拉力型锚杆锚固段拉拔受力的非线性全历程分析
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摘要
针对拉力型锚杆锚固段拉拔受力的非线性全历程分析问题,从锚杆荷载位移关系的指数曲线模型出发,建立锚杆锚固段的双指数曲线剪切滑移模型及其拉拔荷载传递解答,分析拉拔全历程中锚杆锚固段的荷载传递与荷载位移曲线特征,并采用实测数据进行对比验证,结果表明:双指数曲线剪切滑移模型反映了锚固界面的非线性和软化特性,且轴力分布和荷载位移曲线的理论计算值均与实测结果吻合得很好,验证了解析解的有效性。拉拔全历程中,锚杆锚固段荷载传递依次经历加载和滑移破坏2个阶段,锚杆锚固段剪应力分布在加载阶段逐渐从一条最大值在张拉端的单调曲线演变为一条单峰曲线且峰值不断向远端传递,而进入滑移破坏阶段后,则进一步演变为一条最大值在远端的单调曲线且最大值不断降低直至锚杆被拔出。在剪应力的演变过程中,锚杆的荷载位移曲线则相应地表现为一条单峰曲线,锚固长度较大时,该曲线存在近似平台段。该研究成果可为拉力型锚杆锚固段拉拔受力分析和设计提供理论参考。
A novel nonlinear shear-slipping model(named as biexponential model) as well as the load transfer solutions was firstly developed for predicting the full-range interfacial behavior of the tensile anchor. The features of the load transfer and the load-displacement curve during the full-range process of pullout were studied in detail. The measured results from the laboratory and in-situ experiments were used to verify the load transfer solutions and the above predicted features of the tensile anchor. The biexponential model was found to describe reasonably the nonlinear and softening behavior of the anchoring interface of tensile anchor. The axial forces and displacements calculated from the load transfer solutions agree well with the measured values. During the full-range pullout process,the load transfer in the fixed segment of the tensile anchor exhibits a loading and a sliding stage. During the loading stage,the shear stress distribution evolves from a monotone decaying curve with the maximum value at the pull end into a single peak curve,and then further evolves into the other monotone decay curve with the maximum value at the far end during the sliding stage. The load-displacement curve is a single peak curve and the peak is approximately flat when the anchorage length is large.
A novel nonlinear shear-slipping model(named as biexponential model) as well as the load transfer solutions was firstly developed for predicting the full-range interfacial behavior of the tensile anchor. The features of the load transfer and the load-displacement curve during the full-range process of pullout were studied in detail. The measured results from the laboratory and in-situ experiments were used to verify the load transfer solutions and the above predicted features of the tensile anchor. The biexponential model was found to describe reasonably the nonlinear and softening behavior of the anchoring interface of tensile anchor. The axial forces and displacements calculated from the load transfer solutions agree well with the measured values. During the full-range pullout process,the load transfer in the fixed segment of the tensile anchor exhibits a loading and a sliding stage. During the loading stage,the shear stress distribution evolves from a monotone decaying curve with the maximum value at the pull end into a single peak curve,and then further evolves into the other monotone decay curve with the maximum value at the far end during the sliding stage. The load-displacement curve is a single peak curve and the peak is approximately flat when the anchorage length is large.
引文
[1]陆士良,汤雷,杨新安.锚杆锚固力与锚固技术[M].北京:煤炭工业出版社,1998:1–17.(LU Shiliang,TANG Lei,YANG Xinan.Anchorage force and technique of the rockbolt[M].Beijing:Coal Industry Press,1998:1–17.(in Chinese))
[2]曹国金,姜弘道,熊红梅.一种确定拉力型锚杆支护长度的方法[J].岩石力学与工程学报,2003,22(7):1 141–1 145.(CAO Guojin,JIANG Hongdao,XIONG Hongmei.Calculation method of support length for stretched bolts[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(7):1 141–1 145.(in Chinese))
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[4]杨庆,朱训国,栾茂田.全长注浆岩石锚杆双曲线模型的建立及锚固效应的参数分析[J].岩石力学与工程学报,2007,26(4):692–698.(YANG Qing,ZHU Xunguo,LUAN Maotian.Development of hyperbolic model for fully grouting rock bolt and parameters analysis for anchoring effect[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(4):692–698.(in Chinese))
[5]中华人民共和国行业标准编写组.JGJl20—2012建筑基坑支护技术规程[S].北京:中国建筑工业出版社,2012.(The Professional Standards Compilation Group of Peoples Republic of China.JGJl20—2012Technical specification for retaining and protection of building foundation excavation[S].Beijing:China Architecture and Building Press,2012.(in Chinese))
[6]PHILLIPS S H E.Factors affecting the design of anchorages in rock[R]. London:Cementation Research Ltd.,1970.
