Experimental Study on the Impact Dynamics of Cylindrical Baffles with a Rigid Barrier against Debris Flows

Abstract

The use of baffle arrays behind a rigid barrier is an effective method to reduce impact force by dissipating flow energy with filtering boulders from debris flows. To prevent structural damage of the rigid barrier, appropriate configurations of the baffle arrays are needed; however, design guidelines for the geometric construction of baffle arrays have not yet been proposed. One of the major challenges in designing multiple structures (baffles and a rigid barrier, etc.) is to set up a framework for a safe and economical design. The flow–structure interaction and impact force of debris flows on a rigid barrier are affected by the configuration of baffles installed behind the rigid barrier. In this study, to evaluate the flow behavior and the dynamic impact force on the terminal barrier after the flow has passed through the baffle arrays, we conducted a series of small-scale flume tests under various baffle heights and a number of rows. The test results revealed that the installation of baffles reduced the run-up height and the impact force on the terminal rigid barrier. The flow impedance induced by baffles had a significant influence on the dissipation of the kinetic energy of debris flows. Moreover, additional baffle rows produced a greater reduction in the run-up and impact force by decreasing debris flow and boulder mobility.

1. Introduction

Debris flow hazards caused by typhoons and heavy rainfall have significantly increased all over the world. Debris flows with entrained debris, gravel, and boulders mixed with water are extremely fast, have a high impact force, and bring disastrous consequences to urban areas and infrastructure. For this, the installation of a single rigid barrier is a commonly used method for intercepting debris flows [1]. However, such an approach allows debris flows to increase in speed and volume, entraining basal sediments before hitting the barrier [2]. Consequently, multiple structural barriers installed in the flow path of debris flows are necessary, as shown in Figure 1, which demonstrates the cylindrical baffles installed at Umyeon Mountain in Korea and the rectangular baffles installed behind a rigid barrier at Lantau Island in Hong Kong, China.

In mountainous regions with steep slopes, large boulders can be entrained by debris flows. However, because of their rigidity, the rigid structures are prone to damage by large boulders. To reduce potential damage from boulders, installing baffle arrays behind a rigid barrier is also an effective countermeasure because, in the course of debris flow, the baffles can decelerate frontal velocity and filter out boulders [3,4,5]. However, a design guideline for the specifications and arrangement of baffles has not yet been suggested. For the engineering design of such structures, a comprehensive understanding of impact force and run-up characteristics is necessary [6]; however, engineering designs have yet to reach complete agreement on impact behavior and impact force estimation. Meanwhile, there have been many experimental studies that have investigated the effect of debris flow on a rigid barrier. Choi et al. (2015a), Ng et al. (2017), Huang and Zhang (2020), and Shen et al. (2018) [7,8,9,10] studied the flow–structure interaction, such as the run-up, overflow, and impact force characteristics. However, the effect of the installed baffles behind a rigid barrier has not been extensively studied. Baffles are mainly deployed in multiple groups, and the interaction between a debris flow and baffles with a complex flow mechanism is significantly affected by the height, spacing, and number of rows of baffles. Therefore, to control the mobility of debris flows containing boulders, an appropriate arrangement of baffle arrays behind a rigid barrier is needed.

In this study, to investigate the effect of cylindrical baffle arrays behind a rigid barrier on debris flow behavior and dynamic impact force, a series of small-scale flume tests was performed according to the varying the baffle height and number of rows. High-speed cameras used to capture the flow interaction with the baffle arrays and the rigid barrier were installed at the top and side of the flume. Load cells employed to record the dynamic impact force of a debris flow against the terminal barrier after the flow has passed through the baffle arrays were also installed behind the rigid barrier. After the test, we analyzed the run-up and impact force characteristics due to the baffle arrays.

