EXPERIMENTAL INVESTIGATION OF RHEOLOGY AND TRANSPORT CHARACTERISTICS OF HYPERCONCENTRATED FLOW

EXPERIMENTAL INVESTIGATION OF RHEOLOGY AND TRANSPORT CHARACTERISTICS OF HYPERCONCENTRATED

FLOW

Jau-Yau Lu^1*, Chih-Chiang Su², Jian-Hao Hong², Jin-Chuan Yang³, Chia-Yun Wang⁴

ABSTRACT

Due to steep terrain, weak geological formation and high rainfall intensity, hyperconcentrated flows frequently occur during typhoon seasons in Taiwan. The existing hydraulic facilities in Taiwan are usually designed based on the traditional open channel flow theories. The characteristics of the hyperconcentrated flow are quite different from the regular sediment-laden flow. Therefore, it is necessary to further investigate the flow characteristics and the transport mechanism of hyperconcentrated flow to avoid underestimating the flow stages during the floods.

In this study, soil physics tests were performed to investigate the characteristics of the soil samples collected from upstream landslide areas near the Chu-Hsiung Bridge of the Ton-Pu-Rey Creek, a tributary of the Cho-Shui River in Taiwan. The rheology tests were conducted using the Brookfield DV-III rheometer for slurry samples with sediment concentration varying from 24% to 50%. An ANN model with a back-propagation network (BPN) algorithm was adopted in this study to estimate the rheological parameters based on our data and the related existing data in the literature.

In addition, sediment transport experiments for the hyperconcentrated flow were conducted using a re-circulating flume with both mobile and fixed beds. The vertical velocity and concentration profiles were measured for different flow discharges and slopes. A sediment transport relations hip was developed based on our data and the existing closed conduit hyperconcentrated flow data.

Key Words: Hyperconcentrated flow, Reology, Bingham yield stress, Sediment transport

INTRODUCTION

Many hyperconcentrated flow phenomena occur in nature (e.g. rivers and reservoirs) and industry (e.g. sediment transport in pipes). Theoretically, hyperconcentrated flow can not be simply judged by the sediment concentration since the sediment gradation and mineral content may also have significant effects on the flow phenomena (Wan and Wang, 1994).

1 Professor, Dept. of Civil Eng., Nat. Chung Hsing Univ., 250 Kuo-Kuang Rd. Taichung 402, Taiwan.

(*Corresponding Author: Tel and Fax:+886-4-22853695. E-mail: jylu@mail.nchu.edu.tw) 2 Postdoctoral research fellow, Dept. of Civil Eng., Nat. Chung Hsing Univ.

3 Professor, Dept. of Civil Engrg., Natl. Chiao Tung Univ, 1001 University Road, Hsinchu 300, Taiwan 4 Master, Dept. of Civil Eng., Nat. Chung Hsing Univ.

When the volumetric concentration of sediment ranges between 0.02 and 0.2, particles may not disperse in the entire depth. It is called an immature debris flow by Takahashi (2007), and is similar to the hyperconcentrated flow.

Hyperconcentrated flow disasters frequently occur due to the typhoon induced floods or volcano eruptions. Taiwan has steep terrain and weak geological formation. Many debris flows and hyperconcentrated flows occurred after the Chi-Chi Earthquake (7.3 on Ritchter scale, 1999) because of the extreme floods caused by the global climate change, e.g.

Chen-Yu-Lan Creek and Ton-Pu-Rey Creek (tributaries of the Cho-Shui River) disasters due to Typhoon Bilis (2000) and Typhoon Toraji (2001), Tai-Ma-Li Creek disaster due to Typhoon Haitang (2005).

Wang (1984) conducted hyperconcentrated flow tests in a recirculating closed conduit. The velocity distributions and the variation of von Karman constant were discussed and compared with the data for Yellow River tributaries. Winterwerp et al. (1990, 1992) performed hyperconcentrated sand-water-mixture flow tests in a semi-recirculating flume over flat and erodible beds. For the high Froude number tests, it was found that anitidunes occurred on the channel bed. Cao et al. (2006) developed a hydrodynamic model to simulate the hyperconcentrated sediment-laden floods over the erodible bed.

