| Debris flows are classified into some types by flow mechanism. Viscous debris flow and
muddy debris flow have a common important characteristic that lots of surges flow
intermittently. Authors have shown that surges are generated by flow instability as same as
roll waves. This paper is reported the influence of nonuniform solid concentration in the flow
into surge occurrence of muddy debris flow or viscous debris flow. It is difficult to discuss a
general solution of any solid concentration form in the flow. Therefore it is simplified
that the flow has two different concentration layers. The concentration of a lower
layer is C-, thickness h- from bottom to h-, the concentration of an upper layer is
Cu, thickness hu from hl to surface of the flow, and C- is greater than Cu. From
the theoretical consideration, when the concentration is nonuniform, the flow is
stable than uniform concentration. A theoretical result on muddy debris flow is as
follows,
F -¥ ------------1--------------
r { (3 )}2 ( )
Φ + 2 - β - β β - 1
(1)
here,
[ ] [ ]- 1
- ------2 -1{-1-} -1{ 1-} - -----2-
Φ = 1+ Ïm - Ïu à sinh Ïm - sinh Ïu - 1+ Ïm + Ïm
[ { { ( )}2} ( ) ( )- -------
β = a 2+ sinh -1 Y0 - 2 sinh-1 Y0 Ï- + 2 sinh-1 Y0 Ï-2 + a2
Ï- Ï - Ï-
{ -1( Y0) - --2---2} -1( a-) { -1( a-)}2
- 2 a sinh Ï- + Ï- + a -
sinh Ï- + a sinh Ï-
{ (Y0 )}2 { { (Y0 )}2} (Y0) - -------
+2 + sinh-1 Ï-- - a 2+ sinh-1 Ï-- +2 sinh- 1 Ï-- Ïu2 + 1
( ) u- -------- { ( u) - -------} u ( )
- 2 sinh-1 Y0 Ïu2 + a2 - 2 sinh-1 Y0- + Ïu2 + 1 -
sinh-1 -1-
{ ( Ïu)} { ( ) Ï-u-------} ( ) Ïu
+ sinh- 1 1-- 2 + 2 a sinh-1 Y0- + Ïu2 + a2 -
sinh-1 -a-
Ïu Ïu Ïu
{ ( a) }2] [ ( 1 ) ( Y ) - ------- ]-2
- a sinh-1 --- Ã sinh-1 --- - sinh-1 --0 - 1 + Ïm2 + Ïm
Ïu Ïm Ïm
Ï2 = ( )
λ2aisiκn2α, λ = {( ) 1 }
C*C 3 - 1-1 : linear concentration, H = h- + hu :
depth of flow, a = h-
H, d : particle size, ks : equivalent roughness , b=1/30, β :
momentum correction coefficient, Fr : Froude number, κ : Karman constant, Ï : dencity
of solid particle, Ïm : mean density of flow, C* : concentration of packed solid
particles, C : mean concentration, suffix m: mean of depth, -: lower layer, u: upper
layer. |