Dampak Penempatan Groundsill

International Journal of Sediment Research 23 (2008) 28-43

The experimental study for the allocation of ground-sills downstream of check dams Bing-Shyan LIN 1 , Chao-Hsien YEH 2 , and Hui-Pang LIEN 3

Abstract The main purpose of this study is to understand the stabilizing effect of ground-sills on the riverbed through a series of flume model experiments. From results, although check dams have the ability to control upstream sediment transport, the mass energy produced by the free fall of the overtopping discharge still causes strong local scour downstream of the structure, and this scour leads to the instability of the check dam. Therefore, this study conducted model experiments on various types of serial ground-sills to determine the appropriate spacing to best protect the downstream bed. Based on the observations and analysis of channel geomorphology and sedimentation, this study concluded the following results: 1) Serial ground-sills reduces the sediment transport ability perfectly, especially under a mild channel gradient equipped with 2 -4 times the average channel width interval. But for steep slopes, it is suggested that the proper spacing should be shortened to 1 -2 times the average channel width. 2) Ground-sills can effectively protect the streambed from scouring under a suitable equipped condition and the concepts of guiding scour and riverbed inertia were used in the analysis of optimal ground-sill spacing. Key Words: Serial ground-sills, Sedimentation, Strong scour area, Riverbed inertia, Guiding scour

1 Introduction Ground-sills are the most commonly used lateral sediment control structures, combined with series of check dams, in Taiwan’s aiwan’s upstream areas for stopping streambed scour. scour. These structures not only stabilize the streambed against sediment scouring, but also help control the streambed gradient. Normally, the top elevation of the ground-sills is either at the same level or slightly higher (no more than 2m) than the streambed. To increase the effectiveness of streambed protection, ground-sills are normally built in a series for the purpose of longitudinal streambed gradient control, decrease of water energy, and lateral streambed stability. stability. In Fig. 1, hS and l S are the height difference and the distance between two

consecutive ground-sills. However, due to the structures’ blocking effects, water flow increases velocity and causes local scouring at the downstream face of ground-sills, which leads to large amounts of sediment scouring. More seriously, seriously, this strong scouring can easily damage the ground-sills’ foundations, foundations, causing the structures to fail (Pictures 1 through 6 are site examples of broken ground-sills in Taiwan’s channels). Due to the importance of ground-sills as river gradient control structures, this design problem has been an important issue for river stability and sediment control. In this paper, based on the results from flume

1

Ph.D. Candidate, Department of Civil and Hydraulic Engineering Institute and Construction and Disaster Prevention Research Center, Feng-Chia University, University, Taichung, Taiwan Taiwan 407, China, E-mail: [email protected] 2 Associate Professor & Corresponding Author, Department of Water Resources Engineering, Feng-Chia University, University, Taichung, Taiwan 407, China 3 Prof., Department of Water Resources Engineering, Feng-Chia University, Taichung, Taichung, Taiwan 407, China Note: The original original manuscript of this paper was received in June 2007. 2007. The revised version was received received in Nov. Nov. 2007. Discussion open until Dec. 2008. - 28 -

International Journal of Sediment Research, Vol. 23, No. 1, 2008, pp. 28-43

experiments and field investigations, the concept of the moderation of riverbed scouring by ground-sills is proposed and applied for the placement of the structures at appropriate intervals.

Fig. 1

Picture 1

Serial ground-sills

Local scouring at downstream channel bed of ground-sill

Picture 3

Picture 5

Scouring between dense allocation ground-sills

Scouring underneath ground-sill

Picture 2

Damage at the foundation of ground-sill by local scouring, leading to bank failure

Picture 4 Riverbed without ground-sill protect protection, resulting in downstream scouring