2. Methods

2.1. Scaling

Dynamic similarity in the flume is achieved by adopting the Froude number, which is defined as the ratio of inertial force to the gravitational force. In Equation (1), $v$ is the velocity $\left(\mathrm{m}/\mathrm{s}\right), h$ is the flow depth ($\mathrm{m}$), $g$ is the gravitational acceleration ($\mathrm{m}/{\mathrm{s}}^2$), and $\theta$ is the slope angle ($°$).

$$Fr=\frac{v}{\sqrt{ghcos\theta }}$$

(1)

The Froude number has been used to simulate flow dynamics in debris flow such as velocity, flow depth, and inclination of gully. The approaching Froude number based on the previous studies ranges from 0.5 to 7.6 [12,13,14,15,16,17]. In this study, we used an approaching Froude number of 5.0 upstream of the baffles.

2.2. Flume Model

In this study, we conducted a series of small-scale tests using an instrumented flume with flow behavior and an impact force measurement of the debris flows, as shown in Figure 2a. The flume was made of a transparent acrylic plate with an overall length of 4.0 m and a side wall height of 0.45 m and a base width of 0.3 m. To prevent deformation of the flume, a stainless-steel frame was attached with an acrylic plate at the side and the bottom of the flume. A storage container was located at the flume’s most upstream end, with a maximum storage capacity of 0.11 m³. A spring-loaded door with a magnetic lock for the storage container enabled the container to keep the source material before the test. The flume was divided into three main parts: a storage container, baffle arrays, and a rigid barrier with load cells. The baffle arrays and rigid barrier were installed at the middle of flume. To study the influence of baffle height, various baffle heights (60 and 120 mm) were used. To capture the flow kinematics of the debris flow, two high-speed cameras (HAU-U2) were installed at the top and side of the flume, as shown in Figure 2a. They had a resolution of 1920 × 1080 pixels and a sampling frequency of 250 frames per second. The diameter and height for a cylindrical baffle were determined as 30 and 60 mm by the similarity ratio of the cylindrical baffles used in a real-scale experiment [18]. The transverse blockage ratio of the baffles in the flume was 40%, as proposed by Watanabe et al. (1980) and Ikeya and Uehara (1980) [19,20]. The size of the rigid barrier was 0.3 m in width, 0.12 m in height, and 0.05 m in thickness. The rigid barrier was made of stainless-steel. To measure the dynamic force of the debris flow at various locations of the rigid barrier, as shown in Figure 2b, the barrier was divided into six plates, and one load cell per plate was attached. Figure 2b shows the rigid plates with load cells divided into upper load cell parts (UL1, UL2, and UL3) and lower load cell parts (LL4, LL5, and LL6). Figure 2c shows an image of the physical experimental setup.

2.3. Test Conditions and Procedure

Excessive pore fluid pressure is primarily influenced by grain size distribution and the presence of particles in the fluid phase [21]. In this study, to simulate debris flow behavior in a flume, a two-phase debris flow was reproduced with granular materials and fluid mixtures. The debris mixture was composed of 25% gravel (5–10 mm in diameter), 25% coarse sand (2–5 mm in diameter), and 50% medium to fine sand (0.25–2.0 mm in diameter). The debris mixture had a similar grain size distribution as the debris flow hazard site at Samcheock, South Korea, where a debris flow occurred in 2019. According to the Unified Soil Classification System (USCS), the debris mixture in this study and the natural weathered soil collected from the debris hazard site at Samcheock were classified as SP, respectively. Furthermore, glass beads were used to reproduce large boulders entrained by debris flows in nature. The glass beads mixed with the debris mixture had a higher bulk volume and less compressibility, therefore it could be used to represent natural boulders. The diameter of the glass beads was 40 mm (equivalent to a prototype boulder of 0.8 m in diameter), based on a boulder diameter ranging from 0.5 to 2.0 m in previous studies [22,23]; Figure 3 shows the debris materials used in the laboratory test. To reproduce the viscosity of a debris flow caused by fine-grained soil in the flume, glycerin was mixed with the debris mixtures with water. The behavior of a two-phase flow with glycerin is similar to natural debris flows and simulates mobility characterized as a non-Newtonian fluid rheology. The volumetric solid fraction of the tested debris flows was determined to be 50%. The flow mass of the debris mixture was 20 kg; the initial bulk density was about 1925 kg/${\mathrm{m}}^3$; and the viscosity was about 0.05 pa s. From this, the approaching velocity, flow depth, and inclination of flume for the predetermined Froude number (Fr = 5.0) were estimated as 2.2 $\mathrm{m}/\mathrm{s}$, 0.02 $\mathrm{m}$, and 15°, respectively.

