Assessment of Debris Flow Impact Based on Experimental Analysis along a Deposition Area

Abstract

Debris flow is a devastating phenomenon that happens in hilly and mountainous regions and has a serious impact on affected areas. It causes casualties and serious damage to the environment and society. Therefore, a susceptible assessment is necessary to prevent, mitigate, and raise awareness of the impact of debris flows. This paper focuses on evaluating the deposition area along the deposition board. The methodology involved an experiment on a physical model by demonstrating the debris flow based on the steepness of the flume slope at 15°, 20°, and 25° angles. The limestone particles with a total volume of 2.5 × 10⁶ mm³ acted as debris and were released with water from the tank to the deposition board with an area of 10 × 10⁵ mm². The volume, area, and length of particle distribution carried from the flume to the deposition board were then determined. Based on the experimental results, the deposition board is covered with particles of about 696.19 × 10³ mm³, 748.29 × 10³ mm³, and 505.19 × 10³ mm³ volume for each 15°, 20°, and 25° angle, respectively. In actual situations, debris flow is capable of causing significant risk to the affected area. This study can be deemed useful for a risk assessment approach, to help develop guidelines, and to mitigate the regions where debris flows are most probable to occur.

1. Introduction

In mountainous areas where uphill valleys or streams are fed by heavy annual rainfall, debris flow has been recognized as a natural phenomenon in recent years. Due to its size (volume of transported debris) and long runout, the phenomenon is among the most dangerous natural processes that affect the mountainous environment [1]. Debris flow contains multiple mixtures of solids, soil, wood, gravel, rocks, snow, ice, and water that slide down slopes under the driving force of gravity [2]. These flows are frequently reported to result in major property damage, loss of life, and morphological changes along riverbeds and mountain slopes [1,3,4].

In many areas of the country, major flooding and landslides were caused by significant amounts of rain that were recorded as a result of prolonged rainfall events [5,6]. Debris flows are often caused by many different mechanisms, one of which is heavy rain, which turns landslides into fast-moving liquid sediments [6,7,8].

Debris flow formation consists of three stages: the initiation area, the propagation zone, and the deposition area [1,9].

The phase of initiation is where the initial mass is released. The most typical type is debris flow, which is mobilized from a single large landslide or from a large series of smaller landslides. They occur when a landslide or debris slide turns into a debris flow. Mobilization is the process of creating debris flows from a static mass of liquid soil, silt, or rock. A major contributing component to the development of a debris flow is the impact of surface-water runoff [9,10,11,12,13]. Debris flows can also be caused by steep channels with an abundance of sediment, shallow landslides, and frequent in high-mountain regions [14,15,16]. The triggered process depends on several characteristics, including the geomorphology, geotechnical characteristics of slope inclination, hydrological factors, and geological setting [8,17]. It is of utmost importance to investigate and understand the debris flow initiation mechanisms with variously sophisticated circumstances for developing debris flow mitigation [18,19].

Once debris flows initiate, they travel down the channel. The zone of propagation is the path where the debris flow after initiation has been triggered, usually by a few factors. One of the main characteristics of many debris flows is the entrainment of channel path and torrent flank material as well as sediment deposition during runout. Through abrupt changes in the flow volume and its rheological behavior, such entrainment mechanisms have the ability to drastically change the mobility of the flow [1]. For researchers to predict the behavior of a debris flow in this zone, parameters such as runout distance are essential [20]. Efforts to analyze, predict, and evaluate the runout flow are necessary for identifying the hazardous region that can be potentially impacted and determining the intensity of the disaster for hazard and risk assessment. Prevention strategies can also be conducted, as can mitigation designs, through dynamic analysis [21,22].

Deposition zones, also known as alluvial fans, typically have many fan levels that alternate between aggradation and incision. There are situations where it could develop hundreds of kilometers away from its source, and deposition of the debris is the final stage of debris flows [23]. Channelized debris flows can rapidly transport large volumes of sediment to the depositional zone, endangering nearby residents’ infrastructure, such as buildings and roads, as well as the environment [24,25,26].

Mitigation and prevention are necessary as they involve lives and the destruction of property. Therefore, it is very important to understand the initiation, propagation, and deposition of the debris flow, and it can be a dominant tool to reduce and minimize the effects of disasters [27].