[7]何思明.预应力锚索作用机制研究[博士学位论文][D].成都:西南交通大学,2004.(HE Siming.Study on mechanism of prestressed anchoring cable[Ph.D.Thesis][D].Chengdu:Southwest Jiaotong University,2004.(in Chinese))
[8]张季如,唐保付.锚杆荷载传递机制分析的双曲函数模型[J].岩土工程学报,2002,24(2):188–192.(ZHANG Jiru,TANG Baofu.Hyperbolic function model to analyze load transfer mechanism on bolts[J].Chinese Journal of Geotechnical Engineering,2002,24(2):188–192.(in Chinese))
[9]HOLLINGSHEAD G W.Stress distribution in rock anchors[J].Canadian Geotechnical Journal,1971,8(4):588–592.
[10]程良奎,胡建林.土层锚杆的几个力学问题[C]//岩土锚固工程技术.北京:人民交通出版社,1996:1–6.(CHENG Liangkui,HU Jianlin.Some problems about the soil layer bolt[C]//Geotechnical Bolting Technology.Beijing:China Communication Press,1996:1–6.(in Chinese))
[11]顾金才,沈俊,陈安敏,等.锚索预应力在岩体内引起的应变状态模型试验研究[J].岩石力学与工程学报,2000,19(增):917–921.(GU Jincai,SHEN Jun,CHEN Anmin,et al.Model testing study of strain distribution regularity in rock mass caused by prestressed anchorage cable[J].Chinese Journal of Rock Mechanics and Engineering,2000,19(Supp.):917–921.(in Chinese))
[12]张培胜,阴可.拉力型锚杆锚固段传力机制的全过程分析方法[J].地下空间与工程学报,2009,5(4):716–723.(ZHANG Peisheng,YIN Ke.An analysis method of the whole working course for the force transferring mechanism in fixed segment of tensile-type anchor bar[J].Chinese Journal of Underground Space and Engineering,2009,5(4):716–723.(in Chinese))
[13]KIM N K,PARK J S,KIM S K.Numerical simulation of ground anchors[J].Computers and Geotechnics,2007,34(6):498–507.
[14]REN F F,YANG Z J,CHEN J F,et al.An analytical analysis of the full-range behavior of grouted rock bolts based on a tri-linear bond-slip model[J].Construction and Building Materials,2010,24(3):361–370.
[15]SEED H B,REESE L C.The action of soft clay along friction piles[J].Transactions of the American Society of Civil Engineers,1957,122(1):731–754.
[16]张乾青,张忠苗.抗拔单桩受力性状的解析算法[J].岩土工程学报,2011,33(增2):308–313.(ZHANG Qianqing,ZHANG Zhongmiao.Analytical prediction approach for response of single pile under tension[J].Chinese Journal of Geotechnical Engineering,2011,33(Supp.2):308–313.(in Chinese))
[17]ELIGEHAUSEN R,POPOV E P,BERTERO V V.Local bond stress-slip relationships of deformed bars under generalized excitations[R].Berkeley:University of California,1983:162–165.
[18]COSENZA E,MANFREDI G,REALFONZO R.Behavior and modeling of bond of FRP rebars to concrete[J].Journal of Composites for Construction,1997,1(2):40–51.
[19]BENMOKRANET B,CHENNOUF A,MITRI H S.Laboratory evaluation of cement-based grouts and grouted rock anchors[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1995,32(7):633–642.
