Debris flow countermeasures

2.4.1 Proposed framework

To reduce the hazardous consequences of debris flows, countermeasures are introduced.

A suggested countermeasure is the building of barriers. Barriers can be placed in slopes with natural channels to hinder the granular flows (Ng et al., 2018). Mitigation measures can be divided into structural and non-structural countermeasures (Proske et al., 2011;

Takahashi, 2007, p. 336), in which rigid barriers count as structural. Also, the mitigation measures can be either active or passive, where active ones directly influence the

process of a debris flow by preventing or dampening the event (Proske et al., 2011).

Other examples of structural barriers are check dams, baffles or even the planting of trees (Takahashi, 2007, p. 336). In the following, only the use of intermediate rigid barriers will be discussed. In particular, the use of one single intermediate barrier.

According to Kwan (2015), the barrier acts in a way that when the debris flow hits the barrier, a portion of the debris will be held back by the barrier. As a result of the barrier retaining debris, the debris flows loose some of its kinetic energy (Kwan et al., 2015).

Also, the barriers can induce a time delay on the flow front, which results in a slightly longer travel time (Kwan et al., 2015).

Kwan et al. (2015) proposed a framework in which they present a method on assessing the design of multiple intermediate barriers to intercept the debris flows. In their

research, they conducted a debris mobility analysis, which took the effect of obstruction of the debris flows due to multiple intermediate barriers into account. These analyses resulted in the noting of several parameters for a debris flow overflowing barriers. The parameters can be obtained from Figure 7 and are further discussed later.

The mobility assessment (Kwan et al., 2015) considers the debris piling up behind a barrier and launching into a ballistic flight after the overflow of the barrier crest. The

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assessment also considers the energy dissipation upon impact with the channel bed.

These features are shown in Figure 7. When the zone behind the barrier is fully filled, the debris that remains in the flow is launched into a ballistic flight (Kwan et al., 2015). From the crest of the barrier, the remaining debris will then carry the kinetic energy of the remaining landslide (Kwan et al., 2015). It should also be noted that if a barrier is filled prior to the debris flow, e.g. by an earlier debris flow, the capacity of the barrier can be neglected for calculation purposes (Kwan et al., 2015).

Figure 7 The flow path of a debris flow hitting a barrier and the parameters determining the dynamics of the debris flow path (Kwan et al., 2015).

Koo et al. (2017) studied the effect on barrier impact loads, by taking the effect on debris attenuation into consideration, with the help of physical modelling. As a result of this work, they proposed an impact load model which takes the change of momentum flux due to the interaction with a barrier into account. The model that is proposed, is stated to be valid for use on granular flows (Koo et al., 2017). It uses a staged run-up behavior of the flow behind the barrier, which is illustrated in Figure 8.

Figure 8 The impact mode, showing a schematic diagram for the impact of the barrier (Koo et al., 2017).

Ng et al. (2019) uses the work of both Kwan et al. (2015) and Koo et al. (2017), and suggests a new analytical framework for the design of multiple rigid barriers. They use physical experiments to evaluate and validate the framework. The experiments consisted of different flows impacting a barrier. The findings of Ng et al. (2019) are in general that the framework estimates the attenuation of the velocity during impact of the barrier, the

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overflow velocity and landing distance quite well. The tests conducted by Ng et al. (2019) verify this. The overflow distance of the barrier is also given in the model, and the final recommendation is that the actual barrier spacing should be larger than the calculated overflow distance (Ng et al., 2019).

Figure 7 shows the debris flow hitting a barrier and how the debris is retained. Further the figure shows the debris front launching into a ballistic flight and how it will follow the trajectory path. The material can be seen to hit at an angle, 𝛽, at which point the debris flow has a new initial speed.

2.4.2 Barrier design according to framework

The main challenge in designing a barrier is due to the requirement for the barrier to resist quite a large impact velocity (Kwan et al., 2015). According to Kwan (2015), the intermediate barriers should be placed at wide positions that are flat parts of the drainage line. These conditions are favorable for decreasing the hazard of a rapid flow, by slowing it down (Kwan et al., 2015). Due to the launch of ballistic flight over the crest of the barrier, the height of the barrier should be optimized and not excessive (Kwan et al., 2015).

Ng et al. (2019) and Kwan (2015) present the framework for the design of rigid barriers shown in Figure 9. The framework proposed by Ng et al. (2019), consists of three parts:

the impact model, the overflow trajectory and the landing model. The path of the ballistic flight is determined by the height of the barrier the debris material is launched from (Ng et al., 2019). When the ballistic flight comes to an end, at the end of the trajectory path, the velocity is reduced at impact between the debris flow material and the channel bed (Kwan et al., 2015). The velocity reduces, due to the energy dissipation of the flow material as it collides with the channel bed at an angle (Ng et al., 2019).

