Random adaptive finite element limit analysis (RAFELA) is introduced to investigate the stability of the footing-voids system with random soils. The emphasis of this study is, for the footing-void system, on quantifying the influence of spatial variability on its bearing capacity and the failure probability. Of particular interest is that random field theory is utilized to characterize the spatial variability of soil, and at the same time, failure probability is calculated by imposing Monte-Carlo simulations on independent cases. Strict close bearing capacity could be obtained within the scope embraced by upper bound (UB) results and lower bound (LB) results. By imposing the proposed modelling, comprehensive parametric studies were carried out, especially for the soil spatial correlation parameters and geometry parameters. The results indicated that the failure probability would increase with the farther distance between the void and the footing, the greater coefficient of variation (COV) and the smaller vertical correlation length. Detailed design tables were presented to assess potential failure probability under different conditions. Typical failure patterns are also summarized, revealing a positive correlation between the failure probability and the diffusion degree of failure curves.

引入随机自适应有限元极限分析（RAFELA）来研究具有随机土壤的基础空洞系统的稳定性。对于立足空隙系统，这项研究的重点是量化空间变异性对其承载力和失效概率的影响。特别令人感兴趣的是，利用随机场理论来表征土壤的空间变异性，同时，通过对独立案例施加蒙特卡洛模拟来计算破坏概率。在上限（UB）结果和下限（LB）结果所涵盖的范围内，可以获得严格的封闭承载力。通过强加建议的建模，进行了全面的参数研究，尤其是对于土壤空间相关参数和几何参数。结果表明，失效概率将随着空隙与桩基之间的距离越远，变异系数（COV）越大和垂直相关长度越小而增加。提出了详细的设计表，以评估在不同条件下的潜在故障概率。还总结了典型的故障模式，揭示了故障概率与故障曲线扩散程度之间的正相关关系。