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The prediction of incipient motion has had great importance to the theory of sediment transport. The most commonly used methods are based on the concept of critical shear stress and employ an approach similar, or identical, to the Shields diagram. An alternative method that uses the movability number, defined as the ratio of the shear velocity to t...
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... find c θ for a particular set of hydraulic and sediment conditions. Substantially more data has been collected subsequent to Shields' work, significantly expanding the range of experimental conditions. One of the issues that became significant with the arrival of these new experimental sets was the scatter of the data. This scatter is apparent in Fig. 1, where the empirical threshold curves of Paphitis (2001) are plotted against measurement data. Some authors, such as Zanke (2003) and Vollmer and Kleinhans (2007), attempted to explain and predict the disperse nature of the data. However, their analyses are complex and depend on variables that are unknown in most practical ...
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... this study, 517 sets of data obtained from many different sources and distinct physical settings were used. The origin of the data and their main characteristics are presented in Table 1, which includes the data used in the original work of Shields (1936) and plotted in Figs. 1 through 3. Not all the data presented in the original sources were used: the sets that did not contain enough information for an accurate calculation of the particle's settling velocity were discarded. Nonetheless, the sediments associated with the data sets in Table 1, made of natural and artificial grains, offer a variety in shape and density ...
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... provide a comparison with Shields parameter-based methods, the statistical analysis above was extended to the explicit curves of Paphitis (2001) (only the mean threshold curve was considered, which is shown as a solid line in Fig. 1(b)) and Yalin and da Silva (2001) (curve was not shown). The corresponding values of the respective statistical parameters for these two curves are presented in rows 3 and 4 of Table 2. The values of R show a significantly larger bias for these two curves than for Eq. (8). Based on the standard deviation, this bias is statistically ...
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... Table 1 provides an overview of the parameters employed in the model. It is acknowledged that the critical Shields parameter on a flatbed can vary temporally and spatially, contingent on bed particle size under external shear stress (Julien 2010;Simões 2014;Soulsby and Whitehouse 1997). Nevertheless, this study simplifies the application by using a constant critical Shields parameter on the flatbed. ...
This research is dedicated to examining downslope sediment transport on steep shorefaces. We present a model that incorporates nonlinear surface wave profiles, sediment movement thresholds, and slope effects, utilizing a set of semi-empirical formulas. The model quantitatively assesses the disparity between wave-augmented upslope transport and gravity-augmented downslope transport, and computes sediment transport rates using a single calibration coefficient. Validation of the model is carried out in the Fuji coast of Japan, where offshore wave conditions and seabed topography with a uniform grain size distribution serve as inputs. The computational outcomes reveal that sediment transport primarily occurs under high wave conditions, and downslope transport dominates on steep slopes. The calibration coefficient is determined through a comparison with observed data, demonstrating a strong agreement in the average annual sediment loss in the target area. Moreover, the model offers insights into the possible mechanism behind the existence of a transition area between the upper and lower shoreface, marked by an abrupt change in seabed slope.
... Over the past decades, practical experiments and theoretical measures have been performed to determine the threshold bed shear stress at the particle's incipient motion. In order to predict the sediment transport rates, surplus shear stress has played a vital role (Simões 2014). ...
