Modeling and Practice of Erosion and Sediment
Transport under Change

Hafzullah Aksoy, Gil Mahe, Mohamed Meddi

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Modeling and Practice
of Erosion and
Sediment Transport
under Change

Edited by

Hafzullah Aksoy, Gil Mahé and Mohamed Meddi

Printed Edition of the Special Issue Published in *Water*
Modeling and Practice of Erosion and
Sediment Transport under Change
<figure><img src="image_3.png" /></figure>
Modeling and Practice of Erosion and
Sediment Transport under Change

Special Issue Editors

Hafzullah Aksoy

Gil Mahé

Mohamed Meddi

MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade

<figure><img src="image_4.png" /></figure>
Special Issue Editors

Hafzullah Aksoy
Istanbul Technical University
Turkey

Mohamed Meddi
Ecole Nationale Supérieure d'Hydraulique
Blida
Algeria

Gil Mahé
IRD, UMR HSM, Univ. Montpellier, CNRS
France

Editorial Office

MDPI
St. Alban-Anlage 66
4052 Basel, Switzerland

This is a reprint of articles from the Special Issue published online in the open access journal *Water* (ISSN 2073-4441) from 2018 to 2019 (available at: https://www.mdpi.com/journal/water/special-issues/erosion_sediment)

For citation purposes, cite each article independently as indicated on the article page online and as indicated below:

Last Name, A.A.; Last Name, B.B.; Last Name, C.C. Article Title. *Journal Name Year, Article Number, Page Range*.

ISBN 978-3-03921-431-0 (Pbk)

ISBN 978-3-03921-432-7 (PDF)

© 2019 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications.

The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND.
# Contents

<table><tr><td>About the Special Issue Editors</td><td>vii</td></tr><tr><td>Preface to "Modeling and Practice of Erosion and Sediment Transport under Change"</td><td>ix</td></tr><tr><td>Hafzullah Aksoy, Gil Mahe and Mohamed Meddi<br>Modeling and Practice of Erosion and Sediment Transport under Change<br>Reprinted from: Water 2019, 11, 1665, doi:10.3390/w11081665</td><td>1</td></tr><tr><td>Joanna Sziło and Robert Józef Bialik<br>Grain Size Distribution of Bedload Transport in a Glaciated Catchment (Baranowski Glacier, King George Island, Western Antarctica)<br>Reprinted from: Water 2018, 10, 360, doi:10.3390/w10040360</td><td>10</td></tr><tr><td>Yang Ho Song, Eui Hoon Lee and Jung Ho Lee<br>Functional Relationship between Soil Slurry Transfer and Deposition in Urban Sewer Conduits<br>Reprinted from: Water 2018, 10, 825, doi:10.3390/w10070825</td><td>25</td></tr><tr><td>Faiza Hallouz, Mohamed Meddi, Gil Mahé, Samir Toumi and Salah Eddine Ali Rahmani<br>Erosion, Suspended Sediment Transport and Sedimentation on the Wadi Mina at the Sidi M'Hamed Ben Aouda Dam, Algeria<br>Reprinted from: Water 2018, 10, 895, doi:10.3390/w10070895</td><td>41</td></tr><tr><td>Mahrez Sadaoui, Wolfgang Ludwig, François Bourrin, Yves Le Bissonnais and Estela Romero<br>Anthropogenic Reservoirs of Various Sizes Trap Most of the Sediment in the Mediterranean Maghreb Basine<br>Reprinted from: Water 2018, 10, 927, doi:10.3390/w10070927</td><td>73</td></tr><tr><td>Yung-Chieh Wang and Chun-Chen Lai<br>Evaluating the Erosion Process from a Single-Stripe Laser-Scanned Topography: A Laboratory Case Study<br>Reprinted from: Water 2019, 10, 956, doi:10.3390/w10070956</td><td>92</td></tr><tr><td>Shanshan Guo, Zhengru Zhu and Leting Lyu<br>Effects of Climate Change and Human Activities on Soil Erosion in the Xihe River Basin, China<br>Reprinted from: Water 2018, 10, 1085, doi:10.3390/w10081085</td><td>108</td></tr><tr><td>Russell Adams, Paul Quinn, Nick Barber and Sim Reaney<br>The Role of Attenuation and Land Management in Small Catchments to Remove Sediment and Phosphorus: A Modelling Study of Mitigation Options and Impacts<br>Reprinted from: Water 2018, 10, 1227, doi:10.3390/w10091227</td><td>122</td></tr><tr><td>Necati Erdem Unal<br>Shear Stress-Based Analysis of Sediment Incipient Deposition in Rigid Boundary Open Channels<br>Reprinted from: Water 2018, 10, 1399, doi:10.3390/w10101399</td><td>140</td></tr><tr><td>Yi-Chiung Chao, Chi-Wen Chen, Hsin-Chi Li and Yung-Ming Chen<br>Riverbed Migrations in Western Taiwan under Climate Change<br>Reprinted from: Water 2018, 10, 1631, doi:10.3390/w10111631</td><td>150</td></tr></table>
Gergely T. Török, János Józsa and Sándor Baranya
A Shear Reynolds Number-Based Classification Method of the Nonuniform Bed Load Transport
Reprinted from: *Water* **2019**, *11*, 73, doi:10.3390/w11010073
163

Jiří Jakubínský, Vilém Pechanec, Jan Procházka and Pavel Cudlín
Modelling of Soil Erosion and Accumulation in an Agricultural Landscape—A Comparison of Selected Approaches Applied at the Small Stream Basin Level in the Czech Republic
Reprinted from: *Water* **2019**, *11*, 404, doi:10.3390/w11030404
179
## About the Special Issue Editors

**Hafzullah Aksoy** received a BA (1990) in civil engineering and a master's degree (1993) and PhD degree (1998) in hydraulics and water resources from Istanbul Technical University, Turkey. He worked in Germany and the USA during his post-doctoral studies. He was appointed as an assistant professor in 2002 and an associate professor in 2003 at Istanbul Technical University. He spent one year (2009) in Germany as an Alexander von Humboldt guest researcher. Currently, he is a professor of hydrology and water resources in the Hydraulics Unit of the Civil Engineering Department at Istanbul Technical University. His research topics range from statistical methods to process-based modeling techniques for rainfall-runoff-sediment transport in hydrological watersheds and rivers. He was awarded the 2006 Best Paper and 2009 Best Discussion Awards of the ASCE *Journal of Hydrologic Engineering* and the 2011 Engineering Incentive Award of the Scientific and Technological Council of Turkey (TUBITAK). Prof. Aksoy is the universities' representative to the National Hydrology Commission of Turkey and has served as vice president (2007–2011), president elect (2011–2013), president (2013–2017), and past president (2017–2019) of International Commission of Surface Water (ICSW), International Association of Hydrological Sciences (IAHS). He was recently awarded a Fulbright Visiting Researcher Scholarship.

**Gil Mahé** received a BA (1986) in geology and geophysics from Paris XI University and a master's degree (1987) in hydrology. He then studied hydrology, meteorology, climate, and oceanography with the ORSTOM Institute (now IRD, Research Institute for Developing Countries) in France and Senegal to obtain a PhD from Paris XI University in 1992. In 1993, his PhD received the French national prize of "Georges Hachette" from the Société de Géographie of Paris. He is now a research director at IRD. He spent five years in Mali working on the hydroclimatology and sediment transport of the Niger River. He then spent one year in the Climatic Research Unit of University of East Anglia in Norwich, UK, working on the hydrological modeling and impact of climate change on the Niger River. He went back to West Africa for four more years, working in Burkina Faso at the International School of Engineers on the Sahel paradox: less rainfall and more runoff. He then developed research in Maghreb on the impact of climate and human activities on river regimes and sediment transport, with a more recent focus on the impact of dams on sediment transport to the sea. He is currently the president of the International Commission of Surface Water (ICSW), International Association of Hydrological Sciences (IAHS). He is the chair of the International Committee of the FRIEND program of UNESCO (International Hydrological Program) and is responsible for the Mediterranean FRIEND group. He is the coordinator of the French research program SICMED of the MISTRALS CNRS/INSU program for the study of the Mediterranean environment.

**Mohamed Meddi** received his PhD from the University of Strasbourg in France. He is a professor of hydrology and a scientific manager of doctoral training at the National High School of Hydraulics of Blida. Prof. Meddi is a member of the editorial board of several journals. His research focuses on hydrology and water science, and he has written more than 50 publications. Prof. Meddi has organized several international conferences in the field of water science. In addition, he is a member of the National Commission for the implementation of the PNR topics. Prof. Meddi is responsible for several national research and international programs. Currently, he is reviewer for several scientific journals. He is a member of the MEDFRIEND (one of the eight FRIEND programs of
the International Hydrological Program of UNESCO). Most recently, he was a member of the WASER
(World Association for Sedimentation and Erosion Research) Council.
# Preface to “Modeling and Practice of Erosion and Sediment Transport under Change”

This book titled "Modeling and Practice of Erosion and Sediment Transport under Change" is composed of five keywords. Two out of the five keywords—"erosion" and "sediment transport"—are related to processes. They are two consecutive processes; one, the former, comes after the other, the latter. Sediment particles are first detached from their original location by erosion under the effect of different agents, such as wind, rainfall, and runoff, and are then transported. Another two keywords are "modeling" and "practice", which are mutually linked—both based on each other. Good practice is not possible without a theoretically well-established model nor is modeling valuable when it is not applicable to practice. Finally, the crucial keyword, "change", is a kind of mirror to the future of the above four keywords. Erosion and sediment processes should be modeled and practiced considering hydrological conditions under continuous change. "Change" is the most challenging and uncertain keyword of the book title, as it is born not only of natural reasons but also due to anthropogenic disturbances. It is a common belief of the editors that all the papers in this book should be considered a contribution to addressing the erosion and sediment transport problem in hydrological watersheds at different scales of space and time and also under any kind of change. This book is expected to attract the interest of hydrologists, water resources researchers, practitioners, and decisionmakers.

Hafzullah Aksoy, Gil Mahé, Mohamed Meddi

*Special Issue Editors*
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# Modeling and Practice of Erosion and Sediment Transport under Change

Hafzullah Aksoy 1,*, Gil Mahe 2 and Mohamed Meddi 3

Received: 27 May 2019; Accepted: 9 August 2019; Published: 12 August 2019

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check for
updates

**Abstract:** Climate and anthropogenic changes impact on the erosion and sediment transport processes in rivers. Rainfall variability and, in many places, the increase of rainfall intensity have a direct impact on rainfall erosivity. Increasing changes in demography have led to the acceleration of land cover changes from natural areas to cultivated areas, and then from degraded areas to desertification. Such areas, under the effect of anthropogenic activities, are more sensitive to erosion, and are therefore prone to erosion. On the other hand, with an increase in the number of dams in watersheds, a great portion of sediment fluxes is trapped in the reservoirs, which do not reach the sea in the same amount nor at the same quality, and thus have consequences for coastal geomorphodynamics. The Special Issue "Modeling and Practice of Erosion and Sediment Transport under Change" is focused on a number of keywords: *erosion* and *sediment transport*, *model* and *practice*, and *change*. The keywords are briefly discussed with respect to the relevant literature. The papers in this Special Issue address observations and models based on laboratory and field data, allowing researchers to make use of such resources in practice under changing conditions.

**Keywords:** Anthropocene; climate change; deposition; erosion; modeling; practice; sedimentation; sediment transport; watershed

## 1. Keywords of the Special Issue

This Special Issue entitled *Modeling and Practice of Erosion and Sediment Transport under Change* is focused on five keywords. Two out of the five keywords are related to processes, which are *erosion* and *sediment transport*. Sediment particles are first detached from their original location by erosion under the effect of different agents, such as wind, rainfall, and runoff, followed by transportation. Another two keywords are the *modeling* and *practice*, which are mutually linked and both based on one other. Good practice is possible without a theoretically well-established model nor is modeling valuable when it is not applicable to practice. Finally, the crucial keyword, *change*, comes in the title of the Special Issue and serves as a kind of mirror to the future of the previous four keywords. Erosion and sediment processes should be modeled and practiced considering the hydrological conditions under continuous change. The keyword *change* is the most challenging and unclear of the Special Issue as it is born not only of natural reasons but also as a result of anthropogenic disturbances.

## 2. Erosion and Sediment Transport

Erosion is the process of detachment and transportation of soil materials by erosive agents [1] such as wind, rainfall, or runoff. In cold regions, snowmelt can cause significant erosion due to freshet and ice jams during the period of spring break-up [2–5]. Earthy or rock materials are loosened or dissolved, and they are removed from any part of the Earth’s surface by erosion [6]. Erosion is a very important

<footnote n="1">1 Istanbul Technical University, Department of Civil Engineering, 34469 Istanbul, Turkey</footnote>

<footnote n="2">2 IRD, UMR HSM IRD/CNRS/ University Montpellier, Place E. Bataillon, 34095 Montpellier, France</footnote>

<footnote n="3">3 Ecole Nationale Supérieure d'Hydraulique, LGEE, Blida 9000, Algeria</footnote>

<footnote>* Correspondence: haksoy@itu.edu.tr</footnote>
natural phenomenon that ends in soil loss. It causes also storage volume loss in river reservoirs where eroded sediment deposits. Water erosion is affected by the climate, topography, soil, vegetation, and anthropogenic activities such as tillage systems and soil conservation measures [7]. Land use and land cover characteristics are also important in the erosion process [8].

Four different processes that accomplish sediment removal and transport are the detachment by raindrop impact and runoff, and transport by raindrop splash and runoff. Flow and raindrop detachment rates are not simple and are, therefore, given by empirical formulas [9]. Once eroded, sediment is transported. Sediment particles have become detached and are transported within flow as long as sediment load in the flow is smaller than its sediment transport capacity. The shear stress exerted by flow should also be greater than the critical value such that sediment particles are removed from their current locations. Otherwise, deposition takes place, which is the actual rate of mass temporarily reaching the overland surface. Deposition might exceed soil entrainment, which is called the net deposition; the opposite case is called net erosion, where the entrainment is higher than deposition. In the case of an equality of entrainment with sedimentation, equilibrium is reached in terms of erosion [10]. Sediment transport is influenced not only by hydraulic properties of flow but also by the physical properties of soil and surface characteristics.

### 3. Modeling and Practice

There are numerous methods are available in the literature for quantifying sediment transport over watersheds or in streams. The usual practice is to analyze the streamflow and sediment discharge time series statistically [11,12] and to correlate the available streamflow and sediment discharge data [13,14]. Empirical approaches [15] are also frequently used in practice. Statistical analysis and stochastic modeling techniques have always been attractive alternatives because the monitoring and sampling are not easy tasks and, in most cases, the simultaneous streamflow and sediment discharge records are not available for comparatively long periods to enable conclusive deterministic relationships between sediment concentration and streamflow discharge. Therefore, time series models [16], in particular, were found to be useful in dealing with sediment transport problems. Among the many available studies, a number [17–20] are based on the time series modeling technique. However, traditional equations [21] as well as soft computational techniques [22] have also received great attention. In the meantime, monitoring, sampling, and surveying [23] as well as remote sensing and the use of geographical information systems [24] have continued to be important in sediment transport modeling.

As far as modeling is concerned, the Universal Soil Loss Equation (USLE) was designed as a tool to be used in the management practices of agricultural lands. It is one of the earliest attempts to compute the sediment yield in a catchment. Its development is based on data from the United States though it has subsequently been widely used all over the world. The USLE, along with some modifications and revisions (MUSLE and RUSLE), is still a useful tool in watershed management. A large number of the existing erosion and sediment transport models are based on the USLE. Their applications are, however, limited to the environmental circumstances from which the USLE was generated. The WEPP model in the United States and the SHESED and EUROSEM models in Europe were derived based on physical description of the erosion and sediment transport processes. Although preparation of data for physically based models is a hard task, they have been extensively used. It is obvious that a physically based model has much more detail than either USLE or its derivatives. Therefore, there has been a great effort towards developing physically based erosion and sediment transport models.

Due to their importance, hydrological models accommodate erosion and sediment transport modules in which the movement of sediment—that has been eroded by wind, rainfall, or flow, and transported—through the existing river channel to the reservoir is predicted. The SHESED [25], WEPP [26], SWAT [27], and WEHY [28,29] models are some of the well-known examples.

Erosion and sediment transport models are extensions of hydrological models. Therefore, erosion and sediment transport equations are coupled to existing hydrological algorithms. In such a coupling,
the output of the hydrological model becomes the input for the erosion part of the model. In the same
sense, an erosion and sediment transport model can be easily extended to a nutrient transport model,
as it is known that nutrients are mainly transported by sediment particles. It is much easier to extend a
multi-size erosion and sediment transport model to a nutrient transport model since nutrient transport
is a size-selective process. For an extensive review on erosion and sediment transport, please refer
to [30,31].

4. Climatological and Anthropogenic Changes

The world's climate exhibits natural and unnatural variations and changes, with time scales ranging from millions of years down to one or two years. Over periods of several years, fluctuations of a few tenths of a degree in surface air temperatures over continents are common. These changes are related to global, regional, and even local scale events. Not only the climatological changes but also anthropogenic activities that could be superimposed on this varied hydrometeorological basis affect a wide variety of water use and management approaches. The individual components of the hydrological cycle are affected by the change. They might cause hydrological extremes such as droughts and floods, which are environmental issues turning back as direct consequences of natural or anthropogenic changes. Similarly, erosion and sediment transport over hydrological watersheds are heavily affected by such changes. Any change in either of the components of the hydrological cycle affects the hydrological behavior of the watershed and, thus, the erosion and sediment transport from the watershed surface.

