基于六方向贯通式间断线网格的边坡稳定性上限分析  

Upper bound analysis of slope stability based on a six-directionthrough-type discontinuity mesh configuration

作　　者：范佳志 秦傲韩 杨峰[2] 杨鹰[2] 赵炼恒[2] 高益康 FAN Jiazhi;QIN Aohan;YANG Feng;YANG Ying;ZHAO Lianheng;GAO Yikang(Yichun Luming Mining Co.,Ltd.,Yichun 152500,China;School of Civil Enginering,Central South University,Changsha 410075,China)

机构地区：[1]伊春鹿鸣矿业有限公司,黑龙江伊春152500 [2]中南大学土木工程学院,湖南长沙410075

出　　处：《自然灾害学报》2025年第2期110-120,共11页Journal of Natural Disasters

基　　金：湖南省杰出青年基金项目(2021JJ10063);伊春鹿鸣矿业有限公司科技项目(LM(2022)-F-045);中南大学中央高校基本科研业务费专项(2024ZZTS0752)。

摘　　要：边坡潜在滑动面可应用极限分析上限有限元方法,以“常应变率三角形单元及速度间断线”网格模式搜索获取,由此速度间断线的排布方式,成为影响边坡稳定性计算精度的重要因素。文中构思一种六方向贯通式速度间断线排布策略,提出对应三角网的生成流程并编程实现,作为自有上限有限元分析程序的前处理模块。经边坡稳定性算例验证表明:六方向贯通式间断线网格布局,以契合关键边界的多次一分为四及末次一分为六背景网格生成方式,不仅实现整个模型的大区域六方向间断线通路,又能在边坡坡脚处体现出多方向发散特性的网格。提出的模型非关键边界背景网格切割算法,可以局部分割新生单元的方式契合边界,维持边界处网格的六方向间断线通路特性。对于“常应变率三角形单元及速度间断线”网格离散模式,六方向贯通式间断线网格布局,较之三方向贯通及Delaunay三角剖分的情况,能更好地发挥速度间断线的效用,明显提高边坡稳定性问题的计算精度。六方向贯通式间断线网格布局,还可以结合高阶变形单元、网格自适应等措施,扩展其应用范围。The potential sliding surface of the slope can be searched and obtained by the upper-bound finite element method(UBFEM)with the mesh discretization of“constant strain rate triangular elements and velocity discontinuities”.Consequently,the arrangement of velocity discontinuities becomes a crucial factor affecting the calculation accuracy of slope stability.This paper proposes a six-direction through-type velocity discontinuity topology scheme,develops the corresponding triangular mesh generation process with programming implementation,and integrates it as a pre-processing module for an in-house UBFEM program.Slope stability case verifications demonstrate that the six-direction through-type discontinuity mesh configuration,generated through multiple quadri-section operations along key boundaries and a final hexa-section operation,not only achieves six-direction discontinuity pathways across large computational domain but also forms meshes with divergence characteristics along several directions at slope toes.The proposed interactive mesh-cutting algorithm can adaptively match boundaries through local subdivision of new elements while maintaining six-direction discontinuity pathway at boundaries.For the“constant strain rate triangular elements and velocity discontinuities”discretization,the six-direction through-type discontinuity mesh configuration demonstrates superior performance in incorporating velocity discontinuity compared with three-direction through-type discontinuity mesh configuration and Delaunay mesh configuration,significantly improving calculation accuracy for slope stability problems.The six-direction through-type discontinuity mesh configuration can be further extended through integration with higher-order six-node elements and adaptive mesh refinement,broadening its application scope.

关 键 词：边坡稳定性 上限有限元方法 速度间断线 六方向贯通式间断线 网格拓扑结构 交互网格切割 

分 类 号：TU4[建筑科学—土工工程]