A v a l a n c h e

D y n a m i c s

a n d

D e f e n ce

3.3 Effect of number^{tween the smaller group and the main body increaseswith}
The effect of the number of particles on the front velocities^{time.As a result, at a rear end, the group of the particles is}
is shown in Fig.5 as forthe TTB1avalanches.Immedi-^{increasingly extended and becomes a tail (Fig.8b).Thus,}
ately after start, at 2 m down from start point,the effect of^{the head-tail structure is formed (Fig.8c).}
thenumberofparticlesisnotverylarge.Butasthe^{The appearanceof the head-tail structure indicatesthat}
avalanchesflow down the effect becomes larger.The front^{the terminal velocityofthe group have been reached; in}
velocity increaseswith the increasing number of the parti-^{otherwords,the motionissteadyunderthe balance be-}
cleswhosenumberismorethan ahundred.When the^{tween the force of gravity and forces resisting.Airdrag is}
number of balls is less than a hundred, eachparticle moves^{one of the mechanisms that defines the terminal velocity.}
independently.So the effect of the numberis negligible.^{Airdrag is dominant forlight materials.}
Fig.6showsanexampleoftherelations betweenthe^{Phenomena which accelerate to reach a steady motion}
number of particles and velocities of a front end and a rear^{are, in general, characterized by the terminal velocity,V}e ^,
end under an nearly steady motion.In this example,the^{the acceleration of gravity,g,and a systemsize such as a}
frontvelocityishigherthan therearvelocitywhenthe
numberofthe particlesismore thana thousand,sothe
avalanchesincreasinglyelongateunderthehead-tail
structure.When the numberislessthanathousand,a
particle at the rear end is fasterthan that at the front end.
As a result, the length of the group of the particles is main-
tained with circulation of the particles between the front
end and the rear end.

3.4 Effect of inclination of chute

Fig.7 shows the sideviews of SFP avalanchesnear the front
ends with different inclination angles of the chute No.10.
The circulation of the particles at the head dependson the
inclination angle.

4. SIMILARITY OF HEAD-TAIL FORMATION
   
   As shown in Fig.5,a bigger group of particles has a faster
   terminalvelocity.Thusthe frontgroupalways mustbe
   the biggest group of particles when the terminal velocity is
   reached. A smallergroup is overtaken by a biggergroup.
   As aresult,the concentrationofparticlesoccuresat the
   front end,which becomes a head (Fig.8a).On the other
   hand, if a smallergroup is at a rearend, the distance be-

Fig.4 Variation of front velocity of a TTB avalanche with flowF
distance.particles.

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