Picture 6

Scouring beneath riverbed bend ground-sill


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2 Literature review High gradient streams often exhibit a naturally formed step-pool architecture, which likely represents self-adjustment of the stream towards higher bed stability (Lenzi, 2001). From a channel’s longitudinal profile, the river morphology of a reach with ground-sills is similar to that of a channel with step-pools and pool-riffles. Mo (1987) indicates that from field observation of upstream Jhuo-Shuei River in Taiwan, step-pools are channel morphologic features of bed armoring and help decrease the water power which supplies sediment transportation, making the channel more stable. Whittaker and Jarggi (1982) claim that, when a riverbed is in an unstable state, it can easily form step-pools if flow discharge is significant and the size distribution of sediment extends in a relatively wide range. Meanwhile, according to Whittaker and Jarggi (1982) flume experiment results, a channel with a slope gradient over 7.5% and high flow discharge maintains its greatest stability by the formation of large boulder step-pools. Ashida (1983) identified the four requirements for the formation of a step-pool channel as: (1) a mixture of bed materials of different sizes, (2) turbulent flow conditions, (i.e. Froude number > 1), (3) moveable sediments smaller than the mean diameter of bed materials, and (4) a total shear stress of the flow smaller than the critical shear stress of the largest particle on the riverbed. Ho (1987) utilized Ted Yang’s unit stream power theory to calculate the sediment transport rate of a step-pool channel and found that about 50% to 85% of original sediment transport can be reduced by a step-pool sequence. The distance L between works or artificial steps can be estimated by applying the maximum flow resistance criterion, as determined by Abrahams et al (1995) in their laboratory. Abrahams determined that the relationship of the step height H , step length L , and bed mean slope S of the step-pool geometry from field data can be expressed as 1≤

H / L S

≤ 2,

(1)

while Wohl et al (1997) discovered the regression relationship of the step length, step height, and the sediment specific diameter S as p

L H

= 4.55S p−0.42 .

(2)

Chin (1989, 1999) concluded from various step-pool channel field investigations that step-pool channels are often stable channels mainly formed by high speed flow; and that the step length will be longer and the vertical height will be shorter if the channel is located downstream.

Fig. 2

Profile of step-pool structure

Lenzi (2002; 2003a; 2003b) investigated 29 drop structures in a mountain river in the Italian Alps with nondimensional parameters where maximum scour depth and scour length were normalized to the drop height. Prior laboratory data revealed a pattern similar to field scours, where complex interactions occur between drop height, critical flow depth, and step spacing. The linkage between scour length and depth is also discussed, suggesting that there may be a maximum step height for impinging jets that is approximately twice the drop height. This maximum may explain the upper limit of the steepness factor found in high-gradient step-pool streams. Similar to the step-pools formed by natural stream flow, appropriate allocation and design of serial ground-sills shows certain effects on sediment control and channel stabilization. Ikeya (1977) investigated the interval of ground-sills based on the concept of a stable bed gradient.The relationship between the interval of ground-sills and the design channel gradient was explored based on the results of field investigation. Izumi (1984), discussed the function of bed control based on flume experiments with - 30 -


variables of ground-sill interval, height, flow discharge, and bed material composition. He found that a higher effective height of ground-sill and an increased number of structures decreases sedimentation. Kimura, Takahashi and Hisao (1990) derived a theoretical formula of appropriate ground-sill interval under the assumption of a rectangular channel section for meandering streams. Chang (1994) verified that channel-traversing structures like ground-sills can increase the roughness of the streambed, decrease the mean flow velocity, and reduce streambed shear force (thus reducing sedinment movement). They also verified that serial ground-sills outperform a single check dam from the perspective of economy and sediment control in steep and narrow channels. Furthermore, they applied the concept of bed resistance distribution to identify the relationship of the shape resistance of ground-sills and their construction density in a rigid streambed. Huang (1995) determined through flume experiments and field investigation the relationships between ground-sill interval and several physical sediment parameters, including: downstream total sediment transport, velocity of sediment-laden flow, Reynolds number, Froude number, and bases on the dynamic equilibrium theory. In Taiwan, the Technical Regulations for Soil and Water Conservation (2003) defines the design interval of ground-sills with the following formula: 1 (3) L = h n−m where, L is the interval of ground-sills (in meters), m is design channel slope (%), n is the original channel slope, and h is the effective ground-sill height. Although ground-sills have the ability of controlling the riverbed souring problem, they also have a negative impact on the downstream channel stability. Ashida et al., (1983) compared a riverbed before and after the implementation of ground-sills and found that the streambed upstream of the ground-sills received the expected outcome in scouring control, while the average streambed souring depth increased downstream of the protected sections. Lenzi (2004) considered grade-control works in steep rivers which are typically built in staircase like sequences. These are generally called check-dams when their crest is more than 1.5–2 m higher than the original bed level, and bed sills if lower. Jets plunging over structures’ crests diffuse their energy in turbulent rollers inside the pools below. Lenzi (2004) reviewed Gaudio’s (2000) dimensional analysis to obtain predictive formulas for clear-water, long-term scour hole dimensions in gently sloping rivers. Lenzi et al (2002) generalized their result to cover steep channels:

