Influence of particle-size segregation on the impact of dry granular flow

Accepted Manuscript Influence of particle-size segregation on the impact of dry granular flow

Yuan-Jun Jiang, Xiao-Yi Fan, Tian-Hua Li, Si-You Xiao PII: DOI: Reference:

S0032-5910(18)30741-1 doi:10.1016/j.powtec.2018.09.014 PTEC 13688

To appear in:

Powder Technology

Received date: Revised date: Accepted date:

10 June 2018 10 August 2018 6 September 2018

Please cite this article as: Yuan-Jun Jiang, Xiao-Yi Fan, Tian-Hua Li, Si-You Xiao , Influence of particle-size segregation on the impact of dry granular flow. Ptec (2018), doi:10.1016/j.powtec.2018.09.014

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ACCEPTED MANUSCRIPT Influence of particle-size segregation on the impact of dry granular flow Yuan-Jun Jianga [email protected] m, Xiao-Yi Fanb,* [email protected] , Tian-Hua Lic [email protected] m, Si-You Xiaod,e [email protected] Institute of Mountain Hazards & Environment, Chinese Academy of Sciences, 9#, Section 4,

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a

RenMinNanLu Avenue, Chengdu, Sichuan 610041, China b

School of Civil Engineering and Architecture, Southwest University of Science and Technology,

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Shock and Vibration of Engineering Materials and Structures Key Laboratory of Sichuan Province, Mianyang, Sichuan, PR China

School of Civil Engineering and Architecture, Southwest University of Science and Technology,

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c

Mianyang, Sichuan, PR China e

University of Chinese Academy of Sciences, Beijing, 100049, China;

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d

Institute of Mountain Hazards & Environment, Chinese Academy of Sciences, 9#, Section 4,

*

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RenMinNanLu Avenue, Chengdu, Sichuan 610041, China

Corresponding author.

ABSTRACT:

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Even though dry granular flow can cause well-known impact hazards to retaining structures, studies rarely have been conducted to determine the influence of particle-

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size segregation on the impact of dry granular flow. Based on the existing experiments concerning the impact of dry granular flow, we calibrated a code of the Discrete Element Method and designed three numerical simulations. Two types of

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degree of particle-size segregation Ns and Nl were defined to show the extent of particle-size segregation in the depth and flow directions. The results of the simulation indicated that a dry granular flow initiated with different degrees of particle-size segregation (Ns) could develop into very distinctive conditions in terms of the relative positions of different groups of particles in the depth and flow directions. The initial deposition with a higher Ns could make it easier for the coarser particles to be located in the front and top of a dry granular flow, with the finer particles being in the tail and bottom of the flow. In the impact process, the greater the values of Ns and Nl are, the more the coarser particles impact the retaining wall at a higher position at an earlier time during the impact. However, a higher degree of segregation of the particle sizes does not necessarily correspond to a higher impact

ACCEPTED MANUSCRIPT force and action point. It is more rational to use the change of Ns with respect to its initial value as the index to show the influence of particle-size segregation, and a greater change in Ns corresponds to a higher impact force and a higher action point. The greater change of Ns corresponds to a lower energy dissipation, which is accounted for by the friction among the particles in the flow process, i.e., less contacts among the particles correspond to the less dissipation of energy, which means that

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more energy can be converted into impact force.

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Keywords: particle-size segregation, dry granular flow, impact force, action point

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1 Introduction

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Dry granular flow hazards can be severe when they occur in mountainous areas that have experienced earthquakes. Such hazards can develop directly from landslides, and

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they can be triggered by road construction and rainfall. Fig. 1a shows one dry granular flow hazard that blocked one road at the epicenter of the Wenchuan earthquake that occurred in 2008 in China. This earthquake produced more than 1000 landslides and

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unstable slopes [1], many dry granular flows, and many such flows that occurred after the earthquake as a long-lasting hazard. Depending on the type of landslide, the

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volume of a dry granular flow could range from 100 to 1,000,000 cubic meters. Once such a mass of gravel and rock fragments run along a steep mountain slope, it can reach a significant velocity and have a long runout distance, generating a destructive

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impact force on any objects it encounters. Such a force could destroy the infrastructure of villages and towns and kill many people. In addition, the mountain roads, which are the only escape routes during an earthquake, could be blocked by the dry granular flow thereby eliminating the escape routes and causing huge indirect losses.

In order to protect the objects threatened by a dry granular flow, structures such as retaining walls (Fig. 1b), flexible nets (Fig. 1c), and rock sheds (Fig. 1d) are commonly used along mountain roads. Many researchers have studied the interaction between dry granular flow and structures by experiments and numerical simulations using indoor experiments, e.g., Jiang [2,3] studied the impact of a dry granular flow

ACCEPTED MANUSCRIPT on a retaining wall and a rock shed. They proposed a method to estimate the maximum impact force exerted on a retaining wall, a nd they analyzed the effect of a cushion layer on the impact force and the inner force in the rock shed. Besides experimental investigation, several researchers also studied dry granular flow impact by Discrete Element Method (DEM) [4-8], which include the reproduction of experimental results, the micro- mechanism in dry granular flow impact processes against different types of retaining structures, and also the factors influencing energy

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variation in a dry granular flow and impact process. For instance, Valentino [4] studied the impact process of a dry granular flow using both a laboratory flume test

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and the discrete element method. Particular attention was devoted to the validation of

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DEM when used for the prediction of the run-out distance and of the impact force on obstacles. However, the soil used for the small-scale model is a mono- granular

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medium sand, no particle size distribution was considered in both experiment and numerical simulation. Albaba [5,6] tried to reproduce the complexity of granular material and retaining structure in terms of particle shape and structure type by DEM.

