Experimental investigation of hydrodynamic characteristics of overland flow with geocell

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2012,24(5):737-743 DOI: 10.1016/S1001-6058(11)60298-9

EXPERIMENTAL INVESTIGATION OF HYDRODYNAMIC CHARACTERISTICS OF OVERLAND FLOW WITH GEOCELL* WANG Guang-yue School of Civil Engineering, Shandong University, Jinan 250061, China, E-mail: [email protected] LIU Yong-hui School of Automotive Engineering, Shandong Jiaotong University, Jinan 250023, China WANG Xin-hua School of Civil Engineering, Shandong University, Jinan 250061, China

(Received March 4, 2012, Revised March 28, 2012) Abstract: The hydrodynamic characteristics of the overland flow with a geocell slope are different from those of traditional flows because of its special structure. In this paper, a hydraulic flume with different slope gradients is used to study the hydrodynamic characteristics of the overland flow with geocell. The differences of flow characteristics between the overland flow with the geocell slope and the traditional flows are studied, and the hydrodynamic characteristics are obtained, including the flow pattern, the flow velocity and the hydraulic friction factor for the slope flow with geocell under different flow rates and slope gradients. The results show that there is a positive power function relationship between the rill depth of the slope surface (h) and the drag coefficient of the Darcy Weisbach ( f ) . There is a positive logarithmic function relationship between the drag coefficient f number Red , and there is a negative power function relationship between the drag coefficient f

and the Reynolds

and the Froude number Fr .

Key words: geocell, overland flow, hydrodynamic characteristics, preferential flow

Introduction  The geocell, as shown in Fig.1, is a three-dimensional network structure, welded by the strengthened material of high-density polyethylene (HDPE). It can be built into a rigid body structure by stuffing soil material. The combination of geocell and grassland vegetation is a new style of slope protection, as shown in Fig.2. It forms a light mesh structure, to provide the friction and the lateral restriction to the adjacent soil, to decrease the water runoff, to change the slope flow direction and to reduce the flow velocity, resulting in the kinetic energy dissipation and the reduction of the slope erosion. Since the hydrodynamic characteristics of the overland flow on a slope with geocell are quite different from those of other flow types, it is necessary to study them, especially, by experimental * Project supported by the National Natural Science Foundation of China (Grant No.11072133). Biography: WANG Guang-yue (1963-), Male, Professor

methods.

Fig.1 The structure of geocell

In recent decades, the overland flows were much studied, both theoretically and by experiments[1]. The flow pattern is an essential part of the hydrodynamic characteristics of the overland flow, and is a focus issue in research. Jing and Hong[2] studied the flow pattern of the erosive overland flow through the fixed-

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bed resistance test and from the principles of hydraulics, and it is shown that the erosive overland flow virtually combines three kinds of flow patterns, the laminar flow, the transitional flow and the turbulent flow. Zhang[3] suggested that the flow pattern of the overland flow is alternately the transition flow and the turbulence flow. Pan[4] observed in experiments that the flow of the slope surface is almost always a laminar flow. Zhang et al.[5] proposed a new standard to decide the flow state through the theory of hydrodynamics and dynamics of sedimentation. Gao et al.[6] studied the hydrodynamic characteristics of the overland flow of the Yellow River through artificial experimental simulations of rainfall, and the results show that the overland flow is not a laminar flow, but in an unstable state. Sha and Bai[7] used the calculation formula of the kinematic viscosity coefficient of muddy water to study the Reynolds number of the muddy flow, and it is shown that the flow state is in the region of quadratic resistance law( Re ! 500 ), but it may be in the transition region when the slope is not steep. Dunkerley et al.[8] studied the measurement results of the average velocity of the laminar flow, and it is shown that the time range between the laminar flow and the turbulence flow is important in the simulation of the overland flow of a dry land. The drag acted on the slope flow were much studied[9,10], where the Darcy-Weisbach formula was used to calculate the drag coefficient, with the slope flow drag consisting of four parts, the particle drag, the shape drag, the wave drag and the rainfall drag. Wu et al.[11] studied the influence of the surface topography on the slope drag by the scouring experiment for a standard slope in an open country, and the relationship between the drag coefficient and the ratio of soil erosions was found to be one of logarithm. Ding et al.[12] found that the Reynolds number influences the drag coefficient, the variation trend is influenced by the slope gradient And the drag coefficient is reduced with the increase of the Reynolds number for a small slope gradient. Zheng et al.[13] shows that the runoff Reynolds number and the drag coefficient is in a parabola relationship, the drag coefficient and the Reynolds number have a positive power function relationship, the drag coefficient and the Froude number have a negative power function relationship. Cao et al.[14] studied the relationship between the overland flow drag coefficient and the slope, the discharge, the coverage rate and the flow regime systematically. It is indicated that the drag coefficient increases with the coverage rate in a power function manner. The relationship between the drag coefficient and the Reynolds number is in a negative way, which becomes more and more significant with the increase of the flow discharge. And the relationship between the drag coefficient and the Froude number is in a negative way, which becomes more and more significant with the increase of the coverage

