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# Soils removal during reservoir emptying

Didier Marot, Alain Alexis, Jean Pierre Bouchard

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Didier Marot, Alain Alexis, Jean Pierre Bouchard. Soils removal during reservoir emptying. 9th International Symposium on River Sedimentation (ISRS), Oct 2004, Yichang, China. hal-01008923

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# Soils removal during reservoir emptying

Didier Marot, Alain Alexis, Jean Pierre Bouchard

► To cite this version:

Didier Marot, Alain Alexis, Jean Pierre Bouchard. Soils removal during reservoir emptying. 9th International Symposium on River Sedimentation (ISRS), Oct 2004, Yichang, China. hal-01008923

HAL Id: hal-01008923

https://hal.science/hal-01008923v1

Submitted on 10 Feb 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

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Distributed under a Creative Commons Attribution 4.0 International License
# SOILS REMOVAL DURING RESERVOIR EMPTYING

Didier MAROT and Alain ALEXIS

GeM, IUT de Saint-Nazaire, BP 420, F - 44606 Saint-Nazaire Cedex

Jean-Pierre BOUCHARD

LNHE, EDF, 6 Quai Watier, BP 49, F - 78401 Chatou Cedex

E-mail: marot@iutsn.univ-nantes.fr

**Abstract:** In fluvial or littoral environment, submerged ultra-weak cohesive soils are characterized by a very high water content, a great spatial variability and great strains. The study of their instabilities induced by the variation of hydraulic stress requires the modelisation of coupled phenomenon : sliding, erosion and deposition. So for anticipating the impact of a reservoir emptying on the stability of submerged mud banks situated upstream from the dam, we propose a model of these coupled phenomenon. The scientific approach associates : theoretical and numerical modelisations and characterizations of sediments on the selected site. The theoretical study by the slice method allows to propose a flat sliding criteria. This criteria is validated by confrontation of height calculated with the changes of the thickness of sediment layer during partial emptying. In order to deal with the natural instability, we integrate this sliding criteria in a numerical code of erosion-deposition. In this code, hydraulic evolution and the calculation of hydrodynamic transportation of sediments are processed separately. The main originality of the numerical code comes from the calculation of the different modes of transportation : erosion, deposition and sliding. The results of the coupling of these three mechanisms are then confronted with variations of bathymetric profiles carried out on the reservoir.

**Keywords:** Ultra-weak cohesive soils, Bank, Sliding, Erosion, Deposition, Dam reservoir

## 1 INTRODUCTION

The lowering of the reservoir level increases the velocity of the flow, which then causes erosion and moves sediments back in suspension. The emersion of the mud banks and the carving action from the flow, generates instabilities, which result in sediments sliding back into water. To enhance sediment storage controls and develop effective solutions, we need to improve our understanding of the different phases of the sedimentary cycle and the connections between them.

Several authors are concerned with some aspects of the impact of reservoir emptying on mud bank stability. Chang *et al.* (1996), for instance, are interested in the soil erosion caused by emptying processes. Bouchard *et al.* (1997) have developed a numerical code, called Courlis, that combines erosion and deposition phenomena. Paquier and Khodashenas (2002) calculate the volumes of eroded sediments, assuming a specific repartition of the bottom shear stress across the river width. Emptying is also at the origin of the sliding of a large proportion of the mud banks. Zhou et Lin (1998) arbitrarily set a sediment maximum slope, which, however, is not easy to estimate since it depends on the soil characteristics, the soil consolidation, the slope of the bedrock and the thickness of the sediment mass. For accurate representation of slides and consideration of the triple interactions of flow, erosion and sliding, a sliding criterion developed by the authors and based on soil mechanics has been integrated within the Courlis code.
# SOILS REMOVAL DURING RESERVOIR EMPTYING

