Investigation of strain localization in sheared granular layers using 3-D discrete element modeling

In this work, we investigate slip localization in sheared granular faults at seismic velocities using 3-D numerical simulations with the discrete element method (DEM). An aggregate of non-destructive spherical particles is subjected to direct shear by using two moving boundaries in a sandwich configuration to identify the impact of particle-scale parameters on slip localization. We impose a thin layer of fine-grained particles with variable contrast in thickness and grain size adjacent to the boundary as well as in the middle of the granular layer to simulate boundary and Y shears observed in both natural and laboratory fault gouges. The results show that larger amounts of strain is accommodated within the pre-described finer-grained layer even with a small (< 10%) contrast in grain size. Up to 90% of the displacement is localized in a finer-grained layer when the contrast ratio of the grain size is 50%. Based on the concept of the average spreading velocity of particles and squeeze expulsion theory in granular flow, we suggest that the phenomenon of localization is likely from result from the contribution of larger grains collisions with smaller grains. Since the amount of frictional heat generated depends on the degree of localization, the results provide crucial information on the heat generation and associated slip accommodation in sheared gouge zones. We conclude that the occurrence of a weaker, fine-grained layer within a dense fault zone is likely to result in self-enhanced weakening of the fault planes

A grain-scale study of unsaturated flow in highly swelling granular materials

Unsaturated flow in swelling porous materials are common and important phenomena in industrial products and earth materials; for example, in paper, hygienic products, swelling clays, and foods. Swelling causes porous media to expand and to deform, which results in a change in pore structure and thus in distributions of water and air. This work focusses on the swelling of Super Absorbent Polymer (SAP) particles, which are absorbent particles capable of absorbing large amounts of fluids, typically 30x its initial weight, in a relatively short time frame (order of minutes). Characterization of a bed of SAP particles is complex, because of its large deformation in a short time as well as the complexity of the process itself; i.e. unsaturated flow in a deforming and swelling material. To characterize swelling, continuum-scale models can be used, but they require hydraulic parameters to have dependencies on both swelling and state-of-stress of the particle packing. Another approach is to employ a pore-scale model that applies physics and rules at the grain-scale, which can be used to upscale grain-scale processes to continuum-scale phenomena. However, a pore-scale model for unsaturated flow in deformable granular materials does not exist, yet. Therefore, we developed a pore-sale methodology that enables simulation of a deforming and swelling bed of particles and the subsequent redistribution of air and water in the pores. Deformation is simulated using the Discrete Element Method (DEM), which can describe motions of individual particles, while unsaturated flow is simulated using a newly developed Pore-Unit Assembly (PUA) methodology. The specific objects in this work are as follows: i) to study the applicability and versatility of the discrete element method towards simulation of a bed of SAP particles; ii) to identify swelling kinetics of individual SAP particles; iii) to couple the discrete element method with the pore-unit assembly method in order to construct capillary pressure-saturation curves of SAP particle beds; iv) to study the effect of swelling and porosity change on the retention properties of SAP particle beds; v) to investigate the role of particle shape in generating packings of SAP particles, using the discrete element method; and vi) to identify dynamic effects of unsaturated flow in rigid and swelling particle packings

Groundwater flow below construction pits and erosion of temporary horizontal layers of silicate grouting

Injection of silicate grouting materials is widely used to create temporary horizontal layers for reducing inflow of groundwater at construction sites, in regions with shallow water tables. The erosion of a grouting layer was investigated by means of analytical solutions for groundwater flow and transport within a pit after construction finished. Erosion is assumed to occur by dissolution of the temporary injection layer and subsequent advective transport. Thereby, the hydraulic conductivity changes with time. This paper presents novel analytical solutions and approximate solutions for the major fluxes in the construction pit as a function of the domain settings, aquifer gradient and hydraulic conductivity. In addition, the mass flux and the dilution ratio of erosion-related components leaving the construction pit and entering the aquifer are quantified. Derived solutions are verified against numerical simulations. A sensitivity study shows the impact of domain settings on fluxes and dilution ratio. The results confirm that mass flux of grout components increases with ongoing erosion. Thus, its effect on groundwater quality increases with time after construction ceased

Complex wave propagation from open water bodies into aquifers: A fast analytical approach

