Method for predicting sediment sorting and bed variation in river channels with a broad sediment size distribution

2006 Heisei 18 Doctoral Thesis Method for predicting sediment sorting and bed variation in river channels with a broad sediment size distribution Ritsumeikan University Graduate School

2006 (Heisei 18) Doctoral Thesis

Method for predicting sediment sorting and bed variation

in river channels with a broad sediment size distribution

Ritsumeikan University Graduate School of Science and Engineering Doctoral Program in Science and Engineering

Luu Xuan Loc

Chapter 1

Introduction

1.1 General remarks

Mechanics of sediment transport is the study of the laws of sediment movement in fluids and

of the process of erosion, transportation and deposition Various types of sediment movement occur in nature and are encountered in engineering practice These include sediment movement in rivers, in canals, in reservoirs, along the seashore, in desert, and in pipelines They take places as results of stream flow, wind, and

waves It costs the US economy

between 30billion USD (Uri &

Lewis 1998) and 44 billion

(Pimental et al.1993) annually

The annual cost in the UK is

estimated at £90 million

(Environment Agency 2002) In

Indonesia, it costs 400 million

USD per year (Magrath & Arens

1989) These costs results from Fig 1.1 Bank erosion in Mekong River, Vietnam (2000)

both direct and indirect site Some

examples of sediment disaster

event are shown in Fig 1.1, 1.2

and 1.3 (various sources)

Direct effects are particularly

important on agriculture land

where the redistribution of soil

within a field, the loss of soil from

a field, the breakdown structure of

soil and the decline in organic

nutrient result in a reduction of

cultivable soil depth and a decline

in soil fertility Indirect problems

arise from bank erosion,

sedimentation downstream, which

reduces the capacity of rivers and

drainage ditches, enhances the risk

of flooding, blocks irrigation

canals and shortens the design life

of reservoirs Many

hydroelectricity and irrigation

projects have been ruined as a

consequence of sediment

transportation Sediment is also a

pollutant in its own through the

chemicals adsorbed to it can increase the level of nitrogen and phosphorus in water bodies and result in eutrophication Statistics (Ning Chen &Zhaohui Wan 1999) show that 13 of the large rivers in the world carry annual sediment loads of over 5.8 billion tons The water runoff and

sediment loads of some of world’s major rivers are listed in Table 1.1

In summary, on account of sediment transportation, a series of difficult confrontations has been encountered in the exploitation of water resources and the construction of water conservancy

Fig 1.2 Debris flow disaster in Venezuela 1999

(http://pr.water.usgs.gov)

Fig 1.3 Bank erosion in Argentina

(http://www.fao.org)

measures, such as: flood control, reservation sedimentation, sedimentation problems in irrigation canal system, in harbors and estuaries It is imperative to conduct research on the behavior of sediment movement over time Moreover, sedimentation problems are concerning to many departments and branches of government, not limited to those dealing with water resources

In addition, some understanding of fundamentals of the mechanics of sediment transport is indispensable to development of some disciplines of science For example, in the book entitled

“Theoretical Geomorphology” published in 1960s, extended coverage was devoted to discussion

of problems related to sediment movement “The physics of Blown Sand and Desert Dunes” published in 1940s by Bagnold, in which the growth and development process of ground configuration under wind action was clearly explained in terms of its dynamics

Table 1.1 Comparison of annual runoff and sediment load for major rivers in the world

area (1000km2)

An Mean runoff (109m3)

An Mean sediment (109 t)

Average concentration kg/m3

Chapter 2

Thickness In Sediment Transport Model

2 1 Introduction

After the construction of dam, the clear water released from reservoir usually causes the downstream river to degrade One critical ingredient for the successful application of mathematical models to the degradation problem is how to predict the change of bed material size distribution during the degradation process and the final compositions of armoring layer The necessary condition for obtaining a gradual armoring of the bed is that at some time during the degradation process not all particles in a given mixture can be transported with a given flow Under this condition, the medium size of the bed material becomes coarser and coarser, and the total sediment transport rate decrease with time On contrary, if the flow is strong enough so that all the particles in the bed mixture can be moved, and equilibrium sediment transport condition can be obtained, no armoring of the bed takes place under such conditions

