Application of stochastic limit analysis to geotechnical stability problems

Soil is a highly heterogeneous natural material with properties varying from point to point, in contrast to engineered materials like steel and concrete. The variability or uncertainty that exists in characterising the soil properties is usually taken into account by a generous factor of safety in engineering design. Concern has been expressed over the implicit use of a factor of safety alone, due to its inability to explicitly account for soil variability. Therefore, probabilistic methods are required, which can deal with this uncertainty in a systematic manner, and pave the way for more reliable and realistic design approaches. A number of probabilistic approaches have been proposed to analyse the reliability of geotechnical structures. However, the combination of random fields and a deterministic method for stability analysis within a Monte-Carlo framework is being increasingly used for probabilistic stability analysis. Amongst such methods, the Random Finite Element Method (RFEM) is very prominent and has been used extensively in recent times. RFEM combines random field theory with the non-linear finite element method (FEM). However, FEM itself is not the optimum approach for assessing stability. In contrast, finite element limit analysis (FELA) is a superior alternative to predict the collapse state of geotechnical structures in a direct and cost-effective manner. Although FELA has been combined with random fields for stochastic stability assessment recently, the use of adaptive remeshing has still not been considered. For deterministic scenarios, adaptive FELA has been successfully employed to accurately and efficiently assess the collapse state of geotechnical structures. Furthermore, the use of adaptive remeshing absolves the need to evaluate a suitable mesh configuration for complex geometries and is thus more practical. Therefore, the principal aim of this research is to combine adaptive FELA with random fields, as a general tool for stability assessment of geotechnical structures on spatially variable soils. The new technique has then been applied for reliability assessment of footings and tunnels, to gain valuable insights about the influence of spatial variability on these structures.