The existing hydraulic structures in Taiwan are usually designed based on the traditional open channel flow theories. The characteristics of the hyperconcentrated flow can be significantly different from the regular sediment-laden flow, especially for very high sediment concentrations. The main objective of this study is to conduct the reologic and transport tests in the laboratories to increase our understanding of the characteristics of the hyperconcentrated flows. The experimental results can be used to simulate the bed evolutions in hyperconcentrated flow rivers (Yang et al., 2008).

SITE DESCRIPTION

Ton-Pu-Rey Creek is an important tributary of the Cho-Shui River. Fig. 1 shows the location map of the creek. The length, drainage area and the average bed slope of the creek are 18.5 km, 102.3 km², and 2.7%, respectively. The mean sediment size ranges from 53.4 to 108.9 mm after the Typhoon Toraji (2001). The soil belongs to silty sand (SM) according to the Unified Soil Classification.

Fig. 1 Location map of Cho-Shui River basin

METHOD

Rheological experiments

For the reology tests, the soil samples were collected at the landslide area upstream of the Chu-Hsiung Bridge of the Ton-Pu-Rey Creek. Only the sediment particles less than 2 mm were used. Fig. 2 shows a comparison of the particle size distributions for a sample at the landslide area and a laboratory sample to be described in the next section (Flume experiments). The median sediment size is about 0.125 mm for the field sample. The material finer than 0.074 mm (ASTM #200 sieve) for the landslide area upstream of the bridge was 21%. The rheology tests were performed using the Brookfield DV-III rheometer for sediment concentrations of 24%, 30%, 40% and 50%.

0.001 0.01 0.1 1 10

D (mm)

0 20 40 60 80 100

% finer

Ton-Pu-Rey Creek Field sample Laboratory sample

Fig. 2 Comparison of partical size distributions for field (D< 2 mm) and laboratory samples

Flume experiments

The experiments were conducted in a re-circulating flume of the Water Resources Planning Institute, Water Resources Agency in Taichung, Taiwan. Fig. 3 shows the side view of the flume. The flume is 8 m long, 0.5 m wide and 0.45 m high with glass side walls and a steel bottom. A 20 Hp pump was installed in the sediment settling basin to pump the sediment to the upstream end of the flume. In addition, an automatic sediment feeder was installed near the upstream end of the flume to add sediment when needed.

1 2 3 4

5 6 7 8

9 automatic sediment feeder

flume honey tube

downstream fixed bed movable bed

tailwater gate

guide pipe 10 11 12

13 14 15 16 sediment settling basin

trash rack water storage tank PVC pipe

pumping system

hinge supporting frame

head tank flow control

slope control jack 12

1 2

3 4 5

6 7

9

8

11 13

10 14

15

8 m 3.3 m

0.7 m

1 m 16

Fig. 3 Side view of recirculating flume

A Japanese SF-5311 type one-dimensional electro-magnetic velocimeter was used to measure the point flow velocities. A concentration sampler based on the siphon theory was adopted to measure the vertical concentration profile. The sediment used in the flume study was quartz sand with a median size (D50) of about 0.1 mm. The specific gravity (Gs) and the geometric standard deviation (σg) were 2.65 and 1.42, respectively. The particle size distribution of the sediment is plotted in Fig. 2 for comparison. A fairly uniform sediment was selected purposely to minimize the “wash load” problem in the sediment transport relationship. In fact, it has been proved by Wang (1984) that the nondimensional sediment transport relationship for the idealized uniform sand in the closed conduit is reasonably close to that for the graded sediment in the tributary of Yellow River with significant amount of fine material.

Two series of flume experiments were conducted. For the mobile bed experiments, a layer of sediment 0.2 m thick was placed on the flume bottom initially. Three slopes (0.5, 0.75 and 1%) and two flow depths (approximately 5 cm and 10 cm) were selected for the experiments.

However, for the milder slopes (0.75 and 0.5%), the actual flow depths were slightly lower than the designed values to avoid overtopping of the flows. In order to perform experiments with high sediment concentrations without highly unstable antidunes on the flume bed, a series of fixed bed experiments were conducted.

For the fixed bed experiments, the sediment were added gradually in the sediment settling basin, and the flume slopes were adjusted gradually until obvious sediment deposition occurred in the test section. Both vertical velocity and sediment concentration profiles were then measured at the centerline of the section 2 m upstream of the downstream end of the flume.

