摘要
针对传统强度折减法中黏聚力与内摩擦角等比例折减的局限性,将强度折减最短路径理论与极限分析上限定理有效结合,构建基于MATLAB的高阶单元+间断线的上限有限元强度折减程序;结合马蹄形隧道围岩稳定性算例,揭示非等比例强度折减下,黏聚力c_(0)与内摩擦角ϕ_(0)折减比例及围岩破坏范围的演化规律。研究结果表明:所构建的强度折减上限解与极限分析软件OPTUM G2及既有文献结果吻合良好;折减路径长度平方值L^(2)与比例因子ξ=F_(c)/F_(ϕ)呈先降后升的3次函数关系,其极小值点对应围岩最不利失稳状态,印证最短路径强度折减理论的合理性;最短折减路径下,黏聚力折减幅度始终大于内摩擦角,但二者差异随隧道埋深增大而减小;隧道埋深增大导致拱脚处高耗散能区域更加集中,围岩综合安全系数下降5.64%~7.12%,局部失稳风险增加。研究结果可为隧道稳定性极限分析提供新思路。
To address the limitations of the traditional strength reduction method,which equivalent proportional reduction cohesion and internal friction angle,this study effectively combines the strength reduction shortest path theory with the upper bound theorem of limit analysis to develop a high-order element+discontinuous line upper bound finite element strength reduction program based on MATLAB.By applying this to a horseshoe-shaped tunnel surrounding rock stability example,the evolution of the reduction ratio of cohesion(c_(0))and internal friction angle(ϕ_(0))under non-proportional strength reduction,as well as the failure scope of surrounding rock is revealed.The results show that the upper bound solution of the strength reduction in this study aligns well with the limit analysis software OPTUM G2 and existing literature results.The square of the reduction path length(L^(2))and the proportional factorξ=F_(c)/F_(ϕ)exhibit a cubic function relationship,first decreasing and then increasing,with the minimum value corresponding to the most unstable state of the surrounding rock which confirms the validity of the shortest path strength reduction theory.Under the shortest reduction path,the reduction in cohesion is always greater than that of the internal friction angle,but the difference decreases with increasing burial depth.As tunnel burial depth increases,the high energy dissipation area at the arch foot becomes more concentrated,and the comprehensive safety factor of the surrounding rock decreases by 5.64%~7.12%,increasing the risk of local instability.This study can provide new insights for the limit analysis of tunnel stability.
作者
路喆津
周华龙
杨峰
黄鼎中
丁战恒
LU Zhejin;ZHOU Hualong;YANG Feng;HUANG Dingzhong;DING Zhanheng(Shenzhen Transportation&Municipal Engineering Design&Research Institute Co.,Ltd.,Shenzhen Guangdong 518003,China;Central South University,Civil Engineering School,Changsha Hunan 410075,China)
出处
《中国安全生产科学技术》
北大核心
2025年第6期168-174,共7页
Journal of Safety Science and Technology
基金
湖南省杰出青年科学基金项目(2021JJ10063)。
关键词
上限有限元
围岩稳定性
强度折减法
最短路径理论
破坏模式
upper bound finite element
surrounding rock stability
strength reduction method
shortest path theory
failure mechanism
作者简介
路喆津,硕士研究生,高级工程师,主要研究方向为道路工程设计与研究;通信作者:杨峰,博士,副教授,主要研究方向为隧道与地下工程相关研究。