rate.

Fig.2 Slope protection of geocell

Previous studies of the hydrodynamic characteristics of the overland flow focused more on the natural slope flow, the grassland flow, the woodland overland flow, but not so much on the overland flow on a slope with geocell. In this paper, the hydrodynamic characteristics of the overland flow with geocell are experimentally studied, with a hydraulic flume of various slope gradients and flow rates. The hydrodynamic parameters such as the flow pattern, the flow velocity and the hydraulic friction factor are analyzed.

1. Experimental methods The test device consists of a hydraulic flume and a water supply system. The flume is 5.6 m long, 1 m wide and 0.5 m deep, made of plexiglass and steel. A hydraulic rail variable slope system is adopted in order to change the slope gradients. The water supply system consists of a water storage tank, a pump, valves, pipes, and an electromagnetic flowmeter. The water is pumped from the water storage tank to a constant pressure tank, to provide a constant flow rate for the flume. The residual water flows back to the water storage tank through a return pipe. Three baffles are placed at the top of the flume to ensure an even flow, and they are 0.2 m high without openings, 0.5 m high with round openings of 0.01 m in diameter, and 0.5 m high with round openings of 0.005 m in diameter at the outlet, respectively. The testing configuration is shown in Fig.3. The slit has a maximum dry density of 1.869×103 kg/m3 and an optimum moisture content of 12.6% and is obtained through its content being sieved through a 0.01 m sieve before testing. The soil specifications are shown in Table 1. The geocell has a size of 0.4 m×0.4 m×0.15 m and a thickness of 0.0015±0.0001 m. The distribution area of the thread is 1.01 m×5.1 m. The weld pitch is 0.4 m, and the peel strength of solder joints is 104 N/m. The silt is watered to the saturated state so the

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Fig.3 Testing configuration Table 1 Specifications of testing soil 4

2. Experimental results and analyses

Grain diameter (10 m)

Percentage (%)

> 2.5

16.47

2.5-0.75

9.83

0.75-0.05

3.06

0.05-0.02

56.64

< 0.02

14.00

same inertial water content in every case is ensured. A 0.05 m thick slit is placed in the flume to ensure that the geocell is parallel to the slope surface. Then the slit for every cell is weighed. After the filling process, the surfaces of the slit are finished into a smooth shape. The fully saturated soil is kept in that condition for 12 h before the experiment in order to ensure the uniform distribution of the water content. The velocity of the flow is measured by the staining method, and the measurement region is located in a 2 m-3 m scope at the water flume end[15]. The Potassium permanganate is poured into the water flow through the plastic syphon, and the time of the staining water through the measurement region is recorded. The velocity of the water surface is obtained by dividing the measurement region length by the time. The measurement of the velocity is repeated 5 times, and the average is taken as the velocity of the water surface. The flux of the experiment is controlled by the electromagnetic flowmeter. Fifteen different tests were carried out. Five different values of the slope gradient(5o, 10o, 15o, 25o, 35o) and three different values of the flow rate (1.0 m3/h, 1.5 m3/h, 2.0 m3/h) were adopted. The coefficient of the kinematic viscosity  was obtained from the water temperature, and the flow around the Reynolds number was calculated according to the rill depth of the slope surface (h) , the water surface velocity (v ) and the coefficient of the kinematic viscosity.

2.1 Flow patterns of the overland flow The flow pattern is a basic parameter that concerns with hydrodynamic properties of the slope flow and is used to calculate the slope runoff and the sediment transport. Therefore, the study of the flow pattern plays a vital role in understanding the hydrodynamic erosion process of the slope with geocell.

