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Background and Theory
Spontaneous Percolation
Spontaneous percolation is the process of fine particles infiltrating into an immobile coarse bed through the void spaces. Research on spontaneous percolation has been undertaken experimentally (e.g. Einstein, 1968; Sakthivadivel and Einstein, 1970; Beschta and Jackson, 1979; Carling, 1984; Diplas and Parker, 1992; Gibson et al., 2009; 2010; Dermisis and Papanicolaou, 2014), in the field (e.g. Frostick et al., 1984; Carling and McCahon, 1987; Lisle, 1989), and using models (Cui et al., 2008; Wooster at al., 2008).
Einstein (1968) explored the infiltration of suspended silica flour into an initially clean, static, gravel bed. He showed that the fine sediment infiltrated the gravel framework to the base of the deposit without clogging, and proceeded to fill the voids from the base upwards. Since that work, the process of spontaneous percolation has been examined numerous times in a fluvial context. A particular focus of interest has been investigation of the influence of grain size ratio (the ratio between the diameter of the coarse sediment forming the bed framework, Dc, and the fine infiltrating sediment, Df) on this process (e.g. Beschta and Jackson, 1979; Frostick et al., 1984; Diplas and Parker, 1992; Gibson et al., 2009). In these works it has been demonstrated that the larger the grain size ratio (Dc/Df), the greater the amount of fine sediment infiltration. The control of grain size ratio over the amount of fine sediment infiltration is understandable as it dictates how much finer sediment can fit in the voids of a gravel deposit.
The influence of the grain size ratio on the vertical gradational profile formed due to spontaneous percolation has also been investigated. Depending upon the ratio, finer sediment has been shown to undergo ‘unimpeded static percolation’, form a ‘bridge’ layer, or not infiltrate into the bed. Table 1.1 summarizes experiments that have assigned boundaries to the formation of these different types of profile.
The term ‘unimpeded static percolation’ describes fine sediment infiltration to the base of a deposit so that the voids in the matrix fill from the base upward. Gibson et al. (2010) showed that, following unimpeded static percolation, the sand content is relatively constant over the depth and fills nearly all the void space. Einstein (1968), Gibson et al. (2009) and Gibson et al. (2010) observed unimpeded static percolation.
A ‘bridge’ layer is formed when the void geometry causes the fines to become blocked, or lodged, in void throats so that fine sediment can infiltrate only to a limited depth. Bridging has been observed both in the field (Frostick et al., 1984; Lisle, 1989) and in the flume (Beschta and Jackson, 1979; Diplas and Parker, 1992; Allan and Frostick, 1999; Gibson et al., 2009; Gibson et al., 2010; Dermisis and Papanicolaou, 2014). The depth of a bridge layer into the gravel deposit is commonly reported to be between 2.5 and 5 D90 of the gravel (Beschta and Jackson, 1979; Lisle, 1989; Diplas and Parker, 1992). The bridge, or seal, layer prevents infiltration farther into the bed, with additional fine sediment entering the bed being stored above the bridges. Once the bed has become saturated with fine sediment above the bridge layer, if more fines are introduced, then they have been observed to appear on the bed surface (Diplas and Parker, 1992).
Sakthivadivel and Einstein (1970) put forward different theories to explain the formation of these bridges, including two fine particles arriving simultaneously and forming a bridge (their experiments did not support this theory) or, alternatively, one fine particle either moving slowly, or being retained in ‘dead space’, being joined by another particle and forming a bridge. The formation of bridges or ‘arches’ by spherical material is well known in granular mechanics (e.g. To et al., 2002; Pugaloni and Barker, 2004).
