﻿ 水平主应力对锚杆锚固区力学特征影响规律研究
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 哈尔滨工程大学学报  2019, Vol. 40 Issue (6): 1102-1108  DOI: 10.11990/jheu.201804114 0

### 引用本文

TAO Wenbin, CHEN Tielin, TANG Bin. Response law of horizontal principal stress to the mechanical characteristics of anchorage zones[J]. Journal of Harbin Engineering University, 2019, 40(6), 1102-1108. DOI: 10.11990/jheu.201804114.

### 文章历史

1. 北京交通大学 土木建筑工程学院, 北京 100044;
2. 安徽理工大学 土木建筑学院, 安徽 淮南 232001

Response law of horizontal principal stress to the mechanical characteristics of anchorage zones
TAO Wenbin 1, CHEN Tielin 1, TANG Bin 2
1. School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China;
2. School of Civil Engineering and Architecture, Anhui University of Science and Technology, Huainan 232001, China
Abstract: The design of the surrounding rock anchorage of roadway supports under different horizontal principal stresses is unsatisfactory. The numerical simulation, theoretical analysis, and field test conducted in this work show that the stress of the surrounding rock in the anchorage area of a roadway is moderate when the angle between the direction of the maximum horizontal principal stress and the axial of the roadway ranges from 0° to 30°. The maximum horizontal principal stress is transferred to the roof and floor of the roadway with the increase in angle when the angle exceeds 30°. Thus, the range and degree of stress concentration in the roof and floor are significantly increased. The axial force of the nonanchoring section is equal, the axial force of the anchorage section negatively exponentially decreases, and the curve is "乀"-shaped. The axial force of the bolt increases as the angle is increased. The axial force of the roof bolt is positively correlated with the angle. Axial force increases with the increase in the angle. The axial force of the roof bolt gradually increases when the angle falls in the ranges of 0°~30° and 70°~90° and drastically increases when the angle falls in the range of 30°~60°. The axial force of the sidewall bolt is negatively correlated with the angle. The shape of the axial force distribution curves of the bolt changes to concave, mouth-shaped, and convex with the increase in the angle.
Keywords: horizontal principal stress    tunnel direction    surrounding rock stress    anchor system    axial force of bolt    bolt support    support optimization    surrounding rock stability

1 潘三矿巷道概况和数值模拟模型 1.1 工程背景

1.2 数值计算模型及方案

 Download: 图 1 模型示意 Fig. 1 Schematic diagram of model

 $\begin{array}{l} \left[ {\begin{array}{*{20}{l}} {{p_x}}&{{p_{xy}}}&{{p_{xz}}}\\ {{p_{yx}}}&{{p_y}}&{{p_{yz}}}\\ {{p_{zx}}}&{{p_{zy}}}&{{p_z}} \end{array}} \right] = \\ \left[ {\begin{array}{*{20}{c}} {{{\cos }^2}\alpha \cdot {\sigma _3} + {{\sin }^2}\alpha \cdot {\sigma _1}}&0{}&{ - \frac{1}{2}\sin (2\alpha )\left( {{\sigma _1} - {\sigma _3}} \right)}\\ 0&{{\sigma _2}}&0\\ { - \frac{1}{2}\sin (2\alpha )\left( {{\sigma _1} - {\sigma _3}} \right)}&0&{{{\cos }^2}\alpha \cdot {\sigma _3} + {{\sin }^2}\alpha \cdot {\sigma _1}} \end{array}} \right] \end{array}$
2 不同水平主应力下巷道锚固区力学变化规律 2.1 不同水平主应力巷道围岩应力分析

 Download: 图 2 不同夹角巷道顶底板水平集中应力分布曲线 Fig. 2 Horizontal concentrated stress distribution curve of roof and floor of different angle laneway

 Download: 图 3 不同夹角巷道两帮垂直集中应力分布曲线 Fig. 3 Vertical concentrated stress distribution curve of two sides in different angle roadway

 Download: 图 4 最大水平主应力方向巷道围岩应力分布 Fig. 4 Stress distribution of surrounding rock in roadway with different maximum horizontal principal stress
2.2 不同水平主应力锚杆锚固段轴力分析

 Download: 图 5 锚杆锚固系统 Fig. 5 Rock bolt and surrounding rock anchor system

 ${\tau ^{\prime \prime }} + rk{\tau ^\prime } + rk\tau = 0$ (1)
 $k = \frac{{4{\rm{ \mathsf{ π} }}G}}{{(3 - 2\mu ){E_a}A}}$ (2)

 $\tau = \frac{p}{{{\rm{ \mathsf{ π} }}b}}\left( {\frac{1}{2}tx} \right){{\rm{e}}^{\left( { - \frac{1}{2}t\frac{{{E_r}}}{{{E_a}}}{x^2}} \right)}}$ (3)

 $t = \frac{1}{{(1 - \mu )(3 - 2\mu ){b^2}}}$ (4)

 $p(x) = p - \int_{{x_1}}^x 2 \tau {\rm{ \mathsf{ π} }}b{\rm{d}}x = p{{\rm{e}}^{ - \frac{1}{2}t}}^{\left( {\frac{{{E_r}}}{{{E_a}}}} \right)\left( {x - {x_1}} \right)}$ (5)

 Download: 图 6 不同水平主应力方向巷道锚杆轴力分布 Fig. 6 Axial force distribution of roadway bolt with different horizontal principal stress

 Download: 图 7 不同水平主应力方向巷道锚杆分段轴力分布曲线 Fig. 7 Distribution curve of axial force distribution of roadway with different horizontal principal stress
2.3 相同夹角下不同位置锚杆轴力分布规律

2.4 不同夹角相同位置处锚杆轴力分布规律

 Download: 图 8 3#锚杆轴力分布 Fig. 8 Axial force distribution 3# bolt

 Download: 图 9 7#锚杆轴力分布 Fig. 9 Axial force distribution 7# bolt

3 锚杆支护优化设计

 Download: 图 10 现场实测锚杆轴力 Fig. 10 Field measurement of anchor force

 Download: 图 11 巷道顶板下沉量变化曲线 Fig. 11 Roadway roof displacement distribution
4 结论

1) 采用数值模拟得出顶、底板应力分布和应力集中程度及其与最大水平主应力方向变化规律。锚杆轴力与围岩最大水平主应力的方向有相关性，顶部锚杆轴力与夹角呈正相关，而帮部锚杆轴力与夹角呈负相关。

2) 锚杆自由段轴力相等，锚固段轴力沿着围岩内部呈负指数衰减。随着夹角的增大，巷道断面锚杆轴力分布曲线依次向“凹”、“口”、“凸”状演化。

3) 巷道掘进方位与最大水平主应力方向为小夹角的原则进行巷道布置；对于方位与最大水平主应力夹角较大的巷道，顶板与帮部支护参数应进行分类设计。

4) 对于强化顶板支护尤其是加强正顶附近的围岩支护，须加多项措施实现巷道围岩稳定性控制。支护顶板优先选用全长锚固支护方式、提高锚杆预紧力及锚杆杆材强度。

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