# IJEGE-11_BS-Hill-et-alii

*Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza*

*DOI: 10.4408/IJEGE.2011-03.B-049*

**DISCRETE ELEMENT MODELING AND LARGE SCALE EXPERIMENTAL**

**STUDIES OF BOULDERY DEBRIS FLOWS**

**INTRODUCTION**

of potential interstitial fluids – are dramatic features in

steep upland regions (e.g., i

ing the landscape in steep upland regions and have the

potential for causing tremendous loss of damage and

property (e.g., s

complex behaviors exhibited by debris flows. They

exhibit a rich variety of dynamics including complex

solid-like and fluid-like behaviour and dynamic spon-

taneous examples of pattern formation. Debris flows

often start to flow under conditions such as a large

rainfall event, but the initiation point is difficult to pre-

dict. Once they start to move, they exhibit a variety of

behaviours from those similar to a shallow fluid flow,

to that of an energetic granular material. Segregation

of particles by size mediates the behaviour while the

debris flow travels and also in the manner in which it

comes to rest. Like a granular material, debris flows

stop flowing over a bed of nonzero slope; in other

words, they resist macroscopic shear. However, the

angle of the slope at which they stop is significantly

lower than the measured angle of repose of the debris

flow giving rise to a so-called long-runout avalanches

(P

*et alii*, 2006; l

fect giving rise to complex fluid-particle interactions

**ABSTRACT**

spontaneous pattern formation. A predictive model for

these flows is elusive. Among the complicating factors

for these systems, mixtures of particles tend to segre-

gate into dramatic patterns whose details are sensitive

to particle property and interstitial fluids, not fully cap-

tured by continuum models. Further, the constitutive

behaviour of particulate flows are sensitive to the par-

ticle size distributions. In this paper, we investigate the

use of Discrete Element Model (DEM) techniques for

their effectiveness in reproducing these details in debris

flow. Because DEM simulations individual particle tra-

jectories throughout the granular flow, this technique is

able to capture segregation effects, associated changes

in local particle size distribution, and resultant non-uni-

formity of constitutive relations. We show that a simple

computational model study using DEM simulations of

a thin granular flow of spheres reproduces flow behav-

iour and segregation in an experimental model debris

flows. Then, we show how this model can be expanded

to include variable particle shape and different intersti-

tial fluids. Ultimately, this technique presents a manner

in which sophisticated theoretical models may be built

which consider the evolving effects of local particle

size distribution on debris flow behaviour.

*K*

*ey*

*worDS*

*: debris flow, segregation, simulations, rotating*

*drum, dense granular flows*

*k.M. HILL, Y. BEREkET*

*, w.E. DIETRICH & L. HSU*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

particle size distribution at the tail. Field and experi-

mental studies of bedrock erosion associated with de-

bris flows indicate that the particle size distribution in

the segregated course front or snout plays a significant

role in the rate of erosion (s

*et alii*, 2008, H

levees that have a high average particle size compared

tothat of the body of the debris flow.

the relationship between applied stress and flow rate;

segregation affects the local average particle size, so the

dynamics of the flow must vary across the debris flow.

In others words, it is becoming increasingly clear that

one needs to understand the effect of an evolving par-

ticle size distribution to develop a predictive model for

the dynamics of debris flows when some of the particles

are large enough so that interparticle interactions plays

an important role in their constitutive behaviours.

that which occurs in debris flows. (See, for example,

s

*et alii*(1997).) The most successful predictive-

superposed ona continuum model for the average

flow. Examples include themodel first proposed G

*et*

*alii*(1997) applied to chaotic flows in a rotating drum

by H

*et alii*(1999). However, these models are not

particle segregation. One of thecomplicating factors to

the application of these models is the degreeto which

segregation behaviours are sensitive to particle prop-

erty (H

*et alii*,

for them in an empirical manner.

