考虑流变特性的两向不等压巷道围岩塑性区近似解
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摘要
针对巷道围岩受两向不等压地应力作用下的平面应变问题,分析围岩流变特性对其塑性区的影响。深埋巷道围岩因流变的发展而持续变形,其达到稳定后的峰值应力为一定围压下的长期强度。基于此,以皖北恒源煤矿-950 m进风井井底车场巷道为例,通过三轴压缩与蠕变试验测定了巷道岩石的抗压峰值强度、长期强度和残余强度。然后,考虑岩体峰后脆性软化特性将巷道围岩分为弹、塑性区,并从既有文献轴对称应力场塑性区公式出发,结合围岩总荷载不变的规律推导了两向不等压巷道围岩水平(及竖向)轴上的塑性区半径,再结合既有文献求解的塑性区形状,相对准确地给出了两向不等压巷道围岩塑性区边界的近似解。该近似解在不考虑岩体峰后脆性软化时的结果与既有文献给出的相应解析结果完全吻合;并且轴对称应力场圆巷围岩塑性区半径的解析解是该近似解在侧压系数为1时的特例。最后,结合试验数据,就考虑岩体流变特性与否的两种情况进行了对比。结果表明:考虑流变,视岩石长期强度为围岩峰值应力,得到的塑性区范围与工程实际基本吻合;否则围岩仅产生弹性变形,与实际偏差较大。可见,岩体流变特性对围岩塑性区分布具有重要的影响,理论研究及工程实际中,忽视岩体流变特性实则无形中高估了围岩岩性,不利于巷道围岩长期稳定性与安全性的评估。
Based on the plane strain problem of roadway surrounding rock under unequal crustal stresses in two directions,the effect of surrounding rock rheology on its plastic zone is studied.The deep-buried roadway sur-rounding rock usually has the characteristics of continuous deformation due to the development of rheology,and the peak stress after stabilization is the long-term strength under a certain confining pressure.Based on this,taken the surrounding rock from the bottom station roadway of the ventilation shaft at-950 m level in Hengyuan Coal Mine in Northern Anhui,China,the peak compressive strength,long-term strength and residual strength of roadway rock are measured by triaxial compression and creep tests.Considering the rock post-peak brittle softening,the roadway surrounding rock may be divided into elastic zone and plastic zone.On the base of the formulas of plastic zone under axisymmetric stress field in the existing literatures and the constant assumption of the total loads,the plastic zone analytical radius on horizontal( and vertical) axis of roadway surrounding rock under non-uniform stress field is derived. Then combining with the plastic zone shape determined by the method from the existing literatures,the plastic zone of surrounding rock under unequal compression in two directions is relatively accurately determined.The study shows that the result of the proposed algorithm is in perfect agreement with the corresponding analytical one presented in the existing literatures if the post-peak brittle softening of rock mass is not considered.The plastic zone analytical radius of circular roadway surrounding rock under axisymmetric stress field is a special case of the proposed algorithm for the lateral pressure coefficient 1.Finally,together with the experiment data and compared the differences of considering the rock rheology to without it,the results show that the broken rock zone by considering the rock rheology is basically consistent with the engineering practice,which is the long-term strength under a certain confining pressure takes as the peak stress of surrounding rock.Otherwise,there will be only elastic deformation in surrounding rock,which is much different from the actural situation.It can be seen that the rock rheology has great impact on plastic zone of roadway surrounding rock.Therefore,ignoring the influence of surrounding rock rheology is actually overrating the feature of surrounding rock in theoretical research and engineering practice,which is not good for the long-term stability and safety evaluation of roadway surrounding rock.