Aquifers are of particular interest in the vicinity of rivers, lakes and coastal areas due to their extensive usage. Hydraulic properties such as transmissivity and storativity can be deduced from periodical water level fluctuations in both open water bodies and groundwater. Here, we model the effect of complex wave propagation into adjacent isotropic and homogeneous aquifers. Besides confined aquifers, we also study wave propagation in leaky aquifers and situations with flow barriers near open water bodies as encountered in harbours where sheet piling are in place. We present a fast analytical solution for the hydraulic head distribution which allows for determining the hydraulic diffusivity (Ss/K) of the aquifer, with low investigational efforts. We make use of the Fast Fourier Transform to decompose complex wave boundary conditions and derive solutions through superposition. Analytical solutions are verified by comparing to numerical MODFLOW models for three application examples: a tidal wave measured in the harbour of Rotterdam, a synthetic square wave and river fluctuations in the river Rhine near Lobith. We setup a parameter estimation routine to identify hydraulic diffusivity, which can be easily adapted to real observation data from piezometers. Inverse estimates show relative differences of less than 2% to numerical input data. A sensitivity study further shows how to achieve reliable estimates depending on the piezometer location or other influencing factors such as resistance values of the confining layer (for leaky aquifers) and flow barriers

Unsaturated flow in a packing of swelling particles: a grain-scale model

In this work, a grain-scale modelling technique is introduced for the simulation of unsaturated flow in deforming and swelling granular materials. To do so, a pore-scale model for unsaturated flow is coupled to the discrete element method (DEM). It is assumed that initially a dry packing of particles is quickly invaded by a liquid and becomes fully saturated. Particles start absorbing the liquid and this causes a rearrangement of particles, entrance of air into the packing, and a redistribution of the liquid (i.e. unsaturated flow). Flow was computed using a scheme of implicit pressure solver and explicit saturation update (IMPES), whilst particle movement was modelled using DEM. Simulations are continued until the packing is dry again. This is the first time that such a pore-scale model has been developed. We have used the model to investigate unsaturated flow during drying of a bed of swelling particles. Results indicated that the characteristic time scales of unsaturated flow and water absorption determine the swelling behaviour of the particle packing

Capillary pressure–saturation relationships for porous granular materials : Pore morphology method vs. pore unit assembly method

In studies of two-phase flow in complex porous media it is often desirable to have an estimation of the capillary pressure–saturation curve prior to measurements. Therefore, we compare in this research the capability of three pore-scale approaches in reproducing experimentally measured capillary pressure–saturation curves. To do so, we have generated 12 packings of spheres that are representative of four different glass-bead packings and eight different sand packings, for which we have found experimental data on the capillary pressure–saturation curve in the literature. In generating the packings, we matched the particle size distributions and porosity values of the granular materials. We have used three different pore-scale approaches for generating the capillary pressure–saturation curves of each packing: i) the Pore Unit Assembly (PUA) method in combination with the Mayer and Stowe–Princen (MS–P) approximation for estimating the entry pressures of pore throats, ii) the PUA method in combination with the hemisphere approximation, and iii) the Pore Morphology Method (PMM) in combination with the hemisphere approximation. The three approaches were also used to produce capillary pressure–saturation curves for the coating layer of paper, used in inkjet printing. Curves for such layers are extremely difficult to determine experimentally, due to their very small thickness and the presence of extremely small pores (less than one micrometer in size). Results indicate that the PMM and PUA-hemisphere method give similar capillary pressure–saturation curves, because both methods rely on a hemisphere to represent the air–water interface. The ability of the hemisphere approximation and the MS–P approximation to reproduce correct capillary pressure seems to depend on the type of particle size distribution, with the hemisphere approximation working well for narrowly distributed granular materials

Infiltration behaviour of elemental mercury DNAPL in fully and partially water saturated porous media

Mercury is a contaminant of global concern due to its harmful effects on human health and for the detrimental consequences of its release in the environment. Sources of liquid elemental mercury are usually anthropogenic, such as chlor-alkali plants. To date insight into the infiltration behaviour of liquid elemental mercury in the subsurface is lacking, although this is critical for assessing both characterization and remediation approaches for mercury DNAPL contaminated sites. Therefore, in this study the infiltration behaviour of elemental mercury in fully and partially water saturated systems was investigated using column experiments. The properties affecting the constitutive relations governing the infiltration behaviour of liquid Hg0, and PCE for comparison, were determined using Pc(S) experiments with different granular porous media (glass beads and sands) for different two- and three-phase configurations. Results showed that, in water saturated porous media, elemental mercury, as PCE, acted as a non-wetting fluid. The required entry head for elemental mercury was higher (from about 5 to 7 times). However, due to the almost tenfold higher density of mercury, the required NAPL entry heads of 6.19 cm and 12.51 cm for mercury to infiltrate were 37.5% to 20.7% lower than for PCE for the same porous media. Although Leverett scaling was able to reproduce the natural tendency of Hg0 to be more prone than PCE to infiltrate in water saturated porous media, it considerably underestimated Hg0 infiltration capacity in comparison with the experimental results. In the partially water saturated system, in contrast with PCE, elemental mercury also acted as a nonwetting fluid, therefore having to overcome an entry head to infiltrate. The required Hg0 entry heads (10.45 and 15.74 cm) were considerably higher (68.9% and 25.8%) than for the water saturated porous systems. Furthermore, in the partially water saturated systems, experiments showed that elemental mercury displaced both air and water, depending on the initial water distribution within the pores. This indicates that the conventional wettability hierarchy, in which the NAPL has an intermediate wetting state between the air and the water phases, is not valid for liquid elemental mercury. Therefore, for future modelling of elemental mercury DNAPL infiltration behaviour in variably water saturated porous media, a different formulation of the governing constitutive relations will be required