[20]高丹盈,朱海堂,谢晶晶.纤维增强塑料筋混凝土黏结滑移本构模型[J].工业建筑,2003,33(7):41–43.(GAO Danying,ZHU Haitang,XIE Jingjing.The constitutive models for bond slip relation between FRP rebars and concrete[J].Industrial Construction,2003,33(7):41–43.(in Chinese))
[21]王贤能,叶蓉,周逢君.土层抗浮锚杆试验破坏标准选取的建议[J].地质灾害与环境保护,2001,12(3):73–77.(WANG Xianneng,YE Rong,ZHOU Fengjun.Proposals for the selection of failure criteria in soil float-resisting anchor rod test[J].Journal of Geological Hazards and Environment Preservation,2001,12(3):73–77.(in Chinese))
[22]龙照,张恩祥,魏永孝.锚杆极限承载力预测模型及方法研究[J].勘察科学技术,2008,(5):3–6.(LONG Zhao,ZHANG Enxiang,WEI Yongxiao.Study on prediction model of anchor rods ultimate bearing capacity and its method[J].Site Investigation Science and Technology,2008,(5):3–6.(in Chinese))
[23]李成,葛钦存,杨有海.膨胀软岩地层灌浆锚杆拉拔试验研究及抗拔力的可靠度分析[J].兰州铁道学院学报,1994,13(5):19–25.(LI Cheng,GE Qincun,YANG Youhai.Expansive rock anchor pull-out test and research[J].Journal of Lanzhou Railway Institute,1994,13(5):19–25.(in Chinese))
[24]应志民,张洁,尚岳全.锚杆荷载–位移曲线的指数函数模型研究[J].岩土力学,2005,26(8):1 331–1 334.(YING Zhimin,ZHANG Jie,SHANG Yuequan.Exponential model for simulating load-displacement curve of anchor rod[J].Rock and Soil Mechanics,2005,26(8):1 331–1 334.(in Chinese))
[25]欧阳明,丁伯阳,石吉森.单桩荷载–沉降曲线的修正指数曲线模型拟合研究[J].水运工程,2013,(1):31–38.(OUYANG Ming,DING Boyang,SHI Jisen.Application of modified exponential curve model in fitting of loading-settlement curve of single pile[J].Port and Waterway Engineering,2013,(1):31–38.(in Chinese))
[26]VAN DER VEEN C.The bearing capacity of a pile[C]//Proceedings of the Third International Conference of Soil Mechanical and Foundation Engineering.[S.l.]:[s.n.],1953:84–90.
[27]朱训国.地下工程中注浆岩石锚杆锚固机制研究[博士学位论文][D].大连:大连理工大学,2006.(ZHU Xunguo.The reinforcement mechanics of fully grouted rock bolt in underground engineering[Ph.D.Thesis][D].Dalian:Dalian University of Technology,2006.(in Chinese))
[28]荣冠,朱焕春,周创兵.螺纹钢与圆钢锚杆工作机制对比试验研究[J].岩石力学与工程学报,2004,23(3):469–475.(RONG Guan,ZHU Huanchun,ZHOU Chuangbing.Testing study on working mechanism of fully grouted bolts of thread steel and smooth steel[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(3):469–475.(in Chinese))
[29]刘波,李东阳,段艳芳,等.锚杆–砂浆界面黏结滑移关系的试验研究与破坏过程解析[J].岩石力学与工程学报,2011,30(增1):2 790–2 797.(LIU Bo,LI Dongyang,DUAN Yanfang,et al.Experimental study of bond-slip relationship between bolt and mortar and theoretical solution to failure process[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(Supp.1):2 790–2 797.(in Chinese))
[2]曹国金,姜弘道,熊红梅.一种确定拉力型锚杆支护长度的方法[J].岩石力学与工程学报,2003,22(7):1 141–1 145.(CAO Guojin,JIANG Hongdao,XIONG Hongmei.Calculation method of support length for stretched bolts[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(7):1 141–1 145.(in Chinese))
[3]张健超,贺建清,蒋鑫.基于Kelvin解的拉力型锚杆锚固段的受力分析[J].矿冶工程,2012,32(4):16–19.(ZHANG Jianchao,HE Jianqing,JIANG Xin.Mechanical analysis for anchorage segment of tension-type anchor[J].Mining and Metallurgical Engineering,2012,32(4):16–19.(in Chinese))
[4]杨庆,朱训国,栾茂田.全长注浆岩石锚杆双曲线模型的建立及锚固效应的参数分析[J].岩石力学与工程学报,2007,26(4):692–698.(YANG Qing,ZHU Xunguo,LUAN Maotian.Development of hyperbolic model for fully grouting rock bolt and parameters analysis for anchoring effect[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(4):692–698.(in Chinese))
[5]中华人民共和国行业标准编写组.JGJl20—2012建筑基坑支护技术规程[S].北京:中国建筑工业出版社,2012.(The Professional Standards Compilation Group of Peoples Republic of China.JGJl20—2012Technical specification for retaining and protection of building foundation excavation[S].Beijing:China Architecture and Building Press,2012.(in Chinese))
[6]PHILLIPS S H E.Factors affecting the design of anchorages in rock[R]. London:Cementation Research Ltd.,1970.