loods are among the adverse natural events with the possibility of turning into a disaster, causing economic losses and casualties. Flood events can become even more dangerous with the presence of intense sediment transport since the morphologic response of a river can determine erosion and deposition in different areas. In-bed structures can be undermined in erosional reaches, while the riverbed elevation increases in a depositional reach and, consequently, the conveyance of the river decreases. The dynamics of the morphologic processes may be different in lowland and upland reaches due to different sediment, slopes, and flow properties. The aim of the thesis is to study, experimentally and numerically, the bed aggradation process in an overloaded channel with a supercritical flow regime. The aggradation experiments of the study are executed in the Mountain Hydraulics Laboratory of the Politecnico di Milano, located in the Lecco campus. These experiments are characterized by an inflow discharge of sediment material that is larger than the sediment transport capacity, resulting in the deposition of sediment in the studied channel. A series of aggradation experiments are realized varying the water discharge and the inflow sediment discharge. Beyond the observation of the phenomenon in progress, the experiments provide quantitative information. For the purpose of experimental data acquisition, different parts of the experimental system are monitored with different cameras, and measurements are done through some image processing methods, appropriately devised. The experimental campaign is completed by experiments specifically devoted to determining the sediment transport capacity of the flow at the initial condition. The time scales of a considered scenario are of great importance for the goal of emergency planning. For the present experiments, this consideration stimulates a study of the propagation of a sediment aggradation wave, for which a front can be identified and its celerity can be determined. The runs performed in this thesis enable preliminary considerations to be made on how a front celerity may depend on the control parameters of the system. The aggradation process studied by the experimental tests is also reproduced with a numerical simulation. The software used to implement the numerical model is BASEMENT, provided by ETH Zurich. In order to obtain a good correspondence between numerical and experimental results, two parameters are calibrated: the Manning coefficient and a bedload factor for the computation of the sediment transport capacity. Depending on the water discharge, different values for calibration factors are obtained.
... The initiation of motion of particles on the bed is commonly described by the Shields curve, which provides a critical Shields number θ cr for the initiation of motion of each grain size. Over the years, many critical Shields curves have been formulated (Mantz, 1977;Brownlie, 1981;Collins & Rigler, 1982;Komar & Clemens, 1986;Soulsby, 1997;Paphitis, 2001;Zanke, 2003;Cao et al., 2006;Rijn, 2007;Beheshti & Ataie-Ashtiani, 2008;Simões, 2014;Kleinhans et al., 2017;Lapôtre & Ielpi, 2020). Some of these equations have also been used in the past for Mars and Titan (Kleinhans, 2005;Burr et al., 2006;Lamb et al., 2012;Amy & Dorrell, 2021). ...
... The Soulsby (1997) equation is sometimes also cited as Soulsby & Whitehouse (1997) and is for example used in Kleinhans et al. (2017); Lapôtre & Ielpi (2020). Additionally, we plotted more modern equations of the initiation of motion from Zanke (2003); Cao et al. (2006); Rijn (2007); Simões (2014). In addition to the equation in the plot we also considered the Zanke (2003) fit from Kleinhans (2005), but was discarded because of the limited grain size range compared to the original Zanke (2003). ...
... The largest differences occur in the cohesive regime. One equation deviates significantly from the other equations, which is the equation from Simões (2014). In the main part of the paper we used Zanke (2003), because this equation is physicsbased, while many other equations are empirical fits to flume data, which could contain hidden gravity components in the coefficients. ...
Studies of fluvial landforms on the surface of Mars have become more detailed since rover data became available of areas altered by water (e.g. water-deposited sediment in Gale crater by Curiosity and the Jezero delta by Perseverance). As surface interpretations become more detailed, we need to pay more attention to the differences between Earth and Mars to fully describe the processes that determine fluvial geomorphology on Mars. In this study, we isolate and clarify the effect of gravity on fluvial sediment transport by means of an analytical model of a transport capacity limited alluvial channel. We use and compare 32 fluvial sediment transport predictors to calculate the sediment transport rate for a range of grain sizes (clay to boulders) and a lognormal sediment distribution. The results indicate that 1) bigger grain are mobilised on Mars and transported in suspension. 2) The magnitude of suspended sediment transport flux is larger on Mars and therefore the total sediment flux as well. Consequently, the gravity effect on transport rates vary with grain size. The differences are shown to be around 5 times higher for the tested conditions on Mars for grain sizes around the bed load-suspended load transition. We expect that these gravity-driven differences in fluvial sediment transport creates differences in sediment sorting, morphology and stratigraphy between Earth and Mars. Because the effect of gravity varies by grain size and transport mode, it is advised not to use total load predictors in the future for planets besides Earth. Additionally, our results stress the significance of gravity on hydraulic and sedimentary processes in rivers and provide new insights into the use of Earth-derived fluvial sediment transport predictors for estimating transport rates and morphological change on Mars and other planets.