Didier MAROT and Alain ALEXIS

GEM, IUT de Saint-Nazaire, BP 420, F - 44606 Saint-Nazaire Cedex

Jean-Pierre BOUCHARD

LNHE, EDF, 6 Quai Watier, BP 49, F - 78401 Chatou Cedex

E-mail: marot@iutsn.univ-nantes.fr

**Abstract:** In fluvial or littoral environment, submerged ultra-weak cohesive soils are characterized by a very high water content, a great spatial variability and great strains. The study of their instabilities induced by the variation of hydraulic stress requires the modelisation of coupled phenomenon : sliding, erosion and deposition. So for anticipating the impact of a reservoir emptying on the stability of submerged mud banks situated upstream from the dam, we propose a model of these coupled phenomenon. The scientific approach associates : theoretical and numerical modelisations and characterizations of sediments on the selected site. The theoretical study by the slice method allows to propose a flat sliding criteria. This criteria is validated by confrontation of height calculated with the changes of the thickness of sediment layer during partial emptying. In order to deal with the natural instability, we integrate this sliding criteria in a numerical code of erosion-deposition. In this code, hydraulic evolution and the calculation of hydrodynamic transportation of sediments are processed separately. The main originality of the numerical code comes from the calculation of the different modes of transportation : erosion, deposition and sliding. The results of the coupling of these three mechanisms are then confronted with variations of bathymetric profiles carried out on the reservoir.

**Keywords:** Ultra-weak cohesive soils, Bank, Sliding, Erosion, Deposition, Dam reservoir

## 1 INTRODUCTION

The lowering of the reservoir level increases the velocity of the flow, which then causes erosion and moves sediments back in suspension. The emersion of the mud banks and the carving action from the flow, generates instabilities, which result in sediments sliding back into water. To enhance sediment storage controls and develop effective solutions, we need to improve our understanding of the different phases of the sedimentary cycle and the connections between them.

Several authors are concerned with some aspects of the impact of reservoir emptying on mud bank stability. Chang *et al.* (1996), for instance, are interested in the soil erosion caused by emptying processes. Bouchard *et al.* (1997) have developed a numerical code, called Courlis, that combines erosion and deposition phenomena. Paquier and Khodashenas (2002) calculate the volumes of eroded sediments, assuming a specific repartition of the bottom shear stress across the river width. Emptying is also at the origin of the sliding of a large proportion of the mud banks. Zhou et Lin (1998) arbitrarily set a sediment maximum slope, which, however, is not easy to estimate since it depends on the soil characteristics, the soil consolidation, the slope of the bedrock and the thickness of the sediment mass. For accurate representation of slides and consideration of the triple interactions of flow, erosion and sliding, a sliding criterion developed by the authors and based on soil mechanics has been integrated within the Courlis code.
# 2 DESCRIPTION OF THE MODEL

## 2.1 Sliding

The present study is conducted to examine the stability of sediment masses in limit balance conditions, i.e., when failure is about to happen. In order to address the problem, a safety coefficient (F), is introduced. This coefficient, originally defined by Fröhlich and generalized by Bishop (1954), is the ratio of the shear strength to the shear stress at the level of the failure surface. The slice method consists in dividing the unstable volume into a certain number of vertical slices and then studying the limit balance of each slice. Using the observations collected on the experimental site, a flat sliding criterion for a trapezoid soil slice is developed (Marot et al., 2003). The safety factor is then expressed as:

$$F = \frac{C_u L \frac{b}{\cos \alpha}}{W \sin \alpha - \Delta f \cos \alpha + P_w \sin(\alpha - \theta)} \quad (1)$$

with,
$L$: length of the slice,
$b$: width of the slice,
$W$: weight of the slice,
$\Delta f$: horizontal components of the inter-slice forces,
$P_w$: force resulting from the pressure of the water applied to the upper surface of the slice,
$\alpha$ and $\theta$: inclination of the lower and the upper surface of the slice.

When sliding occurs, the remained stable underlying soil course becomes overconsolidated. So as to consider this phenomenon, the shear strength profile on the potential slip line defined by dimensions $T_i$ and $T_{i+1}$ in undrained conditions is defined by:

$$C_u = a \frac{Z_{i+1}^n - T_{i+1} + Z_i^n - T_i}{2} + C_{uo} \quad (2)$$

with: $Z_i^n$ and $Z_{i+1}^n$: elevations of the top slice in configuration $n$,

Coefficient $a$ is measured on the experimental site and, in order to differentiate remolded sediments from undisturbed sediments, critical remolded erosion stress and remolded undrained cohesion values are assumed to be half that of the undisturbed sediments (Marot et al., 1998).

