# Assessment of the sedimentation and trapping efficiency in dam reservoirs by applying the settling basin framework

Bérenger Koffi, Koffi Eugène Kouakou, Alexis Loukou Brou, Martin Sanchez

Angulo, Ouédé Gla Blaise, Brice Wawogninlin Coulibaly, Franck Hervé

Akaffou, Michal Habel, Amani Michel Kouassi, Dibi Brou, et al.

► To cite this version:

Bérenger Koffi, Koffi Eugène Kouakou, Alexis Loukou Brou, Martin Sanchez Angulo, Ouédé Gla Blaise, et al.. Assessment of the sedimentation and trapping efficiency in dam reservoirs by applying the settling basin framework. Journal of Hydrology: Regional Studies, 2025, 57, pp.102172. 10.1016/j.ejrh.2024.102172. hal-04926715

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# Assessment of the sedimentation and trapping efficiency in dam reservoirs by applying the settling basin framework

Bérenger Koffi<sup>a,∗</sup>, Koffi Eugène Kouakou<sup>a</sup>, Alexis Loukou Brou<sup>b</sup>, Martin Sanchez<sup>c</sup>, Ouédé Gla Blaise<sup>b</sup>, Brice Wawogninlin Coulibaly<sup>b</sup>, Franck Hervé Akaffou<sup>b</sup>, Michal Habel<sup>d</sup>, Amani Michel Kouassi<sup>a</sup>, Dibi Brou<sup>b</sup>, Kouakou Lazare Kouassi<sup>b</sup>

## ARTICLE INFO

**Keywords:**

Dam reservoir siltation
Settling basin theory
Peclet number
Gamma distributed
Settling velocity
Lobo River
Tropical regions

## ABSTRACT

**Study region:** The investigated object is the Lobo Dam reservoir, located in the south part of the Lobo River Basin in west-central Côte d'Ivoire, West Africa.

**Study focus:** Dam reservoirs in tropical climates face rapid siltation and eutrophication challenges, necessitating new analytical solutions to understand their capacity to trap sediment inputs. This study presents a hydrosedimentary mathematical model based on the theory of settling basins and Gamma Law approaches to describe the settling velocity of suspended solids. Using field data from the Lobo River reservoir in Côte d'Ivoire.

**New hydrological insights for the region:** The analysis shows that the reservoir's trapping capacity is influenced by settling velocity, critical velocity, shape parameter 1/r, and the Peclet number (Pe). The study found strong synchronization between models for constant settling velocity (CV-NT, CV-CM, CV-Teeter (1986)) and variable settling velocity (VV-NT, VV-CM) with Teeter's (1986) model. This agreement validates the proposed models. However, for Pe > 4, the numerical values and curves fall outside the validity range of Teeter's (1986) model, particularly during dry periods.

The findings provide crucial insights into the hydrosedimentary dynamics of the Lobo River reservoir, emphasizing the need to account for seasonal variations and hydrological conditions. This research offers valuable guidance for sediment and water resource management, contributing to the sustainability of reservoirs in tropical regions facing similar environmental pressures.

## 1. Introduction

Water is an irreplaceable substance essential to life, as it constantly interacts with all the elements of the biosphere. Its management, in conjunction with that of other natural resources, has prompted major international organizations to include it in their sustainable development objectives (Anoh et al., 2021; Diabagaté et al., 2016). Water resources are under increasing pressure in most parts of the world due to population growth, changing lifestyles and climate change uncertainties (Brulebois, 2016; Fowler and

<footnote><sup>a</sup> Institut National Polytechnique Félix Houphouët Boigny (INP-HB), BP 1093, Yamoussoukro, Côte d'Ivoire</footnote>

<footnote><sup>b</sup> Laboratory of Science and Technology of Environment, Université Jean Lorougnon Guédé, BP 150, Daloa, Côte d'Ivoire</footnote>

<footnote><sup>c</sup> Nantes Université, UMR 6112 CNRS, LPG (Lab. Planetology & Geodynamics), 2 rue de la Houssinière, BP 92208, Nantes cedex 44322, France</footnote>

<footnote><sup>d</sup> Faculty of Geographical Sciences, Kazimierz Wielki University, Bydgoszcz 85-033, Poland</footnote>

<footnote>* Corresponding author.
E-mail address: koffi.berenger@inphb.ci (B. Koffi).</footnote>
Ekström, 2009; Stanzel et al., 2018). In addition, the growing demand for different water uses is putting further pressure on already limited freshwater resources.

Almost all drinking water is found underground. However, the low productivity of bedrock aquifers, galloping demographics and the adverse effects of climate change have prompted the use of surface water, which is more accessible as the main source of drinking water supply for populations (Anoh et al., 2021). Thus, water reservoirs are used in several regions of the world to support socio-economic development (Akaffou et al., 2024; Guertault et al., 2018; Koffi et al., 2020). These reservoirs are of economic interest due to the development of certain activities such as fishing, agriculture, livestock breeding and hydropower generation (Akaffou et al., 2024; Kouassi et al., 2013). However, these reservoirs are increasingly threatened by the silting-up phenomena that occur as they age (Tang et al., 2021; Tiron Dutu et al., 2019).

Deforestation and intensive farming activities have exposed the land, leading to erosion upstream of these reservoirs (Andréassian, 2004; Asenso Barnieh et al., 2020; Gupta and Sharma, 2020; Koffi et al., 2023a). In addition, it leads to the regular deposition of sediment in the reservoir during runoff from the catchment.

Most of the sediments carrying pollutants accumulate in reservoirs, continuously, gradually reducing their storage capacity (Lee et al., 2014). In addition, the transport of sediments, which causes nutrient inputs, accelerates the process of silting up, siltation and eutrophication of water reservoirs (Isaac and Eldho, 2016; Shrestha et al., 2022; Susperregui, 2008). While sedimentation is a natural process, it is important to note that human actions can significantly accelerate this process, leading to the premature ageing of water bodies (Aneseyee et al., 2020; Asenso Barnieh et al., 2020; Koffi et al., 2023c). This is a crucial issue for reservoir sustainability (Yang et al., 2014). It is estimated that around 0.5 % ± 1 % of reservoir storage capacity worldwide is lost each year due to sedimentation (Schleiss et al., 2016).

This loss of reservoir capacity threatens the sustainability of water supply as water demand increases. Consequently, studying how to control sedimentation rates and maintain the sustainable use of reservoirs has become a major concern worldwide (Chen and Liu, 2017; Fu et al., 2008). (Hendi et al., 2022; Verstraeten and Poesen, 1999). For small reservoirs, in particular, sedimentation can become a severe problem because the rate of siltation is generally much higher than for large dams. Therefore, the useful life of these ponds is only short if they are frequently dredged. Examples of high sedimentation rates have been shown for flood retardation structures in central Belgium (Hendi et al., 2022; Verstraeten and Poesen, 1999).

The complexity of sediment transport and deposition in reservoir has led to the development of numerous methods for estimating soil erosion and particle movement through to deposition in receiving environments, such as dam reservoirs (Hallouz et al., 2018; Miranda et al., 2021; Ran et al., 2021). These tools include numerical models, regional-scale estimates of sediment flux over catchments (Al-Mamari et al., 2023; Dutta, 2016) and the effectiveness of sediment traps in reservoirs (Brune, 1953).