Debris flow incidents are only investigated and reported when they have already resulted in damage to people or property. Currently, research on debris flows is limited to post-disaster analysis at the catastrophe site. The catastrophes ultimately lead to huge financial losses and fatalities [15]. There have been comparatively few observations of debris flow events in the field. The mechanisms and characteristics of debris flows have long been poorly understood [1]. Given a specific shape and collection of materials, observations of laboratory experiments utilizing model-scale flumes can help us understand the mechanics of debris flows better and, as a result, help us quantify the spatial component of risk. Furthermore, parametric investigations can be carried out in a flume experiment, which is simpler and highly controlled.

2. Materials and Methods

2.1. Physical Model Test

The model for this study was developed with three main components: a water tank, a flume, and a deposition board. In this design, the water tank is filled manually using a pump system, and flow to the tank is controlled by a butterfly valve connected to the pipe. The actual model is 4.55 m long, 1.1 m wide, and 1.5 m high. The water tank is 1 m long, 1 m wide, and 1 m high. The total length of the flume is 2.5 m long, 0.1 m wide, and 0.01 m high. The deposition board dimension is 1 m long and 1 m wide. The model is constructed using a polyvinyl chloride (PVC) sheet with a 10 mm thickness. Figure 1 shows the geometry of the physical model, and Figure 2 shows the physical model in the laboratory.

2.2. Physical Model Configuration

The determination of the design parameters of the model needs to be considered, such as the flume angle and water level in the water tank.

Twelve cases were included in the study and tested at different water levels, flume angles, and water gate openings.

Table 1. Investigated cases.

Case Study	Flume Degree (°)	Water Level (mm)	Gate Opening
A1	15	120	Half
A2	15	120	Full
A3	15	150	Half
A4	15	150	Full
B5	20	120	Half
B6	20	120	Full
B7	20	150	Half
B8	20	150	Full
C9	25	120	Half
C10	25	120	Full
C11	25	150	Half
C12	25	150	Full

summarizes the case studies and operations used in this section.

In this research, the water and sediment are separated in the experiment. In order to study these processes in isolation, we systematically varied the water content (height of water in the tank) of the bed sediment. Through experiments, we were able to observe and measure the effect of different water contents on the process of entrainment. According to Calhoun and Clague [28], water-rich mass flows are one of the causes of debris flow. This process involves the movement of a continuous mass of debris, resembling a flood, which is directed by an inflow. The primary mode of transportation for the majority of sediments within this flow is particle-by-particle movement, forming what is known as a bed load. The water in the tank was used to reproduce the conditions of a debris flow. In their research, [29] utilized this method to study the segregation of particle routing in debris flow mechanisms.

2.2.1. Sediment Particle and Preparation

The limestone used in this study was obtained as a by-product of the marble industry in Ipoh, Malaysia. Prior to undertaking the experiments, a general characterization of the limestone was done to determine its particle size. In order to get the necessary particle size for the media, about 1 kg of limestone was sieved using a sieve shaker. The particles were sieved to pass through a 1.18 mm aperture and be retained in a 2 mm size range. The limestone used in the experiment had a density of 2573 kg/m³. Figure 3 shows the total sample collection as well as the sieve shaker that was used to sieve the samples. The selection of debris flow material offers valuable data insights, especially when focusing on limestone. This is particularly significant in the Malaysian region, where limestone is known to have extensive formation and prevalence [30].

Sediment is filling behind the sediment block in the flume, which is 50 mm high, 500 mm long, and 100 mm wide. The distance between the bottom sediment block and the bottom of the flume is 1250 mm. The sediment block is higher than the sample to maintain its position before the test is carried out. The details of the sediment are shown in Figure 4.

2.2.2. Water Tank

The water in the tank will be filled based on the test that will be conducted according to the height of the water, either 120 mm or 150 mm. The water in this tank resembles the pore water pressure in the soil. The increase in water content leads to a decrease in the shear strength of the soil in the process of rainfall infiltration. Eventually, the balance of the debris source fails, triggering a debris flow [19]. The pump will be turned on to fill the tank with water and controlled using a valve to reach the desired water level. The marker for the water level in the water tank is shown in Figure 5.