A particularly important issue linked to the change in hydrology could be linked to stochastic modeling, which is based on the assumption that the time series is stationary. Generated sequences of any hydrological process under investigation, sediment discharge for instance, are considered stationary; i.e., they have the same statistical characteristics as the observed sequence. On the one hand, the stationarity is considered dead [32] with the change in hydrological processes [33–36]. On the other hand, however, it is still alive and inevitably useful in modeling hydrological processes [37–40] because it is convenient to use for making reliable predictions in engineering design. Also, the modeling concept based on the observed data is a useful practice due to the fact that the past is representative of the future [40]. Yet, any gradual and sudden changes due either to natural variation of the process under investigation or to any anthropogenic intervention should not be ignored. Such changes that could arise in the form of either a trend or a jump could be considered through the existing trend detection mechanisms and segmentation tools [41–44] to eliminate the nonstationarity of the process. Any jump or trend, when they exist, are determined and added into the modeled hydrological variables such that the nonstationary behavior of the process is taken into account.

5. Summary of the Special Issue

Eleven papers have been published in the Special Issue among a much larger collection of submissions. The published papers deal with different aspects of erosion and sediment transport by using different methodologies, through different practices, implementing different scale datasets, collecting in situ data from the field or gathering experimental data, modeling the process with different approaches, and performing case studies from Europe and the Mediterranean North Africa to typhoon-dominated Asia and even to polar Antarctica. The Special Issue therefore represents highly diverse research activities.

A summary of the papers in the Special Issue follows, given in the order in which they appear.

The grain size distribution of bedload transported within a given water discharge has been investigated for two polar catchments in Antarctica [45], aimed at determining how the grain size distribution is modified during times of peak discharge, determining the relationship between the grain size distribution and its parameters, and the amount of transported material in gravel-bed rivers, and examining whether the modification of grain size distribution during efficient bedload transport events allow for the identification of the development stage of river throughs during changing
meteorological conditions. These questions were answered after a measurement campaign in two creeks with proglacial gravel-bed channels. At the end it is confirmed that the variability and modification of grain size distributions are strongly related to the daily variability of bedload transport dynamics. The increased proportion of medium and coarse gravel was strictly proportional to the increase in water discharge. An efficient erosive process, which is confirmed by the general conditions of both streams, is significantly influenced by bedload transport.

Urban sewer conduits prevent flooding in urban areas by discharging runoff generated during rainfall. With an improper design of urban sewer conduits, severe soil sedimentation can occur in the conduits which threatens the capacity and ability of the system to discharge the flood during the rainy season or at localized heavy rainfalls. Soil slurry deposited on the surface of the Earth during rainfall that flows into urban sewer conduits was investigated [46] to propose a functional relationship between critical tractive force in urban sewer conduits and the physical properties of particles in a conduit bed which are taken as the inlet flow velocity of the soil slurry mixture, the volume concentration of the soil, and its particle size. For the two-phase soil slurry flow, a numerical analysis was performed based on various flow conditions to conclude that the findings of this study may be helpful to prevent conduit clogging or conduit damage that may occur during heavy rainfall events. As this study considered only the inflow of a large amount of soil slurry at the beginning of rainfall events, it is open for further investigation to introduce various types of rainfall events by using data from real conduit systems.

Algeria, in northern Africa, has always been confronted with severe periodic droughts as well as catastrophic floods, both being major constraints against the economic and social development of the country [47]. In order to combat both natural hazards, the total number of dams increased quite quickly, from 14 in 1962 to 65 in 2014. The scale of aggradations and the raising of the bottom of these dam impoundments by successive deposits of sediments—brought by the watercourses and the wind—are serious problems whose negative consequences are considerably felt in the agriculture, farming, fishing, electricity, and navigation fields. The sedimentation in North African dams is very high in relation to what is noted in the watershed of Wadi Mina in semiarid northwest Algeria, and it has been the subject of the study of Hallouz et al. [47]. Also, with a trend starting in the late 1980s, the annual production of sediment became seven times larger than the previous period, with a four times greater increase in the rates of contribution in the dry season. By comparing the results, it is observed that the upstream basin is the greatest sediment producer towards the dam.

The Mediterranean Maghreb Basin (MMB), that extends over Morocco, Algeria, and Tunisia, is a region where both mechanical erosion rates and the anthropogenic pressure on surface water resources are high and were subject to analysis [48]. Based on sediment trapping, calculated by the models using information and limited data from 470 out of 670 reservoirs in the area, it is confirmed that natural sediment yields are clearly above the world average, with the largest being in Morocco and the smallest in Tunisia. Trapping rates have an opposite order, being the highest in the Tunisian part of the basin, followed by the Algerian and the Moroccan parts. Trapping of the sediment in their reservoirs greatly reduces the natural sediment flux of the dams in the entire Mediterranean Maghreb Basin to the sea; only slightly more than one-third of the natural river sediment fluxes reaches the coastal Mediterranean waters of the Maghreb [49,50]. The effect of small reservoirs and hillside reservoirs should not be ignored in the interception of sediment compared to large reservoirs, although they have shorter life spans than large reservoirs, and their economic exploitation is limited in time. Understanding the impact of dams and related water infrastructures on riverine sediment dynamics is key in arid zones such as the Mediterranean Maghreb Basin, where global warming is predicted to cause important changes in the climatic conditions and the water availability.

Small-scale laboratory rainfall simulator experimental data based on high-precision DEM are evaluated to provide accurate, but affordable, soil loss estimates [51]. Laser-scanned topography and sediment yields were collected every 5 min in each test. The difference between the DEMs from laser scans of different time steps gives the eroded soil volumes and the corresponding estimates of soil loss in mass. It is seen that sediment yield and eroded soil volume increased with rainfall duration and
slope. It is demonstrated that the stripe laser-scanning method is applicable in soil loss prediction and erosion evaluation in laboratory case studies, and could be taken for further case studies of larger scales such that a method that is useful, in practice, can be generated.

Climate change and human activities are two major factors affecting runoff and sediment load in hydrological basins [52]. Gradual or sudden changes in hydrometeorological characteristics, such as annual rainfall, air temperature, runoff, and sediment load, are important in simulating the watershed hydrological cycle. These gradual and sudden changes are mainly linked to the contributions of climate change and human activities to runoff and sediment load under change. Results showed that both rainfall and air temperature increased whilst runoff and sediment load decreased. The air temperature experienced a sudden increase and sediment load decrease in 1988. Soil erosion was found to be worse in the upper part of the basin than other parts, and it is the highest in cultivated land. Climate change exacerbates runoff and sediment load with overall contribution to the total change while, on the other hand, human activities decreased runoff and sediment load with overall contribution to the total change. The conclusion of the study is that the variation of runoff and sediment load in the Xihe River Basin in China is largely caused by human activities.

Soil, hillslopes, and watercourses in small catchments possess a degree of natural attenuation that affects both the shape of the outlet hydrograph and the transport of nutrients and sediments [53]. The headwaters of such catchments are expected to add additional attenuation primarily through increasing the amount of new storage available to accommodate flood flows. The actual types of so-called natural-based solutions include swales, ditches, and small ponds (acting as sediment traps). A modeling study was performed on a small subcatchment of 1.25 km² in order to address the impacts of land management by altering hydrological flow paths and the overall catchment attenuation capacity on flow rates and nutrient losses. The model results implied that a small decrease in the order of 5%–10% in the peak concentrations of suspended sediment and nutrients was observed with an increase in the catchment storage.

An indoor laboratory-scale experimental study is quite beneficial to the sediment transport problem as the urban drainage and sewer systems are final reaching points for any type of sediment to be washed into the channels or conduits [54]. Using the self-cleansing concept, different cross-section channels were tested to better clarify the fuzziness between the incipient deposition and incipient motion of sediment particles moving within the flow. With this aim, an experimental study carried out in trapezoidal, rectangular, circular, U-shape, and V-bottom channels for four different sizes of sand as the sediment in the experiments was performed in a tilting flume under nine different longitudinal channel bed slopes. The shear stress approach was considered for the analysis in which the well-known Shields and Yalin methods were used. The circular channel was found to be the second most efficient after the rectangular channel, and the V-bottom channel the least in transporting sediment within the drainage system. The outputs of this study are expected to be useful for practical use in the design of urban drainage and sewer systems that collect the sediment load together with nutrients.

Extreme weather phenomena which have been a part of daily hydrometeorological practice worldwide bring catastrophic disasters under the impact of climate change; and Taiwan has no exemption, due to an increase in the frequency of extreme rainfall events [55]. Extreme rainfall events might cause riverbed migrations, such as degradation and aggradation. The extrapolation of typhoon events—observed in the past by the CCHE1D model—under the climate change scenario of representative concentration pathways 8.5 (RCP8.5) and dynamical downscaling of rainfall data in Taiwan shows that the average peak flow during extreme rainfall events will increase by 20% relative to the base period, but the time required to reach the peak will be 8 h shorter than that in the base period. It is expected that the aggradation of the riverbed will increase by the end of the 21st century. It is also foreseen that anthropogenic activities, such as blocking upstream sediment by structures such as a weir, will clearly increase the severity of scouring downstream. The study finally indicates that not only will larger floods occur within a shorter time duration, but that the catchment will also face more severe degradation and aggradation in the future.
In addition to sand-dominated sediment being transported within flow, gravel may also be transported in rivers with mixed-size bed material when dealing with large rivers with complex hydrodynamics and morphodynamics [56]. This is the collapse of the uniform sediment assumption, which then requires a suitable approach to estimate the nonuniform behavior of the sediment transport. Utilizing the shear Reynolds number, a decision criterion which is based on the combined use of several formulas, each of them having a certain application range, was verified with the field and laboratory data of nonuniform bed material compositions. The proposed approach is able to predict domination of sand or gravel transport with an uncertainty of less than 5%.

In central Czech Republic, a small stream catchment with an agricultural and forest-agricultural landscape and relatively rugged topography and riverbed slope [57] make the terrain very vulnerable to water erosion, and this was studied to compare four selected soil erosion and sediment delivery models—WaTEM/SEDEM, USPED, InVEST, and TerrSet, with each working on several different algorithms. The models were compared based on the total volume of eroded and accumulated sediment within the catchment per unit time, and according to the spatial distribution of sites susceptible to soil loss or sediment accumulation. Despite the fact that the models are different in terms of calculation algorithms and data preprocessing requirements, comparable results in calculating the average annual soil loss and accumulation were obtained but they behaved differently in identifying the spatial distribution of specific locations prone to soil loss or accumulation processes.

## 6. Establishment of the Special Issue

**Scope and coverage:** When the Special Issue had been scheduled, it was anticipated to be a collection of contributions focusing on erosion and sediment transport issues in riverbeds or watersheds using analytical, numerical, and in situ experimental tools. However, laboratory experiments were also found to be an important consideration, due to their providing specific details in the transport of sediment.

**Scale:** Another point is the scale issue, that has varied greatly among the papers published in the Special Issue. The erosion and sediment transport issues have been investigated in channels and over watersheds. The channels have been either a prototype natural watercourse [45,54] or an artificial flume of a laboratory model [46,54]. As for the watersheds, the scale has changed from 1.25 km² subcatchments from the United Kingdom [53] to large, millions of km² watersheds in the Maghrib basin that extend over Morocco, Algeria, and Tunisia.

**Geographical diversity:** The Special Issue has not been a collection of studies concentrated on a specific region. The papers have large geographical variability, from the Maghrib area in North Africa to typhoon-dominated Taiwan and even Antarctica. Therefore, the erosion and sediment transport problem has not been limited to a particular region but extends over a geographical scale representing large diversity.

**Large rivers vs. small rivers:** Large rivers carry not only sand-type sediment but also gravel-dominated bedload which contradict with the uniform-size sediment assumption. However, in smaller rivers, the assumption that the sediment has a uniform grain size could be considered valid to a certain degree. In this sense, it is important that bedload sediment models should be dealt with differently when one is interested in a large river where the bedload is gravel-dominated and, thus, no uniformity exists in terms of sediment size.

**In situ measurements and laboratory data:** It is important that any model is validated with real data, which is a headache for all scientists and practitioners who deal with Earth sciences. Hydrology is no exception, and erosion and sediment transport are particular issues which experiences this problem at the highest level, due to the fact that sediment data are not collected as frequently as other hydrometeorological variables, such as precipitation, evaporation, humidity, streamflow, etc. Therefore, in situ problem-specific data collection efforts are quite valuable. Laboratory studies could also be as useful as fields studies. This is a fact that has been touched upon; the former could be replaced by the latter when it is hard to perform field studies and when the latter is possible.
Climate change and anthropogenic activities: It is an inevitable reality that hydrology is under
change that is either linked to the climatology or Anthropocene. More frequent floods with higher
peaks are reached in shorter time intervals than before. This is a challenge that can be associated with
the stationary time series methodologies. The stationarity is now dead, and the past is no longer the
mirror for the future as it was before.

7. Conclusions

The Special Issue has attracted the interest of hydrologists and water resources researchers. It is a
common belief of the authors of this Editorial that all papers in this Special Issue could be considered a
contribution to the erosion and sediment transport problem in hydrological watersheds at different
scales of space and time and also under any kind of change.

**Author Contributions:** Conceptualization, G.M., H.A., M.M.; Writing—Original Draft Preparation, H.A.; Writing—Review & Editing, H.A., G.M., M.M.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors thank editors for their help during the processes for the Special Issue. Yonca Cavus, PhD candidate from Istanbul Technical University, read the draft and edited it carefully. The authors are thankful to her for the time she dedicated to this Editorial.

**Conflicts of Interest:** The authors declare no conflict of interest.

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<figure><img src="image_8.png" /></figure>

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
<figure><img src="image_9.png" /></figure>

Article

# Grain Size Distribution of Bedload Transport in a Glaciated Catchment (Baranowski Glacier, King George Island, Western Antarctica)

Joanna Sziło<fnref n="1" />,* and Robert Józef Bialik<fnref n="2" />

Received: 20 February 2018; Accepted: 20 March 2018; Published: 23 March 2018

<figure><img src="image_10.png" /></figure>

check for
updates

**Abstract:** The relationships among grain size distribution (GSD), water discharge, and GSD parameters are investigated to identify regularities in the evolution of two gravel-bed proglacial troughs: Fosa Creek and Siodło Creek. In addition, the potential application of certain parameters obtained from the GSD analysis for the assessment of the formation stage of both creeks is comprehensively discussed. To achieve these goals, River Bedload Traps (RBTs) were used to collect the bedload, and a sieving method for dry material was applied to obtain the GSDs. Statistical comparisons between both streams showed significant differences in flow velocity; however, the lack of significant differences in bedload transport clearly indicated that meteorological conditions are among the most important factors in the erosive process for this catchment. In particular, the instability of flow conditions during high water discharge resulted in an increase in the proportion of medium and coarse gravels. The poorly sorted fine and very fine gravels observed in Siodło Creek suggest that this trough is more susceptible to erosion and less stabilized than Fosa Creek. The results suggest that GSD analyses can be used to define the stage of development of riverbeds relative to that of other riverbeds in polar regions.

**Keywords:** GSD; proglacial channels; bedload transport; field measurements; fluvial erosion

## 1. Introduction

One of the most important challenges in studies of bedload transport is investigating the differences between mobile and bottom particle sizes and taking these relations into account in new transport models [1–4]. This problem is mostly based on the lack of complex datasets for flow velocity, transport, and grain size distribution (GSD) of the bedload and bottom particles [2]. The lack of sufficient field observations and datasets collected during high flows when active transport is observed [5,6] is not the only problem associated with model development and geomorphological process assessments in Arctic or Antarctic catchments. The limited application of current models to natural gravel-bed rivers [7], and methods of predicting the sediment flux to the global ocean from small rivers [8] represent other problems that remain to be resolved.

Bedload transport is one of the main factors associated with changes in the morphology of troughs [9–14], and the difficulty describing the relationships among water flow conditions, GSD, and deposition processes was identified decades ago (e.g., [15–18]). Although a substantial amount of progress has been made in this field because of research conducted in laboratory channels (e.g., [19–21]) and field studies (e.g., [22–26]) and with the use of bedload transport models (e.g., [1,2,27–30]), the relationships among the factors associated with bedload transport are poorly understood in natural gravel-bed channels in general and in those located in polar regions in particular [31].

<footnote n="1">¹ Institute of Geophysics, Polish Academy of Sciences, 01-452 Warsaw, Poland</footnote>

<footnote n="2">² Institute of Biochemistry and Biophysics, Polish Academy of Sciences, 02-106 Warsaw, Poland;
rbialik@ibb.waw.pl</footnote>

<footnote>* Correspondence: jszilo@igf.edu.pl; Tel.: +48-504-595-266</footnote>
Ghoshal et al. [32] claimed that the bedload has a large influence on the GSD and determines the concentration of each size fraction of noncohesive particles under changing hydrological conditions. GSD analyses have frequently been used as indicators of the threshold for the initiation of particle motion, and shear stress dictates the specific role of particles in this process [10,33–37]. Johnson [38] suggested that the geomorphology of the bed as well as the sediment transport rate should be considered because of their relationship with grain size and shape. Moreover, the distribution of particles also depends on the mechanism of fluvial transport and can be used to define the influence of flow conditions on the geomorphology of the channel, as stated by Kociuba and Janicki [31] or Lisle [23]. Although the coarser fraction is entrained with greater discharge [39], because of protrusion and hiding effects, particles larger than the mean grain size are easier to move than smaller ones [40–42]. The above-mentioned situation may be understood by using the GSD for the analysis of selective bedload transport in natural gravel-bed channels [43] or by performing a direct analysis of certain parameters, such as the mean grain size, sorting, or skewness, which can be used to predict the direction of sediment transport [27,44]. These parameters allow us to obtain information about the predominant size of the transported particles, their dispersal during this process, and their symmetry or preferential dispersal to one side of the average. Ashworth et al. [45] concluded that sediment sorting can occur during entrainment, transport, or deposition. In this research, sediment sorting is calculated based on the sediment caught in traps during bedload transport.

