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

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

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
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- 被引次数: 0
出版历程
- 收稿日期: 2022-08-22
- 修回日期: 2022-11-28
- 网络出版日期: 2023-08-06
- 刊出日期: 2023-09-19

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

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

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图 1 边坡锚固系统受力机理与位移协调示意图

Figure 1. Sketch map of loading mechanism and displacement compatibility of the anchorage system used to reinforce slopes

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图 2 锚索结构-边坡体系的整体串联流变模型

　　注：E_a1、E_a2分别为坡面抑制构件、锚索的弹性模量；E_h1、E_h2分别为自由段滑体和锚固段地层岩土体的瞬时弹性模量，反映了其在外力作用下的瞬时弹性效应；E_k1、E_k2分别为自由段滑体和锚固段地层的滞后弹性模量，反映了其在外力作用下的滞后弹性效应；η₁、η₂分别为自由段滑体和锚固段地层的黏滞系数；P为锚索拉力。

Figure 2. General series rheological model for prestressed anchor cable-slope system

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图 3 模型布置示意图（单位：cm）^[10]

Figure 3. Model layout diagram (unit: cm)^[10]

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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. Comparison of the measured and calculated values of anchor cable tension in laboratory model test

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图 5 现场多点位移计布设示意图^[15]

Figure 5. Layout diagram of multi-point displacement meters^[15]

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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. Comparison of the measured and calculated values of cable tension of intact rock high slope

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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. Comparison of the measured and theoretical calculation of anchor cable tension in a high slope with broken rock

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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. Comparison between the measured and theoretical calculation of anchor cable tension in a high accumulation slope

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图 9 锚索拉力松弛率随锚索直径变化曲线

Figure 9. Variation of anchor tension relaxation rate with the diameter

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图 10 锚索拉力松弛率随锚孔间距变化曲线

Figure 10. Variation of anchor tension relaxation rate with anchor hole spacing

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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. Variation of anchor tension relaxation rate with the elastic modulus

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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. Variation of anchor tension relaxation rate with rheological parameters of a stable layer

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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. Curve of cable tension relaxation rate vs elastic modulus of slope restraint

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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. Variation of anchor tension relaxation rate with rheological parameters of potential slide mass

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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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