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He simulated dry granular flow impact events by using poly-dispersed non-spherical particles and with concern of particle size distribution. Besides rigid retaining wall, he

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also used DEM to simulate flexible net with concern of the complex structure detail in terms of cable, ring and net composition. Meanwhile he studied the relationship between the microstructure and the impact load produced by a dry granular flow.

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Zhao [7,8] also studied the flow and impact behavior of dry granular flows by DEM simulations. Special attention was paid to the way energy dissipation by the granular flows. It was revealed that most of the energy of the granular columns was dissipated

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by inter-particle friction, to calculate the destructive power of a granular flow slide, only the translational contribution of the kinetic energy is relevant, and a methodology was presented to calculate the flux of kinetic energy over time carried by the granular flow. In addition, during the impact process, the majority of initial total energy was dissipated by particle-particle and particle-flume interactions, while only a negligibly small amount of energy was dissipated by particle-barrier interaction. To date, most of the literature concerning the impacts of dry granular flows has focused on the impact of the flow against a retaining wall. Such research generally can be categorized into two classes, the first of which is concerned with the impact mechanism, e.g., dead- zone development [5,9,10], runup [11,12], overflow

ACCEPTED MANUSCRIPT [13-15], and the influence of the characteristics of the particles [3]. The second class deals with the estimation of the force of the impact by theoretical and empirical solutions. For instance, on the basis of several sets of flume experiments in which a dry granular flow impacted a rigid wall, Faug [16] made certain simplifications and assumptions and proposed a depth-averaged analytical solution that described the dynamics of the impact, thereby reproducing the variations of the impact force during the entire impact process. However, among many other researchers, most of t he

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equations for calculating the force of the impact have been based on hydrodynamics [2,17,18]. This approach assumes that the pressure at impact is proportional to the

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square of the velocity of the flow and that this pressure should be calibrated by an

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empirical coefficient, which is a function of the Froude number. Other studies specifically related to snow avalanches have been conducted to investigate the

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correlation between the calibration coefficient and Froude number based on data acquired from field and laboratory tests [19-22].

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Figure 1

The impact of a dry granular flow against a retaining wall has been studied

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extensively. However, the present studies of dry granular flow impact have never taken into account the influence of particle-size segregation. While particle-size

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segregation significantly and inevitably occurs in the process of a dry granular flow [23-25], it is well known that the mixtures of coarse and fine particles segregate to develop an inversely graded (upward coarsening) particle‐size distribution. For a dry

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granular flow that is sheared down a slope, the main mechanisms of segregation include kinetic sieving and squeeze expulsion [26,27]. These processes result in the larger particles moving to the front and to the top surface, while the smaller particles accumulate at the bottom and in the rear part of the flows [28], which inevitably influences the interaction of a dry granular flow against an obstacle. Many different types of studies have been done in attempts to determine the mechanism of particlesize segregation, e.g., 1) experimental studies [26,27,29-31] and 2) analytical and numerical models [26,32-36]. However, it is rare to see any of them have related particle-size segregation to dry granular flow impact.

ACCEPTED MANUSCRIPT Therefore, in this study, we used discrete element simulation to investigate the influence of particle-size segregation on the impact of a dry granular flow and to estimate the differences of the impact forces based on the different degrees of segregation. In this paper, the Introduction provides a review of the state of art of based on the existing research related to the impact of dry granular flows and particlesize segregation. The methodology chapter (Chapter 2) introduces the theoretical model of the Discrete Element Method (DEM) used in the present research and the

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design and calibration of the numerical simulations. In Chapter 3, we present and discuss our analysis of the results of the DEM simulations and of the influence of

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particle-size segregation. Our conclusions based on the DEM results and analyses are

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presented in Chapter 4.

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2 Numerical Simulation via Discrete Element Method The Discrete Element Method (DEM) has been used successfully to investigate the

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flow mechanism of dry granular flows, including small- scale laboratory experiments in which such flows were reproduced [37-40] and simulation of the natural rock avalanche hazard process [41]. DEM also has become a powerful tool for studying the

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mechanisms involved when a dry granular flow interacts with a retaining structure. For instance, based on the DEM simulation results of a free-surface, gravity-driven,

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dense flow overflowing a wall, Faug [42] proposed a hydrodynamic model to predict the impact force produced by a dry granular flow against a rigid retaining wall. Several researchers have used DEM to study the influence of the shape and size of the

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particles and the angle of the slope on the impact process [7,43,44]. A new modelling technique of DEM also was proposed by Albaba [5] and Albaba [6] to study the impact of a dry granular flow against a rigid wall and a flexible net barrier. In our study, we used a discrete element tool named as EDEM 2.5 to conduct the discrete element simulations. EDEM is the market- leading software for bulk material simulation powered by state-of-the-art Discrete Element Modeling (DEM) technology, EDEM can quickly and accurately simulate and analyze the behavior of bulk materials such as coal, mined ores, soil, tablet, and powders. Eqs. 1 and 2 are the governing equations for the translational and rotational motion of particle i:

ACCEPTED MANUSCRIPT  dv  n mi  i  g     Fijn  Fijt   dt  j

Ii

(1)

d i n   M ij j dt

(2)

where vi and i are the translational and angular velocities of particle i,

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respectively; mi is mass of particle i; Ii is the moment of inertia of particle i; Fijn and

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Fijt are the normal and tangential contact forces between particle i and particle j or the

wall; Mij is the torque acting on particle i by particle j or the wall; g is the acceleration

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of gravity; and t is time.