These methods can be divided into direct and indirect approaches. The indirect approach can be subdivided into theoretical and empirical or semi-empirical approaches. Empirical relationships are more common than theoretical relationships for determining deposition rate or reservoir storage capacity reduction, as these procedures are developed from field data. Moreover, empirical methods require less data and are comparatively more accessible and uncomplicated. It is also difficult to calibrate theoretical approaches or models (Alves E Santos et al., 2024; Liu et al., 2022). As a result, numerous empirical and semi-empirical methods have been developed based on reservoir sedimentation data. The simplest method is that in which the efficiency of the sediment curve is evaluated (Endalew and Mulu, 2022; Smith, 1990).

Furthermore, Xu et al., (2006) and Randle et al. (2013) have suggested that the most important characteristic of a reservoir is its trapping efficiency (TE) in retaining sediment. This value corresponds to the proportion of incoming sediment deposited or trapped in a reservoir. For most reservoirs, the water-holding capacity must be maintained at its highest level for as long as possible. This means that the TE must be low. For sedimentation basins, on the other hand, the TE must be high. For a pond or reservoir to be economically viable, its TE must be designed carefully. It is, therefore, necessary to understand the TE of a proposed pond or reservoir and the factors that influence it. TE is also very important in sediment yield studies. If a pond retains only a small proportion of incoming sediments, the result will be a serious underestimate of sediment production. Therefore, siltation rates in reservoirs must be corrected for TE.

The reason for carrying out the work is the need to define the most convenient location for the water intake on the dam reservoir located in the central-western of Côte d'Ivoire, the Lobo River. It supplies fresh water to the third largest city (Daloa) in Côte d'Ivoire. Siltation and eutrophication of the reservoir are due to the enrichment of the water body by pesticides from agricultural activities in the basin (Groga et al., 2017) and land use. This led the managers to conduct dredging work in 2011 to renovate the reservoir's storage capacity and move the freshwater intake.

The primary goal of our research is to estimate the sediment mass and thickness trapped in dam reservoirs with high silting index. Our study introduces a mathematical model based on the theory of settling basins to describe the settling velocity of suspended solids, employing four Gamma Law approaches for purpose. Field observations provided unique data that allowed us to test the created hydrosedimentary mathematical model. The experiment was implemented on a small dam reservoir facility in a tropical climate zone with a high sediment supply index. This study applies the author's earlier work to estimate the settling velocity of suspended solids and the trapping capacity of the Lobo River dam (Koffi et al., 2023b). Proposed new analytical solutions are crucial to comprehending the impoundment's capacity to trap solid inputs and the impoundment's capacity to trap solid inputs to the reservoirs.

## 2. Material and methods

### 2.1. Study area

A main tributary of the Sassandra River, the Lobo River is the main source of drinking water for Côte d'Ivoire's third-largest city
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Study area: (a) Côte d'Ivoire in Africa, (b) geographical position of the Lobo basin in Côte d'Ivoire. (c) Lobo basin at Nibéhibé. (d) Lobo dam reservoir.</figcaption></figure>
(Daloa). The Lobo River reservoir (Fig. 1), which is the subject of this study, is located 25 km from the city of Daloa (Koffi et al., 2020; Yao et al., 2012). The catchment area of the Lobo River reservoir is approximately 7000 km². The relief of the study area is monotonous overall, with altitudes ranging from 192 to 612 m.a.s.l. (Avenard, 1974). The climate is equatorial with a mild transition, with a rainy season from March to October and a dry season from November to February. The average annual rainfall is around 1150 mm (Koffi et al., 2020). The Lobo River reservoir was commissioned in 1976 (Maiga et al., 2001). According to bathymetric data and previous studies by Koffi et al. (2023a), the reservoir's average depth is 3.5 m, its average width is 74 m, its average length is 4.3 km, and its average surface area is 0.3 km². The dam's volume at spillway elevation (231.03 m) is 360,000 m³. Agriculture is the population's main activity. The population of the Lobo River watershed is estimated at around 1103,059, with an average density of 165.67 individuals per square kilometre. The annual growth rate is around 3.72 % (INS, 2022).

## 2.2. Data

The data used in this study are of two categories: hydrometric (flow and water level) and bathymetric. The flow and water level data come from the Andjoukro-Sikaboutou hydrometric station supported by the General Directorate of Hydrology (DH) and from the water level station of the Lobo reservoir, located around 8 km upstream of the reservoir. The hydrometric data covers 2019–2022, with a daily measurement frequency. Bathymetric data collected on the Lobo reservoir were used to estimate the average depth of the dam reservoir (Fig. 2a,b). The Environmental Science and Technology Laboratory of the Jean Lorougnon Guédé University collected this information.

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Water velocity profiling by ADCP profiler on the Andjoukro-Sikaboutou gauging station hydrometric profile (a) and cross-profile with velocity distribution (b, c).</figcaption></figure>
## 2.3. Analysis of suspended and bottom solids data

Data were collected in the middle and upstream of the dam reservoir to assess sediment flux. Forty-two water samples were taken at fourteen stations in the dam reservoir and the Andjoukro-Sikaboutou hydrometric station upstream of the Lobo River impoundment. At each sampling station, samples were collected at the surface, at mid-depth and at the bottom using a Van Dorn hydrological bottle. The water samples were filtrated using a membrane filters 47 mm in diameter with a porosity of 0.45 µm. After filtration, the samples were dried at 105°C in an oven and weighed using a precision balance to determine total suspended solids concentrations (Koffi et al., 2023b). Twelve sediment samples were also taken from the Lobo reservoir using a Van Veen grab sampler. The aim was to determine the dry density of sediments deposited in the dam reservoir. The methodology used to assess the organic matter content of the sediments involved measuring mass loss due to high-temperature calcination. Samples were placed in porcelain crucibles, and the masses of empty and full crucibles were recorded. The calcination temperature of the organic material was set at 550°C, in accordance with standard NF EN 12–879. After several trials to determine the optimum calcination time, a 24-hour treatment was selected (Heiri et al., 2001). Quantification of loss on ignition, corresponding to the percentage of organic matter, was deduced from the difference in mass between the initial dry sample and the calcined sample.

To determine the current volume, it was necessary to measure the depth of the reservoir. Bathymetric surveys were carried out using a single-beam echo sounder. Depth measurements were taken at a frequency of 450 kHz dedicated to low-depth aqueous (Lowrance, 2019). The bathymetric data were used to calculate the reservoir's average monthly depth based on reference elevation.

## 2.4. Settling velocity of sediments and trapping efficiency

### 2.4.1. Settling velocity

Gravimetric analyses based on the Owen tube approach (Owen, 1976) were used to study the vertical distribution of suspended solids (SS) and their settling velocities under steady-state water conditions. Twelve tests were carried out on monthly samples taken from January to December at characteristic depths (surface, mid-depth, bottom) at the hydrometric profile on the Sikaboutou-Andjoukro gauging station.

