Analytical Solution of Surrounding Rock Stress and Displacement in Bidirectional Unequal Pressure Stope Under Supporting Stress

doi:10.12068/j.issn.1005-3026.2024.12.011

Abstract

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

CLC Number:

TD 355

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.

Figures/Tables 11

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

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

Fig.3 Conformal transformation of the inclined rectangular stope

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

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

Fig.5 FLAC numerical model and boundary conditions

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

Table 2 Average relative deviation coefficients for different transformation functions

应力、位移

3项

映射函数

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

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

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

References 22

1	Yang K Y， Chen C X， Xia K Z，et al.Stability analysis and failure mechanism of the hanging wall in a sublevel caving mine based on microseismic monitoring［J］.Bulletin of Engineering Geology and the Environment，2024，83：259.
2	Xie P S， Luo Y， Wu Y P， Gao X C，et al.Roof deformation associated with mining of two panels in steeply dipping coal seam using subsurface subsidence prediction model and physical simulation experiment［J］.Mining，Metallurgy & Exploration，2020，37（2）：581-591.
3	施耀斌.缓倾斜页岩矿床上向条带回采采场围岩变形特征及破坏判据［D］.武汉：武汉科技大学，2022.
	Shi Yao‑bin.Deformation characteristics and failure criterion of stope surrounding rock in upward strip mining of gently inclined shale deposit［D］.Wuhan：Wuhan University of Science and Technology，2022.
4	Ravandi E G， Rahmannejad R.Wall displacement prediction of circular，D shaped and modified horseshoe tunnels in non‑hydrostatic stress fields［J］.Tunnelling and Underground Space Technology，2013，34：54-60.
5	Abbo A J， Wilson D W， Sloan S W，et al.Undrained stability of wide rectangular tunnels［J］.Computers and Geotechnics，2013，53：46-59.
6	Zheng M Z， Li S J， Feng Z J，et al.Three‑dimensional stress variation characteristics in deep hard rock of CJPL-II project based on in‑situ monitoring［J］.International Journal of Mining Science and Technology，2024，34（2）：179-195.
7	Wang H N， Zeng G S， Jiang M J.Analytical stress and displacement around non‑circular tunnels in semi‑infinite ground［J］.Applied Mathematical Modelling，2018，63：303-328.
8	肖建清，冯夏庭，张腊春，等.均匀地应力场下圆形隧道静态弹塑性解析方法［J］.岩石力学与工程学报，2013，32（sup2）：3466-3477.
	Xiao Jian‑qing， Feng Xia‑ting， Zhang La‑chun，et al.Static elastoplastic analytical method of circular tunnel under uniform geostress field［J］.Chinese Journal of Rock Mechanics and Engineering，2013，32（sup2）：3466-3477.
9	覃爱民，骆汉宾.基于Mohr-Coulomb准则寒区隧道围岩应力弹塑性解析［J］.地下空间与工程学报，2018，14（2）：395-402.
	Qin Ai‑min， Luo Han‑bin.Analytical elasto‑plastic solution for stress of surrounding rock based on Mohr-Coulomb criterion［J］.Chinese Journal of Underground Space and Engineering，2018，14（2）：395-402.
10	Muskhelishvili N I.Some basic problems of the mathematical theory of elasticity［M］.Groningen：Noordhoof Ltd，1954.
11	李元辉，刘明飞，李坤蒙，等.矩形采场支护作用下围岩周边应力复变函数解析解［J］.金属矿山，2021（4）：20-26.
	Li Yuan‑hui， Liu Ming‑fei， Li Kun‑meng，et al.Analytical solution of complex function of surrounding rock stress under supporting action of rectangular stope［J］.Metal Mine，2021（4）：20-26.
12	Huo H， Bobet A， Fernández G，et al.Analytical solution for deep rectangular structures subjected to far‑field shear stresses［J］.Tunnelling and Underground Space Technology，2006，21（6）：613-625.
13	Zhao G P， Yang S L.Analytical solutions for rock stress around square tunnels using complex variable theory［J］.International Journal of Rock Mechanics and Mining Sciences，2015，80：302-307.
14	Lei G H， Ng C W W， Rigby D B.Stress and displacement around an elastic artificial rectangular hole［J］.Journal of Engineering Mechanics，2001，127（9）：880-890.
15	Ng C W W， Lei G H.An explicit analytical solution for calculating horizontal stress changes and displacements around an excavated diaphragm wall panel［J］.Canadian Geotechnical Journal，2003，40：780-792.
16	李坤蒙，李元辉，王者超，等.硬岩采场新型预应力膨胀支柱的研发及应用［J］.东北大学学报（自然科学版），2021，42（2）：213-219.
	Li Kun‑meng， Li Yuan‑hui， Wang Zhe‑chao，et al.Development and application of a new pre‑stressed expandable pillar in hard rock stope［J］.Journal of Northeastern University （Natural Science），2021，42（2）：213-219.
17	Wang M B， Li S C.A complex variable solution for stress and displacement field around a lined circular tunnel at great depth［J］.International Journal for Numerical and Analytical Methods in Geomechanics，2009，33（7）：939-951.
18	Wang H N， Jiang M J， Zhao T，et al.Viscoelastic solutions for stresses and displacements around non‑circular tunnels sequentially excavated at great depths［J］.Acta Geotechnica，2019，14（1）：111-139.
19	Gao X， Wang H N， Jiang M J.Analytical solutions for the displacement and stress of lined circular tunnel subjected to surcharge loadings in semi‑infinite ground［J］.Applied Mathematical Modelling，2021，89：771-791.
20	Dong X J， Karrech A， Qi C C，et al.The critical behaviour of finite thickness lining systems in tunnels［J］.European Journal of Environmental and Civil Engineering，2022，26（8）：3313-3330.
21	Savin G N.Stress concentration around holes［M］.New York：Pergamon Press，1961.
22	Yang S X， Huang L Y， Xie F R，et al.Quantitative analysis of the shallow crustal tectonic stress field in China mainland based on in situ stress data［J］.Journal of Asian Earth Sciences，2014，85：154-162.