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2.1 No-slip Hertz–Mindlin contact model

The no-slip Hertz-Mindlin model [45] was selected to describe the contacts in the

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DEM simulations. This model combines Hertz's theory in the normal direction and the Mindlin's no-slip model in the tangential direction. As shown in Eqs. 3 and 4 both the

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normal total force ( Fn ) and the tangential total force ( Ft ) have elastic and damping force components. The elastic component provides a spring repulsive force to push the colliding particles apart; while the damping component provides a dashpot to

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dissipate a portion of the relative kinetic energy. It is also noteworthy that the No-slip Hertz–Mindlin contact model evaluates the tangential force without considering micro-slip phenomena, which is a simplification of the full Hertz-Mindlin model [46].

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However, as shown in Eq. 4 there is indeed relative tangential motion, and the tangential force–displacement relation is linear. But the tangential elastic stiffness constant ( Kt ) depends upon the normal displacement as shown in Table 1, correctly accounting for the different tangential behavior for different normal displacement states. While the full Hertz-Mindlin model takes concern of the influence of microslip on the microscopical tangential interactions regarding the non- linear tangential force–displacement relation and the hysteretic behavior for oscillating conditions. In the full Hertz-Mindlin model the normal and tangential displacements vary simultaneously, an incremental procedure must be used in general, relating the change in tangential force to the change in tangential displacement. The actual tangential

ACCEPTED MANUSCRIPT force is calculated considering the previous tangential force and the change of the tangential displacement through an incremental stiffness, which complexes the algorithm and increases the cost of computation. Therefore, the No-slip Hertz– Mindlin contact model was proposed to simulate the macroscopic behavior of bulk granular material, such as granular flow, which was validated to be successful [45]. For both the No-slip Hertz–Mindlin contact model and the full Hertz–Mindlin contact model, the gross sliding condition provided by Coulomb's law of friction is imposed

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as a constraint to the tangential force calculation (Eq. 4) [46]. The constraint is the upper bound of the tangential force must be applied to a motionless object to make it

Fn   K n n  Cn vnrel

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start moving [47], therefore, the coefficient of static friction s was used in Eq. 4. (3)

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Ft  min  s Fn , K t t  Ct vtrel 

(4)

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where Kn and Kt are the spring stiffness constants in the normal and tangential directions, respectively; Cn and Ct are damping coefficients;  n and  t are

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overlaps or displacements in normal and tangential directions; vnrel and vtrel are the relative velocities; and s is the coefficient of static friction, which corresponds to

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the scalar value that is used to determine the magnitude of the force that must be applied to a motionless object to make it start moving. Also, a rolling torque was

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introduced to account for the rolling friction:

Tr  r Fn Rii

(5)

where r is coefficient of rolling, and Ri is the distance from the center of particle i to the contact point. The equations for the other parameters are listed in Table 1. Table 1. Equati ons for the parameters in the no-slip Hertz-Mindlin model Normal direction Spring stiffness constant

Kn 

4 * * E R n 3

Tangential direction

Kt  8G* R* n

ACCEPTED MANUSCRIPT 5  Sn m* 6

Cn  2

Equivalent Young’s modulus

1 E

(E )

Ej are the Young’s modules of particles i and j; vi and vj are the

2 i

1

2 j

1

Ei

Ct  2

5  Kt m* 6

Damping coefficient

Ej

, where i, j are number of particles; Ei and

Poisson’s ratioes of particles i and j shear

modulus

(G )

1 G

2 i

1 Gi

2 j

1

, where Gi and Gj are the shear modules of

Gj

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Equivalent

particles i and j

1 , where Ri and Rj are the radiuses of particles i Rj

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Equivalent radius ( R )

1 Ri

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1 R

and j

Equivalent mass ( m )

Parameter related to restitution



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G

ln e

ln 2 e   2

and j

Sn  2E* R* n , where e is the restitution coefficient

E , where E is elastic modulus; G is shear modulus; v 2(1 )

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coefficient (  )

Relation between E and G

1 , where mi and mj are the masses of particles i mj

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Normal damping stiffness ( Sn )

1 mi

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1 m

is Poisson’s ratio

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2.2 Design of the numerical simulation The setup of the numerical model in EDEM was based on the experiment conducted by Jiang and Towhata [2] (Fig. 2) in which they studied the impact behavior of dry granular flow against a rigid retaining wall by using a poly-dispersed mixture of limestone gravel (Gravel 1 in Fig. 3); the Gravel 1 had a measured angle of repose of 53˚. The experimental flume which had a length of 2.93 m, a height of 0.35 m, and a width of 0.30 m, was titled to 35˚ in experiments. The friction angles of the flume base, flume sides, and the rigid wall were 25˚, 15˚, and 21˚, respectively. A rigid retaining wall model with a height of 0.40 m and a width of 0.30 m was installed at the lower end of the flume. The gravel material (Gravel1) used to produce dry

