锚固长度对锚杆受力影响分析及其临界值计算
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摘要
基于锚固界面的一种非线性剪切滑移模型,采用荷载传递方法分析了锚固长度对锚杆受力特性的影响,建立了锚杆临界锚固长度的计算方法,并通过工程案例检验其可行性。结果表明:锚固长度较小时,锚杆荷载-位移曲线为承载力较小的单峰曲线;随着锚固长度的增加,逐渐衍生出一个平缓变化区段;锚固长度越小,界面剪应力分布越均匀,但整体承载力也越小;随着锚固长度增加,界面剪应力分布的不均匀特征逐渐明显,整体承载力也随之提高;锚固长度超过一定取值时,锚固界面软化荷载、抗拔荷载以及整体承载力均趋于定值,与锚固长度无关;计算得到的临界锚固长度与工程实际的锚固长度具有较好的一致性,验证了方法的可行性。
Aiming at the influence of anchorage length on stress conditions in bolt as well as the calculation method for its critical value, a nonlinear stress-slipping model of anchorage interface was introduced to develop shear stress, axial force and displacement solutions of bolts using load transfer method. The influence of anchorage length on stress conditions in bolt, mainly including load-displacement relationship, shear stress distribution as well as softening load and ultimate bearing capacity, was discussed. The calculation method for critical anchorage length was proposed and verified by the engineering applications. The results indicate that the load-displacement relationships of bolts with small anchorage length perform as unimodal curves with low bearing capacities. A slowness changing of the segment aroused accompanying with the increasing of anchorage length. Shear stress distributes uniformly along bolts with small anchorage length and the bearing capacity is very small. The non-uniform characteristics occur with the anchorage length increase and the bearing capacity also increases. The softening loads, ultimate bearing capacities and the bearing capacities of bolts approximate toward constant values after the anchorage length reaches critical value. The calculation results of the critical anchorage lengths show good agreement with the actual values in engineering cases for bearing tests, thus this proposed method is feasible and effective.
Aiming at the influence of anchorage length on stress conditions in bolt as well as the calculation method for its critical value, a nonlinear stress-slipping model of anchorage interface was introduced to develop shear stress, axial force and displacement solutions of bolts using load transfer method. The influence of anchorage length on stress conditions in bolt, mainly including load-displacement relationship, shear stress distribution as well as softening load and ultimate bearing capacity, was discussed. The calculation method for critical anchorage length was proposed and verified by the engineering applications. The results indicate that the load-displacement relationships of bolts with small anchorage length perform as unimodal curves with low bearing capacities. A slowness changing of the segment aroused accompanying with the increasing of anchorage length. Shear stress distributes uniformly along bolts with small anchorage length and the bearing capacity is very small. The non-uniform characteristics occur with the anchorage length increase and the bearing capacity also increases. The softening loads, ultimate bearing capacities and the bearing capacities of bolts approximate toward constant values after the anchorage length reaches critical value. The calculation results of the critical anchorage lengths show good agreement with the actual values in engineering cases for bearing tests, thus this proposed method is feasible and effective.
引文
[1]程良奎,张培文,王帆.岩土锚固工程的若干力学概念问题[J].岩石力学与工程学报,2015,34(4):668-682.CHENG Liang-kui,ZHANG Pei-wen,WANG Fan.Several mechanical conceptions for anchored structures in rock and soil[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(4):668-682.
[2]曾宪明,赵林,李世民,等.锚固类结构杆体临界锚固长度与判别方法试验研究[J].岩土工程学报,2008,30(增刊):404-409.ZENG Xian-ming,ZHAO Lin,LI Shi-ming,et al.Critical rod anchorage length and discrimination method of anchorage type structure[J].Chinese Journal of Geotechnical Engineering,2008,30(Supp.):404-409.
[3]曾宪明,林大路,李世民,等.锚固类结构杆体临界锚固长度问题综合研究[J].岩石力学与工程学报,2009,28(增刊2):3609-3625.ZENG Xian-ming,LIN Da-lu,LI Shi-min,et al.Comprehensive research of critical anchorage length problem of rod of anchorage structure[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(Supp.2):668-682.