The objective of this study is to answer the following questions: (1) How is GSD modified during the times of peak discharge in a polar catchment? (2) What is the relationship between the GSD and GSD parameters and the amount of transported material in gravel-bed rivers? (3) Does the modification of GSDs during efficient bedload transport events allow for the identification of the development stage of river troughs during changing meteorological conditions?

To answer these questions, insightful measurements have been performed in Fosa and Siodło creeks, two proglacial gravel-bed channels located on the forefield of the Baranowski Glacier on King George Island in Western Antarctica (Figure 1). This study is a continuation and development of the results presented by Sziło and Bialik [46], who identified the relationship between bedload transport and rapid outflow and high water discharge in the form of eight-loop hysteresis for these creeks.

<figure><img src="image_11.png" /><figcaption>**Figure 1.** Location of the study site: (a) King George Island; (b) Baranowski Glacier catchment; (c) forefield of the glacier and measurement sites. Reference system: WGS 1984, UTM zone 21S, geoid EGM96.</figcaption></figure>
## 2. Materials and Methods

The field campaign was conducted at two sites established in Fosa and Siodło creeks from 9 January to 11 February 2016 (Figure 1). Data on the bedload transport associated with water flow conditions measurements were collected at 24 h intervals over 35 days in both creeks. However, the measurements in Fosa Creek were extended to 2 March, and during those additional 14 days, bedload transport was not observed.

### 2.1. Study Site

The Antarctic Peninsula region, where the study site is located, is prone to climatic fluctuations [47–52]. The total catchment area of the creeks is 6.8 km² of which 69.1% (4.7 km²) is covered by the glacier (including Windy Glacier). The area of the forefield is 2.1 km² and is expanding yearly (status for 2017). The frontal part of the glacier is divided into two tongues: Northern and Southern. The Northern tongue is currently terminating on a narrow strip of land close to the shallow lagoon, and the Southern tongue presents several creeks flowing through the forefield. All measurements were initiated in two gravel-bed troughs of the Fosa and Siodło proglacial creeks, which were selected because of their continuous and dynamic water flows during the entire summer season. Fosa Creek receives water mainly from Ginger Lake and the Baranowski Glacier, whereas Siodło Creek is a subglacial outflow from the Baranowski Glacier. Both creeks are fed by meltwater from the glacier in the ablation season (which may represent the primary source of water) and intensive rainfalls. The measurement site in Fosa Creek was established in a location where ablation water cut the trough into moraine cover between 1988 and 1995, whereas in Siodło Creek, this trough was cut between 2001 and 2005. The total lengths (L) of Fosa and Siodło creeks are 1.40 km and 0.42 km, respectively; the longitudinal water surface slopes (S) are 0.07 mm⁻¹ and 0.08 mm⁻¹ for Fosa Creek and Siodło Creek, respectively (Table 1). Furthermore, Reynolds and Froude numbers are also presented for both creeks (Figure 2a,b).

<table><caption>Table 1. Basic hydraulic parameters of Fosa and Siodło creeks.</caption><thead><tr><th>Parameter</th><th>Total Length (L) [km]</th><th>Average Bankfull Width (w) [m]</th><th>Average Bankfull Depth (d) [m]</th><th>Longitudinal Water Surface Slope (S) [mm<sup>-1</sup>]</th><th>Maximum Discharge (Q<sub>max</sub>) [m<sup>3</sup> s<sup>-1</sup>]<sup>1</sup></th><th>Maximum Velocity (V<sub>max</sub>) [ms<sup>-1</sup>]<sup>2</sup></th></tr></thead><tbody><tr><td>Fosa Creek</td><td>1.40</td><td>2.82</td><td>0.14</td><td>0.07</td><td>0.75</td><td>0.91</td></tr><tr><td>Siodło Creek</td><td>0.42</td><td>2.15</td><td>0.09</td><td>0.08</td><td>0.26</td><td>1.25</td></tr></tbody></table>

Note: ¹ Qmax: maximum water discharge measured at one day during field campaign; ² Vmax: maximum water velocity measured at one point during field campaign.

<figure><img src="image_12.png" /><figcaption>Figure 2. *Cont.*</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>**Figure 2.** Temporal changes in (a) Reynolds number and (b) Froude number for both creeks.</figcaption></figure>

The period of the field campaign was characterized by higher air temperatures relative to other summer months over the last decade [49,50,53]. The mean monthly air temperature was +1.0 °C in January and +1.1 °C in February for the period from 2007 to 2016 [54]. However, the mean air temperature during the field campaign was +1.8 °C, with a maximum of +5.9 °C on 29 January. On the same day, the highest precipitation of 8.8 mm was recorded. During the 35 days of continuous measurements, 16 days were without precipitation and 12 days had precipitation >1.0 mm. The total precipitation over the whole period was 47.7 mm. Meteorological conditions that contributed to greater water discharge were observed 2 days after intense rainfall (Figure 3) [46].

<figure><img src="image_14.png" /><figcaption>**Figure 3.** Mean daily air temperature, precipitation, and discharge during the field campaign in 2016 from Bellingshausen Station.</figcaption></figure>

## 2.2. Bedload Transport Measurements

To collect the transported material, River Bedload Traps (RBT) [55,56] were anchored at the bottoms of the troughs in two cross sections (Figure 4). In Fosa Creek, a set of two RBT modules at a distance of 300 m from the forehead of the glacier was installed, and in Siodło Creek, a set of three RBT modules at a distance of 15 m from the front of the glacier was installed. One additional module was established in Siodło Creek because less rinsing of the bottom of the trough occurred in this creek compared with in Fosa Creek and a finer bedload was visible at the beginning of the measurements. The assumption was that the bedload can move more easily in a trough in an early stage of development (Siodło Creek) than in a later stage of development [46]. The locations of the modules in the profiles were chosen based on the most intense currents.
<figure><img src="image_15.png" /><figcaption>Figure 4. River Bedload Traps (RBT) in (a) Fosa Creek and (b) Siodło Creek (modified from Szilo and Bialik [46]); (c) schematic diagram for the bedload transport technique (Kociuba [56]).</figcaption></figure>

## 2.3. Sieve Method and GSD Analysis

To obtain the GSD, each of the collected samples of the bedload was transported, drained, sieved, and weighed in the laboratory of the Henryk Arctowski Polish Antarctic Station. Furthermore, a comparison of the dry and wet sample weights was performed to determine the most reliable method of preparing the data for further analysis. Each sample that had a greater than 1% proportion of grain size <2 mm was truncated to exclude sediment that was predominantly suspended and because of limitations of the mesh diameter of the net. The upper limit to remove the samples because of the selective rejection of particles by the sample was set up at 32 mm [23]. Furthermore, for the GSD analysis, average weight values lower than 3% (chosen arbitrarily) for all collected data were rejected as not statistically important. To obtain information on the sedimentary environment, such as the sediment provenance, transport, and deposition conditions (e.g., [15,18,24]), the GSD parameters were evaluated. The Folk and Ward [15] method was employed to obtain the GSD parameters of mean grain size (Mz), standard variation ($\sigma_{\phi}$), sorting ($\sigma$), skewness (Skl), and kurtosis (KG), which according to Blot and Pye [57] describe (a) the average size of grains (Mz); (b) the spread of the sizes around the average ($\sigma$); (c) the preferential spread to one side of the average (Skl); and (d) the degree of concentration of the grains relative to the average (KG). As suggested by Blot and Pye [57], the Folk and Ward [15] method provides the most robust basis for routine comparisons of compositionally variable sediments in the cases when the skewness or kurtosis of grain sizes are calculated. It should be noted that besides the presentation of grain diameters in metric units, according to standard procedure [15,57], data will be also shown and analyzed in $\phi$ (φ) units, which is the negative log to base 2 of the diameter in mm.

## 2.4. Bedload Transport Rate

The bedload transport rate ($q_b$) was calculated from the weighted arithmetic mean formula [46] given in Equation (1):

$$q_b = \frac{G_s}{S_w t} \cdot W_t \qquad (1)$$

where $G_s$ represents the bedload material (kg), $S_w$ represents the width of the module inlet (m), $W_t$ represents the width of the trough (m), and $t$ represents the measurement time (day). In addition, the water velocity was measured with an Electromagnetic Open Channel Flow Meter (manufactured by Valeport, model 801). For details, see Szilo and Bialik [46]. The average water velocity was measured at least two times [46] at each measurement section for 30 seconds [58]. If the standard deviation of the measurement values was higher than 10%, the measurements were repeated until an acceptable standard deviation was obtained. Based on the values of creek bathymetry and water velocities for each section, the water discharge was calculated following the standard procedure [58]. The accuracy of equipment employed for measurements was ±0.5% of reading values plus 5 mm/s.
## 2.5. Statistical Analysis

An analysis of variance (ANOVA) test was performed to determine whether or not the two investigated creeks had statistically significant differences in terms of bedload transport and hydrological conditions. The Anderson-Darling test was used to check for normality, and Bartlett's test was used to check for the homogeneity of variance to meet the assumptions of the ANOVA. To provide a better description of the changes that occurred in the channels of both creeks, sediment samples from the individual traps were analyzed independently even when collected from the same creek.

# 3. Results

## 3.1. Statistical Analysis: Water Discharge, Flow Velocity, and Bedload Transport

Figure 5 shows the bedload transport, water discharge, and flow velocity data for Fosa and Siodło creeks. Unfortunately, the assumptions of normality and homogeneity of variance were not observed for all presented data. When a variable does not fit the assumptions required for the ANOVA test, the data are usually transformed (log or square root) [59]. The square root transformation was used for water discharge and flow velocity, and the double square root transformation was used for bedload transport; the transformed variables met the above assumptions. A comparison of the results of all transformed data indicated only one of the variables (flow velocity) between the creeks presented statistically significant differences (*p*-value < 0.05).

<figure><img src="image_16.png" /><figcaption>**Figure 5.** Bedload transport (a), water discharge (b), and flow velocity (c) data for Fosa Creek (1) and Siodło Creek (2).</figcaption></figure>

## 3.2. Sieving Procedure Comparison (Wet and Dry)

Although standard procedures for wet sieving are acceptable for determining the GSD (e.g., [31]), the form of sieving (wet or dry) may influence the particle distribution [60,61]. To investigate how the drying process can influence the GSD, the weights of randomly chosen wet and dry bedloads not lower than 10 kg were compared (Figure 6). The results of the analysis revealed that the difference between the weights ranged from 15% to 28% (Figure 6). Hence, in this research, only the dried bedload was considered in further analyses.

<figure><img src="image_17.png" /><figcaption>**Figure 6.** Weight fractions of the wet and dry samples.</figcaption></figure>
### 3.3. GSD Parameters and Variation of Characteristic Diameters (D) of the Bedload Transport Rate

Figures 7 and 8 show the relationship between $\sigma$ and Mz for all data, for both creeks separately, and for the individual traps. The analysis of the $\sigma$ and Mz in the profiles established in the Fosa and the Siodło troughs suggested that linear correlations occurred with those indicators, and the correlation coefficients ($R^2$) were 0.82–0.92 (Figure 7). Moreover, an increase in Mz presents a corresponding increase in grain variability. The mean diameter of sediment from Fosa Creek for all measurement days varied from 2.9 mm to 6.2 mm and was higher than that in Siodło Creek, which varied from 1.5 mm to 3.6 mm. Furthermore, larger ranges of Mz values were observed for the individual traps in Siodło Creek than for those in Fosa Creek, and a maximum of 10.4 mm was observed on 6 February (Figure 8a,b). The strongest correlation for the material collected in the trap occurred in the Siodło middle (M) at $R^2 = 0.96$ (Figure 8b), for which 77% of the data ranged from 2.3 to 3.9 mm, whereas for the Siodło left (L), 80% of the data were in the interval from 4.1 to 8.9 mm.

<figure><img src="image_18.png" /><figcaption>Figure 7. Relation between sorting ($\sigma$) and mean grain size (Mz) in Fosa and Siodło creeks in all profiles.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>Figure 8. Relation between sorting ($\sigma$) and mean grain size (Mz) in Fosa (a) and Siodło (b) creeks in individual traps.</figcaption></figure>

The temporal changes in bedload transport and $\sigma$ for the studied creeks are presented in Figure 9. The $\sigma$ in individual traps varied from 1 mm to 1.5 mm in 93% of the samples, which means that the collected sediments in both cross sections were poorly sorted (Figure 9a,b). Furthermore, after the peak bedload transport, which appeared from 29 to 30 January, an inversion of $\sigma$ occurred from lower values in the Fosa right (R) section compared with in the Fosa left (L) section, where higher values were observed (Figure 9a). A similar situation occurred in the Siodło trough: after both of the bedload transport peaks (on 1 and 5 February), inversions of $\sigma$ in the left trap from highest to lowest and then to highest values again were noticed (Figure 9b). Furthermore, the results suggest that better $\sigma$ occurred in both troughs after each peak in bedload transport (Figure 9a,b).
<figure><img src="image_20.png" /><figcaption>Figure 9. Bedload transport and sorting in individual traps in the Fosa (a) and Siodło (b) creeks.</figcaption></figure>

The relation between bedload transport and $\sigma$ was inversely proportional before and directly proportional after the peaks in bedload transport (Figure 10a,b). All bedload transport data from Siodło Creek were negatively skewed, which means that a large proportion of coarse sediment occurred (Figure 10c), and this finding is also confirmed based on the percentage of gravels in the collected material (Figure 11a,b). An increase in water discharge and a consequential increase in bedload transport resulted in symmetrical *Skl* and leptokurtic *KG* (Figure 10c,d). Before 31 January and after 4 February, when the maximum discharge was observed, strongly negative *Skl* was observed in Siodło (Figure 10c). Under low discharge conditions, leptokurtic *KG* was observed.

The bedload transport rate and grain size variation analyses indicate that an inverse correlation occurred for both creeks. In Fosa Creek, the grain size variations decrease when the bedload transport rate increases, whereas in Siodło Creek, the grain size variations are directly proportional to increases in bedload transport rate. Furthermore, in Fosa Creek, the D-value correlations increase from 0.15 for $D_{50}$ to 0.26 for $D_{95}$, which is inconsistent with the data from Siodło Creek, where the correlation for $D_{50}$ of 0.29 decreases to 0.11 for $D_{95}$ (Figure 11a,b).

<figure><img src="image_21.png" /><figcaption>Figure 10. *Cont.*</figcaption></figure>
<figure><img src="image_22.png" /><figcaption>**Figure 10.** Grain size parameters (by Folk and Ward, 1957) for Fosa and Siodło Creeks: bedload transport rate and sorting for Fosa (a) and Siodło (b); skewness (c); and kurtosis (d).</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>**Figure 11.** Correlation between bedload transport rate and characteristic diameters D<sub>b</sub> for Fosa (a) and Siodło (b) creeks, where b stands for the percentage of the weight of the sample finer than this value.</figcaption></figure>

### 3.4. *Selective Transport and Bedload Transport versus Water Discharge and Water Velocity*

Fine (4–8 mm) and very fine (2–4 mm) gravel accounted for 40 to 99% of the total sample weight in the troughs for each day of the measurement campaign. Nevertheless, a higher proportion of these gravels (2–8 mm) was observed in Siodło Creek, with the value reaching at least 63%. This increase was especially clear before the peaks of water discharge on 19 and 29 January, when the fine and very fine gravel constituted almost the entirety of the Siodło Creek samples. Furthermore, because of the increase in water discharge, the proportion of medium (8–6 mm) and coarse (16–22 mm) gravel also increased in both creeks, particularly on 29 to 31 January and 4 to 5 February (Figure 12a,b), when the highest water discharge occurred. In addition to the previously mentioned periods when the low water discharge was observed, certain coarse sediment samples were identified. Nonetheless, these samples had insignificant weight fractions and were disrupted by the presence of a few coarse pebbles. A similar situation was observed when the water discharge peaked. At that time, several boulders were caught in the Siodło trough, which contributed more than 50% of the sample in certain cases, although the water discharge was two times lower than that in Fosa Creek.
<figure><img src="image_24.png" /><figcaption>Figure 12. Percentage of bedload vs water discharge for Fosa (a) and Siodło (b) creeks.</figcaption></figure>

Because of the high proportions of fine and very fine gravel in each sample, those grain sizes have been chosen for our examination of the correlation between bedload transport and water discharge or water velocity (Figures 13 and 14). The correlation between water discharge and bedload transport was equal to 0.65 in the Fosa and 0.55 in the Siodło, and these correlations were stronger than those between bedload transport and water velocity, which were 0.53 in Fosa and 0.28 in Siodło; this is likely due to the changes of the creek beds and shapes, due to the existence of scouring effects [56] and because only grains with diameter lower than 22 mm were taken into account for the analysis. Thus, the increase in water discharge was observable with the simultaneous increase in bedload transport, and the intensity or correlation in the relations between water velocity and bedload transport was lower.

<figure><img src="image_25.png" /><figcaption>Figure 13. Relationship between water discharge and quantity of fine and very fine gravel in Fosa (a) and Siodło (b) creeks.</figcaption></figure>
<figure><img src="image_26.png" /><figcaption>**Figure 14.** Relationship between water velocity and quantity of fine and very fine gravel in Fosa (a) and Siodło (b) creeks.</figcaption></figure>

**4. Discussion**

The weights of the wet and dry samples differ significantly—by as much as 28% and by an average of 21.5%. These results are inconsistent with those of Kociuba and Janicki [31], who reported that the average water amount in a natural gravel-bed channel was 6%. In this situation, the error in the calculation can reach maximum values of 20.1–21.3 kg d⁻¹ for the mean transport rate [31] and 33.3–67.8 kg d⁻¹ for the mean daily bedload flux [62] based on exemplary data from the Scott River (Svalbard).