ACCEPTED MANUSCRIPT granular flow had particles that ranged in size from 10 to 20 mm in diameter and had a specific weight of 13.5 kN/m3 . Fig. 2 shows that, in the experiment, the deposition of Gravel1, with a length of 0.44 m, a width of 0.30 m, and a height of 0.20 m, was released at the upper end of a flume, at a distance of 2.19 m from the retaining wall. In the experiment, the normal impact force variation with time was measured and recorded. The experimental data was selected for our model calibration.

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Figure 2

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The same flume model was built and used in the DEM simulation, but the granular material in DEM, defined as Gravel_DEM, was a little different from Gravel1 in that

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the particle size distribution was different. Fig. 3 shows that Gravel1 had a very uniform particle size of approximately 20 mm, which was not suitable for producing

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particle-size segregation in the flow process. Therefore, to widen the distribution of particle sizes in the DEM simulation, four distinctively different groups of particle

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sizes, defined as KL1, KL2, KL3, and KL4, were used to compose Gravel_DEM (Fig. 3). Table 2 shows that the particles in the group KL1 ranged from 1 to 2 mm, whereas KL2 ranged from 2 to 10 mm; KL3 ranged from 10 to 20 mm; and KL4 ranged from

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20 to 40 mm. Gravel_DEM was made up of the same weight percent of the four sizes

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of particles.

Figure 3

Table 2. Particle size distribution of Gravel_DEM

Particle diameter/mm Percent by weight/%

1~2（ KL1）

2~10（ KL2）

10~20（ KL3）

20~40（ KL4）

25

25

25

25

The initial depositions of Gravel_DEM were constructed in three ways according to the different arrangements of the particle groups. For example, in Fig. 4a, the particle groups KL1, KL2, KL3 and KL4 were arranged layer by layer from top to bottom in a size descending order for the case of M1. For the case of M2, the four groups of particles were distributed randomly in the initial deposition. While for the case of M3, the four groups of particles were arranged in a size ascending order like KL4, KL3,

ACCEPTED MANUSCRIPT KL2 and KL1 from top to bottom. Considering the degree of particle-size segregation, M1 had the highest degree of particle segregation, i.e., full segregation; M3 had the lowest degree of particle segregation, i.e., no segregation; and M2 had a degree of particle segregation between those of M1 and M3. From Fig. 4b it seems that the KL1, KL2, and KL3 particles were distributed mainly in the lower zone of the deposition, whereas the KL4 particles were distributed throughout the whole deposition, especially in the upper zone, which is not a perfect random distribution for the four

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groups of particles. However, this does not hinder the fact that the degree of

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segregation of M2 is between those of M1 and M3.

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Figure 4

From Section 2.1, we know that the no-slip Hertz-Mindlin contact model requires the

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input of material properties and contact parameters. By reproducing the experimental results of Jiang and Towhata [2] in terms of final deposition of granular material (Fig.

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5) and impact force history (Fig. 6), these parameters were calibrated as listed in Tables 3 and 4. Fig. 5 shows that the shape of final deposition produced by the DEM simulation was very similar to that of the experiment. However, the impact force

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produced by the DEM simulation was a little smaller than that of the experiment. Since the goal of this study was to investigate the effect of particle-size segregation on

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dry granular impact, the exact reproduction of experimental results was not a necessity. It is reasonable to conclude that the DEM simulation was conducted properly and that the study of particle-size segregation could rely on the settings of

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the numerical parameters that were used. Figure 5 Figure 6

Table 3. Properties of the materials Material

Poisson’s ratio

Elastic modulus

Density（kg∙m-3 ）

(MPa) Gravel_DEM Flume

0.25 0.3

8.5×102 3

1.23×10

1969 7900

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3.85×103

0.3

7900

Table 4. Contact parameters Particle-Particle

Particle-Flume

Particle-Wall

Restitution coefficient

0.6

0.6

0.6

Friction coefficient

1.33

0.453

0.453

Rolling friction coefficient

0.23

0.05

0.05

Hertz-Mindlin (no slip)

Hertz-Mindlin (no slip)

Hertz-Mindlin (no slip)

Contact model

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Parameter

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3 Numerical Simulation Results and Analyses

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3.1 Particle-size segregation and its quantitative description

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Based on the above model and the parameters that were set, three DEM simulations (M1, M2, and M3) were conducted to produce the processes of the initiation, flow, and impacts of a dry granular flow. For each case, Fig. 7 shows snapshots at three

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times that show the states of flow, impact, and final deposition. Figs. 7a, b, and c show the flow states of the three cases when the dry granular flow reached the

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retaining wall. For the three cases, it is clear that the segregation of particles developed in different degrees. For M1 and M2, the coarser particles, mainly of groups KL4 and KL3, obviously were on the top and the front of the flow, and this