[4]FUJITA K,UEDA K,KUSABUKA M.A simplified method of predicting load-displacement relationship of ground anchors[C]//Proceedings of the 9th International Conference on Soil Mechanics and Foundation Engineering,Tokyo:The Japanese Society of Soil Mechanics and Foundation Engineering,1977:58-62.
[5]程良奎,胡建林.土层锚杆的几个力学问题[C]//岩土工程中的锚固技术.北京:人民交通出版社,1996:1-6.CHENG Liang-kui,HU Jian-lin.Several mechanism problems of soil nail[C]//Anchor Techniques of Rock and Soil Engineering.Beijing:China Communication Press,1996:1-6.
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[7]白晓宇,张明义,匡政,等.光纤光栅传感技术在GFRP抗浮锚杆现场拉拔试验中的应用[J].岩土力学,2018,39(10):1-9.BAI Xiao-yu,ZHANG Ming-yi,KUANG Zheng,et al.Application of fiber grating sensing technology in pullout test on glass fiber reinforced polymer anti-floating anchor[J].Rock and Soil Mechanics,2018,39(10):1-9.
[8]付世雄,郜志强,岳炜.基于锚杆拉拔的临界锚固长度测试研究[J].煤炭技术,2016,35(11):46-49.FU Shi-xiong GAO Zhi-qiang YUE Wei.Research on critical anchorage length test based on anchor pull-out[J].Coal Technology,2016,35(11):46-49.
[9]杨校辉,朱彦鹏,郭楠,等.软岩深基坑预应力锚杆承载特性与滑移面确定试验研究[J].岩石力学与工程学报,2014,33(增刊2):4287-4298.YANG Xiao-hui,ZHU Yan-pen,GUO Nan,et al.Experimental research on bearing behavior of prestressed anchor and determination of slip surface in deep excavation of weak rock[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(Supp.2):4287-4298.
[10]LI C C,GUNNAR K,ARE H H.Critical embedment length and bond strength of fully encapsulated rebar rockbolts[J].Tunnelling and Underground Space Technology,2016,59:16-23
[11]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):1141-1145.CAO Guo-jin,JIANG Hong-dao,XIONG Hong-mei.Calculation method of support length for stretched bolts[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(7):1141-1145.
[12]张洁,尚岳全,叶彬.锚杆临界锚固长度解析计算[J].岩石力学与工程学报,2005,24(7):1134-1138.ZHANG Jie,SHANG Yue-quan,YE Bin.Analytic calculations of critical anchorage length of bolts[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(7):1134-1138.
[13]赵明华,刘峻龙,龙照.锚杆变形分析与临界锚固长度计算[J].建筑科学与工程学报,2008,25(3):17-21.ZHAO Ming-hua,LIU Jun-long,LONG Zhao.Deformation analysis of bolt and calculation of critical anchorage length[J].Journal of Architecture and Civil Engineering,2008,25(3):17-21.
[14]龙照,赵明华,张恩祥,等.锚杆临界锚固长度简化计算方法[J].岩土力学,2010,31(9):2991-2994.LONG Zhao,ZHAO Ming-hua,ZHANG En-xiang,et al.A simplified method for calculating critical anchorage length of bolt[J].Rock and Soil Mechanics,2010,31(9):2991-2994.
[15]李怀珍,李学华.基于界面滑移脱黏的锚杆合理锚固长度研究[J].岩土力学,2017,38(11):3107-3112.LI Huai-zhen,LI Xue-hua.Determination of rational anchorage length of bolt based on slip-debonding failure mode of interface[J].Rock and Soil Mechanics,2017,38(11):3107-3112.
[16]ZHENG J J,DAI J G.Analytical solution for the fullrange pull-out behavior of FRP ground anchors[J].Construction&Building Materials,2014,58(10):129-137.
[17]MA S Q,ZHAO Z Y,NIE W,et al.A numerical model of fully grouted bolts considering the tri-linear shear bondslip model[J].Tunnelling and Underground Space Technology,2016,54:73-80.