little investigation as to how theparticle size affects

important rheological relationships. Analternative

approach to a continuum model for understanding-

*et alii*, 2006) but also possibly due to

(l

of debris flows. Examples include non-Newtonian

fluid-like models to capture certain details of the con-

stitutive behavior such as the generalized Bingham

or Herschel-Buckley model (e.g., i

*et alii*, 2007). These models don’t take into

haviors and therefore are probably most appropriate

for debris flows comprised primarily of finer particles

or even for the interior of bouldery debris flows where

finer particles are most highly concentrated (e.g., i

interparticle interactions including Coulomb stress

and collisional stress appears important for determin-

ing internal stress and other details. Collisional stress

in sheared granular flows, first modelled by b

behaviour of a wide variety of granular flows (e.g.,

s

*et alii*, 2001, b

*et alii*, 2008). Exam-

stresses are dominated by Coulomb friction include

those by s

behaviour of mixtures of debris flows consisting of

gravels and larger particles where segregation be-

comes increasingly important in determining local

and global constitutive behavior. For example, an

apparent feedback mechanism between local particle

size distribution and the constitutive behavior ap-

pears to be a primary driving mechanism for some

pattern formation problems such as a fingering phe-

nomenon observed in some large scale pyroclastic

flows (P

length scales that shapes the behaviours of the debris

flows. Large particles tend to segregate to the free sur-

face. They also segregate to the front and sides of de-

bris flows. The segregation of large particles to the front

gives rise to a course front or “snout” where the particle

**DISCRETE ELEMENT MODELING AND LARGE SCALE EXPERIMENTAL STUDIES OF BOULDERY DEBRIS FLOWS**

*Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza*

granular systems where particles undergo enduring

interaction with one another, often with more than

one particle at a time.

tions are modelled with an effective overlap between

the particles (Fig. 1). The force exerted by the parti-

cles on one another is estimated based on the effective

deformation or overlap of each particle in contact. The

resulting interparticle force is dependent on the mag-

nitude and rate change of the overlap tangential and

normal to the line connecting the particles. This may

be thought of as a relative movement of the contact

points between the particles normal and tangential to

the plane of overlap, δ

only on the amount of deformation or overlap, and a

damping mechanism, dependent on the rate change of

deformation or overlap:

respectively.

*F*

*n*

*and*

*F*

*t*

tions in debris flowsis the Discrete Element Method

(DEM). First proposed in the late1970’s by Cundall

and Strack, the DEM approach has the capabilityof

tracking individual particles throughout a simula-

tion. Rather thana bulk model for rheological rela-

tionships, the DEM approach relieson simple models

describing interactions between particles and the-

nobtains the resulting motion through numerical in-

tegration of theaccelerations of the particles derived

from the total force on eachparticle, as detailed in

the next section. The technique therefore hasthe ca-

pability of capturing segregation effects and subse-

quentchanges in the local rheological behaviour of a

particulate flow andeven forces and stresses between

the particles and the boundaryrather than imposing

rules based on, for example, empirical data. Inthis

paper, we first provide an overview of the DEM for

dry granularflows. Then we present results compar-

ing data from these DEMsimulations with model

experimental debris flows and discuss howthe DEM

simulations can be made to more realistically repre-

sent debris flows.

**DISCRETE ELMENT METHOD SIMULA-**

**TIONS**

to Molecular Dynamics (MD), (e.g., a

roscopic particles rather than molecules are treated as

distinct objects; in other words, the interaction between

two particles is modelled as a single force (rather than

a sum of all the molecular forces associated with atoms

and molecules composing each particle). Additionally,

in DEM simulation of macroscopic dry granular sys-

tems, only particles in direct contact with one another

interact and may repel and rotate one another.

is called a “soft sphere” model (e.g., C

*et alii*, 1992) which takes into

during particle-particle interactions. While this detail

is not always important for relatively sparse granular

materials where interparticle interactions are relative-

ly rare and typically binary, the details of interpar-

*Fig. 1 - Illustration of the interaction of two particles in*

*a soft sphere DEM model. (a) Two particles ap-*

*proach each other at velocities of V1 and V2 and*

*rotational speeds of ω1 and ω2. (b) During colli-*

*sion the particles the deformation is represented*

*by the normal overlap (δn) between the two cir-*

*cular particles. The plane of contact is assumed*

*to be flat and perpendicular to the line joining the*

*centers of the two particles. n is the axis perpen-*

*dicular (normal) to the contact plane and t is the*

*axis parallel (tangential) to the contact plane in*

*the direction of relative movement normal to n. δt*

*is not shown*

*k.M. HILL, Y. BEREkET*

*, w.E. DIETRICH & L. HSU*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

ton’s and Euler’s second laws. We use the Fourth Order

Runge Kutta numerical scheme to integrate the particle

accelerations to determine the rotational and transla-

tional velocities and displacement of the particles at

each instant in time. To assure numerical stability we

use a time step of approximately 1.4 μs for these calcu-

lations (m

**PRELIMINARY RESULTS: DRY SPHERI-**

**CAL PARTICLES IN A DRUM**

used for studying model debris flows at the University

of California at Berkeley described in detail in H

*et*

*alii*, (2008). The drum diameter D = 0.56 m and its

width w = 0.15m. The front vertical wall is made of

clear acrylic, so quantities such as surface profile and

particle location for those particles adjacent to the wall

are accessible. The flat vertical sidewalls are relatively

smooth. For the experiments described here, the outer

curved boundary over which the particles move – i.e.,

the bed – was roughened with attached sandpaper but

otherwise is not bumpy.

