考虑受压侧岩体反力非线性作用的锚杆抗剪理论
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摘要
针对锚杆受压侧岩体或砂浆体反力非线性作用及结构面的剪胀效应问题,基于经典梁理论推导锚杆轴力与轴向变形及横向剪切力与横向变形的理论公式,建立了锚杆抗剪力计算公式。通过加锚结构面直剪试验验证理论计算有效性,并分析结构面剪胀系数、围岩强度、锚杆安装角(倾角)对锚杆变形和抗剪力的影响。结果表明:锚杆抗剪理论计算与室内试验结果吻合较好;结构面剪胀系数越大,越能较快调动锚杆抗剪作用,相反锚杆塑性强化特征越不明显,改善加锚结构面的阻滑抗剪作用,主要依靠结构面固有抗剪强度;随着围岩强度降低,锚杆需经一定变形才能发挥较大抗剪作用,而随着围岩强度增大,锚杆将迅速达到屈服状态,并且锚杆由轴向张拉破坏逐渐转为拉剪破坏;锚杆最优安装角随结构面内摩擦角增大而增大,依据实际工程中结构面内摩擦角取值范围,可估算锚杆最优安装角为30°～68°。
This study aims to solve the problems on the nonlinear behaviour of rock mass or mortar against the pressure side of the bolt and the dilatancy effect of the structural surface. Theoretical formulas for the axial force and axial deformation, transverse shear force and transverse deformation of anchor bolts were derived, and the formula for the shear resistance of anchor bolts was also established based on the classical beam theory. The validity of the theoretical solutions was verified by the direct shear test on bolted structures. Furthermore, this study performed the effects of joint dilatancy coefficient, joint friction angle, surrounding rock strength and bolt installation angle on the deformation and shear resistance of anchor rods. The results showed that the theoretical calculation results were in good agreement with the experimental results. The higher dilatancy coefficient led to the higher shear resistance of the bolt, but less significant of plastic behaviour. Thus, the shear resistance of bolted joint can be improved by the inherent shear strength of the structural surface. When the strength of surrounding rock decreased, the anchor bolt had to undergo specific deformation to exert a large shearing effect. The higher strength of rock resulted in the yield failure of the bolt within a shorter time, and the damage of the anchor bolt was gradually transformed from the axial tensile failure into tensile shear failure. The optimal installation angle of the bolt increased with the increase of the internal friction angle of the structure. The optimal installation angle of the bolt was estimated within the angle ranging from 30° to 68° in working joint conditions.
This study aims to solve the problems on the nonlinear behaviour of rock mass or mortar against the pressure side of the bolt and the dilatancy effect of the structural surface. Theoretical formulas for the axial force and axial deformation, transverse shear force and transverse deformation of anchor bolts were derived, and the formula for the shear resistance of anchor bolts was also established based on the classical beam theory. The validity of the theoretical solutions was verified by the direct shear test on bolted structures. Furthermore, this study performed the effects of joint dilatancy coefficient, joint friction angle, surrounding rock strength and bolt installation angle on the deformation and shear resistance of anchor rods. The results showed that the theoretical calculation results were in good agreement with the experimental results. The higher dilatancy coefficient led to the higher shear resistance of the bolt, but less significant of plastic behaviour. Thus, the shear resistance of bolted joint can be improved by the inherent shear strength of the structural surface. When the strength of surrounding rock decreased, the anchor bolt had to undergo specific deformation to exert a large shearing effect. The higher strength of rock resulted in the yield failure of the bolt within a shorter time, and the damage of the anchor bolt was gradually transformed from the axial tensile failure into tensile shear failure. The optimal installation angle of the bolt increased with the increase of the internal friction angle of the structure. The optimal installation angle of the bolt was estimated within the angle ranging from 30° to 68° in working joint conditions.
引文
[1]刘华丽,李宏伟,朱大勇.锚固力在边坡加固中的工程应用[J].岩土力学,2015,36(2):509-514.LIU Hua-li,LI Hong-wei,ZHU Da-yong.A method for calculation of anchor force in slope reinforcement[J].Rock and Soil Mechanics,2015,36(2):509-514.
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[4]HAAS C J.Shear resistance of rock bolts[M].Rolla:University of Missouri,1976.
[5]DIGHT P M.Improvements to the stability of rock walls in open pit mines[D].Melbourne:Monash University,1983.
[6]YOSHINAKA R,SKAGUCHI S,SHIMIZU T.Experimental study of the bolt reinforcement in discontinuous rock[C]//Proceeding of 6th International Conference on Rock Mechanics.Rotterdam:A.A.Balkema,1987:117-127.
