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# Interaction Mechanisms between Natural Debris Flow and Rigid Barrier Deflectors: A New Perspective for Rational Design and Optimal Arrangement

1 Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, Shanghai, 200092, China

2 Department of Hydraulic Engineering, College of Civil Engineering, Tongji University, Shanghai, 200092, China

* Corresponding Author: Dianlei Feng. Email:

(This article belongs to the Special Issue: Recent Advances in Computational Methods for Performance Assessment of Engineering Structures and Materials against Dynamic Loadings)

*Computer Modeling in Engineering & Sciences* **2024**, *139*(2), 1679-1699. https://doi.org/10.32604/cmes.2023.044094

**Received** 20 July 2023; **Accepted** 31 October 2023; **Issue published** 29 January 2024

## Abstract

Rigid barrier deflectors can effectively prevent overspilling landslides, and can satisfy disaster prevention requirements. However, the mechanisms of interaction between natural granular flow and rigid barrier deflectors require further investigation. To date, few studies have investigated the impact of deflectors on controlling viscous debris flows for geological disaster prevention. To investigate the effect of rigid barrier deflectors on impact mechanisms, a numerical model using the smoothed particle hydrodynamics (SPH) method with the Herschel–Bulkley model is proposed to simulate the interaction between natural viscous flow and single/dual barriers with and without deflectors. This model was validated using laboratory flume test data from the literature. Then, the model was used to investigate the influence of the deflector angle and multi-barrier arrangements. The optimal configuration of multi-barriers was analyzed with consideration to the barrier height and distance between the barriers, because these metrics have a significant impact on the viscous flow pile-up, run-up, and overflow mechanisms. The investigation considered the energy dissipation process, retention efficiency, and dead-zone formation. Compared with bare barriers with similar geometric characteristics and spatial distribution, rigid barriers with deflectors exhibit superior effectiveness in preventing the overflow and overspilling of viscous debris flow. Recommendations for the rational design of deflectors and the optimal arrangement of multi-barriers are provided to mitigate geological disasters.## Graphic Abstract

## Keywords

Rigid barriers can effectively prevent natural hazards caused by mass-wasting debris flows in mountainous regions [1,2]. In large-scale natural debris flow disasters, bare barriers cannot retain flow material, and do not satisfy existing disaster protection requirements. Many design recommendations have been proposed to prevent debris flows from overflowing and overspilling [3,4]. For mitigation purposes, deflectors positioned atop the wall stem can redirect debris flows. The parapets in coastal structures are prototypes of these deflectors, and were initially designed to minimize water overspill and splash back [5,6]. The reduction factor quantifies the effectiveness of deflectors by measuring the discharge that overtops a barrier with a deflector in place and dividing this amount by the discharge that overtops a barrier without a deflector [7]. The comparison of bare barriers and rigid barriers with deflectors is shown in detail in Fig. 1, where

The interactions between debris flows and deflectors have been investigated using both physical and numerical models. Choi et al. [12] conducted preliminary small-scale flume experiments to investigate dry granular flow interaction with deflectors that had different angles. Ng et al. [4] conducted flume tests to investigate the flow kinematics of dry sand flows and the energy dissipation under the influence of deflectors. The results obtained by previous studies have revealed that conditions for adverse overflow strongly depend on the effective barrier height and length, and deflector angle. Notably, the flow characteristics of viscous debris flow differ significantly to those of dry granular flow, resulting in overspilling and hydrodynamic dead-zone formation [13–15]. Ng et al. [16] discussed the impact kinematics of fluids, including water and slurry, under different deflector geometries. A modified impact equation considering the flow-deflector interactions has been proposed. The impact, run-up, and pile-up mechanisms of saturated debris flow exhibit significant differences compared with those of dry granular flows in flow–barrier interactions. Consequently, research on the influence of deflectors on natural debris flow remains limited. Moreover, an appropriate constitutive model is required to capture the dynamic behavior of natural debris flow accurately and elucidate the flow–deflector interaction mechanisms.

