基于串联流变模型的锚拉力松弛分析方法

邓益; 肖世国

doi:10.16030/j.cnki.issn.1000-3665.202208062

基于串联流变模型的锚拉力松弛分析方法

邓益^1,,
肖世国^2, ,

1.
西南交通大学地球科学与环境工程学院，四川成都　610031

2.
西南交通大学高速铁路线路工程教育部重点实验室，四川成都　610031

基金项目: 四川省交通运输科技项目（2020-A-01）；国家自然科学基金项目（51578466）

详细信息

作者简介: 邓益（1997-），男，硕士研究生，主要从事边坡工程研究。E-mail：1427091785@qq.com

通讯作者: 肖世国（1973-），男，博士，教授，博导，主要从事边坡稳定性与支挡结构研究。E-mail：xiaoshiguo@swjtu.cn

中图分类号: TU443

收稿日期: 2022-08-22

修回日期: 2022-11-28

刊出日期: 2023-09-15

Analysis method for relaxation effect of prestressed anchor cable tension based on a series rheological model

DENG Yi^1,,
XIAO Shiguo^2, ,

1.
Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu, Sichuan　610031, China

2.
Key Laboratory of High-speed Railway Engineering, Ministry of Education, Southwest Jiaotong University, Chengdu, Sichuan　610031, China

More Information

Corresponding author: XIAO Shiguo, xiaoshiguo@swjtu.cn

Received Date: 22 August 2022

Revised Date: 28 November 2022

Publish Date: 15 September 2023

摘要

摘要:
加固坡体的预应力锚索结构存在锚索拉力随时间松弛问题，为了合理预测分析锚索拉力松弛，基于锚索-边坡体系中滑床、锚索、滑体、坡面抑制构件之间的相互作用与锚固系统受力、变形基本机理，建立了一种采用虎克体模拟锚索或坡面抑制构件、开尔文体模拟滑床、开尔文体或广义开尔文体模拟土质或岩质滑体的锚索-滑床-滑体-坡面抑制件的四体串联式流变模型，推导了锚索拉力松弛的计算方程。实例分析表明：所提出模型的锚索拉力松弛计算值与试验或实测结果的误差小于既有模型的计算误差，计算得到的锚索拉力松弛收敛值的最大计算误差约为11%，松弛历时的最大误差约为10%；锚索拉力松弛率随锚索的直径和弹性模量的增大呈线性增大，随锚孔间距、滑床和滑体的滞后弹性模量与黏滞系数（尤其初期阶段）的增大呈非线性减弱，而滑床和滑体的瞬时弹性模量、坡面抑制构件的弹性模量均对锚索松弛效应影响很小。所建立的方法可用于定量评估预测预应力锚索加固坡体的锚拉力松弛效应，进而可用于分析锚固边坡长期稳定性。
- 边坡 /
- 预应力锚索 /
- 锚索拉力 /
- 松弛效应 /
- 串联流变模型
Abstract:
Anchor cable tension relaxation with time is a typical problem in the prestressed anchor cable structure used to reinforce slopes. In order to reasonably predict the tension relaxation of anchor cable, based on the interaction among the stable layer, anchor cable, slide mass and constraint components on the slope face in the anchor cable-slope system and the basic loading and deformation mechanism of the anchorage system, a four-body series rheological model composed of anchor cable, slide bed, slide body, and constraint components is established, in which the anchor cable and constraint components are simulated with Hooke body, the slide mass is simulated with Kelvin body or generalized Kelvin body, and the stable layer is simulated with generalized Kelvin body. The calculation equation of the anchor cable tension relaxation is accordingly derived. Some examples show that the error between the proposed value of cable tension relaxation and the observed results is smaller than those using the existing calculation methods. The maximum error of cable tension relaxation convergence value using the proposed method is about 11%, and the maximum error of the relaxation duration is about 10%. The relaxation rate of the anchor cable tension increases linearly with the diameter and elastic modulus of the anchor cable, and decreases nonlinearly with the increasing anchor hole spacing, the hysteresis elastic modulus and the viscosity coefficient (particularly in the initial stage) of the stable layer and slide mass. The instantaneous elastic modulus of the stable layer and the slide mass as well as the elastic modulus of the constraint components have little effect on the tension relaxation of the anchor cable. The proposed method can be used to quantitatively evaluate the anchor tension relaxation of slopes reinforced with prestressed anchor cables in practical engineering, which naturally allows to analyze the long-term stability of the anchored slopes.
- slope /
- prestressed anchor cable /
- anchor tension /
- relaxation effect /
- series rheological model