The flow velocity analysis for both creeks suggests that a statistically significant difference (*p*-value < 0.05) occurred in the hydraulic conditions. A stronger correlation with bedload transport was revealed for water discharge than for water velocity, which was estimated based on the measured values of the water velocity. This result explained the previously reported findings of Sziło and Bialik [46], who suggested that a similar relationship occurred between water discharge and bedload transport for Fosa and Siodło creeks. Moreover, the lack of significant differences in bedload transport clearly indicated that this catchment process was strongly associated with meteorological conditions, as presented in Figure 2. Certain differences noted by the authors in their previous work were likely caused by differences in the geomorphological features of the analyzed troughs, which could be explained based on the GSD analysis.

The detailed GSD analysis has shown that *σ* is inversely proportional to Mz, which is consistent with the results of studies in the Scott River performed by Kociuba and Janicki [31]. Kociuba and Janicki suggested that the bed material was poorly sorted, which is similar to the results from the Fosa and Siodło creeks (Figure 8a,b). Moreover, grains in the investigated troughs were finer (3 mm) than those in the Scott River (10 mm) [31]), which is likely because both creeks in this study are in the earlier stages of formation and more sensitive to morphological changes (especially Siodło Creek, as suggested by Sziło and Bialik [46]) in relation to the Scott River. These troughs were cut down into moraine cover later (in recent decades, Figure 1) than was the trough of the Scott River [63]. Poorly sorted bedload (Figure 9a,b) suggests high energetic differentiation of the particles and rapid changes in the geomorphology of both troughs. Significant bedload transport rates based on the definition of Batalla et al. [36] of 1 gm⁻¹s⁻¹ were observed on 30 January and 1 February in the troughs. Nevertheless, the bedload transport peak was defined as qb > 0.1 gm⁻¹s⁻¹. As a consequence, the sizes of movable grains are more variable and present a larger proportion of finer grains compared with that in the bed channels, where they could have already been rinsed. This finding could be related to the higher transport of the bedload and faster changes in the morphology of the troughs. Other GSD parameters, e.g., negative Skl, are typical for natural gravel-bed channels [23,31,64,65].
The investigation of the correlation between grain size variations and bedload transport rate revealed that both troughs were characterized by an inverse correlation. In Fosa Creek, this correlation increased proportionally to the D values and was strongest for D<sub>95</sub>, which is more sensitive to water flow as concluded by Batalla et al. [36]. This result is similar to findings for the Salty River [36] and the Scott River [31]. Nevertheless, for Siodło Creek, a higher value was observed for D<sub>50</sub> than for D<sub>95</sub>.

For both creeks, finer bedload is transported before the peak of water discharge than that transported during and after this phenomenon, which is consistent with findings of the previous studies (e.g., [23]). Generally, two phases of selective transport can be distinguished in both creeks (Figure 11). In the first phase, very fine gravel was predominantly entrained; this was followed by the second phase, where gravel dominated. Similar observations of two-phase selective transport have been reported in previous studies of other natural gravel-bed channels [31, 36, 66, 67]. Furthermore, the higher proportions of fine and very fine gravel in Siodło Creek compared with those in Fosa Creek over the entire field campaign confirm the previous hypothesis posed by Szilo and Bialik [46], who assumed that the Siodło trough may be in an earlier stage of formation than the Fosa trough and thus exhibit a more obvious erosive process. In addition, fine material collected from the Siodło, which constituted at least 63% in each sample, can also provide evidence that the channel is not yet armored and paved like the Fosa trough, and bottom erosion may occur faster [33]. Moreover, the presence of boulders (>64 mm) during the peaks of water discharge not exceeding even one-fourth bankfull, mostly in the Siodło trough [46], may suggest that the greater part of the sediment was entrained rather than laterally eroded, as has been observed in other gravel-bed channels during near-bankfull discharge [23, 31].

**5. Conclusions**

According to the aims of this study, the analysis confirmed that the variability and modification of GSDs are strongly related to the daily variability of bedload transport dynamics, which was suggested for the first time for polar catchments by Kociuba and Janicki [31]. During the measurement period, i.e., the ablation period, the weather conditions played a significant role in the processes observed in the bed channels of streams, especially when low water discharge occurred. In addition, the increased proportion of medium and coarse gravel was strictly proportional to the increases in water discharge. The simultaneous measurements performed in two creeks that are located in the same catchment but present partial differences in the sources of the material (i.e., Fosa Creek was also fed with lake material) indicated the processes occurring in both troughs. The bedload material from Siodło Creek consisted mostly of fine and very fine gravels, suggesting an early stage of formation and an efficient erosive process, which is confirmed by the general conditions of both streams. Fosa Creek has been free of ice cover for more than 30 years and is at a more stable development stage in which water discharge is the predominant control mechanism for the channel geometry. However, the GSD analysis showed that bedload transport can also significantly influence this process.

**Acknowledgments:** This publication has been partially financed by funds from the Leading National Research Centre (KNOW) received by the Centre for Polar Studies for the period 2014–2018.

**Author Contributions:** J.S. and R.J.B. designed the study and conducted the field campaign and laboratory analysis. J.S. conducted the majority of the data analysis and wrote the majority of the paper. J.S. and R.J.B. both contributed to the final version of the manuscript.

**Conflicts of Interest:** The authors declare no conflicts of interest.

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© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
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Article

# Functional Relationship between Soil Slurry Transfer and Deposition in Urban Sewer Conduits

Yang Ho Song<fnref n="1" /> ID, Eui Hoon Lee<fnref n="2" /> ID and Jung Ho Lee<fnref n="1" />,*

Received: 5 May 2018; Accepted: 21 June 2018; Published: 22 June 2018

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**Abstract:** Soil slurry deposited on the surface of the Earth during rainfall mixes with fluids and flows into urban sewer conduits. Turbulent energy and energy dissipation in the conduits lead to separation, and sedimentation at the bottom lowers the discharge capacity of conduits. This study proposes a functional relationship between shear stress in urban sewer conduits and the physical properties of particles in a conduit bed containing less than 20 mm of soil. Several conditions were implemented for analyzing two-phase flow (soil slurry and fluid in urban sewer conduits) in terms of turbulent flow by considering soil slurry flowing into urban sewer conduits. The internal flows of fluid and soil slurry in urban sewer conduits were numerically analyzed and modeled by applying the Navier-Stokes equation and the $k-\epsilon$ turbulence model. The transfer deposition of the soil slurry in the conduits was reviewed and, based on the results, a limiting tractive force was calculated and used to propose criteria for transfer deposition occurring in urban sewer conduits.

**Keywords:** soil slurry; sedimentation; two-phase flow; transfer; deposition; limiting tractive force

## 1. Introduction

It is important to understand the flow characteristics of urban sewer conduits to maintain their flow control capacity and prevent flooding during rainfall. In the case of localized and heavy rainfall, soil slurry separates from the Earth's surface through outflows and flows into drainage. This lowers the discharge capacity of drains. Delaying the outflow leads to overflow that causes flooding. Under a balanced condition, sediments accumulated at the bottom of urban sewer conduits are directly related to a reduction in discharge capacity, and leads to system overload and flooding.

The purpose of urban sewer conduits is to prevent flooding in urban areas by discharging runoff generated during rainfall. Together with the design and construction of such urban sewer conduits, maintaining their discharge capacity is the most important factor influencing continual maintenance. If urban sewer conduits are not designed, constructed, and maintained properly, severe soil sedimentation can occur in them during or after rainfall events, which threatens their discharge capacity and ability to properly handle sediments. Reduced discharge capacity of urban sewer conduits can cause flooding during the rainy season or localized heavy rainfalls.

In general, soil slurry flowing into urban sewer conduits forms a layer of solid particles at the bottom of the conduit leading to deposition [1–4]. In terms of flow characteristics, when particles are transferred, the fluid and solid particles interact in a complex manner. Past research has relied on experiments [5], but it is challenging in experimental analyses to review the independent influence of each variable on transfer deposition. Moreover, soil slurry has a dynamic flow in the transfer process. In the case of particles, it is difficult to measure the internal flow velocity of a conduit because of their

<footnote n="1">¹ Department of Civil and Environmental Engineering, Hanbat National University, Daejeon 34158, Korea; syho@daum.net</footnote>

<footnote n="2">² Research Center for Disaster Prevention Science and Technology, Korea University, Seoul 02841, Korea; hydrohydro@naver.com</footnote>

<footnote>* Correspondence: leejh@hanbat.ac.kr; Tel.: +82-042-821-1106</footnote>
own viscosities, particle sizes, and fluid drag forces [6,7]. Using experimental results, many studies have analyzed the fundamental aspects of sediment transfer in turbulent flow conditions [8]. However, they propose representing sediment flow as an induction equation to relate it to flow velocity [9–12]. Knowledge of the characteristics of internal flow is critical. However, the internal flow of urban sewer conduits is completely different from that of a river, making it difficult to obtain accurate predictions. For this purpose, existing empirical equations based on flow along a river may be applicable if modified according to the hydraulic features of urban sewer conduits.

It is difficult to determine the initiation of particle movement because of various issues. The Shields diagram is a typical criterion for the incipient motion of sediments [13]. Shields suggested fundamental concepts for initiating the motion of a bed comprising non-cohesive particles resistant to erosion by flowing water. This is indicated by critical shear stress, which is commonly assumed to be a constant for a given sediment mixture and can be determined through laboratory experiments [14]. However, the proposed results cannot be directly applied owing to some limitations. Shields did not provide any method to obtain critical shear stress for transfer and deposition. Accordingly, Brownlie fitted a curve to the representative line using the Shields relationship [15]. In this study, the precise moment of incipient motion is suggested, mainly based on numerical modeling, and transport rate measurements are used for a more objective evaluation of the various conditions of the deposition environment.

To efficiently model the transfer deposition of soil in a conduit, it is necessary to determine the shear stress to smoothly model the transfer of particles without deposition in the conduit. To review the characteristics of the transfer deposition of particles in turbulent flow, some studies have applied obstacles in pipes or conduits, attended to the flow of particles in the relevant region, and applied the results to various technologies [16–18]. Some of these studies focused on one phase of the fluid to analyze the mechanism of its continuity and momentum equations, and applied the advection–diffusion equation to the soil slurry sediment. However, such methods are limited to the analysis of particle deposition and sedimentation.

Studies based on numerical analysis to reflect the conditions of turbulent flow have modeled the transfer deposition of soil and correlations among multiple parameters. The results have been compared with those of the above-mentioned empirical equation to suggest a proper method of application [19–22].

This study proposes a functional relationship between critical tractive force in urban sewer conduits and the physical properties of particles in a conduit bed containing less than 20 mm of soil. The inlet flow velocity (1.0, 2.0 and 3.0 m/s) of the soil slurry mixture, the volume concentration of the soil (10%, 30% and 50%), and its particle size were set as variables. Soil slurry flowing into urban sewer conduits was analyzed based on the two-phase flow (soil slurry and fluid in urban sewer conduits) as turbulent flow. In a relevant work, Song et al. studied the flow of soil slurry in urban sewer conduits [23]. In reviewing flow, the shear flow velocity and shear stress were found to be critical. Therefore, the results of Song et al. were applied in this study. The purpose was to review the criteria of deposition in the transfer process by assuming that soil slurry can flow in urban sewer conduits and by changing its flow conditions. It is noteworthy that the observation and analysis of the two-phase flow are difficult, and no relevant study has considered this for soil slurry. This study made the following assumptions:

1. The flow of a mixture of fluid and soil slurry in urban sewer conduits was considered, similar to simulating the mixing and flowing of a large amount of soil slurry and runoff.

2. In conditions of turbulent flow, it was assumed that flow in the conduit consisted of fluid and solid phases.

3. For accurate flow analysis, incidental simulations were excluded, and a method for reducing the time needed to analyze a short conduit was considered.

4. Soil flowing in a sewer conduit consists of particles of different sizes. For modeling, it is necessary to consider this distribution of particle size. In this study, it was assumed that the soil slurry had a uniform particle size distribution.
A commercial analysis tool ANSYS FLUENT 13.0 was used in this study [24]. This study analyzed the characteristics of flow in urban sewer conduits of 10 m length and 0.6 m diameter in light of the inlet flow velocity of the soil-fluid mixture (v), size of the soil particle (d), and the volume fraction in the soil mixture (v/f). The simulation results were used to investigate the limiting tractive force. Based on the results of a hydrodynamic analysis using 2D modeling, the limiting tractive force was calculated depending on the particle size of the soil slurry, and an equation for the functional relationship based on a different particle size was proposed. The limiting tractive force was found to be related to the physical properties of non-cohesive soil.

## 2. Numerical Method

In past studies on two-phase flow, the sensitivity of each phase was analyzed to propose the mechanism of their interaction [25–28]. These results provided a considerable amount of information concerning two-phase flow that was used to define the phenomenon for a variety of flows using a diversity of numerical analysis models. A few recent studies have proposed a functional equation based on particle density to define the criteria for sediment movement based on the flow velocity distribution of urban sewer conduits, in the context of two-phase flow containing a mixture of fluid and soil slurry [29–31].

### 2.1. Governing Equations and Mathematical Model

In this study, the models were constructed in FLUENT 13.0 to analyze two-phase flow using the ANSYS solver [32]. The control equations consisted of continuity and momentum equations and particle component conservation equations of mass and momentum [33]. The continuity and momentum equations can be implemented using Reynolds’ transport theorem, and by applying Newton’s second law [34,35].

The continuity equations are shown as Equation (1) and compressible fluid is presented as Equation (2). In Equation (3), the equations of momentum yield the volume fraction and density per unit time for each phase based on velocity. In the equation, $x_i(i = 1, 2, 3)$ represents the orthogonal coordinates, $u_i$ the orthogonal (directional) element of the velocity vector that represents average flow velocity, $\rho$ is fluid density, $p$ is pressure, and $F_i$ is the sum of influential forces, such as gravity, deflecting force, and centrifugal force.

$$ \frac{\partial \rho}{\partial t} + \frac{\partial (\rho u_i)}{\partial x_i} = \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \bar{u}) = 0 \quad (1) $$

$$ \nabla \cdot (\rho \bar{u}) = 0 \quad (2) $$

$$ \frac{\partial(\rho u_i)}{\partial t} + \frac{\partial(\rho u_j u_i)}{\partial x_j} = \frac{\partial \tau_{ij}}{\partial x_j} - \frac{\partial p}{\partial x_i} + F_i \quad (3) $$

In Equation (4), $\tau_{ij}$ represents a viscous stress tensor representing Newtonian flow fluid, including the velocity of the deformed stress tensor; and $ii$ represents structural correlation. In Equation (5), $\delta_{ij}$ represents the ratio of the strain (deformation) tensor described in Equation (4):

$$ \tau_{ij} = 2\mu\delta_{ij} - \frac{2}{3}\mu\delta_{ij}\frac{\partial u_i}{\partial x_j} \quad (4) $$

$$ \delta_{ij} = \frac{1}{2} \left( \frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i} \right) \quad (5) $$

### 2.2. Turbulence Model

To analyze the effect of turbulence in a conduit with soil slurry, a turbulence model is required. The shear force owing to the laminar viscous force of the neighboring fluid becomes its driving force
and, consequently, a laminar flow with a certain layer appears. However, if the shear stress increases with increasing flow velocity, viscous force transmission becomes challenging to maintain. As a result, the shear stress breaks into very small turbulent eddies and ends up being transmitted inside the fluid.

In general, the Reynolds stress-based model is used to simulate turbulent flow [36–39]. To analyze turbulent flow, the authors used Launder and Spalding’s standard k-ε model, the universally used turbulence model [40]. In the model used to calculate the Reynolds factors, two equations representing the turbulent kinetic energy and the rate of dissipation of energy were calculated to represent turbulent viscosity. It is well known that the prediction of rotational flow or vortex flow, generated when particles of the fluid rotate about a certain axis, and the analysis of an area near a wall with a low Reynolds’ number is inaccurate. However, the model is excellent at convergence in basic turbulent analysis and shortening calculation time [32].

To analyze fluid flow in the standard k-ε model, two equations of turbulent energy and dissipation rate as well as a general transfer equation should be applied separately. These equations are called the turbulent kinetic energy equation and the turbulent kinetic energy dissipation equation, respectively, and are used as a two-equation model. C_μ is a model constant, which is generally 0.09. In this study, based on Equations (6) and (7) in the analysis of the transfer deposition of soil in a tube, k and ε are calculated in two separate transport equations (k-equation and ε-equation) to model turbulent stress [32].

$$ \frac{\partial(\rho k)}{\partial t} + \frac{\partial(\rho \overline{u_j} k)}{\partial x_j} = \frac{\partial}{\partial x_j} \left[ \left( \mu + \frac{\mu_t}{\delta_k} \right) \frac{\partial k}{\partial x_j} \right] + P_k - \rho \epsilon \quad (6) $$

$$ \frac{\partial(\rho\epsilon)}{\partial t} + \frac{\partial(\rho\overline{u_j}\epsilon)}{\partial x_j} = \frac{\partial}{\partial x_j} \left( \mu + \frac{\mu_t}{\delta_\epsilon} \frac{\partial\epsilon}{\partial x_j} \right) + C_{\epsilon1} P_k \frac{\epsilon}{k} - C_{\epsilon2} P_k \frac{\epsilon^2}{k} \quad (7) $$

$$ P_k = \mu_t \left( \frac{\partial \overline{u_i}}{\partial x_j} + \frac{\partial \overline{u_j}}{\partial x_i} \right) \frac{\partial \overline{u_i}}{\partial x_j} \quad (8) $$

In Equation (8), P_k reflects the influence of viscous force, and each value represents the coefficient of the standard values of k and ε, which are obtained through experiments in a wide range of the turbulent area as proposed by Versteeg and Malalasekera (Table 1) [41]. The parameters presented in Table 1 were used to predict the shear flow of basic turbulence, including homogeneous and heterogeneous flows, and yield highly reliable results in terms of the boundary of the wall and free shear flow. C_μ, C_ε1, and C_ε2 are empirical constants determined through experiments, and δ_k and δ_ε are turbulent Prandtl numbers for turbulent kinetic energy and the rate of energy dissipation, respectively [42].

