Introduction

Debris flow is a common geological disaster that occurs in mountainous areas. Debris flow has the characteristics of high velocity, large density, and strong impact that pose serious threats to properties and people on the path of its movement (Iverson et al. 1997). Engineering measures are used to mitigate the risk of debris flow, which include check dams (Huebl and Fiebiger 2005; Mizuyama 2008), slit dams (Armanini and Larcher 2001), flexible net dams (Bichler et al. 2012; Volkwein et al. 2015), drainage channels (Chen et al. 2001; Wang et al. 2012a, b), debris-flow basins (Gems et al. 2014), and debris-flow deceleration baffles (Choi et al. 2014; Ng et al. 2015a, b; Wang et al. 2017a).

Debris-flow countermeasures can be selected from the aspects of structure, material, deformation, size of the opening, and cost of construction. For example, check dams are mainly concrete gravity dams, which can retain solid materials through the storage capacity, and can effectively prevent gully erosion. However, the check dam has deep-buried depth, large cross section, long construction time, and relatively high cost (Chen et al. 2013; Cui et al. 2018). The slit dam has a good effect of blocking coarse and discharging fine particles. This type of dam can block the boulders larger than the width of the slit and effectively reduce the risk of debris flow (Lien 2003; Zhou et al. 2019). The flexible net dam is suitable for the small width of the valley, which is used to block the boulders or solid materials with large particle size in the debris flow. Moreover, it has the characteristics of convenient construction and a good landscape (Ashwood and Hungr 2016). The drainage channel can make the debris flow leave the protected area quickly, which has the characteristics of simple structure and good protection effect (You et al. 2006). Baffles can be used to reduce the velocity and impact force of debris flow. It has the characteristics of a flexible layout and convenient construction (Choi et al. 2020). There are many types of debris flow engineering measures, and each structure has its own function and application conditions. In engineering practice, one or more structures can be used together according to the needs of debris-flow prevention.

A debris-flow deceleration baffle is a kind of energy dissipation engineering countermeasure structure constructed in mountainous areas or a drainage channel (Choi et al. 2015). They are used to reduce the velocity and impact of debris flow to protect people’s life and property. Moreover, the baffle models are used to study the phase separation mechanism of debris flows (Wang et al. 2019; Liu et al. 2020). The drainage channel is an engineering system for a debris flow to pass through the protection zone rapidly (Chen et al. 2017; Li et al. 2020). It is a simple structure, convenient for construction, and it plays an important part in the comprehensive prevention and control of debris flow. In certain specific cases, the deceleration baffles are arranged in the debris-flow drainage channel to reduce the velocity and energy of debris flows (Chen et al. 2015).

The construction design of the debris-flow drainage channel is related to the terrain conditions (Li 1997). Presently, there are two types of drainage channels that can meet the demand of most conditions: (a) V-type drainage channel with a design gradient of 0.01–0.05 and a V-type bottom that can increase the transport capacity of debris flow and (b) the Dongchuan-type drainage channel with a design gradient of 0.05–0.20, which installs transverse sills at the bottom to reduce velocity, and these sills, can also effectively prevent the bottom concrete from being eroded. These two types of drainage channels mainly change the hydraulic conditions of the debris-flow movement through structural design based on the terrain slope (Chen et al. 2001; You and Liu 2008; You et al. 2011). After the 5/12 Wenchuan earthquake in the Sichuan Province, many landslides and collapses were accumulated in the gullies. Under such circumstances, short and steep drainage channels are more suitable to drain the debris flow. For example, the gradient of the Xiaogangjian debris-flow drainage channel in the Sichuan Mianmao–Hanqing highway reached 34%, which significantly reduced the burial risk that was caused for the road and river because of debris flow. Therefore, the “V” and Dongchuan drainage channels may not meet the demands of the discharge (Li 1997; Chen et al. 2014).