RESULTS AND DISCUSSION

Rheological properties of hyperconcentrated flow for fine particles (D < 2 mm)

Based on the experimental results for the landslide area near the Chu-Hsiung Bridge of the Ton-Pu-Rey Creek, two expressions were derived for the Bingham yield stress τ_B and Bingham viscosity μ_B as follows

[

]

exp 157 . 0 ) /

( ² _v

B dyne cm = × ×C

τ (1)

[

]

exp 047 . 0 )

( _v

B cp = × ×C

μ (2)

Eqs. (1) and (2) can only be applied to the landslide area near the Chu-Hsiung Bridge of the Ton-Pu-Rey Creek because of the complexity of the rheological behavior.

Recently, Artificial Neural Networks (ANNs) are widely applied to various disciplines to overcome the nonlinear relationships. Wang (2007) found that both the Bingham yield stress τB and Bingham viscosity μ_B can be expressed as functions of P0.01, P0.02 and Cv, i.e.

(

)

B = f P_0.01,P_0.02,C

τ (3)

(

)

B = f P_0.01,P_0.02,C

μ (4)

in which P_0.01 and P_0.02 are the cumulative percentages for particle sizes less than 0.01 mm and 0.02 mm, respectively, and Cv is the volumetric concentration (%). Similar to Eqs. (3) and (4), in this study the P0.01, P0.02, and Cv were selected as the input variables to predict the output variables τ_B and μ_B.

An ANN model with a back-propagation network (BPN) algorithm from the Matlab7.0 was adopted in this study to estimate the rheological parameters. Table 1 gives the ranges of the data collected by Wang (2007). The parameters including numbers of input data, hidden layer, and the neurons in the hidden layer for the best fitting of the results are given in Table 2. Figs.

4(a) and 4(b) are the comparisons of the measured and predicted Bingham yield stress and Bingham viscosity. For the verifications, the correlation coefficients are 0.932 and 0.939 for Fig. 4(a) and 4(b), respectively.

Laboratory hyperconcentrated flow experiments

Table 3 summarizes the experimental conditions of the laboratory hyperconcentrated flow experiments, in which S= bed slope, h= flow depth, C_v= average volumetric sediment concentration in the vertical, u = average flow velocity in the vertical, q = unit flow discharge, Fr = Froude number. The maximum average volumetric concentration was 25.4% for the fixed bed experiments. The Froude number ranges from 0.8 to 2.31. In general, the bed form was ripple for the subcritical flow condition, and it was antidune for the supercritical flow condition, which were consistent with Wintewerp et al.’s (1990, 1992) experimental findings.

(a)

1 10 100 1000 10000 100000

Measured, τ_Β (dyne/cm²)

1 10 100 1000 10000 100000

Predicted, τΒ (dyne/cm2)

Verification data, 50 sets I3H9O1, r = 0.932 Training data, 143 sets

I₃H₉O₁, r = 0.968 (b)

1 10 100 1000 10000 100000 1000000

Measured, μ_Β (cp)

1 10 100 1000 10000 100000 1000000

Predicted, μΒ (cp)

Verification data, 54 sets I3H13O1, r = 0.939 Training data, 139 sets I₃H₁₃O₁, r = 0.945

Fig. 4 Performances of ANN model for (a) Bingham yield stress; (b) Bingham viscosity

Table 1 Summary of available data

Data ranges for Bingham yield stress

P0.01 (%) P0.02 (%) Cv (%) τ_B(dyne/cm²)

13.5 – 69.8 21 – 76.7 12 – 62.5 5.7 – 9200.7 Data ranges for Bingham viscosity

P0.01 (%) P0.02 (%) Cv (%) μ_B(cp=0.01dyne/cm²⋅s)