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was even more significant for M1. For M3, the finest, macroscopic particles were on the top and at the front of the flow. This indicated that the extent of particle segregation of the initial deposition indeed influenced the development of particle

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segregation in a dry granular flow. Figs. 7d, e, and f show the moment when the maximum impact force occurred on the retaining wall and the particle segregation phenomenon had already occurred significantly in the three granular flows, respectively. What was different was that, for M1, most of the coarser particles (KL4 and KL3) were distributed in the front and at the top of the deposition; for the part that was flowing after the deposition, there were very few coarser particles. For M2, there was mostly a very thick layer of coarser particles distributed on the top of the deposition, and a thin layer was observed in the flowing part. For M3, a thin layer of coarser particles was distributed on the top of the deposition, and a thick layer is on the part that was still flowing. The particle distributions in the final depositions of the

ACCEPTED MANUSCRIPT three cases also were very distinctive (Figs. 7g, h, i). For M1, most of the coarser particles accumulated in the front and top of the deposition, while the finer particles were in the rear and at the bottom. For M2, most of the coarser particles accumulated in the top of the deposition, while the finer particles were at the bottom. For M3, most of the coarser particles accumulated in the top and at the rear of the deposition, while the finer particles were in the front and at the bottom. Fig. 7 shows that the different particle distributions in the initial depositions impacted the process of a dry granular

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Figure 7

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flow and affected the distributions of the particles in the final depositions.

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By setting initial depositions with different degrees of particle-size segregation for three cases, it was observed that particle segregations had distinguishing developments in M1, M2, and M3. In addition, there was evidence that the degree of

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particle-size segregation indeed influenced the impact mode of a dry granular flow against a retaining wall. However, in the above analysis the degree of particle-size

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segregation was described only qualitatively. The degree to which the particle-size segregation developed in each case and how the variation process occurred were not clear. In order to portray the development of particle-size segregation in a dry

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granular flow and the impact process in more quantitative terms, two non-dimensional numbers were defined to describe the degree of particle-size segregation in the depth direction (Ns) and along the flow direction (Nl). Since the segregation of the particle

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based on their sizes causes the coarser particles to move upward, the basic idea of Ns was to demonstrate the degree of segregation of the particles based on their sizes by showing the relative differences in the heights of the coarser particles and the finer particles. Eq. 6 was used to normalize the average height of the coarsest particle group (KL4) with the average heights of the other, finer particle groups (KL3, KL2, and KL1) and to summarize these normalized numbers. In Eq. 6, hi is the vertical distance between particle i and the base of the flume, as defined previously; nKL1 ,

nKL 2 , nKL3 , and nKL 4 are the number of particles of particle groups KL1, KL2, KL3, and KL4, respectively. Ns is not an absolutely physical non-dimensional number; however, it does show the relative change of particle-size segregation with respect to

ACCEPTED MANUSCRIPT the initial state of a granular mass. Note that Ns cannot be used to compare the degree of particle-size segregation between different granular masses with different particle size distributions because Ns only indicates the relative change of a single system. In Eq. 6, the greater Ns is, the more significant the degree of particle-size segregation becomes. As shown in Eq. 7, a similar concept was used to define the degree of particle-size segregation in the flow direction by Nl; in Eq. 7, li is the distance of particles move forward to the front of a dry granular flow.

nKL 4 nKL 4 i 1

nKL 4

(6)

n

 li

 i 1 , n  nKL1 , nKL 2 , nKL 3 n

(7)

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Nl  

 li

 i 1 , n  nKL1 , nKL 2 , nKL3 n

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i 1

n

 hi

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Ns  

 hi

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nKL 4

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particle i from the back wall of the flume. The greater Nl is, the more the coarser

Fig. 8a shows the variation of Ns in the process of a dry granular flow for the cases of M1, M2, and M3. It is clear that M1 has the largest Ns; M3 has the smallest Ns; and M2

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has a Ns between the largest and smallest values in the beginning, which is identical to the initial state of particle-size segregation shown in Fig. 4. It was known that M1 had

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the most complete particle-size segregation; M3 had no segregation; and M2 had a random particle distribution in Fig. 4. Fig. 8a shows that, when a dry granular flow was initiated, Ns generally increased to a

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peak in the impact process and then increased to a constant value until the end of the impact. The increase of Ns indicates that the degree of particle-size segregation for M1, M2, and M3 were developed substantially in the flow and impact processes, as shown in Fig. 7. The decrease after the peak can be interpreted from two aspects, i.e., 1) that with reaching the end of an impact process, the co llisions or jumping of the coarser particles in the top layer (Fig. 7) gradually disappeared, which caused the average height of the coarser particles to become low, and, consequently, according to Eq. 6, Ns gradually became small and 2) that particle-size segregation made coarser particles run to the front and finer particles stay in the tail of a flow. Then, after the coarser particles were resting on the deposition, the finer particles finally arrived and

ACCEPTED MANUSCRIPT somehow climbed up onto the deposition, which increased the average height of the finer particles, and, as a consequence, Ns decreased according to Eq. 6. While it is noteworthy that for M3, after a short decrease, Ns kept increasing until it assumed a constant value, which was due to the fact that, in the case of M3, the finer particles run to the front (Fig. 7c). First, they come to rest in the front of the wall, and, as more and more coarser particles arrive and rest on the finer particles, the average height of the coarser particles increased, which, in turn, caused Ns to increase. Also, for the case

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of M1, there was a brief decrease of Ns after the initiation of flow because the initial deposition was spread out and caused the average height of the coarser particles

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decreased.