Considering the serious erosion of the large gradient drainage channel, we proposed to set multiple groups of staggered baffles at the bottom of the drainage channel to reduce the velocity of the debris flow on the basis of field investigation and engineering experience without affecting the discharge capacity of debris flow and simultaneously enabling the structure to reduce the flow velocity (Wang et al. 2017a; Yan et al. 2020, b). Similar structures of baffles are used to change the direction of the impending fluid and reduce its velocity to manage avalanche, water conservancy, and other debris flow projects (Peterka 1984; Jóhannesson et al. 2009; Choi et al. 2014). We have studied the deceleration effect of debris-flow density, baffle shape, and row spacing under 12° channel slope conditions (Wang et al. 2017a), and the deceleration effect of debris-flow density, channel slope, and row spacing with cube baffles (Wang et al. 2017b). However, due to the time relationship, the research conditions in the above papers are relatively limited, and there are still some deficiencies in the study about the energy dissipation properties and the application of the baffles. For example, the variation characteristics of the velocity reduction ratio under the action of slopes and shapes of the baffles have not been studied. Moreover, the above researches only focus on the combination of each parameter variable of a single group of energy dissipation baffles and do not consider the situation that multiple groups of energy dissipation baffles need to be arranged as the length of the debris-flow drainage channel increases. The deceleration characteristics and arrangement method of multiple groups of energy dissipation baffles have important guiding significance for engineering practice.

To further study the above issues, a 6-m long flume was used to study the velocity control mechanism of the single-group and double-group baffles. A series of flume experiments were conducted at the Dongchuan Debris Flow Observation and Research Station with the debris-flow deposits in the Jiangjia Gully. Based on the existing research and supplementary tests, the influences of debris-flow density, baffle row spacing, baffle shape, and movement slope on the velocity reduction ratio of the baffles are analyzed. In addition, the double-group baffles were compared with single-group baffles in terms of the flow pattern and the velocity control effect. Finally, we summarized the design process of the multiple groups of baffles. The research results may provide references for the design of the velocity reduction baffles in a large gradient drainage channel.

Experimental equipment and procedure

A series of experiments were conducted at the Dongchuan Debris Flow Observation and Research Station, Chinese Academy of Sciences (Wang et al. 2017a, b). The debris-flow flume mainly includes four parts: a 6-m-long flume with a rectangular cross section of 0.45 m × 0.40 m (width × height); a reservoir at the topside of the flume; a tailing pool with length, width, and height of 1.2 m, 1.2 m, and 0.8 m, respectively. Several rows of deceleration baffles are installed at the bottom of the flume. Both sides of the flume are reinforced glass, which is convenient for photographing the movement of debris flow. The deceleration baffles are installed in the bottom by screws. Figure 1 provides the schematic diagram of the double group experiment. L is the adjacent row spacing in the experiment; the values in the test are 0.10 m, 0.15 m, and 0.25 m, respectively. D is the width and the spacing of the adjacent baffles in the same row, which is a constant of 0.05 m in the experiment. Figure 2 is a picture of the experimental equipment.

Fig. 1
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Schematic diagram of the double group experiments (unit: mm, unless otherwise stated)

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Fig. 2
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Photo of the experimental flume. a Front view. b Lateral view

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In the experiment, we used three different shapes of baffles according to the diversion direction, namely, cube, trapezoid, and triangular prism baffles. The cube baffles represent the front collision, the triangular prism baffles represent the lateral collision, and the trapezoid can be treated as a transitional form. The schematic diagrams of the three baffles are shown in Fig. 3.

Fig. 3
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Model size and layout of the three baffles (unit: m)

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In the experiment, we used soil deposition from the Jiangjia Gully, Yunnan Province. The area is located on the Xiaojiang Fault, which is affected by the movement of the Indian Ocean and the Eurasian plate, so the rocks are fragmented. In addition, this area is a typical dry-hot valley with discernible dry and wet seasons. The rocks are mainly slate and dolomite, and the surface of the mountain is severely weathered. Therefore, the soil is a well-graded mixture with pre-dominantly sands and gravels. Due to the frequent occurrence of various types of debris flows in this area, we chose the soil here as the test material to make the prepared debris flow much closer to natural debris flow in property, movement characteristics, and viscosity (Li et al. 2013, 2015). According to test requirements, a 25 mm × 25 mm steel mesh was used to remove the big gravels with diameters larger than 25 mm. Figure 4 shows the particle size distribution of the soil materials.

Fig. 4
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Particle size distribution curve of the experimental soil

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The experimental parameters include the baffle shape, flow density, row spacing, and channel slope in the experiment for a single group of baffles. In the experiment, 9°, 12°, and 15° were adopted as a reasonable slope of the drainage channel lies generally between 5 and 20% (Li 1997). In the experiment, four representative densities of debris flows were adopted: 1200 kg/m3, 1500 kg/m3, 1800 kg/m3, and 2100 kg/m3 according to the scope of the debris-flow density in the Jiangjia Gully. The slurry is mainly formed by mixing the filtered soil and water. Due to the pores in the soil, the total density of the soil-water mixture must reach the specific density of debris flow, before the test, try to mix evenly to make it meet the requirements. Table 1 shows the properties of experimental debris flows. The row spacing of the baffles was maintained at 0.10 m, 0.15 m, and 0.25 m, respectively. Table 2 details the experimental parameters of the single-group baffles.

