E3S Web of Conferences 415, 06019 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341506019

Static and dynamic impact forces on a rigid barrier due to drydebris flow simulated by a DEM-based granular column collapse
Aman Ujjwal1, S. Sureka1, Govind Kant Mishra2, Mousumi Mukherjee2*, and Arindam Dey1
1Indian Institute of Technology, Guwahati, India.
2Indian Institute of Technology, Mandi, India.

Abstract. Geophysical flows like debris flows require protective barriers so as to scale down theirdisastrous effects. The impact force exerted on these barriers depends upon several factors like the velocity
and height of flowing debris, the density and other associated characteristics of flowing mass, and the heightof the sediment deposited behind the barrier. These factors are found to vary with time during the debris
flow process, thereby causing significant temporal variations in the magnitude of impact force. Assessing
the impact force on a barrier is a prerequisite for its design. In this work, the impact of dry debris flow,
emanating from a granular column collapse, on a rigid barrier has been investigated using 3-D Discrete
Element Method (DEM). It has been found that the impact force is predominantly influenced by dynamic
thrust at the initial stages, which, with elapse time, subsequently transits to the sole contribution of staticpressure. The applicability of the existing hydraulic models comprising hydrostatic and hydrodynamic
formulae has also been analysed in this exercise. Furthermore, the empirical coefficients associated withthese formulae have been evaluated for the dry debris flow impacting the rigid barrier.

1 Introduction
Debris flows constitute a class of devastating
geophysicalflows
thatmostlycomprises
inhomogeneous material mixture. The flowing debris
engulfs everything that comes in its trajectory, thus
leading to volume augmentation during the flow [1].
Due to such increased bulk volume, the flowing debris
characteristically exhibits high velocity and pressure,thereby posing a compounded threat to lives,infrastructure and environment. Debris flow control
structures in form of protective barriers are often used tocreate obstruction along the pathway of the flowing
debris, thereby aiding in reducing the potential damage[1]. These protective structures should be designed foradequate strength or capacity so as to restrain thedislodged mass moving with high kinetic energy. Inturn, as the flowing mass is hindered by the barrier, theobstructed debris transfer a temporally varying impact
force to such structures [2]. Thus, estimation of theimpact force is a prerequisite for the design of suchbarriers [1] and requires a comprehensive understandingof the mechanism and dynamics of the debris flow.
Impact force exerted by the flowing debris depends
on various factors like velocity and height of flowing
mass along with the density, particle size and otherassociated characteristics of debris [3]. Recent studies
have also revealed that initial inclination of flow front,intergranular friction and porosity of flowing mass, andmass length significantly influence the impact force,
wherein the inclination of the front plays a dominant rolewith the maximum impact force experienced for an
initial inclination angle of 90º [4]. Continuum-based
numerical analyses have been extensively conducted in
the past to assess the impact of flowing debris on thebarriers [2]. The studies indicate that the kinetic energy
carried by the flow, which reflects the flow velocity, hasa direct implication on the magnitude of the thrust
imparted on the obstructing barrier. Furthermore, theheights of flow and sediment (settled mass) also affects
the impact force exerted on the barrier. These analyses
confirm that the impact force essentially comprises twocomponents, a static part and a dynamic part. The
deposited mass behind the barrier structure primarily
contributes to the static part; whereas, the flowing mass
striking against the structure is responsible for thedynamic component. However, such continuum-based
impact force estimation often assumes a single phase
idealisation for the flowing debris mass, wherein thevariability in flow is taken into account throughempirical constants, which are difficult to calibrate.
Dry debris flows have predominant granularbehaviour with only frictional inter-particle contacts
controlling the mobility [1]. Such a flow can be easily
replicated by causing an instantaneous collapse of
granular column and can be investigated numericallyusing Discrete Element Method (DEM) [5]. DEM is anumerical modelling technique based on Langrangian
approach and deals with the particle level responses [5].
It helps in comprehending large deformation problems
such as debris flows with detailed and intricate insights.
This approach has been recently used for understanding* Corresponding author: mousumi.ju06@gmail.com© 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, 06019 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341506019

the micro and macro mechanical behaviour in reference
to the dynamic interaction between dry granular flow
and rigid barrier [4, 6]. The present study aims to assess
the characteristics of the impact of dry debris flow on arigid barrier using 3D – DEM with due consideration toestimation of its dynamic and static components. In thisregard, applicability of the existing continuum based
hydraulic models has also been analysed along with theestimation of associated empirical parameters.