## 2.2 Hydrodynamic and Sediment Transport

COURLIS has been developed at the Laboratoire National d'Hydraulique et d'Environnement (LNHE), a department of Electricité De France. It is based on the external coupling of a hydraulic unit and a sedimentary unit described in Bertier et al. (2002).

The sedimentary unit calculates an advection-diffusion equation for the concentration of fine sediment, written as follow:

$$\frac{\partial C_M}{\partial t} + \text{div}(u_f C_M) = \text{div}(q) + S_v \quad (3)$$

with, $C_M$: suspended matter mean concentration, $u_f$: flow velocity, $q$: diffusion flux, $S_v$: volume sources.

Krone's law is used to model the deposition surface flux ($q_{deposition}$). We write:

$$q_{deposition} = C_M v_s \left(1 - \frac{\tau}{\tau_{cd}}\right) \quad (4)$$

with, $v_s$: settling velocity, $\tau_{cd}$: critical shear stress for deposition.

$\tau(v)$, shear stress defined by:
## 2 DESCRIPTION OF THE MODEL

### 2.1 Sliding

The present study is conducted to examine the stability of sediment masses in limit balance conditions, i.e., when failure is about to happen. In order to address the problem, a safety coefficient (F), is introduced. This coefficient, originally defined by Fröhlich and generalized by Bishop (1954), is the ratio of the shear strength to the shear stress at the level of the failure surface. The slice method consists in dividing the unstable volume into a certain number of vertical slices and then studying the limit balance of each slice. Using the observations collected on the experimental site, a flat sliding criterion for a trapezoid soil slice is developed (Marot et al., 2003). The safety factor is then expressed as:

$$F = \frac{C_u L \frac{b}{\cos \alpha}}{W \sin \alpha - \Delta f \cos \alpha + P_w \sin(\alpha - \theta)} \quad (1)$$

with,
$L$: length of the slice,
$b$: width of the slice,
$W$: weight of the slice,
$\Delta f$: horizontal components of the inter-slice forces,
$P_w$: force resulting from the pressure of the water applied to the upper surface of the slice,
$\alpha$ and $\theta$: inclination of the lower and the upper surface of the slice.

When sliding occurs, the remained stable underlying soil course becomes overconsolidated. So as to consider this phenomenon, the shear strength profile on the potential slip line defined by dimensions $T_i$ and $T_{i+1}$ in undrained conditions is defined by:

$$C_u = a \frac{Z_{i+1}^n - T_{i+1} + Z_i^n - T_i}{2} + C_{uo} \quad (2)$$

with: $Z_i^n$ and $Z_{i+1}^n$: elevations of the top slice in configuration $n$,

Coefficient $a$ is measured on the experimental site and, in order to differentiate remolded sediments from undisturbed sediments, critical remolded erosion stress and remolded undrained cohesion values are assumed to be half that of the undisturbed sediments (Marot et al., 1998).

### 2.2 Hydrodynamic and Sediment Transport

COURLIS has been developed at the Laboratoire National d'Hydraulique et d'Environnement (LNHE), a department of Electricité De France. It is based on the external coupling of a hydraulic unit and a sedimentary unit described in Bertier et al. (2002).

The sedimentary unit calculates an advection-diffusion equation for the concentration of fine sediment, written as follow:

$$\frac{\partial C_M}{\partial t} + \text{div}(u_f C_M) = \text{div}(q) + S_v \quad (3)$$

with, $C_M$: suspended matter mean concentration, $u_f$: flow velocity, $q$: diffusion flux, $S_v$: volume sources.

Krone's law is used to model the deposition surface flux ($q_{deposition}$). We write:

$$q_{deposition} = C_M v_s \left(1 - \frac{\tau}{\tau_{cd}}\right) \quad (4)$$

with, $v_s$: settling velocity, $\tau_{cd}$: critical shear stress for deposition.