For the small-scale test, firstly, a debris mixture of 20 kg was prepared. Then, the inclination of the flume was set to 15°, and the cylindrical baffle arrays and the rigid barrier with the load cells were installed at the middle of the flume, as shown in Figure 2a. To prevent the rotation and bending of the cylindrical baffles during the test, the cylindrical baffles were fixed by dual-threaded screws at the base of the acrylic flume. To measure the dynamic impact load from debris flows, a data logger connected to load cells was set with a sampling rate of 20 kHz. After the rigid barrier was installed, as shown in Figure 2a, high-speed cameras were also installed at the top and side of the flume. Subsequently, the debris mixture of 20 kg was moved to the storage container, and the debris was continuously stirred by a hand-held electric mixer. Once the debris preparation from the storage container was completed, the debris was released toward the barrier arrays by opening the spring-loaded door by deactivating the magnetic lock. During the test, the flow–structure interaction and impact force were measured by high-speed cameras and load cells, respectively. Particle image velocimetry (PIV) analysis [24] was utilized to investigate the effect of velocity attenuation and the deposition process behind the barrier. Five tests in total were conducted according to various baffle configurations. Each test was repeated two times to eliminate errors and to obtain precise results from the experiments. The test conditions are summarized in

Table 1. Test conditions.

Baffle Condition	Baffle Height (H)	Number of Rows (R)	Spacing between Successive Rows (L)	Transverse Blockage Ratio (B)	Amount of Soil (kg)	Designation
Without baffles	-	—	—	—	20	H0
With baffles	60 mm	1	200 mm *	40%		H60-R1
		2				H60-R2
	120 mm	1				H120-R1
		2				H120-R2

* Spacing from the final row of baffles to the rigid barrier: 200 mm.

.

3. Results

3.1. Run-Up Height

Figure 4 shows a comparison between the observed kinematics captured at the maximum run-up using the high-speed camera for each test. As shown in Figure 4, the flow piled up to form a gradual increase in dead zones behind baffles, after which the flow was deflected upwards along the surface of the rigid barrier. In each experiment, the arrival time for the maximum run-up height ranged from 0.50 to 1.46 s (time from entering the baffles to the maximum run-up height at the rigid barrier), and the maximum run-up height was significantly different according to the presence of baffles. In Figure 4a, because of the absence of the interference of baffles, the maximum run-up height was observed, which was much higher than the height of the rigid barrier. In Figure 4b–e, with the baffle arrays, the flow was affected by the first and second rows of baffles, and then the flow dispersed around the baffle arrays. Subsequently, there was a relatively lower run-up height behind the rigid barrier. Figure 5 shows a comparison of the maximum run-up height measured at the rigid barrier. The run-up height for each test was measured at the maximum vertical height for the flow process and was normalized with the flow depth ($h_a)$ before the flow entered the baffles. A horizontal reference line was also plotted for the height of the rigid barrier. The maximum run-up height for the case with no baffles (H0) increased up to 2.65 times that of the rigid barrier height. Meanwhile, the run-up height for cases with baffles (H60 and H120) decreased by an average of 40% compared with the case of no baffles. This can be considered to be the effect of flow impedance caused by the impact with the baffles. Furthermore, taller baffles had a negligible effect on the run-up height, while increasing the number of rows of baffles from one row (R1) to two rows (R2) led to an additional 23% of run-up height reduction. Likewise, the addition of baffle rows exhibited a gradual reduction in the maximum run-up to the height of the rigid barrier ($h_r/h_a=6)$. This was because an additional staggered row of baffles decreased the flow discharge, and the energy of the debris flow approaching the rigid barrier decreased thereafter.

