Bayesian inference of spatially varying parameters in soil constitutive models by using deformation observation data

Abstract

Parameters of soil constitutive models are usually identified through laboratory tests. The spatial variability of these parameters is generally not considered due to the limitation of the test scale. This study proposes a data-driven approach to infer the spatially varying parameter of the modified Cam-clay model from limited field observations and subsequently improves soil settlement predictions. The observation data and numerical results of random finite element method are assimilated in an inverse modeling process based on the iterative Ensemble Kalman filtering (iEnKF). Different unknown variables and number of observations are used to study their effects on parameter estimations and settlement predictions. The effectiveness of the proposed approach is illustrated through a synthetic partial-loading test. The results show that the site-specific spatial variability can be estimated reasonably, and predictions of settlement can be improved by using the inferred parameter field. When the variables to be inferred change from all 60 variables to the selected 17 important variables, the average error of the estimated fields increases, but the variance decreases. A reduction in the observation spacing and an increase in the number of observations lead to a slightly smaller error of the mean and considerably reduced uncertainties of soil parameters. Although the inferred results of parameter field show different accuracies, the corresponding calculated settlements are generally similar and satisfactory.

Identification of Nonlinear Soil Properties from Downhole Array Data Using a Bayesian Model Updating Approach

“…In this study, an unscented Kalman filtering (UKF) [28] method is used to update the unknown parameter vector at each iteration. While other methods, such as sampling techniques (e.g., particle filters, Markov chain Monte Carlo) or ensemble-based Kalman filters, can be used for uncertainty propagation and posterior PDF estimation (see, e.g., [29][30][31][32][33]), the UKF is employed here to reduce the computational costs, which could be cumbersome for large-scale problems. To do so, the nonlinear FE model is evaluated in parallel at a set of 2n ψ + 1 deterministically selected realizations of the unknown parameter vector around the prior mean estimate ψ− , which are called sigma points (SPs) and are denoted by ϑ j .…”

A bi‐fidelity inverse analysis method for deep excavations considering three‐dimensional effects

“…34 Ensemble Kalman filter (EnKF) is one of the commonly used ensemble-based data assimilation methods in geotechnical problems. 16,[35][36][37][38][39] Liu et al 36 updated the estimates of soil hydraulic parameter based on EnKF by using the time-series observations of pore water pressure. Ju et al 39 regarded the cone penetration test data as sequentially obtained and used them to estimate the soil total unit weight along the depth.…”

“…Ensemble‐based data assimilation methods have been widely used in inverse analyses because they can achieve uncertainty quantification at a computational cost considerably less than the exact Bayesian inference with Markov chain Monte Carlo sampling 34 . Ensemble Kalman filter (EnKF) is one of the commonly used ensemble‐based data assimilation methods in geotechnical problems 16,35–39 . Liu et al 36 .…”

Reliability analysis of PVD-improved soft soil settlement prediction using Bayesian back analysis framework and simplified Hypothesis B method

“…Inverse analysis should be used to optimize the model parameters and, as a result, to update the predicted settlement (class C prediction). The Bayesian framework has been widely used in geotechnical engineering in recent years [15,16,18,24,27].…”

“…= 𝜇 𝐶 𝛼𝑒 + 𝜎 𝐶 𝛼𝑒 𝑍 𝐶 𝛼𝑒(15) where 𝑍 𝐶 𝑐 , 𝑍𝐶 𝑒 ,𝑍 𝐶 𝛼𝑒 are standard Gaussian random variables; 𝜇 𝐶 𝑐 ,𝜇 𝐶 𝑒 , 𝜇 𝐶 𝛼𝑒 are the means of random variables . Based on the formula for calculating settlement in the previous section, the calculated value of the settlement can be considered a Gaussian random variable with the following mean 𝜇 𝑦 𝑡 and standard deviation 𝜎 𝑦 𝑡 :…”