[18]黄明华,周智,欧进萍.拉力型锚杆锚固段拉拔受力的非线性全历程分析[J].岩石力学与工程学报,2014,33(11):2190-2199.HUANG Ming-hua,ZHOU Zhi,OU Jin-ping.Nonlinear full-range analysis of load transfer in fixed segment of tensile anchors[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(11):2190-2199.
[19]黄明华.岩土锚杆拉拔荷载传递分析与FRP智能锚杆监测验证[D].哈尔滨:哈尔滨工业大学,2014.HUANG Ming-hua.Analysis on pullout load transfer mechanism of geotechnical anchor and its validating monitor with smart frp anchor[D].Harbin:Harbin Institute of Technology,2014.
[20]张季如,唐保付.锚杆荷载传递机理分析的双曲函数模型[J].岩土工程学报,2002,24(2):188-192.ZHANG Ji-ru,TANG Bao-fu.Hyperbolic function model to analyze load transfer mechanism on bolts[J].Chinese Journal of Geotechnical Engineering,2002,24(2):188-192.
[21]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(增刊1):2790-2797.LIU Bo,LI Dong-yang,DUAN Yan-fang,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):2790-2797.
[22]荣冠,朱焕春,周创兵.螺纹钢与圆钢锚杆工作机理对比试验研究[J].岩石力学与工程学报,2004,23(3):469-475.RONG Guan,ZHU Huan-chun,ZHOU Chuang-bing.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.
[2]曾宪明,赵林,李世民,等.锚固类结构杆体临界锚固长度与判别方法试验研究[J].岩土工程学报,2008,30(增刊):404-409.ZENG Xian-ming,ZHAO Lin,LI Shi-ming,et al.Critical rod anchorage length and discrimination method of anchorage type structure[J].Chinese Journal of Geotechnical Engineering,2008,30(Supp.):404-409.
[3]曾宪明,林大路,李世民,等.锚固类结构杆体临界锚固长度问题综合研究[J].岩石力学与工程学报,2009,28(增刊2):3609-3625.ZENG Xian-ming,LIN Da-lu,LI Shi-min,et al.Comprehensive research of critical anchorage length problem of rod of anchorage structure[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(Supp.2):668-682.
[4]FUJITA K,UEDA K,KUSABUKA M.A simplified method of predicting load-displacement relationship of ground anchors[C]//Proceedings of the 9th International Conference on Soil Mechanics and Foundation Engineering,Tokyo:The Japanese Society of Soil Mechanics and Foundation Engineering,1977:58-62.
[5]程良奎,胡建林.土层锚杆的几个力学问题[C]//岩土工程中的锚固技术.北京:人民交通出版社,1996:1-6.CHENG Liang-kui,HU Jian-lin.Several mechanism problems of soil nail[C]//Anchor Techniques of Rock and Soil Engineering.Beijing:China Communication Press,1996:1-6.
[6]张福明,梁仕发,林大路,等.土中锚杆临界锚固长度的试验研究[J].煤矿开采,2015,20(5):97-100.ZHANG Fu-ming,LIANG Shi-fa,LIN Da-lu,et al.Test of critical anchorage length of anchored bolt for soil[J].Coal Mining Technology,2015,20(5):97-100.
[7]白晓宇,张明义,匡政,等.光纤光栅传感技术在GFRP抗浮锚杆现场拉拔试验中的应用[J].岩土力学,2018,39(10):1-9.BAI Xiao-yu,ZHANG Ming-yi,KUANG Zheng,et al.Application of fiber grating sensing technology in pullout test on glass fiber reinforced polymer anti-floating anchor[J].Rock and Soil Mechanics,2018,39(10):1-9.
[8]付世雄,郜志强,岳炜.基于锚杆拉拔的临界锚固长度测试研究[J].煤炭技术,2016,35(11):46-49.FU Shi-xiong GAO Zhi-qiang YUE Wei.Research on critical anchorage length test based on anchor pull-out[J].Coal Technology,2016,35(11):46-49.
