Semi-analytical study on mechanical model of vertical shaft surrounding rock reinforcement considering the lagging support of anchor bolts

ZHANG Ji-wei; ZHANG Jia-xin; MA Wen-zhuo; JIA Hong-xue; WU Wei-dong; WANG Chuan-bao

doi:10.16285/j.rsm.2024.1508

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Semi-analytical study on mechanical model of vertical shaft surrounding rock reinforcement considering the lagging support of anchor bolts

更新时间：2026-06-25

- Semi-analytical study on mechanical model of vertical shaft surrounding rock reinforcement considering the lagging support of anchor bolts
- Vol. 46, Issue 11, Pages: 3395-3409(2025)
- 作者机构：
  
  1. 北京科技大学资源与安全工程学院,北京,100013
  2. 中国建筑第八工程局有限公司,上海,200120
  3. 中建八局天津建设工程有限公司,天津,300450
  4. 新疆兵团水利水电工程集团有限公司,新疆,乌鲁木齐,830000
  5. 新疆兵团勘测设计院集团股份有限公司,新疆,乌鲁木齐,830000
- 作者简介：
- 基金信息：
- DOI：10.16285/j.rsm.2024.1508
  CLC： TU45
- Online First：11 November 2025，
  
  Published：11 November 2025
- 稿件说明：
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ZHANG Ji-wei, ZHANG Jia-xin, MA Wen-zhuo, et al. Semi-analytical study on mechanical model of vertical shaft surrounding rock reinforcement considering the lagging support of anchor bolts[J]. 2025, 46(11): 3395-3409.
DOI：

ZHANG Ji-wei, ZHANG Jia-xin, MA Wen-zhuo, et al. Semi-analytical study on mechanical model of vertical shaft surrounding rock reinforcement considering the lagging support of anchor bolts[J]. 2025, 46(11): 3395-3409. DOI： 10.16285/j.rsm.2024.1508.

摘要

中国西部地区的能源开发项目，需要在稳定性较差的弱胶结砾石层中建设大量竖井。锚杆支护是控制围岩变形的重要手段。然而，目前的锚杆加固理论大都忽略了锚杆的滞后支护。为此，基于工作面的空间约束效应、弹塑性理论和锚杆应力均布法，提出了考虑锚杆滞后支护的竖井锚杆围岩变形和应力半解析计算方法，而后通过有限单元法验证了其正确性。基于所提出的半解析解，进一步探讨了锚杆参数的影响性。研究结果表明：锚杆滞后距离越大，围岩变形越大，锚杆等支护结构所承受的围岩压力越小，当锚杆滞后支护距离xgs＜1.5rA（rA为竖井开挖半径）时，围岩变形ur（r=rA，r为围岩中任何一点的半径）及安全系数s变化较大，当锚杆滞后支护距离xgs＞3.0rA时，围岩变形ur(r=rA)及安全系数s基本不变；增大锚杆直径可提高抗剪强度但影响逐渐减小；当锚杆长度L＜1.0rA时，围岩变形ur(r=rA)及安全系数s变化较大，当锚杆长度L＞1.0rA时，则变化缓慢，因此不建议过度使用长锚杆。研究指出，在选择支护参数时，需考虑支护滞后距离以确保围岩稳定。本研究将该理论成功应用于压力管道竖井工程中，研究成果为竖井围岩的锚杆支护设计提供了坚实的理论依据。

Abstract

The energydevelopment projects in western China require the construction of a largenumber of vertical shafts in weakly cemented gravel layers with poor stability.Anchor rod support is an important means of controlling the deformation ofsurrounding rock. However

most of the current theories on anchor reinforcementhave overlooked the lagging support of anchor rods. Therefore

based on thespatial constraint effect of the working face

elastic-plastic theory

and theanchor rod stress uniform distribution method

this study proposes asemi-analytical calculation method for the deformation and stress of thesurrounding rock of vertical shaft anchor bolts considering the lag support ofanchor bolts. The correctness of this method was verified by finite elementmethod. Based on the proposed semi analytical solution

the influence of anchorparameters was further explored. The research results show that the larger thelag distance of the anchor rod

the greater the deformation of the surroundingrock

and the smaller the surrounding rock pressure borne by the anchor rod andother supporting structures. When the lag distance of the anchor rod is less than 1.5 ( represents the excavation radius of the vertical shaft)

the deformation (=)and safety factor of the surrounding rock change greatly. When the lagdistance of the anchor rod is greaterthan 3.0

the deformation (=)and safety factor of the surrounding rock remain basically unchanged.Increasing the diameter of the anchor rod improves the shear strength

but theimpact gradually decreases. When the length of the anchor rod is less than 1.0

the deformation of the surrounding rock (=)and the safety factor change greatly. When the length of the anchorrod is greater than 1.0

the change is slow

so itis not recommended to excessively use long anchor rods. Research suggests thatwhen selecting support parameters

consideration should be given to the supportlag distance to ensure the stability of the surrounding rock. This studysuccessfully applied this theory to the vertical shaft engineering of pressurepipelines

and the research results providea solid theoretical basis for the design of anchor rod support for thesurrounding rock of the vertical shaft.

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