... The incipient motion condition is the critical condition where critical bed shear stress is represented as 2 * , c τ ρu = where u *c is the critical shear velocity. Many researchers have used another parameter for the threshold of the sediment motion, the Movability Number Λ, which is the ratio of the shear velocity of the flowing stream to the settling velocity w s of the sediment under observation (Collins and Rigler, 1982;Komar and Clemens, 1986;Paphitis, 2001;Beheshti and Ataie-Ashtiani, 2008;Simoes, 2014;Rieux et al., 2019). The incipient motion condition is represented by the critical Movability Number given by ...
... Even though Λ 2 considers the effect of all important settling velocity, but still, it is not as better parameter as Λ. As per Simoes (2014), Λ reduces the scatter of the experimental data around the empirical curves as it is proportional to the square root of θ, hence τ as per the following equation. ...
... Various researchers have replaced the traditional Shields parameter with the Movability Number, citing the inclusion of the shape effects by having settling velocity in the denominator of the dimensionless ratio as the reason (Collins and Rigler, 1982;Paphitis, 2001;Simoes, 2014). The varying shapes and texture of the sediment used in this study (Fisher et al., 1983;Paphitis et al., 2002;Rieux et al., 2019) provide varying hydrodynamic behaviour while settling or moving on the sediment bed. ...
... Finally, they were able to determine a certain value of critical shear stress for both uniform and non-uniform flow of the sediment transition. Simoes [5] showed that this method can also be commonly used to determine threshold conditions of the sediment motion using a parameter called the number of movable particles and changing the parameters of the Shields graph. Wang et al. [6] studied experimentally the presence of submerged flexible vegetation in the open channels and found with their equation, that the threshold velocity of sediment motion in the presence of the vegetation was lower than when the vegetation does not exist. ...
... Novak and Nalluri [7,8] showed that the threshold velocity of motion in circular and rectangular channels with rough and flat and a stable invert bed follows the following equation: (4) Where is the threshold velocity of motion, = sediment density, g = gravity acceleration, d 50 = average diameter of the sediment, R = the hydraulic radius of the cross sectional area of flow. El-Zaemey (1991) in an experimental test on rectangular and circular channels with a flatbed showed that the critical velocity equation is the following formula: (5) Where is the threshold velocity of motion, = sediment density, g = gravity acceleration, d 50 = average diameter of the sediment, R = the hydraulic radius of the cross sectional area of flow that are performed for both stable rough and flat beds. ...
One of the common methods to prevent the erosion of the furrows’ bed is to enter the water flow with a discharge less than the maximum of eroding discharge. Accordingly, it is important to determine the threshold velocity of the bed particle motion. In the current study, the average diameter of particles in each soil class was determined using 12 available classes in the soil texture triangle and then in an irrigation furrow with a fixed bed and triangular cross section, the threshold velocities were calculated using the equations provided by El-Zaemey, Novak, Nalluri and Charles Heinz Bong and compared them with proposed values of Walker et al and the US Department of Soil Conservation. The results were also compared with the Shields graph by determining the Shields parameter and boundary layer Reynolds number in the slope range of 0.5% to 1% for each soil texture class. A graph was presented based on all the above mentioned methods to simplify the use of the results. In addition to specifying the difference in velocity values predicted by different methods, the graph can be also used to determine the maximum permissible velocity in furrows.
... Shear Stress (To) The force per unit wetted area that acts on a surface is defined as shear stress (Gilley, et al. 1993) that force to the incipient soil particle movement. The concept of excess shear stress has played a major role in the prediction of sediment transport rates (Simoes, 2014). Due to the force vector component, shear stress occurs which is parallel to the cross-section of the initial sediment movement and perpendicular to cross-section of the bed (Dey 2021). ...