A probability density function $F(V)$ of the settling velocity $V$ was obtained by monitoring over time the evolution of matter remaining in suspension in a sedimentation column of height $H_{init} = 2$ m (Owen tube) in which a sample of water. The Owen tube (Owen, 1976) has a capacity of 3.4 liters and is positioned vertically. Samples of a tenth of the initial volume are then taken from the bottom of the tube at different times (2 min, 4 min, 8 min, 15 min, 30 min, 60 min, 120 min, 240 min, 480 min), to estimate the concentration of particles settling in each time interval. A final sample is taken to recover the remaining liquid in the tube and calculate the total solid mass of the sample. The concentrations of suspended solids in the various samples were then determined by the filtration method, using WHATMAN GF/F circular filters with a diameter of 47 mm and a porosity of 0.45 µm.

After drying at 105°C, the filters were carefully recovered and marked to determine the total suspended solids concentrations expressed in kg/m³ (AFNOR, 1994). Using Owen's (1976) tube measurements, a distribution curve was obtained representing the percentage by weight (V%) of grains with a settling velocity less than $Vd = H/t$, where $H$ is the settling height and $t$ is the falling time measured since the start of the test. The settling velocity distribution function curve is plotted as follows: The initial $C_{init}$ concentration in the Owen tube (Owen, 1976) is estimated and then the total mass (MT) suspended in the tube at time $t = 0$ is calculated.

The proportion of total suspended solids (TSS) remaining in suspension at time $t_i$ of each sample is obtained by the ratio $P(t_i)=C/C_{init}$. If the height $H$ remained constant during the test, the ratio $P(t)=C/C_{init}$ would be given by Eq. 1:

$$P = \int_{0}^{H/t} \left(1 - \frac{Vt}{H}\right) f(V) dV = \int_{0}^{H/t} f(V) dV - \int_{0}^{H/t} \frac{Vt}{H} f(V) dV \quad (1)$$

Knowing that the height $H$ of the column varies during the test, we establish a relationship between $F(V)$ and $P(t^c)$ where $t^c = t \cdot H_{init}/H$ is:

$$P = \int_{0}^{H_{init}/t^c} \left(1 - \frac{Vt}{H_{init}}\right) f(V) dV = \int_{0}^{H_{init}/t^c} f(V) dV - \int_{0}^{H_{init}/t^c} \left(\frac{Vt}{H_{init}}\right) f(V) dV \quad (2)$$

On the other hand, we have the following equality:

$$t^c \frac{dP}{dt^c} = t^c \frac{d}{dt^c} \left[ \int_{0}^{H_{init}/t^c} f(V) dV - \int_{0}^{H_{init}/t^c} \frac{Vt^c}{H_{init}} f(V) dV \right] \quad (3)$$

Eq. (2) has been developed using the following Leibnitz rule:

$$\frac{d}{dt^c} \int_{0}^{\beta(t^c)} \phi(V, t^c) dV = \phi(\beta(t^c), t^c) \beta'(t^c) + \int_{0}^{\beta(t^c)} \frac{\partial \phi(V, t^c)}{\partial t^c} dV \quad (4)$$

Where $\beta(t^c) = H_{init}/t^c$ we obtain:

$$\frac{dP}{dt^c} = t^c \left[ f\left(H_{init}/t^c\right) \beta'(t^c) - \frac{H_{init}/t^c}{H_{init}} f\left(H_{init}/t^c\right) \beta'(t^c) - \int_{0}^{H_{init}/t^c} \frac{w}{H_{init}} f(w) dw \right] \quad (5)$$
With:

$$t^c \frac{dP}{dt^c} = t^c \frac{dP}{d(\ln t^c)} = -t^c \int_0^{H_{init}/t^c} \frac{V}{H_{init}} f(V) dV \qquad (6)$$

The equation can then be written as:

$$F(V = H_{init} / t^c) = \int_0^{H_{init}/t^c} f(V) dV = P + \int_0^{H_{init}/t^c} \frac{Vt^c}{H_{init}} f(V) dV \qquad (7)$$

Using Eqs. 5 and 7, we finally obtain the relationship between F(V) and P(t^c):

$$F(V = H_{init} / t^c = H / t) = \int_0^{H_{init} / t^c} f(V) dV = P - \frac{dP}{d(\ln t^c)} \qquad (8)$$

The expression of Eq. (9) is obtained by the finite-difference method for the numerical calculation of the derivative dP/d (ln t^c) using an off-center scheme.

$$\frac{dP}{d(\ln t^c)} |_{t^c = t^c_i} = \frac{P(t^c_{i+1}) - P(t^c_{i-1})}{\ln(t^c_{i+1}) - \ln(t^c_{i-1})} \qquad (9)$$

The distribution function F(V) of the settling velocity (Fig. 3) of suspended solids was obtained after plotting the P function as a function of t^c for each sample taken. Most authors characterize the fall velocity by its median value V50%, which is always lower than the local mean fall velocity V (Sanchez et al., 2005), which gives a better description of vertical sediment dynamics. This study studies the settling velocity V of suspended solids is studied as a stochastic variable. According to the studies of Sanchez et al. (2005), the settling velocity follows a probability law by the Gamma law, with a shape parameter r characterizing the range of settling velocity values for all aggregates simultaneously in suspension. However, all suspended particles fall with a variable velocity, depending on their concentration and weight.

Calculation of the average fall velocity involves the following steps:

* the settling velocity V50% and V90% are determined on the curve of the settling velocity distribution function. On this curve, V50% and V90% represent, for a given sample mass, 50 and 90 percent of sediment settling at a known settling velocity;

* the ratio of V50% / V90%

* The calculation of the shape parameter r and the ratio of V/V50% by iteration;

* Based on knowledge of the ratio of the mean settling velocity (V̄) and the settling velocity V50%, the mean settling velocity of suspended solids is obtained.

<figure><img src="image_5.png" /><figcaption>Fig. 3. Gamma distribution function of settling velocity for five values of parameter r (Sanchez, 2018).</figcaption></figure>
### 2.4.2. Evaluation of sedimentation and trapping rates using settling basin theory

Settling basin theory, a fundamental principle in dam design and management, is a key strategy for reducing sediment accumulation in reservoirs and improving downstream water quality. This method finds application in various areas, including wastewater treatment (Cripps and Bergheim, 2000; Lee et al., 2014), drinking water treatment, and the reclamation process of suspended solids. This study is not a standalone effort, but a continuation of the work of Koffi et al. (2023b), focusing on the assessment of the settling velocity and trapping capacity of the Lobo River reservoir. It represents a step forward in our understanding and application of this theory.

Four main hypotheses were used to set up the various mathematical models:

**Hypothesis 1.** settling velocity is constant;

**Hypothesis 2.** settling velocity is constant with Teeter (1986) mixture;

**Hypothesis 3.** settling velocity is Gamma-distributed;

**Hypothesis 4.** settling velocity is Gamma-distributed with Teeter (1986) mixing.

This method makes it possible to estimate the thickness of monthly deposits by taking into account the settling velocity of suspended solids distributed according to Gamma's law and also to assess reservoir's capacity to trap sediment. To set up the mathematical model, cross-sections were defined as every fifty meters over four kilometers, i.e. eighty profiles (Fig. 4).

