Analytical solution of load transfer of inclined partial-cohesive anchor cable during the whole pull-out process
HAN Jianyong1, 2, ZHAO Wen3, CHEN Yang4*, BAI Xiaoyu5, JIA Pengjiao6, LI Tianliang7
(1. School of Civil Engineering, Shandong Jianzhu University, Jinan, Shandong 250101, China; 2. Key Laboratory of Building Structural Retrofitting and Underground Space Engineering of Ministry of Education, Shandong Jianzhu University, Jinan, Shandong 250101, China; 3. School of Resources and Civil Engineering, Northeastern University, Shenyang,
Liaoning 110004, China; 4. School of Civil Engineering and Architectural, Xi?an University of Technology, Xi?an,
Shanxi 710048; 5. School of Civil Engineering, Qingdao University of Technology, Qingdao, Shandong 266033,
China; 6. School of Rail Transportation,Soochow University, Suzhou, Jiangsu 215002, China;
7. PipeChina Engineering Technology Innovation Co., Ltd., Tianjin 300457, China)
Abstract:Due to the nonlinear characteristics of the pullout behavior of partially cohesive anchor cables, developing a theoretical analytical method for their load transfer mechanism poses certain challenges. This study focuses on the mechanical behavior of the anchorage interface and proposes a shear stress calculation method for the grout-soil interface. Based on the typical pullout failure characteristics of anchor cables, analytical solutions for the load transfer of inclined partially cohesive anchor cables are derived for both the elastic stage and the slippage development stage. On this basis, the distribution characteristics of axial stress and interfacial shear stress of the partial cohesive anchor cable in soil under pullout load are systematically analyzed, revealing the failure evolution throughout the pullout process. The results indicate that the grout in the free section of the partially cohesive anchor cables provides significant resistance to overall pullout performance. The axial stress in the steel strand of the anchorage section follows a hyperbolic sine distribution, while the maximum axial compressive stress of the grout occurs at the junction between the free and anchorage sections, with a tensile stress zone emerging at the bottom of the anchorage section. During the slippage development stage, the length of the interfacial plastic zone at both the free and anchorage sections generally demonstrates a linear relationship. The proposed analytical method effectively captures the shear slip behavior at the anchorage interface of inclined partially cohesive anchor cables and elucidates the corresponding load transfer mechanism, thereby providing theoretical support for understanding their pullout failure evolution and for the design of temporary reinforcement systems in slopes or excavations.
韩健勇1,2,赵 文3,陈 阳4*,白晓宇5,贾鹏蛟6,李天亮7. 倾斜型非全长黏结锚索拉拔全过程荷载传递解析方法[J]. 岩石力学与工程学报, 2026, 45(S1): 81-93.
HAN Jianyong1, 2, ZHAO Wen3, CHEN Yang4*, BAI Xiaoyu5, JIA Pengjiao6, LI Tianliang7. Analytical solution of load transfer of inclined partial-cohesive anchor cable during the whole pull-out process. , 2026, 45(S1): 81-93.
[1] 郭盼盼,龚晓南,魏支援. 锚固段穿越双地层拉力型锚索拉拔力学模型及应用[J]. 中国公路学报,2022,35(12):144–153.(GUO Panpan,GONG Xiaonan,WEI Zhiyuan. A pullout mechanical model for tension-type ground anchor penetrating two soil stratums and its application[J]. China Journal of Highway and Transport,2022,35(12):144–153.(in Chinese))
[2] 尤春安. 全长黏结式锚杆的受力分析[J]. 岩石力学与工程学报,2000,19(3):339–341.(YOU Chun′an. Analysis on bolt strain with large deformation under shearing-tensile load[J]. Chinese Journal of Rock Mechanics and Engineering,2000,19(3):339–341.(in Chinese))
[3] 黄明华,李嘉成,赵明华,等. 层状地基中锚杆拉拔荷载传递非线性分析[J]. 中国公路学报,2019,32(1):12–20.(HUANG Minghua,LI Jiacheng,ZHAO Minghua,et al. Nonlinear analysis on load transfer mechanism of bolts in layered ground[J]. China Journal of Highway and Transport,2019,32(1):12–20.(in Chinese))
[4] 周炳生,王保田,梁传扬,等. 全长黏结式锚杆锚固段荷载传递特性研究[J]. 岩石力学与工程学报,2017,36(增2):3 774–3 780. (ZHOU Bingsheng,WANG Baotian,LIANG Chuanyang,et al. Study on load transfer characteristics of wholly grouted bolt[J]. Chinese Journal of Rock Mechanics and Engineering,2017,36(Supp.2): 3 774–3 780.(in Chinese))
[5] 中华人民共和国行业标准编写组. JGJ 120—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 People?s Republic of China. JGJ 120—2012 Technical specification for retaining and protection of building foundation excavations[S]. Beijing:China Architecture and Building Press,2012.(in Chinese))
[6] 肖世国,周德培. 非全长粘结型锚索锚固段长度的一种确定方法[J]. 岩石力学与工程学报,2004,23(9):1 530–1 534.(XIAO Shiguo,ZHOU Depei. Calculation method of length of anchoring segment for partial-cohesive cable[J]. Chinese Journal of Rock Mechanics and Engineering,2004,23(9):1 530–1 534.(in Chinese))
[7] 李怀珍. 煤巷非全长锚固单元体锚杆滑移脱黏机制及应用研究[博士学位论文][D]. 徐州:中国矿业大学,2018.(LI Huaizhen. Research on slipping mechanism of bolt in non full length anchorage unit and engineering application[Ph. D. Thesis][D]. Xuzhou:China University of Mining and Technology,2018.(in Chinese))
[8] ZHU B L,LI Q,WU Y,et al. Analytical model for predicting stress distribution and load transfer of tension-type anchor cable with borehole deviation[J]. International Journal of Geomechanics,2020,20(7):04020085.