Based on the plane strain problem of roadway surrounding rock under unequal crustal stresses in two directions,the effect of surrounding rock rheology on its plastic zone is studied.The deep-buried roadway sur-rounding rock usually has the characteristics of continuous deformation due to the development of rheology,and the peak stress after stabilization is the long-term strength under a certain confining pressure.Based on this,taken the surrounding rock from the bottom station roadway of the ventilation shaft at-950 m level in Hengyuan Coal Mine in Northern Anhui,China,the peak compressive strength,long-term strength and residual strength of roadway rock are measured by triaxial compression and creep tests.Considering the rock post-peak brittle softening,the roadway surrounding rock may be divided into elastic zone and plastic zone.On the base of the formulas of plastic zone under axisymmetric stress field in the existing literatures and the constant assumption of the total loads,the plastic zone analytical radius on horizontal( and vertical) axis of roadway surrounding rock under non-uniform stress field is derived. Then combining with the plastic zone shape determined by the method from the existing literatures,the plastic zone of surrounding rock under unequal compression in two directions is relatively accurately determined.The study shows that the result of the proposed algorithm is in perfect agreement with the corresponding analytical one presented in the existing literatures if the post-peak brittle softening of rock mass is not considered.The plastic zone analytical radius of circular roadway surrounding rock under axisymmetric stress field is a special case of the proposed algorithm for the lateral pressure coefficient 1.Finally,together with the experiment data and compared the differences of considering the rock rheology to without it,the results show that the broken rock zone by considering the rock rheology is basically consistent with the engineering practice,which is the long-term strength under a certain confining pressure takes as the peak stress of surrounding rock.Otherwise,there will be only elastic deformation in surrounding rock,which is much different from the actural situation.It can be seen that the rock rheology has great impact on plastic zone of roadway surrounding rock.Therefore,ignoring the influence of surrounding rock rheology is actually overrating the feature of surrounding rock in theoretical research and engineering practice,which is not good for the long-term stability and safety evaluation of roadway surrounding rock.
引文
[1]侯公羽,李晶晶,赵伟伟,等.两向不等压圆形巷道弹塑性摄动解[J].岩石力学与工程学报,2014,33(S2):3639-3647.HOU Gongyu,LI Jingjing,ZHAO Weiwei,et al. Perturbation solutions for elasto-plastic problems of circular tunnel under unequel compression[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(S2):3639-3647.
[2]马念杰,赵希栋,赵志强,等.均质圆形巷道蝶型冲击地压发生机理及其判定准则[J].煤炭学报,2016,40(10):2287-2295.MA Nianjie,ZHAO Xidong,ZHAO Zhiqiang,et al. Stability analysis and control technology of mine roadway roof in deep mining[J].Journal of China Coal Society,2016,40(10):2287-2295.
[3]郭晓菲,马念杰,赵希栋,等.圆形巷道围岩塑性区的一般形态及其判定准则[J].煤炭学报,2016,41(8):1871-1877.GUO Xiaofei,MA Nianjie,ZHAO Xidong,et al. General shapes and criterion for surrounding rock mass plastic zone of round roadway[J].Journal of China Coal Society,2016,41(8):1871-1877.
[4]赵志强,马念杰,郭晓菲,等.大变形回采巷道蝶叶型冒顶机理与控制[J].煤炭学报,2016,41(12):2932-2939.ZHAO Zhiqiang,MA Nianjie,GUO Xiaofei,et al. Falling principle and support design of butterfly-failure roof in large deformation mining roadways[J]. Journal of China Coal Society,2016,41(12):2932-2939.
[5] KASTNER H.隧道与坑道静力学[M].同济大学,译.上海:上海科学技术出版社,1980:56-61.
[6]魏悦广.两向不等压作用下圆形巷道弹塑性分析摄动解[J].岩土工程学报,1990,12(4):11-20.WEI Yueguang. Perturbation solutions for elasto-plastic analysis of circular tunnel under unequal compression in two directions[J].Chinese Journal of Geotechnical Engineering,1990,12(4):11-20.
[7]孙金山,卢文波.非轴对称荷载下圆形隧洞围岩弹塑性分析解析解[J].岩土力学,2007,28(S1):327-332.SUN Jinshan,LU Wenbo. Analytical elastoplastic solutions to supporting rock masses of circular tunnels under asymmetric load[J].Rock and Soil Mechanics,2007,28(S1):327-332.
[8]潘阳,赵光明,孟祥瑞.非均匀应力场下巷道围岩弹塑性分析[J].煤炭学报,2011,36(S1):53-57.PAN Yang,ZHAO Guangming,MENG Xiangrui.Elasto-plastic analysis on surrounding rock mass under non-uniform stress field[J].Journal of China Coal Society,2011,36(S1):53-57.
[9]吕爱钟,张晓莉,王少杰.两向不等压圆形隧洞弹塑性解析分析[J].岩石力学与工程学报,2018,37(1):14-22.LAizhong,ZHANG Xiaoli,WANG Shaojie. Analytic method for elasto-plastic analysis of circular tunnels under non-axisymmetric stresses[J]. Chinese Journal of Rock Mechanics and Engineering,2018,37(1):14-22.