2 Methodology
In this study, a DEM platform has been used toinvestigate a dry debris flow simulated through thecollapse of a granular column. The simulations havebeen carried out using LIGGGHTS [7]. The efficacy of
the granular column collapse simulations has beenvalidated against the experimental results from Shi et al.
[8, 9].
In the present study, a granular column of aspectratio (height/width) as 4 has been allowed to collapse
freely over a planar horizontal frictional bed. The dry
debris flow emanating from the collapsing mass has
been made to impact a rigid barrier placed at a certaindistance away from the granular column. Fig. 1
represents the initial geometry of the granular column
and the final settled state of the particles behind the rigidbarrier. Table 1 depicts the geometrical details of thecolumn and barrier. It also includes the micromechanical properties of the column particles, whichhave been calibrated iteratively against the granularcolumn collapse experiment reported in Shi et al. [8].

Fig. 1. Initial geometry of granular column and final deposited
mass behind the rigid barrier.

3 Results and Inferences
The variation of total impact force (F) is plottedwith respect to time in Fig. 2. In order to calculate theimpact force, the barrier has been discretised withmultiple mesh elements in LIGGGHTS [7]. At any time
instant, the total impact force (F) is a cumulative sum of
the product of impact pressure over each mesh elementwith the area of that element, thereby, causing an
undulating yet less noisy plot for F. The beginning of
the plot represents the time at which the confining gateof the column has been instantaneously removed, i.e.,
when the collapse of the granular column has begun andthe material have started to flow towards the barrier. The
touchdown impact of the flowing particles on the rigidbarrier occurs at a later time (~ 0.19 s) that is demarcatedby a sudden rise in the impact force. In the succeedingtime instants, the undulating impact peaks are witnessedas the continually flowing particles transfers thedominant dynamic impact to the barrier. Further, thedynamic impacts gradually decrease with thecomplementing attainment of a static impact force fromthe particles settled behind the barrier, as can be noted
approximately beyond a time instant of 0.4 s.

Table 1. Micro-mechanical properties and the geometry
details used in this study.
Parameters/Properties
ValuesMicro-mechanical properties
Particle diameter (d) (m)0.004

Particle density (ρs) (kg/m3)

2700

Modulus of Elasticity of particles (E) (N/m2)

5 × 106
0.7

0.31

Coefficient of restitution (e)0.7

Packing porosity (n)0.43Bulk density (ρ) (kg/m3)

1539
HertzMindlin

Contact Model

2.50.424

Total impact force (F)(N)

Coefficient of friction for interaction between
column particles (μ)
Coefficient of friction for particle-wall andparticle-gate interactions (μ’)
Poisson’s ratio (ν)

0.06

Column thickness (m)0.04

Aspect ratio (a)40.096Barrier width (b) (m)0.04

Distance of the barrier from the column (m)

0.12

1
0.5
00.1

0.2

0.3
0.4
Time (s)0.5

0.6

Fig. 2. Variation of total impact force (F) with respect to time.

Details of the rigid barrier
Barrier height (m)1.50Details of the granular column collapse model
Column width (Li) (m)2Fig. 3 represents the variation of average impact
pressure with the height of barrier at some specific timeinstants. These are developed by averaging the values ofimpact pressure along the width of the barrier for thecorresponding chosen height along the barrier.

2

E3S Web of Conferences 415, 06019 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341506019

It can be inferred from Fig. 3(a) that initially theimpact pressure on the barrier is primarily governed by
the dynamic thrust of the flowing particles, which isreflected by higher pressure magnitudes on the lower
level of the barrier. As the particles start settling behindthe barrier, the dynamic component experiences atransition to the static counterpart, and thereby withtime, the impact pressure exerted over the lower levelsof barrier reduces due to the predominant contribution
from the static lateral pressures (Fig. 3b).