Fig.4 Roll wave

Fig.5 Preferential flow

At the beginning of the experiment, the inertia force is larger than the viscous force, which leads to the unstable water movement. Then the roll wave

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Table 2 Testing results of hydrodynamic properties of overland flow Slope gradient

o

5

10o

o

15

o

25

o

35

Flow rate (m³/h)

Temperature (oC)

Velocity (m/s)

Rill depth (10–2m)

Red

1

18

0.3736

05902

2 071.578

1.5

11

0.3569

0.8819

2 464.376

2

18

0.3661

0.9356

3 217.993

1

18

0.3479

0.8806

2 878.248

1.5

11

0.3380

1.2764

3 335.909

2

18

0.3389

1.4654

4 665.765

1

15.5

0.2982

1.1945

3 145.531

1.5

11

0.2833

1.7189

3 812.750

2

16.5

0.3377

2.0318

6 208.278

1

15

0.3062

1.7488

4 672.623

1.5

14

0.3610

2.6812

8 211.004

2

16.5

0.3538

3.1030

9 933.418

1

15

0.3599

2.0595

6 467.836

1.5

13

0.3955

3.0489

9 952.459

2

16.5

0.4101

3.4119

12 660.33

appears, as shown in Fig.4. As the erosion progresses, especially, after the exposure of the geocell, the disturbance of the geocell on the flow becomes so significant that the flow direction changes, the water moves along the geocell edge, and a preferential flow is formed. A part of the kinetic energy of the flow is consumed on the geocell, resulting in the kinetic energy dissipation and the reduction of the slope erosion, and no continuous rills appear on the slope, as shown in Fig.5. With the increase of the erosion depth, a drop-sill type flow is formed, resulting in more significant flow disturbance and energy dissipation. The low Reynolds number in the traditional fluid mechanics can not be applied to a flow with the drop-sill pattern. The bed roughness becomes a major influential factor of the overland flow pattern[16]. Therefore, a Reynolds number for the turbulent flow in the sediment transportation mechanics is adopted here for the analysis of the overland flow pattern, Red =

and a turbulent flow pattern is shown. At the early stage of the discharge, the surface water loses its stability and roll waves are formed, resulting in a mixed flow and suspended sediments. The main reason of the water encroach and the silt transport is the emergence of roll waves[18]. In the later stage, a preferential flow is formed due to the increased drag from the geocell. The results are obtained in an ideal hydraulic flume. A turbulent flow pattern would be more prominent on a real slope with complicated topography. 2.2 The variations of flow velocity in runoff process The velocity is the most influential factor of the flow pattern and the sediment transport pattern. The variation of the velocity is not only related to the erosion mechanism, but also provides information for the water erosion prediction. The variations of the flow velocity (v) over time are shown in Figs.6-10.

ud

Q

where u is the average flow velocity, v is the kinematic coefficient of viscosity, and d is the bed roughness, which is equal to the rill depth (the erosion depth). As shown in Table 2, no laminar flow appears in all 15 tests since their Reynolds numbers are all larger than the critical value ranging from 800 to 1 000[17],

Fig.6 Flow velocity vs. time for a 5o slope

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the erosion, the geocell is exposed, resulting in the prolonged flow path and the increased flow resistance, so the flow velocity decreases. As the erosion progression is stabilized, the velocity eventually is leveled off. In addition, for a fixed slope gradient, the flow rate increases as the velocity increases. This is because that, at the inertial stage, the inertia force is dominant, and then the resistance from the geocell becomes much greater than the inertia force due to the increased erosion, and the influence of the flow rate on the velocity is reduced. Fig.7 Flow velocity vs. time for a 10o slope

2.3 Rill depth on geocell The flow on the slope with geocell is very different from other overlands. The water flowing along the geocell edge is a preferential flow. The rill depth is an important hydraulic parameter, which is determined according to a balance between the degree of the erosion and that of the scouring, and affects the energy dissipation and the flow velocity.