[10]蔡美峰,何满潮,刘东燕,等.岩石力学与工程[M].北京:科学出版社,2002:50-51.
[11]严克强.不对称荷载作用下圆洞围岩塑性区的估算方法[J].岩土工程学报,1980,2(2):74-79.YAN Keqiang.Estimation method of circular hole’s plastic zone under asymmetric load[J].Chinese Journal of Geotechnical Engineering,1980,2(2):74-79.
[12]蔡晓鸿,蔡勇平.水工压力隧洞结构应力计算[M].北京:中国水利水电出版社,2004:74-76.
[13]彭瑞,赵光明,孟祥瑞.基于D-P准则的两向不等压受扰动轴对称巷道安全性分析[J].中国安全科学学报,2014,24(1):103-108.PENG Rui,ZHAO Guangming,MENG Xiangrui. Analysis of safety of disturbed and axisymmetric roadway under non-uniform stress field based on D-P criterion[J]. China Safety Science Journal,2014,24(1):103-108.
[14]经纬.圆形巷道围岩变形分区的理论与试验研究[D].淮南:安徽理工大学,2017:36-37.JING Wei. Theoretical and experimental research on deformation partition of circular roadway[D].Huainan:Anhui University of Science&Technology,2017:36-37.
[15] S K SHARAN.Exact and approximate solutions for displacements around circular openings in elastic-brittle-plastic Hoek-Brown rock[J].International Journal of Rock Mechanics&Mining Science,2005,42(4):542-549.
[16] KYUNG HO PARK,YONG JIN KIM.Analytical solution for a circular opening in an elastic-brittle-plastic rock[J]. International Journal of Rock Mechanics&Mining Science,2006,43(4):616-622.
[17]张常光,赵均海,孙珊珊.隧道围岩弹-脆-塑性应力的三剪统一解[J].应用力学学报,2012,29(5):530-534,627.ZHANG Changguang,ZHAO Junhai,SUN Shanshan. An analytical solution for tunnel stress in an elastic-brittle-plastic rock based on the triple-shear unified strength criterion[J].Chinese Journal of Applied Mechanics,2012,29(5):530-534,627.
[18]张善彪.线荷载荷载定义与平行分布荷载简化计算[J].力学与实践,2005,27(5):72-74.ZHANG Shanbiao. Definition of line load intensity and simplified calculation of parallel distributed load[J].Mechanics in Engineering,2005,27(5):72-74.
[19]李桂臣,张农,王成,等.高地应力巷道断面形状优化数值模拟研究[J].中国矿业大学学报,2010,39(5):652-658.LI Guichen,ZHANG Nong,WANG Cheng,et al. Optimizing the section shape of roadways in high stress ground by numerical simulation[J]. Journal of China University of Mining&Technology,2010,39(5):652-658.
[20]董方庭.巷道围岩松动圈支护理论及应用技术[M].北京:煤炭工业出版社,2001.
[2]马念杰,赵希栋,赵志强,等.均质圆形巷道蝶型冲击地压发生机理及其判定准则[J].煤炭学报,2016,40(10):2287-2295.MA Nianjie,ZHAO Xidong,ZHAO Zhiqiang,et al. Stability analysis and control technology of mine roadway roof in deep mining[J].Journal of China Coal Society,2016,40(10):2287-2295.
[3]郭晓菲,马念杰,赵希栋,等.圆形巷道围岩塑性区的一般形态及其判定准则[J].煤炭学报,2016,41(8):1871-1877.GUO Xiaofei,MA Nianjie,ZHAO Xidong,et al. General shapes and criterion for surrounding rock mass plastic zone of round roadway[J].Journal of China Coal Society,2016,41(8):1871-1877.
[4]赵志强,马念杰,郭晓菲,等.大变形回采巷道蝶叶型冒顶机理与控制[J].煤炭学报,2016,41(12):2932-2939.ZHAO Zhiqiang,MA Nianjie,GUO Xiaofei,et al. Falling principle and support design of butterfly-failure roof in large deformation mining roadways[J]. Journal of China Coal Society,2016,41(12):2932-2939.
[5] KASTNER H.隧道与坑道静力学[M].同济大学,译.上海:上海科学技术出版社,1980:56-61.