Table 1 Properties of the experimental debris flows
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Table 2 Experimental parameters of single-group baffles
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To verify the deceleration effect of the baffles, we also conducted four double group experiments with each group having three rows of cube baffles and four controlled trials without baffles in the flume. The experimental results can be compared with each other in terms of flow pattern and velocity regulation mechanism. The specific parameters are shown in Table 3.

Table 3 Experimental parameters for the double group of baffles
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Four digital cameras were used to record the progress of the movement of the debris flow during the experiment on the double-group baffles. Three of these cameras were fixed above the baffles to obtain the average velocity of the flow before and after encountering the baffles. Although there is a lot of turbulence in the debris flow, the surface velocity of the fluid can be obtained by observing the movement of some bright spots, dark spots, or specks of a particular shape in the image over a short period of time. The other camera was used to record the mobility characteristics and flow pattern when the debris flow passes over the two groups of baffles. According to Formula (1), the speed can be calculated from the image taken by the cameras.

$$ v=\Delta L/\Delta t $$
(1)

where ΔL is the distance of movement in time Δt. The movement distance and time can be obtained from the images captured by the cameras. There are several methods to study the interaction effect of debris flow and prevention of engineering structure such as energy dissipation, velocity distribution, and the change of debris-flow density (Spurr 1985; Pan et al. 2013; Chen et al. 2015, Chen et al. 2018). In this study, we used the velocity reduction ratio (n) to reflect the velocity reduction effect, which represents the percentage of velocity attenuation before and after the baffles. The velocity reduction ratio (n) is obtained from the following formula:

$$ n=\left({v}_1-{v}_2\right)/{v}_1\times 100\% $$
(2)

where v1 is the surface velocity of debris flow at the upstream centerline position of the first row of baffles; v2 is the surface velocity of debris flow at the downstream centerline position of the third row of baffles.

The equivalence of Froude number (Fr) is the key to ensure the dynamic similarity between the test model and natural debris flow. The Froude number (Fr) is a nondimensional quantity used to measure the relative value of fluid inertial force and gravity (Iverson 2015; Lanzoni et al. 2017), which is expressed as follows:

$$ \mathrm{Fr}=\frac{v}{\sqrt{gh\ \cos\ \theta }} $$
(3)

where v is the velocity before the baffles (m/s), g is the gravitational acceleration (m/s2), h is the flow depth (m), and θ is the channel slope (°). According to the control test results, the averaged Froude numbers are 3.46, 4.3, and 4.74 for the flume slopes of 9°, 12°, and 15°, respectively. The Froude number of natural debris flow ranges from 0 to 4.5, which indicates that the text model is basically similar to that of natural debris flow in dynamics (Arattano et al. 1997; Hubl et al. 2009).

Results and analysis

Flow pattern of double-group baffles

Wang et al. (2017a, b) studied the flow pattern of debris flow over the single group of velocity reduction baffles. The experimental results showed that the debris flow passed through the single group of baffles as jet flow, and the flow surface showed a large fluctuation and turbulence. Moreover, the flow velocity appears to be attenuated obviously when it encounters the baffles. This is consistent with the movement pattern of dry sand passing through the baffles (Ng et al. 2015a, b). Figure 5 is the movement process of the debris flow passing through the two groups of cube deceleration baffles. It can be seen from Fig. 5 that the debris flow had a strong interaction with the baffles during the progress of the movement, and it was akin to waves. However, the jet flow height of debris flow under the action of the single group of baffles is significantly higher than that under the action of the two groups of baffles (Wang et al. 2017a, b). This implies that the two groups of deceleration baffles can effectively reduce the velocity and impact the height of debris flows.