Depending on the mathematical problem posed, the parameters of the problem configuration are as follows:

H = depth of the reservoir

B = width of the reservoir

C = concentration of suspended solids (SSL)

L = length of settling zone

Q = inflow

S₁, S₂...Sₙ = cross section

T = residence time

u = velocity

v_c = critical velocity

V = Settling velocity of SSL

V_r = reservoir volume

Three important relationships between mean flow velocity (u), critical velocity and sediment residence time in the reservoir of the Lobo reservoir are presented:

$$u = \frac{Q}{HB} \qquad (10)$$

Residence time is:

$$T = \frac{L}{u} = \frac{V_r}{Q} \qquad (11)$$

For the purposes of this study, all suspended matter settling at a settling velocity V equal to or greater than the critical velocity v_c

<figure><img src="image_6.png" /><figcaption>Fig. 4. Concept diagram against the background of the longitudinal section of the dam reservoir.</figcaption></figure>
settles in the settling zone. Suspended particles with a settling velocity v below the critical velocity (v_c) settle only below level H=v_cT at the entrance to the settling zone. It's worth noting that the trapping capacity of a reservoir is influenced by turbulence and the statistical distribution of settling velocities.

A critical settling velocity v_c is defined by Eq. 12:

$$v_c = \frac{H}{T} \qquad (12)$$

### 2.4.2.1. Constant settling velocity of suspended solids and no turbulence.
Concentration near the bottom remains constant until the total settling of suspended solids, assuming constant settling velocity and unmixed flow in the Lobo River reservoir. However, the surface concentration is zero, and the interface between zero and bottom concentration propagates from the surface to the bottom with the same settling velocity as the suspended matter. Under calm water conditions, in the absence of turbulence, Eqs. 13, 14 and 15 describe this hypothesis perfectly.

$$C\begin{pmatrix} x, y \end{pmatrix} = \begin{cases} 0 & \text{for } \left(1 - \frac{\bar{V} \times T}{H}\right) H < y < H \\ C_0 & \text{for } 0 \le y \le \left(1 - \frac{\bar{V} \times T}{H}\right) H \end{cases} \qquad (13)$$

As a function of residence time (T), the solid mass (M) remaining suspended in the water column is: $M(T) = \begin{cases} \left(1 - \frac{\bar{V} \times T}{H}\right) H C_0 & \text{for } T \le \frac{u \times H}{\bar{V}} \\ 0 & \text{for } T > \frac{u \times H}{\bar{V}} \end{cases}$ (14)

The percentage of sediment trapped is obtained by:

$$\eta = \frac{M(0) - M(L)}{M(0)} = \begin{cases} \frac{\bar{V}}{v_c} & \text{for } \bar{V} \le v_c \\ 1 & \text{for } \bar{V} > v_c \end{cases} \qquad (15)$$

With:

T, the residence time of suspended solids in water reservoir; u, the flow velocity; H, the average depth of water reservoir; C_0, the average concentration of the suspended solids at reservoir inlet; L, the length of water reservoir; V̄, the average settling velocity of the suspended solids; η, trapping capacity of the water reservoir; v_c, critical velocity.

### 2.4.2.2. Constant settling velocity of suspended solids with turbulence.
Assuming perfect mixing over the vertical, with constant concentration over depth for each value of y (C(x,y)= C̄(x), C̄(x) where represents the local average concentration over the vertical), an observer moving through the settling zone at the same horizontal velocity as the flow (u), the temporal variation of the suspended solid mass M at the local level is expressed by Eq. 16.

$$\left. \frac{dM(x)}{dt} \right|_{\text{following the horizontal flow}} = \left. \frac{d(H \times \bar{C}(x))}{dt} \right|_{\text{following the horizontal flow}} = - \bar{V} \times \bar{C}(x) \qquad (16)$$

The variation on x of C̄(x) is described by:

$$\frac{d\bar{C}(x)}{dx} = - \frac{\bar{V}}{uH} \times \bar{C}(x) \qquad (17)$$

and the solution is:

$$\bar{C}(x) = \bar{C}(0)\exp\left(-\frac{\bar{V} \times T}{H}\right) \qquad (18)$$

As a function of x, the solid mass M remaining in suspension in the water column is:

$$M(x) = H\bar{C}(0)\exp\left(-\frac{\bar{V} \times T}{H}\right) \qquad (19)$$

And the collection efficiency is:

$$\eta = \frac{M(0) - M(L)}{M(0)} = 1 - \exp\left(-\frac{\bar{V}}{v_c}\right) \qquad (20)$$

### 2.4.2.3. Constant settling velocity with the Teeter model in the turbulence environment.
Many of the actions in fine sediment dynamics
occur at the suspension/sediment bed interface. Using analytical and numerical approaches to examine vertical transport relation-
ships, Teeter (1986) established a relationship between near-bed concentration and Peclet number (P^e). The vertical variation of
suspended solids in the Lobo River impoundment for a constant settling velocity in the presence of turbulence is analyzed in this note.
Teeter's (1986) solution is as follows:

$$
C_0 \left( z = 0 \right) = \bar{C}(x) * \left( 1 + \left( \frac{P^e}{1.25 + 4.75(P^{2.5}_d)} \right) \right) = f(P^e) \quad (21)
$$

With P<sup>e</sup>, the Peclet number is characteristic of vertical sediment transfer by convection-diffusion. Assuming deposition of all suspended sediments, P = 1 (P is the Krone number), in calm water conditions:

$$
C \left( z = 0 \right) = \bar{C}(x) * \left( 1 + \left( \frac{P^e}{6} \right) \right) = f(P^e) \quad (22)
$$

The variation over time of the local suspended solid mass M taking into account the Peclet function (f(P^e)) is given by:

$$
\frac{dM(x)}{dt} = \frac{d(H * \bar{C}(x))}{dt} = - \frac{\bar{V}}{u * H} * \bar{C}(x) * f(P^e) \quad (23)
$$

And the variation over x of the concentration of the suspended solids:

$$
\bar{C}(x) = \bar{C}(0) * e \left( \frac{\bar{V} * f(P^e) * X}{u * H} \right) \quad (24)
$$

With:

$P^e = \frac{\bar{V}H}{K_c}$, the Peclet number constructed with $\bar{V}$. This number represents vertical sediment transfer.

The capacity of the reservoir to trap sediment is then:

$$
\eta = 1 - \left( - \frac{\bar{V} * f(P^e)}{V_c} \right) \qquad (25)
$$

With:

$\bar{V}$is the average settling velocity of suspended solids, $f(Pe)$, the Peclet function, $\eta$, the trapping capacity of the water retention; $V_c$, critical velocity; H: water depth.

2.4.2.4. Gamma Law distribution of settling velocity and no turbulence. In the case of variable settling velocity in the absence of turbulence, this approach is based on the work carried out by Sanchez (2006) and Koffi et al. (2023), has practical implications. According to these two authors, settling velocity is considered a stochastic variable that follows a Gamma-like probability law with a shape parameter *r* that characterizes the set of suspended aggregates.