13.5 – 69.8 21 – 79.5 12 – 62.4 7.5 - 183814

Table 2 Parameters of networks Rheological

parameters

Input data

Number of hidden layer

Number of neurons in the

hidden layer

Number of iterations training testing

τB 143 50 1 9 10000

μB 139 54 1 13 10000

Table 3 Experimental conditions of current hyperconcentrated flow study

Run No. h (m) S (%) Cv (％) u (m/s) q (m³/s/m) Fr Bed form

Mobile bed

M1 0.050 1 7.3 0.87 0.044 1.25 Antidune

M2 0.100 1 6.0 1.00 0.100 1.01 Antidune

M3 0.050 0.75 4.9 0.83 0.042 1.19 Antidune

M4 0.095 0.75 6.1 1.04 0.099 1.07 Antidune

M5 0.045 0.5 2.4 0.53 0.024 0.80 Ripples

M6 0.080 0.5 5.0 0.88 0.070 0.99 Antidune

Fixed bed

F1 0.053 1 1.8 1.56 0.083 2.16 －

F2 0.100 1 1.5 1.43 0.014 1.44 －

F3 0.058 1.25 3.5 1.72 0.100 2.28 －

F4 0.052 1.48 14.0 1.64 0.085 2.30 －

F5 0.049 1.66 25.4 1.60 0.078 2.31 －

Figs. 5(a) and 5(b) show the vertical sediment concentration profiles for the mobile bed and fixed bed experiments, respectively. The maximum sediment concentration for the fixed bed experiment ( = 25.4%) was higher than that for the mobile bed experiments ( = 7.3%). In Fig. 5(a), most of the concentration profiles are concave upward except Run M1, which has the highest concentration ( = 7.3%) and is slightly concave downward. In Fig. 5(b), the profile for Run F3 is also concave upward. However, the profiles for F4 and F5 ( = 14 and 25.4%) are concave downward, which are consistent with Wang (1984) and Chien’s (1989) finding that there was an inflection point in the concentration profile for the high concentration condition due to the sediment deposition. For Runs F1 and F2 with low concentrations ( = 1.8 and 1.5%) and a high slope gradient (S= 1%), the vertical concentration profiles are relatively uniform, indicating that the sediment particles behave like wash load.

Cv C_v

C Cv

v

Cv

Based on the open channel measurements with a laser Doppler anemometer, Nezu (1986) found that for clear water the mean value and standard deviation of the von Karman constant

= 0.412 0.11. In general, the velocity gradient of the vertical velocity profile increases and the von Karman constant decreases with an increase of the sediment concentration due to the damping of the turbulent intensity by the suspended sediment. The variation of

κ ±

κ κ

with sediment concentration was developed by Einstein and Chien (1954) based on the energy consideration, as shown in Fig. 6. The κ values obtained by regression for the mobile bed experiments are also plotted in Fig. 6 for comparison. The envelope curves (dotted curves) are added to the figure by the writers based on their original data in the figure. In general, it can be seen that results of our data are reasonably close to the original -E relationship developed by Einstein and Chien (1995).

κ

(a)

0 100000 200000 300000 400000

C (ppm) 0

0.2 0.4 0.6 0.8 1

y/H

mobile bed

S (%) h (cm) C_v(%) M1 1 5 7.3 M2 1 10 6.0 M3 0.75 5 4.9 M4 0.75 9.5 6.1 M5 0.5 4.5 2.4 M6 0.5 8 5.0

(b)

0 200000 400000 600000

C (ppm) 0

0.2 0.4 0.6 0.8 1

y/H fixed bed

S (%) h (cm) C_v(%) F1 1 5.3 1.8 F2 1 10.0 1.5 F3 1.25 5.8 3.5 F4 1.48 5.2 14.0 F5$ 1.66 4.9 25.4

Fig. 5 Vertical sediment concentration distributions for (a) mobile bed; (b) fixed bed

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 von Karman constant, κ

0.0001 0.001 0.01 0.1

0.0002 0.0004 0.0006 0.0008 0.002 0.004 0.006 0.008 0.02 0.04 0.06 0.08 0.2

E = ρs-ρ ρsΣωC uS

Hyperconcentrated flow Mobile bed 0.3

0.00004 0.00006 0.00008

Fig. 6 Comparison of measured κ values with Einstein and Chien’s (1955) relationship

Fig. 7 shows a comparison of the computed ( ) and measured ( ) sediment concentration profile exponents, Rouse number Z values (Rouse, 1937) for the mobile bed experiments. The

values were obtained from the measured velocity profiles. The fall velocity values were calculated based on Richardson and Zaki’s (1954) formula for concentration corrections, i.e.

Zc Z_m

κ ω

m

Cv) . 1 (

0

− ω =

ω (5)

in which is the fall velocity for clear water calculated by Rubey’s (1933) equation. An exponent m value of 7 was adopted in this study. The computed values, in general, are fairly consistent with the measured values, though slightly lower than the 45° line. In fact, qualitatively this is consistent with Eistein and Chien’s (1954) finding.