$\tau(v)$, shear stress defined by:
$$ \tau(y) = \frac{\rho.g.h(y) V^2 n^2}{R^{4/3}} \qquad (5) $$

with, $\rho$: density,

$g$: gravity,

$V$: mean fluid velocity,

$h(y)$: local water depth

$n$: manning roughness coefficient,

$R$: hydraulic radius.

The erosion flux is represented by Partheniades' law :

$$ q_{\text{erosion}} = M_e \left( \frac{\tau}{\tau_{ce}} - 1 \right) \qquad (6) $$

with, $\tau_{ce}$: critical shear stress for erosion

$M_{ce}$: erosion rate.

Bottom sediment are described more accurately by discretizing the cross-sections transversally to the flow axis. Exchange flux with the bottom are then computed on each element along the cross section with the local expression of the shear stress (Eq. 5) and added to get a total sediment flux (kg·m·s⁻¹) available for a 1D transport equation. Sediment deposit is described vertically by different layers of matter where sediment characteristics and properties are assumed to be homogeneous. At each time step, the geometry of the bottom sediment is updated and hydrodynamic calculation relaunched. This exchange between both codes allows to adapt the hydraulic to the bottom evolution due to both sediment transport and bank sliding.

## 2.3 Modelling Bank Deformation

The bottom cross section is divided in a set of finite elements (segments). When a segment is unstable, sliding will result in a smoothing of the bottom elevation values. For example, if the element (i, i+1) is unstable, sliding would induce a decrease of $Z_i^n$ value and an increase of $Z_{i+1}^n$. Mathematically, such a smoothing can be simulated by a diffusion operator applied to the bottom elevation of the unstable parts of the cross section. It can be written as :

$$ Z_{i}^{n+1} = (1-\lambda) Z_{i}^{n} + \lambda M Z_{i}^{n} \qquad (7) $$

$M$ is a diffusion matrix, the coefficients of which are fixed according to the stability of the element and $\lambda$ is a numerical parameter which controls the deformation speed. This parameter is calibrated to avoid any time lag between the loading condition variations and the bottom shape adaptations. Such a description implies that at each time step, under variable external conditions, the cross section tends to come back to the stability of all the segments and that no inertial effect exists in the movement (slow deformation).

The diffusion matrix is built following the finite elements formalism :

$$ M = \begin{bmatrix} B & C \\ A & B & C \\ & A & B & C \end{bmatrix} $$

The contribution of segment $[i, i+1]$ is defined according to two configurations:

$$ \text{if the segment is stable: } \quad B(i) = \frac{1}{2} \qquad C(i) = 0 $$
$$ \tau(y) = \frac{\rho.g.h(y) V^2 n^2}{R^{4/3}} \qquad (5) $$

with, $\rho$: density,

$g$: gravity,

$V$: mean fluid velocity,

$h(y)$: local water depth

$n$: manning roughness coefficient,

$R$: hydraulic radius.

The erosion flux is represented by Partheniades' law :

$$ q_{\text{erosion}} = M_e \left( \frac{\tau}{\tau_{ce}} - 1 \right) \qquad (6) $$

with, $\tau_{ce}$: critical shear stress for erosion

$M_{ce}$: erosion rate.

Bottom sediment are described more accurately by discretizing the cross-sections transversally to the flow axis. Exchange flux with the bottom are then computed on each element along the cross section with the local expression of the shear stress (Eq. 5) and added to get a total sediment flux (kg·m·s⁻¹) available for a 1D transport equation. Sediment deposit is described vertically by different layers of matter where sediment characteristics and properties are assumed to be homogeneous. At each time step, the geometry of the bottom sediment is updated and hydrodynamic calculation relaunched. This exchange between both codes allows to adapt the hydraulic to the bottom evolution due to both sediment transport and bank sliding.

