Suffusion of gravel–sand mixtures under cyclic hydraulic gradient with emphasis on tracking the migration of fine particles

Different layers of soil often have distinct particle sizes. When exposed to the natural environment, soil is easily affected by natural rainfall, rising groundwater levels and human activities, leading to particle contact erosion, which reduces the safety and service performance of the soil structure. In this paper, a coupled computational fluid dynamics–discrete-element method (CFD–DEM) model was employed to investigate the particle migration phenomena, mechanical response of contact interfaces, variations in flow fields and macroscopic deformation during the contact erosion process under cyclic loads at different frequencies and amplitudes. The conclusions are presented as follows. (a) Within one cycle of cyclic loading, both compression during loading and stress relaxation during unloading are the main factors triggering the migration of fine particles. (b) The migration and loss of fine particles mainly occur in the early stages of cyclic loading, where strong contact force chains are formed within the fine particle layer, leading to significant plastic deformation of the soil at the macroscopic level. (c) Under cyclic loading, changes in the soil pore structure cause an upwards hydraulic gradient in the initial quiescent water flow field. This hydraulic gradient can rupture weak contact force chains and cause particle pumping. (d) Increasing the frequency and amplitude of cyclic loading intensifies the erosion of fine particles, causing greater axial deformation of the soil. Compared to cyclic loading frequency, the amplitude of cyclic loading has a greater impact on contact erosion.

Most groundwater equations for flow toward wells use a set of assumptions and idealizations about the aquifer–well configuration so that analytical expressions can be derived for steady-state and unsteady-state flows. In this article, the main assumption in these equations is that constant hydraulic conductivity is relaxed and instead allows radial variability. The basic question is how the hydraulic conductivity gradient affects groundwater flow. Changes in hydraulic conductivity influence groundwater flow; any local changes in the hydraulic conductivity cause local changes in hydraulic gradient and in groundwater velocity. This problem is solved using water balance equations with changes in linear radial hydraulic conductivity. Simple but more general equations for groundwater flow toward wells are derived and applied to steady-state groundwater flows in a confined aquifer. This formulation reduces to the classical Theim solution for constant hydraulic conductivity. The use of this methodology is presented for steady-state groundwater measurement from a well in the Arabian Peninsula. It is observed that constant hydraulic conductivity underestimates transmissivity, compared to the numerical example given in this article, by about 41%.

Numerous incidents and failures of earth slopes, dykes, levees and embankment dams are caused by internal erosion. At a time of global climate change, rapid pore-water pressure changes in soil masses are frequently induced by extreme rainfall, storm surges, waves, flash floods and so on. Under such complex cyclic hydraulic conditions, the soil erodibility, hydraulic conductivity and subsequent stress–strain behaviour may differ from those under the monotonic seepage condition, and are still poorly understood. In this study, preliminary laboratory tests have been conducted to investigate the development of internal erosion and changes in hydraulic conductivity under one-way cyclic seepage, and the post-erosion stress–strain behaviour. Representative internally stable and unstable soils were tested. The effects of mean hydraulic gradient and cyclic gradient amplitude were investigated in detail. Results show that the erosion development is significantly influenced by both the initial grain size distribution and the pattern of imposed cyclic hydraulic gradient. The cyclic seepage promotes the loss of fine particles and leads to larger hydraulic conductivity. For the internally unstable soil, the eroded soil mass and hydraulic conductivity increased significantly with increasing cyclic gradient amplitude. Nevertheless, the internally stable soil experienced a small amount of particle loss, even under large cyclic gradients. For both types of soil, a larger cyclic gradient amplitude corresponds to a stronger post-erosion contractive shearing behaviour and a smaller critical friction angle.