Fig. 5
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Debris-flow movement in the flume with two group cube deceleration baffles

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Velocity control effect of single-group baffles

Influence of debris-flow density

Density is one of the most important parameters of debris flow, which can be used for debris-flow risk assessment, velocity calculation, and design of debris flow engineering measures such as check dams and drainage channels (Fuchs et al. 2007; Lin et al. 2008; Li et al. 2012; Chen et al. 2014). Debris-flow density not only represents the content of the solid matter but can also affect the movement and phase separation characteristics of debris flows (Wang et al. 2019). To study the relationship between flow density and the average velocity reduction ratio of the baffles, a series of flume experiments were conducted. Figure 6 shows the lines of best fit representing the relationships between flow density and velocity reduction ratio for all the experimental conditions of the single group of baffles. In Fig. 6, only the relationship between debris-flow densities and velocity reduction ratios under different slope conditions are considered, while the shape and row spacing of the baffles are ignored. According to the results of the regression analysis, the slopes of the lines of best fit of 9°, 12°, and 15° are 0.00143, 0.0040, and 0.00135, respectively, which means that the velocity reduction ratio increases with the increase in density of debris flow. However, the value of the fitting slope does not increase with the increase of the movement slope. The density has a much greater impact on the velocity reduction ratios at the 9° and 15° conditions than that of the 12° condition. This may be caused by the nonlinear change of debris-flow properties. Because there is an upper limit on the density of debris flow, the deceleration effect of the velocity reduction baffles is also limited. Calculations suggest that the average velocity reduction ratio range of 9°, 12°, and 15° conditions are 7.76–20.63%, 17.98–21.58%, and 13.97–25.80%, respectively. Increasing the flow density from 1200 to 2100 kg/m3 can lead to an increase in the average velocity reduction ratio by 12.87%, 3.6%, and 11.83%, correspondingly.

Fig. 6
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Relationship between debris-flow density and velocity reduction ratio under different flume slopes

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The debris-flow density can affect the viscosity coefficient, the distribution of solid particles, and the velocity of debris flows. In general, the viscosity coefficient is proportional to the debris-flow density. The increase of viscosity coefficient will not only reduce the velocity of debris flow, but it will also reduce the jet height of debris flow caused by the baffles. It can be seen from the observation of the experiments that viscous debris flow has a lower jet height due to its high viscosity. Therefore, debris flow can fully collide with the energy dissipation baffles, which is more conducive to the decrease of velocity and energy dissipation.

Influence of baffle shape

The shape of the baffles can change flow direction and promote energy dissipation, thereby reducing the flow velocity. The index of the effective area of frontal impact (S) was used to explore the influence of baffle shape on the velocity reduction ratios. The effective area of the frontal impact is the cross section that is perpendicular to the direction of the fluid at the centroid, that is, the red cross section as shown in Fig. 7. The effective area of the frontal impact of the cube (S1), trapezoid (S2), and three prism baffles (S3) is 0.0025 m2, 0.0021 m2, and 0.0017 m2, respectively.

Fig. 7
figure 7

Effective area of a frontal impact

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Figure 8 shows the relationship between velocity reduction ratio and the effective area of frontal impact under 15° experimental conditions without considering the influence of row spacing and debris-flow density. The dotted line nsmooth = − 17.5% is the velocity reduction ratio in the controlled test where no baffles were installed in the experimental flume. In this study, the relative velocity reduction ratio (nrelative) was used to represent the velocity reduction effect compared with the controlled test, which can be calculated by Formula (4).

$$ {n}_{\mathrm{relative}}={n}_{\mathrm{absolute}}+{n}_{\mathrm{smooth}} $$
(4)

where nabsolute is the velocity reduction ratio in a flume where different shapes of staggered baffles were installed in the flume and nsmooth is the velocity reduction ratio of the controlled test where no baffle was installed in the flume.

Fig. 8
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Relationship between the effective area of a frontal impact of cubic baffles and the velocity reduction ratio at the 15° condition

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According to Formula (4), the relative velocity reduction ratio range of the triangular prism, trapezoid, and cubic baffles under the 15° condition was 30.00–42.50%, 36.00–43.82%, and 28.03–41.31%, respectively. The mechanism of energy dissipation between debris flow and velocity reduction ratio is very complex, which includes the collision energy dissipation between the baffles and fluid, the mixed energy dissipation between the fluids, and the trajectory energy dissipation. Due to the opacity of the debris flow and the limitation of test facilities, it is impossible to reveal the relationship between the shape of the energy dissipator and the effect of fluid deceleration. Therefore, the velocity reduction effect that is influenced by the baffle shape cannot be explored solely by this experiment. Table 4 shows the ranges of the relative velocity reduction ratio for the three shapes of baffles, which can serve as a quantitative reference for the design of energy dissipation baffles in a debris-flow drainage channel. Because debris flow is a complex solid–liquid mixture, the energy dissipation of debris flow not only needs to consider the energy dissipation from the perspective of fluids but it also needs to consider the interaction between the solid particles and baffles such as abrasion and structural stability of the baffles.

