A Probabilistic Cut Finite Element Method With Random Field Generator and Bayesian Model Calibration for Flow Through Rough Cracks

Abstract

A new model for the simulation of fluid flow through rough cracks is presented. The model combines a probabilistic cut finite element method (PCutFEM) to capture the unfitted boundary condition at the fluid interface, with a stochastic random field generator to represent the crack asperities. A key feature of the model is the consideration of the crack roughness and tortuosity, which are calculated from the crack asperities. This approach avoids the need for empirical reduction factors, whilst allowing for the heterogeneity of the flow processes. In addition to this, the model considers the spatially varying crack width associated with material loss during the fracture process, which is represented using a smoothed Gaussian noise. To determine the statistical parameters that describe the crack asperities, a Bayesian statistical inference is employed. The statistical inference considers the uncertainty in measured values, observations of crack permeabilities and the stochastic nature of the random field model. The performance of the model is assessed via comparison with new experimental data of the flow of tap water (TW) and a ground‐granulated blast furnace slag (GGBS) suspension through concrete cracks. In addition, a statistical analysis is employed to quantify the level of uncertainty in the predictions. The results of the validation show that the model is able to accurately reproduce the observed experimental behaviour and that a confidence level in the results of 95% is achieved in eight simulations.