<table><caption>**Table 1.** Parameters of the standard k-ε model.</caption><thead><tr><th>Parameter</th><th>C<sub>μ</sub></th><th>C<sub>ε1</sub></th><th>C<sub>ε2</sub></th><th>δ<sub>k</sub></th><th>δ<sub>ε</sub></th></tr></thead><tbody><tr><td>Value</td><td>0.09</td><td>1.44</td><td>1.92</td><td>1.0</td><td>1.3</td></tr></tbody></table>

Data collected through experimental research on turbulent energy and the rate of dissipation were first applied as parameters in the model. Nevertheless, as this study focuses on analyzing phenomena based on modeling, the reliability of the parameters to be applied were not validated, and experimentally acquired values proposed in a manual were applied because the range of each parameter and ground for its application were required [32].

## 2.3. Setup and Boundary Conditions

In this study, the inlet, outlet, side wall, and symmetry of the entire conduit (volume) were defined as boundary conditions to consider the flow of particles and soil slurry in urban sewer conduits. The authors used ANSYS-FLUENT 13.0 for the analysis. In repeated numerical calculations,
the relative error of a numerical solution was made to converge to 0.001. The relative error of the schemes is computed by comparing the result of the integration step. Reduce step size by half refine the step such that the change of outcome can be identified [24]. It took 17 h on average on an Intel(R) Xeon(R) CPU E5-2630, 2.40 GHz, with 16 GB RAM. The boundary conditions of the numerical model in this study are presented in Table 2.

<table><caption>**Table 2.** Boundary conditions for analysis.</caption><thead><tr><th>Classification</th><th>Boundary Conditions</th></tr></thead><tbody><tr><td>Multiphase flow</td><td>Fluid (water)-Solid (soil)</td></tr><tr><td>Applied models and flow conditions</td><td>Euler-Euler model<br>Standard k-ε model<br>Turbulent flow<br>Unsteady and turbulent</td></tr><tr><td>Inlet conditions</td><td>Inlet velocity<br>Inlet volume fraction<br>Soil diameter</td></tr><tr><td>Outlet condition</td><td>Free fall</td></tr><tr><td>Wall condition</td><td>Non-slip</td></tr><tr><td>Convergence</td><td>0.001</td></tr></tbody></table>

It was assumed that the flow conditions did not change, and no deformed flow occurred. The authors simulated phenomena by analyzing various runoff flows in the conduit. This method helped reduce calculation time and implement an optimal solution through repeated calculations.

The inlet flow velocity of the soil slurry mixture, the volume concentration of the soil, and its particle size were set as variables. The flow velocity and particle distribution of the mixtures in all 63 conditions were compared and reviewed. Table 3 lists the values of parameters of the fluid and soil slurry mixture, which are similar to those used by Song et al. [23]. To simulate the soil slurry transfer and deposition in urban sewer conduits, short conduits were used, as shown in Figure 1. A mesh structure consisting of 140,000 rectangular meshes, each of 0.6 m in diameter and 10 m in length, was implemented. Wall boundary conditions were applied to confine fluid and soil regions. In viscous flows, the non-slip boundary condition is enforced at walls by default; no symmetrical boundaries were applied but the shape of the entire conduit was represented.

<table><caption>**Table 3.** Basic information concerning the parameters for analysis.</caption><thead><tr><th>Parameter</th><th>Units</th><th>Value</th></tr></thead><tbody><tr><td>Conduit specification</td><td>m</td><td>0.6 (D) × 10 (L)</td></tr><tr><td>Mesh specification</td><td>grid</td><td>140,000</td></tr><tr><td>Inlet velocity condition</td><td>m/s</td><td>1.0, 2.0, 3.0</td></tr><tr><td>Inlet volume fraction condition</td><td>%</td><td>10, 30, 50</td></tr><tr><td>Fluid density</td><td>kg/m³</td><td>998.2</td></tr><tr><td>Fluid kinematic viscosity</td><td>Pa·s</td><td>0.001003</td></tr><tr><td>Soil density</td><td>kg/m³</td><td>2,650</td></tr><tr><td>Soil diameter</td><td>mm</td><td>0.5, 1.0, 3.0, 5.0, 7.0, 15.0, 20.0</td></tr></tbody></table>

<figure><img src="image_30.png" /><figcaption>**Figure 1.** 2D mesh containing 140,000 cells.</figcaption></figure>
As for the cross-section, the fluid and soil slurry flowed into the initial flow section (0 m), where the flow rate was constant for a certain period (500 s). The sectional volume fraction of the cross-section of the conduit was assumed to be the volume fraction of particles in the total flow. For the outlet (10 m), the results of the flow field and volume fraction in nine sections (1–9 m inside) were reviewed. In the case of the inlet, the flow velocity was constant, and thus flow field could be neglected. In the case of the outlet, the two-phase flow was such that the distribution of the flow field and volume fraction tended to be scattered. Therefore, it was excluded. Shields performed experiments in flumes with widths of 0.8 m and 0.4 m and beds composed of particles with diameters from 0.36 mm to 3.44 mm; mean velocity was increased in steps of 0.1 m/s to 0.6 m/s [13]. Brownlie conducted studies on the Colorado River, Mississippi River, and Red River. In his study, the flow velocity had minimum and maximum values of 0.37 m/s and 2.42 m/s, respectively, and beds were composed of particles ranging from 0.08 mm to 1.44 mm in diameter [15]. In this study, the same specification was applied to a sewer based on a numerical model. In the analysis, the particle size and inflow rate were changed to reflect the runoff condition in actual sewers. The transport and erosion phenomena in the conduit were reviewed. For discharge flowing into sewer pipes, most flow in as a mixture of fluid and soil slurry depending on the occurrence of rainfall, showing characteristics of turbulent flows. Accordingly, for soil slurry flowing into conduits, this study investigated the characteristics of flows inside conduits by determining the rate of flow corresponding to outflow and that to inflow occurred in mixed forms. The soil slurry flowing into the conduit contained particles of different sizes. The slurry was modeled by considering the dispersion of particle size. However, only particle size influenced velocity and particle distribution of the mixture. Therefore, we assumed particles of uniform size by considering a single particle size [23].

## 2.4. *Model Validation*

Song et al. [23] developed a model based on the experimental results obtained by Nabil et al. [43]. Based on the correction process, they suggested that the distribution of flow velocity and the changing pattern of the volume fraction of soil slurry were consistent in a conduit in their model. They reported experimental results for soil particles 1.4–2.0 mm in size, as used by Matousek [44].

Figure 2 shows the transfer of particles of size 1.4–2.0 mm in urban sewer conduits, with a volume concentration of 26% and flow velocities of 2.5 m/s and 3.0 m/s. A significant of the resulting flow was consistent. The internal distribution under the two conditions of flow velocity and volume concentration, which were used for examination, tended to be the same. Therefore, the analysis model was considered verified.

<figure><img src="image_31.png" /><figcaption>**Figure 2.** Results of examination using data obtained by Matousek. Results corresponding to flow velocities of: (a) 2.5 m/s; and (b) 3.0 m/s.</figcaption></figure>
3. Numerical Modeling

3.1. *Analysis of Flow Characteristics in Conduit Depending on Inlet Flow Velocity*

The transfer of soil slurry in a conduit influences flow velocity under the action of inertia and gravity. Figures 3 and 4 show changes in the flow velocity in a conduit depending on the volume fraction at the same flow velocity for 1.0 mm and 20.0 mm of slurry. As shown in Figure 3, in the case of the flow velocity distribution of a single fluid, the flow velocity converged to zero at the bottom of the conduit, and then assumed the maximum value at the center with a rise in the diffusion coefficient through the volume fraction grade of soil slurry. However, this study analyzes two-phase flow rather than that of a single fluid, and revealed that the maximum value of flow velocity increased in the upper part of the conduit with changes in the volume fraction. The maximum flow velocity should have been observed at the center of the conduit because of the soil slurry deposited at its bottom.

In Figure 4, the flow velocity at the bottom changes slowly because of the soil slurry. In the upper part of the conduit, where the volume fraction had been reduced, the flow velocity tended to increase. With a rise in the volume fraction of the soil slurry in the lower part of the conduit, the damping effect of turbulence due to fluid friction largely worked and, consequently, the maximum value of flow velocity moved to the upper part of the conduit. Depending on deposition, the volume fraction of the soil slurry in the upper part of the conduit was smaller than that in the lower part. It was analyzed to be ideally consistent with the flow of a single fluid.

<figure><img src="image_32.png" /><figcaption>**Figure 3.** Vertical profile of longitudinal flow velocity of 1.0 mm of slurry in a conduit: (a) 1.0 m/s, 10% volume fraction; (b) 1.0 m/s, 30% volume fraction; and (c) 1.0 m/s, 50% volume fraction.</figcaption></figure>

<figure><img src="image_33.png" /><figcaption>**Figure 4.** Vertical profile of longitudinal flow velocity of 20.0 mm of slurry in a conduit: (a) 1.0 m/s, 10% volume fraction; (b) 1.0 m/s, 30% volume fraction; and (c) 1.0 m/s, 50% volume fraction.</figcaption></figure>
The distributions of the flow velocity of 1.0 mm and 20.0 mm of slurry were used in this study to verify that relatively smaller particles changed rapidly in the lower part of the conduit with a large volume fraction of soil slurry. It is fair to attribute this result to relative density. In general, the higher the volume fraction of soil slurry, the greater the interaction of particles in the mixture and the higher their viscosity. As a result, the flow velocity of the fluid in a relevant section decreases and, if the volume fraction decreases, flow velocity increases.

## 3.2. Analysis of Flow Characteristics of Conduit Depending on Inlet Volume Fraction

The most significant change with changing volume fraction of the inlet occurred in the distribution of flow velocity in the conduit. The volume fraction influenced the flow of each particle and changed the distribution of the flow velocity. The homogeneity of the distribution of flow velocity thus represented the homogeneity of the particle distribution. Figures 5 and 6 show the changes depending on volume fraction at velocities of 1.0 mm and 20.0 mm of the slurry. As shown in the results, the volume fraction in the upper part was close to zero, and a large volume fraction was observed only in the lower part of the conduit. The frictional force arising in the lower part did not significantly influence the center of the conduit with the maximum turbulence and flow velocity.

<figure><img src="image_34.png" /><figcaption>**Figure 5.** Vertical profile of the longitudinal volume fraction of 1.0 mm of slurry in the conduit: (a) 1.0 m/s, 10% volume fraction; (b) 1.0 m/s, 30% volume fraction; and (c) 1.0 m/s, 50% volume fraction.</figcaption></figure>

<figure><img src="image_35.png" /><figcaption>**Figure 6.** Vertical profile of the longitudinal volume fraction of 20.0 mm of slurry in the conduit: (a) 1.0 m/s, 10% volume fraction; (b) 1.0 m/s, 30% volume fraction; and (c) 1.0 m/s, 50% volume fraction.</figcaption></figure>
Figure 5 shows the influence of the particle size of the soil slurry. As shown, when particle diameter was small, the distribution of volume fraction altered from heterogeneous to homogeneous along with a change in flow velocity. When the particles were small, they were easily moved by the eddy of the fluid. As shown in Figure 6, this was because particle movement was determined by gravity, which is based on unit particle weight. In general, with an increase in flow velocity, the fluid force became greater than the resistance of the hardened deposit and, thereby, moved the soil slurry. Friction increased with rising tractive force. Based on the change in flow velocity observed at the bottom of the conduit, the limiting tractive force could be estimated by calculating the shear flow velocity and shear stress in the conduit.

To sum up the numerical analysis, the larger the particle size of the soil slurry and the greater the increase in volume fraction, the greater the deposition. The higher the flow velocity, the smaller the deposition. An increase in the layer deposited led to increased flow velocity in the upper part of the conduit. With increased particle size of the soil slurry, deposition was evident.

# 4. Functional Relationship of Soil Slurry Transfer Deposition in Urban Sewer Conduits

## 4.1. Calculation and Review of Limiting Tractive Force

The major parameters needed to determine transfer deposition in the fluid transfer process are the vertical distribution of soil slurry in the conduit and the shear flow velocity ($u_*$) along the floor boundary. The shear flow velocity causes the soil slurry deposited at the bottom of the conduit to float in the re-floating process. At this time, the volume concentration can induce a smooth transfer or re-sedimentation. Accordingly, the shear flow velocity influenced by the layer of deposit was reviewed to measure the change in shear flow velocity at the bottom of the conduit. In general, this change in shear flow velocity represents a change in kinetic energy.

The characteristics of soil slurry include physical, such as particle size ($d$), density ($\rho$) and settling velocity ($v_s$), and volumetric constituents, such as the volume fraction of flow and the unit weight of mixed fluid flow. Raudkivi claimed that sediment transfer depends on shearing speed and the relative particle settling velocity [45]. Shearing speed can be calculated using Equations (9) and (10), and the settling velocity of the particle can be calculated using Equation (11). Shear stress is calculated through conversion. ($\rho_s - \rho_s$) / $\rho_s$ is the specific gravity of the sediment (submerged) in fluid, $\rho_s$ is its density (kg/m³), $\rho$ is the density of water (kg/m³), $g$ is the acceleration due to gravity (m/s²), $d$ the particle diameter (m), and $C_D$ is the coefficient of drag, which varies depending on the free motion of a particle but generally converges to 0.44 in turbulent flow. It is known that the drag coefficient of particles in a turbulent fluid may be significantly different, depending on concentrations and particle characteristics. The viscosity of the mixture, however, increases rapidly with volumetric sand concentrations beyond 20% [46,47]. For mixture flow, pressure drops could not be predicted accurately. The amount of error increased rapidly with the slurry concentration. These problems will be addressed through further research. The objective of this study is to provide a better description of the physical properties in agreement with numerical data. Accordingly, the average drag coefficient was considered to be 0.44 of a perfect sphere with the same volume and density depending on the particle diameter. Therefore, it was assigned a fixed value without any separate calculation. The particle settling velocity to be applied in this study was calculated using Equation (11). The weight of a submerged particle was calculated by $4/3(\rho_s - \rho_s)/\rho_s = 2.2$. Subsequently, calculations using particle size could be performed with $(gd/C_D)$.

$$ \tau_b = \rho g R_h S_f \qquad (9) $$

$$ \tau_c^* = \frac{\tau_b}{\rho \left( \frac{\rho_s - \rho}{\rho} \right) g d} = \frac{u_*^2}{\rho \left( \frac{\rho_s - \rho}{\rho} \right) g d} \qquad (10) $$

$$ v_s = \sqrt{\frac{4}{3} \left( \frac{\rho_s - \rho}{\rho} \right) \left( \frac{gd}{C_D} \right)} \qquad (11) $$
$$ \frac{u}{u_{*}} = \frac{1}{\kappa} \ln\left(\frac{z}{z_{o}}\right) \qquad (12) $$

Given the distribution of flow velocity in a certain cross-section, such as flow in the conduit, Shear flow velocity in Equation (12) could be calculated, where *u* is the average flow velocity at the upper distance *z* relative to the bottom, *z*<sub>o</sub> is the distance from the bottom, where the flow velocity is zero, *u*<sub>*</sub> is the flow shear speed, and *κ* is the von Kármán constant, which is approximately 0.41 [48,49]. In the case of shear flow velocity using Equation (12), assuming a certain flow velocity distribution in a certain cross-section, an approximate value of velocity can be estimated using the equation below. It can also be calculated using the law of the wall, which was used to explain the relatively thin layer (*z*/*H* < 0.2) at the bottom [29].

Therefore, by applying the change owing to an increase in continuous velocity occurring along the boundary of the bottom of the conduit, the shear flow velocity and shear stress in transfer deposition can be calculated. If *y* increases discontinuously at a certain calculation point, ∂*u*/*∂*y in Equation (13) increases infinitely. Therefore, the shear stress at the point where there is no change in flow velocity can be defined as the limiting shear stress. In Equation (13), *μ* is the dynamic viscosity of the fluid. Shear force is the value of friction generated along the side wall due to the velocity of fluid flow in a cross-section of the conduit. Therefore, this friction is proportional to flow velocity and inversely proportional to the cross-sectional area of a conduit, and is used as shear rate or shear stress. In Equation (13), τ<sub>b</sub> represents shear stress at the bottom. In Equation (14), τ<sub>c</sub><sup>*</sup> is the critical shear stress at the bottom to initiate motion in the sedimentation layer (*z*) in the conduit, and is used to calculate the limiting tractive force that forms the basis of transfer deposition.

$$ \tau_b = \mu \frac{\partial u}{\partial y} = \rho g \sin\theta (h - y) \qquad (13) $$

$$ \tau_c^* = \frac{\tau_b}{(\rho_s - \rho)g d} \qquad (14) $$

Table 4 lists the results of shear stress based on shear flow velocity in 63 cases. Soil slurry of 0.5 mm diameter had a shear stress of 0.030–0.060 at a velocity of 1–2 m/s. Although there were slight deviations, it generally remained stable at 0.043. At a velocity of 3 m/s, the soil slurry had a value of over 0.284, which means that at relatively high flow velocity, the soil slurry was deposited more rapidly at the bottom of the conduit. Given that the amount of soil slurry (flow amount defined as the mass of soil slurry per total volume in unit flow) flowed in proportion to the inlet flow velocity, a larger deposit was expected when a large amount of slurry flowed in. This means that small particles could be deposited in the conduit. Soil slurry of 20.0 mm diameter had an average value of 0.053, which was maintained even with changes in flow velocity. The probability of sedimentation based on deposition was 0.056, the value suggested by Shields [13]. Given these results, if particle size increased, the density and specific gravity of the soil slurry increased. Deposition thus easily occurred and the settling velocity increased.