2.2.3. Water Gate Opening

For this study, there are two openings (50 mm and 100 mm) controlled by a water gate using pneumatic actuators. The pneumatic actuators converted the energy of compressed air into a mechanical motion that regulates the water gate. This opening is to see the influence of the amount of water on the sediment on the dynamics of debris flow, where water has an extensive influence on it [31]. Figure 6 shows the position of the water gate system and water opening on the physical model.

The pneumatic actuator is connected to the control box with a push button to control the opening and closing of the water gate. The control box comprises a solenoid valve, circuit board, power supply, and push button that have their respective functions to ensure that it works as desired. Figure 7 indicates the electronic device on the control box.

2.2.4. Inclination of Flume

The degree of the slope on the flume is adjusted depending on the case. Prior to conducting the test procedure, the slope of the flume is set. In this study, three levels of flume angle (°) were studied to represent the initiation level of debris flow: high (25°), intermediate (20°), and low (15°) levels. This is based on the fact that the average slope angle of the channel bed at the prospective area for debris flows typically ranges from 10° to 25° [8,20,32,33,34]. The inclination of the flume is shown in Figure 8.

2.2.5. Deposition Board

A deposition board is located at the end of the flume to receive particle deposits from the flow current. An alluvial fan will be formed, and the contour will be measured as a grid. The boards are kept in clean condition, in good alignment, and positioned properly to avoid data distortion.

Equation (1), developed by [20], was used to determine the position and volume of the sediment in the flume and the size of the deposition board. Three runout distances calculated for three different slopes met the equation with a runout distance of less than 1000 mm.

L = 1.9V^0.16 H^0.83

(1)

where L is the propagation distance, H is the height where the debris flow occurred, and V is the volume of the debris flow. Based on the height and volume of the debris flow occurrence, the behavior of the debris flow was studied. As a result, the outcomes were based on a topographical viewpoint.

2.3. Data Collection

2.3.1. Shape and Thickness

In order to have an accurate condition of the sediment deposit, the grid method is used. In this method, a rigid bamboo stick with a diameter of 4 mm and a length of 15 mm with red and white colors is used as the interval measurement. Each interval is 20 mm to facilitate the process of retrieving data for thickness. The stick is placed as a grid on a board, 50 × 50 mm for the middle part and 100 × 100 mm for the right, left, and end parts of the board. The middle part of the grid is smaller because more deposits occur in this part than in other parts. Figure 9 shows the grid points on the deposition board and the labels on the deposition board for data retrieval purposes. In research conducted by researchers [35], it was determined that bamboo sticks have no impact on the runout and pattern of debris flows. The study aimed to investigate the efficacy of tree stems in intercepting debris flows in forested fan areas. The researchers observed that the high-forest management type, which was represented by bamboo sticks in this study, did not appear to have a significant impact on reducing debris-flow motion for solid concentrations greater than or equal to 0.60.

A measuring tape was used to measure the shape deposit of each grid on the x and y axes. A digital caliper depth rod was used to measure the thickness of the deposit on the deposition board and lower jaws were used to measure the deposit shape for parts that required high-accuracy readings to get the actual shape.

2.3.2. Contour Sketch and Visualize

Once the data were collected, they were processed to generate a contour map using the Kriging method. One of the advantages of kriging is that it allows for quantifying the estimation uncertainty, which is important for decision-making processes. Kriging is often regarded as an effective approach because it can produce accurate maps for a wide range of datasets. Additionally, it has the capability to compensate for clustered data by assigning less weight to the cluster in the overall prediction [36].

The resulting contour maps were used to further understand deposition shapes and patterns. Cross-sectional profiles, volumes, areas, and distances can also be computed and exported. This can simplify the analysis process. In this study, Surfer was utilized as a software tool for post-processing and analysis of the collected data. Surfer is a comprehensive and powerful software package developed by Golden Software, which specializes in providing advanced scientific data visualization tools. Specifically, Surfer is designed to create and visualize high-quality 2D and 3D maps, models, and analyses of spatial data, making it a suitable choice for a wide range of scientific applications [37,38]. Figure 10 shows some examples of post-processing results.

2.4. Test Procedure

This section explains the process of the experiment. The stages of the experimental process chart are shown in Figure 11. This chart shows how the experiment is carried out.