[7]何思明.预应力锚索作用机制研究[博士学位论文][D].成都:西南交通大学,2004.(HE Siming.Study on mechanism of prestressed anchoring cable[Ph.D.Thesis][D].Chengdu:Southwest Jiaotong University,2004.(in Chinese))
[8]张季如,唐保付.锚杆荷载传递机制分析的双曲函数模型[J].岩土工程学报,2002,24(2):188–192.(ZHANG Jiru,TANG Baofu.Hyperbolic function model to analyze load transfer mechanism on bolts[J].Chinese Journal of Geotechnical Engineering,2002,24(2):188–192.(in Chinese))
[9]HOLLINGSHEAD G W.Stress distribution in rock anchors[J].Canadian Geotechnical Journal,1971,8(4):588–592.
[10]程良奎,胡建林.土层锚杆的几个力学问题[C]//岩土锚固工程技术.北京:人民交通出版社,1996:1–6.(CHENG Liangkui,HU Jianlin.Some problems about the soil layer bolt[C]//Geotechnical Bolting Technology.Beijing:China Communication Press,1996:1–6.(in Chinese))
[11]顾金才,沈俊,陈安敏,等.锚索预应力在岩体内引起的应变状态模型试验研究[J].岩石力学与工程学报,2000,19(增):917–921.(GU Jincai,SHEN Jun,CHEN Anmin,et al.Model testing study of strain distribution regularity in rock mass caused by prestressed anchorage cable[J].Chinese Journal of Rock Mechanics and Engineering,2000,19(Supp.):917–921.(in Chinese))
[12]张培胜,阴可.拉力型锚杆锚固段传力机制的全过程分析方法[J].地下空间与工程学报,2009,5(4):716–723.(ZHANG Peisheng,YIN Ke.An analysis method of the whole working course for the force transferring mechanism in fixed segment of tensile-type anchor bar[J].Chinese Journal of Underground Space and Engineering,2009,5(4):716–723.(in Chinese))
[13]KIM N K,PARK J S,KIM S K.Numerical simulation of ground anchors[J].Computers and Geotechnics,2007,34(6):498–507.
[14]REN F F,YANG Z J,CHEN J F,et al.An analytical analysis of the full-range behavior of grouted rock bolts based on a tri-linear bond-slip model[J].Construction and Building Materials,2010,24(3):361–370.
[15]SEED H B,REESE L C.The action of soft clay along friction piles[J].Transactions of the American Society of Civil Engineers,1957,122(1):731–754.
[16]张乾青,张忠苗.抗拔单桩受力性状的解析算法[J].岩土工程学报,2011,33(增2):308–313.(ZHANG Qianqing,ZHANG Zhongmiao.Analytical prediction approach for response of single pile under tension[J].Chinese Journal of Geotechnical Engineering,2011,33(Supp.2):308–313.(in Chinese))
[17]ELIGEHAUSEN R,POPOV E P,BERTERO V V.Local bond stress-slip relationships of deformed bars under generalized excitations[R].Berkeley:University of California,1983:162–165.