Infiltration behaviour of elemental mercury DNAPL in fully and partially water saturated porous media

Mercury is a contaminant of global concern due to its harmful effects on human health and for the detrimental consequences of its release in the environment. Sources of liquid elemental mercury are usually anthropogenic, such as chlor-alkali plants. To date insight into the infiltration behaviour of liquid elemental mercury in the subsurface is lacking, although this is critical for assessing both characterization and remediation approaches for mercury DNAPL contaminated sites. Therefore, in this study the infiltration behaviour of elemental mercury in fully and partially water saturated systems was investigated using column experiments. The properties affecting the constitutive relations governing the infiltration behaviour of liquid Hg-0 and PCE for comparison, were determined using P-c(S) experiments with different granular porous media (glass beads and sands) for different two- and three-phase configurations. Results showed that, in water saturated porous media, elemental mercury, as PCE, acted as a non-wetting fluid. The required entry head for elemental mercury was higher (from about 5 to 7 times). However, due to the almost tenfold higher density of mercury, the required NAPL entry heads of 6.19 cm and 12.51 cm for mercury to infiltrate were 37.5% to 20.7% lower than for PCE for the same porous media. Although Leverett scaling was able to reproduce the natural tendency of Hg to be more prone than PCE to infiltrate in water saturated porous media, it considerably underestimated Hg infiltration capacity in comparison with the experimental results. In the partially water saturated system, in contrast with PCE, elemental mercury also acted as a nonwetting fluid, therefore having to overcome an entry head to infiltrate. The required Hg entry heads (10.45 and 15.74 cm) were considerably higher (68.9% and 25.8%) than for the water saturated porous systems. Furthermore, in the partially water saturated systems, experiments showed that elemental mercury displaced both air and water, depending on the initial water distribution within the pores. This indicates that the conventional wettability hierarchy, in which the NAPL has an intermediate wetting state between the air and the water phases, is not valid for liquid elemental mercury. Therefore, for future modelling of elemental mercury DNAPL infiltration behaviour in variably water saturated porous media, a different formulation of the governing constitutive relations will be required

The impact of water saturation on the infiltration behaviour of elemental mercury DNAPL in heterogeneous porous media

Industrial use has led to the presence of liquid elemental mercury (Hg-0) worldwide in the subsurface as Dense NonAqueous Phase Liquid (DNAPL), resulting in long lasting sources of contamination, which cause harmful effects on human health and detrimental consequences on ecosystems. However, to date, insight into the infiltration behaviour of elemental mercury DNAPL is lacking. In this study, a two-stage flow container experiment of elemental mercury DNAPL infiltration into a variably water saturated stratified sand is described. During the first stage of the experiment, 16.3 ml of liquid Hg-0 infiltrated and distributed into an initially partially water saturated system. Afterwards, during the second stage of the experiment, consisting of the simulation of a "rain event" to assess whether the elemental mercury already infiltrated could be mobilized due to local increases in water saturation, a significant additional infiltration of 4.7 ml of liquid mercury occurred from the remaining DNAPL source. The experiment showed that, under conditions similar to those found in the field, Hg-0 DNAPL infiltration is likely to occur via fingers and is strongly controlled by porous medium structure and water saturation. Heterogeneities within the porous medium likely determined preferential pathways for liquid Hg-0 infiltration and distribution, as also suggested by dual gamma ray measurements. Overall, this study highlights that the infiltration behaviour of mercury DNAPL is strongly impacted by water saturation. In the field, this may result in a preferential infiltration of Hg-0 DNAPL in wetter areas or in its mobilization due to wetting during a rain event, as indicated by this study, or a groundwater table rise. This should be considered when assessing the likely distribution pathways of historic mercury DNAPL contamination as well as the remediation efforts