Sediment sorting and armoring has long been studied by many researchers in relation to river bed stability, sediment transportation and associated bed evolution, longitudinal and transverse bed topography, etc (Raudkivi et al., 1982; Shen et al.,1983; Ashida et al, 1971; Suzuki et al.,

19884); Parker, 1990 and Egashira et al., 1990) As far as bed-load and corresponding problems

are concerned, these have been solved numerically using governing equations for water as well as for a bed load equation of non-uniform sediment and mass conservation equations of bed sediment In the methods employed therein, it is very important how to evaluate bed-load transport rate of each grain size and sediment size distribution of bed surface

The study of bed armoring has progressed rapidly in terms of “so called exchange layer” proposed first by Hirano (1971) He introduced an exchange layer thickness in order to develop the mass conservation equation of each grain size in the bed surface layer, which enables us to compute sediment size distribution and bed load rates of non-uniform sediment bed In addition to this, Egiazaroff’s formula (1965) and its modified formula by Ashida and Michiue (1972) which predict incipient motion of individual particles were a key for developing these studies Since then, many valuable results have been proposed, and are illustrated in many textbooks, Walter (1984), Ning (1999)

In above mentioned studies, the exchange layer thickness is treated as a constant value in relation to reference sediment size; i.e maximum grain size, although it might be specified sometimes in situproblems, referring to height of sand waves Nevertheless, we have obtained valuable results on sediment armoring and sorting, lowering processes, etc However, most researchers may not think that “constant value” for the exchange layer thickness is reasonable from a view of sediment dynamics principle, because the bed-load layer thickness changes with bed shear stress In fact, it is well known that propagation speed of armor coat and lowering process of bed elevation (Hirano, 1971; Garde et al., 1977 and Little et al, 1976), formation process of sand bars (Jeaggi et al, 1982; Parker, 1991 and Takebayashi et al 1997), stability of river bends (Bridge, 1992) etc are very sensitive to the thickness of the exchange layer

2 2 Description of sediment transport models

2 2 1 Exchange Layer Model

Fig 2.1 Schematization of sediment exchange process on channel bed in an exchange layer model

In treating the sediment sorting numerically, a concept of the exchange layer (active layer) has been widely used in mobile-bed with sediment mixtures The exchange layer is defined as a upper

layer of stationary layer In this model, as shown in Fig.2.1, it is assumed that all material in the

exchange layer (denoted by E t) is homogeneously mixed, and all sediment particles of a given size class inside the exchange layer are equally exposed to the flow irrespective of their location in the layer It is difficult to determine the thickness of exchange layer Several relations are used in one-dimensional models (Mohamed-Abdalla et al 1986, Rahauel et al 1989) Many experiences suggest that the general method predicts experimental data well when the exchange layer thickness is specified properly, i.e to be equal to the maximum grain diameter, although there is not a universal criterion for determining it The governing equations are described as follows

A continuity equation of each grain size for the exchange layer is formulated as follows:

∂

∂ +

∂

∂

− +

z F f

E t

bk b

tk tk

x x

q

q bk bk ∆

∂

∂+

Et

(2.1)

the first deposited layer

A bed elevation is estimated by means of the following formula

k

bkx

q

1

0

The bed load transport rate for sediment of size class-k is estimated by the following relation

(Ashida and Michiue 1971, Liu 1991)

k

ck k

ck ek

/ 3

* 3

1 1

17

τ

τ τ

τ

In these equations, λ is the porosity of material of the bed layer (λ=0.4 as constant for simplify);

q bk is the sediment transport rate for size class-k ; s is the submerged specific weight of sediment;

d k is the diameter of sediment size class-k ; τ *k is the non-dimensional shear stress of sediment size

class-k; τ *ck is the non-dimensional critical shear stress of sediment size class-k ; τ *ek is the

non-dimensional effective shear stress of sediment size class-k

The non-dimensional critical shear stress of size class-k is estimated as follows (Ashida and