Natural debris flow, which is a typical non-Newtonian fluid, has the characteristics of shear thinning or shear thickening behavior [17]. Various non-Newtonian rheological models, such as the Bingham model [18,19], power-law model [20], and Herschel–Bulkley model [21,22], have been proposed. Moreover, the constant threshold of yield stress (

The grid-based method and particle-based method are often used for modeling flow–structure interactions. For large-deformation debris flows, mesh-free methods can avoid the grid distortion in grid-based methods. Methods such as the discrete element method (DEM) [24], coupled computational fluid dynamics and discrete element method (CFD-DEM) [25], material point method (MPM) [26], and smoothed particle hydrodynamics (SPH) [27] are typical particle-based methods for capturing the complicated flow–barrier interactions of classic geomechanical problems. Among them, the SPH method has many advantages in solving large deformation problems over traditional grid-based methods [24–26]. This method has become widespread owing to its accuracy and stability under complex boundary conditions for the quantitative analysis of the mechanisms of dynamic interaction between natural debris flows and rigid barriers [27–29]. Wang et al. [30] investigated the flow behavior of debris flows using SPH, focusing on the propagation analysis of debris flows in terms of run-out distance and flow velocity. Dai et al. [31] used SPH to investigate the interaction between debris flows and structures, and estimated the impact force. Sun et al. [32,33] proposed the particle shifting technique (PST) to maintain the numerical stability and accuracy of the δ-plus-SPH scheme. Notably, the δ-SPH scheme introduces an artificial diffusive term to improve the high-frequency noise in the pressure field. Relevant results have revealed that δ-plus-SPH is feasible and reliable for investigating the dynamic interaction between debris flows and structures.

This study developed a δ-plus-SPH method and used it to investigate the influence of deflectors on the dynamic behavior of viscous debris flow. The primary objective of this study was to investigate the influence of deflector angles on viscous debris flow in both single-barrier and dual-barrier systems. The presentation and validation of the numerical results are obtained by using the δ-plus-SPH model, followed by the discussion of energy dissipation process, retention efficiency, and run-up and overflow mechanisms of viscous debris flow in rigid barriers with and without deflectors.

In the domain of computational fluid dynamics, the SPH method has emerged as a prominent mesh-free Lagrangian approach [28]. Central to the SPH method is the utilization of kernel functions to compute particle interactions, ensuring both consistency and stability in the numerical representation. This subsection presents the fundamental principles and mathematical formulations of the SPH method. Each equation is systematically introduced, accompanied by a rigorous exposition of its derivation, underlying assumptions, and its role within the overarching SPH framework.

The governing equations (Eq. (1)) include the mass and momentum balance, and require numerical solutions.

Eq. (1) has the derivative form of density and velocity;

Recently, the SPH method has been widely used to simulate large-deformation natural debris flows, because it can capture free surfaces and large deformable geomaterial boundaries [34]. By using the SPH method, the governing equations can be efficiently solved. The physical properties carried by the arbitrarily distributed discrete particles of debris flow are based on the distributed particles within a smoothing length. The field function

where

In Eqs. (3) and (4),

In Eq. (5),

In this study, the particle shifting technique (PST) and

In two-dimensional problems, the coefficient of the viscous term

where

The PST method is used to avoid arbitrary particle configuration, and the shifting velocity

In Eq. (9),

In Eq. (11),

This study employed the generalized wall boundary method and 4th-order Runge–Kutta time-integration technique to model intricate geometries. Notably, dummy particles can be used to model the interactions between the fluid phase and a solid boundary [42].

2.2 Numerical Model Setup and Rheological Model

Because deflectors are an efficient debris flow deflection method, a previous study [12] conducted flume tests to investigate the influence of different rigid barrier deflector angles. The overflow mechanisms are characterized by viscous flow launching off ramp-like dead zones, launch length

The setup of the 3D numerical flume models of the single barrier with deflectors and dual-barrier system are illustrated in Figs. 2a and 2b, and the detailed geometry of the 2D dual-barrier system with deflectors is shown in Fig. 2c. A rigid barrier with a 65-mm-long deflector (

The Herschel–Bulkley (HB) model was used to model the debris flow. The HB model has been widely used to investigate the rheological behavior of natural debris flow [47,48]. The deviatoric viscous stress tensor τ is expressed as follows:

In Eq. (12),

The apparent viscosity

The above model is singular in the static state when

The dam break test reported by a previous study [50] was first used to calibrate the proposed numerical models. Fig. 3 shows the geometry of the dam break test and monitoring locations H1 and H4. Additionally, the physical and rheological parameters of the test fluid are listed in Table 2. As mentioned in the description of the rheological model in the Subsection 2.2, the debris flow viscosity is calculated by

The simulated results obtained by the proposed model were compared to the experimental results and are presented in Figs. 4 and 5. Fig. 4 mainly compares the relative flow elevation (

Unlike water, when a viscous debris flow collides with an obstacle, the flow velocity decreases dramatically, leading to an approximately triangular zone of a fluid at rest forming upstream of the obstacle. This deposited zone is referred to as a “dead zone” in mudflow [51]. The ensuing flow mounts this dead zone and expends part of its energy before hitting the barrier [1,24,52]. When the barrier’s retention capacity is reached, an overflow effect occurs: the debris flow material begins to escape from the barrier and flows forward through the barrier crest [53]. A dimensionless parameter

To gain a better understanding of the deflector’s robustness against disasters, the kinetic energy

Here,

This study investigated the effect of single and dual-barrier systems with a deflector angle of 26° on viscous debris flow. To investigate the interaction between the viscous debris flow and the dual-barrier system, upstream and downstream barriers with different heights (

At the upstream barrier position, the flow thickness and front flow velocity were measured in the open-channel test (H0-WD) to calculate

Based on the simulation results, the rest of this paper focuses on the overflow pattern and pile-up mechanisms, and discusses the energy dissipation under the influence of the deflector angles, dead zone, and retention ability of the barrier with different barrier heights and location setups.

3.1 Overflow Pattern and Energy Dissipation

Fig. 8 illustrates the dynamic behavior of viscous flow overflow with and without deflectors. A single barrier with a height of 100 mm and deflector angles ranging from 0° to 60° was considered. Orthogonal deflectors (0°) and 30° deflectors caused the viscous flow to overflow the barrier quickly, resulting in higher velocity magnitude. The distance traveled by the overflow and its points of impact on the channel base are defined as the launch length (

Deflectors with larger angles lead to a shorter launch length and larger launch angles when the viscous debris flow overflows the barrier and lands on the flume base. As shown in Fig. 9a, the launch length decreased from 1.845 to 1.273 m as the deflector angle increased from zero to 45°. However, the effect was less pronounced when the deflector angle exceeded 45°. The launch length of a barrier without deflectors (1.715 m) is marginally shorter compared with that of orthogonal deflectors (0°). The launch angle increased from approximately 20° to 35° as the deflector’s angles (ranging from 0° to 60°) increased (Fig. 9b).

In Fig. 10, the size of the dead-zone area markedly increases with the introduction of a barrier equipped with deflectors. Additionally, the dimensionless length of the dead-zone is positively correlated with the deflector angles. When the deflector angle exceeds 30°, the dimensionless length of the dead-zone increases significantly, reaching values above 3.5.

Fig. 11 illustrates the general evolution of overflow kinetic energy with various deflector angles, which can be categorized into three phases. Before impacting on the barrier, there is a kinetic energy peak in the process, owing to the acceleration of the debris flow. Phase 2 involves the dissipation process of the kinetic energy induced by the deflectors. Compared with barriers with deflectors, the kinetic energy of barriers without deflectors immediately increases, indicating a significant increase in the particle velocity. However, barriers with deflectors experience a period of zero kinetic energy when entering Phase 2 of dissipation, primarily because the deflectors directly intercept the impacting particles and then create a dead zone.