this paper we focus instead on the kinematic behav-

iour of the particles. For this, we model thebehaviour

of 13.8mm spherical glass marbles that were sheared

in the experimental drum and also the behaviour of

very simple mixtures – a single larger particle among

the 13.8mm particles. The 13.8 mm “matrix” particles

had a measured polydispersity of 10%, so in reality

they ranged from approximately 12.4 mm – 15.2 mm.

ties are shown in Table I. In all cases, the particles may

be considered in the hard sphere limit as we discuss in

Hill and Yohannes (2010, under review). The particle

*k*

*n*

*k*

*t*

*δ*

*n*

*δ*

*t*

*are the overlaps between particles and*

*γ*

*n*

*γ*

*t*

*μ*is the coefficient of fric-

*R*

*eff*

*E*

*eff*

*G*

*eff*

*r*

*i*

*v*

*i*

lar to t

*et alii*(1992):

*m*

*eff*

*is the effective mass of two particles*

*m*

*eff*

*m*

*1*

*m*

*2*

solution by t

*et alii*(1992).

or walls) is similar to the inter-particle force model

described by Equations 1(a) and 1(b). The dimensions

of the walls are usually much larger than the particle

sizes, so wall mass and radius are considered infinite.

Therefore, the effective radius during a particle-wall

contact is considered equal to the radius of the particle.

masses of those particles, we calculate the net force

and net moment on each object and, from this, the

*Tab. 1 - Properties of the simulated particles*

**DISCRETE ELEMENT MODELING AND LARGE SCALE EXPERIMENTAL STUDIES OF BOULDERY DEBRIS FLOWS**

*Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza*

to the motion associated with levy formation in debris

flows in nature. Individual particle trajectories in this

general circulation pattern vary depending on particle

size, as we describe shortly.

is sheared, and there is no plug-like section that is com-

mon in deeper flows. From the side view, there is a

steady, spatially varying velocity field from the top to

the bottom of the flow between the upstream and down-

stream moving particles. The movement of the particles

in the drum is analogous to that the flow of particles

down a hillslope, with two chief exceptions. First, the

hillslope is stationary, so none of the particles are mov-

ing backwards except in a relative sense, for example,

to the direction of motion of the particles on the top of

the debris flow. Second, the bed at the back of the flow

in the drum reaches unreasonably high slopes com-

pared to that of real debris flows. We limit ourselves to

the front and middle of the flow in the drum for making

analogies to real debris flows.

sample surface profiles derived experimentally (a) and

computationally (b) and (c) for the same mass of 13.8

mm spherical glass particles (3.13 kg). As qualitatively

apparent from the snapshots in Fig. 2, the model de-

bris flows are bulky at the front and diminish toward

the back. The similarity between the results from the

physical and computational models over the whole

field of particles gives credence to the effectiveness of

the DEM simulations in modelling these systems. The

those in the physical experiments: d = 13.8 mm ±10%

for most of the experiments. The values of the numeri-

cal parameters for the nonlinear force model between

individual particles [Equation 2(a) and 2(b)] were de-

rived from the formulas detailed in the previous section.

cm. The walls of the drum are physically smooth (i.e.,

without bumps), and the wallparticle frictional coeffi-

cient is slightly greater than that between particles to

account for the additional friction associated with the

sandpaper. All other material properties of the walls are

the same as that for the particles. Snapshots from one of

these computational experiments are shown in Fig. 2.