The experiment is conducted as follows. Firstly, the water gate was closed using the pneumatic actuator with an on/off switch button. The flume is tilted to the desired inclination according to the case to be carried out. The water tank is filled with water at the desired level, according to the case. The deposition board is ensured to be in its proper position and in good alignment by using a spirit level. The sediment is then prepared in the flume. Once everything is ready, the switch is pressed to open the water gate for 5 s. Then, the switch is pressed again to close back the water gate.

The next step is to take data for the sediment contour on the deposition board using an electronic caliper and measuring tape. Contour data are recorded in x, y, and z coordinate formats. The recorded data will then visualize the contour in 3D.

3. Results and Discussions

3.1. Deposition Observation

A total of 12 cases were analyzed. The contouring was performed with a measuring tape and digital calipers. As a result of the data analysis, a 3D contour map was generated to represent the spatial distribution of the sampled data. Then, a planar (2D) view of the cross-section of the 3D contour was created to provide a more detailed view of the distribution pattern along a specific axis or plane. Each color in the contour line represents an elevation value, which is measured in millimeters (mm). According to [21], the deposition pattern is unaffected by any obstructions or discrete channels on the fan. Typically, the topography causes the material to rise over the channel and begin to spread over the fan.

Table 2. Debris flow deposition pattern categorization [21].

Type	Remarks
A	Represents an ideal shape for uniform runout patterns with no obstructions or distinct channels on the fan affect deposition. Typically, the topography causes the material to rise over the channel and begin to spread over the fan.
B1	Obstructions such as structures or mitigation measures in the lower part of the deposition region affect the deposition pattern.
B2
C1	Linear structures crossing the deposition zone, such as roads, railway tracks, or receiving streams that caused a pronounced lateral spreading in the lower part of the deposition region.
C2
D

displays the deposition pattern as classified by the observations of [21]. Table 2 categorizes the results of the deposition pattern from the experimental observation. This process is necessary to comprehend the particle characteristics, particle distribution, and physical data of the deposited material.

The researchers [21] made an important observation regarding the debris-flow deposition pattern known as type A. They identified a distinct correlation between the properties of the circle sector (specifically the radius, denoted as L_f, and the aperture angle, denoted as Ψ) and the volume of the event (V). This correlation allowed them to propose a theoretical approximation for the radius, L_f in Equation (2). Moreover, they conducted data analysis and successfully fitted the data with a power-law function, resulting in a coefficient of determination (R²) value of 0.78. As depicted in Figure 12, it was determined that type A represents an ideal shape for achieving uniform runout patterns.

$${\mathrm{L}}_{\mathrm{fpred}}=65.3{\left(\frac{\mathsf{\Psi }}{{\mathrm{V}}^{2/3}}\right)}^{-0.49}\approx 65.3{\mathsf{\Psi }}^{-1/2}{\mathrm{V}}^{1/3}$$

(2)

Due to the observational outcomes being nearly identical for all four cases, only two of the four cases on each slope of the flume (15°, 20°, and 25°) representing the water level (120 mm, 150 mm) with half gate opening are displayed in Figure 13.

As shown in Figure 13, the deposition trajectory reaches the end of the deposition board for all 6 cases. From case A1 to case C11, the deposition pattern reveals that the fan size is decreasing. According to the details, A1 recorded the highest estimated total volume of deposition, which is 1.677518 × 10³ mm³, with a surface area of 537.07 × 10³ mm². The total volume of particles on the deposition board decreases as the inclination angle increases, and this trend can be seen in all conditions.

In every case, the pattern type is categorized as type A because it represents the ideal shape for uniform runout patterns because there are no obstacles or distinct channels on the fan affecting deposition.

In the conducted research, Figure 14 visually presents the outcome following the completion of each case. Mainly, no sediment remains either behind the sediment block or in front of it once the water gate is closed, as clearly depicted in Figure 14a. Furthermore, Figure 14b effectively illustrates the condition of the deposition board subsequent to the complete deposition of sediment. The deposit’s shape on the board is clearly observable without any obstructions caused by the bamboo stick. Additionally, the total volume of sediment that traverses over the board is visibly captured and measured through the retention on the strainer, with the corresponding values recorded in Table 2.

