Although numerous studies have been paid much attention to rainfall-induced instability of multilayered slopes, the interface between layers is generally considered to be “zero thickness”, and the layer transition zone between layers is neglected. In this study, the influence of the layer transition zone on the rainfall-induced instability of multilayered slope was investigated. A model was developed to simulate the rainfall infiltration process, the distribution of pore water pressure, and the stability of multilayered slope by coupling the unsaturated seepage model and the slope stability analysis method. Based on the analysis of the multilayered slopes with the different thickness ratios of the layer transition zone, a method for determining the critical thickness of the layer transition zone was proposed. The results showed that the layer transition zone had a significant influence on the stability of multilayered slope. It was found that the presence of the layer transition zone in the multilayered slope reduced the hydraulic conductivity of the slope and increased the rate of formation of transient saturated zone, which contributed to excess pore water pressure at the toe of the slope. The analysis of the local factor of safety (LFS) showed that when the thickness ratios of the layer transition zone were between 2.5% and 5%, the corresponding hydraulic conductivity of the slope decreased by 1%-2.5% and the maximum failure area of the slope during the rainfall was 25% of the slope. Our study highlighted the importance of the layer transition zone for the rainfall-induced instability of the multilayered slope.

Understanding solute transport in fractured rocks is of particular importance in many applications. Aperture values ranging from 4.7 to 8.7 mm and Reynolds number (R_e) values at 9.38~1743.8 were set for investigating fluid flow through synthetic horizontal single smooth and rough fractures. The Brilliant Blue FCF dye was chosen as the tracer to visualize the transport process. This paper focuses on the dispersion process in rough single fractures under non-Darcian flow conditions. Non-Darcian flow existed in both smooth and rough single fractures and the average flow velocity–hydraulic gradient (V–J) relationships were best described by the Forchheimer equation. The main objectives were to check the existing flow and transport models and to study possible correlations between fitting parameters and heterogeneities. The classical advection dispersion equation (ADE) model failed to capture the long-tailing of breakthrough curves (BTCs). Instead, the continuous time random walk (CTRW) model was better at explaining BTCs in both smooth and rough fractures, especially in capturing the long-tailing feature. The non-Darcian coefficient β_c in the Forchheimer equation and the coefficient β in the CTRW model appeared to be most relevant for characterizing the heterogeneity of the rough single fractures.

Abrupt changes in aperture (sudden expansion and contraction) are commonly seen in naturally occurred or artificial single fractures. The relevant research mainly focuses on the changes in fluid properties caused by the sudden expansion of the aperture in smooth parallel fractures. To investigate the effects of roughness on the nonlinear flow properties in a single rough fracture with abruptly aperture change (SF-AC), the flow characteristics of the fractures under different Reynolds numbers $Re$ (50~2000) are simulated by the turbulence $k‐ε$ steady-state modulus with the Naiver-Stokes equation. The results show that, in a rough SF-AC, the growth of the eddy and the flow path deflection of the mainstream zone are more obvious than those in a smooth SF-AC, and the discrepancies between the rough and smooth SF-ACs become even more obvious when the relative roughness and/or $Re$ values become greater. The increase of the fracture roughness leads to the generation of more local eddies on the rough SF-ACs and enhances the flow path deflection in the sudden expansion fracture. The number of eddies increases with $Re$⁠, and the size of eddy area increases linearly with $Re$ at first. When $Re$ reaches a value of 300-500, the growth rate of the eddy size slows down and then stabilizes. Groundwater flow in a rough SF-AC follows a clearly visible nonlinear (or non-Darcy) flow law other than the linear Darcy’s law. The Forchheimer equation fits the hydraulic gradient-velocity (⁠ $J‐v$⁠) better than the linear Darcy’s law. The corresponding critical $Re$ value at which the nonlinear flow starts to dominate in a rough SF-AC is around 300~500.

Soils and other geologic porous media often have contrasting grain size layers associated with a grain size transition zone between layers. However, this transition zone is generally simplified to a plane of zero thickness for modeling assumption, and its influence has always been neglected in previous studies. In this study, an approach combining a deposition process and a random packing process was developed to generate 3D porous media without and with consideration of the transition zone. The direct numerical models for solving the flow and concentration fields were implemented to investigate the influence of the grain size transition on flow and solute transport. Our results showed that although the transition zone occupied 13.6% of the entire layered porous medium, it had little influence on the distribution of flow velocity at the scale of the entire layered porous medium. However, the transition zone had a significant influence on the local flow field, which was associated with the increased spatial variability of velocity and the varied distribution of flow velocity. This varied local flow field could increase the solute residence time and delay the breakthrough time for solute transport. Although using both the advection-dispersion equation (ADE) and the mobile and immobile (MIM) models to fit the breakthrough curves (BTCs) for solute transport through layered porous media resulted in trivial errors, the ADE model failed to capture the influence induced by the local flow field, especially the influence of the transition zone. In contrast, the MIM model was shown to be able to capture the influence of the transition on solute transport. It was found that the mass transfer rate $α$⁠, a parameter of the MIM model, was significantly improved by the presence of the transition zone, while it decreased as the transition zone fraction increased. Our study emphasized that the transition zone can vary the local flow field at the pore scale, while it has little influence on the hydraulic properties (e.g., hydraulic conductivity) of the macroscale flow field. However, the local flow field varied by the transition zone has a significant influence on solute transport.