Probabilistic estimation of thermal crack propagation in clays with Gaussian processes and random fields

Prediction of thermal crack propagation in desiccated soils is imperfect due to the obscure field measurements, modeling approximations, and the underlying soil uncertainties. To address these issues, a probabilistic framework is developed to quantify the uncertainties and enhance the crack estimation reliability. Hence, the uncertainties associated with the soil properties, including the tensile strength, matric suction, Poisson's ratio, elastic modulus and suction ratio are associated in a probabilistic model. Then, the probabilistic model is utilized with the improved Monte Carlo simulation to calculate the failure probability due to the exceedance of the crack propagation. Furthermore, failure probability optimization is exemplified by evaluating the spatial correlation between variables. The Bayesian optimization is employed to optimize the covariance kernels via the Gaussian process regression. Then, the covariance matrices are decomposed to generate random fields to further enhance the calculated failure probabilities. The results indicate that the cracking probability in near-surface layers is imminent. However, with the increase of the tensile strength and decrease in the matric suction, a sharp drop in crack propagation is highly expected. The findings also suggest that the importance of variable uncertainties is in the order of Matric suction> Elastic modulus and Suction ratio > Tensile strength> Poisson's ratio. Also, the operation of the probabilistic model with different random field sampling outperforms the improved and directed Monte Carlo simulations because of the comprehension of the spatial correlation. However, the Gaussian fields are restricted to the second-order statistics, while lognormal fields show relatively lesser constraints. Hence, the random field sampling with a larger length scale as well the Karhunen–Loève expansion followed by the approximated eigenvalue decomposition offer viable options for the probabilistic estimation of the crack depth.