Table 3. Summary of the results.

Case Study	Total Volume of Deposited Sediment (mm3)	Total Volume of Sediment Retained in Strainer (mm3)	Planar Area (mm2)	Surface Area (mm2)	Aperture Angle (°)	Highest Point (mm)	Percentage Particle on Deposition Board (%)	Type of Pattern	Lfpred [21] (mm)
A1	1.677518 × 103	2498.322 × 103	536.79 × 103	537.07 × 103	90.19	7.5	53.68%	A	884.87
A2	1.508610 × 103	2498.491 × 103	436.93 × 103	437.13 × 103	86.63	6.5	43.69%	A	902.50
A3	1.656639 × 103	2498.343 × 103	488.42 × 103	488.65 × 103	81.83	6.5	48.84%	A	928.07
A4	1.544908 × 103	2498.455 × 103	402.34 × 103	402.61 × 103	67.87	7.5	40.23%	A	1017.15
B5	1.497587 × 103	2498.502 × 103	461.38 × 103	461.57 × 103	124.88	5.5	46.14%	A	754.44
B6	1.730672 × 103	2498.269 × 103	447.06 × 103	447.57 × 103	98.87	7	44.71%	A	845.91
B7	1.54 × 103	2498.460 × 103	415.86 × 103	416.17 × 103	85.46	7	41.59%	A	908.54
B8	1.048050 × 103	2498.951 × 103	290.03 × 103	290.33 × 103	84.00	6.5	29.00%	A	916.24
C9	1.312914 × 103	2498.687 × 103	367.62 × 103	367.87 × 103	86.52	6.5	36.75%	A	903.07
C10	1.251489 × 103	2498.748 × 103	321.46 × 103	321.93 × 103	73.17	11	32.15%	A	980.36
C11	1.377437 × 103	2498.622 × 103	485.07 × 103	485.23 × 103	102.45	4.4	48.51%	A	831.30
C12	1.179189 × 103	2498.820 × 103	298.70 × 103	299.02 × 103	65.86	7	29.87%	A	1032.24

shows the summary results for all experimental cases. The table consists of the total volume of deposited sediment, total volume of sediment retained in the strainer, planar area, surface area, aperture angle, highest point, and percentage of particles on the deposition board. The effect of the slope gradient on the flume and water level inside the tank can be seen in Table 3.

From Table 3, the maximum percentage of particles covering the sedimentation board is 53.68% for A1 and the minimum percentage is 29.00% for B8, respectively, at angles of 15° and 25°. The decrease in the percentage of particles on the deposition board from case A1 to case C12 can be attributed to the change in slope gradient (15° to 25°) at the flume and water level (120 to 150 mm) in the tank. This decrease in the percentage of particles on the deposition board could be related to an increase in pore water pressure, causing entrainment to occur and separating the particles, making them liquefy and accelerate in motion during runout. This causes the sediment to flow out of the deposition board, as supported by the total volume results. This situation shows a higher mobility and results in flatter deposits, with only one case recording the highest point on the contour at 11 mm and the rest below 7 mm. Additionally, larger flume slopes produce larger runout distances and reduce the area due to greater gravitational potential energy.

According to our observations, the deposition fan in case B5 exhibits the widest aperture angle, measuring 124.88°, while the smallest aperture angle of 65.86° is found in case C12. In case C5, there is a flume inclined at 20° with a water level of 120 mm and the water gate partially open. Similarly, in Case C12, the flume has a 25° inclination, a water level of 150 mm, and the gate is fully open. By examining the case with a 15° inclination, we can observe a reduction in angle from Case A1 to A4. This pattern of angle reduction is also evident in cases with 20° and 25° of inclination.

As a result of predicting the debris flow length using Equation (2), it was found that there were only two cases where the runout length exceeded 1000 mm compared to all the other cases. During the observation, it was found that some of the sediment that has been deposited will be carried to the end of the board by the excess water flowing from the flume after the gate is open for 5 s. This indicates that the duration of the open gate affects the movement of sediment in the flume.

3.2. Statistical Analysis

This analysis explores the relationships between flume inclination (θ_d) and fluid volume (V_W) as independent variables and total volume of deposited sediment (V_T), total volume of sediment retained in strainer (V_out), planar area (P_A), surface area (S_A), aperture angle (Ψ), highest point (H_P) and percentage particle on deposition board (P_B) as dependent variables using Pearson’s correlation coefficient (r) and regression analysis.