HTML全文

图 1 边坡锚固系统受力机理与位移协调示意图

Figure 1.

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图 2 锚索结构-边坡体系的整体串联流变模型

Figure 2.

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图 3 模型布置示意图（单位：cm）^[10]

Figure 3.

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图 4 室内模型试验锚索拉力实测与计算值对比

Figure 4.

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图 5 现场多点位移计布设示意图^[15]

Figure 5.

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图 6 完整岩质高边坡锚索拉力实测与计算值对比

Figure 6.

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图 7 较破碎岩质高边坡锚索拉力实测与理论计算对比

Figure 7.

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图 8 某堆积层高边坡锚索拉力实测与理论计算对比

Figure 8.

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图 9 锚索拉力松弛率随锚索直径变化曲线

Figure 9.

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图 10 锚索拉力松弛率随锚孔间距变化曲线

Figure 10.

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图 11 锚索拉力松弛率随锚索弹性模量变化曲线

Figure 11.

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图 12 锚索拉力松弛率随锚固段地层流变参数变化曲线

Figure 12.

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图 13 锚索拉力松弛率随坡面抑制件弹性模量变化曲线

Figure 13.

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图 14 锚索拉力松弛率随自由段滑体流变参数变化曲线

Figure 14.

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表 1 模型岩体的流变参数

Table 1. Rheological parameters of model rock mass

组号	E_k/MPa	η/（MPa∙h⁻¹）
2	9.187	582.101
3	9.340	597.862
平均值	9.264	589.982

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表 2 锚索拉力松弛历时及本法计算误差

Table 2. Relaxation duration of anchor tension and proposed calculation errors

锚索编号	锚拉力初始值/kN	松弛历时/d	确定方法	本法误差/%
2#	0.054	5.1	试验值	9.8
2#	0.054	5.6	本文值	9.8
3#	0.083	5.2	试验值	9.6
3#	0.083	5.7	本文值	9.6
2-4-A	600	52	试验值	7.7
2-4-A	600	56	本文值	7.7
2-4-B	600	50	试验值	8.0
2-4-B	600	54	本文值	8.0
BZ16-23	850	62	试验值	3.2
BZ16-23	850	60	本文值	3.2

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参考文献(28)