Fig. 8a shows that the particle-size segregation with increasing depth was significant for the three cases, and the development of particle-size segregation in the flow

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direction also was very obvious. In Fig. 8b for M1 and M2, Nl went through a process of increasing and then decreasing, which corresponded to two states, i.e., the first state

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was before the granular flow reached the retaining wall, and the coarser particles were moving in the front of the granular flow, i.e., the relative average distance between the coarser particles and the finer particles was getting larger. After the impact started, the

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coarser particles rested and formed the dead zone, and the finer particles arrived afterwards and rested on top of the coarser particles, i.e., the relative average distance

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between the coarser particles and the finer particles became smaller. These two states occurred in the reverse sequence for M3.

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Figure 8

3.2 Influence of particle-size segregation on the impact process In addition to the snapshots in the flow and impact processes, the contact forces generated by the particles and their interaction with the wall in the dry granular flow impact process also were recorded and plotted as a cloud picture in Fig. 9, and Figs. 9a, b, and c correspond to the time point when the maximum impact force occurred in each case, respectively. By integrating the particle-wall contact forces based on Eq. 8, the total impact force or the resultant force were obtained as an output, as shown in Fig. 11. In Eq. 8, Ftotal is the total force of all of the particles that are in contact with

ACCEPTED MANUSCRIPT the retaining wall; Fi is the contact force between particle i and the wall; nc is the total number of particles contacting the wall; ncKL1 , ncKL 2 , ncKL 3 , and ncKL 4 are the number of particles contacting the wall respectively for particle groups KL1, KL2, KL3, and KL4; and FKL1 , FKL 2 , FKL 3 , and FKL 4 are the integrated impact force of

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each of the particle groups, respectively.

nc

ncKL1

ncKL 2

ncKL 3

ncKL 4

i 1

i 1

i 1

i 1

i 1

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Figure 9

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Ftotal   Fi   Fi   Fi   Fi   Fi  FKL1  FKL 2  FKL 3  FKL 4

(8)

Fig. 10a shows that the three cases had similar impact force-time histories. And the

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time point of peak force occurred (at about 1.6 s) for each case (Fig. 10a), but this time was not the same as that of peak Ns (Fig. 8a). M3 obviously had a greater peak

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value than M2 and M1, which showed that the different particle segregation processes indeed had different effects on the impact of dry granular flow. However, around the time of 1.6 s when the peaks occurred, the Ns values of M1, M2, and M3 were in a

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reverse sequence from that of the peak forces, which does not necessarily indicate that a higher degree of particle-size segregation corresponds to a lower impact force since

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M1, M2, and M3 did not initiate from the same Ns. It may be more rational to use the change of Ns with respect to its initial value as the index to show the influence of particle-size segregation. Around the time of 1.6 s, the changes of the Ns values of

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M1, M2, and M3 were about 2, 4, and 6, respectively, which may suggest that the highest change of Ns corresponded to the higher impact force. To show this difference from the aspect of particle segregation, we also show the components of the total impact force contributed by the different groups of particles for each case (Figs. 10b, c, and d). For M1 (Fig. 10b), which had full particle segregation from its initiation, it was obvious that the different groups of particles made different degrees of contributions to the total impact force. In Fig. 10b, the groups of particles from coarse to fine (i.e., from KL4 to KL1) provided force contributions from high to low. The force components generated by the coarser groups (KL4 and KL3) made up most of the total force. While for the case of M2 (Fig. 10c), which had a random particle distribution from its initiation, it is very interesting

ACCEPTED MANUSCRIPT that KL4 generated the minimum amount of force component, which was very different from the case of M1. Except from KL4, the force component generated by group KL3 was the maximum, followed sequentially by those of KL2 and KL1. For M3, the proportion of the force components was totally opposite that of M1, i.e., the finest particle group (KL1) made the largest contribution to the total force, and particle group KL2 had the second largest contribution. However, particle groups KL3 and KL4 provided almost no contribution to the total force. It is interesting that, for a

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dry granular flow, the different degrees of initial particle-size segregation could result in very different impact force values. Also, the state of particle-size segregation also

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influenced the proportion of impact force contribution from the different groups of

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particles. The mechanism that caused such a difference could be explained more directly by the shape of the distribution of each group of particles, as shown in Fig.

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11. The snapshots at the moment when the maximum impact force occurred were shown in Figs. 7d, e, and f, and the corresponding individual display of each particle group is shown in Fig. 11. Figs. 11a-d show that, for the case of M1, the coarsest

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group, KL4 (Fig. 11d), had the maximum contact area with the retaining wall, and the contact area decreased sequentially from KL4 to KL1, which may explain the decrease

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of force components from KL4 to KL1 in Fig. 11b. For the case of M2 (Figs. 11e- h), it is clear that KL3 had the largest contact area and that the contact area decreased from KL2 to KL1 to KL4, which also was identical to the decrease sequence of the force

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components in Fig. 10c. A very obvious decrease of contact area from KL1 to KL4 also was observed in Figs. 11i- l for the case of M3, which also corresponded to the decrease in the force components from KL1 to KL4 in Fig.10d. Basically, Figs. 10 and

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11 indicate that, for M1 to M3, which had different initial particle-size segregations, the following different degrees of development of particle-size segregation could cause the contact area of each particle group with the retaining wall to vary from case to case, which causes the different particle groups to make different contributions to the force of the impact.

