基于极限平衡法与极限分析法等效性的地基承载力系数N_γ的上限解

针对地基承载力系数Nγ真实解答尚未获得的现状,提出一种计算Nγ上限解的数值计算方法。在论证极限平衡法与极限分析法等效性的基础上,采用一组三角条块逼近满足机动许可的潜在破坏机构,通过极限平衡法建立条间力的递推公式,依据推力最大原理优化条块底线的倾角,得到最危险破坏机构及对应的地基承载力系数Nγ的上限数值解,进而分析地表倾斜情况下的Nγ及其修正方法;最后,为了便于工程应用,给出Nγ及地表倾斜修正系数ξγ的近似表达式。通过与已有研究成果的比较,验证该方法的合理性。研究表明:该方法计算过程简单易于编程实现,能够得到相对小的上限解。研究成果可用于地基承载力的理论分析,为深入研究地基承载力系数Nγ提供参考。

THE UPPER-BOUND SOLUTION FOR BEARING CAPACITY FACTOR OF BY EMPLOYING THE EQUIVALENCE OF LIMIT ANALYSIS AND LIMIT EQUILIBRIUM METHOD

An approach for evaluating the upper-bound for bearing capacity factor Nγ was presented.The equivalence of limit analysis and limit equilibrium method was analyzed,and then a kinematical admissible failure mechanism,which was composed of a sequence of rigid triangles,was considered in the framework of limit equilibrium method.The recursion formula of inter-slice force was deduced according to the force equilibrium conditions of slice,and optimal bottom inclination of each triangle also was obtained by employing the principle of maximum thrust force.Therefore,the critical failure mechanism and corresponding Nγ value were obtained.Then,the influence of inclined ground surface on Nγ value was discussed.These solutions,presented in the form of graphs,were compared against existing semi-empirical expressions and numerical solutions.Finally,approximate analytical expressions for Nγ and ξγ(correction factor of inclined ground surface) were suggested.The present method,which was of simple principle and could be readily implemented into computer software,could solve a lower Nγ value than other's the upper-bound solutions.The study results could be used in theoretical analysis of bearing capacity and provideed some beneficial references for further research on Nγ.