[1]	肖世国,周德培. 岩石高边坡预应力锚索地梁的一种内力计算方法[J]. 岩石力学与工程学报,2003,22(2):250 − 253. [XIAO Shiguo,ZHOU Depei. Internal force calculating method of prestressed-cable beam-on-foundation for high rock slope[J]. Chinese Journal of Rock Mechanics and Engineering,2003,22(2):250 − 253. (in Chinese with English abstract) XIAO Shiguo, ZHOU Depei. Internal force calculating method of prestressed-cable beam-on-foundation for high rock slope[J]. Chinese Journal of Rock Mechanics and Engineering, 2003, 22（2）: 250 − 253. （in Chinese with English abstract）
[2]	付晓,冀文有,张建经,等. 锚索框架梁加固平面滑动型边坡地震动力响应[J]. 岩土力学,2018,39(5):1709 − 1719. [FU Xiao,JI Wenyou,ZHANG Jianjing,et al. Seismic response for plane sliding of slope reinforced by anchor-chain-framed ground beams through shaking table test[J]. Rock and Soil Mechanics,2018,39(5):1709 − 1719. (in Chinese with English abstract) doi: 10.16285/j.rsm.2016.2102 FU Xiao, JI Wenyou, ZHANG Jianjing, et al. Seismic response for plane sliding of slope reinforced by anchor-chain-framed ground beams through shaking table test[J]. Rock and Soil Mechanics, 2018, 39（5）: 1709 − 1719. （in Chinese with English abstract） doi: 10.16285/j.rsm.2016.2102
[3]	YAN Minjia,XIA Yuanyou,LIU Tingting,et al. Limit analysis under seismic conditions of a slope reinforced with prestressed anchor cables[J]. Computers and Geotechnics,2019,108:226 − 233. doi: 10.1016/j.compgeo.2018.12.027
[4]	YANG Guanghua,ZHONG Zhihui,ZHANG Yucheng,et al. Optimal design of anchor cables for slope reinforcement based on stress and displacement fields[J]. Journal of Rock Mechanics and Geotechnical Engineering,2015,7(4):411 − 420. doi: 10.1016/j.jrmge.2015.04.004
[5]	雷军,肖世国. 考虑滑体中锚拉力扩散效应的锚固边坡稳定性分析方法[J]. 岩土工程学报,2019,41(9):1724 − 1730. [LEI Jun,XIAO Shiguo. Stability analysis method for anchored slopes considering stress dispersion effect in sliding mass due to anchor tensile forces[J]. Chinese Journal of Geotechnical Engineering,2019,41(9):1724 − 1730. (in Chinese with English abstract) LEI Jun, XIAO Shiguo. Stability analysis method for anchored slopes considering stress dispersion effect in sliding mass due to anchor tensile forces[J]. Chinese Journal of Geotechnical Engineering, 2019, 41（9）: 1724 − 1730. （in Chinese with English abstract）
[6]	曾宪明,陈肇元,王靖涛,等. 锚固类结构安全性与耐久性问题探讨[J]. 岩石力学与工程学报,2004,23(13):2235 − 2242. [ZENG Xianming,CHEN Zhaoyuan,WANG Jingtao,et al. Research on safety and durability of bolt and cable-supported structures[J]. Chinese Journal of Rock Mechanics and Engineering,2004,23(13):2235 − 2242. (in Chinese with English abstract) doi: 10.3321/j.issn:1000-6915.2004.13.020 ZENG Xianming, CHEN Zhaoyuan, WANG Jingtao, et al. Research on safety and durability of bolt and cable-supported structures[J]. Chinese Journal of Rock Mechanics and Engineering, 2004, 23（13）: 2235 − 2242. （in Chinese with English abstract） doi: 10.3321/j.issn:1000-6915.2004.13.020