<table><caption>**Table 4.** Calculation of shear stress based on results of numerical analysis.</caption><thead><tr><th rowspan="3">d (mm)</th><th colspan="8">τ<sub>c</sub><sup>*</sup></th></tr><tr><th colspan="3">1.0 m/s</th><th colspan="3">2.0 m/s</th><th colspan="3">3.0 m/s</th></tr><tr><th>10% v/f</th><th>30% v/f</th><th>50% v/f</th><th>10% v/f</th><th>30% v/f</th><th>50% v/f</th><th>10% v/f</th><th>30% v/f</th><th>50% v/f</th></tr></thead><tbody><tr><td>0.5</td><td>0.030</td><td>0.060</td><td>0.056</td><td>0.035</td><td>0.040</td><td>0.041</td><td>0.284</td><td>0.308</td><td>0.307</td></tr><tr><td>1.0</td><td>0.036</td><td>0.036</td><td>0.029</td><td>0.074</td><td>0.730</td><td>0.068</td><td>0.224</td><td>0.259</td><td>0.243</td></tr><tr><td>3.0</td><td>0.061</td><td>0.037</td><td>0.041</td><td>0.033</td><td>0.029</td><td>0.028</td><td>0.086</td><td>0.098</td><td>0.102</td></tr><tr><td>5.0</td><td>0.046</td><td>0.051</td><td>0.056</td><td>0.056</td><td>0.032</td><td>0.056</td><td>0.027</td><td>0.036</td><td>0.034</td></tr><tr><td>7.0</td><td>0.047</td><td>0.047</td><td>0.036</td><td>0.045</td><td>0.047</td><td>0.041</td><td>0.035</td><td>0.055</td><td>0.056</td></tr><tr><td>15.0</td><td>0.052</td><td>0.052</td><td>0.060</td><td>0.038</td><td>0.045</td><td>0.048</td><td>0.042</td><td>0.042</td><td>0.051</td></tr><tr><td>20.0</td><td>0.048</td><td>0.060</td><td>0.054</td><td>0.053</td><td>0.048</td><td>0.051</td><td>0.049</td><td>0.055</td><td>0.056</td></tr></tbody></table>
Shear flow velocity and shear stress at the bottom represent the force accompanying and transferring the deposits. The shear stress along the critical boundary or the critical erosion speed is the limiting condition of deposit transfer and shear stress (limiting point of motion) at the start of the yield. The value of roughness at the bottom depends on the size of sediment particles there, and influences changes in the flow velocity distribution and the transfer capability of the soil slurry.

In general, the settling velocity influences the movement of the particles once the dynamic force of the fluid is imposed on them, and thus creates a boundary layer. In turbulent flow, if the flow velocity increases, the amount of force on the particles exceeds a threshold and acts on the sediment particles at the bottom of the conduit under a constant velocity. This means that, when the threshold is reached, shear stress in the conduit dominates the transfer velocity of the deposits, and significantly depends on flow velocity.

## 4.2. Functional Relationship of Transfer Deposition Due to Soil Slurry Particles

The method proposed by Shields [13] is commonly used to calculate the limiting tractive force as it can be used to directly compare the results obtained at different densities and viscosities, and thus makes it possible to easily judge the conditions of flow. However, in this method, the velocity of shear flow and the size of particles belong to both the longitudinal and transverse axes, and thus, the relationship between them is unclear. Therefore, the limiting tractive force for a given particle size could not be directly calculated. Problems and improvements regarding Shields’ methodology have been discussed by Maa [50], Yalin and Karahan [51], and Smith and Cheung [52]. To solve these problems, Julien introduced a dimensionless parameter given by $(0.1Re^2/\tau_c^*)^2$ and proposed the following modified Equation (15) [14]. $d_s$ is defined as exactly analogous to Rouse’s auxiliary parameter or Rouse Reynolds number, eliminating the critical shear stress from the abscissa definition (in Reynolds number coordinates) [53]. Here, “SPG” represents the specific gravity of the particle. The Reynolds number for a multiparticle system, given in Equation (16), is defined in a similar manner as a function of the void fraction [54,55].

$$ \theta_c = \tau_c^* = f(d_*) = f\left[\frac{(SPG - 1)gd}{v^2}\right]^{1/3} \quad (15) $$

$$ R_e = \frac{u_*d}{v} \quad (16) $$

The works by Shields, Brownlie, and Parker et al. have improved and applied the limited diameter-based equation. To review the case where the limited diameter is small, this study used the results of a numerical analysis [15,56].

The results for particles of sizes 0.5–20.0 mm are presented without dimensions and compared with the results reported by Shields’ limiting tractive force as shown in Figure 7. Shields used 15 data items, whereas this study used 63 for comparison.

As shown in Figure 7, the limiting tractive force for relatively smaller particles (0.5 mm and 1.0 mm) was close to the criteria suggested by Shields’ curve. A velocity of 1.0 m/s was obtained for consistent conditions. The pattern of the increasing amount of soil slurry flowing with increased flow velocity was different from that in Shields’ diagram. The range of limiting tractive force was 0.224–0.307, which means that with increasing flow velocity, the inflow of a large amount of soil slurry led to higher sedimentation. In a turbulent state, high flow velocity leads to a more active deposition of particles, which means that small particles can be deposited in the conduit.

With increasing particle size, a pattern similar to that in Shields’ diagram was observed. In the case of a relatively larger particle of diameter of 20.0 mm, the variable for transfer deposition was calculated to be 0.053, identical to the result suggested by Shields’ curve even with changes in flow velocity. This means that, if the particle size increased, the density and specific gravity of the soil slurry also increase, and particles are rapidly deposited at the bottom of the conduit regardless of the values
of other variables. Therefore, particle size is the basic criterion for soil slurry transfer in calculating the limiting tractive force, but its influence is considered to be little to negligible if particle size is greater or less than a particular value. Small particles flowing into an urban sewer conduit constitute an important variable, and, thus, the conduit must be designed considering its discharge capacity.

<figure><img src="image_36.png" /><figcaption>**Figure 7.** Shields' diagram depending on the boundary Reynolds number and comparison results of the particles.</figcaption></figure>

To account for measurement errors in Table 5, the evaluation accuracy was examined by calculating two different evaluation statistics: SSQ (the sum of the squares) and RMSE (root mean squared error). These are expressed as Equations (17) and (18).

$$SSQ(x_1, x_2) = \sum (x_1 - x_2)^2 \qquad (17)$$

$$RMSE(x_1, x_2) = \sqrt{\frac{\sum_{i=1}^{n} (x_1 - x_2)^2}{n}} \qquad (18)$$

where $x_1$ is the amount of observed values, $x_2$ is the amount of calculated values (Table 5), subscript i indicates $i_{is}$ data in the set, and n is the number of data [57–60]. The results of the numerical model were compared with those of Shields and Brownlie [13,15]. To measure errors, we compared the values obtained in Table 5 with those of Shields and Brownlie, as shown in Table 6.

<table><caption>**Table 5.** Functional relationship of transfer deposition in a conduit using particle size.</caption><thead><tr><th>d (mm)</th><th>d<sub>*</sub> (non-dimensional)</th><th>Relationship Equation</th></tr></thead><tbody><tr><td>d &le; 0.5</td><td>d<sub>*</sub> &le; 9.4</td><td>&theta;<sub>c</sub> = 0.280 &times; d<sub>*</sub><sup>-0.288</sup></td></tr><tr><td>0.5 &lt; d &le; 1.0</td><td>9.4 &lt; d<sub>*</sub> &le; 18.8</td><td>&theta;<sub>c</sub> = 2.336 &times; d<sub>*</sub><sup>-1.248</sup></td></tr><tr><td>1.0 &lt; d &le; 3.0</td><td>18.8 &lt; d<sub>*</sub> &le; 56.4</td><td>&theta;<sub>c</sub> = 0.135 &times; d<sub>*</sub><sup>-0.306</sup></td></tr><tr><td>3.0 &lt; d &le; 5.0</td><td>56.4 &lt; d<sub>*</sub> &le; 94.0</td><td>&theta;<sub>c</sub> = 0.012 &times; d<sup>0.288</sup></td></tr><tr><td>5.0 &lt; d &le; 7.0</td><td>94.0 &lt; d<sub>*</sub> &le; 131.6</td><td>&theta;<sub>c</sub> = 0.032 &times; d<sub>*</sub><sup>0.067</sup></td></tr><tr><td>7.0 &lt; d &le; 15.0</td><td>131.6 &lt; d<sub>*</sub> &le; 282.1</td><td>&theta;<sub>c</sub> = 0.029 &times; d<sup>0.086</sup></td></tr><tr><td>15.0 &lt; d &le; 20.0</td><td>282.1 &lt; d<sub>*</sub> &le; 376.1</td><td>&theta;<sub>c</sub> = 0.007 &times; d<sub>*</sub><sup>0.345</sup></td></tr><tr><td>20.0 &lt; d</td><td>376.1 &lt; d<sub>*</sub></td><td>&theta;<sub>c</sub> = 0.056</td></tr></tbody></table>
<table><caption>**Table 6.** Comparison between the results of this study and those of Shields and Brownlie.</caption><thead><tr><th>d (mm)</th><th>d<sub>*</sub> (non-dimensional)</th><th>Shields and Brownlie (x<sub>1</sub>)</th><th>This Study (x<sub>2</sub>)</th></tr></thead><tbody><tr><td>0.5</td><td>9.4</td><td>0.0334</td><td>0.1468</td></tr><tr><td>1.0</td><td>18.8</td><td>0.0298</td><td>0.0600</td></tr><tr><td>3.0</td><td>56.4</td><td>0.0419</td><td>0.0395</td></tr><tr><td>5.0</td><td>94.0</td><td>0.0485</td><td>0.0438</td></tr><tr><td>7.0</td><td>131.6</td><td>0.0535</td><td>0.0450</td></tr><tr><td>15.0</td><td>282.1</td><td>0.0556</td><td>0.0478</td></tr><tr><td>20.0</td><td>376.1</td><td>0.0556</td><td>0.0530</td></tr><tr><td></td><td>SSQ</td><td></td><td>0.0020</td></tr><tr><td></td><td>RMSE</td><td></td><td>0.0446</td></tr></tbody></table>

The overall SSQ and RMSE values were found to be 0.0020 and 0.0446, respectively. Theoretically, a functional relationship equation is accepted as excellent when RMSE and SSQ values are equal to zero. The RMSE and SSQ values in this study indicate that the assessed results were highly correlated. Accordingly, this study proposed a functional relationship of the limiting tractive force for particles of different sizes, as shown in Table 5. The functional relationship can be used as the criterion to assess the transfer deposition of soil slurry in a conduit. The modified equation proposed in this study expresses this criterion and can be used to calculate the amount of sedimentation in a conduit.

Nevertheless, further studies should focus on analyzing errors considering various diameters and mathematical representation of the curve of critical tractive force results, such as flow conditions and other derived particle parameters.

## 5. Conclusions

In this study, a numerical analysis was performed to investigate the influence of the transfer deposition of soil slurry in urban sewer conduits. The results were analyzed based on various flow conditions. Particle size was set as the main parameter and settling velocity was applied to analyze deposition behavior in the conduit. By considering the turbulence model, the shear flow velocity was investigated according to flow velocity and volumetric concentration. Accordingly, a functional relationship used to identify the boundary of the transfer deposition of soil slurry in urban sewer conduits. Based on the entire process of the numerical analysis, the following conclusions can be drawn:

1. Particle size is the basic criterion for soil slurry transfer in calculating the limiting tractive force, but its influence is little to negligible if particle size is greater or less than a particular value. Nevertheless, small particles flowing into urban sewer conduits are an important variable, and thus conduits must be designed considering their discharge capacity.

2. A turbulence model was applied to calculate average flow velocity, shear flow velocity, and shear stress. In a conduit with sedimentation, the distribution of flow velocity was weakened overall by a similar drag-based volume fraction, and a slant in the flow velocity in the conduit increased due to deposition. The shear flow velocity and turbulent stress were large when a large value was calculated around the boundary of the bottom of the conduit. Therefore, it was estimated by applying an overall inclination.

3. Based on the results, the authors proposed a functional relationship between the limiting tractive and particle size. This relationship can be used as criterion to judge the transfer deposition of soil slurry in a conduit, and can be applied to urban sewer conduits, unlike previous studies. If the phenomena in urban sewer conduits are measured for comparison in an improved study, a more reasonable research method can be devised.

4. The results of this study can help overcome inaccuracy in simulating particles of small diameters in one-dimensional models, which are used to estimate the flow of sediment in urban sewer conduits. In future work, it will be necessary to further investigate the deposition rate of soil in conduits and the pattern of cohesion of each particle.
The findings of this study may be helpful in designing conduits with the aim of preventing conduit clogging or conduit damage that may occur during heavy rainfall events. To analyze drainage flow under the influence of various soil shapes and floating particles, it is necessary to consider different conditions through model experiments and numerical modeling. This study considered only the inflow of a large amount of soil slurry at the beginning of rainfall events. Therefore, the proposed method must be further investigated by introducing various types of rainfall events. Moreover, to validate the results of this study, data from real conduit systems must be collected and analyzed using a rainfall-runoff model. Overall, further research is required to determine the relationship considering the volume fraction of small particles.

**Author Contributions:** Y.H.S. carried out the literature survey and wrote the draft of the manuscript. Y.H.S. and E.H.L. worked on subsequent drafts of the manuscript. Y.H.S. and J.H.L. performed the simulations. Y.H.S., E.H. and J.H.L. conceived the original idea of the proposed method.

**Funding:** This research was supported by a grant (MOIS-DP-2015-03) from the Disaster and Safety Management Institute funded by the Ministry of Interior and Safety of Korea.

**Acknowledgments:** This research was supported by a grant (MOIS-DP-2015-03) from the Disaster and Safety Management Institute funded by the Ministry of Interior and Safety of Korea

**Conflicts of Interest:** The authors have no conflict of interest to declare.

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Article

# Erosion, Suspended Sediment Transport and Sedimentation on the Wadi Mina at the Sidi M'Hamed Ben Aouda Dam, Algeria

Faiza Hallouz<sup>1,2,*</sup> ●, Mohamed Meddi<sup>1</sup>, Gil Mahé<sup>3</sup>, Samir Toumi<sup>1</sup>
and Salah Eddine Ali Rahmani<sup>4 ID</sup>

Received: 28 March 2018; Accepted: 26 June 2018; Published: 4 July 2018

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**Abstract:** The objective of this study was to follow-up on the evolution of the hydro-pluviometric schemes and particular elements of Wadi Mina (6048 km<fnref n="2" />) to the Sidi M'Hamed Ben Aouda Dam to evaluate the silting origin and status of this dam situated in the northwest of Algeria. The pluviometric study targeted a series of rains during 77 years (1930–2007), the liquid discharge data cover a period of 41 years (1969–2010) and the solids and suspended sediment concentrations data cover very variable periods, starting from 22 to 40 years for the entire catchment area. The statistical tests for ruptures detection on the chronological series of rains and discharges indicate a net reduction of rains of more than 20% on the entire basin since 1970. The evolution of solids inputs was quantified: the maximum values are registered on autumn start and at the end of spring. The Wadi Mina basin brings annually 38 × 10⁶ m<fnref n="3" /> of water with a specific degradation of 860 t·km⁻<fnref n="2" />·year⁻<fnref n="1" />. By comparing the results found, we thus observe that the basin upstream of SMBA (1B) Dam is the greatest sediment producer towards the dam because it shows a specific degradation equal to 13.36 t·ha⁻<fnref n="1" />·year⁻<fnref n="1" />.

**Keywords:** Wadi Mina; Algeria; sediment; ruptures; SMBA Dam; specific degradation

## 1. Introduction

Algeria has always been confronted with extreme phenomena: periodic droughts which were sometimes severe and lasting and floods that are more often than not catastrophic. These events constitute a major constraint for the economic and social development and have been the subject of numerous studies [1–12].

Following a rain over a catchment area, a complex mechanism of interactions between hydrological and erosive phenomena is started. The streaming related to strong precipitations entails the soil slide by erosion in quantities that are sometimes very abundant. This has an impact on the environment and one of the results is the soils fertility loss and the early filling of water impoundments (dams, ponds, lakes), thus reducing their storing capacity and possibly entailing as well as degradation of the water quality and usage conflicts [13].

Since the Independence of Algeria, the total number of dams in exploitation at national level increased from 14 in 1962 to 65 in 2014 and, if we add the inter-basin water transfer major works,

<footnote n="1">1 Laboratoire Génie de l’Eau et de l’Environnement, Higher National School of Hydraulic, 09000 Blida, Algeria; m.meddi@ensh.dz (M.M.); s.toumi@ensh.dz (S.T.)</footnote>

<footnote n="2">2 University of Khemis Miliana, 44225 Ain Defla, Algeria</footnote>

<footnote n="3">3 IRD Hydrosciences, 34090 Montpellier, France; gilmahe@hotmail.com</footnote>

<footnote n="4">4 Geo-Environment Laboratory, Faculty of Earth Sciences, Geography and Spatial Planning, University of Sciences and Technology Houari Boumediene, 16111 Bab Ezzouar Algiers, Algeria; alirahmani101990@gmail.com</footnote>

<footnote>* Correspondence: hallouzfaiza@gmail.com; Tel.: +213-660-319-854</footnote>
there are 7 billion m³ of water that are mobilized to be used for drinking water supply, irrigation and industry [14].

The scale of aggradations and the raise of the bottom of these dam impoundments by successive deposits of sediments brought by the watercourses and the wind are a serious problem whose negative consequences are considerably felt in the agriculture, farming, fishing, electricity and navigation fields [15–17]. The study on the silting of lakes, catchment areas or dams is of considerable interest for attempting to explain the complex mechanisms of solid transport and to quantify the volumes of transported sediments [18–21] and for a potential dredging of the impoundment [22].