The permeability of crushed coal bodies plays a bottom neck role in seepage processes, which significantly limits the coal resource utilisation. To study the permeability of crushed coal bodies under pressure, the particle size distribution of crushed coal body grains is quantitatively considered by fractal theory. In addition, the parameters of the percolation characteristics of crushed coal body grains are calculated. Moreover, the permeability of the crushed coal body during recrushing is determined by the fractal dimension and porosity. A lateral limit compression test with the crushed coal bodies was carried out to illustrate the effect of the porosity on the permeability, In addition, a compressive crushed coal body size fractal–permeability model was proposed by combination of the fractal dimension and the non-Darcy equivalent permeability. The results show (1) the migration and loss of fine particles lead to a rapid increase in the porosity of the crushed coal body. (2) Increases in the effective stress cause the porosity and permeability to decrease. When the porosity decreases to approximately 0.375, its effect is undermined. (3) The migration and loss of fine particles change the pore structure and enhance the permeability properties of the skeleton, causing sudden seepage changes. (4) At low porosity, the permeability k is slightly larger than the non-Darcy equivalent permeability ke. Thus, the experimental data show an acceptable agreement with the present model. A particle size fractal–percolation model for crushed coal bodies under pressure provides a solution for effectively determining the grain permeability of the crushed coal bodies. The research results can contribute to the formation of more fractal-seepage theoretical models in fractured lithosphere, karst column pillars and coal goaf, and provide theoretical guidance for mine water disaster prevention.

Darcian flow law in aquifers assumes that the aquifer hydraulic conductivity is constant and the groundwater movement is due only to the piezometric level changes through hydraulic gradient. In practice, after the well development the aquifer just around the well has comparatively larger hydraulic conductivity and gradient. Patchy aquifer solutions in the literature consider sudden hydraulic conductivity changes with distance for the steady state flow. The change of transmissivity is demonstrated by the application of slope-matching procedure to actual field data. It is the main purpose of this paper to derive simple analytical expressions for aquifer parameter evaluations with steadily decreasing hydraulic conductivity around the well. Spatial nonlinear hydraulic conductivity changes around a large-diameter well within the depression cone of a confined aquifer are considered as exponentially decreasing functions of the radial distance. Copyright © 2010 John Wiley & Sons, Ltd.

Cyclic hydraulic loading frequently affects embankment dams during reservoir regulation, tidal fluctuations, and intense rainfall. It potentially worsens fine particle migration during internal erosion and increases dam failure risks. This study is the first to systematically explore the influence of cyclic hydraulic loading on the critical hydraulic gradient (icr) of gap-graded soils, providing new insights into suffusion behavior. Transparent soil experiments, which enable direct observation of soil structural evolution, are combined with coupled DEM–Darcy simulations that offer microscopic mechanical insights, marking the first integrated use of these two approaches to investigate suffusion behavior. To quantify fine particle migration, we propose a novel modified grayscale threshold segmentation (MGTS) method for analyzing cross-sectional images captured during transparent soil experiments. The results from both methods show consistency in fine particle migration, clogging formation, and failure, with differences in permeability and icr remaining within acceptable limits. Fine particle content significantly influences the post-cyclic icr of internally unstable soils. For soils with lower fine particle content (15%), icr increases after cyclic hydraulic loading and rises with the mean hydraulic gradient during cycling. Conversely, soils with higher fine particle content (20%) exhibit a decrease in post-cyclic icr. This behavior is explained by changes in the average contact force between fine particles (Fff) observed in DEM simulations.

Tidal fluctuations in surface‐water bodies produce progressive pressure waves in adjacent aquifers. As these pressure waves propagate inland, ground‐water levels and hydraulic gradients continuously fluctuate, creating a situation where a single set of water‐level measurements cannot be used to accurately characterize ground‐water flow. For example, a time series of water levels measured in a confined aquifer in Atlantic City, New Jersey, showed that the hydraulic gradient ranged from. 01 to. 001 with a 22‐degree change in direction during a tidal day of approximately 25 hours. At any point where ground water tidally fluctuates, the magnitude and direction of the hydraulic gradient fluctuates about the mean or regional hydraulic gradient. The net effect of these fluctuations on ground‐water flow can be determined using the mean hydraulic gradient, which can be calculated by comparing mean ground‐ and surface‐water elevations. Filtering methods traditionally used to determine daily mean sea level can be similarly applied to ground water to determine mean levels. Method (1) uses 71 consecutive hourly water‐level observations to accurately determine the mean level. Method (2) approximates the mean level using only 25 consecutive hourly observations; however, there is a small error associated with this method. The exact magnitude of this error is usually unknown, and therefore the accuracy of the mean level is also unknown. Method (1) should be used if a higher degree of accuracy is required.