[7]	付晓,张建经,周立荣. 多级框架锚索和抗滑桩联合作用下边坡抗震性能的振动台试验研究[J]. 岩土力学,2017,38(2):462 − 470. [FU Xiao,ZHANG Jianjing,ZHOU Lirong. Shaking table test of seismic response of slope reinforced by combination of anti-slide piles and multi-frame foundation beam with anchor cable[J]. Rock and Soil Mechanics,2017,38(2):462 − 470. (in Chinese with English abstract) doi: 10.16285/j.rsm.2017.02.020 FU Xiao, ZHANG Jianjing, ZHOU Lirong. Shaking table test of seismic response of slope reinforced by combination of anti-slide piles and multi-frame foundation beam with anchor cable[J]. Rock and Soil Mechanics, 2017, 38（2）: 462 − 470. （in Chinese with English abstract） doi: 10.16285/j.rsm.2017.02.020
[8]	丁多文,白世伟,罗国煜. 预应力锚索加固岩体的应力损失分析[J]. 工程地质学报,1995,3(1):65 − 69. [DING Duowen,BAI Shiwei,LUO Guoyu. Analysis on the load losses of prestressed rock cablle bolts[J]. Journal of Engineering Geology,1995,3(1):65 − 69. (in Chinese with English abstract) DING Duowen, BAI Shiwei, LUO Guoyu. Analysis on the load losses of prestressed rock cablle bolts[J]. Journal of Engineering Geology, 1995, 3（1）: 65 − 69. （in Chinese with English abstract）
[9]	SHI Keyou,WU Xiaoping,LIU Ze,et al. Coupled calculation model for anchoring force loss in a slope reinforced by a frame beam and anchor cables[J]. Engineering Geology,2019,260:105245. doi: 10.1016/j.enggeo.2019.105245
[10]	陈安敏,顾金才,沈俊,等. 软岩加固中锚索张拉吨位随时间变化规律的模型试验研究[J]. 岩石力学与工程学报,2002,21(2):251 − 256. [CHEN Anmin,GU Jincai,SHEN Jun,et al. Model testing research on the variation of tension force of anchor cable with time in reinforcement of soft rocks[J]. Chinese Journal of Rock Mechanics and Engineering,2002,21(2):251 − 256. (in Chinese with English abstract) doi: 10.3321/j.issn:1000-6915.2002.02.020 CHEN Anmin, GU Jincai, SHEN Jun, et al. Model testing research on the variation of tension force of anchor cable with time in reinforcement of soft rocks[J]. Chinese Journal of Rock Mechanics and Engineering, 2002, 21（2）: 251 − 256. （in Chinese with English abstract） doi: 10.3321/j.issn:1000-6915.2002.02.020
[11]	杨栋,王全成,姜昭群. 高强大变形屈服锚索承载特性室内试验研究[J]. 水文地质工程地质,2022,49(3):79 − 86. [YANG Dong,WANG Quancheng,JIANG Zhaoqun. Laboratory test on the mechanical behavior of high-strength and large-deformation yield anchor cable[J]. Hydrogeology & Engineering Geology,2022,49(3):79 − 86. (in Chinese with English abstract) YANG Dong, WANG Quancheng, JIANG Zhaoqun. Laboratory test on the mechanical behavior of high-strength and large-deformation yield anchor cable[J]. Hydrogeology & Engineering Geology, 2022, 49（3）: 79 − 86. （in Chinese with English abstract）
[12]	李涛,蔡海波,刘波,等. 膨胀土地层锚索预应力损失与流变耦合模型研究[J]. 岩石力学与工程学报,2020,39(1):147 − 155. [LI Tao,CAI Haibo,LIU Bo,et al. Study on prestress loss and rheological coupling model of anchor cables in expansive soil layers[J]. Chinese Journal of Rock Mechanics and Engineering,2020,39(1):147 − 155. (in Chinese with English abstract) doi: 10.13722/j.cnki.jrme.2019.0491 LI Tao, CAI Haibo, LIU Bo, et al. Study on prestress loss and rheological coupling model of anchor cables in expansive soil layers[J]. Chinese Journal of Rock Mechanics and Engineering, 2020, 39（1）: 147 − 155. （in Chinese with English abstract） doi: 10.13722/j.cnki.jrme.2019.0491