tion patterns. Particles in contact with the bed and walls

are dragged upstream in the direction of the walls,

though there is some slip between the walls and the par-

ticles so that the particles immediately adjacent to the

walls are not dragged as quickly upstream as the bed is

moving. The particles adjacent to the bed are carried to

the back where they then flow down the top surface of

the particles. In other words, the top and bottom sur-

faces move like two sides of a conveyor belt relative to

one another. From a plan view, lateral motion toward

*Fig.2 - Snapshots from two different perspectives from an*

*instant in time from a simulation performed mod-*

*eled after physical experiments in the drum de-*

*scribed in the text with 3.13 kg of 13.8 mm spheri-*

*cal glass particles. Rotation direction indicated*

*by the vectors outside of the drums. Movement of*

*the particles indicated by arrows drawn over the*

*beads*

*Fig. 3 - Surface profiles of the particles in the physical and*

*computational experiments described in the text.*

*(a) the longitudinal profile from the physical ex-*

*periments at one instant in time. (b) the same from*

*the computational experiments. (c) the average*

*over 20 rotations from the computational experi-*

*ments*

*k.M. HILL, Y. BEREkET*

*, w.E. DIETRICH & L. HSU*

*5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011*

of the bulk granular flow are well-represented by the

interparticle force model within the DEM simulation.

3, but there are marked differences in the behaviour of

individual particles that vary with particle size. For ex-

ample, while larger particles roughly follow the circula-

tion of the general flow at the front, once they start to

move back, they quickly segregate upward toward the

free surface, as is typical of mixtures of different sized

particles (e.g., k

*et alii*, 1997). Once at the top,

neighbors at the top of the flow and return to the front.

tive concentration in the bulk. Particles that are only

moderately larger than their neighbors take longer to

segregate to the free surface and therefore, they typi-

cally have a higher concentration slightly further back

in the flow. In other words, while the segregation be-

haviour is similar for all larger particles, it is most

dramatic for the largest particles. The relationship

between this segregation pattern and particle size is

“mixtures” consisting primarily of 13.8mm spherical

“matrix” particles and a single larger “intruder” parti-

cle. We kept the mass constant for each mixture so that

in each case a quantity of matrix particles whose mass

equalled that of the intruder particles was removed.

Figure 4 illustrates the longitudinal position of relative-

ly large intruder particles using a probability distribu-

tion (pdf) of the intruder particle in each case. Similar

to large-scale bouldery debris flows with a much wider

particle size distribution, the large particles are found

toward the front of these physical (Fig 4.a) and com-

putational (Fig. 4.b) model debris flows. The top figure

in each pair shows the pdf of the intruder particle loca-

tion for the experiments using a single 50 mm spherical

particle among the 13.8 mm particles. The next three

rows show results the same total mass of particles, but

the size of the intruder particle decreases in each subse-

quent panel to 40mm, 34mm, and then 25mm.

of the flow, and relatively narrow. For smaller intruder

particles (though still larger than the matrix particles),

the peak broadens, and the tail of the distribution thick-

ens toward the back of the flow. For the 25 mm intruder

particle experiments and simulations, the front peak is

notably farther back and broader, and there appears to

be a secondary peak two thirds of the way back in the

flow. (The latter is likely related to the complications

that arise from the anomalously high slopes and not

relevant for real debris flows).

results are somewhat noisier and the peaks are broader.

We believe these differences are primarily due to sub-

tle differences between the physical experiments and

the simulations. First, the simulated particles do not

capture all details of the experimental particles which

are slightly aspherical and have slight asperities. The

experimental drum also is not perfectly true as it is in

the simulations. Finally, while we can follow a particle

throughout the simulations, no matter where it is lo-

cated, we can only see the particles in the physical ex-

periments if they are immediately adjacent to the wall.

However, we feel the trends are similar enough to say

that trends associated with particle size distribution are

*Fig.4 - Results from (a) physical and (b)computational*

*experimentsusing particles of total mass 3.13 kg*

*rotated in a drum of dimensions D = 0.56m, w =*

*0.15m. The particles in each experiment consisted*

*of a single large particle (size indicated in the fig-*

*ures) in a matrix of 13.8 mm particles. The plots*

*are the probability distribution function (pdf) of*

*the location of the large intruder particle. Please*

*see Figs. 2 and 3 for definition of θ*

**DISCRETE ELEMENT MODELING AND LARGE SCALE EXPERIMENTAL STUDIES OF BOULDERY DEBRIS FLOWS**

rougher form of asphericity, such as those described

in u

ficult to implement efficiently. Further, both methods

for representing aspherical particles in DEM simula-

tions take significant additional computational time.