⎛ a ⎞ = 0.4359 + 1.4525⎜⎜ 1 ⎟⎟ H S ⎝ H S ⎠ y S

0.8626

1.4908

⎛ a ⎞ + 0.0599⎜⎜ 1 ⎟⎟ ⎝ Δ D95 ⎠

(4)

where ys = maximum scour depth; H s = specific critical energy; D95 = grain size for which 95% of the sediment in weight is finer; D = sediment relative submerged density; and a1 = morphological jump given by a1=(S-S eq)/L (5) where S = slope between bed sill crests; S eq = bed slope at the equilibrium; and L = sill spacing. Eq. 4 was obtained by multiple regression on low and high-gradient flume data with the experimental range: 0.225
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6) implies that, beyond a certain value of hc /L, the relative scour length can be increased only by much larger flow rates than below that point; that is, a physical upper limit may exist to the ratio l /L s . Moreover, the scour length would not be related to the channel slope. From all the non-dimensional plots shown above, it is apparent that bed slopes – initial and at the equilibrium – affect scour dimensions and act together to the creation of the morphological jump a1 (Equation 5). The above mentioned results of Lenzi et al (2002; 2003c; 2004) were basically based on a single length of bed sills or step pool structure, and water depth was considered an important factor of the bed scouring effect. Therefore, in this research, only the discharge for sediment transport was added. For the literature described previously, the discussion of ground-sills focused mostly on the interval, streambed scouring problems, and bed stabilization; while the scouring discussion about unprotected channels is seldom found. Therefore, this study, based on flume experiments and field investigation, intended to achieve several objectives: (1) define the effectiveness of serial ground-sills on bed scouring mitigation, (2) solve the local scouring problem at the downstream end of ground-sills, and (3) provide an appropriate design interval for ground-sill construction.

Fig. 3

Comparison of riverbed difference with and without ground-sill setup

3 Flume experiment Flume experiments were used in this study to explore the relationship between the configuration of serial ground-sills and the process of scouring.

3.1 Assumptions Several assumptions were made to simplify this complex problem for the flume experiments as follows: (1) Non-sediment-laden flow: This assumption often fails in natural streams. However, clear water carries more sediment than sediment-laden flow. Therefore, the channel erosion under clear water can be thought of as the maximum erosion in this study. (2) When the sediment output is less than 5% of the maximum sediment output in that single run, it is assumed that the channel is under the static equilibrium of sediment transport and the experiment stops. (3) If the interval of ground-sills is larger than 20 times the bed width, the downstream local scouring of one single ground-sill is not affected by the next downstream ground-sill. (4) The shear stress of the glass flume side wall is neglected as long as the water depth and channel width ratio is under 0.2 (Zuo, 1984; Hui and Wang, 1999). (5) For field practice, flume scaling is considered referring to relative bed width. Therefore, the restriction for our flume setup was 20 times bed width, and bed slope was limited to 3 degree (5.24%). 3.2 Experiment settings The inclined flume used in the study is 5.76 meters long, 0.08 meter wide and 0.25 meter high. Before the experiment, the experimental portion of the flume was paved with 15 cm of loose bed materials, ranging in size from 0.15 mm to 6.3 mm, for a 3.2 meter length. With boards, 2 mm thick, as ground-sills. The observed channel was equipped every 0.2 meter, 0.4 meter, 0.8 meter, 1.6 meters, and 3.2 meters for - 32 -


different serial ground-sill settings. The top of each ground-sill was controlled to the elevation of the streambed. For comparison, three kinds of channels were used in the research to define the scouring mitigation efficiency of ground-sills: no ground-sills, partial-region with ground-sills, and full-region, shown in Fig. 4, Table 1 and Fig. 5. With saturated sediment at the observation zone, the flume was supplied with a pre-defined discharge for the scouring process. The scouring sediment was collected every 30 second at the end point of the flume until the sediment output dropped to less than 5% of the maximum level of sediment output for that run. At that point, the water supply was disconnected, the scouring time was recorded, and longitudinal cross sections of the flume bed were surveyed at 1 centimeter intervals. By changing one of the experimental variables (i.e. the flume gradient, ground-sill interval, or discharge) the flume experiment was repeated until all the combinations were observed.