[13]	李安润,邓辉,王红娟,等. 水-岩作用下粉砂质泥岩含水损伤本构模型[J]. 水文地质工程地质,2021,48(2):106 − 113. [LI Anrun,DENG Hui,WANG Hongjuan,et al. Constitutive model of water-damaged silty mudstone under water-rock interactions[J]. Hydrogeology & Engineering Geology,2021,48(2):106 − 113. (in Chinese with English abstract) doi: 10.16030/j.cnki.issn.1000-3665.202004007 LI Anrun, DENG Hui, WANG Hongjuan, et al. Constitutive model of water-damaged silty mudstone under water-rock interactions[J]. Hydrogeology & Engineering Geology, 2021, 48（2）: 106 − 113. （in Chinese with English abstract） doi: 10.16030/j.cnki.issn.1000-3665.202004007
[14]	郭长宝,王磊,李任杰,等. 西藏贡觉粉砂质泥岩工程地质特性与蠕变强度研究[J]. 水文地质工程地质,2021,48(5):54 − 64. [GUO Changbao,WANG Lei,LI Renjie,et al. Engineering geology properties and creeping strength characteristics of the silty mudstone in Gongjue County in Tibet of China[J]. Hydrogeology & Engineering Geology,2021,48(5):54 − 64. (in Chinese with English abstract) doi: 10.16030/j.cnki.issn.1000-3665.202107012 GUO Changbao, WANG Lei, LI Renjie, et al. Engineering geology properties and creeping strength characteristics of the silty mudstone in Gongjue County in Tibet of China[J]. Hydrogeology & Engineering Geology, 2021, 48（5）: 54 − 64. （in Chinese with English abstract） doi: 10.16030/j.cnki.issn.1000-3665.202107012
[15]	陈沅江,尹进,胡毅夫. 软岩边坡锚索预应力定量损失规律研究[J]. 岩石力学与工程学报,2013,32(8):1685 − 1691. [CHEN Yuanjiang,YIN Jin,HU Yifu. Research on prestress quantitative loss law of soft rock slope anchor cable[J]. Chinese Journal of Rock Mechanics and Engineering,2013,32(8):1685 − 1691. (in Chinese with English abstract) CHEN Yuanjiang, YIN Jin, HU Yifu. Research on prestress quantitative loss law of soft rock slope anchor cable[J]. Chinese Journal of Rock Mechanics and Engineering, 2013, 32（8）: 1685 − 1691. （in Chinese with English abstract）
[16]	朱晗迓,尚岳全,陆锡铭,等. 锚索预应力长期损失与坡体蠕变耦合分析[J]. 岩土工程学报,2005,27(4):464 − 467. [ZHU Hanya,SHANG Yuequan,LU Ximing,et al. Coupling analysis of long-term prestress loss and slope creep[J]. Chinese Journal of Geotechnical Engineering,2005,27(4):464 − 467. (in Chinese with English abstract) ZHU Hanya, SHANG Yuequan, LU Ximing, et al. Coupling analysis of long-term prestress loss and slope creep[J]. Chinese Journal of Geotechnical Engineering, 2005, 27（4）: 464 − 467. （in Chinese with English abstract）
[17]	王清标,张聪,王辉,等. 预应力锚索锚固力损失与岩土体蠕变耦合效应研究[J]. 岩土力学,2014,35(8):2150 − 2156. [WANG Qingbiao,ZHANG Cong,WANG Hui,et al. Study of coupling effect between anchorage force loss of prestressed anchor cable and rock and soil creep[J]. Rock and Soil Mechanics,2014,35(8):2150 − 2156. (in Chinese with English abstract) doi: 10.16285/j.rsm.2014.08.006 WANG Qingbiao, ZHANG Cong, WANG Hui, et al. Study of coupling effect between anchorage force loss of prestressed anchor cable and rock and soil creep[J]. Rock and Soil Mechanics, 2014, 35（8）: 2150 − 2156. （in Chinese with English abstract） doi: 10.16285/j.rsm.2014.08.006
