Theoretical solutions of geotechnical engineering problems are generally based on simplifying assumptions about soil homogeneity and isotropy. In reality, soil masses are usually both anisotropic and heterogeneous in situ and thus, the effects of soil deposition orientation and stratification should be taken into account. In this context, the present paper describes a contribution towards a general probabilistic limit analysis of geotechnical stability problems dealing with clays having inherent spatial variability and anisotropy of the undrained shear strength simultaneously. The static lower-bound theorem in conjunction with the finite element method and mathematical programming are utilized to provide limit analysis approach. Anisotropy of clay is imposed by the application of an iterative scheme and, its spatial variability has been considered via the application of random field theory. Based on the proposed method, the bearing capacity of a strip footing and the stability of a square tunnel have been investigated and the effects of simultaneous consideration of non-homogeneity and anisotropy of soil’s shear strength on collapse load have been studied.

岩土工程问题的理论解决方案通常基于简化的关于土壤均质性和各向同性的假设。实际上，土壤质量通常既是各向异性的又是非均质的，因此，应考虑土壤沉积取向和分层的影响。在这种情况下，本论文描述了对岩土工程稳定性问题的一般概率极限分析的贡献，该问题涉及同时具有固有空间变异性和不排水抗剪强度各向异性的粘土。静态下界定理与有限元方法和数学编程相结合，提供了极限分析方法。粘土的各向异性是通过应用迭代方案来实现的，通过应用随机场理论已经考虑了其空间变异性。在此基础上，研究了条形基础的承载力和方型隧道的稳定性，研究了同时考虑非均质性和土的抗剪强度各向异性对破坏荷载的影响。