Figure 9 The framework of multiple barrier design (Ng et al., 2019).

Kwan (2015) presents the design equations for assessing the dynamic motion of the landslide debris overflowing a barrier. Figure 7 in the previous section presents the parameters in the model. 𝑥_𝑖 represents the horizontal length projected by the debris flow trajectory path. 𝑣_𝑚 is the horizontal velocity of the debris flow launched from the crest of the barrier. 𝑣_𝑟 is the velocity of the debris material right before impact with the channel bed. The velocity is given at an angle to the slope. 𝑣_𝑖 gives the velocity after impacting

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the channel bed. This velocity is parallel with the slope. 𝜃 represents the angle of inclination of the channel and ℎ is the height of the barrier.

The trajectory path projection, 𝑥_𝑖, is obtained from energy conservation principle and is given by the following formula (Kwan et al., 2015):

(2.8) 𝑥𝑖=^𝑣𝑚2

𝑔 ⋅ [𝑡𝑎𝑛𝜃 + √tan²𝜃 +^2𝑔ℎ

𝑣_𝑚² ]

The debris flow velocity prior to landing is from Kwan et al. (2015) derived based on the kinetic energy of the debris and the kinetic energy that is gained from a drop in height:

(2.9) 𝑣_𝑟= √^{2[𝐾𝐸𝑟+𝑚𝑟𝑔(ℎ+𝐶𝑥𝑥𝑖𝑡𝑎𝑛𝜃)]}

𝑚_𝑟

In this equation, 𝐾𝐸_𝑟, represents the kinetic energy of the remaining debris after the first barrier. 𝐶_𝑥 is a correction factor for the horizontal length of the trajectory path and 𝑚_𝑟 is the mass of the remaining debris after passage of the first barrier. 𝑔 is the gravitational acceleration.

The velocity parallel to the slope after impact with the channel bed is given by Kwan et al. (2015) as follows:

(2.10) 𝑣_𝑖= 𝑣_𝑟cos 𝛽 Where 𝛽 is given as

(2.11) 𝛽 + 𝜃 = tan⁻¹√^{𝑚𝑟𝑔(ℎ+𝐶𝑥𝑥𝑖𝑡𝑎𝑛𝜃)}

𝐾𝐸_𝑟 ]}

𝑅 represents the velocity correction factor and the value is correlating with the material used at the channel base. All other parameters are previously described.

Combining equations (2.10) and (2.11), the final expression for this velocity is obtained:

(2.12) 𝑣_𝑖= 𝑅𝑣_𝑟cos{[tan⁻¹√^{𝑚𝑟𝑔(ℎ+𝐶𝑥𝑥𝑖𝑡𝑎𝑛𝜃)}

𝐾𝐸_𝑟 ] − 𝜃}

Figure 9 contains also a model for the impact on the barrier, in addition to the overflow trajectory and landing model. As some of the material starts to arrest behind the barrier, the rest of the material has to climb upon it, resulting in a drag between the resting and flowing material (Ng et al., 2019). The event of attenuation is hence described by Koo et al. (2017) with help of the run-up velocity, 𝑣𝑑, and factor of attenuation, 𝑅𝑑:

(2.13) 𝑣_𝑑= 𝑣(1 − 𝑅_𝑑) (2.14) 𝑅𝑑= 1 − √1 −^{2𝑔(𝑡𝑎𝑛𝜙𝐿𝑇+ℎ𝑑)}

𝑣²

𝐿_𝑇 represents the travel distance of the debris flow in the run-up behind the barrier. 𝜙 is described by Ng et al. (2019) as the angle of repose, and is in Koo et al. (2017)

described as the internal friction angle of the retained material. ℎ_𝑑 is the height of the retained granular material behind the barrier. Ng et al. (2019) present a modified figure of the depositing mechanism behind the barrier, see Figure 10. The original one is presented in Koo et al. (2017).

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Figure 10 Parameters of the retained material behind the barrier (Koo et al., 2017; Ng et al., 2019).

𝜃𝑑 is the deposition angle of the material, which makes 𝜃_𝑑− 𝜃 the net deposition angle. 𝑣 is the free flow velocity and ℎ_𝑜 is the free field thickness. Lastly, ℎ is given as the run -up thickness (Koo et al., 2017).