[9]杨校辉,朱彦鹏,郭楠,等.软岩深基坑预应力锚杆承载特性与滑移面确定试验研究[J].岩石力学与工程学报,2014,33(增刊2):4287-4298.YANG Xiao-hui,ZHU Yan-pen,GUO Nan,et al.Experimental research on bearing behavior of prestressed anchor and determination of slip surface in deep excavation of weak rock[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(Supp.2):4287-4298.
[10]LI C C,GUNNAR K,ARE H H.Critical embedment length and bond strength of fully encapsulated rebar rockbolts[J].Tunnelling and Underground Space Technology,2016,59:16-23
[11]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):1141-1145.CAO Guo-jin,JIANG Hong-dao,XIONG Hong-mei.Calculation method of support length for stretched bolts[J].Chinese Journal of Rock Mechanics and Engineering,2003,22(7):1141-1145.
[12]张洁,尚岳全,叶彬.锚杆临界锚固长度解析计算[J].岩石力学与工程学报,2005,24(7):1134-1138.ZHANG Jie,SHANG Yue-quan,YE Bin.Analytic calculations of critical anchorage length of bolts[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(7):1134-1138.
[13]赵明华,刘峻龙,龙照.锚杆变形分析与临界锚固长度计算[J].建筑科学与工程学报,2008,25(3):17-21.ZHAO Ming-hua,LIU Jun-long,LONG Zhao.Deformation analysis of bolt and calculation of critical anchorage length[J].Journal of Architecture and Civil Engineering,2008,25(3):17-21.
[14]龙照,赵明华,张恩祥,等.锚杆临界锚固长度简化计算方法[J].岩土力学,2010,31(9):2991-2994.LONG Zhao,ZHAO Ming-hua,ZHANG En-xiang,et al.A simplified method for calculating critical anchorage length of bolt[J].Rock and Soil Mechanics,2010,31(9):2991-2994.
[15]李怀珍,李学华.基于界面滑移脱黏的锚杆合理锚固长度研究[J].岩土力学,2017,38(11):3107-3112.LI Huai-zhen,LI Xue-hua.Determination of rational anchorage length of bolt based on slip-debonding failure mode of interface[J].Rock and Soil Mechanics,2017,38(11):3107-3112.
[16]ZHENG J J,DAI J G.Analytical solution for the fullrange pull-out behavior of FRP ground anchors[J].Construction&Building Materials,2014,58(10):129-137.
[17]MA S Q,ZHAO Z Y,NIE W,et al.A numerical model of fully grouted bolts considering the tri-linear shear bondslip model[J].Tunnelling and Underground Space Technology,2016,54:73-80.
[18]黄明华,周智,欧进萍.拉力型锚杆锚固段拉拔受力的非线性全历程分析[J].岩石力学与工程学报,2014,33(11):2190-2199.HUANG Ming-hua,ZHOU Zhi,OU Jin-ping.Nonlinear full-range analysis of load transfer in fixed segment of tensile anchors[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(11):2190-2199.
[19]黄明华.岩土锚杆拉拔荷载传递分析与FRP智能锚杆监测验证[D].哈尔滨:哈尔滨工业大学,2014.HUANG Ming-hua.Analysis on pullout load transfer mechanism of geotechnical anchor and its validating monitor with smart frp anchor[D].Harbin:Harbin Institute of Technology,2014.
[20]张季如,唐保付.锚杆荷载传递机理分析的双曲函数模型[J].岩土工程学报,2002,24(2):188-192.ZHANG Ji-ru,TANG Bao-fu.Hyperbolic function model to analyze load transfer mechanism on bolts[J].Chinese Journal of Geotechnical Engineering,2002,24(2):188-192.
[21]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(增刊1):2790-2797.LIU Bo,LI Dong-yang,DUAN Yan-fang,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):2790-2797.
[22]荣冠,朱焕春,周创兵.螺纹钢与圆钢锚杆工作机理对比试验研究[J].岩石力学与工程学报,2004,23(3):469-475.RONG Guan,ZHU Huan-chun,ZHOU Chuang-bing.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.