[18]	邓东平,李亮. 锚索预应力长期损失与岩土体蠕变耦合模型研究[J]. 长江科学院院报,2015,32(8):65 − 71. [DENG Dongping,LI Liang. Coupled model for the long-term pre-stress loss of anchor cable and geotechnical creep[J]. Journal of Yangtze River Scientific Research Institute,2015,32(8):65 − 71. (in Chinese with English abstract) DENG Dongping, LI Liang. Coupled model for the long-term pre-stress loss of anchor cable and geotechnical creep[J]. Journal of Yangtze River Scientific Research Institute, 2015, 32（8）: 65 − 71. （in Chinese with English abstract）
[19]	高大水,曾勇. 三峡永久船闸高边坡锚索预应力状态监测分析[J]. 岩石力学与工程学报,2001,20(5):653 − 656. [GAO Dashui,ZENG Yong. Monitoring analysis on prestress state of anchor cable of high slope of the tgp permanent shiplocks[J]. Chinese Journal of Rock Mechanics and Engineering,2001,20(5):653 − 656. (in Chinese with English abstract) doi: 10.3321/j.issn:1000-6915.2001.05.010 GAO Dashui, ZENG Yong. Monitoring analysis on prestress state of anchor cable of high slope of the tgp permanent shiplocks[J]. Chinese Journal of Rock Mechanics and Engineering, 2001, 20（5）: 653 − 656. （in Chinese with English abstract） doi: 10.3321/j.issn:1000-6915.2001.05.010
[20]	王军,曹平,林杭. 锚土界面位移特征及其蠕变损伤耦合效应研究[J]. 中国矿业大学学报,2018,47(2):289 − 295. [WANG Jun,CAO Ping,LIN Hang. Characteristic of displacement on the interface between bolt and soil and damage transfer based on the coupling effect of creep and damage[J]. Journal of China University of Mining & Technology,2018,47(2):289 − 295. (in Chinese with English abstract) doi: 10.13247/j.cnki.jcumt.000838 WANG Jun, CAO Ping, LIN Hang. Characteristic of displacement on the interface between bolt and soil and damage transfer based on the coupling effect of creep and damage[J]. Journal of China University of Mining & Technology, 2018, 47（2）: 289 − 295. （in Chinese with English abstract） doi: 10.13247/j.cnki.jcumt.000838
[21]	徐毅青,邓绍玉,葛琦. 锚索预应力初期与长期损失的预测模型研究[J]. 岩土力学,2020,41(5):1663 − 1669. [XU Yiqing,DENG Shaoyu,GE Qi. Prediction models for short-term and long-term pre-stress loss of anchor cable[J]. Rock and Soil Mechanics,2020,41(5):1663 − 1669. (in Chinese with English abstract) doi: 10.16285/j.rsm.2019.0099 XU Yiqing, DENG Shaoyu, GE Qi. Prediction models for short-term and long-term pre-stress loss of anchor cable[J]. Rock and Soil Mechanics, 2020, 41（5）: 1663 − 1669. （in Chinese with English abstract） doi: 10.16285/j.rsm.2019.0099
[22]	冯忠居,江冠,赵瑞欣,等. 基于多因素耦合效应的锚索预应力长期损失研究[J]. 岩土力学,2021,42(8):2215 − 2224. [FENG Zhongju,JIANG Guan,ZHAO Ruixin,et al. Study on pre-stress long term loss of anchor cable considering coupled multiple factors[J]. Rock and Soil Mechanics,2021,42(8):2215 − 2224. (in Chinese with English abstract) FENG Zhongju, JIANG Guan, ZHAO Ruixin, et al. Study on pre-stress long term loss of anchor cable considering coupled multiple factors[J]. Rock and Soil Mechanics, 2021, 42（8）: 2215 − 2224. （in Chinese with English abstract）
[23]	周德培,朱本珍,毛坚强. 流变力学原理及其在岩土工程中的应用[M]. 成都:西南交通大学出版社,1995:29 – 31. [ZHOU Depei,ZHU Benzhen,MAO Jianqiang. Rheological mechanics principle and its application in geotechnical engineering [M]. Chengdu:Southwest Jiaotong University Press,1995:29 – 31. (in Chinese) ZHOU Depei, ZHU Benzhen, MAO Jianqiang. Rheological mechanics principle and its application in geotechnical engineering [M]. Chengdu: Southwest Jiaotong University Press, 1995: 29 – 31. （in Chinese）