Internal erosion involves the loss of fine particles within the matrix of coarse particles under seepage flow, posing a severe threat to hydraulic structures. This paper focuses on internal erosion considering anisotropic stress conditions. The influence of the anisotropic stress state, represented by vertical stress equal to, bigger than, or smaller than horizontal stress, was investigated using coupled computational fluid dynamics (CFD) and the discrete element method (DEM). Results show that the loss of fine particle specimens under anisotropic stress conditions is greater than that for samples under isotropic stress states, as the loss of fine particles leads to an evolution of anisotropy into isotropy, with local contact force chains gradually forming spatially isotropic structures. The strong force chains of specimens under triaxial compression were also found to develop a dominant orientation in the vertical direction, leading to clogging in the upward migration of fine particles and increasing the critical hydraulic gradient. In addition, the evolution of void ratio, hydraulic drag force, connectivity, and coordination number has also been analyzed to exhibit the influence of stress anisotropy on internal erosion.

Experimental Study on the Migration and Clogging of Fine Particles in Coarse-Grained Soil with Seepage

Mass migration and loss in fractured rock during seepage processes are considered to cause seepage instabilities, which can lead to seepage catastrophes. In this study, the migration and loss of fine particles in fractured rock during seepage are theoretically and experimentally investigated. We analyze the characteristics of lost and migrated mass obtained from the experiments over time, as well as the effect of initial compression. A linear relationship is found to best describe the difference of migrated versus lost mass and Talbot power exponent (TPE), with the slope and intercept related to initial compression. The lost and migrated mass are described mathematically based on the TPE and initial compression. We quantify the behavior of mass migration and loss, which allows calculation of the possibility of seepage instability and water inrush. A seepage instability occurs if the lost mass ratio is greater than 4.90%. The results presented here provide important insight into the water inrush mechanism in geotechnical engineering applications.

It is very common in geotechnical engineering with Karst geological conditions that the fine particles migrate and lose continuously with water flow in the fractured rock mass, which will lead to the water-mud-inrush accident. In this paper, the time-varying characteristics of fine particles’ migration and loss in fractured mudstone under water flow scour were investigated experimentally and theoretically. Considering the continuous gradation of fractured mudstone, taking Talbot power exponent as the influencing factor, the time-varying features of the total lost mass were described. Based on the total lost mass, the mass-loss rate and the mass-migration rate of fine particles were proposed, and their time-varying features were compared and analyzed. The loss-migration-ratio was defined, and the water-mud-inrush risk was assessed by the relationships between loss-migration-ratio and time. The research showed that (1) the lost mass resulted from the fine particles’ migration, and the migrated mass was affected not only by lost fine particles but also by the water flow velocity. The rules of the fine particles’ migration and loss in the fractured mudstone had the non-linear and time-varying characteristics. (2) For samples with the smaller Talbot power exponent of n = 0.1–0.5, the fine particles splashing phenomenon occurred, and quite a lot of migrated fine particles were lost. The loss-migration-ratio attenuated with time by a power function. Fractured mudstone with this continuous gradation had a high water-mud-inrush risk. (3) For samples with n = 0.6–1.0, large numbers of fine particles migrated with water flow, but only a few rushed out from the fractured mudstone. The loss-migration-ratio attenuated with time by an exponent function. Fractured mudstone with this continuous gradation had a stable inner structure; therefore, the water-mud-inrush risk was very low. The results will help geotechnical practitioners to assess the water-mud-inrush risk and provide some references for the water-mud-inrush accidents prevention in geotechnical engineering with Karst geological conditions.

