Displacement-Based Back-Analysis Frameworks for Soil Parameters of a Slope: Using Frequentist Inference and Bayesian Inference
Yibiao Liu, Weizhong Ren, Chenchen Liu, Simin Cai, Wenhui Xu
Abstract
The displacement-based back-analysis is an effective approach to determine the values of soil parameters of a slope. However, the applicability of different methods of the displacement-based back-analysis varies. This paper divides the displacement-based back-analysis into the deterministic back-analysis under frequentist inference and the probabilistic back-analysis under Bayesian inference. A framework for the deterministic back-analysis is proposed using the maximum likelihood estimation, which is a typical method of frequentist inference. In the framework for the deterministic back-analysis, the dual annealing (DA) algorithm is applied to search for the globally optimal solution. A framework for the probabilistic back-analysis considering spatial variability is proposed based on the Bayesian theory, random field theory, and truncated Karhunen–Loève expansion (KLE), which overcome the “curse of dimensionality.” It is explained that this framework will also work in the probabilistic back-analysis based on the random variable model. In the two frameworks, metamodels are constructed by gradient boosting decision trees (GBDT). This algorithm perfectly fits the relationship between parameters and displacements of a slope, which replaces the time-consuming finite-element simulations. The adaptability of the two proposed frameworks is illustrated with a real case study of a highway slope. The case study also proves that the fitting accuracy of metamodels constructed by the GBDT algorithm is higher than those constructed by the neural network (NN) and the random forests (RF). Processes of frequentist inference and Bayesian inference show that the difference in their results originates from the different perceptions of the parameter space. However, the two different back-analysis results are not in competition but should be complementary. They both play an important role in slope parameter determination and slope stability analysis.