Fig.8 Flow velocity vs. time for a 15o slope

Fig.11 Rill depth vs. slope gradient

Fig.9 Flow velocity vs. time for a 25o slope

Figure 11 shows the relationship between the average rill depth (d ) and the slope gradient for different flow rates, which indicates a positive power function relationship between the average rill depth and the slope gradient. The effect of the flow rate on the average rill depth is related to the slope gradient. Table 3 Statistic analysis of formulas used to estimate the relationship between average rill depth and slope gradient

o

Fig.10 Flow velocity vs. time for a 35 slope

It is shown that the flow velocity decreases as the erosion progresses and reaches a stable value in about fifteen minutes. This behavior is related to the special structure of the geocell. At the early stage of the discharge, the slope is relatively smooth and thus its resistance to the flow is moderate. With the progress of

Flow rate (m3/h)

Regression

Coefficient of determination r 2

1.0

h = 0.1996 S 0.6616

0.996

1.5

h = 0.2899 S

0.6684

0.989

h = 0.3041S

0.6971

0.990

2.0

Table 3 lists the formulas used to estimate the relationship between the rill depth and the slope gradient, obtained through a statistical analysis. 2.4 Hydraulic friction factor The hydraulic friction factor can be expressed by

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the Chezy factor, the Maning factor and the Darcy Weisbach factor f [19]. The Darcy Weisbach factor is more accurate in describing the drag due to its good dimensional description. Therefore, the formula of the Darcy Weisbach factor f = 8 gR J / u 2 is adopted in this analysis, where f is the Darcy weisbach factor, J is the hydraulic gradient for an even flow, J = i = sin T , T is the slope gradient of the flume and R is the hydraulic radius. A thin water flow can be regarded as a two dimensional flow, and the hydraulic radius is approximately equal to the water depth h . The calculation results show that the Darcy Weisbach drag coefficient is related to the flow states, and the drag coefficient increases with the Red by a positive logarithmic function relationship, as shown in Fig.12. Figure 13 shows the relationship between the friction factor and the slop gradient.

friction factor and the slope gradient are in a power functional relationship for different flow rates. Although the regression coefficients for these formulas are different from one another, the coefficients of determination r 2 are all greater than 0.95. Since the rill depth increases as the slope gradient increases, the influence of the slope gradient on the resistance to the overland flow is reduced. The configuration resistance is dominant in our tests.

Fig.14 Hydraulic friction factor vs. Froude number

Figure 14 shows a negative power function relationship between the hydraulic friction factor and the Froude number. The hydraulic friction factor decreases as the Froude number increases. A larger hydraulic friction factor is resulted with a slower flow.

Fig.12 Hydraulic friction factor vs. high Reynolds number

Fig.13 Hydraulic friction factor vs. slope gradient Table 4 Statistic analysis of formulas used to estimate the relationship between rill depth and slope gradient Flow rate (m3/h)

Regression

Coefficient of determination r 2

1.0

h = 0.1995S 1.7343

0.976

1.5

h = 0.0461S

1.5412

0.962

h = 0.0434 S

1.5757

0.976

2.0

Figure 13 and Table 4 indicate that the hydraulic

3. Conclusions This paper mainly studies the hydrodynamic properties including the flow pattern, the flow velocity and the hydraulic friction factor of the slope flow with geocell under different flow rates and slope gradients. Fifteen different tests were carried out. Five different values of the slope gradient (5o, 10o, 15o, 25o, 35o) and three different values of the flow rate (1.0 m3/h, 1.5 m3/h, 2.0 m3/h) were adopted. The main conclusions are: (1) At the early stage of the discharge, because of the existence of geocell, the roll wave is firstly formed on the slope. As the erosion progresses, the disturbance of geocell on the flow becomes so significant that the flow path is getting longer, the water moves along the geocell edge, and a preferential flow is formed. Its flow pattern is turbulent. (2) Under the same slope gradient condition, the overland flow velocity decreases over time and then reaches a stable value in about fifteen minute. (3) Under the same flow rate condition, with the increase of the slope gradient, a positive power function relationship between the rill depth and the Darcy Weisbach hydraulic friction factor exists. (4) There is a positive logarithmic function relationship between the hydraulic friction factor and the

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Reynolds number, which means that the larger the drag, the larger the extent of turbulence will be. Also, there is a negative power function relationship between the Darcy Weisbach hydraulic friction factor and the Froude number, which means that the larger the drag, the smaller the velocity becomes.

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