what one might call “computationally gluing” spheri-

cal particles together (t

*et alii*, 2004; y

to one another into a rigid-body cluster. When a sphere

in one cluster contacts a sphere in another cluster, the

forces between them are calculated as if they were in-

dividual spheres using Equations 1(a) and 1(b). The

primary difference between simulations involving sin-

gle spherical particles and these aspherical particles

comprised of clusters of spherical particles arises from

the calculation of the kinematics of the aspherical par-

ticle clusters. To calculate the movements of the parti-

cle clusters at each time step, first all the forces on all

particles in a cluster are used to calculate the resultant

force for the cluster and the resultant force moment

about the mass center of the cluster. Then, the rota-

tional and translational acceleration of each individual

particle cluster is determined from the force and force

moments using the cluster mass and moment ofinertia

of each cluster particle.

ticles offers flexibility without significant additional

computational cost. Any number of particles with dif-

ferent sizes can be glued together to form a wide vari-

ety of particle shapes. (A few are illustrated in Fig. 5.)

C

*et alii*(2004) showed that by using aspheri-

per cluster, one can reproduce such macroscopic

flows, there are several simplifications in the simula-

tions compared with real debris flow systems. We are

currently working to build the level of sophistication

of our model to address some of the more complicated

effects. We describe our efforts in the next section..

**ADDITIONAL EFFECTS: PARTICLE**

**SHAPE AND INTERSTITIAL FLUIDS**

ever, particles in natural debris flows are aspherical,

real debris flows involve particles that are distributed

over a wide range of particle size and involve millions

of particles, and typically interstitial fluid influences

the behaviour of debris flows through effects such as

cohesivity and pore pressure. While current compu-

tational power limits the number of particles that we

can simulate, we can address some of the other issues

through various computational techniques. We de-

scribe our preliminary efforts to simulate debris flows

that have aspherical particles and interstitial fluids that

alter the dynamics of the flow briefly in this section

*PARTICLE ASPHERICITY IN DEBRIS FLOwS*

granular materials in debris flows are, in general, as-

pherical. Compared with aspherical particles, spheri-

cal particles tend to roll and slide past other spheri-

cal particles relatively easily. This difference leads to

discrepancies in bulk macroscopic properties and is

generally believed to cause an unphysically low stiff-

ness in some DEM models (t

*et alii*, 2001 and

*et alii*, 1995), subsequently, an unreasonably low

*et alii*, 2004). A number

effect of the asphericities.

tion of the shape of the primary entities of the parti-

cles from spheres to aspherical particles. This requires

changing the algorithm and force contact model de-

scribed above depending on the orientation of the par-

ticles. The most widely used aspherical particle shape

for DEM simulations is an ellipse (t

*et alii*, 1995).

*Fig. 5 - Particles that may be created from glued spheri-*

*cal particles that (a) may not or (b) may overlap,*

*and (c) may even be of different sizes*

*k.M. HILL, Y. BEREkET*

*, w.E. DIETRICH & L. HSU*

*et alii*, 1974). The liquid forms

of closely-spaced particles, as sketched in Fig. 6. Liq-

uid bridges are responsible for an apparent attractive

force between neighboring particles associated with

two effects: (1) the surface tension of the interstitial

fluid and (2) the pressure gradient between the fluid

in the liquid bridge and the “void space,” occupied by

air (H

*et alii*, 1974). The resulting force Fc can be

*et alii*(1974):

*a*is the half filling

angle and

*β*is the contact angle formed between the

liquid and a particle (please see Fig. 6). ΔP

and the atmosphere (determined by the radius of cur-

vature of the liquid bridge), and is computed from the

Laplace-Young equation:

spatial derivative of Y with respect to X, and Y′′ is the

spatial derivative of Y′ with respect to X. The size of

each liquid bridge is determined by the level of satura-

tion and the number of particles close enough for liq-

uid bridges to form. The effect of the liquid bridges is

more pronounced on smaller size particles (maximum

size of about 2 mm). Therefore for bouldery debris

flows this method is primarily helpful for understand-

ing the effect of cohesivity on debris flows. Previously,

the angle of repose. In addition, inter-particle contact

detection can be performed easily, and calculating in-

terparticle forces is simply a matter of using the equa-

tions described above for spherical particles, though

in the case of the clusters, one must consider contacts

between individual particles in a one cluster with

those in another. Admittedly, there is additional com-

putational time associated with the number of parti-

cles in a cluster. Nevertheless, the computational time

requirement is significantly less than other methods

for simulating aspherical particles described above.

plets to sufficiently reproduce tests of the strength of

materials, as described in y

fect particle asphericity on the kinematics of gravity-

driven debris flows.