## 2.3 Modelling Bank Deformation

The bottom cross section is divided in a set of finite elements (segments). When a segment is unstable, sliding will result in a smoothing of the bottom elevation values. For example, if the element (i, i+1) is unstable, sliding would induce a decrease of $Z_i''$ value and an increase of $Z_{i+1}''$. Mathematically, such a smoothing can be simulated by a diffusion operator applied to the bottom elevation of the unstable parts of the cross section. It can be written as :

$$ Z_{i}^{n+1} = (1-\lambda) Z_{i}^{n} + \lambda M Z_{i}^{n} \qquad (7) $$

$M$ is a diffusion matrix, the coefficients of which are fixed according to the stability of the element and $\lambda$ is a numerical parameter which controls the deformation speed. This parameter is calibrated to avoid any time lag between the loading condition variations and the bottom shape adaptations. Such a description implies that at each time step, under variable external conditions, the cross section tends to come back to the stability of all the segments and that no inertial effect exists in the movement (slow deformation).

The diffusion matrix is built following the finite elements formalism :

$$ M = \begin{bmatrix} B & C \\ A & B & C \\ & A & B & C \end{bmatrix} $$

The contribution of segment $[i, i+1]$ is defined according to two configurations:

$$ \text{if the segment is stable: } \quad B(i) = \frac{1}{2} \qquad C(i) = 0 $$
$$A(i+1) = 0 \qquad B(i+1) = \frac{1}{2}$$

$$\text{if the segment is unstable} \qquad B(i) = \frac{1}{3} \qquad C(i) = \frac{1}{6}$$

$$A(i+1) = \frac{1}{6} \qquad B(i+1) = \frac{1}{3}$$

The matrix is then formed by adding the contributions of each segments. For a clearer definition of the matrix, point i is studied depending on the stability or the instability of segments [i-1, i] and [i, i+1].

Whatever the configuration, the total sum of each line of the matrix is equal to one, which guarantees sediment volume conservation.

At each time step, erosion and settling is computed and the sediment transport equation is solved. The cross section shape is then modified according to the stability criterion to sliding. The final cross section geometry, is then sent to the hydraulic code for flow characteristic updating.

Finally, the presence of a specific configuration arising from the coupling of erosion and sliding cannot be ignored. Until now, indeed, sliding has been considered along slopes with the same signs than the topographic profile. Erosion, however, can create channels, the side slopes of which can be the opposite of that of the topographic profile. In this case, the stability of the upper part of the slice is studied.

# 3 APPLICATION TO A SELECTED SITE

## 3.1 Site Features

The Grangent storage reservoir is located near Saint Etienne (France) on the longest French river, the Loire river (1,020 km). The dam structure is a cylindrical concrete vault with a height of 55 m and a crown length of 200 m. The storage reservoir has a length of 23 km, a volume of 57 Mm³ whereas the surface area of the total catchment is 3,850 km². During partial emptying processes (October 1995-May 1996), the level of the reservoir was depleted down to an elevation of 404 m NGF, i.e., 16 m below its nominal elevation. Upon completion of the partial emptying, upstream end of the reduced reservoir was exactly at the confluence of the Loire and the Ondaine. The study zone spreads upstream and downstream from the junction over approximately 4 km. Four zones are distinguished: upstream, Ondaine, after confluence and downstream (Fig. 1).

<figure><img src="image_3.png" /><figcaption>Fig. 1 Location Map of Sampling and P 27 to P 42 Bathymetric Profile Stations.</figcaption></figure>
$$A(i+1) = 0 \qquad B(i+1) = \frac{1}{2}$$

$$\text{if the segment is unstable} \qquad B(i) = \frac{1}{3} \qquad C(i) = \frac{1}{6}$$

$$A(i+1) = \frac{1}{6} \qquad B(i+1) = \frac{1}{3}$$

The matrix is then formed by adding the contributions of each segments. For a clearer definition of the matrix, point i is studied depending on the stability or the instability of segments [i-1, i] and [i, i+1].

Whatever the configuration, the total sum of each line of the matrix is equal to one, which guarantees sediment volume conservation.

At each time step, erosion and settling is computed and the sediment transport equation is solved. The cross section shape is then modified according to the stability criterion to sliding. The final cross section geometry, is then sent to the hydraulic code for flow characteristic updating.

Finally, the presence of a specific configuration arising from the coupling of erosion and sliding cannot be ignored. Until now, indeed, sliding has been considered along slopes with the same signs than the topographic profile. Erosion, however, can create channels, the side slopes of which can be the opposite of that of the topographic profile. In this case, the stability of the upper part of the slice is studied.

