-0.073 8	-0.033 0	-0.014 1	-0.004 1
9∶1	0.858	10.892	0.770 8	-0.067 7	-0.031 3	-0.014 3	-0.005 0

图4 不同映射函数确定的宽高比为8:1条件下采场

Fig.4 Inclined rectangular stopes with width‑height ratio of 8∶1 mapped by different conformal transformation functions

图5 FLAC数值模型及边界条件

Fig.5 FLAC numerical model and boundary conditions

图6 采场顶板围岩水平应力及垂直位移分布曲线（a）—水平应力；（b）—垂直位移.

Fig.6 Horizontal stress and vertical displacement distribution curves of surrounding rock for stope roof

表2 不同映射函数的平均相对偏差系数 (%)

Table 2 Average relative deviation coefficients for different transformation functions

应力、位移

3项

映射函数

图7 不同倾角条件下顶板垂直应力和垂直位移分布曲线（a）—垂直应力；（b）—垂直位移.

Fig.7 Distribution curves of vertical stress and displacement of stope roof for different dip angles

图8 不同宽高比条件下采场顶板垂直应力和垂直位移曲线（a）—垂直应力；（b）—垂直位移.

Fig.8 Distribution curves of vertical stress and displacement of stope roof with different width‑height ratios

图9 不同支护力作用下采场顶板垂直应力和垂直位移分布曲线（a）—垂直应力；（b）—垂直位移.

Fig.9 Distribution curves of vertical stress and displacement of stope roof with different supporting stress

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