ω0

It was found that for the mobile bed experiments antidunes occurred periodically except for Run M5, which has the lowest Froude number (Fr = 0.8, see Table 3). Fig. 8 shows the comparisons of our data with three graphical solutions, including Simons and Richardson (1966), Garde and Albertson (1959) and Athaullah (1968). It can be seen from Fig. 8(c) that Athaullah’s (1968) method gives fairly consistent predictions with our observations.

0 0.4 0.8 1.2 Z_c=

1.6 ω

κu_* 0

0.4 0.8 1.2 1.6

Zm

Hyperconcentrated flow Mobile bed

Fig. 7 Comparison of measured and computed Z values for the mobile bed experiments

(a)

0 0.10.20.30.40.50.60.70.80.9 1 D50 (mm)

0.001 0.01 0.1 1

0.002 0.004 0.006 0.008 0.02 0.04 0.06 0.08 0.2 0.4 0.6 0.8 2

Stream power(τ0u ) in foot pounds per second per square foot

Antidunes & Flat bed

Tranisition

Dunes

Flat Ripples

3 (b)

0.01 0.1 1

Fr= u

√gh 0.01

0.1 1 10

τ∗= τ (γs−γ)D50

Ripples &

Dunes

Tranisition Antidunes

(c)

10 100 1000 10000

R/D50 0.1

1

0.2 0.4 0.6 0.8 2 4 6 8

Fr

Antidunes Tranisition

Dunes

Fig. 8 Comparisons of measured data with different bed form graphical solutions: (a) Simons and Richardson (1966); (b) Garde and Albertson (1959); (c) Athaullah (1968)

Fig. 9 gives a comparison of the sediment transport relationships for our experiments and Wang’s (1984) closed conduit hyperconcentrated flow study using a dimensionless stream power type parameter [γ_m/(γ_s −γ_m)⋅(U³/ghω)], in which γ_m and γ_s are the specific weight of water sediment mixture and specific weight of sediment particles, respectively. The median sizes of the sediment (0.1 and 0.15 mm) for both studies are reasonably close. It can be seen that for [γ_m /(γ_s −γ_m)⋅(U³/ghω)]< 1000, the data points for the mobile bed (solid

circles) and the fixed bed (hollow circles) can be considered as the upper envelope and lower envelope curves, respectively for Wang’s closed conduit data. In other words, for a given flow condition, the sediment concentration for the mobile bed was higher than that for the fixed bed. This is probably due to the fact that the measuring section located on the downstream side of a sand wave may have significant amount of overloading sediment entrained by the flow from the lee side of an antidune occurring periodically. Based on Wang’s (1984) closed conduit data and the data collected in this study, an empirical sediment transport relationship for the hyperconcentrated flow is developed as follows

[

]

ln

3

⎟⎟−

⎠

⎜⎜ ⎞

⎝

⎛

ω γ

− γ

× γ

= gh

C U

m s

m

v (6)

The correlation coefficient is 0.76. The equation can be further improved when more data for wider flow and sediment ranges are available in the future.

1 ^{2 5} 10 ^{20 50} 100 ^{200 500} 1000 ^{2000 5000}10000

γ_m γs-γm ^U

3

ghω 1

10 100

2 3 5 20 30 50

0.5 Cv(%)

Wang (1984): closed conduit, D50 = 0.15 mm, Gs = 2.92 mobile bed

ln[Cv (%)] = 0.501×ln( γ_m γ_s-γ_m ^U

3

ghω) -0.98 fixed bed

Current study: flume, D50 = 0.1 mm, Gs = 2.65

Fig. 9 Comparison of sediment transport relationships for current study and Wang’s (1984) closed conduit hyperconcentrated flow study

CONCLUSIONS

Both rheology and sediment transport experiments were conducted to explore the characteristics of the hyperconcentrated flow. A Back-Propagation Neural Network (BPN) mode was adopted and gave reasonably good predictions for the rheological parameters (Bingham yield stress τ_B , and Bingham viscosity μ_B ). In addition, a sediment concentration-flow intensity relationship (Eq. 6) was derived based on the data collected in an open channel and a closed conduit. The results can offer useful information for the development of a numerical model for simulating the bed evolutions in hyperconcentrated flow rivers.

ACKNOWLEDGMENTS

This research was supported by the Water Resource Agency, Ministry of Economic Affairs of

R.O.C.

REFERENCES

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