Thus, the proportion of suspended matter whose settling velocity is less than *v* is given by the cumulative distribution function of *V*,
which is also a function *F*<sub>*V*</sub>(*v*) of the possible values *v* of *V* described by:

$$
F_v(v) = \int_0^v f_v(v) \, dv \tag{26}
$$

The probability density function of V described by the Gamma distribution law (Sanchez, 2006) is:

$$
f_v(v) = \frac{\lambda^r v^{-1} \exp(-\lambda v)}{\Gamma(r)}, \quad 0 \le v < \infty \qquad (27)
$$

With Γ which is the Gamma function. The parameters r and λ are associated with the average
settling velocity V̄of suspended solids and the dispersion V̄ of V values, as indicated by Spiegel (1975).And

$$
\lambda = \frac{\bar{V}}{\sigma^2} = \frac{r}{\bar{V}} \quad \text{et} \quad r = \frac{\bar{V}^2}{\sigma^2} \qquad (28)
$$

Assuming that the fluid is uniform in depth at the entrance to the settling zone (at x = 0), the probability density function of V is assumed to be constant over the vertical. After a lapse of time t, particles with a settling velocity V>V'=H/T are settled from a height H. In addition, a fraction V×T/H of particles with a settling velocity V lower than V' is also settled (from a variable height, V×T ≤ H). According to Jones and Jago (1996); Malarkey et al. (2013), the proportion P of solids still in suspension (not yet settled) is calculated as follows:

$$
P = \frac{M(x = uT)}{M(0)} = \int_{0}^{v} \left(1 - \frac{vT}{H}\right) f_v(v) \, dv \qquad (29)
$$

Applying the Gamma law yields the following calculation:
$$ \int_{0}^{V} \frac{v T}{H} f_{v}(v) dv = \frac{T}{H} \int_{0}^{V} v \frac{\lambda^{r} v^{-1} \exp(-\lambda v)}{\Gamma(r)} dv, \qquad (30) $$

If, $\alpha - 1 = r$, we get:

$$ \int_{0}^{V} \frac{v T}{H} f_{v}(v) dv = \frac{T}{H} \frac{\lambda^{r}}{\lambda^{r+1}} \frac{\Gamma(r+1)}{\Gamma(r)} \int_{0}^{V} \frac{\lambda^{\alpha} v^{\alpha-1} \exp(-\lambda v)}{\Gamma(\alpha)} dv, \qquad (31) $$

With, $r + 1/r$, and $\bar{V} = r/\lambda$, we have:

$$ \int_{0}^{V} \frac{v T}{H} f_{v}(v) dv = \frac{T}{H} \times \bar{V} \int_{0}^{V} \frac{\lambda^{\alpha} v^{\alpha-1} \exp(-\lambda v)}{\Gamma(\alpha)} dv \qquad (32) $$

For an observer moving with the flow from $x = 0$ at time $t = 0$, these two variables are linked by $x = ut$. The proportion $P$ of solids still in suspension for an observer moving in the flow from $x = 0$ at time $t = 0$, with $x = ut$, is obtained by the following equation:

$$ P = \int_{0}^{V/\bar{V}} \frac{r^r (v_*)^{r-1} \exp(-rv_*)}{\Gamma(r)} dv_* - \frac{uT}{L} \times \frac{\bar{V}}{v_c} \int_{0}^{V/\bar{V}} \frac{r^\alpha (v_*)^{\alpha-1} \exp(-rv_*)}{\Gamma(\alpha)} dv_* \qquad (33) $$

The trapping capacity of the reservoir is:

$$ \eta = \frac{M(0) - M(L)}{M(0)} = 1 - \int_{0}^{v_c/\bar{V}} \frac{r^r (v_*)^{r-1} \exp(-rv_*)}{\Gamma(r)} dv_* + \frac{\bar{V}}{v_c} \int_{0}^{v_c/\bar{V}} \frac{r^\alpha (v_*)^{\alpha-1} \exp(-rv_*)}{\Gamma(\alpha)} dv_* \qquad (34) $$

### 2.4.2.5. Gamma law distribution of settling velocity with turbulence.
The settling process, as a function of the local settling velocity of the suspended sediment mass, follows a Gamma distribution (Sanchez, 2006). The parameter $r$ and the average settling velocity are sufficient to define a Gamma distribution. Indeed, in the presence of turbulence, with a constant concentration over the entire depth, Sanchez (2018) has demonstrated the variation in the average concentration of suspended solids and the ability to trap sediment in settling basins.

In the case of perfect mixing over the water column with a constant concentration ($C(x,y) = \bar{C}(x)$). The variation in concentration over $x$ is governed by:

$$ \frac{d\bar{C}(x)}{dx} = - \frac{\bar{V}}{uH} \times \bar{C}(x) \qquad (35) $$

The variation in the average settling velocity $\bar{V}$ of suspended solids was demonstrated by Sanchez (2006). The average settling velocity of suspended solids decreases with concentration and follows the following law:

$$ \bar{V}(x) = \bar{V}(0) \left( \frac{\bar{C}(x)}{\bar{C}(0)} \right)^{1/r} \qquad (36) $$

From Eqs. 35 and 36 we obtain:

$$ \frac{d\bar{C}(x)}{dx} = - \frac{\bar{V}(0)}{u \times H \times \bar{C}(0)^{1/r}} \times \bar{C}(x)^{(1+r)/r} \qquad (37) $$

When the residence time of suspended solids is taken into account, the average concentration $\bar{C}(x)$ is:

$$ \bar{C}(x) = \bar{C}(0) \left( \frac{r \times H}{r \times H + \bar{V}(0) \times T} \right)^{r} \qquad (38) $$

The trapping capacity of the reservoir is:

$$ \eta = \frac{M(0) - M(L)}{M(0)} = 1 - \left( \frac{r}{r + \bar{V}(0)/v_c} \right)^r \qquad (39) $$

With $\bar{V}(0)$, the average settling velocity of suspended solids at $x = 0$.

### 2.4.2.6. Gamma law distribution of settling velocity with Teeter model.
The hypotheses used in this note are those of Teeter (1986) and the Gamma distribution law (Sanchez, 2006). According to the Gamma distribution law, all particles settle with a variable settling velocity following a stochastic law. An analytical solution for the average suspended solids concentration in the reservoir is obtained. The capacity of the impoundment to trap solid inputs to the reservoir in the Lobo River catchment area is also analyzed. The law governing the variation in average concentration was demonstrated by Sanchez (2006). However, taking into account the Peclet function, the variation over $x$ of the suspended solids concentration is obtained by the following equation:

$$ \bar{C}(x) = \bar{C}(0) \left( \frac{r \times H}{r \times H + f(P^e) \times \bar{V}(0) \times T} \right)^r \qquad (40) $$
<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Seasonal-spatial variability of SSL (a) and water flow conditions during the year of the Lobo River (b). The vertical axis for (a) shows the numbers of measurement stations (cross-sections), while the x-axis shows the months of the year.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Curves of the proportions (P) of sediments remaining in suspension as a function of time (t<sup>c</sup>) for monthly observation on the Lobo River reservoir.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Fig. 7. Settling velocity distribution functions for suspended solids for monthly observation on the Lobo River reservoir.</figcaption></figure>
The capacity of the reservoir to trap sediment is:

$$ \eta = 1 - \left( \frac{r}{\frac{\overline{V(0)} \times f(\rho^*)}{v_c} + r} \right)^r \quad (41) $$

The coefficient of local friction (Eq. 42) and shear rate (Eq. 43) were also used to calculate the various parameters.

$$ C_f = \frac{2 \times g}{K_s^2 \times H^{1/3}} \quad (42) $$

$$ U^* = \left( \frac{C_f}{2} \right)^{1/2} \times U \quad (43) $$

Where, U is the flow velocity, H is the average depth of the water reservoir, Ks is the Strickler coefficient, and U* is the shear velocity.