The sedimentation in North Africa dams is very high in relation to what is noted at international level. According to Lahlou [23], the 23 major dams that are being exploited in Morocco lose annually 50 Mm³ of their storage capacity. In Tunisia, the annual loss of the storage capacity is estimated between 0.5% [24] and 1% for a total initial capacity of about 1430 Mm³ [25]. Algeria's rivers transport a large quantity of sediments [26,27]. The sediment deposited in Algerian dams is estimated to be 20 million m³·year⁻¹ [28]. Competition for water among agriculture, industry, and drinking water supply—accentuated by a drought in Algeria—has shown the need for greater attention to be paid to water [29] and for it to be managed at the large basin scale [30]. Surface water resources in Algeria are evaluated to be approximately 8376 billion m³ for an average year [31]. These water resources in Algeria are characterized by wide variability—the resources for the last nine years have been significantly below this average [32]. Under these circumstances, several dams were built in Algeria to ensure water resources for the supply of drinking water to all its cities and allowed approximately 12,350 km² of irrigated land to be developed [31–33]. However, the sediments deposits in the dam reservoirs are estimated, on average, at 20 million m³ per year [34]. The high efficiency of sediments transport of the Algerian rivers [27,35] encouraged numerous authors to study the transfer of sediments in suspension in this area [36–41]. Considering these problems and to establish the lifespan of dams and to implement a better strategy of water resources management, research on the dynamics of sediments underlines the need to better understand the variations of erosion, deposits and dynamics of storage of sediments in a variety of catchment areas and rivers [42]. In this context, a certain number of studies used the relation of concentration of suspended particles matters (SPM) for acquiring a more complete understanding of the drainage basins processes [19,43,44].

Among the factors that favor erosion (slope, nature of rocks, hilly area, climate, and human activities), climate is recognized as the main factor in the semiarid Mediterranean regions of Algeria that go through short and intense rain episodes, a strong power of evaporation of the wind, prolonged droughts and freezing cycles [45,46]. The erosion is extremely active and the average concentration is at least higher than the global average [42].

Indeed, the main works for surface waters mobilization (big dams, dams and small lakes) were built on the watercourses of basins situated in the northern part of the country. These basins are characterized by various hilly areas dominated, on the one side, by marly lands and soils vulnerable to erosion and, on the other side, by a forest cover limited in the most watered parts and a seasonal vegetation cover. To these natural conditions is added the torrential nature of precipitations that fall at the end of the dry season and that would be responsible for a major part of the erosion and the solid load of water [21].

This article presents a study of erosion, sedimentation and climate change on Wadi Mina, at the Sidi M'Hamed Ben Aouda Dam in the northeast of Algeria, in a semiarid area. It is essential to know the evolution of water resources available for this dam in a variable climatic environment. In addition, since 1976 the rains reduction starting [47] and the increase in extreme events [48], the erosion and solids transport conditions were modified. The first results of the SIGMED (Approche Spatialisée de l'Impact des activités aGricoles au Maghreb sur les transports solides et les ressources en Eau De grands bassins versants) program showed as well the impact of human activities on environment and erosion [49,50], but it is still difficult to quantify the anthropogenic and climatic parts responsible for the recent modifications of the dynamic erosion on the basin [51].
The watershed of Wadi Mina (6048 km², northwest Algeria) is the subject of numerous works in the field of water erosion and siltation of dams [52–67].

The hydrologic part was a study on the rain and water flows in the basin towards available stations supplied by ANRH (National Agency for Hydraulic Resources). The solid transport of suspended particles matters (SPM) was estimated based on specific measures taken by the hydrological services of ANRH during the period 1969–2010. The water volume of the SMBA (Sidi M'Hamed Ben Aouda) Dam was estimated based on the results of the bathymetric measures supplied by ANBT (National Agency for Dams and Transfers) in the period 1978–2004.

In the last part, we studied the sedimentation study on the SMBA Dam and the origin of sediments, comparing the soil loss measured at the hydrometric stations with the dam silting data (bathymetry) with the results of a study of soils erosion by the USLE (Universal Soil Loss Equation) method carried out by Toumi et al. [66]. This is the first comparative study in Algeria which compares the erosion and sedimentation rates on a river basin and the associated reservoir, from several different approaches; this is the originality of this article in relation to the literature.

## 2. Materials and Methods

### 2.1. Study Area

Situated in a semiarid area, the catchment area of Wadi Mina presents strong erodibility and the good availability of pluviometric and hydrometric data. Situated at around 300 km west of Algiers, the catchment area Wadi Mina drains, at the level of the Sidi M'Hamed Ben Aouda (SMBA) Dam, a surface of 6048 km² (Figure 1). Wadi Mina is among the main tributaries of Wadi Cheliff. There are two dams on Wadi Mina, the SMBA Dam, subject of our study, and the Bakhadda Dam, situated at 90 km. The topographic study [68] allowed classifying the studied sub-basins in the hard hilly landscape class, in accordance with the IRD (French National Institute for Research for Sustainable Development) classification [69]. The basin of Wadi Mina spreads on dissimilar natural units:

* In the south, the Tellian plateaus also include the mountains of Frenda and Saida, with an altitude ranging from 900 to 1300 m, where limestone shows on the surface.

* In the north, a unit of mountain ranges and basins, generally of inferior altitude of 900 m, within a complex geological structure, individualized in blocks, where Ouarsenis is one of the most remarkable. They are characterized by an abundance of outcrops of marls, very sensible at hydric erosion.

<figure><img src="image_40.png" /><figcaption>**Figure 1.** Localization of the catchment area of Wadi Mina.</figcaption></figure>
The climate of the region is Mediterranean semi-arid with an annual average precipitation of 305 mm, marked by an irregularity which is both seasonal and inter-annual [68]. Moreover, the analysis of geographical repartition and the diversity of vegetal formations on the basin showed the existence of two parts clearly distinct [59,70]: the north area which is purely marlacious, strongly eroded and lacking vegetation, except for a few small islands of reforestation and plantations of fruit trees in the valley and the south area which is less eroded and where about 50% of the surface is covered by scattered vegetation with very variable density, ranging from the localized forest (pine of Alep) to the very scattered covering scrub. It must be noted that subsistence agriculture reigns with excessive exploitation of soils, a permanent clearing and an intensive overgrazing.

## 2.2. Acquisition and Preparation of Data

The pluviometric data came from the National Agency of Hydraulic Resources (ANRH). They are registered at 26 pluviometric posts (Table 1) distributed on the catchment area and the related observation duration is variable. The longest chronicles (1930–2007) are registered at the pluviometric stations in the south of the basin (Figure 2).

<figure><img src="image_41.png" /><figcaption>**Figure 2.** Localization of pluviometric and hydrometric stations (group of regions: E: east; NW: northwest; CW: center-west; and SW: southwest).</figcaption></figure>

For the entire 26 stations of the basin of Wadi Mina over a period of 77 years (1930–2007), it has been estimated at around 4% the total number of gaps on all the time series of monthly and annual precipitation. Gaps in rainfall series were filled using the method of the regional vector to facilitate the use of rupture tests [47].
<table><caption>**Table 1.** Inventory of pluviometric stations (latitudes and longitudes in decimal degrees, altitude in m).</caption><thead><tr><th>N°</th><th>ANRH Station Code</th><th>Name</th><th>Latitude</th><th>Longitude</th><th>Altitude</th><th>Period</th></tr></thead><tbody><tr><td>1</td><td>012507</td><td>Wadi Lili</td><td>35.50417</td><td>1.288056</td><td>588</td><td>1969–2007</td></tr><tr><td>2</td><td>012703</td><td>Djdiouia<br>amont</td><td>35.6525</td><td>0.8277778</td><td>562</td><td>1930–2003</td></tr><tr><td>3</td><td>012901</td><td>Bakhadda<br>Bge</td><td>35.35444</td><td>1.035</td><td>572</td><td>1972–2007</td></tr><tr><td>4</td><td>012909</td><td>Sidi Ali<br>Benamar</td><td>35.32444</td><td>1.129722</td><td>630</td><td>1971–1994</td></tr><tr><td>5</td><td>012917</td><td>Tiaret-ANRH</td><td>35.38528</td><td>1.306944</td><td>1106</td><td>1990–2007</td></tr><tr><td>6</td><td>013302</td><td>Ain Hamara</td><td>35.38028</td><td>0.6797222</td><td>288</td><td>1968–2007</td></tr><tr><td>7</td><td>013306</td><td>Wadi<br>El-Abtal</td><td>35.46056</td><td>0.6972222</td><td>354</td><td>1952–1968</td></tr><tr><td>8</td><td>013401</td><td>Sidi AEK<br>Djilali</td><td>35.48555</td><td>0.5877778</td><td>236</td><td>1968–2007</td></tr><tr><td>9</td><td>013410</td><td>SBMA</td><td>35.58528</td><td>0.5944445</td><td>195</td><td>1968–2007</td></tr><tr><td>10</td><td>013505</td><td>Relizane</td><td>35.76278</td><td>0.5347222</td><td>58</td><td>1966–2005</td></tr><tr><td>11</td><td>013506</td><td>DEMRH</td><td>35.72333</td><td>0.4847222</td><td>70</td><td>1990–2007</td></tr><tr><td>12</td><td>013507</td><td>El Matmar<br>L'Hillil</td><td>35.72556</td><td>0.3480555</td><td>120</td><td>1968–2006</td></tr><tr><td>13</td><td>013511</td><td>Relizane<br>aval</td><td>35.73695</td><td>0.5336111</td><td>69</td><td>1938–1969</td></tr><tr><td>14</td><td>111401</td><td>Mascara</td><td>35.38278</td><td>0.2408333</td><td>487</td><td>1930–1961</td></tr><tr><td>15</td><td>111404</td><td>Aouf</td><td>35.18639</td><td>0.3688889</td><td>968</td><td>1930–1959</td></tr><tr><td>16</td><td>111405</td><td>Matmor</td><td>35.33333</td><td>0.2</td><td>470</td><td>1930–2003</td></tr><tr><td>17</td><td>111407</td><td>Tighenif</td><td>35.42417</td><td>0.3252778</td><td>540</td><td>1938–1969</td></tr><tr><td>18</td><td>111418</td><td>Nesmoth</td><td>35.25945</td><td>0.3913889</td><td>906</td><td>1990–2007</td></tr><tr><td>19</td><td>111609</td><td>Bouguirat</td><td>35.76472</td><td>0.2291667</td><td>65</td><td>1930–2003</td></tr><tr><td>20</td><td>080504</td><td>Bled Bel<br>Hammar</td><td>34.73583</td><td>0.22</td><td>1170</td><td>1970–2006</td></tr><tr><td>21</td><td>080606</td><td>Maamora</td><td>34.68389</td><td>0.5269445</td><td>1148</td><td>1974–2007</td></tr><tr><td>22</td><td>080701</td><td>Medrissa</td><td>34.89611</td><td>1.233333</td><td>1110</td><td>1930–2006</td></tr><tr><td>23</td><td>111216</td><td>Med El<br>Habib</td><td>34.8</td><td>0.2541667</td><td>1106</td><td>1930–2007</td></tr><tr><td>24</td><td>013201</td><td>Ain Kermès</td><td>34.90861</td><td>1.1025</td><td>1112</td><td>1976–2007</td></tr><tr><td>25</td><td>013204</td><td>Sidi Yousef</td><td>34.80056</td><td>0.5944445</td><td>1091</td><td>1930–2007</td></tr><tr><td>26</td><td>013304</td><td>Takhmert</td><td>35.115</td><td>0.6913889</td><td>663</td><td>1930–2007</td></tr></tbody></table>

The longest possible series of hydrometric data (1969–2010) were used (Table 2). We have at our disposal five hydrological series on the Wadi Mina basin, with little or no gaps (Figure 3).

The solid discharges and concentrations of SPM data cover 40 years periods from 1970/1971 to 2009/2010 for the Wadi El Abtal and Sidi Abdel Kader Djilali stations, from 1975/1976 to 2009/2010 for the Ain Hamara station (35 years old), from 1985/1986 to 2005/2006 for the Sidi Ali Ben Amar station, and from 1972/1973 to 1993/1994 for the Takhmert station (22 years old).

The measurement of suspended sediment concentrations (C) consists of a systematic sampling of water samples using a 500 cL bottle. These samples are taken at a single point, either on the edge or in the middle of the Wadi. Samples are more numerous during floods, while in low water or when the liquid discharge (Q) is constant during the day, only one sample is taken. The difficulty of the measurement is the non-uniformity of the sediment concentration in the measurement section. The turbidity measurement procedure used by ANRH is developed in the work of Bourouba [35] and Meddi [68].

C and Q measurements were used to define rating curves that estimate C from measured values of Q on the Wadi Mina, according to a common approach [71–76]. The curves most commonly used to estimate sediment transport is a power function [77–79]: $Q = aC^b$, where a and b are regression coefficients determined empirically that account for the effectiveness of erosion and transport [42].
<table><caption>**Table 2.** Inventory of hydrometric stations used for the study.</caption><thead><tr><th>Basin</th><th>S/Basin</th><th>Stations</th><th>Surface (km²)</th><th>Latitude</th><th>Longitude</th><th>Altitude</th><th>Period</th><th>Number of Instantaneous Solid Flow Measurements</th></tr></thead><tbody><tr><td>Wadi Haddad</td><td>2B</td><td>Sidi Aek Djilali: I</td><td>499</td><td>35.48555</td><td>0.5877778</td><td>236</td><td>1969/2010</td><td>6262</td></tr><tr><td>Wadi Mina</td><td>1B</td><td>Wadi El Abtal: II</td><td>5365</td><td>35.58528</td><td>0.5944445</td><td>195</td><td>1969/2010</td><td>17,692</td></tr><tr><td rowspan="2">Wadi Abd Aval</td><td>3B</td><td>Ain Hamara: III</td><td>2474</td><td>35.38028</td><td>0.6797222</td><td>288</td><td>1969/2010</td><td>10,222</td></tr><tr><td>4B</td><td>Takhmert: IV</td><td>1488</td><td>35.115</td><td>0.6913889</td><td>663</td><td>1969/2007</td><td>737</td></tr><tr><td>Upstream Wadi Mina</td><td>5B</td><td>Sidi Ali Ben Amar: V</td><td>1163</td><td>35.32444</td><td>1.129722</td><td>630</td><td>1969/2007</td><td>848</td></tr><tr><td>Wadi Mina</td><td>6B</td><td>Intermediary zone: VI</td><td>192</td><td>/</td><td>/</td><td>/</td><td>/</td><td>/</td></tr></tbody></table>

## 2.3. Methods Used

The main objective of the analysis of a chronological series, in accordance with Kendall and Stuart [80], is to bring clarity on the statistical mechanisms generating this series of observation.

Discontinuities in the studied datasets were analyzed using the rupture tests of Pettitt, Buishand, Lee, and Heghinian and the segmentation procedure of Hubert [81]. The null hypothesis tested is that there is no rupture in the series and a rupture is considered as very likely when it is statistically significant and is detected by two tests or two stations. These procedures are well defined by Maftei et al. [82] and in Khomsi et al. [83]. The choice of retained methods is based on the robustness of their foundation and the conclusions of a simulation study of artificially disturbed random series [84]. The study was performed with the software KHRONOSTAT [85], developed by IRD [86].

These tests were applied on the precipitations series in Algeria [87], Morocco [88] and Sub-Saharan Africa [89] as well as on the hydro-pluviometric studies series of the Sudan-Sahelian area [89,90], in West and Central Africa [91], and Tunisia [92]. These methods are thus largely validated in many regions of the world, on rains, discharges or temperatures series.

### 2.3.1. Flood Frequency Analysis (FFA)

The HYFRAN-PLUS software (version-V2.1) developed by the Canadian Institute (INRS-ETE, Eau Terre Environnement Research Centre of Institut national de la recherche scientifique), is designed for Hydrological Frequency Analysis (FFA) especially for extreme value. In the FFA, data corresponds to observations $X_1, \dots, X_N$ which are independent and identically distributed (IID), i.e., verify the hypothesis of homogeneity, stationarity and independence. Several models are available to fulfill this task and the selection of the most robust approach to fit the model to data is a great challenge [93]. The prediction procedure is mainly based on the selection of the best fit for a given dataset. Conventional estimates of flood exceedance quantiles are highly dependent on the form of the underlying flood frequency distribution [94]. Several frequency distributions have been developed to fit different probability shapes, especially for extreme values. The first models related to extreme value theory (EVT) are the Generalized Extreme Value distribution [95], Gumbel [96] and then other models such as Lognormal distribution, Pearson family, Halphen family, Logistic distribution related models are proposed to give more flexibility when the EVT hypotheses are not fulfilled [97].

A decision support system (DSS) has been developed in the HYFRAN-PLUS software [98] to discriminate the different classes of the statistical distributions, and especially to estimate the quantiles for high return period $T$. Note that, for a random variable $Q$, the quantile $Q_T$ with a return period $T$ is the solution of the equation: $Pr[Q > Q_T] = 1/T$. DSS is mainly based on the classification of statistical distributions according to their asymptotic behavior. DSS is mainly based on the classification of statistical distributions according to their asymptotic behavior [99].

There are three nested classes of distributions that are commonly used for extremes [94,100] and implemented in the HYFRAN-PLUS software: Class C (regularly varying distributions) containing Fréchet (EV2), Halphen Inverse B (HIB), Log-Pearson type 3 (LP3) and Inverse Gamma (IG)
distributions, class D (the sub-exponential distributions) involving Halphen type A (HA) and B (HB), Gumbel (EV1), Pearson type 3 (P3) and Gamma (G) distributions and the class E of distributions with inexistent exponential moments (Figures 3 and 4). The Log-Normal (LN) distribution has an asymptotic behavior between the C and D classes [94]. However, the use of the Generalized Extreme Value (GEV) distribution is currently a standard, thanks to the simplicity of its quantile function and the availability of software for parameter estimation [94].

