Information Technology Reference
In-Depth Information
debris outflows determination by application of the minimisation algorithm;
debris inflows determination, debris and run up variation due to outflows.
In the following, a sketch of the local elementary processes will be given, which is
sufficient to capture the mechanisms of the transition function.
_Q
x
means variation
of the substate
Q
x
; the energy associated to the debris inside a cell is measured by the
value
Q
r
[
0
]
*Q
th
[
0
]; the execution of an elementary process updates the substates.
Mobilisation Effects.
When the energy value overcomes an opportune threshold
(
Q
r
[
0
]
*Q
th
[
0
]
>p
mt
), depending on the soil features and its saturation state then a
mobilisation of the detrital cover occurs proportionally to the quantity overcoming the
threshold. The depth of the erosion (altitude variation
_Q
a
) is given by the following
expression
(
_Q
a
=-(Q
r
[
0
]
*Q
th
[
0
]
-p
mt
)*p
er
; then trivially
_Q
th
=-
_Q
a
;
_Q
r
=-
_Q
a
.
Friction Effect.
The effect of the friction is modelled, considering a constant run up
loss
p
rl
at each SCIDDICA step.
Outflows Determination
. Very rapid debris flows imply often a run up effect,
depending on the energy associated to debris flow. So the height minimisation
algorithm [4] is applied, considering the height fixed part of the central cell as
q
[
0
]
=Q
a
[
0
]
+p
adh
[
0
], the height mobile part as
p
[
0
]
=Q
r
[
0
]
-p
adh
[
0
], the height of the
adjacent cell
i
,
1
6
, as
q
[
i
]=
Q
a
[
i
]
+Q
th
[
i
].
A preliminary test is executed in order to account the friction effects, that prevent
debris outflows, when the height difference between the two cells is insufficient; the
condition is expressed by the formula
(q
[
0
]
+p
[
0
]
-q
[
i
]
)<p
f
.
Note that in order to account for the ability of the flowing debris of climbing a
slope of given partial height, the volume occupied by the debris in the central cell is,
ideally, assumed to be equal to cell area multiplied by run-up. In this way, given an
amount of debris in the cell, its volume (and then its thickness - which we use in the
computation) enlarges to a higher value (fictitious swelling).
The minimisation algorithm then returns outflows values that are fictitious swelling
and must be normalised by the multiplicative factor
(Q
th
[
0
]
-p
adh
[
0
]
)/(Q
r
[
0
]
-p
adh
[
0
]
)
;
furthermore another multiplicative factor must be considered: the relaxation rate
p
r
.
Outflows Effects.
Debris inflows are trivially derived by the outflow values: cell A
outflow toward adjacent cell B is cell B inflow from adjacent cell A.
The new value of
Q
th
[
0
] is given, considering the balance of inflows and outflows:
i
6
[]
[]
[
)
Q
0
+
(
Q
j
−
Q
j
∑
(
2
)
th
i
o
j
=
1
The run-up determination is calculated as the average weight of Q
r
, by considering
both the remaining debris in the central cell and the inflows:
6
6
6
[]
[]
[]
[]
[]
[]
[]
[]
(
3
)
(
Q
0
−
Q
j
)
×
Q
0
+
(
Q
j
×
Q
j
Q
0
+
(
Q
j
−
Q
j
)
∑
∑
∑
th
o
r
i
r
th
i
o
j
=
1
j
=
1
j
=
1