A coastal beach is the most dynamic field in the world. Being the transition zone between land and sea, the beach is a coastal
landform facing the open sea and it is a gently sloping flat plain between low water lines of spring tide to the upper limit of
wave action. It could be defined as a sloppy sand platform towards the sea. About 45 km long Kanthi coast stretches from the
mouth of the tidal river Rasulpur in the east to the mouth of Subarnarekha River in the west. Kanthi Coast is associated with
seven beaches, viz. Junput Beach, Shoula Beach, Mandarbani Beach, Tajpur Beach, Shankarpur Beach, Digha Beach and
Talsari Beach from east to west. Beach is shaped by the coastal wave. Wave is the source of energy that dissipates on the
beach. Sediment textural distribution influences the work of waves on the beach. Burrowing activity by the crab is governed
the beach sediment textural distribution. In this research work, it has been observed that crab-burrowing activity pronounced
mean sediment grain size and pronounced the sediment movement by the marine agents. To trace the said things mean grain
size assessment by Folk and Ward method (1957) and sediment transportation model of Inman and Bagnold (1963) and the
model of Bagnold (1941) are used. It has been examined that the crab burrowing activity on the beach is very important for
the beach environment. But the crab habitat in the study area is under threat for unscientific tourism development that
directly influences beach health.
... There is another sediment threshold parameter which can be mentioned here, the movability number. This, which has been considered a potential replacement of the Shields parameter (Paphitis 2001;Paphitis et al. 2002;Simões 2014) and explored by many researchers in studying the sediment threshold in the field of sediment hydraulics (Paphitis 2001;Paphitis et al. 2002;Beheshti and Ataie-Ashtiani 2008;Simões 2014;Bhat and Ahanger 2021), is the shear velocity, proportional to the square root of stress, non-dimensionalized with respect to grain settling velocity: ...
... There is another sediment threshold parameter which can be mentioned here, the movability number. This, which has been considered a potential replacement of the Shields parameter (Paphitis 2001;Paphitis et al. 2002;Simões 2014) and explored by many researchers in studying the sediment threshold in the field of sediment hydraulics (Paphitis 2001;Paphitis et al. 2002;Beheshti and Ataie-Ashtiani 2008;Simões 2014;Bhat and Ahanger 2021), is the shear velocity, proportional to the square root of stress, non-dimensionalized with respect to grain settling velocity: ...
... The particle Reynolds number is expressed as R * = u * d∕ where is the kinematic viscosity of the flowing fluid. The dimensionless grain diameter (e.g., Paphitis 2001;Beheshti and Ataie-Ashtiani 2008;Simões 2014) is given by ...
Shields dimensionless stress and particle Reynolds number have been used since their introduction into sediment threshold studies. They do not separate forcing and resisting quantities so that both shear velocity and particle grain size occur in each. This study considers two different combinations of those traditional parameters to give two dimensionless variables, a dimensionless grain size independent of flow, and a dimensionless shear stress independent of the size. Considering observed data from various sources, the scatter around the new dimensionless threshold curve was found to be less than around the traditional Shields form. Simple explicit rational approximations were obtained between the new dimensionless stress and dimensionless grain size. They describe experimental results better than arbitrary formulae for the traditional Shields parameter. That, with the separation of flow and resistance, makes the solution of practical problems simpler.
... The hydraulic ratio is different from the one considered in the scour process, and S is the slope of the hydraulic grade line. A shear velocity criterion for incipient motion of sediment is used as follows [36]: ...