[18]COSENZA E,MANFREDI G,REALFONZO R.Behavior and modeling of bond of FRP rebars to concrete[J].Journal of Composites for Construction,1997,1(2):40–51.
[19]BENMOKRANET B,CHENNOUF A,MITRI H S.Laboratory evaluation of cement-based grouts and grouted rock anchors[J].International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts,1995,32(7):633–642.
[20]高丹盈,朱海堂,谢晶晶.纤维增强塑料筋混凝土黏结滑移本构模型[J].工业建筑,2003,33(7):41–43.(GAO Danying,ZHU Haitang,XIE Jingjing.The constitutive models for bond slip relation between FRP rebars and concrete[J].Industrial Construction,2003,33(7):41–43.(in Chinese))
[21]王贤能,叶蓉,周逢君.土层抗浮锚杆试验破坏标准选取的建议[J].地质灾害与环境保护,2001,12(3):73–77.(WANG Xianneng,YE Rong,ZHOU Fengjun.Proposals for the selection of failure criteria in soil float-resisting anchor rod test[J].Journal of Geological Hazards and Environment Preservation,2001,12(3):73–77.(in Chinese))
[22]龙照,张恩祥,魏永孝.锚杆极限承载力预测模型及方法研究[J].勘察科学技术,2008,(5):3–6.(LONG Zhao,ZHANG Enxiang,WEI Yongxiao.Study on prediction model of anchor rods ultimate bearing capacity and its method[J].Site Investigation Science and Technology,2008,(5):3–6.(in Chinese))
[23]李成,葛钦存,杨有海.膨胀软岩地层灌浆锚杆拉拔试验研究及抗拔力的可靠度分析[J].兰州铁道学院学报,1994,13(5):19–25.(LI Cheng,GE Qincun,YANG Youhai.Expansive rock anchor pull-out test and research[J].Journal of Lanzhou Railway Institute,1994,13(5):19–25.(in Chinese))
[24]应志民,张洁,尚岳全.锚杆荷载–位移曲线的指数函数模型研究[J].岩土力学,2005,26(8):1 331–1 334.(YING Zhimin,ZHANG Jie,SHANG Yuequan.Exponential model for simulating load-displacement curve of anchor rod[J].Rock and Soil Mechanics,2005,26(8):1 331–1 334.(in Chinese))
[25]欧阳明,丁伯阳,石吉森.单桩荷载–沉降曲线的修正指数曲线模型拟合研究[J].水运工程,2013,(1):31–38.(OUYANG Ming,DING Boyang,SHI Jisen.Application of modified exponential curve model in fitting of loading-settlement curve of single pile[J].Port and Waterway Engineering,2013,(1):31–38.(in Chinese))
[26]VAN DER VEEN C.The bearing capacity of a pile[C]//Proceedings of the Third International Conference of Soil Mechanical and Foundation Engineering.[S.l.]:[s.n.],1953:84–90.
[27]朱训国.地下工程中注浆岩石锚杆锚固机制研究[博士学位论文][D].大连:大连理工大学,2006.(ZHU Xunguo.The reinforcement mechanics of fully grouted rock bolt in underground engineering[Ph.D.Thesis][D].Dalian:Dalian University of Technology,2006.(in Chinese))
[28]荣冠,朱焕春,周创兵.螺纹钢与圆钢锚杆工作机制对比试验研究[J].岩石力学与工程学报,2004,23(3):469–475.(RONG Guan,ZHU Huanchun,ZHOU Chuangbing.Testing study on working mechanism of fully grouted bolts of thread steel and smooth steel[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(3):469–475.(in Chinese))
[29]刘波,李东阳,段艳芳,等.锚杆–砂浆界面黏结滑移关系的试验研究与破坏过程解析[J].岩石力学与工程学报,2011,30(增1):2 790–2 797.(LIU Bo,LI Dongyang,DUAN Yanfang,et al.Experimental study of bond-slip relationship between bolt and mortar and theoretical solution to failure process[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(Supp.1):2 790–2 797.(in Chinese))