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[9]韦四江,勾攀峰.锚杆预紧力对锚固体强度强化的模拟实验研究[J].煤炭学报,2012,37(12):1987-1993.WEI Si-jiang,GOU Pan-feng.Analogy simulation test on strengthening effect for pretention of bolts on anchorage body[J].Journal of China Coal Society,2012,37(12):1987-1993.
[10]张伟,刘泉声.节理岩体锚杆的综合变形分析[J].岩土力学,2012,33(4):1067-1074.ZHANG Wei,LIU Quan-sheng.Synthetical deformation analysis of anchor bolt in jointed rock mass[J].Rock and Soil Mechanics,2012,33(4):1067-1074.
[11]张伟,刘泉声.基于剪切试验的预应力锚杆变形性能分析[J].岩土力学,2014,35(8):2231-2240.ZHANG Wei,LIU Quan-sheng.Analysis of deformation characteristics of prestressed anchor bolt based on shear test[J].Rock and Soil Mechanics,2014,35(8):2231-2240.
[12]刘泉声,雷广峰,彭星新,等.锚杆锚固对节理岩体剪切性能影响试验研究及机制分析[J].岩土力学,2017,38(增刊1):27-35.LIU Quan-sheng,LEI Guang-feng,PENG Xing-xin,et al.Experimental study and mechanism analysis of influence of bolt anchoring on shear properties of jointed rock mass[J].Rock and Soil Mechanics,2017,38(Supp.1):27-35.
[13]葛修润,刘建武.加锚节理面抗剪性能研究[J].岩土工程学报,1988,10(1):8-19.GE Xiu-run,LIU Jian-wu.Study of the shear resistance behaviour of bolted rock joints[J].Chinese Journal of Geotechnical Engineering,1988,10(1):8-19.
[14]PELLET F,EGGER P.Analytical model for the mechanical behaviour of bolted rock joints subjected to shearing[J].Rock Mechanics and Rock Engineering,1996,29(2):73-97.
[15]陈文强,贾志欣,赵宇飞,等.剪切过程中锚杆的轴向和横向作用分析[J].岩土力学,2015,36(1):143-148.CHEN Wen-qiang,JIA Zhi-xin,ZHAO Yu-fei,et al.Analysis of axial and transverse effects of rock bolt during shearing process[J].Rock and Soil Mechanics,2015,36(1):143-148.
[16]LI XUWEI,JAN NEMCIK,ALI MIRZAGHORBANALI,et al.Analytical model of shear behaviour of a fully grouted cable bolt subjected to shearing[J].International Journal of Rock Mechanics&Mining Sciences,2015,80:31-39.
[17]宋宏伟.非连续岩体中锚杆横向作用新研究[J].中国矿业大学学报,2003,32(2):161-164.SONG Hong-wei.New study on transverse effect of rock bolts in discontinuous rock mass[J].Journal of China University of Mining&Technology,2003,32(2):161-164.
[18]HOLMBERG M.The mechanical behavior of untensioned grouted rock bolts[D].Stockholm:Royal Institute of Technology,1991.
[19]JALALIFAR H,AZIZ N.Analytical behaviour of bolt-joint intersection under lateral loading conditions[J].Rock Mechanics&Rock Engineering,2010,43(1):89-94.
[20]李华,曾庆元.关于考虑剪切变形的影响计算梁挠度方法的综述[J].工程力学,1999,16(增刊):141-145.LI Hua,ZENG Qing-yuan.A review of the beam deflection method considering shear deformation effects[J].Engineering Mechanics,1999,16(Supp.):141-145.
[21]杨松林,徐卫亚,朱焕春.锚杆在节理中的加固作用[J].岩土力学,2002,23(5):604-607.YANG Song-lin,XU Wei-ya,ZHU Huan-chun.Reinforcement of bolt in joints[J].Rock and Soil Mechanics,2002,23(5):604-607.
[2]周浩,肖明,陈俊涛.大型地下洞室全长黏结式岩石锚杆锚固机制研究及锚固效应分析[J].岩土力学,2016,37(5):1503-1511.ZHOU Hao,XIAO Ming,CHEN Jun-tao.Study of anchoring mechanism and analysis of anchoring effect of fully grouted rock anchor in large-scale underground caverns[J].Rock and Soil Mechanics,2016,37(5):1503-1511.
[3]BJURSTR?M S.Shear strength of hard rock joints reinforced by grouted un-tensioned bolts[C]//Proceedings of the 3rd International Congress on Rock Mechanics.Denver:[s.n.],1974,2(B):1194-1199.
[4]HAAS C J.Shear resistance of rock bolts[M].Rolla:University of Missouri,1976.