*INTERSTITIAL FLUIDS IN DEBRIS FLOwS*

granular flows. The presence of a fluid introduces a

cohesivity between particles, provides lubrication

allowing particles to more easily slide past one an-

other, and can be the source of anomalous effects as-

sociated with pressure in the fluid that is greater than

the hydrostatic pressure. Modelling these effects are

somewhat more complicated than modelling dry par-

ticles alone as they involve longer-range interactions

between particles.

presence of an interstitial fluid in debris flows and

some preliminary results from simulations employing

these methods. In each case, we investigate a method

for reproducing the effect of a fluid at the scale of par-

ticle-particle interactions and investigate the resulting

change in dynamics at the scale of the system.

*MODELING COHESION ASSOCIATED wITH*

INTERSTITIAL FLUIDS

INTERSTITIAL FLUIDS

tial fluid at the scale of individual particles is prima-

rily associated with a cohesivity between particles that

is not present in dry granular materials (e.g., m

*Fig. 6 - Liquid bridge between two spherical particles. R1*

*and R2 are the longitudinal and meridian radius*

*of the curvature of the surface of liquid*

**DISCRETE ELEMENT MODELING AND LARGE SCALE EXPERIMENTAL STUDIES OF BOULDERY DEBRIS FLOWS**

address in the next subsection.

*HIGH MOISTURE CONTENT*

the interparticle interactions is not limited to cohesiv-

ity. The large-scale mechanics of the particle-fluid

interactions in this case are not fully understood, but

they are generally linked to the effect of the variability

of pore pressure (e.g., s

*et alii*, 2000).

particles are mutually connected and entirely filled

with a liquid. In this case, the pressure in the liquid,

the pore pressure, is typically equal to what it would

be in a static fluid, its hydrostatic pressure:

*p*

*h*

*ρ*

*L*

*gh,*

*ρ*

*L*

*g*is gravitational

*h*is depth beneath the free surface.

However, in a sheared (or in some case, even slightly

disturbed) fluid-particle flow the pore pressure can in-

crease in part due to relative fluid and particle motion.

In addition to their movement associated with the av-

erage flow, particles tend to approach and recede from

one another. The presence of liquid in the pores damp-

ens this somewhat, particularly when the liquid is un-

able to move through the pores rapidly enough to ac-

commodate relative particle movement. This tends to

reduce contact between particles. When this happens,

the interstitial liquid rather than interparticle contacts

supports the particles, resulting in pore pressure in ex-

cess of hydrostatic pressure.

ity leading to long run-out avalanches (C

a strong effect on details such as particle segregation

(l

force associated with Equation (6) (with the solution

for pressure difference described by Equation (7)) as

an additional normal force between separated particles.

fluid and when there is 10% water in among relatively

small particles. The picture is representative of a near

steady state for both systems. Two differences are ap-

parent. First, the segregation is clearly affected by the

presence of liquid. In the case of the system shown in

Fig. 7(b), the larger particles no longer segregate all the

way to the front of the flow. Second, the longitudinal

profile is altered, suggesting the internal stresses of the

granular assembly as a whole are affected by the local

interactions between individual particles.

is the profile of the particles alone, while Fig. 7(b)

shows the profile for the case with some fluid. The

fluid in this case reduces the maximum velocity and

the average shear rate by approximately 1/3. All of

this information is useful in considering the possible

modifications one could make to continuum models

for particle/fluid mixtures. However, additional ef-

*Fig. 7 - Snapshots from simulations of relatively small*

*particles (a) without interstitial fluid and (b)*

*with 10% interstitial fluid. In both case, the drum*

*diameter D = 140 mm; the drum thickness: w =*

*37.5 mm; and the particle diameters are: 1.25*

*mm, 3.0mm and 6.25mm; total mass of particles:*

*0.0524 kg; rotational speed: 48 rpm*

*Fig. 8 - Velocity profiles from two different locations*

*in the model debris flows depicted in Fig. 7(a)*

*without and (b) with 10% interstitial fluid.*

*Results from two different positions in the drum*

*are shown for values of θ indicated in the legend.*

*(Please see Figs. 2 and 3 for definition of θ)*

*k.M. HILL, Y. BEREkET*

*, w.E. DIETRICH & L. HSU*

excess pore pressure occurs and influences the behav-

iour of a debris flow, particularly factors that modify

the permeability including void ratio, particle size

distribution of the granular material and fine particle

content (w

respondingly, the dissipation of excess pore pressure

generated due to some deformation in saturated granu-

lar materials. To better understand the effects of the

pore-pressure on flow properties, models that account

specifically for the modified particle-particle and par-

ticlefluid interactions are helpful.

