复合地基极限承载力的变分极限平衡法分析——竖向增强  

Variational limit equilibrium method analysis of ultimate bearing capacity of composite foundation:vertical reinforcement

作　　者：周志雄 周凤玺[1,2] 曹小林[1] 汪镇 ZHOU Zhi-xiong;ZHOU Feng-xi;CAO Xiao-lin;WANG Zhen(School of Civil Engineering,Lanzhou University of Technology,Lanzhou,Gansu 730050,China;Western Engineering Research Center of Disaster Mitigation in Civil Engineering of Ministry of Education,Lanzhou University of Technology,Lanzhou,Gansu 730050,China;CCCC First Highway Fifth Engineering Co.Ltd.,Beijing 100024,China)

机构地区：[1]兰州理工大学土木工程学院,甘肃兰州730050 [2]兰州理工大学西部土木工程防灾减灾教育部工程研究中心,甘肃兰州730050 [3]中交一公局第五工程有限公司,北京100024

出　　处：《岩土力学》2024年第12期3748-3754,3778,共8页Rock and Soil Mechanics

基　　金：国家自然科学基金(No.12362032,No.51978320);甘肃省重点研发计划(No.23YFFA0063);甘肃省优秀博士生项目(No.24JRRA209)。

摘　　要：基于变分极限平衡法,对设置竖向增强体的复合地基极限承载力开展了理论研究。首先,以竖向增强体复合地基中滑动土体的静力学平衡方程为基本方程,结合变分原理建立了地基极限承载力泛函极值的等周约束模型。在此基础上,利用欧拉方程得到了以潜在滑动面、滑面上法向正应力以及拉格朗日乘子等为基本未知量的控制方程,并通过引入辅助变量将可动边界转化为固定边界。最后,利用打靶法对该耦合的两点边值问题进行了数值求解,得到了问题的精确解答,并与复合地基设计中简化的等效强度指标法进行了比较,且分析了置换率、增强体黏聚力和内摩擦角对地基极限承载力的影响。数值分析结果表明,简化的等效强度指标法可以有效分析竖向增强复合地基极限承载力。Based on the variational limit equilibrium method,the ultimate bearing capacity of composite foundation with vertical reinforcement is studied.Firstly,based on the static equilibrium equation of sliding soil in composite foundation with vertical reinforcement and combined with the variational principle,an isoperimetric constraint model for the functional extremum of the ultimate bearing capacity of foundation is established.On this basis,the control equations with potential sliding surface,normal stress on sliding surface,and Lagrange multiplier as basic unknowns are obtained using the Euler equation,and the movable boundary is transformed into a fixed boundary by introducing auxiliary variables.Finally,the shooting method is used to numerically solve the coupled two-point boundary value problem,obtaining an accurate solution and comparing it with the simplified equivalent strength index method in composite foundation design.Simultaneously,the numerical examples are used to analyze the effects of displacement rations,reinforcement cohesion,and internal friction angle on the ultimate bearing capacity of the foundation.The numerical results show that the simplified equivalent strength index method can effectively analyze the ultimate bearing capacity of composite foundation with vertical reinforcement.

关 键 词：复合地基 竖向增强体 极限承载力 变分极限平衡法 打靶法 

分 类 号：TU432[建筑科学—岩土工程]