The overflow velocity magnitude and viscous debris direction are largely influenced by the deflector angles. The barrier with orthogonal deflectors exhibits a dissipation process similar to that of a barrier without a deflector, leading to the longest launch length. Although the 45° deflector significantly reduces the launch length, its capability of energy dissipation is inferior to that of the 60° and 30° deflectors within the monitored section. In the H10-D45 test program (Fig. 12), the dead zone starts to form when the flow impacts the barrier, and gradually grows and controls the overflow behavior observed around

The energy dissipation of the dual-barrier system exhibits characteristics similar to the three stages observed in the single barrier structure described earlier (Fig. 13). The energy accumulation phase follows a pattern of initial increase and subsequent decrease. Compared with the upstream barrier with a height of 100 mm, the barrier with a height of 180 mm exhibits a zero-energy zone owing to the formation of a larger dead zone. The distance between barriers affects the energy dissipation process. A shorter distance results in a larger proportion of particles flowing back to the upstream barrier with higher velocity. In contrast, the downstream barrier with a height of 180 mm effectively intercepts the released viscous debris flow.

3.2 Pile-Up Mechanism and Retention Efficiency

The barrier height, barrier location, and deflector angles greatly influence the control of the dynamic behavior of viscous flow. As shown in Fig. 14, increasing the height of a single barrier from 100 mm (

In this study, barriers with heights of 100 and 180 mm were investigated at distances of 400 and 700 mm, respectively. When the upstream barrier was equipped with deflectors, a downstream barrier height of 250 mm could intercept the entire debris volume in four test programs. The deflector angle influenced the formation of the dead zone near the deflectors, with larger angles resulting in more pronounced ramp-like dead zones. The results are presented in Fig. 15, illustrating that the dead zone serves as cushion layer at the upstream barrier. The impact of the overflowing debris flow on the downstream barrier results in the formation of dead zones with different sizes. Particularly, the upstream barrier equipped with an orthogonal deflector exhibits the highest momentum, leading to the rapid interception of viscous flow by the downstream barrier.

Larger deflector angles can effectively retain a larger amount of debris flow. Fig. 16 shows that the deflector’s debris flow interception capability increases and then stabilizes starting from approximately 1.5 s. As shown in Fig. 17, when the deflector angle

In a dual-barrier system without deflectors, the ramp-like dead zones become steeper as the height of the upstream barrier increases (Fig. 18). Although the barrier distance is reduced by 42.9% to 300 mm, the downstream barrier retains the highest debris flow volume. Compared with the single barrier with retention efficiency (Fig. 19), the upstream barrier with a height of 180 mm intercepted over 90% of the debris flow, exceeding the interception of approximately 40% achieved by the upstream barrier with a height of 100 mm.

This study investigated the interaction of viscous debris flow with barriers that have different deflector angles, and the impact of a dual-barrier system with different barrier heights and distances. The main conclusions are as follows:

(1) The interaction between viscous debris flows and barriers is largely determined by the deflector angles. Specifically, a deflector angle below 45° forms shallow ramp-like zones, promoting a thick and high-speed overflow downstream. The dimensionless length of the dead zone increases significantly when the deflector angle exceeds 30°. Moreover, the overflow mechanisms vary owing to the intricacies of viscous debris flows, with back-flows becoming more obvious when the flow velocity increases and the launch length decreases. There are three stages of energy in the dissipation process: the cumulative phase, interaction phase, and plateau phase.

(2) The barrier’s height and downstream positioning profoundly influence the effectiveness of single barriers in retaining flows. For instance, a barrier height decreasing from 250 to 180 mm cuts the retained flow volume by approximately one tenth, while a height reduction to 100 mm decreases the volume by approximately 40%. In dual-barrier systems, the spacing between the barriers also affects the dead-zone formation.

Although this study provides insights into the role of deflectors and dual-barrier systems against debris flows, further research into other influencing factors and the three-dimensional effects during viscous debris flow–structure interactions is required.

Acknowledgement: The authors thank the editor and the reviewers for their help to improve the quality of our manuscript.

Funding Statement: This study was supported by the National Natural Science Foundation of China (Grant Nos. 42120104008 and 42207198).

Author Contributions: Conceptualization, Y.H. and D.F.; methodology, B.L. and H.S.; formal analysis, B.L. and H.S.; investigation, B.L.; writing—original draft preparation, B.L.; writing—review and editing, Y.H. and D.F.; visualization, B.L.; supervision, D.F.; funding acquisition, Y.H. and D.F. All authors have read and agreed to the published version of the manuscript.

Availability of Data and Materials: The data sets used and analysed during this study are available from the corresponding author upon reasonable request.

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.

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