# 3 APPLICATION TO A SELECTED SITE

## 3.1 Site Features

The Grangent storage reservoir is located near Saint Etienne (France) on the longest French river, the Loire river (1,020 km). The dam structure is a cylindrical concrete vault with a height of 55 m and a crown length of 200 m. The storage reservoir has a length of 23 km, a volume of 57 Mm³ whereas the surface area of the total catchment is 3,850 km². During partial emptying processes (October 1995-May 1996), the level of the reservoir was depleted down to an elevation of 404 m NGF, i.e., 16 m below its nominal elevation. Upon completion of the partial emptying, upstream end of the reduced reservoir was exactly at the confluence of the Loire and the Ondaine. The study zone spreads upstream and downstream from the junction over approximately 4 km. Four zones are distinguished: upstream, Ondaine, after confluence and downstream (Fig. 1).

<figure><img src="image_3.png" /><figcaption>Fig. 1 Location Map of Sampling and P 27 to P 42 Bathymetric Profile Stations.</figcaption></figure>
## 3.2 Topography and Bathymetry

A topographic survey carried out in 1952 at every four hundred meters was used to know the elevation of the Loire coarse alluvial deposit before the construction of the dam. In order to assess the impact of the lowering of the reservoir level on the stability of the mud banks, bathymetric surveys using sonic depth-sounders are carried out on the site before and after partial emptying. So as to limit uncertainties for the bathymetric profile comparative study, positioning is achieved by satellite (GPSD).

## 3.3 Geotechnical Characterization

To characterize the submerged soils before the beginning of the emptying process, a core sampling campaign is conducted and eleven samples with a diameter of 6 cm and a mean length of 2.5 m are taken. These samples are subjected to measurement every 10 cm on undisturbed then remolded sediments. The correlation analysis conducted on all the parameters (Marot et al., 1998) allows for the expression of a linear relationship between undrained shear strength and depth :

$$ cu(h) = a h + cu_0 \qquad (8) $$

with $a = 1.47 \text{ kPa} \cdot \text{m}^{-1}$ and $c_{u0} = 0.16 \text{ kPa}$ ($r = 0.858; n = 48; \xi = 8.9 \ 10^{-11}$)

# 4 COMPARISON BETWEEN MODELLING AND EXPERIMENTAL MEASUREMENTS

## 4.1 Comparison Between Sliding and Bathymetry

The sliding criterion has been first validated by comparing measured (hm) and modelled (he) displaced heights under both limit loading conditions exclusively, i.e., completely submerged or completely emergent massif (Marot et al., 2003). The sliding criterion gives a satisfactory estimate of displaced heights. However, the computation produces a height, which is systematically underestimated by 0.3 m. In order to perform a continuous survey of mud bank geomorphologic changes and validate the integration of the sliding criterion into Courlis, computations are made by neglecting both erosion and deposition phenomena (Fig. 2).

<figure><img src="image_4.png" /><figcaption>Fig. 2 P32 Profile Modelling Using Courlis (Sliding)</figcaption></figure>

The results obtained make it possible to estimate a sliding height on the order of 60 % to 70% of the real actual displaced mud thickness.
## 3.2 Topography and Bathymetry

A topographic survey carried out in 1952 at every four hundred meters was used to know the elevation of the Loire coarse alluvial deposit before the construction of the dam. In order to assess the impact of the lowering of the reservoir level on the stability of the mud banks, bathymetric surveys using sonic depth-sounders are carried out on the site before and after partial emptying. So as to limit uncertainties for the bathymetric profile comparative study, positioning is achieved by satellite (GPSD).