19 log

ck

d d

τ

k

m cm ck

cm

*

τ

(2.6)

d h

.2

1ln5.26

=

ττ

2 2 2 A new treatment of exchange layer thickness

Sediment transportation in rivers shows various regimes as general bed load and massive movement In an uni-direction of open channel where water discharge is supplied at some

constant rate, sediment flow over eroded bed is schematically shown in Fig 2.2 ( Egashira and

Ashida, 1992) If the bed slope θ is greater than some critical value θ c, sediment particles can be dispersed in whole flow area, for simplicity, called as a debris flow While the bed slope takes

value smaller than θ c, the upper clear water flow zone will separate from water sediment mixture area with the decreasing of bed slope, and then a bed load-layer will be seen clearly The motion

of each sediment particles takes such forms as saltation, sliding and rolling, when the thickness of sediment movement is in order of magnitude of particle size Generally, this regime of sediment transportation is called bed-load Finally, a pure water flow is formed over rigid bed if a bed slope decreases enough to small value so that all sediment particles can not be transported

Following above mechanism of sediment transportation, author tries to introduce a new idea,

a temporally and spatially changing bed-load layer instead of the constant exchange layer, into a general method as follows

(2.7)

Fig 2 2 Schematic of sediment transportation regimes

In Fig 2.3, the bed-load layer, bed surface and under-laying bed layers are shown

schematically In comparison with the exchange layer model, the present model can define the bed surface clearly as the boundary between the bed-load layer and the stationary layer, because the

thickness of the bed-load layer, denoted by E s, is evaluated to be a function of bed shear stress,

using a formula proposed by Egashira and Ashida (see Eq 2.11)

The continuity equation of each grain size for the bed load layer is given as follows

∂

∂

− +

∂

∂

x

q t

z F t

E f

bk s

∂

∂

t

E F f

t

f

dk k d k d

k

bkx

q

1

0

In these equations, f bk is the fraction of size class-k in the bed load layer, E d1 is the thickness of first

deposited layer, c b is the sediment concentration of the bed-load layer, E s is the bed-load layer thickness, estimated by the following equation (Egashira and Ashida, 1990):

(2.8)

(2.9)

(2 10)

b m

s

c d

E

*tantan

cos

θφ

=

in which d m is the mean sediment size of bed load, θ is the local bed slope, is the friction angle of

sediment and τ*m is the non-dimensional bed shear stress specified by d m

2 3 Prediction of sediment sorting and armoring

2.3.1 Experiment

To obtain flume data for testing two methods, an experiment was conducted in a straight open

channel, 14m long and 0.4m wide, which is shown in Fig 2.4 An initial bed which is 12cm thick

and 12m long is made smoothly, using non-uniform sediment whose size ranges from 0.5mm to

12mm The sediment size distribution is illustrated in Fig 2.5 A part of upstream reach is fixed to

avoid disturbances from upstream entrance, and at the downstream end, a controller is mounted to obtain uniform flow The flow condition was set so as to form parallel degradation as follows Unit width flow discharge and the initial bed slope are 0.075 m2/s and 0.0025, respectively Initial bed shear stress is almost equal to τ*c90, in which τ*c90 is the critical non-dimensional bed shear

stress of d90 Bed degradation processes were observed with no sediment supply

Measurements were conducted temporally for the water and the bed surface elevations, sediment transport rate at the flume end, grain size distribution of the bed surface material and so

on

The water surface elevation and the bed surface profile were measured at 1m interval along working area by using a point depth gauge with an accuracy of 0.1mm Sediment transport rate was measured by collecting sediment at downstream end Bed material was sampled in the surface area of about 49cm2 (7cm x 7cm) with the thickness of 1.2cm after measuring the bed surface profile at 3m, 8m and 13m from the upstream end The sampling tools are illustrated in