However, there is yet a remnant effect of dynamic
impact in the lower levels as the succeeding flow thrusts
behind the settled particles and indirectly transmits areduced dynamic impact over the barrier. Additionally,
these flowing particles, having high kinetic energy,
jump over the settled particles and exert an extended
dynamic impression over the barrier at the immediate
upper level. This is apparent from the kink illustrated inFig. 3b, which has been discussed explicitly in [2]. As
time further elapses, more and more particles startsettling behind the barrier, thereby, augmenting thecontribution of static pressure over the extended heightof barrier. In such scenario, the direct impact of dynamic
pressures from the flowing particles contracts meagrely
in higher elevations of the barrier (as apparent from Fig.
3d), and eventually converges to the imparted timeindependent static pressure.
In order to assess the impact of debris flows, certain
hydraulic models are available that include the relations
for estimating hydrostatic and hydrodynamiccomponents of the impact force. The expression forhydrostatic part (Eqn. 1) is based upon the height ofdeposition behind the barrier; whereas, the relation forhydrodynamic component estimation (Eqn. 2) is pivoted
around the flowing velocity and height [3].

Height (z) (m)

0.08
0.06
0.04
0.02
00500 1000 1500 2000 2500
Average Impact pressure (p) (Pa)

3000(a)Height (z) (m)

0.08
0.06

Fs = 1⁄2 kρghs 2 b
Fd = αρv2 hf b

0.04
0.02

where Fs and Fd are the hydrostatic and hydrodynamic
components of impact forces, respectively, k and α are
the empirical coefficients for hydrostatic andhydrodynamic formulae respectively, ρ is the density of
the flowing mass, hs is the height of flow with static
behaviour, i.e., the height of settled mass behind thebarrier, hf is the height of flow, v is the flowing velocity
and b is the width of the barrier.
Fig. 4 shows the variation of average flow velocity(v) with time. For determining the average flow velocity,a threshold velocity has been first identified. By
averaging out the particle velocities with magnitude
greater than the threshold velocity, average flow
velocity has been obtained. The threshold velocity has
been fixed at 1% of maximum of average particle
velocity.

00250 500 750 1000 1250 1500 1750
Average Impact pressure (p) (Pa)(b)
Height (z) (m)

0.08

0.06
0.04
0.02
00250500
750 1000 1250
Average Impact pressure (p) (Pa)

1500(c)t = 0.35 st = 0.4 s
t = 0.5 s

0.06

Average flow velocity (v)(m/s)

Height (z) (m)

0.08

0.04
0.02
00250
500
750 1000 1250
Average Impact pressure (p) (Pa)

(1)
(2)

1500(d)Fig. 3. The variation of average impact pressure (p)with respect to height (z) of the rigid barrier for time(a) 0.2 s, (b) 0.25 s, (c) 0.3 s, (d) 0.35 s, 0.4 s and 0.5 s.

0.6
0.4
0.2
00

0.1

0.2

0.3
0.4
Time (s)0.5

0.6

Fig. 4. Variation in average flow velocity (v) fordifferent time instants.
Fig. 5 shows the variation of average height of flow(hf) with time that has been determined by considering
the average height of all the flowing particles, i.e.,3E3S Web of Conferences 415, 06019 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341506019

0.08

0.08

hf
hs

0.06

0.06

0.04

0.04

0.02

0.02

00
0

0.1

0.2

0.3 0.4
Time (s)0.5coefficients, as well as the applicability of the type of
hydraulic models, is dependent on the predominant
forcing behaviour (dynamic or static) that changes andevolves with time; similar inference has been reported
by Leonardi et al. [10]. Based on the present study, therange of k values is estimated as 0.93 – 67.52 and that ofα values is estimated as 0.27 – 13.62. Since the designof such barriers is governed by maximum impact force(indicated in Fig. 2) [1], the estimated values of k and αcoefficients at the time instant of maximum impact force
as illustrated in Table 2. Within the limits of thisparticular study, the obtained values of the empiricalcoefficients are in reasonable agreement with theavailable ranges as mentioned by Lee and Jeong [2]. It
is to be noted that the impact force exerted by a dry
debris mass has been investigated here. However, a true
debris flow may also contain fluid part leading to a more
complex impact force variation over the rigid barrier,that is beyond the scope of this study.