Fig. 4

Lab flume graph (A: Water tank B: Water pump C: Stainless filter net D: Inlet pipe E: Backwater pipe F: Bee cone type water control device G: Head water controller H: Backwater tank)

Fig. 5A

No ground-sill equipped

Fig. 5B

Fig. 5C

Full-region test

Partial region test


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Table 1

Flume test control factor

Variable

Quantity

Discharge ( l / s )

0.540 (Large)

0.290 (Median)

、

20

Ground-sill interval L (cm)

40

、

Protection length Lo (cm)

80

、

160

、

160

320

、

320

、

Gradient ( o )

Sed.

0.089 (Small)

、

1, 2, 3

D50 (mm)

Dm (mm)

D90 (mm)

Dmin (mm)

Dmax (mm)

1.11

2.05

5.12

0.15

6.3

3

ρ S (g/cm

2.28

)

σ g =

d 84 d 16

3.16

3.3 Average scouring rate To define the amount of sediment scoured from the flume, the average scouring rate ( S r ) was calculated as the scouring sediment volume in unit time using the following formula. V S = s

r

(7)

A t

where, V s is the scouring sediment bulk volume, A is the scoured area, and t is the equivalent total scouring time. With this formula, S ro , S rf , and S rh represent the average scour rates of the flume conditions without ground-sills, full region, and partial region, respectively. The reduction rates of the sediment scouring rate can be expressed as: X = 1 − S rf / S ro (8) Y = 1 − S rh / S ro .

(9)

The larger X or Y , the more stable of the flume is protected by the ground-sills for controlling and ceasing sediment transport. (Consider: Greater values of X and Y correspond to increased stability of the flume bed, and increased ground sill protection for controlling and stopping sediment transport.) 4 Discussion From the results under different experimental conditions, the responses of the flume riverbed in terms of morphology are discussed in the following sections.

4.1 Local scouring phenomenon Lateral structure on a riverbed are mainly for the purposes of preventing longitudinal scour and decreasing the river’s kinetic energy. But in fluvial channels, local scouring often occurs downstream of the lateral structure, (Figs. 6 -8). As the slope increases, the depth and length of the local scouring area increases (Table 2). From analyzing riverbed scouring and equivalent slopes, the gradient downstream from the local scouring area becomes more mild than the original bed slope. Therefore, the tendency of the bed slope is to adjust toward a more stable slope.

Fig. 6

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Channel profile under slope of 1°


Table 2

Bed slope 1 degree(0.0175) 2 degree(0.0349) 3 degree(0.0524)

Fig. 7


Fig. 8


Scour hole diameter under different gradient and flow condition Scour depth / Scour length (cm) / Equivalent slope Large flow Medium flow 3.6 / 14 / 1.12 2.2 / 12 / 0.96 8.2 / 16 / 1.82 5.1 / 15 / 1.66 15.6 / 28 / 2.45 8.2 / 18 / 2.11

Small flow 1.5 / 10 / 0.79 2.8 / 12 / 1.05 5.9 / 12 / 1.37

4.2 Scouring patterns of serial ground-sills To mitigate local scouring and its threat to structure safety protection facilities are often applied to control the scouring at the downstream face of the structure. Based on experimental results (Figs. 9 to 17), the channel bed profiles under different combinations of variables (i.e. bed slope, flow discharge, and ground-sill interval) indicated that the magnitudes and depths of the local scouring area downstream from the serial ground-sills decreases with increasing resistance of the water flow over the ground-sills. Table 3 and Table 4 are the tabulated results of the experimental data illustrated in Figs. 9 to 17. Status regression reveals that relative scour depth increases as the ground-sill interval lengthens, so does the relation appear as bed slope increases. However, a bed slope of 2 degrees produce the scour hole length of less than twice the bed width, positioned furthest from the ground sill, and with the greatest depth. When the bed slope is mild (1 degree), the respective scour hole becomes the smallest―which indicates that the lateral structure has the ability to control sediment under the above mentioned conditions. Table 3

