The aim of this study is to investigate the applicability of reliability theory on surface square/rectangular footing against bearing capacity failure using fuzzy set theory in conjunction with the finite element method. Soil is modeled as a three-dimensional spatially varying medium, where its parameters (cohesion, friction angle, unit weight, etc.) are considered as fuzzy variables that maintain some membership functions. Soil is idealized as an elastic-perfectly plastic material obeying the Mohr-Coulomb failure criterion, where both associated and non-associated flow rules are considered in estimating the ultimate bearing capacity of the footing. The spatial variability of the soil is incorporated for both isotropic and anisotropic fields, which are determined by the values of scales of fluctuation in both the horizontal and vertical directions. A new parameter namely, limiting applied pressure at zero failure probability is proposed, and it indirectly predicts the failure probability of the footing. The effect of the coefficient of variation of the friction angle of the soil on the probability of failure is analyzed, and it is observed that the effect is significant. Furthermore, the effect of the scale of fluctuation on the probability of failure is investigated, and the necessity for considering spatial variability in the reliability analysis is well proven.

这项研究的目的是结合模糊集理论和有限元方法，研究可靠度理论在表面正方形/矩形基础上对承载力破坏的适用性。土壤被建模为三维空间变化的介质，其中的参数（内聚力，摩擦角，单位重量等）被视为保持某些隶属函数的模糊变量。遵循Mohr-Coulomb破坏准则，理想地将土壤作为一种具有弹性的完美塑性材料，在评估基础的最终承载力时，应同时考虑关联流规则和非关联流规则。对于各向同性和各向异性场，都考虑了土壤的空间变异性，这由水平和垂直方向上的波动尺度值决定。提出了一个新的参数，即以零失效概率限制施加压力，它可以间接预测立足点的失效概率。分析了土壤摩擦角的变化系数对破坏概率的影响，发现该影响是显着的。此外，研究了波动幅度对失效概率的影响，并充分证明了在可靠性分析中考虑空间变异性的必要性。