Unsteady overflow behavior of polydisperse granular flows against closed type barrier

Highlights

• The overflow behavior of polydisperse granular flows against closed type barrier is investigated.

• The morphology of dead zone regulates overflow behavior.

• The overflow enhanced particle-size segregation can lead to local damage of the downstream barrier.

• Too steep or gentler barrier configuration should be avoided in the field.

Abstract

The overflow behavior of polydisperse granular flows against closed type barrier is a crucial yet poorly understood aspect of multiple-barrier design. We use a robust numerical model based on the three-dimensional discrete element method (DEM) to simulate polydisperse granular flows and identify fundamental mechanisms. The morphology of the dead zone behind the upstream barrier significantly influences the overflow behavior of granular flows. This implies that aside from the case of a gentler barrier (<70°), the launch direction is controlled by the inclination surface of the dead zone. We identified a three-stage evolution process of the overflow velocity. The velocity component in the z-direction controls the first stage, whereas the latter two stages are controlled by the velocity component in the x-direction. The launch angle is usually larger than 45° during the initial overflow stage. Such a high launch angle is maintained for about 0.2–0.3 s. Boulders are transported downstream by the overflow process owing to particle-size segregation and a more concentrated load is received by the downstream barrier, which can lead to localized barrier damage. A different overflow mechanism would result in a different launch distance. Steeper (135°) and gentler (70°) barrier configurations are dangerous because the normalized launch distance is up to 20% larger than that of a barrier with a medium inclination. And a point-mass based assumption is used to estimate the maximum launch distance with the use of maximum overflow velocity and a single launch angle. In addition, we discuss some limitations of numerical modelling, including the effect of fluid phase on overflow, as well as the direct application of our results in engineering design.

Introduction

A large-scale granular assembly that surges downslope driven by gravity (e.g., debris flows, granular avalanches, lahars) often leads to catastrophic disaster (Thouret et al., 2020; Wang, 2013; Zhan et al., 2018). Substantial preventative design efforts have therefore been made to mitigate flowing geo-disasters, among which check dams are most commonly used because they are engineered to fully capture the flow debris (Albaba et al., 2018; Armanini et al., 2020; Chen et al., 2019; Jiang et al., 2018; Remaître et al., 2008; Shen et al., 2019; Shen et al., 2018; Zhou et al., 2018). Nevertheless, the design of check dams faces considerable scientific challenges because the flow-structure interaction mechanism remains poorly understood (Chen et al., 2019; Huang and Zhang, 2020). A lot of physical modeling and numerical simulation researches have been conducted to address this issue, but mostly focused on the impact dynamics of granular flows on a single barrier (Ahmadipur et al., 2019; Albaba et al., 2018; Calvetti et al., 2019; Jiang et al., 2018; Jiang and Towhata, 2013; Moriguchi et al., 2009; Ng et al., 2016; Shen et al., 2018; Zhou et al., 2018); however, in the field, multiple-barrier systems comprised of rows of single barriers with different configurations installed along the flow path are preferred to intercept the huge volume of flowing debris (Piton et al., 2017; Remaître et al., 2008; Shen et al., 2019; Wang, 2013). A multiple-barrier system is considered to stepwise reduce the kinetic energy and volume of granular flows. However, multiple-barrier system design has not been properly solved.

Koo (2017) presented a systematic design framework for multiple-barrier systems, including the flow impact process on the upstream barrier, overflow, landing, convergence, and impact on the downstream barrier. An appropriate estimate of barrier spacing is also important in multiple-barrier system design (Fig. 1). Kwan et al. (2015) proposed a simplified model to estimate the launch distance of overflowed materials based on a point mass assumption (Eq. (1)), in which the barrier spacing is required to be no less than the launch distance. In China's design code for debris flow disaster mitigation measures (CGS, 2004), the barrier spacing is determined by the upstream barrier height (H_dl′) and overflowed material depth (H_c) (Eq. (2)). Consequently, the overflow mechanism of granular flows is important but not well understood.

$$L=\frac{v_c^2}{g}\left(\sqrt{{\mathit{tan}}^2\theta +\frac{2g{H}_{\mathit{dl}}^{\prime }}{v_c^2}}+tan\theta \right)$$

$$L=\left(1.5~2\right)\times \left(H_{\mathit{dl}}^{\prime }+H_c\right)$$

where L is the launch distance, v_c is the overflow velocity, θ is the slope angle, and g is gravitational acceleration.

To prevent overflow, some analytical solutions have been proposed to estimate the flow run-up height (Choi et al., 2015; Iverson et al., 2016; Zhou et al., 2020b). Hákonardóttir et al. (2003) showed the relationship between barrier slope and overflow launch angle. Faug et al. (2015) demonstrated that the shape of a standing jump (overflow) is affected by flow conditions (e.g., slope and flow mass discharge), and proposed an analytical model to describe the overflow process, although this is limited to steady flow conditions. Ng et al. (2017) investigated the influence of deflectors on granular overflow kinematics. Ng et al. (2018) showed that the barrier height significantly influences the launch distance of the overflowed material. The overflow behavior encompasses multiple physical mechanisms, especially for dry granular flows because of the formation of a dead-zone structure (Faug et al., 2002; Ng et al., 2017; Ng et al., 2016; Song et al., 2019b). Some studies have already pointed out that a dead zone exerts a crucial effect on the impact dynamics of barrier structures (Albaba et al., 2018; Tan et al., 2020). However, a quantitative description of the dead-zone influence on the overflow behavior of granular flow remains unreported.

To address these scientific research gaps, we conduct a series of numerical simulation based on DEM modeling. We focus on the overflow behavior, which is a typical time-dependent process. The details of influence of debris-barrier interaction on overflow process has been elucidated. Our results may be useful to understand the granular flow overflow process, which may serve as the basis of engineering design of multiple barrier system in field.