Depth 2X 2XNPA 4X 4XNPA 7X 7XNPA

SF 0.063 0.000 0.050 0.013 0.150 0.000

Test results of the largest relative bed-surface scour-hole depth downstream of the ground-sill series with different equipped ground-sill setup interval 1 degree 2 degree 3 degree MF LF SF MF LF SF MF 0.125 0.288 0.150 0.225 0.350 0.188 0.238 0.025 0.063 0.088 0.288 0.563 0.275 1.450 0.125 0.350 0.163 0.350 0.575 0.350 0.575 0.038 0.150 0.013 0.238 0.700 0.750 1.300 0.225 0.338 0.100 0.163 0.613 0.600 0.675 0.000 0.000 0.000 0.325 1.175 0.038 0.100


LF 0.263 1.675 0.738 1.963 0.950 0.525 - 35 -

Table 4

Test results of relative bed-surface scour-hole position downstream of the ground-sill series with different equipped ground-sill setup interval 1 degree 2 degree 3 degree Position SF MF LF SF MF LF SF MF 2X 0.375 0.750 1.250 0.500 1.000 1.250 0.375 0.750 2XNPA 0.125 0.125 0.188 0.250 1.250 1.500 0.375 0.625 4X 0.500 0.625 1.125 0.625 0.750 1.063 1.000 1.625 4XNPA 0.063 0.125 0.500 0.013 0.375 0.625 0.500 0.625 7X 0.750 1.000 1.250 0.375 0.625 0.688 0.875 1.063 7XNPA 0.000 0.000 0.000 0.000 0.250 0.750 0.013 0.063 *Small flow (SF), Medium flow (MF), Large flow (LF) *Non-protected area (NPA) *16cm = 2 times bed width interval, 32cm = 4 times bed width interval, 56cm = 7 times bed width interval.

LF 0.875 0.750 2.000 0.875 1.375 0.275

4.3 Guiding (transferring) scour Although serial ground-sills do have the ability to increase the resistance force of the flow and reduce the total sediment transported within the protected reach, the scouring downstream of the last ground-sill becomes enormous, as shown in Figs. 9 to 17 for the flume bed with partial-region ground-sills. Defined as the reduction rates of the sediment scouring rate, Equation (6) and (7) were applied to compare the results from the conditions of full region ground-sills and partial region ground-sills. As shown in Fig. 3, the channel with partial region ground-sills encountered higher sedimentation than that with full region ground-sills under the same experimental settings. This means that the ground-sills controlled the riverbed scouring in the protected reach, but more sediment was scoured away at the unprotected area resulting in a deeper crater. This phenomena was also reported by Michiue and Susuki (Ashida et al, 1983). This special relocation and increased scouring accompanying ground-sills is termed “transferring scour” in this paper. Even though it is impossible to establish ground-sills throughout the entire channel, an appropriate allocation of partial ground-sills can transfer the energy for potential scouring from one area to another with a more solid riverbed, milder slope, or larger bed materials so that the energy will not cause uncontrollable sedimentation.

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Fig. 9

Channel profile with 16cm ground-sill interval under slope of 1° (No ground sill setup downstream 160cm)

Fig.10

Channel profile with 16cm ground-sill interval under slope of 2° (No ground sill setup downstream 160cm) International Journal of Sediment Research, Vol. 23, No. 1, 2008, pp. 28-43

Fig. 11


Fig. 12


Fig. 13


Fig. 14



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Fig. 15


Fig. 16


Fig. 17


4.4 Average scour rate and ground-sill interval relationship From the perspective of potential energy, the motion of sediment particles is caused by shear force from the flowing water such that the flow loses energy to provide the kinetic energy needed for bed load sedimentation. Therefore, the loss of potential energy for the unit width and length of water can be expressed as (10) W = γ RUS 0 = γ q S o . where W is the energy loss for transporting bed load over a unit of bed width and length with dimension of [ M / T 3 ]; γ [ M / L2T 2 ] is the water density; and q [ L2 / T ] is the unit width discharge (q = Q / B) ; S o

is the slope gradient of the riverbed. Chain and Wan (1991) defined the critical unit width and length energy loss for bed load transport W C based on the following formula: γ ⎛ γ s

W c = k ⎜⎜ g ⎝

where, - 38 -

γ S

is the sediment particle density;

− γ γ

γ

⎞ gd ⎟⎟ ⎠

3/ 2

(11)

is the water density; d is the specific sediment


diameter; and k is an undefined constant number. From Equations (10) and (11), the effective bed load transport per unit bed width and length energy is defined as W − W C , where sediment particles begin to transport as the value of W − W C increases.