Fig 2.6

2 3.2 Computational method and prediction conditions

A backward difference numerical scheme is employed for the governing equations of flow,

(2 11)

φ

and a forward difference scheme is employed for the equations associated with sediment

Numerical computations are conducted using the present model (PM for simplicity) as well as the

well known exchange layer model (ELM for simplicity) In ELM method, the thickness of the

exchange layer is specified as 0.5dmax (dmax=1.2cm),dmax and 2dmax , respectively The

non-dimensional critical bed shear stress of d m is specified as 0.062 in all computations (1-λ)/2 is used

as c b in PM for simplicity

Fig 2.4 Experimental facilities

0 10

chemical parameters (e.g cation exchange, sodium absorption, pH) and physical

processes (e.g settling, deposition, consolidation, erosion)

It is hardly to take into account all of parameters in developing a numerical model to simulate the sediment transport problems Since the pioneer works in the 1970’s, numerous cohesive sediment transport models have been developed, the most popular for engineering applications being depth integrated models The last ten years have seen the emergence of efficient 3D models for estuarine applications or more complex situations (Sheng, 1983; Markofsky et al., 1986; Hayter and Pakala, 1989; Lanormant et

al., 1993; Teisson, 1997) But there are few models that can predict the sediment transport in a river reach with co-presence of non-cohesive and cohesive material alternatively

The main goal of the present chapter is to develop a numerical model which can predict the bed evolutions and bank shifting of alluvial rivers with material including non-cohesive and cohesive material In order to evaluate the influence of existing of cohesive material on bed variation, the model is constructed by adding alternatively

some cohesive material layers into bed layers of the model which stated in Chapter 2

In addition, the erosion rate formula for cohesive material is introduced, and a coefficient to describe the unsaturated bed load transport is proposed All equations are described in the boundary fitted orthogonal curvilinear coordinate system This method allows the model to be able to easily treat the computation of two dimensional bed deformations with complicate boundaries

3 2 Characterictics of Tan Chau Reach of Mekong River

Mekong River is the longest river in

South East Asia and twelfth longest in

the world It has great values to the

nature and the societies of the

Indo-China Peninsula The source of

Mekong River is in Tibet Mountains

and is called Dza Chu River (River of

Rock) After running through narrow

valley (paralleling Yangz Jiang and

Salween River), it reaches to

Yung-Nan Province of China where it is

called Lancang Jiang (Turbulent

River) Via Golden Triangle, the

crossing of China, Myanmer and Laos

boarder, then it flows into Vientiane

Plain and the last segment is Mekong

Fig 3.1 Mekong River basin

(Source: WUP-JICA report)

Delta in Viet Nam, which distributes grate influences to agriculture, especially paddy fields there With overall length of 4,800km, the catchments area of Mekong River is approximately 795,000km2 and an average annual runoff of 475,000 million m3 annually Fig.3.1 shows the morphology of Mekong River

River bank 1970 River bank 1990 River bank 2003 National Border

Downstream boundary

Upstream boundary

Study Reach

Fig 3.2 Bank lines measured in 1970, 1990 and 2003

The study reach is about 18km long, a part of the Mekong River, which is located at Tan Chau near the national border with Cambodia and 190km away from coast as

shown in Fig 3.2 Left bank of the reach in Thuong Phuoc has received strongest and

fastest erosion which takes place frequently not only in flood season but also in dry season Annual averaged erosion rate is estimated at about 30-50m/year Such bank erosion causes damages of more than 100 houses a year The bank erosion at northwest side of Tan Chau City is estimated at about 6m per year, which is not so large comparing to other places However, Tan Chau is populated densely and urbanized

much more than others Therefore, damages due to the bank erosion are serious As above circumstances, it is emphasized that bank protections and preferable countermeasures should be conducted