creased pore pressure for a single particle approach-

ing or departing from a group of other particles. A

particle approaching a group of other particles needs

to push out a pocket of interstitial fluid and thus that

particle and the group of particles feels a mutually

repellent force. DEM models that incorporate this ef-

fect of pore pressure have been proposed by t

spaces between particles. For example, if volume of a

pore space decreases, the pressure gradient forces the

fluid to flow to adjacent pore spaces. These models

were capable of demonstrating the evolution of pore-

pressure associated with applied stresses in saturated

granular materials. However, tracking the pore spaces

in DEM models is computationally very intense and

these two DEM models are limited to 2D set up or to a

very few particle in 3D. This makes their implementa-

tion into debris flow models impractical.

additional computational intensity. This model cap-

tures the “action at a distance” for particles moving

relative to one another as suggested by the sketches

in Fig. 9. As we noted above, the presence of fluid

dampens relative particle motion for particles in close

proximity. A model that captures this basic idea can be

written as follows:

*F*

cles moving relative to one another, increases as their

relative velocities increase and decreases with dis-

tance to one another.

*v*

*n*

similar to the definition of

*δ*

*n*

*r*

*12*

thought of as a “pore pressure coefficient” that varies

with fines content and other details that influence the

permeability of the particle network. We expect

*k*to

vary with details of the system including fines content

and more general considerations of the particle size

distribution.

with more detailed comparisons with experimental

and field data. We consider it a first order attempt to

represent the action at a distance brought about by the

saturated interstitial fluid in a DEM that facilitates in-

vestigations of this effect on larger systems.

rates the system as modelled by Equation 8. Figure

10(a) shows the velocity profile of a system that does

not include consideration of any fluid effects and is

thus fully represented by Equation 1 and Fig. 10(b)

includes the additional normal force described in (8)

added to Equation 1(a). For the system where an ex-

tra term is added to account for pore pressure effects,

the flow is slowed by approximately 30%. More no-

tably, however, there is a qualitative difference with

the additional pore pressure effect. The flow profile

concavity has changed and it resembles slightly more

the plug flow expected by excess pore pressure effects

and observed in experimental flows in large scale ex-

perimental drums.

*Fig. 9 - Sketches illustrating the effect of a pore-filling*

*liquid on damping relative particle motion. The*

*liquid can either work to create a repulsiveforce*

*between particles if they are approaching or to*

*effectively attract them if they are moving away*

*from one another*

**DISCRETE ELEMENT MODELING AND LARGE SCALE EXPERIMENTAL STUDIES OF BOULDERY DEBRIS FLOWS**

Ongoing work includes the following:

interstitial fluids Initial comparison of these results

with large scale experiments with aspherical particles

and different interstitial fluid is ongoing. Preliminary

results indicate the simple modifications suggested in

this paper have potential for reproducing some of the

complicated effects in natural debris flows. In the long

run, results from Fig. 10 Velocity profiles from model

debris flows where particle interactions are modelled

as (a) dry, completely described by Equation (1) and

(b) saturated, where the additional long range force

described by Equation (8) is added to the normal

force. (a) (b) simulations such as those described here

can inform the development of sophisticated con-

tinuum models for debris flows that better represent

evolving particle size distributions and solid and fluid

concentrations.

**ACKNOWLEDGEMENTS**

California – Berkeley, and by the National Center for

Earth Surface Dynamics (NCED), a NSF Science and

Technology Center funded under agreement EAR-

0120914.

**DISCUSSION AND CONCLUDING RE-**

**MARKS**

debris flows including the following:

the size of particles in the bulk;

dry spherical particles, suggesting that the constitu-

tive behaviour is well-represented by the DEM model;

While the results of this model to date are primarily

from dry flow of spherical particles, implementation

of additional modelling techniques show promise for

simulating more sophisticated flows. These include

more details associated with realistic particles and in-

*Fig. 10 - Velocity profiles from model debris flows whe-*

*re particle interactions are modelled as (a) dry,*

*completely described by Equation (1) and (b)*

*saturated, where the additional long range force*

*described by Equation (8) is added to the normal*

*force*

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