Several variables exhibited a significant correlation with the inclination of the flume. For instance, a weak positive correlation was observed between flume inclination and the aperture angle (r = 0.302, p < 0.05). Furthermore, the inclination demonstrated a weak negative correlation with the total volume of sediment retained in the strainer (r = −0.005, p < 0.05), as shown in

Table 4. Statistical analysis for correlation coefficient, θ_d, V_w, and other variables based on Pearson analysis.

	θd (°)	Vw (mm3)	VT (mm3)	Vout (mm3)	PA (mm2)	SA (mm2)	Ψ (°)	HP (mm)	PB (%)
θd (°)	1
Vw (mm3)	0.000	1
VT (mm3)	−0.637 *	−0.260	1
Vout (mm3)	−0.005	0.783 **	−0.315	1
PA (mm2)	−0.527	−0.210	0.844 **	−0.410	1
SA (mm2)	−0.527	−0.210	0.844 **	−0.411	1.000 **	1
Ψ (°)	0.302	−0.285	−0.078	−0.305	0.130	0.129	1
HP (mm)	−0.248	0.107	−0.308	0.107	−0.418	−0.418	−0.565	1
PB (%)	−0.527	−0.210	0.844 **	−0.410	1.000 **	1.000 **	0.129	−0.418	1

* Correlation is significant at the 0.05 level (2-tailed). ** Correlation is significant at the 0.01 level (2-tailed).

. Notably, a strong negative correlation was found between the flume inclination and the total volume of deposited sediment (r = −0.637, p < 0.05). It was evident that the distribution of sediment deposition in terms of total volume was influenced by the inclination of the flume and indicated that when θ_d is increased, there is a clear correlation with a decrease in the volume of deposits present on the board. In a study conducted by [39], the experimental findings provided support for the idea that as the channel slope, which represents the flume inclination, increased, the total travel distance of debris flow also increased. Aside from flume inclination, fluid volume also showed a significant association with V_T (r = −0.260, p < 0.05), V_out (r = 0.783, p < 0.01), P_A (r = −0.210, p < 0.05), S_A (r = −0.210, p < 0.05), Ψ (r = −0.285, p < 0.05), H_p (r = 0.107, p < 0.05), and P_B (r = −0.210, p < 0.05). A significant positive correlation between V_out (fluid volume) and the runout distance of debris flow, suggesting that higher fluid volumes contribute to increased travel distances. According to a study carried out by [40], it has been demonstrated that the phenomenon of entrainment exerts a noteworthy impact on flow depths and runout. The study reveals a substantial augmentation in both maximum flow heights and the distance covered by the flow when entrainment is taken into consideration. In fact, the calculated maximum height of the flow, when entrainment is absent, can be multiplied by two or even three times when compared to the estimated maximum heights that incorporate the entrainment process. Similarly, the length of the runout distance traveled can be expanded by nearly one-third. Moreover, this study reveals that a higher fluid volume also leads to a greater retention of sediment on the strainer.

In [41], the researchers mentioned that the polynomial regression model has the potential to accurately predict responses in certain data segments. Therefore, for the analysis of θ_d and V_w, this research explored alternative regression models, including linear, quadratic, and nonlinear approaches. The subsequent equations were formulated to account for each type of response.

$$\mathrm{y}=\mathrm{a}+\mathrm{b} \times \mathrm{t},$$

(3)

$$\mathrm{y}=\mathrm{a}+\mathrm{b} \times \mathrm{t}+\mathrm{c} \times {\mathrm{t}}^2,$$

(4)

$$\mathrm{y}=\exp \left(-\mathrm{b}1 \times \mathrm{x}\right)/\left(\mathrm{b}2+\mathrm{b}3 \times \mathrm{x}\right)$$

(5)

Several datasets exhibit poor conditioning when applied to a quadratic model. Fits for the linear and quadratic are reasonably comparable for the θ_d with V_T (R² = 40.6, 40.7). The comparative analysis of the nonlinear model reveals its superiority in estimating the values of θ_d and V_W for the aperture angle data, as indicated by its significantly lower standard error of the regression (S) when compared to alternative models. However, it should be noted that the nonlinear model does not provide a coefficient of determination (R²) to assess the goodness of fit.