<figure><img src="image_42.png" /><figcaption>**Figure 3.** Distributions ordered with respect to their right tails [94].</figcaption></figure>

The methods developed in the DSS allow identifying the most adequate class for adjusting a given sample. These methods are (Figure 4) [94]:

* the test Jarque–Bera (JB test): considered to test the log-normality with selected a priori based on the diagram (represented by coefficients of variation Cv and skewness Cs);

* the graphic log-log: used to discriminate firstly the class C and secondly D and E classes;

Mean Excess Function (MEF) used to discriminate the classes D and E; and two statistics: the ratio of Hill and Jackson statistics that can be used to perform a confirmatory analysis of suggested conclusions from the two previous methods (log-log graph and MEF).

<figure><img src="image_43.png" /><figcaption>**Figure 4.** Diagram for class discrimination used in the DSS (according to [94]).</figcaption></figure>
### 2.3.2. Generalized Extreme Value (GEV) Distribution and the Extreme Value Theory (EVT)

The generalized extreme value (GEV) distribution appears to be a universal model for hydrological extremes in several regions of the world (in particular in the United Kingdom), the same as the Log-Pearson type 3 distribution in the USA and Australia or Lognormal distribution in China [94].

When modeling the maxima of random variables, extreme value theory plays the same fundamental role as the central limit theorem when modeling sums of variables. In both cases, the theory tells us what are the limiting distributions. Generally, there are two main ways to identify extremes in real data. Let $Y_1, \dots, Y_N$, be a sequence of $N$ random variables, and $X$ their maximum:

$X = \max\{Y_1, \dots, Y_N\}$ taken in successive periods. If the variables $Y_1, \dots, Y_N$ are independent and identically distributed and $F_0$ is their distribution function (referred here as parent distribution), the distribution of the maximum $X$ is given by:

$$ 
\begin{aligned}
H_N(x) &= P(X = \max(Y_1, \dots, Y_N) < x) \\
&= P(Y_1 < x, \dots, Y_N < x) \\
&= \prod_{i=1}^{N} P(Y_i < x) \\
&= [F_0(x)]^N
\end{aligned} 
\quad (1) $$

Let $X_1, \dots, X_N$ constitute the extreme events, also called block of maxima, taken in $n$ successive periods, for example $n$ years. The limiting distribution for the block of maxima is given by Fisher and Tippett [101]. The Fisher-Tippett theorem states that if the sequence $Y_1, \dots, Y_N$ are Independent and Identically Distributed (IID) and if there exist constants $C_N > 0, d_N \in R$ and some non-degenerate function $H$ such that $H_N$ converges, when $N$ tends to infinity, towards $H$ in distribution $(H_N \to H)$, then $H$ corresponds to one of the three standard extreme value distributions:

$$ \text{Gumbel (EV1): } A(x) = \exp(-e^{-x}), \quad x \in R \quad (2) $$

$$ \text{Fréchet (EV2): } \Phi_k(x) = \begin{cases} 0 & x \le 0 \\ \exp(-x^k) & x > 0 \end{cases} \quad k < 0 \quad (3) $$

$$ \text{Reverse Weibull (EV3): } \Psi_k(x) = \begin{cases} \exp(-(-x^k)) & x \le 0 \\ 0 & x > 0 \end{cases} \quad k > 0 \quad (4) $$

Depending on each case, the distribution of the original observation $F_0$ belongs to the Max-Domain of Attraction (MDA) of $A, \Phi_k$ or $\Psi_k$:

* The Gumbel MDA contains a great variety of distributions such as Normal, Gamma, Exponential and Gumbel.

* The Fréchet MDA contains distributions with power decay tail as the Pareto, Student, Cauchy, Inverse Gamma and Fréchet.

* The Weibull MDA distributions are light tailed with finite right endpoint. Such domain of attraction encloses Uniform and Beta distributions and is not of interest in FFA. The Weibull distribution has an upper bound and is not considered for high extremes.

Von Mises [101] proposed the generalized extreme value (GEV) distribution, which includes the three limit distributions EV1, EV2 and EV3. Another re-parameterization given by Fisher and Tippett [102] is generally used in hydrology:

$$ F_{\text{GEV}}(x) = \begin{cases} \exp\left[-\left(1 - \frac{k}{\alpha}(x - \mu)\right)^{\frac{1}{k}}\right] & k \neq 0 \quad (\text{EV2 and EV3}) \\ \exp\left[-\exp\left(-\frac{(x-\mu)}{\alpha}\right)\right] & k = 0 \quad (\text{EV1}) \end{cases} \quad (5) $$
whenever $1 - k \frac{(x - \mu)}{\alpha} \ge 0$. When the shape parameter $k$ is positive (respectively negative), the GEV corresponds to the inverse Weibull (EV3) (respectively Fréchet, EV2) distribution. The limiting case, $k = 0$, corresponds to the Gumbel (EV1) distribution. The simplicity of the GEV distribution function lead to an explicit expression of the quantile function to compute quantile for a given non-exceedance probability $p$:

$$x_p = \begin{cases} \mu + \frac{\alpha}{k}(1 - (-\ln p)^k) & k < 0 \ (\text{EV2}) \\ \mu - \alpha \ln(-\ln p) & k = 0 \ (\text{EV1}) \\ \mu + \frac{\alpha}{k}(1 - (-\ln p)^k) & k > 0 \ (\text{EV3}) \end{cases} \quad (6)$$

This explicit quantile formula is also useful to generate a GEV samples by inversion method based on the generation of uniform distribution.

### 2.3.3. USLE Method

A classic example is the Universal Soil Loss Equation (USLE) [103]. This method expresses the long-term average annual soil loss as a product of rainfall erosivity factor (R factor), soil erodibility factor, slope length factor, slope steepness factor, cover-management factor, and support practice factor. USLE only predicts the amount of soil loss that results from sheet or rill erosion on a single slope and does not account for additional soil losses that might occur from gully, wind or tillage erosion. This erosion model was created for use in selected cropping and management systems, but is also applicable to non-agricultural conditions such as construction sites. The USLE can be used to compare soil losses from a particular field with a specific crop and management system to “tolerable soil loss” rates. Alternative management and crop systems may also be evaluated to determine the adequacy of conservation measures in farm planning. However, erosion is seen as a multiplier of rainfall erosivity (the R factor, which equals the potential energy); this multiplies the resistance of the environment, which comprises K (soil erodibility), SL (the topographical factor), C (plant cover and farming techniques) and P (erosion control practices). Since it is a multiplier, if one factor tends toward zero, erosion will tend toward zero.

## 3. Results

### 3.1. Analysis of Precipitations

At the monthly scale, some significant patterns arise. There are two periods of maximum occurrence of rupture in the rainfall time series of the stations studied, Autumn until January, which concentrate more than 40% of the annual amount of precipitation, with a peak in December and January, and Spring between April and June with more than 20% of the annual amount and two peaks in June and April. Intermediate seasons show much less occurrences of ruptures during the 1970s. However, during the 1980s the maximum of occurrence of ruptures is in August, and similarly during the 2000s in August and September, while during the 1990s the maximum is in March (Table 3).

The pluviometric posts for which a rupture could be detected are more numerous in the north than in the south. The pluviometric deficits noted are frequently close to 19–20%. This pluviometric deficit is thus felt for more than three decades and seems to be accentuated during the 1970–1980 decade. The areas in the west center and northwest have higher totals ruptures than the other areas on a monthly and yearly scales.
<table><caption>**Table 3.** Ruptures detected at the level of each pluviometric station. Ruptures dates detected by three statistical tests (red: strong rupture), by at least two statistical tests (dark gray: probable ruptures), by at least one statistical test (light gray: weak rupture) on the catchment areas (in bold: the ruptures dates detected for more than one catchment area the same year or the same month) (empty box = no probable rupture detected).</caption><thead><tr><th>Station</th><th>Region</th><th>Groups</th><th>N</th><th>D</th><th>J</th><th>F</th><th>M</th><th>A</th><th>M</th><th>J</th><th>J</th><th>A</th><th>Annual</th></tr></thead><tbody><tr><td>Oued lili</td><td></td><td>72</td><td></td><td>75</td><td>77</td><td></td><td>80</td><td>75</td><td>85</td><td>71</td><td>82</td><td>70</td><td>74</td></tr><tr><td>Djdiouia amont</td><td></td><td>75</td><td>01</td><td>81</td><td>72</td><td>86</td><td>96</td><td></td><td></td><td>76</td><td></td><td>01</td><td>76</td></tr><tr><td>Bekhadda bge</td><td></td><td></td><td></td><td>74</td><td>76</td><td>77</td><td>76</td><td>76</td><td>70</td><td></td><td></td><td></td><td>69</td></tr><tr><td>Sidi Ali Ben Amar</td><td>E</td><td>75</td><td></td><td>74</td><td>78</td><td></td><td>81</td><td></td><td></td><td>78</td><td>78</td><td></td><td>81</td></tr><tr><td>Tiaret-ANRH</td><td></td><td>84</td><td></td><td>73</td><td>74</td><td></td><td></td><td>79</td><td></td><td>78</td><td>76</td><td>02</td><td>93</td></tr><tr><td>Medrissa</td><td></td><td>93</td><td></td><td></td><td>01</td><td></td><td>99</td><td></td><td></td><td>96</td><td>96</td><td>01</td><td>98</td></tr><tr><td>Ain kermes</td><td></td><td>92</td><td>80</td><td>71</td><td>72</td><td></td><td>75</td><td>79</td><td></td><td>76</td><td></td><td>84</td><td></td></tr><tr><td>Total ruptures by region</td><td></td><td>04</td><td>04</td><td>04</td><td>03</td><td>07</td><td>02</td><td>06</td><td>04</td><td>02</td><td>06</td><td>05</td><td>06</td></tr><tr><td>Relizane demrh</td><td></td><td>71</td><td>83</td><td>00</td><td>87</td><td>72</td><td>95</td><td>74</td><td>75</td><td>70</td><td>76</td><td>03</td><td>93</td></tr><tr><td>El Matmar</td><td></td><td>02</td><td>80</td><td>71</td><td>03</td><td>72</td><td>06</td><td>05</td><td>79</td><td>06</td><td>76</td><td>06</td><td>87</td></tr><tr><td>Hillil</td><td></td><td>02</td><td>70</td><td>00</td><td>81</td><td>72</td><td>70</td><td>74</td><td>75</td><td>71</td><td>76</td><td>03</td><td>75</td></tr><tr><td>Relizane aval</td><td>NW</td><td>81</td><td></td><td>82</td><td>78</td><td>70</td><td>81</td><td></td><td>73</td><td>77</td><td>80</td><td>02</td><td>82</td></tr><tr><td>Mascara</td><td></td><td></td><td>72</td><td></td><td>74</td><td>81</td><td>77</td><td>82</td><td>73</td><td>70</td><td></td><td>01</td><td>65</td></tr><tr><td>Motmor</td><td></td><td></td><td>75</td><td>99</td><td>74</td><td></td><td></td><td>96</td><td></td><td></td><td>76</td><td>01</td><td>76</td></tr><tr><td>Tighenif</td><td></td><td>82</td><td>80</td><td>71</td><td>72</td><td></td><td></td><td></td><td>79</td><td>02</td><td>76</td><td>80</td><td>67</td></tr><tr><td>Bouguirat</td><td></td><td></td><td></td><td>01</td><td>74</td><td>01</td><td></td><td>96</td><td></td><td></td><td>76</td><td>01</td><td>76</td></tr><tr><td>Total ruptures by region</td><td></td><td>05</td><td>06</td><td>07</td><td>07</td><td>07</td><td>05</td><td>06</td><td>06</td><td>06</td><td>07</td><td>08</td><td>08</td></tr><tr><td>Ain Hamara</td><td></td><td>84</td><td>80</td><td>06</td><td>70</td><td>06</td><td>68</td><td>74</td><td>81</td><td>70</td><td>76</td><td></td><td>75</td></tr><tr><td>Oued El Abtal</td><td></td><td>02</td><td></td><td></td><td>74</td><td>71</td><td></td><td>80</td><td>74</td><td>92</td><td>75</td><td>78</td><td>64</td></tr><tr><td>Sidi Aek Djilali</td><td>CW</td><td>02</td><td>06</td><td>02</td><td>03</td><td>72</td><td>68</td><td>74</td><td>02</td><td>71</td><td>03</td><td>05</td><td>87</td></tr><tr><td>Sidi M'Hamed Ben Aouda</td><td></td><td>02</td><td>80</td><td>71</td><td>03</td><td>72</td><td>06</td><td>05</td><td>79</td><td>06</td><td>76</td><td>06</td><td>87</td></tr><tr><td>Aouf</td><td></td><td>81</td><td></td><td>71</td><td>77</td><td>72</td><td></td><td>94</td><td>79</td><td></td><td>82</td><td>81</td><td>69</td></tr><tr><td>Nesmoth</td><td></td><td></td><td>80</td><td>74</td><td>83</td><td>72</td><td></td><td>79</td><td></td><td>76</td><td></td><td>80</td><td>04</td></tr><tr><td>Total ruptures by region</td><td></td><td>05</td><td>04</td><td>05</td><td>05</td><td>06</td><td>04</td><td>04</td><td>06</td><td>05</td><td>05</td><td>04</td><td>06</td></tr><tr><td>Bled Bel Hammar</td><td></td><td>78</td><td>74</td><td></td><td>73</td><td>75</td><td>76</td><td>76</td><td>80</td><td>75</td><td>76</td><td>81</td><td>77</td></tr><tr><td>Maamora</td><td></td><td>92</td><td></td><td></td><td>74</td><td>82</td><td>71</td><td></td><td>72</td><td>74</td><td>80</td><td>79</td><td>70</td></tr><tr><td>Med El Habib</td><td>SW</td><td></td><td>75</td><td>99</td><td>81</td><td>72</td><td></td><td>96</td><td>98</td><td></td><td>96</td><td>96</td><td>76</td></tr><tr><td>Sidi Youcef</td><td></td><td>06</td><td></td><td></td><td>74</td><td></td><td></td><td>96</td><td></td><td>96</td><td></td><td>96</td><td>76</td></tr><tr><td>Takhmert</td><td></td><td></td><td>75</td><td></td><td>74</td><td></td><td></td><td>96</td><td>98</td><td></td><td>76</td><td></td><td>76</td></tr><tr><td>Total ruptures by region</td><td></td><td>03</td><td>03</td><td>01</td><td>05</td><td>03</td><td>02</td><td>04</td><td>04</td><td>02</td><td>05</td><td>04</td><td>05</td></tr><tr><td>% of annual rain</td><td></td><td>06</td><td>08</td><td>11</td><td>13</td><td>11</td><td></td><td>12</td><td>13</td><td>08</td><td>02</td><td>01</td><td>02</td></tr><tr><td>Number of ruptures</td><td>1960</td><td>03</td><td>09</td><td>08</td><td>12</td><td>18</td><td>05</td><td>07</td><td>15</td><td>09</td><td>17</td><td>07</td><td>03</td></tr><tr><td>in the decades</td><td>1970</td><td>05</td><td>07</td><td>01</td><td>05</td><td>02</td><td>02</td><td>04</td><td>01</td><td>02</td><td>02</td><td>03</td><td>09</td></tr><tr><td>1980</td><td></td><td>03</td><td></td><td>02</td><td></td><td></td><td>02</td><td>07</td><td>03</td><td>01</td><td>03</td><td>03</td><td>02</td></tr><tr><td>1990</td><td></td><td>06</td><td>01</td><td>05</td><td>03</td><td>03</td><td>02</td><td>02</td><td>03</td><td>01</td><td>05</td><td>06</td><td>03</td></tr><tr><td>2000</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

Indeed, 13 stations present a considerable rupture during the 1970–1980 decade for the entire catchment area of Wadi Mina, which represents 50% of the pluviometric stations used in this study (Figure 5).

It is equally interesting to note that the stations that present ruptures are localized differently during each decade: in the northwest of the basin before the 1970 decade, on the entire basin, except for the highlands of south and southeast, between the years 1970 and 1980, and on the entire basin, except for the center, after 1980, but in proportion representing less than half.
<figure><img src="image_44.png" /><figcaption>**Figure 5.** Ruptures detected at rainfall stations: (a) before 1970; (b) 1970–1980; and (c) after 1980. Rupture dates were detected: by three statistical tests (black: strong ruptures); by two statistical tests (dark grey: probable rupture); or by at least one statistical test (light grey: weak rupture).</figcaption></figure>

Indeed, we have noted a rupture corresponding to a decrease of precipitations during the mid-1970s over the whole Wadi Mina basin (58% series present a rupture in 1976) (Table 3), date presented by numerous researchers [6,104], who already indicated the tendency towards drought starting with 1970 in north Algeria. These results are compliant with the recent works in Algeria [8,11] and which concluded to a rains decrease noted during the last thirty years which hit the entire country of Algeria, but especially its western part, adding up to: (a) 30–40% at annual level and more than 40% during winter and spring in the Mascara region; (b) 20–30% on the littoral, starting from the center to the western part of the country; and (c) 20% at annual level and 25% during winter in the center of the country. They confirm as well the results of works carried out on the basins of the extreme west in Algeria [6,11] which concluded to a decrease of rainfall. A rupture in the rainfall time series is frequently observed in 1979–1980, except 1972 for the Wadi Mina basin, at the Wadi El Abtal and Ain Hamara stations, and 1976 for the west-central part of Algeria. These results confirm as well the occurrence in Morocco of a pluviometric deficit starting with 1970 and its continuation during the 1980s, an extremely severe and long drought episode [105]. At the level of North Africa, the results obtained by Meddi et al. [11] in Algeria and by Bouzaiane and Laforgue [106] in Tunisia indicate the same rupture period and show the spatial extension of the drought, accompanied by a net pluviometric reduction. The conclusions of the Intergovernmental group on the climate evolution from 2001 and 2007 [107] and those of the regional report of the United Nations on the changes in North Africa [108], go in the same direction.