[6]魏悦广.两向不等压作用下圆形巷道弹塑性分析摄动解[J].岩土工程学报,1990,12(4):11-20.WEI Yueguang. Perturbation solutions for elasto-plastic analysis of circular tunnel under unequal compression in two directions[J].Chinese Journal of Geotechnical Engineering,1990,12(4):11-20.
[7]孙金山,卢文波.非轴对称荷载下圆形隧洞围岩弹塑性分析解析解[J].岩土力学,2007,28(S1):327-332.SUN Jinshan,LU Wenbo. Analytical elastoplastic solutions to supporting rock masses of circular tunnels under asymmetric load[J].Rock and Soil Mechanics,2007,28(S1):327-332.
[8]潘阳,赵光明,孟祥瑞.非均匀应力场下巷道围岩弹塑性分析[J].煤炭学报,2011,36(S1):53-57.PAN Yang,ZHAO Guangming,MENG Xiangrui.Elasto-plastic analysis on surrounding rock mass under non-uniform stress field[J].Journal of China Coal Society,2011,36(S1):53-57.
[9]吕爱钟,张晓莉,王少杰.两向不等压圆形隧洞弹塑性解析分析[J].岩石力学与工程学报,2018,37(1):14-22.LAizhong,ZHANG Xiaoli,WANG Shaojie. Analytic method for elasto-plastic analysis of circular tunnels under non-axisymmetric stresses[J]. Chinese Journal of Rock Mechanics and Engineering,2018,37(1):14-22.
[10]蔡美峰,何满潮,刘东燕,等.岩石力学与工程[M].北京:科学出版社,2002:50-51.
[11]严克强.不对称荷载作用下圆洞围岩塑性区的估算方法[J].岩土工程学报,1980,2(2):74-79.YAN Keqiang.Estimation method of circular hole’s plastic zone under asymmetric load[J].Chinese Journal of Geotechnical Engineering,1980,2(2):74-79.
[12]蔡晓鸿,蔡勇平.水工压力隧洞结构应力计算[M].北京:中国水利水电出版社,2004:74-76.
[13]彭瑞,赵光明,孟祥瑞.基于D-P准则的两向不等压受扰动轴对称巷道安全性分析[J].中国安全科学学报,2014,24(1):103-108.PENG Rui,ZHAO Guangming,MENG Xiangrui. Analysis of safety of disturbed and axisymmetric roadway under non-uniform stress field based on D-P criterion[J]. China Safety Science Journal,2014,24(1):103-108.
[14]经纬.圆形巷道围岩变形分区的理论与试验研究[D].淮南:安徽理工大学,2017:36-37.JING Wei. Theoretical and experimental research on deformation partition of circular roadway[D].Huainan:Anhui University of Science&Technology,2017:36-37.
[15] S K SHARAN.Exact and approximate solutions for displacements around circular openings in elastic-brittle-plastic Hoek-Brown rock[J].International Journal of Rock Mechanics&Mining Science,2005,42(4):542-549.
[16] KYUNG HO PARK,YONG JIN KIM.Analytical solution for a circular opening in an elastic-brittle-plastic rock[J]. International Journal of Rock Mechanics&Mining Science,2006,43(4):616-622.
[17]张常光,赵均海,孙珊珊.隧道围岩弹-脆-塑性应力的三剪统一解[J].应用力学学报,2012,29(5):530-534,627.ZHANG Changguang,ZHAO Junhai,SUN Shanshan. An analytical solution for tunnel stress in an elastic-brittle-plastic rock based on the triple-shear unified strength criterion[J].Chinese Journal of Applied Mechanics,2012,29(5):530-534,627.
[18]张善彪.线荷载荷载定义与平行分布荷载简化计算[J].力学与实践,2005,27(5):72-74.ZHANG Shanbiao. Definition of line load intensity and simplified calculation of parallel distributed load[J].Mechanics in Engineering,2005,27(5):72-74.
[19]李桂臣,张农,王成,等.高地应力巷道断面形状优化数值模拟研究[J].中国矿业大学学报,2010,39(5):652-658.LI Guichen,ZHANG Nong,WANG Cheng,et al. Optimizing the section shape of roadways in high stress ground by numerical simulation[J]. Journal of China University of Mining&Technology,2010,39(5):652-658.
[20]董方庭.巷道围岩松动圈支护理论及应用技术[M].北京:煤炭工业出版社,2001.
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