Ultraslow diffusion is characterized by a logarithmic growth of the mean squared displacement (MSD) as a function of time. It occurs in complex arrangements of molecules, microbes, and many-body systems. This paper reviews mechanical models for ultraslow diffusion in heterogeneous media from both macroscopic and microscopic perspectives. Macroscopic models are typically formulated in terms of a diffusion equation that employs noninteger order derivatives (distributed order, structural, and comb models (CM)) or employs a diffusion coefficient that is a function of space or time. Microscopic models are usually based on the continuous time random walk (CTRW) theory, but use a weighted logarithmic function as the limiting formula of the waiting time density. The similarities and differences between these models are analyzed and compared with each other. The corresponding MSD in each case is tabulated and discussed from the perspectives of the underlying assumptions and of real-world applications in heterogeneous materials. It is noted that the CMs can be considered as a type of two-dimensional distributed order fractional derivative model (DFDM), and that the structural derivative models (SDMs) generalize the DFDMs. The heterogeneous diffusion process model (HDPM) with time-dependent diffusivity can be rewritten to a local structural derivative diffusion model mathematically. The ergodic properties, aging effect, and velocity autocorrelation for the ultraslow diffusion models are also briefly discussed.

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.

The safety of groundwater resources in coastal areas is related to the sustainable development of the national economy and society. Seawater intrusion is a serious problem threatening the groundwater environment in coastal areas. Climate change, tidal effects and groundwater exploitation may destroy the balance between salt water and fresh water in coastal aquifers, leading to seawater intrusion. The threat of seawater intrusion has attracted close attention, especially in the coastal areas of northern China, and the accuracy and efficiency of seawater intrusion monitoring need to be improved. The aim of this study was to fill the blanks in seawater intrusion research in the coastal aquifer of the Daqing River Catchment, northeastern Liaodong Bay, China, and determine the extent and evolutionary characteristics of seawater intrusion in this area. In this study, historical chloride concentration data were used to trace the evolution of the salinization, and electrical resistivity tomography (ERT) was used to supplement the data in areas with limited hydrochemical data and to detect the saltwater/freshwater interface, especially in the area near the Xihai Sluice. The results show that seawater intrusion in the Daqing River Catchment is mainly caused by overexploitation of groundwater. Since 2012, strict controls have been placed on the groundwater exploitation rate, and the chloride concentration of 250 mg/L has receded year by year, with saltwater being significantly reduced by 2018. The Daqing River plays an important role in the saltwater distribution. The Xihai Sluice, located in the lower reaches of the Daqing River, intercepts and controls the seawater intrusion in a certain range by raising the level of fresh groundwater to intercept and control saltwater intrusion within a certain range. The research results also confirmed that a combination of geophysical and geochemical methods is of great value in studying seawater intrusion, especially in areas with limited available hydrochemical data. A monitoring network with ERT instruments and wells should be established to collect regular measurements of the electrical resistivity distribution, as well as the groundwater level and chemical composition.

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.

Time fluctuations of groundwater flux are known to affect solute transport and thus the width and penetration of seawater intrusion. Yet, most theoretical and laboratory studies of the mixed‐convective processes accompanying seawater intrusion assume constant extraction rates, even though real‐world pumping is usually intermittent. In this study, dynamic changes to an experimental saltwater wedge caused by intermittent pumping were explored using sand tank experiments and numerical simulation. Three different aquifer systems were assessed: a homogeneous unconfined aquifer, and two stratified systems (aquifer‐aquitard‐aquifer), with the latter having an aquitard of lower permeability. Both fully and partially penetrating wells were used. The effects of the pumping period and no‐pumping period were explored, with nine laboratory experiments performed in total. The overall finding is that the impact of intermittent pumping is non‐trivial. Under the laboratory conditions, where head was prescribed inland (representative of a surface water body) intermittent pumping allowed larger volumes of freshwater to be extracted before well salinization. This reflects that non‐pumping periods allow the aquifer to recover. Additional experiments and numerical modeling, which reproduced reasonably well the experimental observations, showed that well salinization could be avoided altogether with sufficient periods of recovery. Numerical models were also used to compare intermittent and constant pumping for the same total extraction rate, showing that intermittent pumping caused earlier well salinization compared to constant pumping, although the aquifer contained a greater mass of salt under constant pumping.

The problem of the groundwater dynamics and water balance of a confined aquifer in the aquifer system has been solved in previous studies, whereas that in the aquitard adjacent to the confined aquifer has seldom been considered. In reality, the groundwater dynamics of the aquitard are closely related to the exploitation of groundwater resources, groundwater contamination, underground storage utilization and land subsidence. In this paper, an analytical solution is derived to describe the drawdown variation in the aquitard when the head in the adjacent confined aquifer declines by a constant value. The characteristics of groundwater dynamics and water balance of the aquitard are analyzed using a dimensionless analytical solution. There is obvious delayed behavior in the response of groundwater dynamics in the aquitard, which is characterized by the delay index τ ₀. The delayed behavior in the response of groundwater dynamics is not only dependent on the properties of the aquitard, but also proportional to the square of the thickness of the aquitard. The law of the delayed release of water is described in terms of the ratio of the delayed release of water. A water balance equation for the aquitard is established. Three stages of the water balance and the corresponding characteristics are presented with the water balance curves of the aquitard. The analytical solution is given to analyze the flux per unit horizontal area of the aquitard. The hydrogeological parameters of the aquitard, namely the hydraulic conductivity, specific storativity and hydraulic diffusivity, are estimated according to type-curve fitting between the analytical solution and observed flux. The parameters are identified and validated in an experiment.