Fractured rocks in the subsurface are ubiquitous, and the dynamics of mass transfer in fractured rocks plays an important role in understanding the problem in engineering geology and environmental geology. In this study, the influence of shear displacement on fluid flow and solute transport in a 3D rough fracture was investigated. A 3D self-affine rough fracture was generated using the modified successive random addition (SRA) technology, and three sheared fractures with different shear displacements were constructed based on the mechanistic model. A direct numerical model based on the Navier-Stokes equation and the advection-diffusion equation was developed to solve the fluid flow and the solute transport. The results showed that shear displacement had a significant influence not only on the fluid flow but also on the solute transport. A global measure of the spatial variability of the flow velocity showed that the heterogeneity became weaker with decreasing shear displacement. All measured BTCs deviated from the Gaussian profile and exhibited the typical anomalous behaviors, such as the long tail and the early arrival. Although the best-fitted results of the advection-dispersion equation (ADE) model and mobile-immobile model (MIM) were generally consistent with those of the BTCs, the MIM was more capable than the ADE model for characterizing the shear-induced anomalous behavior of the BTCs. It was found that the mass exchange process between the immobile and mobile domains was enhanced in the sheared fractures while the fraction of the advection-dominant mobile domain decreased as the shear displacement increased. Furthermore, the deviation of the Taylor dispersion coefficient from the fitted dispersion coefficient by the ADE model and MIM in the sheared fractures was confirmed due to the influence of shear displacement.

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.

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.

The cementation of porous media leads to the variation of the pore space and heterogeneity of the porous media. In this study, four porous media (PM1, PM2, PM3, and PM4) with the different radii of solid grains were generated to represent the different cementation degrees of the porous media. The direct simulations of flow and conservative solute transport in PM1–4 were conducted to investigate the influence of the cemented porous media and Peclet number (Pe) on the temporal mixing behavior. Two metrics, scalar dissipation rates (SDR) and dilution index, were employed to quantify the temporal mixing behavior. It was found that the spatial velocity variability of the flow field was enhanced as cementation degree increased. The results of the coefficient of velocity variation ( $C{V}_U$ ) increased from 0.943 to 2.319 for PM1–4. A network consisted of several preferential flow paths was observed in PM1–4. The preferential flow enhanced the mixing of the conservative solute but had a negative influence on the mixing of the solute plume when the cemented solid grains formed several groups, and there were some stagnant regions where the flow was almost immobile. As the Pe increased, for PM1–3, the exponent of the best-fitting power law of the global SDR decreased. At the case of Pe = 400, the slope of the global SDR reduced to around −1.9. In PM4 where the preferential flow was enhanced by the cemented solid grains, the slope of the global SDR increased as the Pe increased. The global SDR results indicated that the temporal mixing behavior followed a Fickian scaling ( $SDR\propto p{v}^{-1.5}$ ) in the early stage (Pv < 0.05), while the mixing behavior turned to be non-Fickian in the late stage. The transition time from the Fickian scaling to the non-Fickian scaling was found to be sensitive to the cementation degree of the porous media.

Clay is widely encountered in nature and directly influences seepage behaviors, exerting a crucial impact on engineering applications. Under low hydraulic gradients, seepage behaviors have been observed to deviate from Darcy’s law, displaying a non-linear trend. However, the impacts of clay content on non-linear seepage behavior and its pore-scale mechanisms to date remain unclear. In this study, constant-head seepage experiments were conducted in sand–clay porous media under various hydraulic gradients. Low-field nuclear magnetic resonance (LF-NMR) technology was utilized to monitor the bound-water and free-water contents of sand–clay porous media under different seepage states. The results show a threshold hydraulic gradient (i₀) below which there is no flow, and a critical hydraulic gradient (i_cr) below which the relationship between the hydraulic gradient (i) and seepage velocity (v) is non-linear. Both hydraulic gradients increased with clay content. Moreover, the transformation between bound water and free water was observed during the seepage-state evolution (no flow to pre-Darcy or pre-Darcy to Darcy). As the hydraulic gradient reached the i₀, the pore water pressure gradually overcame the adsorption force of the bound-water film, reducing the thickness of the bound-water film, and causing non-linear seepage behavior. When i₀ < i < i_cr, the enlarging hydraulic gradient triggers the thinning of bound water and enhances the fluidity of pore water. Moreover, the increasing clay content augments the bound-water content required for the seepage state’s change.