Consequently, the average riverbed scour rate is related to

the flow conditions and characteristics of channel bed materials. This relationship can be expressed as (12) S r = f 1 (W , W c ) . In addition, after setting up ground-sills at different specific intervals, the riverbed scour rate changes due to the changes in flow conditions and the critical condition of sediment transport, such that the average riverbed scour rate can be formulated as S r = f 2 (W , W c , l , l o , g ) (13) where, l o is the ground-sill protected range,

l

is the ground-sill interval, and g is the gravitational

acceleration. In Figs. 9 to 17, the relationships among average scour rates and stream power under different ground-sill intervals, sediment size, and slope gradients illustrated that a higher stream power corresponds to a higher scour rate. With experimental data, the constant number k in Equation (11) was calculated as an average value of 1.08. When different ground-sill intervals and riverbed gradients were applied, the slopes of the curves varied and these results revealed that the average scour rate is affected by the factors in Equation (14) as well as the riverbed gradient. Therefore, the difference in average scour rate can be expressed as a function including the slope gradient of the reach where the ground-sill series is constructed: ΔS r = S r ο − S rf = f 3 (W , W c , l , l o , S o , g ) . (14) where S ro and S rf represent the average scour rates of the flume conditions without ground-sill and full region. Four dimensionless parameters were further formulated through dimensional analysis as W − W c l o − l ΔS r , , S o ) = f 4 ( W c lo gl

(15)

Based on the flume experiment results, the coefficients were determined and used to modify the theoretical Equation (13) into a compound regression equation; W − W c 0.83 l o − l 2.81 ΔS r = 8 ×10 −5 ( ) ( ) ( S o )1.23 (r 2=0.92) .(16) W c lo gl with the coefficient of determination of the Equation (16) equals to 0.90, shown in Fig. 18. The regression

Fig. 18

Relationship of average scour rate to the combination of unit area energy loss due to ground-sill interval and slope gradient


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equation can define the scouring rate

S rf

under the conditions of

S o = 3.49 - 6.98% . Additionally, for a zero ground-sill interval (i.e.,

l = l o

0.0625 < l / l o < 1.0

and

) the average scour rate S ro

is equal to the scour rate S rf . 5 Optimal design interval for ground-sill series

5.1 Reasonable ground-sill interval The major function of ground-sills is to stop the longitudinal scour of the riverbed, to stabilize the riverbed, or to greatly increase riverbed resistance. In other word, the best interval for ground-sills must stop the scouring of the riverbed and yield the largest impedance. From test results shown in Table 3 (the geometric analysis of local scour ditches) the comparisons of the positions and depths of the largest scour ditches clearly shows the following: (1) As slope gradient increases, the riverbed scour depth increases and its location moves closer to the structure─affecting structural stability. (2) The optimal interval for mild slope (<2 degrees) ground-sills is 2 -4 times the river width. This interval can efficiently control the scour depth and guide away the plunging tail waters. (3) In steep gradient rivers ( ≥ 2 degree), condensed equipped ground-sill interval is not the best policy. But a ground sill interval less than 2 times the relative bed width shows better sediment control. (4) At the unprotected section, the scour depth also increases with the bed slope gradient. But the ground still interval under steep slope conditions must be changed to 1-2 times bed width for the greatest control of scour depth. 5.2 Riverbed scour resistant inertia (SRI) Laursen (1952) noted that the riverbed sediment scour rate is the difference between area sediment scour rate and upstream input sediment laden rate. As the scour depth and cross section increases, the scour rate decreases and approaches a constant value which is normally lesser than sediment-laden flux and runoff rate. However, different riverbed materials and boundary conditions will effect the riverbed scour rate. Therefore, the bed material and boundary condition make the river resistant to the deformation of the riverbed. As determined by Laursen (1952) and Wang(1998a & b), the riverbed inertia is expressed as dD = qb − qin . (17) I SRI dt where I SRI is the riverbed inertia; dD / dt is the deformation rate of riverbed average scour depth; qb is sediment-laden flux; and qin is the upstream sediment runoff rate. Because the dimensions of qb and qin are equal to [ M / TL ] and the dimension for [ dD / dt ] equals [ L / T ], the dimension for riverbed

