非均质与各向异性黏土基坑抗隆起稳定分析

经典的Prandtl 机构不能很好地反映支护结构入土深度的影响，也不能反映土体强度非均质和各向异性的影响。根据塑性极限分析上限定理，基于修正的Prandtl机构，推导了既可以合理反映支护结构入土深度影响，又可以反映土体强度非均质和各向异性特性的基坑抗隆起稳定的上限解公式，同时基于商业化程序的二次开发，建立了可以考虑土体强度非均质和各向异性影响的强度折减弹塑性有限元方法。通过提出的修正Prandtl机构上限解与强度折减有限元方法以及多块体上限解的对比，验证了修正机构上限解以及强度折减有限元法的合理性和可行性，最后讨论了非均质系数、各向异性系数、支护机构入土深度等因素对基坑抗隆起稳定性的影响，并通过了实例的验证，相关结论可供工程参考。

Analysis for basal stability of braced excavation in nonhomogeneous and anisotropic clay

The classical Prandtl mechanism could not reflect the effects of inserted depth of wall penetration well and has limitation to reflect the effects of the nonhomogeneity and anisotropy of the clay. An improved analytical formula based on a modified Prandtl mechanism is given, which obeys the upper bound theorem of plastic limit analysis. This formula could reflect the effects of inserted depth of wall penetration well, and the effects of the nonhomogeneity and anisotropy of the clay could also be considered. In the meantime, considering the effects of the nonhomogeneity and anisotropy of the clay, a shear strength reduction finite element method (SSRFEM) is developed through the secondary development of commercialized software. The reasonability and reliability of the proposed modified mechanism and SSRFEM are verified by compared with the multi-block upper bound method. And the formula which is verified by a case study can give proper safety factors considering the influence of inserted depth of wall penetration, nonhomogeneity and anisotropy. Related conclusions can bring references for excavation designs.