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.

Rigid barriers can effectively prevent natural hazards caused by mass-wasting debris flows in mountainous regions [

The interactions between debris flows and deflectors have been investigated using both physical and numerical models. Choi et al. [

Natural debris flow, which is a typical non-Newtonian fluid, has the characteristics of shear thinning or shear thickening behavior [

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) [

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 [

The governing equations (

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 [

In

In

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

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

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

In

In

This study employed the generalized wall boundary method and 4^{th}-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 [

Because deflectors are an efficient debris flow deflection method, a previous study [

The setup of the 3D numerical flume models of the single barrier with deflectors and dual-barrier system are illustrated in ^{−3} for natural debris flow containing fine-grained pyroclastic soil in southern Italy, as estimated from

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 [

In

Rheological properties | Parameters |
---|---|

1135 | |

90 | |

4.526 | |

0.795 |

The apparent viscosity

The above model is singular in the static state when ^{−1} to prevent singular viscosity at zero shear rates [

The dam break test reported by a previous study [

Rheological properties | Parameters |
---|---|

997 | |

0 | |

0.001 | |

1 | |

0.6; 0.3 /0.6 |

Test ID | Deflector |
Upstream barrier height (mm) | Distance between barriers | Downstream barrier height (mm) |
---|---|---|---|---|

H0-WD |
No deflector | / | / | / |

H10-WD1 | No deflector | 250 | / | / |

H10-WD2 | No deflector | 100 | / | / |

H10-D0 | 0 | 100 | / | / |

H10-D30 | 30 | 100 | / | / |

H10-D45 | 45 | 100 | / | / |

H10-D60 | 60 | 100 | / | / |

H10-D0-H25 | 0 | 100 | 700 | 250 |

H10-D30-H25 | 30 | 100 | 700 | 250 |

H10-D45-H25 | 45 | 100 | 700 | 250 |

H10-D60-H25 | 60 | 100 | 700 | 250 |

H10-WD1-H25 | No deflector | 100 | 700 | 250 |

H10-WD-H18 | No deflector | 100 | 700 | 180 |

H10-WD2-H25 | No deflector | 100 | 400 | 250 |

H18-WD-H25 | No deflector | 180 | 400 | 250 |

The simulated results obtained by the proposed model were compared to the experimental results and are presented in

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 [_{.} 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 [

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.

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

In

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 (

The energy dissipation of the dual-barrier system exhibits characteristics similar to the three stages observed in the single barrier structure described earlier (

The barrier height, barrier location, and deflector angles greatly influence the control of the dynamic behavior of viscous flow. As shown in

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

Larger deflector angles can effectively retain a larger amount of debris flow.

In a dual-barrier system without deflectors, the ramp-like dead zones become steeper as the height of the upstream barrier increases (

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:

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.

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.

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

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

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.

The data sets used and analysed during this study are available from the corresponding author upon reasonable request.

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