The analytical approach for run-up height is based on the conservation of mass and momentum. Two methods for the energy principle and momentum-based approach were proposed by Jóhannesson et al. (2009) and Kwan (2012) [5,25], respectively, to predict the trend line for the run-up height of debris flows. The energy principle proposed by Kwan (2012) [5] is given as:

$$\frac{h_f}{h}=1+\frac{v^2}{2gh}$$

(2)

where $h_f$ is the final run-up height ($\mathrm{m})$, $h$ is the approaching flow height ($\mathrm{m})$, $v$ is the flow velocity ($\mathrm{m}/\mathrm{s}$), and $g$ is the acceleration of gravity ($\mathrm{m}/{\mathrm{s}}^2$). The momentum-based approach [25] is given as:

$$\frac{{\rho }_f}{{\rho }_i}{\left(\frac{h_f}{h_i}\right)}^2-\frac{h_f}{h_i}-1+{\left(\frac{{\rho }_f{h}_f}{{\rho }_i{h}_i}\right)}^{-1}-2N_{Fr}^2=0$$

(3)

where ${\rho }_f$ is the density of the flow after the run-up, ${\rho }_f$ is the density of the approaching flow before the run-up, and $N_{Fr}$ is the Froude number of the approaching flow, indicating the ratio of inertial force to gravitational force. The adopted predictive models can be characterized as two flow states, which are governed by inertial force and frictional force. These two states show the difference in energy dissipation depending on the flow interaction such as fluid conditions or grain contact and friction. Based on the maximum run-up height for the flow process, the energy dissipation characteristics according to different baffle configurations can be explained. Figure 6 shows the comparison of the approaching Froude number ($F_r)$ and the normalized run-up height for various heights and numbers of the rows of baffles. The run-up height ($h_f)$ for each test was normalized with an approaching flow depth ($h_a)$ upstream. Moreover, we added to the figure results of previous studies on the effect of the run-up height on the rigid barrier conducted under various flow conditions [7,8], and the two reference lines based on the energy principle [5] and the momentum-based approach [25] models were also added for comparison. As shown in Figure 6, a comparison of water and dry sand from prior studies [7,8] showed that the water flow induced a significantly higher run-up height than the dry sand flow because water has a lower dynamic viscosity and the dry sand flow was governed by frictional resistance by grain contacts. The results of the run-up for both water flow and dry sand flow were in good agreement with the trend lines estimated by the energy principle and momentum-based approach, respectively. In comparison with the two-phase flow condition, the results revealed that the no baffle case (H0) agreed well with the trend line by the energy principle model, which was dominated by inertial stress, whereas the case with baffles (H60 and H120) approached the trend line by the momentum-based approach model, which was dominated by the frictional force. Moreover, additional numbers of rows of baffles produced a greater run-up height reduction.

