E3S Web of Conferences 415, 06022 (2023)
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https://doi.org/10.1051/e3sconf/202341506022

Impact dynamics of debris flow against slit dam: experimental
and numerical investigation
Gordon G.D. Zhou1,2,3*, Kahlil F. E. Cui1,2, Junhan Du1,2, Nanjun Li1,2, Xueqiang Lu1,2, and Yunxu Xie1,2
1Key Laboratory of Mountain Hazards and Earth Surface Process / Institute of Mountain Hazards and Environment, Chinese

Academy of Sciences, Chengdu 610000, China
2University of Chinese Academy of Sciences, Beijing 100000, China
3China-Pakistan Joint Research Center on Earth Sciences, CAS-HEC

Abstract. Debris flows are gravity-driven phenomena common in mountainous regions that are hazardous
to downstream facilities. To mitigate the impacts of these disastrous processes, structural countermeasures
such as slit dams are constructed in gullies and along mountain slopes. Existing studies on the impact
dynamics of debris flows against slit dams typically focus only on the flow characteristics but fail to takethe geometry of the structure into account. Here we develop an analytical model, derived from themomentum approach, that allows for the estimation of the runup height and impact load of debris flows on
slit dams. The model is validated against discrete element simulations and small-scale flume experiments.
It is found that the runup height is controlled by both the Froude number and slit size. The proposed
analytical model can predict the runup height well within a certain range of Froude numbers. Results fromexperiments further reveal that the fontal dynamic pressure is sensitive to the flow properties whereas thepeak dynamic pressure is strongly affected by the slit size.

1 Introduction
Debris flows are gravity-driven mixtures ofdifferently sized particles (from sand to boulders)saturated in muddy slurry [1]. These flows are massive
and highly mobile and therefore pose significant risks tohuman lives and facilities downstream [2,3]. Mitigation
structures, such as slit dams [4], are commonly installed
strategically along the expected flow path to mitigate
such destructive hazards. Such structures, which consistof rigid planes (posts) and openings (slits), disperse flowenergy thereby arresting the flows [5].
The interaction between debris flows and structuralcountermeasures is a complex process involving impact,
deceleration, deposition, and discharge. For engineering
design and hazard mitigation, it is essential tocomprehendrunupbehaviors
andimpactmechanisms [6]. Several analytical models have been
proposed to predict the runup height of debris flows
against obstacles [7] and a wide range of continuumloading models have been used to calculate impact
loads. However, the dynamic interaction between debris
flows and slit dams, which significantly affects therunup height and impact load, is still poorly understood.
Here, we propose an analytical model based on themomentum approach to predict the impact dynamics ofdebris flows on slit dams. The interaction between
debris flows and slit dams are studied numerically using
the Discrete Element Method (DEM). Simulations ofdebris flows with varying Froude numbers NFr
impacting slit dams with different slit sizes are carriedout. In addition, a series of flume experiments of debris
flow impacting model check dams and slit dams arecarried out to study the influence of slit size on theimpact loads.

2 Theoretical model and simulations
2.1 Analytical model for the run-up height
Using the momentum approach, a depth-averaged
continuum model has been developed to estimate therunup height. This analytical model is based on shock
theory [8]. It is predicted that a flow impinging on anobstacle is a one-dimensional dynamic problem that canbe interpreted from the emergence of a shock. When asteady flow encounters a vertical obstacle, a shock (orshock wave) develops instantly and travels upstream.
Shocks are characterized by abrupt jumps in thevelocity, density, and height. It is assumed that theincoming flow on a horizontal channel is continuous,
steady, uniform, compressible, and unaffected by thebackwater effect.
Fig. 1(a) illustrates a shock that forms when a debris
flow impacts a check dam as viewed from the (top) sideand (bottom) from the top. A shock forms and travels
upstream with depth-invariant velocity 𝑢, height ℎ, andbulk density 𝜌 . A granular dead zone develops
simultaneously between the shock and the dam. The
conservation of mass and momentum across the shock
travelling at a speed 𝑠 can be expressed as:
𝜌0 ℎ0 (𝑢0 + 𝑠) = 𝜌1 ℎ1 (𝑢1 + 𝑠)ℎ0