To understand spontaneous percolation behavior as a function of grain size ratio, the geometry of the grain arrangements and void spaces must be known. As an ideal case, the packing of uniform spheres has been studied for a long period of time. In 1611, Johannes Kepler hypothesized that the densest packing arrangement for cannonballs yields a void fraction of approximately 0.26 (Andreotti et al., 2013), yet this was not proven until recently by Hales (2005). This packing arrangement is the theoretically densest possible packing, and would be difficult to achieve in a real system. In contrast, the loosest possible packing arrangement in which the system is stable was shown by Onoda and Liniger (1990) to have a void fraction of approximately 0.45 (but see next paragraph regarding cubic packing); this state is termed ‘random loose packing’. Between these two extremes, Scott and Kilgour (1969) defined ‘random close packing’, which is formed by spheres randomly arranged in a rigid container and vibrated to ensure close packing; this has a void fraction of approximately 0.36. Between the limit states, there exists a wide range of stable packing arrangements (see Allen, 1982).
Allen (1982) summarized work undertaken by Manegold et al. (1931), Horsfield (1934) and White and Walton (1937) on the size of the largest sphere which could fit into the largest void space for various packing arrangements. For cubic, orthorhombic and rhombohedral packing arrangements, the void fractions are 0.4764, 0.3954 and 0.2595, respectively. If Dc is the diameter of the spheres forming the packing arrangement, and Df,max is the size of the largest sphere which can fit into the largest void space, values of Dc/Df,max for the different packing arrangements are 1.366, 1.895 and 2.414, respectively. These values are much smaller than those reported from fluvial experiments in Table 1.1, demonstrating that factors other than grain size ratio play a role in the infiltration behaviour.
Other factors which have been shown to modify the amount of fine sediment infiltration into a static coarse bed include:
(1) Flow conditions: Huston and Fox (2015) undertook a macroanalysis and statistical analysis of multiple previously published studies on fine grain infiltration into gravel beds in hydraulically rough turbulent open flows. They discovered that, whilst the grain size ratio was a good predictor for whether a bridge layer would form, it was not a good predictor of the maximum depth of bridging. Instead, they found that a combination of the bed porosity and the roughness Reynolds number, which indicates a control of the pore water velocity distribution, was a better predictor of maximum bridging depth.
(2) Fine feed rate: Wooster et al. (2008) undertook experiments wherein sand at varying feed rates was input to a clean gravel bed. Higher sand feed rates resulted in less infiltration into the bed.
(3) Other sediment properties: It has been noted that the framework packing arrangement is influenced by sediment shape (Frostick et al., 1984) and the grain size distribution (Lisle, 1989). These, in turn, influence the void sizes and consequently the infiltration behavior.
A great deal is known about spontaneous percolation, however the question arises, how would this grain sorting process change if the surface of the gravel bed were in motion, as is often the case in nature? Would the moving surface layer cause changes to the spontaneous percolation process in the underlying static bed?
Kinetic Sieving
Kinetic sieving occurs when granular materials containing particles of different sizes are in motion. The process of kinetic sieving has been extensively addressed in granular physics literature to gain insight for industrial purposes. For example, research has been undertaken to improve understanding on the segregation of granular materials in hoppers and of medical ingredients for the pharmaceutical industry.
Savage and Lun (1988) used different sizes of dry granular material to experimentally and theoretically study the process of kinetic sieving in an inclined free surface flow. They assumed that flow within a granular medium takes place in layers which move relative to each other. For relatively slow flows, where collisions are not too vigorous, they proposed two mechanisms to explain the transfer of particles between the layers:
(1) The particles are continually rearranging as the layers are moving relative to one another. If a void space opens up into which a particle from the layer above is able to fall, the particle will change layers. There is a higher probability of finding a void space for a small particle to fall into than a larger one. Therefore fines move towards the base of the deposit.
(2) As the fine sediment is moving towards the channel base in (1), there must be some mechanism that moves particles upward to preserve mass conservation. They attributed this to an imbalance of instantaneous forces acting on a particle, which causes it to be squeezed into a different layer. This process has no preference for direction of movement, or size of grain involved.
Although the majority of research on kinetic sieving has been focused in industrial contexts, there is an increasing body of literature documenting the process in a fluvial context.