Table 4 Ranges of relative velocity reduction ratios under different slope conditions
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Influence of channel slope

Debris flow movement slope is an important parameter for the calculation of flow velocity and design of drainage channels. The flow velocity increases with the gradient. Figure 9 a, b, and c provide the charts of the velocity reduction ratios that change with the channel slope at row spacings of 0.10 m, 0.15 m, and 0.25 m, respectively. The results show that the velocity reduction ratio of the cubic baffles increases with an increase in slope. However, the change of row spacing will have a certain influence on the increasing trend. Generally speaking, when the row spacing is small, the debris flow will pass over the second and third row of baffles in the form of jet flow, so the deceleration effect will be weakened (Fig. 9 a). With the increase of row spacing, the interaction between the baffle and debris flow is more sufficient, which can effectively reduce the velocity of debris flow (Fig. 9c). When the row spacing is larger than a certain distance, the debris flow will accelerate between two rows of baffles, so the deceleration effect of the baffles will gradually disappear.

Fig. 9
figure 9

Relationship between movement slope and velocity reduction ratio at different row spacings for cubic baffles. a Row spacing L = 0.10 m. b Row spacing L = 0.15 m. c Row spacing L = 0.25 m

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Figure 10 shows the regression fitting lines of the velocity reduction ratios of the three types of baffles affected by slope without considering the density change of debris flow. According to the fitting results, the fitting lines for the average velocity reduction ratios of the cube, trapezoid, and triangular baffles with the change of slopes are n = 2.191 + 1.241θ, n = 8.171 + 0.888θ, and n = 6.021 + 1.062θ, and the determination coefficients (R2) of these equations are 0.217, 0.133, and 0.199, respectively. This means that the velocity reduction ratio increases with the increase of slope, but the fitting degree is not remarkably high. It can be seen from the calculation that the range of the velocity reduction ratio is almost the same under the three shape conditions in the process of the slope increasing from 9° to 15°, which are 13.36–20.81%, 15.51–21.61%, and 15.58–21.95%, respectively.

Fig. 10
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Fitting curves of velocity reduction ratios changing with the movement slopes for different shapes of baffles. a Cube. b Trapezoid. c Triangular prism

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The movement slope has a significant influence on the velocity of debris flow before the baffles, and then, it indirectly affects the velocity reduction ratio. This is because the velocity of the fluid in front of the baffles is positively correlated with the slope. When the debris flow passes through the baffles, it will have a higher velocity attenuation, resulting in a much higher velocity reduction ratio. These results can be used as reference values for the design of the debris-flow drainage channel with a large gradient.

Influence of row spacing

Figure 11 shows regression lines of best fit for the velocity reduction ratios changing with an increase in the row spacing for movement slope of 9°, 12°, and 15°. It shows that the velocity reduction ratio decreases gradually with the increase of row spacing for the three slope conditions. Based on the equations for the lines of best fit, it can be inferred that the average variation range of the velocity reduction ratio is relatively small as the row spacing increases from 0.10 to 0.25 m at 9°, 12°, and 15°, which are 13.26–14.78%, 18.28–22.30%, and 20.25–20.67%, respectively. As for the reason why the velocity reduction ratio decreases with the increase of row spacing, we consider that the reacceleration of debris flow between the adjacent rows of baffles is the main reason.

Fig. 11
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Fitting curve of velocity reduction ratio changing with row spacing under different slope conditions

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A similar study was conducted by Choi et al. (2015) to explore the velocity reduction effect by dry sand in a 26° flume. To compare our experimental results with their research, a transformation can be made for the fitting line of the velocity reduction ratio by Formula (5), and the transformation equation for each fitting line is shown in Table 5.

$$ \frac{{\mathrm{E}}_k}{{\mathrm{E}}_a}=\frac{v_k^2}{v_0^2}={\left(1-0.01n\right)}^2 $$
(5)

where Ek = 1/2 mvk2 is the debris-flow kinetic energy after the baffles, Ea = 1/2 mvk2 is the initial debris-flow kinetic energy, and n is the fitting line equation between the average velocity reduction ratio and row spacing.

Table 5 Fitting equations between row spacing and the velocity reduction ratios
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The relationship of the normalized row spacing and normalized kinetic energy is arrived by transforming the fitting equation of the velocity reduction ratio to the normalized kinetic energy and by changing the abscissa of the row spacing to the normalized row spacing of L/W (W is the flume width). This is shown in Fig. 12.