𝜌0 ℎ0 𝑢0 (𝑢0 + 𝑠) + ∫ 𝜎0 𝑥𝑥 dz =0ℎ1

𝜌1 ℎ1 𝑢1 (𝑢1 + 𝑠) + ∫ 𝜎1 𝑥𝑥 d𝑧0(1)(2)* Corresponding author: gordon@imde.ac.cn© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0(https://creativecommons.org/licenses/by/4.0/).

E3S Web of Conferences 415, 06022 (2023)
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https://doi.org/10.1051/e3sconf/202341506022𝐹𝑟0 2 [1 − 2𝐵𝛼 + 𝐵𝛼 2 − 𝐴𝐵𝛼 2 + 𝐴𝐵2 𝛼 2 ]1ℎ1 ℎ1− 𝑘 [𝐴 − − 1 + 𝐴−1 ] = 02ℎ0 ℎ0(5)Fig.1. A (top) side-view and (bottom) plan-view
schematic diagram of runup against (a) a check dam and(b) a slit-dam.
In the case of slit dams (Fig. 1(b)), a more complex
process that involves flow deceleration, redirection, anddownstream discharge is observed. As the incoming
flow encounters the slit dam, a shock forms and rapidly
travels upstream. In contrast to the check dam case, theslit dam's regulation causes the downstream flow fromthe shock to change into two types: (i) one slows down
and deposits with speed 𝑢1 , creating a granular deadzone between the shock and the dam similar to the checkdam case; (ii) another propagates downstream withspeed 𝑢2 and then passes through the slit. The
conservation of mass and momentum across the shock
travelling at speed s can be expressed as:
𝜌0 ℎ0 (𝑢0 + 𝑠) = (1 − 𝐵)[𝜌1 ℎ1 (𝑢1 + 𝑠)]+𝐵[𝜌2 ℎ2 (𝑢2 + 𝑠)]ℎ0

𝜌0 ℎ0 𝑢0 (𝑢0 + 𝑠) + ∫ 𝜎0 𝑥𝑥 dz = (1 − 𝐵)
0(3)

ℎ1

[𝜌1 ℎ1 𝑢1 (𝑢1 + 𝑠) + ∫ 𝜎1 𝑥𝑥 d𝑧]
0ℎ2+ 𝐵 [𝜌2 ℎ2 𝑢2 (𝑢2 + 𝑠) + ∫ 𝜎1 𝑥𝑥 d𝑧]
0Fig. 2. Comparison of theoretical normalized runup
height predicted by (a) the energy approach and (b) themomentum approach with the DEM results.

(4)

where 𝐹𝑟0 is the Froude number of the incoming flow,
indicating the ratio of inertial forces to gravitationalforces. Equation (5) yields a runup formula based on themomentum approach and takes into account both theupstream Froude conditions (NFr) and the slit size (B).
Finally, the solutions of the runup formula can beobtained. Consequently, if the Froude number ofincoming flow and the geometry of slit dam are known
in advance, the runup height of debris flows against it
can be predicted.

where subscript 0 denotes properties of the flow
upstream of the shock, subscript 1 denotes properties ofthe (i) retarding flow downstream of the shock while 2
denotes properties of the (ii) outgoing flow. 𝐵 = 𝑏/𝑤,
where b is the width of the spacing between posts and w
is the width of the channel, is the transverse blockage ofthe slit dam, 𝜎𝑥𝑥 is the longitudinal normal stress.
It is reasonable to assume that the density and theheight of the flows downstream of the shock are equal,i.e., 𝜌1 = 𝜌2 and ℎ1 = ℎ2 . Downstream of the shock,the flow deposits at a speed 𝑢1 , forming a granular deadzone between the shock and the dam. The velocity 𝑢1
can then be supposed to be equal to 0. The outgoing flow
between the shock and the slit dam is characterized bystrong flow curvatures, flow redirection, and theformation of dead zones in the corners. Without athorough theory for the outgoing flow, we consider an
empirical linear relationship between the outgoingvelocity 𝑢2 and the velocity of the incoming flow 𝑢0 . By
combining these simplifications, the momentum jumpcondition equation (4) reduces to:

2.2 Comparison of runup prediction models
The comparison between the simulated normalized
runup heights and the analytical model of [4] is shownin Fig. 2(a). The results show that this approach isunable to accurately predict the runup heights of thesimulated granular flows. The predictions are either
overestimated when the relative post spacing is low or
too conservative when it is high. This is because thisstrategy assumes that the runup process is under thehydraulic jump condition, making it inappropriate for
frictional dense granular flows, where the pileup

2

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load exerted on the dam. However, the momentum of
the flow impact is not always along the direction of thechannel. When 𝛼1 < 1 part of the impact load istransferred vertically along the dam surface due tosignificant run-up [4]. In addition, 𝛼1 is mainly related
to the momentum of frontal debris flow instead of𝑏/𝐷𝑚𝑎𝑥 , which means that 𝛼1 does not change with𝑏/𝐷𝑚𝑎𝑥 . Consequently, it can be said that the peakfrontal impact pressure is not affected by slit size.
Debris flows with low solid fraction (𝐶𝑠 = 0.4) arecontrolled by strong inertial stresses, resulting in large
𝛼1 . Dilute debris flows easily deflect upward along thedam surface and the momentum of the flow istransferred to the base of dam efficiently during thecollision. Meanwhile, debris flows with 𝐶𝑠 = 0.6 havelarger frictional stresses resulting from the increased
interaction between particles. This leads to greater
energy dissipation within the flow and consequently theattenuation of the frontal impact pressures.

mechanism dominates the flow-structure interaction
process.
The momentum approach is said to be able toaccurately predict runup heights and capture the runup
behavior of granular flows [9]. Figure 2(b) compares
the simulated normalized runup heights with predictions
obtained from equation (5). Results indicate that ourproposed model can accurately predict the runup heights
of debris flows against slit dams. The numericalsimulation results and the runup heights predicted by themodel exhibit similar tendencies: higher Froudenumbers (NFr) and lower transverse blockage (B) lead tohigher runup heights. The maximum deviation of thecalculated results from the predicted runup heights isless than 15.6%. Therefore, engineers anticipating adense granular debris flow can safely estimate the heightneeded for the slit dam to prevent hazardous
overtopping using the proposed equation. In addition,
the results show the influence of the upstream Froude
conditions (NFr) on runup heights for granular flows
against slit dams. The maximum runup height increases
monotonically with the Froude number of incoming
flows, which is consistent with [10].

3 Small-scale flume experiments
3.1 Experimental parameters
Designing safe and effective countermeasuresagainst debris flows involves accurate predictions of theimpact load. Currently, there has been abundantresearch focused on the mechanisms of debris flows
impacting structures. Impact loads can be estimatedusing existing hydrodynamic models. However, lessattention has been paid to the effect of slit size on theimpact load. In this section, the frontal impact pressure
and the total impact force influenced by slit size andsolid volume fraction will be discussed.
The relative post spacing 𝑏/𝐷𝑚𝑎𝑥 , where 𝑏 is thesize of slit and 𝐷𝑚𝑎𝑥 is the maximum particle diameter,
is a dimensionless parameter that characterizes the slitsize. During the frontal impact, the peak impact pressure
𝑃𝑝𝑒𝑎𝑘 can be detected by force sensors positioned at thebottom of the dam [6]. The frontal dynamic pressure
coefficient 𝛼1 , a dimensionless parameter that quantifies
the dynamic load, is expressed as function of 𝑃𝑝𝑒𝑎𝑘 , i.e
𝛼1 = 𝑃𝑝𝑒𝑎𝑘 /(𝜌𝑣 2 ) , where 𝜌 is bulk density, 𝑣 is thefrontal velocity. An important parameter considered in
the design of mitigation structures is the peak total
impact force acting on them 𝐹𝑝𝑒𝑎𝑘 ′ . The peak impact
force is calculated by integrating the impact pressure
along the dam height. The peak dynamic pressure
coefficient 𝛼2 , which encodes information on thedynamic and static load, can be calculated through𝐹𝑝𝑒𝑎𝑘 ′ , i.e 𝛼2 = 𝐹𝑝𝑒𝑎𝑘 ′ /(𝜌𝑣 2 ℎ) , where ℎ is themaximum approaching flow depth.