The process of ‘kinetic sieving’ was introduced into fluvial sedimentology as an explanation for inverse sorting observed in sediment deposits (Middleton, 1970). Since then the process has been invoked to partly explain the formation of bed pavements (Parker and Klingeman, 1982) and ‘mobile armour layers’ (Mao et al., 2011). Additionally, kinetic sieving in coastal environments, due to waves, is becoming an increasingly explored topic (e.g. Calantoni and Thaxton, 2008).
Allan and Frostick (1999) investigated how the formation of a fine sediment matrix is influenced by flows that are capable of entraining the gravel bed compared to flows which cannot. They observed that, when the coarse particles ‘jostle’ and ‘shake’, the fine sediment is able to fall past the surface layer into the subsurface. Then, just before the coarse particle is entrained, the framework1 lifts and dilates, and fluid is drawn into the space created, along with fine sediment.
Bacchi et al. (2014) undertook experiments comparing the size sorting behavior between a run with mobile coarse material and a run with static coarse material. The two runs led to different bed behaviours and morphologies, and in the run in which kinetic sieving was possible, it was noted that highly efficient vertical sorting occurred.
Whilst awareness of kinetic sieving is increasing, we do not have a complete description of this process in a fluvial context. This research will contribute to an improved understanding by examining how the grain size ratio between the segregating grains impacts upon the behaviour.
1 Coarse grains forming the structure of the bed.
Sediment Mobility
In addition to examination of the size sorting processes, investigation of the consequences of a fine grain input to a channel has been undertaken due to observed impacts upon sediment mobility. Imagine a channel with a mobile uniform bed (constant grain diameter) in equilibrium, whereby the sediment input rate is equal to the sediment output rate. An increase in sediment supply to the channel, with the additional material being finer than that forming the bed, has been shown to cause an increase in the coarse sediment transport rate in comparison to the preceding uniform conditions. The superior mobility of grain size mixtures was first demonstrated by Gilbert (1914), and has since been explored experimentally (Jackson and Beschta, 1984; Iseya and Ikeda, 1987; Ikeda and Iseya, 1988; Wilcock et al., 2001; Cui et al., 2003; Curran and Wilcock, 2005b; Venditti et al., 2010a, 2010b), and also observed in the field (e.g., Ferguson et al., 1989; Montgomery et al., 1999; Major et al., 2000).
The increase in transport rates resulting from a fine sediment addition may even be so large as to increase the sediment output rate above the sediment input rate, despite the increased supply to the system, which leads to channel degradation and a reduced equilibrium bed slope (Iseya and Ikeda, 1987; Ikeda and Iseya, 1988; Curran and Wilcock, 2005b). In contrast, an increase in sediment supply to the channel with the additional material being the same size as that forming the bed, would result in a steeper channel slope (Lane, 1955), as more energy would be required to transport the larger load.
The superior mobility of mixtures has been attributed to several causes. (1) Enhanced entrainment potential: Houssais and Lajeunesse (2012) demonstrated that, in a bimodal bed, an increasing fraction of fine sediment on the bed surface leads to a reduction in the critical Shields number for the coarse component. (2) Elimination of ‘deposition’ locations: infilling of the bed surface with fines will remove potential ‘deposition’ locations (Venditti et al., 2010b), consequently once a particle is entrained, it is less likely to stop again. (3) Changes in the flow structure: infilling of fines on the bed surface will result in a smoother top layer, which has been observed to cause flow acceleration close to the bed, resulting in an increased drag force on the coarse particles (Venditti et al., 2010b). (4) Pivoting angle: Komar and Li (1986) examined the pivoting angle required for the threshold of motion. For a grain to be entrained, it must pivot about a contact point with an underlying grain; the angle through which it must rotate is the ‘pivoting angle’. The pivoting angle of a grain is, amongst other things, a function of the ratio of the diameter of the grain to the diameter of the underlying grain, with a greater difference in diameter leading to a smaller pivoting angle (Komar and Li, 1986). (5) Exposure: the projection of a larger grain above a bed formed of finer material increases the exposure of the grain to the flow (Fenton and Abbott, 1977), therefore resulting in a lower critical Shields number for the larger grain when compared to uniform conditions (Parker and Klingeman, 1982). However, the finer grains have a higher critical Shields number as they are ‘hidden’ from the flow.