## 3.3 Geotechnical Characterization

To characterize the submerged soils before the beginning of the emptying process, a core sampling campaign is conducted and eleven samples with a diameter of 6 cm and a mean length of 2.5 m are taken. These samples are subjected to measurement every 10 cm on undisturbed then remolded sediments. The correlation analysis conducted on all the parameters (Marot et al., 1998) allows for the expression of a linear relationship between undrained shear strength and depth :

$$cu(h) = a h + cu_0 \quad (8)$$

with $a = 1.47 \text{ kPa} \cdot \text{m}^{-1}$ and $c_{u0} = 0.16 \text{ kPa}$ ($r = 0.858; n = 48; \xi = 8.9 \ 10^{-11}$)

# 4 COMPARISON BETWEEN MODELLING AND EXPERIMENTAL MEASUREMENTS

## 4.1 Comparison Between Sliding and Bathymetry

The sliding criterion has been first validated by comparing measured (hm) and modelled (he) displaced heights under both limit loading conditions exclusively, i.e., completely submerged or completely emergent massif (Marot et al., 2003). The sliding criterion gives a satisfactory estimate of displaced heights. However, the computation produces a height, which is systematically underestimated by 0.3 m. In order to perform a continuous survey of mud bank geomorphologic changes and validate the integration of the sliding criterion into Courlis, computations are made by neglecting both erosion and deposition phenomena (Fig. 2).

<figure><img src="image_4.png" /><figcaption>Fig. 2 P32 Profile Modelling Using Courlis (Sliding)</figcaption></figure>

The results obtained make it possible to estimate a sliding height on the order of 60 % to 70% of the real actual displaced mud thickness.
## 4.2 Comparison Between Erosion-Deposition-Sliding and Bathymetry

Fig. 3 presents the results achieved when the three phenomena are combined. The upper part of slided mud layer is not modified whereas erosion computational results are characterized by the presence of a too deep and too narrow channel.

This first comparison proves that the sliding criterion satisfactorily characterizes mud bank stability. The results, however, are strongly dependent on the coupled erosion computations. The emergent massif sliding initiated on the right of the profile could develop further if erosion had removed the passive earth pressure formed by the submerged massif. Furthermore, the presence of an erosion channel up to bedrock is probably due to shear stress repartition on the bottom. According to relation (5), the local shear stress strongly increases with the flow depth. Some variations in the local stress expression could improve the erosion computations and, consequently, improve the coupled sliding results.

<figure><img src="image_5.png" /><figcaption>Fig. 3 P32 Profile Modelling Using Courlis (Erosion-Deposition-Sliding Coupling)</figcaption></figure>

## 5 CONCLUSION

The aim of this study is to simulate soils removal during a dam reservoir emptying. The submerged fine matter mud banks are characterized by a high water content, a great spatial variability and a strong deformability. A coupled modelling of sliding, erosion and deposition mechanisms is necessary to account for such instabilities. The flat sliding criterion proposed here takes the specific features of high water content soils and the particularities arising from the combination of phenomena into account. The theoretically achieved sliding criterion is validated by comparison with unstable mud height measurements on a selected site. For more accuracy in the representation of the natural events, the sliding criterion is then integrated within an erosion-deposition code. Finally, the results of the combination of all three mechanisms are compared with the variations in the experimental bathymetric profiles. This comparison confirms the validity of the simulation used and gives a satisfactory estimated of displaced thicknesses.

## REFERENCES

* Bertier, C., Bouchard, JP., Dumond, L., 2002, One dimensional model for reservoir sedimentation management, *Proceedings of the International Conference on Fluvial Hydraulics River Flow 2002*, Louvain la Neuve Belgium. Bousmar & Zech (eds.) Balkema publishers.

* Bishop A.W., 1954, The use of slip circle in the stability analysis of slopes, *Géotechnique*, Vol. 5, pp. 7-17.

* Bouchard, J.P., Maurel, F., and Petitjean, A., 1997, Sedimental impact of reservoir emptying prediction tools and site investigation, *In Proceedings of the International Water Research Symposium*, Aachen.
## 4.2 Comparison Between Erosion-Deposition-Sliding and Bathymetry

Fig. 3 presents the results achieved when the three phenomena are combined. The upper part of slided mud layer is not modified whereas erosion computational results are characterized by the presence of a too deep and too narrow channel.

This first comparison proves that the sliding criterion satisfactorily characterizes mud bank stability. The results, however, are strongly dependent on the coupled erosion computations. The emergent massif sliding initiated on the right of the profile could develop further if erosion had removed the passive earth pressure formed by the submerged massif. Furthermore, the presence of an erosion channel up to bedrock is probably due to shear stress repartition on the bottom. According to relation (5), the local shear stress strongly increases with the flow depth. Some variations in the local stress expression could improve the erosion computations and, consequently, improve the coupled sliding results.