### 2.4.3. Mass and thickness deposition

The mass of deposits in the reservoir is estimated by the relationship:

$$ M_d = \left( \frac{Q \times (C_0 - C_n) \times T}{S_r} \right) \times \eta \quad (44) $$

The relationship between deposit mass and deposit thickness is:

$$ h = \frac{M_d}{\rho_s} \quad (45) $$

With:

S<sub>r</sub>(m<sup>2</sup>), Area of water reservoir; C<sub>0</sub> and C<sub>n</sub> (kg/m<sup>3</sup>), Concentration of suspended solids between two sections of the reservoir; η(%), Water reservoir trapping capacity; T (day), Residence time;

h (m), the thickness of the deposit (m); M<sub>d</sub> (kg/m<sup>2</sup>), the mass of the deposit, ρ<sub>s</sub>, Dry density (kg/m<sup>3</sup>).

## 3. Results

### 3.1. Monthly variation in concentrations of suspended solids

Depending on the measuring stations, suspended solids concentrations exhibit significant variations throughout the year and across different locations. During the dry season (December-January and February), SSL concentrations are relatively low, with monthly averages ranging from 4 to 20 mg/L. At the beginning of the rainy season (March-April), SSL levels gradually increase, reaching values between 22 and 36 mg/L. The initial rains cause a resuspension of sediments accumulated in the water column. From April to November (rainy season), SSL concentrations peak, with values fluctuating between 37 and 58 mg/L due to the intensity of rainfall and soil erosion. The highest SSL values are observed in September and October (Fig. 5), the wettest months. During this period, the Lobo River reaches its highest levels. Between November and December, a gradual decrease in SSL is observed, with values dropping from 42 to 18 mg/L due to reduced water flow. Differences between measuring stations reveal significant spatial variations from one location to another. Measuring stations upstream (river section) exhibit higher concentrations than those in the lacustrine section of the reservoir.

### 3.2. Proportion of suspended solids remaining in suspension

The results of the twelve-column settling tests conducted in the laboratory reveal significant variations in the proportions of sediments remaining in suspension over time, as illustrated in Fig. 6. It is noteworthy that the proportions fluctuate not only from month to month but also according to the seasons. During periods of maximum flooding, particularly in September and October, a high proportion of sediments remains in suspension (approximately 60 %). However, the dry season is marked by lower proportions, particularly in January, February, and December (28 %). Moreover, at the beginning of the rainy season in March, the intensity of the rainfall causes a significant resuspension of particles that had settled during the long dry period (Fig. 6). These results highlight the impact of seasonal variations and weather events on the settling velocity of suspended materials, underscoring the importance of understanding these variations for effective water resource management. This spatial variation in sediments shows that the vertical distribution of suspended materials in the Lobo River can gradually vary over time.

### 3.3. Settling velocity distribution

The results of the various suspended matter distribution functions as a function of particle fall velocity for twelve laboratory tests in a settling column are shown in Fig. 7. It can be seen that there is a good distribution of suspended solids. Most of the curves obtained are
similar: they have the same profile and the same trend, but each speed corresponds to a particle size. When the concentration changes from low to high, the curves migrate downwards, increasing the particles' settling velocity and the settling mass of settleable particles. By differentiating the settling velocities by class, it is possible to plot the distribution curves of the SSL as a function of their settling velocities. The median settling velocity of $V_{50}$ % and the settling velocity of $V_{90}$ % are obtained from the SSL distribution function curves. Overall, the suspended solids distribution functions vary from month to month. This spatial variation in sediments shows that the vertical distribution of suspended solids in the Lobo River can be considered to be gradually varied over time.

### 3.4. Variation of concentrations of suspended solids as a function of inflow and settling velocity

Analysis of the monthly variation in the settling velocity of suspended solids in relation to the shape parameter *r* reveals a dynamic relationship that evolves over the months, following seasonal fluctuations and flood peaks. These findings have direct implications for water management and hydrology, providing valuable insights into the behavior of suspended solids in water bodies. At the start of the rains in March, there was an upward trend in both the shape parameter *r* and the settling velocity, followed by a marked decrease during April, May, June and July. This trend peaks during the period of maximum flooding, generally between August, September and

<figure><img src="image_10.png" /><figcaption>**Fig. 8.** Monthly variations in suspended solids concentration (SSL) and inflow (a), and in parameter *r* and settling velocity (b) on the Lobo River reservoir.</figcaption></figure>
October. Thereafter, there is a decrease in the $r$ parameters during the drop in water level phase observed in November and December (Fig. 8a). In addition, a close relationship is demonstrated between the inflows into the Lobo reservoir and the concentration of suspended solids. The initial rainfall, which was particularly intense in March and April, contributed significantly to the increase in the concentration of suspended solids in the reservoir. This upward trend also persisted during the periods of maximum flooding (Fig. 8b),

<figure><img src="image_11.png" /><figcaption>Fig. 9. Trapping capacity of the Lobo River reservoir between January and December.</figcaption></figure>
before falling sharply between November and December.

### 3.5. Capacity of the reservoir to trap sediment

The trapping capacity of the Lobo River reservoir is analysed (Fig. 9). The capacity of the reservoir to trap sediment depends on the head velocity, the critical velocity and the shape parameter $1/r$. There is good synchronisation between the models used for constant settling velocity (CV-NT, CV-CM, CV-Teeter 1986) and variable settling velocity (VV-NT, VV-CM) and the model proposed by Teeter (1986) (CV-Teeter1986, VV-Teeter1986). This good synchronisation with the model proposed by Teeter (1986) shows the reliability of the analytical solutions of the models proposed in this study. Furthermore, the results show that for a Peclet number ($P^e$) greater than 4, the numerical values of the Peclet number fall outside the range of validity of the Teeter (1986) solution. In fact, for these Peclet numbers greater than 4, the curve of the Teeter (1986) solution falls outside the range of validity of the models for a constant and variable fall speed. This invalidity of the numerical values of the Peclet number is strongly observed during dry periods. This method makes it possible to assess the capacity of the Lobo River reservoir to trap sediments and the flow of suspended matter that the reservoir has not trapped. This perfect continuity between the plotted points corresponds to a deposit with constant settlement. Thus, for a constant head speed $\bar{V}/v_c \ge 40f$, almost all the sediment (95–100 %) tends to be trapped by the reservoir during the low-water period.