Average height ofsettled mass (hs) (m)Average height offlow (hf) (m)particles with velocity greater than the thresholdvelocity. Similarly, Fig. 5 also illustrates the variation inthe height of flow with static behaviour, i.e., averageheight of settled debris mass behind the barrier (hs) withtime. The same has been ascertained by considering theheight of all those particles that are near to the barrier
and have velocity lesser than the threshold velocity.

0.6

Fig. 5. Variation in average height of flow (hf) andaverage height of settled debris mass (hs) behind thebarrier for different time instants.
Value of empiricalcoefficients

100Table 2. Estimation of k and α coefficients of the hydraulicmodels corresponding to maximum impact force
Parameters/Coefficients
Values
Impact force (F) (N)
1.98
Average flow velocity (v) (m/s)
0.27
Average height of flow (hf) (m)0.057
Average height of settled debris mass
0.015
behind the barrier (hs) (m)
k
29.13
α0.79

'k''k''a''α'

101
0.1
0

0.1

0.2

0.3
0.4
Time (s)0.5

0.6

References

Fig. 6. Variation of k and α coefficients with time for thedry debris flow.

1.

W. Shen, T. Zhao, J. Zhao, F. Dai, G.G.D. Zhou,
Eng. Geol., 241, 86-96 (2018).
2. K. Lee, S. Jeong, Comp. and Geotech., 116, 103214(2019).
3. Y. Cui, C.E. Choi, L.H.D. Liu, C.W.W. Ng, Nat.
Haz., 91, 1179-1201 (2018).
4. F. Calvetti, C. G. D. Prisco, E. Vairaktaris, Acta
Geotech., 12, 129-144 (2017).
5. S. Utili, T. Zhao, G.T. Houlsby, Eng. Geol., 186, 316 (2015).
6. W, Shen, G. Luo, X. Zhao, Landslides, 19, 479-489(2022).
7. LIGGGHTS, DCS Computing GmbH, Linz,
Austria.
https://www.cfdem.com/liggghts-opensource-discrete-element-method-particlesimulation-code. Last accessed 31/08/22.
8. B. Shi, Y. Zhang, W. Zhang, Int. J. of Geo., ASCE,
18, 04018092 (2018).
9. A. Ujjwal, A DEM based study of dry debris flow
through granular column collapse over a horizontal
bed and its interaction with a rigid barrier, Masters
Dissertation, Department of Civil Engineering,
Indian Institute of Technology Guwahati (2022).
10. A. Leonardi, M. Pirulli, M. Barbero, F.Barpi, M.
Borri-Brunetto, O. Pallara, C. Scavia, V.Segor,
Environ. Eng. Geosci, 27(2), 195–212 (2021).

Using the magnitudes of impact force from Fig. 2,
the values of the coefficients, k and α, are calculated for
different time instants, i.e., 0.2, 0.25, 0.3, 0.35, 0.4 and0.5 s, and are plotted in Fig. 6. While estimating thevalues of empirical coefficients, certain truncation
criteria have been considered for v, hf and hs, in order toeliminate any unrealistic or spurious values mostly for
extreme time instants. It can be observed from Fig. 6 thatfor initial time instants, where the impact ispredominantly dynamic (hf > hs), the value of α is lesser
than or nearly equal to 1, whereas the value of k issignificantly large. Since the initial impact force ismostly governed by the flow velocity, the hydrodynamic
formula (Eqn. 2) suitably represents the impact force
that is indicated by a lesser α value. However, as the time
progresses, the contribution of static pressure enhances.
As hs builds up and hf gradually diminishes over thetime, the k value decreases and α value increases.
Finally, for the time instants of 0.4 s and beyond, thevalue of k coefficient becomes near to 1 while that of αcoefficient is extremely high. During these later times,
the force experienced by the barrier is derived solely
from the static impression of the deposited mass behindthe barrier (as seen from Fig. 5). Hence, the lateralstresses on the barrier could be better represented byhydrostatic formula (Eqn. 1), as indicated by lesser kvalue (nearly equal to 1). Thus, the range of k and α4