Continuum Modeling of Suffusion and Filtration in Underfilled Gap-Graded Soils with an Immobile Skeleton

This study investigated the performance of a continuum approach to modeling the internal erosion processes of suffusion and filtration. Building on the framework in prior studies, the model is formulated based on mass conservation of a four-phase system with modifications presented for erosion and deposition rate models. The continuum approach was assessed by comparing with experimental data from permeameter tests that were augmented with spatial time domain reflectometry, which enabled measurements of porosity and fines content at a relatively high spatial and temporal resolution. Given that porosity and fines content are key variables within the continuum approach, the ability to assess the model based on their internal measurements was a key novel contribution, as prior studies focused on macroscale features such as eroded mass and hydraulic conductivity. The experimental data encompassed a range of fines content and hydraulic loading rates, and the unique sample configuration enabled the process of suffusion and filtration to be investigated simultaneously, which was also a key contribution. The model considered a simplified one-dimensional representation of the experiment with a saturated underfilled gap-graded soil that experienced no deformation of the coarse skeleton. Suffusion was solely modeled using an erosion rate model, while filtration only considered a deposition rate model. Despite these simplifying assumptions, the continuum approach was able to broadly capture both mechanisms, particularly when the fines migration was gradual, whilst discrepancies were noted for rapid transitions. Moreover, modeling the suffusion process was relatively insensitive to model choices, which were more critical for capturing the filtration process. The modifications to the erosion and deposition rate models with the inclusion of a critical flow rate and higher time-scale of deposition were found to have an important impact on the internal spatial fines migration. In addition, the model parameters showed some dependence on the rate of hydraulic loading that was not captured in prior studies.