Fig. 12
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Relationship between the normalized kinetic energy and the normalized row spacing

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Figure 12 shows the relationship between the normalized kinetic energy and the normalized row spacing at the 9°, 12°, and 15° conditions and that of dry sand at 26°. Figure 12 shows that the normalized kinetic energy of the debris flow is proportional to the row spacing under the same slope, which means that the deceleration effect of the velocity reduction baffles gradually decreases with the increase of row spacing. By comparing the change curves of debris flow and dry sand, it can be concluded that the deceleration effect of debris flow is relatively smaller than that of dry sand due to the rheological characteristics of debris flow. In addition, according to the change of the normalized kinetic energy of 9°, 12°, and 15° of debris flow, the normalized kinetic energy decreases with the increase of slope under the same normalized row spacing, which is consistent with the result that the deceleration ratio increases with the increase of slope.

Generally speaking, the value of the normalized kinetic energy should be less than 1; that is, the velocity of debris flow after passing through the baffles should be less than that before the baffles. However, according to the analysis in Fig. 11, with the increase of row spacing, the velocity of debris flow will also increase when the distance is greater than a certain distance. When the velocity of debris flow behind the baffles is greater than that in front of the baffles, the value of normalized kinetic energy will be greater than 1. In the test, the maximum row spacing of the baffles is 0.25, so the maximum of L/w is 0.56, and the corresponding value is not greater than 1. As for the normalized kinetic energy greater than 1, it can be verified in the future when the test conditions are available.

Velocity control effect of a double group of baffles

According to the requirements of engineering, many groups of baffles must be arranged in the drainage channel to continuously reduce the flow velocity of debris flow. In this section, the velocity control effect of a single group and a double group of velocity reduction baffles is studied. Three cameras were installed at 2 m, 4 m, and 6 m away from the flume outlet, as shown in Fig. 1. The distance and time of debris-flow movement were obtained from the videos; then, the velocity of debris flow at each point was calculated by Formula (2). Figure 13 shows the curves of the debris-flow velocity of single and double-group baffles, and the control tests for flow densities of 1200 kg/m3, 1500 kg/m3, 1800 kg/m3, and 2100 kg/m3 at a flume slope of 15°. Figure 13 shows that the flow velocity of debris flow in the control test shows a tendency to increase gradually with the displacement. However, the velocity of debris flow in the single group and double group experiment first increased and then decreased. At the displacement of 6 m (in Fig. 13c), the flow velocity in the double group experiment is reduced by 27.3% compared to the control test. This means that the flow velocity of the debris flow can be obviously reduced by the velocity reduction baffles.

Fig. 13
figure 13

Velocity variation curves on the condition of a single group, double group of cubic baffles, and the control test at 15° a 1200 kg/m3, b 1500 kg/m3, c 1800 kg/m3, d 2100 kg/m3

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By comparing the deceleration effect of the single-group and double-group baffles at the displacement of 6 m, it can be found that the double-group baffles do not show a better deceleration effect than that of the single-group baffles. This is because the slowing effect of the baffles is limited. After the fluid passed through the baffles, there is a process of continuous acceleration, and the flow velocity is controlled in a reasonable range by the continuous action of acceleration and deceleration caused by the velocity reduction baffles. Although the decelerating effect of the baffles is limited, this deceleration effect is helpful to reduce the bottom abrasion of the drainage channel and increase the service life in a long period of operation.

Design case of a drainage channel with velocity control baffles in the Xiaogangjian Gully

Study area

The Xiaogangjian Gully is located on the right side of the Mianmao-Hanqing highway in Sichuan Province, China, on the left bank of the Mianyuan River, about 5 km away from the Qingping township. The area of the Xiaogangjian watershed is small, about 1.36 km2, and the longitudinal gradient of the gully is 412‰. The altitude of the Xiaogangjian watershed is 810–1987 m. The valley is deeply V-shaped. The Xiaogangjian basin is characterized by precipitous topography, aerial surface development, and many geological disasters such as collapse and landslide, which provide a large number of soil sources for the outbreak of debris flows (Yang et al. 2012).

Before the “5.12” earthquake, the gully was well vegetated and the ecological environment was good, but the free surface was developed in the lower reaches of the basin. After the earthquake, the collapse and landslide accumulated in the gully, and the debris flow broke out frequently, resulting in the valley cutting down, road interruption, and the formation of barrier lake on the Mianyuan River many times (Chen et al. 2015).