In 2001, Southern Institute of Water Resource Research - River Training Center conducted a research about erosion problems at several places But unfortunately, no reasonable methods have been proposed except temporary bank protections

3.2.1 Hydrology characteristics

Data of hydrograph and water surface elevation were provided by Mekong River

Commission Figure 3.3 shows water discharge at Neak Luong gauge station, located at

about 80 km upstream from Tan Chau reach The maximum discharge is 31,799m3/s in September and minimum one is 3,050m3/s in April, respectively Flood duration is about 7 months in which water level is rising during 3 to 4 months and lowering during

3 months Its maximum difference can be 4.5m between dry and flood seasons, as

shown in Fig 3.4 and 3.5 Therefore, flow velocity in flood season at some river reach

exceeds the specific critical velocity for long time The specific critical velocities that

are criterions causing active erosion are shown for bed and bank regions in Table 3.1

(Le, 1997)

Table 3.1 Cross-sectional average flow velocity and specific critical velocity for

threshold of active erosion

Specific critical velocity of bed erosion 0.5 0.43

Specific critical velocity of bank erosion 0.58 0.78

On the other hand, the Mekong Delta was formed in the duration from Old-Tertiary Period of Cenozoic (ten million years ago) to Pleistocene when the Himalaya Mountains appeared Thereafter, in the Quaternary Period, Indochina region was affected by sea expanding and 80% of the present Mekong Delta was submerged (Pham et al 1991)

Since then, the Mekong Delta may have been influenced by seasonal and daily changes

of hydrological quantities as well as by associated sediment transportation

0 5000 10000 15000 20000 25000 30000 35000

07/01 /80

07/22 /82

08/11 /84

09/01 /86

09/21 /88

10/12 /90

11/01 /92

11/22 /94

12/12 /96

01/02 /99

01/22 /01

02/12 /03

Fig 3.3 Water discharge of the Mekong River at Neak Luong gauge station (about

80km upstream from Tan Chau reach)

0.00 1.00 2.00 3.00 4.00 5.00 6.00

1979

1981

1-Jan- 1983

1985

2-Jan- 1987

1989

3-Jan- 1991

1993

4-Jan- 1995

1997

5-Jan- 1999

2001

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Jan

01- Jan

31- Mar

01- Mar

31- Apr

May

30- Jun

Jul

29- Aug

28- Sep

Oct

27- Nov

Dec

Fig 3.5 Water surface elevation at Tan Chau gauge station in 2000

3.2.2 Material distribution characteristics

Field surveys were performed in 2003 and 2005 to measure topography of river and

to collect bank and bed material Especially bed sediment was collected by diver along a deepest line at every 1 km spacing

Figures 3.6, 3.7 and 3.8 show the size distribution curves at left bank, right bank

and river bed, respectively As shown in these figures, the bank’s sediment is composed

of wide range of particle size from clay to fine sands, and the medium size is almost smaller than 0.1mm Whereas the bed sediment is much coarser than the bank’s one, and the medium size ranges 0.15 mm to 0.3mm These differences can be seen clearly in

Fig 3.9 in which distributions of mean diameter measured along study reach Such

differences in sediment size between banks and river bed suggests that fine sediment included in side banks , i.e finer than 0.1mm in diameter, is released once into flow, and thus transported far as wash load and that the sediment coarser than 0.1mm deposits onto bed and is transported as bed loads and suspended loads In addition, bank material

was investigated by core sampling as shown in Fig 3.10 It suggests that sediment at

side banks are affected much by erosion, deposition and channel shifting Coarse

sediment included in side banks, which can be seen partly in Fig 3.6 and 3.7, are may

deposited by flow recently

Fig 3.6 Grain size distribution of left bank material (surveyed on February in 2005)

Fig 3.7 Grain size distribution of right bank material (surveyed on February in 2005)

Fig 3.8 Grain size distribution of bed material (surveyed on February in 2005)