基于复变理论的不同断面巷道围岩塑性区演化特征及支护优化

doi:10.3724/1000-6915.jrme.2025.0965

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摘要为研究主应力方向偏转对围岩塑性区形态及尺寸的影响，采用复变函数保角映射方法，在远场应力中引入主应力偏转角（?），推导不同侧压力系数（?）和?作用下圆形、椭圆形、矩形及直墙半圆拱形4种断面巷道边壁环向应力解，揭示不同断面围岩环向应力分布规律。基于Mohr-Coulomb强度准则，建立围岩塑性区边界隐式方程，分析不同?和?组合下4种断面塑性区形态与尺寸的演化特征，并通过数值模拟验证了理论计算结果。结果表明：（1）?主导巷道边壁环向应力的分布形态与应力集中位置，?使应力场发生定向旋转，破坏应力分布的对称性。含有几何拐点或曲率突变的非圆形断面，对主应力方向变化更为敏感，易产生局部应力集中。（2）围岩塑性区演化可归纳为六类典型形态。?控制塑性区的基本扩展类型，?决定塑性区的偏转方向，两者共同决定塑性区的最终扩展形态、范围及方位。（3）最大塑性区半径（Rpmax）对主应力方向变化的敏感性受断面形态影响显著，圆形和椭圆形断面呈弱敏感性，矩形和直墙半圆拱形断面呈强角度依赖性，且受?影响较大。基于上述围岩塑性区演化特征，提出“长短锚杆索协同+钢筋网喷联合+浅层注浆加固”的靶向支护方案，并以红庆梁煤矿11302回风巷为工程背景，验证了该方案的可靠性。

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	刘家顺1
	2*
	王思宇1
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	左建平2
	郑智勇1
	贾宝新1

关键词 ：采矿工程, 主应力方向, 侧压力系数, 复变函数, 巷道断面, 围岩塑性区

Abstract：To investigate the effects of rotation of the principal stress direction on the morphology and size of the plastic zone in surrounding rock, a conformal mapping method based on complex variable theory was adopted. The principal stress rotation angle ? was introduced into the remote stress field, and analytical solutions for the circumferential stress at the boundaries of four roadway sections, namely circular, elliptical, rectangular, and straight wall semicircular arch sections, were derived under different lateral pressure coefficients ? and principal stress rotation angles ?. The circumferential stress distribution in the surrounding rock of different roadway sections was then investigated. Based on the Mohr-Coulomb strength criterion, an implicit equation for the boundary of the plastic zone in surrounding rock was established. The evolution of the morphology and size of the plastic zone for the four roadway sections under different combinations of ? and ? was analyzed, and the theoretical results were verified by numerical simulation. The results show that: (1) ? governs the distribution pattern of circumferential stress and the locations of stress concentration at the roadway boundary, whereas ? causes directional rotation of the stress field and breaks the symmetry of the stress distribution. Noncircular sections with geometric corners or abrupt changes in curvature are more sensitive to changes in the principal stress direction and are more prone to local stress concentration. (2) The evolution of the plastic zone in surrounding rock can be classified into six typical morphologies. ? controls the basic propagation pattern of the plastic zone, whereas ? determines its deflection direction. Their combined effects determine the final propagation morphology, extent, and orientation of the plastic zone. (3) The sensitivity of the maximum plastic zone radius Rpmax to changes in the principal stress direction is significantly affected by the roadway section shape. Circular and elliptical sections show relatively low sensitivity, whereas rectangular and straight wall semicircular arch sections exhibit a strong dependence on the principal stress rotation angle and are also strongly affected by ?. Based on these evolution characteristics of the plastic zone, a targeted advance support scheme integrating coordinated long and short bolts and cables, steel mesh and shotcrete, and shallow grouting reinforcement was proposed. The 11302 return airway of Hongqingliang Coal Mine was used as an engineering case to verify the reliability of the proposed support scheme.

Key words： mining engineering principal stress direction lateral pressure coefficient complex variable function roadway cross-section plastic zone in surrounding rock

引用本文:

刘家顺1，2*，王思宇1，2，左建平2，郑智勇1，贾宝新1. 基于复变理论的不同断面巷道围岩塑性区演化特征及支护优化[J]. 岩石力学与工程学报, 2026, 45(11): 3386-3402.
LIU Jiashun1, 2*, WANG Siyu1, 2, ZUO Jianping2, ZHENG Zhiyong1, JIA Baoxin1. Evolution characteristics of the plastic zone in surrounding rock for different cross-sectional shapes via complex variable theory and support optimization. , 2026, 45(11): 3386-3402.

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https://rockmech.whrsm.ac.cn/CN/10.3724/1000-6915.jrme.2025.0965 或 https://rockmech.whrsm.ac.cn/CN/Y2026/V45/I11/3386

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