The annual average temperature of the Xiaogangjian basin is 15 °C, the annual average rainfall is about 1500 mm, and the 24-h maximum rainfall is about 160 mm. The rainy season of this basin is the summer and autumn, which is prone to flash floods and debris flows. Before the Wenchuan earthquake, there were few debris flows in this area. However, after the Wenchuan earthquake, the surface vegetation of the mountain was seriously destroyed and a large number of landslides were accumulated in the gully. The frequency of the debris flow obviously increased, and the downstream roads were often blocked.

Introduction of the debris flow mitigation project

To protect the downstream highway from the threat of debris flow, a series of systematic mitigation project had been built. The design standard of debris flow mitigation measures is to resist rainstorm debris flow once in 20 years. The mitigation project includes the following parts: (1) five check dams with various opening sizes, which are used to block the stones of different particle diameters; (2) a 131.75-m-long drainage channel with energy dissipation cabinets; (3) a debris-flow basin between the highway and the Mianyuan River, which is used to store the debris flow acclamation to prevent the risk of river blocking; (4) a drainage ditch on the left of the gully, which is built to lead the rainwater (Chen et al. 2015).

Due to the small area, rich soil resources and large longitudinal slope of the Xiaogangjian watershed, the drainage channel can only be arranged between the forming area and the accumulation area. Compared with the layout of the drainage channel in other mitigation projects, the Xiaogangjian drainage channel has certain particularity. The drainage channel has a relatively large longitudinal gradient of 34.9%, a total length of 131.75 m, and a depth of 3.50 m. The energy dissipation cabinets were used in the section from 40.02 to 60.06 m to dissipate the kinetic energy of debris flows, and the open tunnel aqueduct from 116.75 to 126.75 m is used for the highway to pass under the diversion channel.

Operating conditions of the drainage channel

The Xiaogangjian debris flow mitigation project was completed in May 2012. Although the abrasion of the debris flow had been considered and the corresponding engineering protection measures were taken, the abrasion of the drainage channel was still inevitable in the working conditions. Chen et al. (2014) summarized the operation and maintenance of the drainage channel in 2012 and 2013. The results showed that this type of drainage channel can effectively discharge the debris flow into the debris-flow basin and protect the highway. However, the abrasion problem of the concrete at the bottom of the drainage channel cannot be effectively solved.

To reduce the wear of debris flow, railway tracks were embedded along the drainage channel in the follow-up maintenance. Although the debris flow has less wear on the railway tracks, the abrasion of the surrounding concrete made some railway tracks hang in the air. The debris flow caused an erosion depth of about 0.2 m at the bottom of the drainage channel, and the maximum erosion on both sides of the drainage channel reached 0.08 m. On July 9, 2013, a 432 mm rainfall caused a total of 100,000 m3 of debris flow, with the maximum flow of 180 m3/s. The bottom of the drainage channel was seriously eroded, and many scour pits appeared, among which the largest erosion pit was 2.5 m long, 1.2 m wide, and 0.75 m deep, and the maximum scouring depth of the sidewall of the drainage channel reached 0.15 m. Detailed introduction and photos of the drainage channel were provided by Chen et al.

The serious erosion of the drainage channel in the Xiaogangjian Gully is mainly due to the topographic conditions. The longitudinal gradient of the drainage channel reached 34.9%, which exceeded the erosion threshold of the concrete, resulting in high debris-flow velocity and serious abrasion. In addition, because the debris flow contains a high concentration of sand and a large number of stones, the cutting action would have a greater effect on the bottom and sidewall of the concrete. Therefore, there is still a need for further research on the use of materials and structural design of debris-flow drainage channels.

Drainage channel design with multi-groups of baffles

Considering the operation conditions of the large gradient drainage channel in the Xiaogangjian mitigation object, this study proposed to install multi groups of baffles at the bottom of the drainage channel, so as to reduce the flow velocity and the concrete erosion rate. This type of drainage channel is designed for the drainage channel with a gradient generally between 15 and 35%. The design method and steps of multi groups of baffles are as follows:

  1. a)

    According to the topography, rainfall, and the design standard, determine the slope of the drainage channel, flow discharge and the type of the cross section;

  2. b)

    Calculate the flow depth and velocity of debris flow under the flow discharge and longitudinal gradient of the designed drainage channel;

  3. c)

    Calculate the jet height (H1) when the debris flow flows over the baffles, H1 = (u1sinα)2/2 g, u1 is the maximum anti-erosion abrasion velocity of the concrete, α is the angle between the rising section and the horizontal line, which can be obtained by experiment or numerical simulation;

  4. d)