Figure 10

ACCEPTED MANUSCRIPT Figure 11

Fig. 9 shows that the force produced by the contact between a particle and the retaining wall was recorded in terms of force value, direction, and coordinates. Using this information and by Eq. 9, the action point ( htotal ) of the total impact force can be

htotal 

i

nc

 Fi



 Fi hi

i 1 nc

 Fi hi

i 1

ncKL 2



 Fi hi

i 1 nc

ncKL 3



 Fi hi

 Fi hi

i 1 nc

ncKL 4



 Fi hi

i 1

i 1

 Fi hi

i 1 nc

 Fi hi

i 1

 hKL1  hKL 2  hKL 3  hKL 4 , (9)

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i

ncKL 1

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nc

 Fi hi

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calculated.

where hi the vertical distance between particle i and the base of the flume; hKL1 ,

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hKL 2 , hKL3 and hKL 4 are the integrated action point of each of the four particle groups, respectively. In the previous analysis, the value of the impact force was compared among M1, M2, and M3, after which the influence of particle-size

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segregation on the action point also was analyzed. Fig. 12a shows that the case with lower degree of particle-size segregation has a higher action point, i.e., M3 has the

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highest action point; M2 has the second highest action point, and M1 has the lowest action point, which is similar to the situation of the impact force. Also, this may

force.

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suggest that greater changes in Ns correspond to higher action points of the impact

The action points of different particle groups were different from case to case. Since M1 has the most substantial particle-size segregation (Figs. 7 and 8), different particle

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groups were distributed from coarse to fine from the top to the bottom of the granular flow, consequently the coarser group of particles impacted at a higher point on the retaining wall, and the finer group of particles acted at a lower point (Fig. 12b). Fig. 12c shows that, for M2, the KL3 group had a much higher action point than the other groups, but this cannot be interpreted directly from Figs. 7 and 11. This may be because the degree of particle-size segregation of M2 was not high enough, which caused only the KL3 group to make a larger upward movement than the other groups, which were still distributed at similar heights. For the case of M3, it is quite clear that particles ranging in size from fine to coarse were distributed from top to bottom in the

ACCEPTED MANUSCRIPT flow and deposition processes, which is identical to the weakest particle-size segregation shown in Figs. 7, 8, and 11.

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Figure 12

3.3 Energy evolution in the particle-size segregation process

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The analysis above demonstrated that greater changes of the degree of particle-size segregation (Ns) can cause higher impact force and higher action point. However, the

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mechanisms by which these effects occur are not clear. Therefore, the kinetic energy of each case was calculated according to velocity and mass of the particles. Fig. 13a shows that M3 had the highest peak kinetic energy in the entire flow and impact

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process, while M2 had a lower peak kinetic energy than M3, and M1 had the lowest value. Thus, we concluded that greater changes in the degree of particle-size

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segregation corresponds to a lower energy dissipation process, and the impact of granular flow with a higher kinetic energy is more likely to produce a higher impact force and point of action. As shown in Fig. 13b, while the different evolutions of

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kinetic energy caused by different energy dissipations may be attributable to the friction among the particles, before a granular flow reached the retaining wall (1 s), the case of M1 had the largest contact number, and M3 had the smallest number. This means that the granular flow of M3 had the lowest energy dissipation by friction and more energy was available to contribute to the force of the impact. Figure 13

4 Conclusions

ACCEPTED MANUSCRIPT Based on the dry granular flow impact experiments, three DEM simulations were designed and calibrated to investigate the influence of particle-size segregation on the impact process of a dry granular flow. It was proven that the different particle-size segregation processes indeed produced different impact processes and affected the variables associated with the impact. Our conclusions are listed below: (1) A dry granular flow initiated with different degrees of particle-size segregation (Ns) can produce very distinctive effects in terms of the relative positions of different

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groups of particles in the depth and flow directions. The initial deposition with a higher Ns can make it easier for the coarser particles to move in the front and top of a

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dry granular flow, with the finer particles being left in the tail and on the bottom.

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(2) In the impact process, the higher the values of Ns and Nl are, the more the coarser particles will impact the retaining wall at a higher position and the earlier the impact

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of these coarser particles will occur. However, near the time of the peak impact force occurred, the Ns values of M1, M2, and M3 were totally in a reverse sequence from that of the peak forces, which does not necessarily indicate that a higher degree of

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particle-size segregation corresponds to a lower impact force. Similar situations occurred concerning the action point of the impact force.

