Multiple debris-resisting barriers with basal clearance: a study on impact force

. Optimising debris-resisting barriers is of paramount importance on constructing cost-effective and eco-friendly mitigation works. Multiple barriers with basal clearance can potentially serve as an optimal approach because they can facilitate flow energy dissipation, reduce the impact force on each barrier, ease the maintenance and resist a large flow volume. However, the design impact force of multiple barriers with basal clearance remains empirical. In this study, physical model tests were carried out to investigate the impact force of idealised dry granular flow against dual rigid barriers with basal clearance using a 5-m-long flume model. Measured impact forces show that basal clearance attenuates the impact force exerted on the second barrier by apportioning the impact forces from basal discharge and overflow. Basal discharge dissipates the kinetic energy of landing flow and reduces the impact force of overflow. A rational design of basal clearance serves as an efficient measure for optimising the design of multiple barriers.


Introduction
Multiple barriers are advantageous on retaining large volumes of debris avalanches and debris flows compared with a single barrier because they can progressively arrest the flow and minimise the flow acceleration by facilitating the energy dissipation, thereby reducing barrier sizes. For closed-type multiple barriers [1], even flow with a small volume can be resisted by upstream barriers, resulting in an increase of maintenance work or a decrease of total retention capacity for next flow event. To optimise the design of multiple barriers, basal clearance [2][3][4] is usually constructed beneath the barriers to allow for discharge of flow (Fig. 1). Moreover, a basal clearance also serves to reduce the impact forces on barriers [5]. Despite the value of basal clearance, the design remains empirical.
In this study, impact dynamics of debris flow against multiple barriers have been investigated by conducting laboratory-scale flume model tests. The debris flows and multiple barriers were simplified as monodisperse dry granular flow and dual rigid barriers. The effects of basal clearance height on the impact dynamics are examined.

Flume modelling
The experiments were carried out in a rectangular flume model. The flume had a total length of 5 m, a width of 0.2 m and a depth of 0.5 m. A storage container at the upstream of the flume had a length of 0.5 m to retain the * Corresponding author: hliubc@connect.ust.hk test material with a gate. A pneumatic device was installed on the flume to control the gate. The pneumatic device was activated during the test to lift the gate and release all the source material down the flume.  Figure 2 shows a schematic side view of the test setup and instrumentation. The flume was inclined at 25º . The first and the second rigid barriers were installed 1100 and 2500 mm away from the storage container, respectively. A load cell was installed on the second barrier to measure the flow impact force. High-speed cameras served to measure the flow impact velocity, flow depth and impact kinematics. A video camera (model no.: GoPro Hero7) served to provide an overall view of the impact kinematics in a qualitative manner. Ultrasonic sensors were mounted to measure the flow depth.
A total mass of 50 kg of monodisperse glass beads with a diameter of 3 mm were adopted for each test. Before carrying out tests for flow-barrier interaction, a control test without installing any barrier was conducted https://doi.org/10.1051/e3sconf/202341506013 , 06013 (2023) E3S Web of Conferences 415 DFHM8 to obtain the flow velocity and flow depth along the flume using high-speed camera. Then, the location of the first barrier was determined by targeting the Froude number of the flow as 3. The first barrier had a barrier height of 2h0 to allow for both overflow and basal discharge. Basal clearance height Hc beneath the first barrier was varied from 0 to 0.8h0. Details of the test setup, instrumentation and plan were reported by [6].  Figure 3 shows the observed impact kinematics captured by the video camera for test where the first barrier had a height of HB1 = 2h0 and basal clearance of Hc = 0.6h0. A wide field of view was adopted to enable capturing the impact kinematics on both barriers. At t = 0.5 s, the basal discharge was approaching to the second barrier and the overflow occurred on first barrier. At t = 1.2 s, the basal discharge impacted on the second barrier and the overflow from the first barrier landed on the basal discharge. The landed flow interacted with the basal discharge and flowed downstream to the second barrier (Fig. 3c). The initially arrested basal discharge by the second barrier formed a deposition and cushioned the subsequent impact. As the impact process continued, the deposited material behind the second barrier continued to accumulate and pileup to the upstream direction ( Fig.  3d). At the end of the impact, the deposited material reached the basal clearance of the first barrier and blocked the discharge (Fig. 3e).

Observed impact kinematics
The observed impact kinematics indicate that the presence of a basal clearance can apportion the impacting flow against the first barrier from basal discharge and overflow. The basal discharge served as a soft loose material for the overflow to land and attenuate the kinetic energy. The basal discharge deposited on the second barrier also acted as a cushion layer for the subsequent overflow impact. Figure 4 shows the time histories of measured impact force on the second barrier for basal clearance heights beneath the first barrier ranging from 0.2h0 to 0.8h0. The impact force is normalised by the theoretical hydrodynamic impact force F = αρv1 2 h0w, where α is the impact coefficient and is selected as unity, ρ is the bulk density of the flow; v1 is the impact velocity at the first barrier; h0 is the impact flow depth at first barrier; w is the flow width. The normalised impact force indicates the ratio of impact force between the two barriers. With the presence of basal clearance, the impact force on the second barrier is influenced by both the basal discharge and overflow from the first barrier. As a result, the time history of the impact force shows two peaks during the impact, where the first peak is caused by the basal discharge and the second peak is caused by the overflow. With the increase of basal clearance beneath the first barrier, the impact force from basal discharge increases while the impact force from overflow decreases.  The maximum impact force on the second barrier decreases when Hc ranges from 0.0 to 0.6h0 due to the reduced overflow and the cushioning effect from the deposition of the basal discharge (Fig. 3b). When Hc = 0.8h0, the impact force on the second barrier increases because the impact force by basal discharge surpassed the impact force by overflow. This implies that the impact force on the second barrier for Hc/h0 ≤ 0.6 and Hc/h0 > 0.6 can be estimated from the impact forces of overflow and basal discharge, respectively.

Measured impact force
To characterise the governed impact force on the second barrier, Ng et al. [6] proposed an analytical approach to estimating the impact forces of overflow and basal discharge considering basal clearance height beneath the first barrier. The maximum impact force on the second barrier was considered as the maximum estimated impact force from overflow and basal discharge. By comparing with the measured maximum impact forces in this study as shown in Fig. 5, this proposed method performs reasonably well. More importantly, the proposed method captures the minimum impact force at Hc/h0 = 0.6, indicating the potential for optimising the design of multiple barriers with an optimal basal clearance.

Conclusions
In this study, physical flume experiments were carried out to study the effects of basal clearance beneath the first barrier on the impact dynamics against dual rigid barriers. The basal clearance of the first barrier can regulate the impact force exerted on the second barrier by dissipating the kinetic energy of landing flow and apportioning the load contributions from basal discharge and overflow. The basal discharge governs the impact force when Hc/h0 ≥ 0.8, whereas the overflow governs the impact force when Hc/h0 ≤ 0.6. These two features indicate a minimum impact force on the second barrier when Hc/h0 = 0.6. The two features also have been well captured by an analytical approach, which can serve to optimise the impact force on multiple barriers considering basal clearance height.