Table 5. Regression goodness of fit for θ_d, V_W with other variables.

		θd (°)			Vw (mm3)
Variable	Regression Type	R2 (%)	S	Equation	R2 (%)	S	Equation
VT (mm3)	Linear	40.6	171.288	VT = 2077 − 31.67θd	6.75	214.616	VT = 1918 − 3.514Vw
	Quadratic	40.7	180.357	VT = 1840 − 69θd − 0.620θd2	N/A	N/A	N/A
	Nonlinear	N/A	180.835	VT = exp(−0.0218546θd)/(0.000449157 + 1.72044 × 10−12θd)	N/A	1157.87	VT = exp(−0.0172781Vw)/(−1.1024 + 0.00918734Vw)
Vout (mm3)	Linear	0.0	222.246	Vout = 2,498,562 − 0.27θd	138.18	61.34	Vout = 2,497,126 + 10.59Vw
	Quadratic	0.01	234.261	Vout = 2,498,510 + 5.2θd − 0.136θd2	N/A	N/A	N/A
	Nonlinear	N/A	234.268	Vout = exp(−1.0799 × 10−7θd)/(4.0023 × 10−7 − 3.31555 × 10−16θd)	N/A	2,040,192	Vout = exp(−0.0296687Vw)/(−1.10221 + 0.00918512Vw)
PA (mm2)	Linear	27.78	70,606.7	PA = 608,453 − 9791θd	4.4	81,234.5	PA = 555,753 − 1060Vw
	Quadratic	28.49	74,057.8	PA = 816,737 – 31,525θd + 543θd2	N/A	N/A	N/A
	Nonlinear	N/A	74,057.8	PA = exp(0.0223781θd)/(3.74916 × 10−7 + 1.7508 × 10−7θd)	N/A	335,061	PA = exp(−0.0277149Vw)/(−1.10245 + 0.00918709Vw)
SA (mm2)	Linear	27.77	70,574.4	SA = 608,634 − 9785θd	4.41	81,187.1	SA = 556,277 − 1062Vw
	Quadratic	28.48	74,026.5	SA = 816,075 − 31,431θd + 541θd2	N/A	N/A	N/A
	Nonlinear	N/A	74,026.5	SA = exp(0.0222817θd)/(3.83081 × 10−7 + 1.74142 × 10−7θd)	N/A	335,257	SA = exp(−0.0276883Vw)/(−1.10245 + 0.00918709Vw)
Ψ (°)	Linear	9.14	16.1373	Ψ = 64.42 + 1.145θd	8.11	16.2287	Ψ = 126.9 − 0.2934Vw
	Quadratic	29.92	14.9388	Ψ = 293.6 − 22.77θd + 0.5978θd2	N/A	N/A	N/A
	Nonlinear	N/A	14.9388	Ψ = exp(0.134118θd)/(−0.221576 + 0.0205293θd)	N/A	17.1065	Ψ = exp(0.0274097Vw)/(−1.48245 + 0.0147908Vw)

shows the regression goodness of fit for several variables.

4. Conclusions

Data collected on all 12 cases were used as input to be analyzed and visualized. The results from the analysis of all 12 cases show the maximum percentage of particles covering the deposition board is 1.677518 × 10³ mm³ (53.68%) for A1 and the minimum percentage is 1.048050 × 10³ mm³ (29.00%) for B8. The decrease in the percentage of particles on the deposition board from case A1 to case C12 can be attributed to the change in slope gradient (15° to 25°) at the flume and water levels (120 to 150 mm) in the tank. Evidently, an increase in water content and pore water pressure leads to entrainment, which separates the particles, causes them to liquefy, and accelerates the motion during runout. As a result, the sediment was driven off the deposition board.

The research concludes that even though the affected area comprises only 29% or the minimum with a small aperture angle, the strainer retains a larger amount of sediment. This suggests that the debris flow has the potential to travel longer distances. These findings have significant implications for the development of guidelines, mitigation plans, and risk assessment techniques in regions with extensive limestone formations and where debris flows are expected to occur.