Scour is the most frequent cause of bridge collapses in Mexico. Bridges located along the
Mexican Pacific coast are exposed to extreme rainfall originating from tropical storms and hurricanes. Such environmental phenomena trigger sediment loss, which is known as scour. If maintenance actions are not taken after scouring events, the scour depth increases over time until the bridge collapses. A methodology to estimate the scour hazard considering both the scour–fill interaction and the Monte Carlo simulation method is proposed. The general extreme value probability distribution is used to characterize the intensity of the scouring events, the lognormal distribution is used to characterize the sedimentation process (fill), and a homogeneous Poisson process is used to forecast the occurrence of both types of events. Based on the above, several histories of scour–fill depths are made; such simulations are then used to develop time-dependent scour hazard curves. Different hazard curves associated with different time intervals are estimated for a bridge located in Oaxaca, Mexico.
... Forces on bed particle: If the average tractive bed shear stress is not able to move the bed particles, the grains or river bed will be on rest. Hence it doesn't accelerate the river bed because all resultant force on it must be in balance [1][2][3]. There are 3 main types of forces acting on the particle: I. Submerged weight of the particle: It is simply a total downward weight of particle minus upward buoyant force. ...
Entrainment of river bed particles by turbulent flow is a core matter of study in river hydrodynamics. It is of great interest to river engineers to evaluate the shear stress for initiating river bed motion. The main objective is to calculate transport rates for bed load, to predict changes in bed level which are scoured or aggraded and to design a stable channel. Forces acting upon the particle especially fluid forces which give a major role in the incipient motion of the particle on the rough boundary. For calculation generally use shield’s diagram but some other modified methods and approaches are discussed. Modeling criteria are discussed for the hydraulically smooth and rough boundary depending on Reynolds number. In the past, experimental studies on tractive shear stress have been done by many researchers but consideration of lift force to analyze the movement of sediment is very limited. For suspended load transport, a detailed analysis of lift force is required. Based on the study it has been observed that shear stress depends on channel slope not only due to gravitational force but also many other factors like drag force, lift force, friction angle, fluctuations, velocity profile, etc. Complete analysis of these factors provides slope dependency over shear stress. To improve past studies, some factors have been discussed, to give a more correct force balance equation. This is very difficult task to analyze more and more variable’s dependency on the slope. Consideration of the possible number of variable holds complete analysis of experimental study. This paper also reviews the effect of particle Reynolds number and relative submergence over critical shield stress. Doi: 10.28991/cej-2021-03091700 Full Text: PDF
... Flemming (2000) identified a relationship between the particular grain size and critical shear velocity. This phenomenon was principally based on incipient motion, through the transition from a stationary to an initial (incipient) motion state as a response to increased hydrodynamic forces acting on a bed of unconsolidated deposits (Simões 2014). Folk (1974) suggested the concept of sediment textural maturity, based on the effect of coastal hydrodynamic processes on texture distribution. ...
Panjang Island Reef Flat is a remote area on Berau Continental Shelf with pristine ecological conditions. This site was selected to study the nature of sediment dynamics in tropical shallow waters. In addition, the sediment textural parameters provide good proxies for long term hydrodynamic process within the marine ecosystem. The aims of this study were to determine: (1) sediment textural parameters; (2) the transport mechanism of sediment particles; and (3) the depositional environment characteristics of the Panjang Island reef flat. The grain size parameters were further analysed to reveal the transport mechanism and energy regime. The results show the presence of coarse to fine sand sediments transported predominantly by rolling and suspension, with a sedimentary environment classified as Inner Shelf. These findings imply the incidence of gradual hydrodynamic energy attenuation at the shelf edge, characterized by breaking waves, followed by extensive seagrasses bed; these are collectively assumed to retard flow. This study suggests the subdivision of Panjang Island reef flat into two distinctive zones based on the ecological engineering capacity of seagrass, particularly regarding the influence on sediment particle distribution. The first comprises fine sand, and is associated with medium to large sized canopy seagrasses vegetation, while the second consists of medium to coarse sand, which is colonized by small to medium canopy sized seagrasses beds.