inertia I SRI is therefore [ M / A ]. From Equation (17), since the riverbed inertia relates to the riverbed components and boundary conditions, therefore, in a reach containing ground-sills with different intervals, the riverbed inertia can be rewritten as q − qin = f (l / B) . (18) I SRI = b dD / dt Under a constant flow and sediment-laden flow condition, where qb is constant and qin is zero, the riverbed inertia for a riverbed without any ground-sills equals 1( I b = 1.0 ). Furthermore, the riverbed inertia for a riverbed with ground-sills can be expressed as (dD / dt ) n I SRI = . (dD / dt ) w

(19)

where, (dD / dt ) n is the average scour rate without ground-sills; (dD / dt ) w is the average scour rate with ground-sills; and I SRI is the ground-sill bed inertia which represents the increased resistance given to the riverbed by installing ground-sills. If the actual scour rate is less than that of the ground-sill protected - 40 -


reach under a given river flow and bed condition, the ground-sill riverbed inertia becomes very large. On the contrary, if the ground-sill riverbed inertia is small, the scour rate becomes remarkably high even with a small discharge. This implies that the riverbed can be easily scoured. In Figs. 19 and 20, the ground-sill riverbed scour resistant inertia is calculated for normal discharge and high stage water conditions; and varying bed slope gradients and ground-sill intervals. Based on the results from our flume experiments, the recommended optimal interval for ground-sills under mild slope conditions is between 2 -4 times the relative bed width; and 2 times the bed width for steep bed slopes. As noted previously, bed inertia can be estimated by the total scour depth. However, each riverbed has a maximum scour limit, therefore, ground-sills not only efficiently stop/reduce riverbed scouring, they also form a relative scour and deposit equilibrium state to protect the riverbed by increasing resistance or riverbed inertia, resulting in greater river or channel stability. Therefore, under a given flow condition, riverbed inertia is the indicator of riverbed stability or resistance. If the original difference between average scour rate and upstream sediment-laden flux is large but the actual measurement for scour rate is small, then this means that the riverbed inertia is significant. But if the riverbed inertia is small, then the riverbed can be easily scoured.

Fig. 19

Ground-sill riverbed scour resistant inertia (large discharge)

Fig. 20

Ground-sill riverbed scour resistant inertia (small discharge)

Acknowledgments Great gratitude first goes to the National Science Council of Taiwan, China for its funding of this study. The authors also express their appreciation to the graduate students of the Soil and Water Conservation Research Laboratory of Feng-Chia University for their efforts on flume experiments. Appreciation also goes to Jacob Christensen; an English native speaker currently lives in Taiwan for assistance in improving the English language in this paper. Reference Abrahams A. and Li G. 1995, Step-pool streams: adjustment to maximum flow resistance. Water Resources Research, Vol. 31, No. 10, pp. 2 593-2602. Ashida K., Takahashi T., and Michiue M. 1983, River sediment disaster and its’ treatment. Shen Ba Publish, pp. 255-321 (in Japanese). Chain N., Chang L., and Chow T. D. 1986, Riverbed Morphology. Science Publish (in Chinese). Chain N. and Wan T. H. 1991, Sediment Transport Mechanic. Science Publish, 3rdEd, Bejing, pp. 229 -261. (in Chinese). Chang H. H. 1980, Geometry of gravel streams. Journal of Hydraulics Division, ASCE, Vol. 106, No. HY9, pp. 1443–1457. Chanson H. 1994, Hydraulics of skimming flows over stepped channels and spillways. Journal of Hydraulic Research., IAHR, Vol. 32, No. 3, pp. 445– 460. Chanson H. 1995, Hydraulic design of stepped channels cascades, Channels, Weirs and Spillways. Pergamon Press: Oxford. Chanson H. 1996, Prediction of the ttransition nappe/skimming flow on a stepped channel. Journal of Hydraulic Research IAHR, Vol. 34, No. 3, pp. 421– 429. Chanson H. 1999, The hydraulics of open channel flows: an introduction. Butterworth-Heinemann: Oxford.


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