[24]	陈拓,陈国庆,黄润秋,等. 考虑高边坡强卸荷的锚索锚固力耦合变化模型[J]. 岩土力学,2018,39(11):4125 − 4132. [CHEN Tuo,CHEN Guoqing,HUANG Runqiu,et al. A model of anchorage force loss of anchor cable during high slope strong unloading[J]. Rock and Soil Mechanics,2018,39(11):4125 − 4132. (in Chinese with English abstract) doi: 10.16285/j.rsm.2017.0514 CHEN Tuo, CHEN Guoqing, HUANG Runqiu, et al. A model of anchorage force loss of anchor cable during high slope strong unloading[J]. Rock and Soil Mechanics, 2018, 39（11）: 4125 − 4132. （in Chinese with English abstract） doi: 10.16285/j.rsm.2017.0514
[25]	王国富,李强,路林海,等. 考虑锚索松弛特性的预应力损失计算模型研究[J]. 地下空间与工程学报,2017,13(6):1585 − 1591. [WANG Guofu,LI Qiang,LU Linhai,et al. A coupled model research of anchor prestress loss considering the relaxation characteristics of anchor[J]. Chinese Journal of Underground Space and Engineering,2017,13(6):1585 − 1591. (in Chinese with English abstract) WANG Guofu, LI Qiang, LU Linhai, et al. A coupled model research of anchor prestress loss considering the relaxation characteristics of anchor[J]. Chinese Journal of Underground Space and Engineering, 2017, 13（6）: 1585 − 1591. （in Chinese with English abstract）
[26]	肖世国,曹顺利,赵琳智. 加固岩体的预应力锚索拉力松弛分析模型[J]. 北京工业大学学报,2020,46(8):940 − 947. [XIAO Shiguo,CAO Shunli,ZHAO Linzhi. Analysis model for relaxation effect of pulling force of prestressed anchor cables used in reinforcing rock mass[J]. Journal of Beijing University of Technology,2020,46(8):940 − 947. (in Chinese with English abstract) XIAO Shiguo, CAO Shunli, ZHAO Linzhi. Analysis model for relaxation effect of pulling force of prestressed anchor cables used in reinforcing rock mass[J]. Journal of Beijing University of Technology, 2020, 46（8）: 940 − 947. （in Chinese with English abstract）
[27]	董旭光,马子涵,李峥,等. 锚固力损失与岩土体时效变形耦合模型研究[J]. 岩石力学与工程学报,2022,41(6):1093 − 1102. [DONG Xuguang,MA Zihan,LI Zheng,et al. Study on coupling model of anchorage force loss and time-dependent deformation of rock-soil mass[J]. Chinese Journal of Rock Mechanics and Engineering,2022,41(6):1093 − 1102. (in Chinese with English abstract) DONG Xuguang, MA Zihan, LI Zheng, et al. Study on coupling model of anchorage force loss and time-dependent deformation of rock-soil mass[J]. Chinese Journal of Rock Mechanics and Engineering, 2022, 41（6）: 1093 − 1102. （in Chinese with English abstract）
[28]	李习平,阳军生,王立川,等. 三联隧道凝灰岩流变试验及其本构模型研究[J]. 铁道科学与工程学报,2015,12(1):137 − 144. [LI Xiping,YANG Junsheng,WANG Lichuan,et al. Research on rheological tests and constitutive models of tuff in trigeminy tunnels[J]. Journal of Railway Science and Engineering,2015,12(1):137 − 144. (in Chinese with English abstract) doi: 10.19713/j.cnki.43-1423/u.2015.01.022 LI Xiping, YANG Junsheng, WANG Lichuan, et al. Research on rheological tests and constitutive models of tuff in trigeminy tunnels[J]. Journal of Railway Science and Engineering, 2015, 12（1）: 137 − 144. （in Chinese with English abstract） doi: 10.19713/j.cnki.43-1423/u.2015.01.022