During the period of maximum high water (September-October), the percentage of sediment trapped in the reservoir is between 88 % and 97 %. In other words, around 3 % and 12 % of suspended solids are not trapped and pass over the spillway of the reservoir. However, for a variable settling speed of the sediments, there is a decrease in the trapping capacity of the sediments during dry periods, but it still remains high. It is between 68 % and 92 %. A large proportion of the sediment passes over the weir. In addition, peak flood periods are marked by increased hydrodynamic action in the dam, which leads to a drop in the percentage of sediment trapped, with greater solid input. This decrease in sediment trapping during peak flood periods highlights the challenges the reservoir faces. r. A large proportion of the sediment passes over the spillway. The proportion of sediments trapped is between 59 % and 64 %; 63 %-73 % and between 54 % and 62 % for the months of August, September and October (Fig. 9). There was also a drop in the percentage of sediments trapped during the period of low water (November) of around 52 % and 58 %. During this period, liquid and solid inputs from the river are very high and the reservoir does not trap a large quantity of sediment but passes over the weir. The increase in inflows is accompanied by an increase in sediment transport, which accelerates the silting up of the reservoir, reducing its storage capacity.

### 3.6. Relationship between the hydrodynamic parameters of the models

Fig. 10 shows the correlation matrix between several variables: suspended solids concentration, solid flow rate, flow velocity, liquid input, critical velocity, shape parameter r, residence time, local friction coefficient and Peclet number. The analyses reveal a significant correlation between the local friction coefficient and sediment residence time (0.79), and the shape parameter r (0.66). In addition, the residence time is strongly correlated with the Peclet number. In addition, the settling velocity of suspended solids showed a significant

<figure><img src="image_12.png" /><figcaption>Fig. 10. Correlation matrix between hydrodynamic model parameters.</figcaption></figure>
correlation with the Peclet number (0.84). The critical velocity of suspended solids shows a very strong correlation with the solid flow rate (0.97), the flow velocity (1), and the liquid inputs (1) to the reservoir of the Lobo River water reservoir. Finally, liquid flows are closely correlated with the concentration of suspended solids (0.67), solid flow (0.97), and flow velocity (1).

### 3.7. Relationship between residence time and sediment discharge

Fig. 11 shows the monthly change in sediment discharge (Qs) as a function of residence time (T). Residence time increases gradually from January to March, reaching a maximum of around seven days. It then decreases steadily from April to May, stabilizing at a low level from May to August. In September, the residence time slightly increases before and remains low and stable until November. In December, it increases again. Sediment discharge (Qs) remains low and stable from January to August. However, Qs increases considerably in September, reaching a peak of around 200 tonnes. After this peak, Qs gradually decrease from October to December. An apparent correlation between residence time and Qs is observed in some months. In September, when Qs peaks, residence time increases slightly, suggesting a potential link between these two parameters. However, residence time peaks in March, a dry period, when Qs are low, indicating that different factors may influence these two parameters. During dry or wet periods, a decrease or increase in solid inputs does not necessarily lead to a corresponding variation in residence time. This highlights the complexity of the interactions between hydrological conditions and sediment dynamics.

### 3.8. Deposit estimates

The models are used to estimate deposits, which are expressed in terms of mass and thickness, based on the data collected in the field. Fig. 12 shows the average variation in deposits in the Lobo River reservoir. The results of the models are obtained according to two hypotheses for a constant and variable settling velocity of suspended solids, with or without efficiency consideration. Our observations revealed a significant increase in deposits in the dam before considering the reservoir's efficiency, underscoring the importance of our findings.

The results show that for a constant settling velocity, the surface masses of the deposits vary from 0.076 to 48.88 kg/m²/month for the CV-NT model, from 0.076 to 47.75 kg/m²/month for the CV-Teeter (1986) model and from 0.076 to 47.57 kg/m²/month for the CV-CM model. For an annual deposit of between 85.18 and 96.05 kg/m²/year. We observe a decrease in the mass of deposits in the reservoir for variable settling velocities distributed according to Gamma law. The surface masses of the deposits are between 0.072 and 33.28 kg/m²/month for the VV-NT model. The VV-Teeter model (1986) shows surface deposits range from 0.067 to 29.95 kg/m²/month. The VV-CM model estimates surface deposition between 0.066 and 29.71 kg/m²/month for an annual deposition of 36.38 and 45.72 kg/m²/year (Fig. 12a).

Fig. 12b shows the monthly sediment deposition thicknesses in the Lobo River reservoir before considering efficiency. Deposits vary temporarily from month to month. For a constant settling velocity, deposit thicknesses range from 0.152 to 97.77 mm/month for the CV-NT model, from 0.152 to 95.50 mm/month for the CV-Teeter (1986) model and from 0.152 to 95.142 mm/month for the CV-CM model. For an annual deposition of between 188.56 and 192.11 mm/year. A decrease in deposit thickness is observed for variable

<figure><img src="image_13.png" /><figcaption>Fig. 11. Monthly changes in residence time and sediment discharge (Qs).</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>**Fig. 12.** Seasonal changes of deposited sediment layers in the Lobo River reservoir: mass (a) and thickness (b) considering the impoundment's effectiveness, mass (c) and thickness (d) after factoring in the reservoir's efficiency.</figcaption></figure>

settling velocities distributed according to Gamma law. The VV-NT model's deposit thicknesses range from 0.145 to 66.57 mm/month. The VV-Teeter model (1986) shows that deposits range from 0.134 to 59.91 mm/month. The VV-CM model estimates deposition between 0.132 and 59.42 kg/m²/month. Annual deposition is between 124.32 and 137.51.

After considering the impoundment's effectiveness in the various mathematical models, there is a noticeable decrease in the mass and surface deposit thicknesses. Under the assumption of a constant settling velocity, the surface masses of the monthly deposits are between 0.076 and 96.05 kg/m²/month with an annual average of between 85.18 and 96.05 kg/m²/year. The thickness of surface deposits ranged from 0.152 to 97.77 mm/month, with a yearly average of between 170.37 and 192.11 mm/year. For a variable settling velocity of suspended solids, the surface mass of monthly deposits ranged from 0.055 to 20.63 kg/m²/month, with an annual average of 36.38 and 45.72 kg/m²/year. The thickness of surface deposits ranged from 0.111 to 41.27 mm/month, with a yearly average of 72.75 and 91.44 mm/year. Our results clearly demonstrate that not factoring in the reservoir's efficiency leads to a notable increase in deposits in the Lobo River reservoir, highlighting the necessity of a comprehensive analysis.