Seepage-induced internal instability is a phenomenon whereby fine particles are transported from a non-plastic soil. A distinction can readily be made between a washed-out soil structure that remains intact and one in which some form of destruction or collapse of the structure accompanies the migration of fine particles. The three variables of a measured value of mass loss, a measured value of volume change and a value of change in hydraulic conductivity, deduced from measurements of hydraulic gradient and flow rate, are sufficient to quantify, and hence distinguish between, seepage-induced internal instability phenomena. The term ‘suffusion’ is advocated to describe the non-destructive response, which may be quantified by a mass loss, no change in volume and an increase in hydraulic conductivity. The term ‘suffosion’ is recommended to describe the instability phenomenon whereby the transport of fine particles by seepage flow is accompanied by a collapse of the soil structure. Accordingly, this distinct internal instability phenomenon may be quantified by a mass loss, a volumetric contraction and a change in hydraulic conductivity.

The infiltration and distribution of water through unsaturated soil determine its mechanical and hydrological properties. However, there are few methods that can accurately capture the spatial distribution of moisture inside soil. This study aims to demonstrate the use of actively heated fiber optic (AHFO) and Brillouin optical time domain analysis (BOTDA) technologies for monitoring soil moisture distribution as well as strain distribution. In addition to a laboratory model test, finite element analyses were conducted to interpret the measurements. During the experiment, the fine particle migration was also measured to understand its influence on soil hydraulic conductivity. The results of the experiment indicate that (i) for a soil that has never experienced a watering-dewatering cycle, water infiltration can be accurately calculated using the Richards’ equation; (ii) migration of fine soil particles caused by the watering-dewatering cycle significantly increases the hydraulic conductivity; and (iii) two critical zones (drainage and erosion) play significant roles in determining the overall hydraulic conductivity of the entire soil. This study provides a new method for monitoring the changes in soil moisture, soil strain, and hydraulic conductivity. The observations suggest that the effect of fine particles migration should be considered while evaluating soil moisture distribution and water movement.

Under complex hydraulic conditions, such as extreme rainfall, water level fluctuations and wave surges, the hydraulic load exerted on the soil differs from constant or monotonically varying hydraulic gradient loads, resulting in more complex contact erosion responses between soil layers. In this study, a coupled computational fluid dynamics–discrete element method (CFD–DEM) was employed to investigate the effects of different mean hydraulic gradients and cyclic hydraulic gradient amplitudes. The research focused on the macroscopic deformation of contact erosion between soil layers under cyclic hydraulic gradients and the underlying microscopic mechanical mechanisms. The findings revealed that under cyclic hydraulic loading, the erosion mass of fine particles significantly increased, with fine particles closer to the contact surface being more susceptible to migration due to the cyclic hydraulic gradients. During the migration process, fine particles were more likely to pack and clog at the bottom of the coarse particle layer. This was primarily due to the increase in both the strength and number of contact forces perpendicular to the seepage direction. Seepage caused the contact forces and their distribution to develop more along the direction of seepage, exhibiting anisotropy. As both the mean hydraulic gradient and the cyclic hydraulic gradient amplitude increased, the particle erosion rate increased, while the shear strength and stability of the sample decreased.

In this work, 3D discrete element method modeling of drained shearing tests with gap-graded soils after internal erosion is carried out based on published experimental results. The erosion in the model is achieved by randomly deleting fine particles, mimicking the salt dissolving process in the experiments. The present model successfully simulates the stress–strain behavior of the physical test by employing the roll resistance and lateral membrane. The case without erosion shows a strain-softening and dilative response, while strain-hardening and contractive response starts to occur as the degree of erosion increases. The dilative to contractive transition is mainly caused by the increase in void ratio due to the loss of fine particles. The change from dilative behavior to contractive behavior is more abrupt for the specimen with larger fine particle percentage because the soil skeleton is mainly controlled by the fine particles instead of by the coarse soil particles. The transition from “fines in sand” to “sand in fines” might be associated with the rapid increasing in the contacts associated with fine particles in the specimen as the percentage of fine content increases. The erosion scenario based on the hydraulic gradient is also modeled by deleting the fine particles based on the ranking of the contact force. Compared with the scenario based on random deletion, the remaining fine particles for the erosion scenario based on the ranking of contact force are more dispersedly distributed, which might benefit the small strain stiffness but result in a smaller strength. This work provides some insights for better understanding the mechanism behind the internal erosion and the associated stress–strain behavior of soil. The gradient of the critical state line increases with more loss of fine particles denoting that the fine particles are helpful for holding the structure of the soils from larger deformation.