    Calculate the size of the baffles, including the length, width, and height. In order to stabilize the operation of the drainage channel, the fluid should pass through the baffles in the way of submergence. The ratio (H/h) between the flow depth (H) and the height of the baffles (h) is less than 1.5, and the height of baffles should be less than 1.0 m;

  5. e)

    Calculate the distance between baffles in the same row. The spacing (l) between the same row of the baffles should be 1~1.5 times of the maximum particle size of the upstream soils;

  6. f)

    Calculate the row spacing of one group of the baffles (L) and the spacing between multi groups of baffles (L1). The row spacing (L) is generally 3~5 times the width of the baffles (D), and the distance between multi-groups of baffles is calculated according to the jet distance along the drainage channel, L1 = u12sin2α/g;

  7. g)

    Determine the position where to start the layout of the baffles. Because the debris flow has an accelerating process in the drainage channel, the baffles are arranged from the position where the concrete allows the maximum velocity of debris flow to pass through. Generally, the maximum anti-erosion abrasion velocity of the concrete is 10–12 m/s (Zhou et al. 1991).

The above is the basic method for the design of the large gradient drainage channel with multi groups of baffles. The design of this type of drainage channel has not been applied in engineering practice, so the operation effect of it cannot be known. Due to the complexity of debris-flow soil sources, the debris flow mitigation project needs to be improved in the course of engineering practice.

Conclusions

In this study, a series of single-group and double-group baffle experiments were conducted to explore the flow pattern, deceleration effect of the baffles influenced by the baffle shapes, flow density, and row spacing, as well as the velocity control effect of the double-group baffles. The results of this study can be summarized as follows:

  1. (1)

    Compared with the single-group baffles, the flow pattern of the debris flow under the action of the double-group baffles presents a state of undulation along the flume with relatively low turbulence intensity and jet height, and there is almost no flushing out of the flume. However, the turbulence of the debris flow after the interaction with the single-group baffles is more intense, and it is easier for it to overflow the flume. Through the comparison of the velocity control effect of the single and double groups of baffles, it is found that the double group of baffles can control the velocity within a certain range in the process of fluid movement, and they cannot continuously reduce the velocity of debris flow. This deceleration effect is helpful in reducing the abrasion at the bottom of the drainage channel, and it prolongs the service time of the drainage channel.

  2. (2)

    The fitting equations of the relationship between debris-flow density and velocity reduction ratios are n = −9.400 + 0.00143ρ, n = 13.180 + 0.0040ρ, and n = −1.811 + 0.00135ρ for the channel slopes of 9°, 12°, and 15°. These results show that the velocity reduction ratio increases with the increase of debris-flow density under three slope conditions. According to the calculation, the average velocity reduction ratio range of the 9°, 12°, and 15° conditions is 7.76–20.63%, 17.98–21.58%, and 13.97–25.80%, respectively.

  3. (3)

    The results of the experiments showed that the range of the velocity reduction ratio of the three shapes of baffles is almost the same under different slope conditions. However, due to the opacity of debris flow, the interaction mechanism between the baffles and fluids is difficult to reveal. In the engineering application, it is necessary to make a comprehensive choice from the aspects of structural stability, construction convenience, and engineering cost.

  4. (4)

    According to the fitting results, the relationships between the velocity reduction ratios and slope under the action of cube, trapezoid, and triangular baffles is n = 2.191 + 1.241θ, n = 8.171 + 0.888θ, and n = 6.021 + 1.062θ, respectively. When the slope increases from 9° to 15°, the corresponding velocity reduction ratio of the three kinds of baffles is 13.36–20.81%, 15.51–21.61%, and 15.58–21.95%, respectively.

  5. (5)

    The results showed that the relationships between the velocity reduction ratios and the row spacing is n = 15.79–10.12 L, n = 24.98–26.80 L, and n = 20.95–2.814 L, which indicates that the velocity reduction ratio of the baffles decreased with the increase of row spacing. When the row spacing increases from 0.10 to 0.25 m, the ranges of the velocity reduction ratios are 13.26–14.78%, 18.28–22.3%, and 20.25–20.67%, respectively.

  6. (6)

    According to the operation of the Xiaogangjian debris-flow drainage channel, this study proposed a structural design method of setting multi-groups of baffles at the bottom of the drainage channel, which can reduce the wear rate of the bottom concrete of the drainage channel and prolong the service life. This kind of baffles is used for the velocity control of debris flow in a large gradient drainage channel. At present, the research is still in the theoretical and experimental stage and has not been applied in engineering practice. The effect of this type of drainage channel needs to be further verified and improved.