The extent of the increase in sediment transport rates following the introduction of fines to a channel has been shown to depend upon the proportion of fines in the total feed (Jackson and Beschta, 1984; Iseya and Ikeda, 1987; Ikeda and Iseya, 1988; Wilcock et al., 2001, Curran and Wilcock, 2005b). However, the relation between the proportion of fines and the equilibrium slope of the bed varies:
(1) Iseya and Ikeda (1987) held the gravel feed rate constant, and varied the sand feed rate between 0 and 58 % of the total feed rate. They observed a reduction in the equilibrium slope between 0 and 48 % sand content, and then a slope at 58 % no different than that at 48 %. During this experiment, the D50 of the gravel was 2.6 mm, and the D50 of the sand was 0.37 mm; therefore a grain size ratio of 7.03.
(2) Curran and Wilcock (2005b), using the same method, saw a reduction in the equilibrium bed slope between 33 and 72 % sand feed content, and then a more gradual decrease between 72 and 86 %. In this experiment the grain size ratio indexed by D50 was approximately 25.
(3) Ikeda and Iseya (1988) held the total feed rate constant, and varied the feed rates of the fine (D=0.2 mm) and coarse (D=1 mm) components (grain size ratio of 5). Between 0 and 43 % fine content, they observed a reduction in the equilibrium bed slope, but above a 43 % content, there was a slight increase in slope.
(4) Ikeda and Iseya (1988) undertook experiments with sand (D50=0.37mm) and gravel (D50=2.6mm) (grain size ratio of 7.03). In this experiment the total feed rate was kept constant. A reduction in the equilibrium bed slope was observed until the sand content reached 54%. As the sand content increased beyond this point, the slope increased slightly.
Table of contents :
Chapter 1: Introduction
1.1 Introduction
1.2 Background and Theory
1.2.1 Spontaneous Percolation
1.2.2 Kinetic Sieving
1.2.3 Sediment Mobility
1.2.4 Research Gaps
1.3 Wider Considerations
1.4 Research Questions
Chapter 2: Infiltration of fines into a coarse mobile bed: a phenomenological study
2.1 Experimental Arrangements
2.2 Experimental Procedure
2.2.1 Supporting Information
2.3 Observations
2.3.1 Coarse Sediment Alone
2.3.2 Experiments: Set 1
2.3.2.1 0.7 mm and 0.9 mm Fine Input: Partially Impeded Static Percolation
2.3.2.2 1.5 mm and 2 mm Fine Infiltration: Bridging
2.3.2.3 3 mm and 4 mm Fine Infiltration: No Spontaneous Percolation
2.3.3 Experiments: Set 2
2.3.3.1 0.7 mm Fine Input
2.3.3.2 2 mm Fine Input
2.4 Discussion
2.5 Conclusion
Chapter 3: Introducing finer grains into bedload: the transition to a new equilibrium
3.1 Experimental Arrangement
3.2 Experimental Procedure
3.3 Results
3.3.1 Experiments: Set 1
3.3.2 Experiments: Set 2
3.4 Discussion
3.5 Conclusions
Chapter 4: Testing reproducibility in a fluvial context
4.1 Experimental Arrangement
4.2 Experimental Procedure
4.3 Results
4.4 Discussion
4.5 Conclusion
Chapter 5: The influence of grain shape
5.1 Experimental Arrangements
5.2 Experimental Procedure
5.2.1 Supporting Information
5.3 Results
5.3.1 Mixed Experiments
5.3.2 Natural Materials
5.4 Discussion
5.5 Conclusion
Chapter 6: Perspectives and Conclusion
6.1 Perspectives
6.2 Conclusions
6.3 Future Work
Bibliography
Appendices