Fig. 3. (a) Frontal dynamic pressure coefficient (𝛼1 )and (b) peak dynamic pressure coefficient (𝛼2 ) at
different relative slit size (𝑏/𝐷𝑚𝑎𝑥 ) . The legend
displays flume inclination angle – solid fraction.
3.3 Total impact load exerted on slit dam
Fig. 3(b) shows the relationship between 𝛼2 and𝑏/𝐷𝑚𝑎𝑥 . Since information on the static load is includedin 𝛼2 , i.e the weight of retained debris flow materials,
𝛼2 is significantly greater than 𝛼1 . For 𝑏/𝐷𝑚𝑎𝑥 ≤ 1.8,

3.2 Frontal impact pressure
Fig. 3(a) shows the relationship between 𝛼1 and𝑏/𝐷𝑚𝑎𝑥 . In theory, 𝛼1 equals unity if there is no static3

E3S Web of Conferences 415, 06022 (2023)
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the slit size has minimal influence on 𝛼2. This means thatthe slit sizes below this limit are too small for debris
flow materials to pass through that they function similar
to check dams. Increasing the relative post spacing to1.8≤𝑏/𝐷𝑚𝑎𝑥≤3.6, decreases 𝛼2 by ~23% for tests with 𝐶𝑠= 0.4, and by 30% ~ 40% for tests with 𝐶𝑠 = 0.6.
However, when 𝑏/𝐷𝑚𝑎𝑥≥3.6, 𝛼2 remains constant whichmeans that 𝑏/𝐷𝑚𝑎𝑥= 3.6 is a critical limit in which slit
dams can still efficiently trap debris flows. Hence, theinfluence of slit size should be considered whenestimating the impact of debris flow.

8.

J.M.N.T. Gray, Y.-C. Tai, S. Noelle, J. Fluid
Mech. 491, 161 (2003)
9. C.E. Choi, G.R. Goodwin, C.W.W. Ng, D.K.H.
Cheung, J.S.H. Kwan, W.K. Pun, GéotechniqueLetters 6, 267 (2016)
10. C.E. Choi, C.W.W. Ng, G.R. Goodwin, L.H.D.
Liu, and W.W. Cheung, Can. Geotech. J. 53, 1751
(2016)

4 Conclusions
An analytical model based on the momentum approach
was derived to predict the runup heights of debris flows
against slit-dams. Debris flows impacting slit-dams areinvestigated through discrete element method (DEM)
simulations. It is found that the runup height iscontrolled by both the Froude number and slit size. The
proposed model captures relevant runup mechanisms ofdebris flows against slit-dams and is able to provide
good predictions of the runup heights within a certain
range of Froude numbers.
To study the influence of slit size on the impact loads, aseries of flume experiments of debris flows impacting
model check dams and slit dams are carried out.
Measurement of the flow velocity, depth, impact load,
total basal normal stress, and basal pore-fluid pressure
enable a comprehensive evaluation of the impact
characteristics. Tests reveal that the peak frontal impact
pressure is largely unaffected by the slit size of structuralcountermeasures but is sensitive to the debris-flow
properties. However, the slit size obviously influences
the peak force experienced by the structures. A critical
relative post spacing of 3.6 is determined wherein slit
dams can effectively mitigate debris-flow hazards.
The authors acknowledge financial support from the National
Natural Science Foundation of China (grant no. 41941017),
the International Science & Technology Cooperation Programof China (No. 2018YFE0100100), CAS "Light of West China"
Program

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