[9] HAN J Y,LIU D,GUAN Y P,et al. Study on shear behavior and damage constitutive model of tendon-grout interface[J]. Construction and Building Materials,2022,320:126223.
[10] HSU S T. Behavior of pressure-grouted anchors in gravel[J]. Canadian Geotechnical Journal,2012,49(6):719–728.
[11] 于远祥,谷拴成,吴 璋,等. 黄土地层下预应力锚索荷载传递规律的试验研究[J]. 岩石力学与工程学报,2010,29(12):2 573– 2 580.(YU Yuanxiang,GU Shuancheng,WU Zhang,et al. Experimental study of load transfer law of prestressed cables under loess stratum[J]. Chinese Journal of Rock Mechanics and Engineering,2010,29(12):2 573–2 580.(in Chinese))
[12] LI T L,ZHAO W,LIU R,et al. Visualized direct shear test of the interface between gravelly sand and concrete pipe[J]. Canadian Geotechnical Journal,2023,61(2):361–374.
[13] 白晓宇,张明义,匡 政,等. 全长黏结GFRP抗浮锚杆荷载分布函数模型研究[J]. 中南大学学报:自然科学版,2020,51(7): 1 977–1 988.(BAI Xiaoyu,ZHANG Mingyi,KUANG Zheng,et al. Load distribution function model of full-length bond GFRP anti-floating anchor[J]. Journal of Central South University:Science and Technology,2020,51(7):1 977–1 988.(in Chinese))
[14] 赵 文,李天亮,韩健勇,等. 砾砂与混凝土管界面剪切力学特性试验[J]. 东北大学学报:自然科学版,2020,41(3):424–429. (ZHAO Wen,LI Tianliang,HAN Jianyong,et al. Experiment of shear properties on the interface between gravelly sand and concrete pipe[J]. Journal of Northeastern University:Natural Science,2020,41(3):424–429.(in Chinese))
[15] 李文轩,卞士海,李国英,等. 粗粒料接触面模型及其在土石坝工程中的应用[J]. 岩土力学,2019,40(6):2 379–2 388.(LI Wenxuan,BIAN Shihai,LI Guoying,et al. Interface model of coarse-grained soils and its application in earth rock dam[J]. Rock and Soil Mechanics,2019,40(6):2 379–2 388.(in Chinese))
[16] 何鹏飞,马 巍,穆彦虎,等. 黄土–砂浆块界面剪切特性试验及本构模型研究[J]. 岩土力学,2019,40(增1):82–90.(HE Pengfei,MA Wei,MU Yanhu,et al. Experimental analysis of interfacial shear behavior of loess-mortar block and construction of constitutive model[J]. Rock and Soil Mechanics,2019,40(Supp.1):82–90.(in Chinese))
[17] HAO Z M,LIU H H,Yan N,et al. In-situ test and numerical simulation of anchoring performance of embedded rock GFRP anchor[J]. Buildings,2023,13(11):2 799.
[18] 李英勇,王梦恕,张顶立,等. 锚索预应力变化影响因素及模型研究[J]. 岩石力学与工程学报,2008,27(增1):3 140–3 146.(LI Yingyong,WANG Mengshu,ZHANG Dingli,et al. Study on influential factors and model for variation of anchor cable prestress[J]. Chinese Journal of Rock Mechanics and Engineering,2008,27(Supp.1):3 140–3 146.(in Chinese))
[19] 丁秀丽,盛 谦,韩 军,等. 预应力锚索锚固机制的数值模拟试验研究[J]. 岩石力学与工程学报,2002,21(7):980–988.(DING Xiuli,SHENG Qian,HAN Jun,et al. Numerical simulation testing study on reinforcement mechanism of prestressed anchorage cable[J]. Chinese Journal of Rock Mechanics and Engineering,2002,21(7):980–988.(in Chinese))
[20] KIM N. Performance of tension and compression anchors in weathered soil[J]. Journal of Geotechnical and Geoenvironmental Engineering,2003,129(12):1 138–1 150.