<figure><img src="image_5.png" /><figcaption>Fig. 3 P32 Profile Modelling Using Courlis (Erosion-Deposition-Sliding Coupling)</figcaption></figure>

# 5 CONCLUSION

The aim of this study is to simulate soils removal during a dam reservoir emptying. The submerged fine matter mud banks are characterized by a high water content, a great spatial variability and a strong deformability. A coupled modelling of sliding, erosion and deposition mechanisms is necessary to account for such instabilities. The flat sliding criterion proposed here takes the specific features of high water content soils and the particularities arising from the combination of phenomena into account. The theoretically achieved sliding criterion is validated by comparison with unstable mud height measurements on a selected site. For more accuracy in the representation of the natural events, the sliding criterion is then integrated within an erosion-deposition code. Finally, the results of the combination of all three mechanisms are compared with the variations in the experimental bathymetric profiles. This comparison confirms the validity of the simulation used and gives a satisfactory estimated of displaced thicknesses.

# REFERENCES

* Bertier, C., Bouchard, JP., Dumond, L., 2002, One dimensional model for reservoir sedimentation management, *Proceedings of the International Conference on Fluvial Hydraulics River Flow 2002*, Louvain la Neuve Belgium. Bousmar & Zech (eds.) Balkema publishers.

* Bishop A.W., 1954, The use of slip circle in the stability analysis of slopes, *Géotechnique*, Vol. 5, pp. 7-17.

* Bouchard, J.P., Maurel, F., and Petitjean, A., 1997, Sedimental impact of reservoir emptying prediction tools and site investigation, *In Proceedings of the International Water Research Symposium*, Aachen.
Chang, H.H., Harrison, L.L., Lee, W., and Tu, S., 1996, Numerical modelling for sediment-pass-through reservoirs, *Journal of Hydraulic Engineering*, ASCE, Vol. 122, pp. 381-387.

Marot, D., Alexis, A., and Thomas, P., 1998, Sedimentological and geotechnical approach of correlations between sediment parameters in a reservoir. In *Proceedings of the 3rd International Conference on Hydroscience and Engineering (ICHE'98) (ASCE, IAHR)*, Cottbus/Berlin, cyber proceedings.

Marot, D., Alexis, A., and Thomas, P., 2003, Towards a better forecast for reservoir slope sliding, *International Journal of Sediment Research*, Vol. 18, pp. 278-289.

Paquier, A. and Khodashenas, S.R., 2002, River bed deformation calculated from boundary shear stress, *Journal of Hydraulic Research*, Vol. 40, pp. 603-609.

Zhou, J., and Lin, B., 1998, One dimensional mathematical model for suspended sediment by lateral integration, *Journal of Hydraulic Engineering*, ASCE, Vol. 124, pp. 712-717.
Chang, H.H., Harrison, L.L., Lee, W., and Tu, S., 1996, Numerical modelling for sediment-pass-through reservoirs, *Journal of Hydraulic Engineering*, ASCE, Vol. 122, pp. 381-387.

Marot, D., Alexis, A., and Thomas, P., 1998, Sedimentological and geotechnical approach of correlations between sediment parameters in a reservoir. In *Proceedings of the 3rd International Conference on Hydroscience and Engineering (ICHE'98) (ASCE, IAHR)*, Cottbus/Berlin, cyber proceedings.

Marot, D., Alexis, A., and Thomas, P., 2003, Towards a better forecast for reservoir slope sliding, *International Journal of Sediment Research*, Vol. 18, pp. 278-289.

Paquier, A. and Khodashenas, S.R., 2002, River bed deformation calculated from boundary shear stress, *Journal of Hydraulic Research*, Vol. 40, pp. 603-609.

Zhou, J., and Lin, B., 1998, One dimensional mathematical model for suspended sediment by lateral integration, *Journal of Hydraulic Engineering*, ASCE, Vol. 124, pp. 712-717.