基于光滑有限元法的岩土体弹塑性分析  

Elastoplastic analysis of rock and soil masses based on smooth finite element method

作　　者：杨茂强 张江辉 王永伟 吕加贺 YANG Maoqiang;ZHANG Jianghui;WANG Yongwei;LÜJiahe(CCCC Second Harbor Engineering Co.,Ltd.No.5 Branch,Wuhan 430050,China;School of Engineering,China University of Geosciences(Wuhan),Wuhan 430074,China)

机构地区：[1]中交第二航务工程局有限公司第五工程分公司,武汉430050 [2]中国地质大学(武汉)工程学院,武汉430074

出　　处：《地质科技通报》2025年第2期330-339,共10页Bulletin of Geological Science and Technology

基　　金：国家自然科学基金项目(52278379)。

摘　　要：随着大型工程项目的日益增多,工程中的岩土极限问题也频繁出现,致使采用数值方法处理时,经常面对极端的模型变形问题。传统有限元法在处理极端的模型变形,特别是采用低阶单元分析时,往往会产生收敛问题、体积锁定问题以及网格严重畸变而导致的应力失准问题。寻找一种新的方法进行数值分析具有重要意义。光滑有限元法是一种有效改进传统有限元法固有缺陷,提高求解精度和收敛速度的算法。基于光滑有限元法,结合一种修正的Mohr-Coulomb屈服准则和线性搜索优化算法,建立了岩土体弹塑性计算模型。最后,针对经典的条形基础承载力模型和边坡模型进行验算,数值计算结果与参考解均吻合较好。结果表明光滑有限元法的计算精度明显优于传统有限元法,验证了本研究算法的可行性和实用性。本研究采用光滑有限元法建立的计算模型进一步提高了岩土体弹塑性问题的计算精度,降低了采用传统有限元法分析时存在的计算误差及网格畸变引起的应力失准问题。[Objective]With the increasing number of large engineering projects,geotechnical limit problems are becoming more common,often leading to extreme model deformation when numerical methods are employed.The traditional finite element method frequently encounters convergence issues,volume locking,and stress misalignment due to severe mesh distortion during the analysis of extreme model deformation,especially when loworder elements are used.Therefore,developing a new method for numerical analysis is of great importance.[Methods]The smooth finite element method is an effective approach to address the inherent defects of the traditional finite element method,enhancing both solution accuracy and convergence speed.Thus,based on the smooth finite element method combined with a modified Mohr-Coulomb yield criterion and a linear search optimization algorithm,an elastoplastic calculation model for rock and soil masses is developed in this study.[Results]The classical bearing capacity model for the strip foundation and slope model was tested,and the numerical results align well with the reference solutions.The findings indicate that the calculation accuracy of the smooth finite element method is clearly superior to that of the traditional finite element method,confirming the feasibility and practicality of the proposed algorithm.[Conclusion]In this work,the calculation model developed using the smooth finite element method significantly improves the calculation accuracy for rock and soil elastoplastic problems,while reducing the calculation error and stress misalignment caused by mesh distortion in traditional finite element methods.

关 键 词：光滑有限元法 弹塑性 岩土体 修正Mohr-Coulomb屈服准则 线性搜索 

分 类 号：TU4[建筑科学—土工工程]