3.2. Impact Force

The impulse load induced by boulders is an important parameter for designing debris flow countermeasures [4,26]. Figure 7 shows a comparison of impact force on the terminal rigid barrier versus time during the experiment, and the impact force was measured under various baffle configurations (H0, H60-R1, R2, and H120-R2, R2). The initial response of the rigid barrier against debris flow impact was set to t = 0.25 s, and the total testing time was 3.0 s. The peak values of the impact force are also marked in each figure. We further investigated the importance of the dynamic and static components of the total impact load recorded at the load cells versus the time. The peak impact force of the debris flow on the terminal rigid barrier showed a distinct change with changes in the baffle configuration. The lower plates of the rigid barrier showed a greater impact force than the upper plates because the debris flow was mainly concentrated at the bottom of the rigid barrier. The case with no baffles (H0) exhibited the largest peak impact force because of the absence of the interference of baffles. Meanwhile, from the case with one and two rows of baffles, a rapid reduction in impact force was observed at the rigid barrier. Figure 8 shows a comparison of the dynamic peak impact force change for all the tests. One row of baffles (H60-R1) exhibited a 85% impact force reduction compared with the case with no baffles. Two rows of baffles (H60-R2) created an additional 47% impact force reduction compared with one row of baffles (H60-R1). This was because the additional staggered row of baffles produced a greater reduction in the gradual mobility of boulders and in the velocity of debris flow through the repeated suppression of the flow. The taller baffles in one row (H120-R1) exhibited an 82% impact force reduction compared with the case of no baffles; however, the impact force showed a negligible difference compared with the case with the shorter baffles (H60-R1). This was because the installed baffles temporarily suppressed the mobility of the boulders, whereas the flow freely passed between baffles without any interference after the baffles. However, increasing the baffle height from 60 mm (H60-R2) to 120 mm (H120-R2) with two rows of baffles decreased the impact force by up to 43%. As observed in previous studies on the debris flow dynamics with baffles by numerical analysis [27,28], the velocity and the impact force of flow significantly decreased with the increase in height and row number of baffles due to the increased flow impedance of baffles. Thus, the energy dissipation of the flow becomes even more obvious for higher heights and more rows of baffles. Figure 9 shows a comparison between the residual static impact force at various locations of the rigid barrier. Because of the formation of dead zones behind the rigid plate, the static force of the lower plates (LL4, LL5, and LL6) was much higher than that of the upper plates (UL1, UL2, and UL3). However, the static force in each test showed relatively few differences compared to the impact force. Comparing the results of the static force and the dynamic force, the baffle arrays had a major effect on the reduction in the dynamic force, while the baffles did not have a significant effect on the dead zone formation and the resultant lower reduction in the static force. As observed in the series of tests, the formation of dead zones for all the tests were similar regardless of the presence of baffle arrays.

4. Discussion

In this study, the two-phase debris flow in the debris hazard site was reproduced by mixing debris materials, glass beads, glycerin, and water, and then a series of small-scale flume tests were performed according to different baffle heights and numbers of rows. The use of baffle arrays decreased the run-up height and impact force on the terminal rigid barrier because of the suppression of boulders and flow dynamics. Moreover, additional baffle rows led to a greater reduction in the run-up and impact force. This means that the flow impedance caused by the baffle arrays can decrease the potential energy of flows and this effect can be augmented by adding a row of baffles. Furthermore, the use of baffles reduced the run-up height and overflow; however, it did not increase deposition on the back of the rigid barrier. As observed in the series of tests, the formation of dead zones for all tests were similar regardless of the presence of baffle arrays. The results of the small-scale test can be utilized to suggest an appropriate specification and arrangements for baffle design. However, the transverse blockage ratio of baffles can be varied depending on the size of the boulders in debris flows because there are boulders with various sizes in mountainous regions. Boulders that have a smaller diameter than the spacing between baffles can have a significant effect on the impact force at a terminal rigid barrier because the boulders can freely pass between baffles without any interference. Therefore, further study is needed to investigate the effect of the impact force characteristics according to the spacing between baffles with various sizes of boulders.

5. Conclusions

In this study, using small-scale flume tests, we evaluated the effect of the configuration of cylindrical baffles behind a rigid barrier on run-up height and the impact force. For this, a series of small-scale flume tests were performed according to different baffle heights and numbers of rows. The findings from this study are as follows:

(1)

The experimental results showed that the use of baffle arrays reduced the run-up height and impact force on the terminal rigid barrier because of the suppression of boulders and flow;

(2)

Increasing the number of baffle rows created a greater run-up and impact force reduction because it impeded the mobility of boulders and flow. In comparison with the existing analytical approaches, the test with no baffles agreed well with the trend line by the energy principle model, whereas the results with baffles approached the trend line by the momentum-based approach model, which was dominated by the frictional force;

(3)

Increasing the number of baffle rows provided more energy dissipation and impact force reduction. Furthermore, the use of baffles promoted a reduction in the run-up height and overflow; however, it did not produce a higher flow deposition on the back of the rigid barrier;

(4)

Cylindrical baffles behind the rigid barrier can be utilized as efficient countermeasures to reduce the high impact forces by boulders entrained by debris flows. For the field application of baffles, however, the transverse blockage ratio of the baffles needs to be varied with the size of boulders. Thus, an additional study on impact force characteristics considering the interaction between baffles and flows including various size of boulders will be needed.