[5]DIGHT P M.Improvements to the stability of rock walls in open pit mines[D].Melbourne:Monash University,1983.
[6]YOSHINAKA R,SKAGUCHI S,SHIMIZU T.Experimental study of the bolt reinforcement in discontinuous rock[C]//Proceeding of 6th International Conference on Rock Mechanics.Rotterdam:A.A.Balkema,1987:117-127.
[7]SPANG K,EGGER P.Action of fully-grouted bolt in jointed rock and factors of influence[J].Rock Mechanics and Rock Engineering,1990,23(3):201-229.
[8]FERRERO A M.The shear strength of reinforced rock joints[J].International Journal of Rock Mechanics and Mining Sciences&Geomechanics Abstracts,1995,32(6):590-600.
[9]韦四江,勾攀峰.锚杆预紧力对锚固体强度强化的模拟实验研究[J].煤炭学报,2012,37(12):1987-1993.WEI Si-jiang,GOU Pan-feng.Analogy simulation test on strengthening effect for pretention of bolts on anchorage body[J].Journal of China Coal Society,2012,37(12):1987-1993.
[10]张伟,刘泉声.节理岩体锚杆的综合变形分析[J].岩土力学,2012,33(4):1067-1074.ZHANG Wei,LIU Quan-sheng.Synthetical deformation analysis of anchor bolt in jointed rock mass[J].Rock and Soil Mechanics,2012,33(4):1067-1074.
[11]张伟,刘泉声.基于剪切试验的预应力锚杆变形性能分析[J].岩土力学,2014,35(8):2231-2240.ZHANG Wei,LIU Quan-sheng.Analysis of deformation characteristics of prestressed anchor bolt based on shear test[J].Rock and Soil Mechanics,2014,35(8):2231-2240.
[12]刘泉声,雷广峰,彭星新,等.锚杆锚固对节理岩体剪切性能影响试验研究及机制分析[J].岩土力学,2017,38(增刊1):27-35.LIU Quan-sheng,LEI Guang-feng,PENG Xing-xin,et al.Experimental study and mechanism analysis of influence of bolt anchoring on shear properties of jointed rock mass[J].Rock and Soil Mechanics,2017,38(Supp.1):27-35.
[13]葛修润,刘建武.加锚节理面抗剪性能研究[J].岩土工程学报,1988,10(1):8-19.GE Xiu-run,LIU Jian-wu.Study of the shear resistance behaviour of bolted rock joints[J].Chinese Journal of Geotechnical Engineering,1988,10(1):8-19.
[14]PELLET F,EGGER P.Analytical model for the mechanical behaviour of bolted rock joints subjected to shearing[J].Rock Mechanics and Rock Engineering,1996,29(2):73-97.
[15]陈文强,贾志欣,赵宇飞,等.剪切过程中锚杆的轴向和横向作用分析[J].岩土力学,2015,36(1):143-148.CHEN Wen-qiang,JIA Zhi-xin,ZHAO Yu-fei,et al.Analysis of axial and transverse effects of rock bolt during shearing process[J].Rock and Soil Mechanics,2015,36(1):143-148.
[16]LI XUWEI,JAN NEMCIK,ALI MIRZAGHORBANALI,et al.Analytical model of shear behaviour of a fully grouted cable bolt subjected to shearing[J].International Journal of Rock Mechanics&Mining Sciences,2015,80:31-39.
[17]宋宏伟.非连续岩体中锚杆横向作用新研究[J].中国矿业大学学报,2003,32(2):161-164.SONG Hong-wei.New study on transverse effect of rock bolts in discontinuous rock mass[J].Journal of China University of Mining&Technology,2003,32(2):161-164.
[18]HOLMBERG M.The mechanical behavior of untensioned grouted rock bolts[D].Stockholm:Royal Institute of Technology,1991.
[19]JALALIFAR H,AZIZ N.Analytical behaviour of bolt-joint intersection under lateral loading conditions[J].Rock Mechanics&Rock Engineering,2010,43(1):89-94.
[20]李华,曾庆元.关于考虑剪切变形的影响计算梁挠度方法的综述[J].工程力学,1999,16(增刊):141-145.LI Hua,ZENG Qing-yuan.A review of the beam deflection method considering shear deformation effects[J].Engineering Mechanics,1999,16(Supp.):141-145.
[21]杨松林,徐卫亚,朱焕春.锚杆在节理中的加固作用[J].岩土力学,2002,23(5):604-607.YANG Song-lin,XU Wei-ya,ZHU Huan-chun.Reinforcement of bolt in joints[J].Rock and Soil Mechanics,2002,23(5):604-607.