## 4. Discussion

This study has provided a comprehensive understanding of the hydrosedimentary dynamics of the Lobo River reservoir. The results, which reveal significant variations in the concentration of suspended solids and the flow rate throughout the year at different measuring stations, are of paramount importance. During the dry season (December-January and February), SSL concentrations are relatively low, with monthly averages of between 4 and 20 mg/L. As the rainy season commences (March-April), SSL concentrations gradually increase, reaching values of between 22 and 36 mg/L. This variability, influenced by land use/land cover dynamics and the aggressiveness of the first rains, is a key finding of this study. Bouguerras and Bouanani, (2019); Koffi et al. (2023b) further report that the extent and nature of suspended sediment discharges are linked to the intensity of erosion by runoff water, the amount of rainfall and the capacity of runoff to transport solids.

There is a strong correlation between sediment discharge variation and inflow variations (Williams, 1989; Zheng et al., 2021). Sediment discharge in the Lobo River reservoir is relatively higher than the sediment discharge obtained by Kouassi et al., (2013) and
Meledje et al. (2021) in Taabo Lake and Ayamé 1 Lake. This difference in results could be due to the degradation and use of the land and the slope, which increases the vulnerability of soils to erosion in the basin. The distribution functions were used to obtain the settling velocity distribution. The results show that the settling velocity varies as a function of SSL concentration. Laboratory studies have shown that the settling velocity of solid suspended solids (SSL) and the settling velocity of silt creams vary mainly as a function of concentration, according to laws specific to each type of sediment (Krone, 1986; Tattersall et al., 2003). These results indicate that the median settling velocity is much lower than the mean settling velocity. According to Sanchez (2006), this variation in velocity could be attributed to the effect of turbulence, which increases as the settling velocity of suspended matter increases. The turbulence generated in the fluid affects the settling dynamics by creating irregular movements and fluctuations in velocity, which explains the differences observed between the median and mean settling velocities. Thus, the observations made by Krone (1986) and Tattersall et al. (2003), corroborated by the conclusions of Sanchez (2006), contribute significantly to the advancement of knowledge in the field of sediment hydrodynamics and suspended particle dynamics.

Six models were developed based on four main hypotheses:

1. settling velocity is constant;

2. settling velocity is constant with Teeter (1986) mixture;

3. settling velocity is Gamma-distributed;

4. settling velocity is Gamma-distributed with Teeter (1986) mixing.

The various scenarios produced good results. These results show that the proposed models follow a similar dynamic to the Teeter (1986) model. In both cases, these models are at the limit for a Peclet number (Pe) less than or equal to 4. This observation is supported by studies on the transport of cohesive sediments, which have shown that when the Peclet number exceeds a critical threshold (Pe > 4), the deposition process ceases (Teeter, 1986). Under these conditions, the Teeter (1986) model loses its validity because, for cohesive sediments, its solution is only applicable in the presence of deposition with a probability equal to 1 (P = 1). Once this range of validity is exceeded, there is no longer any deposition: all the sediment in the water column no longer settles to the bottom but is resuspended. The close correspondence between the proposed models and that of Teeter (1986) attests to the reliability and quality of the analytical solutions developed in this study. This concordance validates the hypothesis underlying these models and reinforces their relevance in the study of settling dynamics. A more in-depth discussion of the implications of these results is required to fully understand the impact of the low current velocities observed in the Lobo reservoir. These low velocities can be attributed to several factors, including seasonal climatic conditions and the specific hydrodynamic characteristics of the site. These factors directly influence sediment trapping capacity during the dry period, when sediment inputs are relatively low. During this period, minimal sediment passes over the reservoir's spillway. This is partly due to the reduction in water flows, which reduces sediment transport capacity (Brune, 1953; Randle et al., 2013; Williams, 1989). As a result, the reservoir has a high capacity to trap a maximum amount of sediment. This observation is crucial for sediment management in reservoirs, as it provides a better understanding of the conditions under which sediment deposition can be maximised. Knowledge of settling dynamics and critical thresholds, such as the Peclet number, is essential for developing effective sediment management strategies. The impact of turbulence on settling is also a crucial aspect to consider. According to Sanchez (2006), the variation in SSL settling velocity could be linked to the phenomenon of turbulence, which increases with settling velocity. This turbulence can influence the distribution and behaviour of suspended particles, thus affecting their ability to settle. Understanding these interactions is essential for improving settling models and predicting the potential impacts of hydrodynamic variations on sediment distribution.

## 5. Conclusion

This study has led to new methods for analyzing steady-flow hydrosedimentary dynamics. These methods are based on four main theories. The results reveal significant seasonal and spatial variations in suspended solids (SS) concentrations, with higher concentrations observed during the rainy season due to increased rainfall intensity and soil erosion. The highest SSL values are recorded in September and October, correlating with the peak flow rates of the Lobo River. The study also highlights the substantial impact of seasonal changes on the proportion of sediments remaining in suspension and their settling velocities, which vary monthly due to changing hydrodynamic conditions. The reservoir's capacity to trap sediments is closely linked to the flow rates, settling velocities, and hydrodynamic parameters such as the Peclet number and critical velocity. During the dry season, the reservoir effectively traps most sediments, with trapping efficiencies ranging from 95% to 100%. However, during periods of maximum flooding, the efficiency decreases, and a more significant proportion of suspended solids bypasses the reservoir. This dynamic relationship underscores the complexity of sediment management in reservoirs, which must account for varying hydrological and climatic conditions. The study's development of six models based on different hypotheses regarding settling velocities provides valuable insights into sediment transport and deposition processes. These models align well with the Teeter (1986) model for cohesive sediments, mainly when the Peclet number is below the critical threshold. The findings emphasize the importance of understanding the interactions between settling dynamics, turbulence, and sediment transport to develop effective sediment management strategies. Overall, this research enhances our understanding of the sediment dynamics in the Lobo River reservoir, providing a basis for improved water resource management and sediment control measures. The insights gained from this study can inform future efforts to mitigate sedimentation impacts, optimize reservoir storage capacity, and enhance the sustainability of water resources. Further research is essential to increase our knowledge of the hydro-sedimentary functioning of the reservoir in the face of climatic and anthropogenic constraints. In future work, this is why we propose to improve the settling basin theory method to visualize the preferential zones of sediment deposition and
the spatial distribution of currents. We also suggest simulating the exceptional phenomena affecting settling in the Lobo River reservoir. In addition, it is crucial to assess future sediment supply and sediment quality in the Lobo River reservoir under various climate change scenarios for better management of the Lobo River reservoir.

### CRediT authorship contribution statement

**Martin Sanchez:** Software, Methodology, Formal analysis, Conceptualization. **Brou Loukou Alexis:** Writing – review & editing.
**Brice W. Coulibaly:** Writing – review & editing. **Gla Blaise Ouédé:** Writing – review & editing. **Michal Habel:** Writing – review & editing. **Franck Hervé Akaffou:** Writing – review & editing. **Kouakou Lazare Kouassi:** Writing – review & editing, Writing – original draft, Visualization, Formal analysis, Data curation, Conceptualization. **Amani Michel Kouassi:** Writing – original draft, Validation.
**Berenger Koffi:** Writing – original draft, Software, Resources, Project administration, Methodology, Formal analysis, Data curation, Conceptualization. **Dibi Brou:** Data curation, Supervision. **Koffi Eugène Kouakou:** Writing – review & editing, Writing – original draft.

### Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Data availability

Data will be made available on request.

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