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(3) It is more rational to use the change of Ns with respect to its initial value as the index to show the influence of particle-size segregation. Around a time of 1.6 s, the change in the Ns of M1 was about 2, whereas it was 4 and 6 for M2 and M3,

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respectively. This may suggest that the greater change of Ns corresponded to a higher impact force and a higher action point. (4) The state of particle-size segregation also influenced the proportion of impact

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force contribution from the different groups of particles. For the different initial particle-size segregations, the following different degrees of development of particlesize segregation could cause the contact area of each particle group with the retaining wall to vary from case to case, which causes the different particle groups to make different contributions to the force of the impact. (5) The greater change in the degree of particle-size segregation corresponded to a higher variation in the kinetic energy or a low energy dissipation, which is attributable to the friction among the particles in the flow process. This means that less contacts between the particles correspond to less energy dissipation by friction, which means that more energy would be available to exacerbate the force of the impact.

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Acknowledgments First, the authors sincerely appreciate the CAS Pioneer Hundred Talents Program for making the completion of this research possible. The research presented in this paper also was supported by

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the National Natural Science Foundation of China (Grant No. 41502334) and the 135 Strategic Program of the Institute of Mountain Hazards and Environment, CAS (Grant No. SDS-135-1705

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and Grant No. SDS-135-1704). The authors gratefully acknowledge these financial contributions

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and convey our appreciation to these organizations for supporting this basic research.

Nomenclature

Fijt Fn Ft Ftotal G G* Gi Gj g hi Ii Kn Kt KLi Mi Mij m* mi mj Ns

the tangential contact forces between particle i and particle j or the wall, N normal total force, N tangential total force, N total force of all of the particles, m shear modulus, Pa equivalent shear modulus, Pa the equivalent shear modulus of particle i, Pa the equivalent shear modulus of particle j, Pa the acceleration of gravity, m/s2 the height of particle i above the base of the flume,m the moment of inertia of particle i, kg·m² the spring stiffness constant in the normal direction, N/m the spring stiffness constant in the tangential direction, N/m particle size range, i=1,2,3,4 group of particles, i=1,2,3,4 the torque acting on particle i by particle j or the wall; N.m equivalent mass, kg the equivalent mass of particle i, kg the equivalent mass of particle j, kg the extent of particle-size segregation in the depth direction

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NU

Fijn

damping coefficient in the normal direction damping coefficient in the tangential direction compression modulus, Pa equivalent Young’s modulus, Pa the Young’s modulus of particle i, Pa the Young’s modulus of particle j, Pa restitution coefficient normal total force, N tangential total force, N the normal contact forces between particle i and particle j or the wall, N

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Cn Ct E E* Ei Ej e Fn Ft

ACCEPTED MANUSCRIPT the extent of particle-size segregation in flow direction the total number of particles contacting the wall the number of particles with size range of Kli the number of particles contacting the wall with size range of KLi the distance from the center of particle i to the contact point, m equivalent radius, m the equivalent radius of particle i, m the equivalent radius of particle j, m normal damping stiffness time, s the translational velocities of particle i, m/s

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Nl nc nKLi ncKLi Ri R* Ri Rj Sn t vi

t n

parameter related to restitution coefficient the overlap in the tangential direction the overlap in the normal direction

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

RI

Greek letters

the relative velocity in the normal direction, m/s

rel t

v

the relative velocity in the tangential direction, m/s

s r i

the coefficient of static friction

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the coefficient of rolling

the angular velocities of particle i, rad/s

References

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Fig. 1. (a) Mountain road destroyed by dry granular flow; (b) retaining wall; (c)

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flexible net; (d) rock shed

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Fig. 2. Schematic diagram of experiment setup

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Fig. 3. Particle size distributions of the experimental granular material (Gravel 1) and the granular material that was used for Discrete Element simulation (Gravel_DEM)

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Fig. 4. Three types of initial deposition: (a) full segregation (M1); (b) random distribution (M2); (c) almost no segregation (M3)

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Fig. 5. Comparison of final depositions between the experiment and the DEM simulation: (a) experimental final deposition; (b) numerical final deposition

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Fig. 6. Comparison of impact force histories between the experiment and the DEM

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simulation

Fig. 7. Impact processes for the three cases: (a) (b) (c) the moment when granular impact started in each simulation; (d) (e) (f) the moment when the maximum impact

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force occurred; (g) (h) (i) final deposition in each simulation Fig. 8. Time histories of Ns and Nl Fig. 9. Force distribution on the retaining wall at the moment of maximum impact force

Fig. 10. Impact force histories from DEM simulations: (a) comparison of total force among three cases; (b) force components in the case of M1; (c) force components in the case of M2; (d) force components in the case of M3 Fig. 11. Snapshots of the impact states of each particle category at the time when the maximum impact force occurred for the three cases

ACCEPTED MANUSCRIPT Fig. 12. Histories of action point of impact force from DEM simulations: (a) comparison of action point among three cases; (b) action points of different particle groups in the case of M1; (c) action points of different particle groups in the case of M2; (d) action points of different particle groups in the case of M3. Fig. 13. (a) The evolution of kinetic energy for the three cases; (b) The evolution of

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particle contacts for the three cases

ACCEPTED MANUSCRIPT Highlights of the paper (1) New index Ns defined as the extent of particle-size segregation in depth direction. (2) New index Nl defined as the extent of particle-size segregation in flow direction. (3) A greater change in Ns corresponds to a higher impact force and a higher action point.

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(4) A greater change of Ns corresponds to a lower energy dissipation

Figure 1

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Figure 4

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Figure 9

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Figure 13