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Presentation given at the second I
1. Using complex models and conceptualizations
for modeling shallow landslides hydrology
R. Magritte - La grande marea, 1951
Riccardo Rigon e Cristiano Lanni
Monday, October 10, 11
2. “Tutto precipita”
Gianni Letta
“Everything falls apart”
Gianni Letta
Panta rei os potamòs
Tutto scorre come un fiume
Everything flows as in a river
Eraclito (Sulla Natura)
Monday, October 10, 11
3. IWL 2 Napoli, 28-30 Settembre 2011
Outline
•Hillslope Hydrology is tricky
•But, as well as landslide triggering, should be simple in simple settings
•About some consequences of the current parameterization of Richards equation
•So, from where all the complexity of real events comes from ?
3
Rigon & Lanni
Monday, October 10, 11
4. IWL 2 Napoli, 28-30 Settembre 2011
Richards
First, I would say, it means that it would be better to call it, for
instance: Richards-Mualem-vanGenuchten equation, since it is:
⇤⇥ ⇥
C(⇥) = ⇥ · K( w ) ⇥ (z + ⇥)
⇤t
n
Se = [1 + ( ⇥) )] m
⇧ ⇤ ⇥ m ⌅2
w) = Ks 1 (1 Se ) 1/m
K( Se
⇤ w () w r
C(⇥) := Se :=
⇤⇥ ⇥s r
4
Rigon & Lanni
Monday, October 10, 11
5. IWL 2 Napoli, 28-30 Settembre 2011
Richards
First, I would say, it means that it would be better to call it, for
instance: Richards-Mualem-vanGenuchten equation, since it is:
⇤⇥ ⇥
C(⇥) = ⇥ · K( w ) ⇥ (z + ⇥) Water balance
⇤t
n
Se = [1 + ( ⇥) )] m
⇧ ⇤ ⇥ m ⌅2
w) = Ks 1 (1 Se ) 1/m
K( Se
⇤ w () w r
C(⇥) := Se :=
⇤⇥ ⇥s r
4
Rigon & Lanni
Monday, October 10, 11
6. IWL 2 Napoli, 28-30 Settembre 2011
Richards
First, I would say, it means that it would be better to call it, for
instance: Richards-Mualem-vanGenuchten equation, since it is:
⇤⇥ ⇥
C(⇥) = ⇥ · K( w ) ⇥ (z + ⇥) Water balance
⇤t
n
Se = [1 + ( ⇥) )] m
⇧ ⇤ ⇥ m ⌅2 Parametric
w) = Ks 1 (1 Se ) 1/m
K( Se Mualem
⇤ w () w r
C(⇥) := Se :=
⇤⇥ ⇥s r
4
Rigon & Lanni
Monday, October 10, 11
7. IWL 2 Napoli, 28-30 Settembre 2011
Richards
First, I would say, it means that it would be better to call it, for
instance: Richards-Mualem-vanGenuchten equation, since it is:
⇤⇥ ⇥
C(⇥) = ⇥ · K( w ) ⇥ (z + ⇥) Water balance
⇤t
n
Se = [1 + ( ⇥) )] m Parametric
van Genuchten
⇧ ⇤ ⇥ m ⌅2 Parametric
w) = Ks 1 (1 Se ) 1/m
K( Se Mualem
⇤ w () w r
C(⇥) := Se :=
⇤⇥ ⇥s r
4
Rigon & Lanni
Monday, October 10, 11
8. Table 12.9: Example of roughness parameters for various surfaces (Evaporation into the Atmosphere, Wilfried Brutsaert, 1984)
IWL 2 Napoli, 28-30 Settembre 2011
Does exist a free available and reliable solver
of Richards equation ?
5
Rigon & Lanni Figure 12.1: Water fluxes
Monday, October 10, 11
9. IWL 2 Napoli, 28-30 Settembre 2011
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Rigon & Lanni
Monday, October 10, 11
10. IWL 2 Napoli, 28-30 Settembre 2011
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Rigon & Lanni
Monday, October 10, 11
11. IWL 2 Napoli, 28-30 Settembre 2011
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Monday, October 10, 11
12. IWL 2 Napoli, 28-30 Settembre 2011
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Monday, October 10, 11
13. IWL 2 Napoli, 28-30 Settembre 2011
igure 2: Experimental set-up.The OpenBook schematization. (b) The initial suction head pr
(a) The infinite hillslope hillslope
il-pixel hillslope numeration system (the case of parallel shape is shown here). Moving from 0 to 900
7
sponds to moving from the crest to the toe of the hillslope
Rigon & Lanni
Monday, October 10, 11
15. IWL 2 Napoli, 28-30 Settembre 2011
Initial Conditions
9
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Monday, October 10, 11
16. IWL 2 Napoli, 28-30 Settembre 2011
- 54
Simulations result
LANNI ET AL.: HYDROLOGICAL ASPECTS IN THE TRIGGERING OF SHALLOW LANDSLIDES
(a) DRY-Low (b) DRY-Med
10
Lanni and Rigon
Rigon & Lanni
Monday, October 10, 11
17. IWL 2 Napoli, 28-30 Settembre 2011
Richards 3D for a hillslope
- 54 Is the flow ever steady state ?
LANNI ET AL.: HYDROLOGICAL ASPECTS IN THE TRIGGERING OF SHALLOW LANDSLIDES
(a) DRY-Low (b) DRY-Med
11
Lanni and Rigon
Rigon & Lanni
Monday, October 10, 11
18. IWL 2 Napoli, 28-30 Settembre 2011
Richards 3D for a hillslope
(a) DRY-Low (b) DRY-Med
Simulations result
(c) DRY-High (d) WET-Low
12
Lanni and Rigon
Rigon & Lanni
Monday, October 10, 11
19. IWL 2 Napoli, 28-30 Settembre 2011
Richards 3D for a hillslope
(c) DRY-High (d) WET-Low
Simulations result
(e) WET-Med (f) WET-High
F T September 24, 2010, 9:13am D 13 A
R
Values of pressure head developed at the soil-bedrock interface at each point of the subcritical parallel hillslope. The
Lanni and Rigon
Rigon & Lanni
e Monday, October 10, 11
head lines represents the mean lateral gradient of pressure
20. IWL 2 Napoli, 28-30 Settembre 2011
Richards 3D for a hillslope
The key for understanding
Three order of magnitude faster !
(a) (b)
14
Lanni andTemporal evolution of the vertical profile of hydraulic conductivity (a) and hydraulic conductivity at the soil-bedrock interface
Rigon & Lanni
Figure 6: Rigon
Monday, October 10, 11
21. IWL 2 Napoli, 28-30 Settembre 2011
When simulating is understanding
•Flow is never stationary
•For the first hours, the flow is purely slope normal with no lateral
movements
•After water gains the bedrock and a thin capillary fringe grows,
lateral flow starts
•This is due to the gap between the growth of suction with respect to
the increase of hydraulic conductivity
15
Rigon & Lanni
Monday, October 10, 11
22. IWL 2 Napoli, 28-30 Settembre 2011
The Richards equation on a plane hillslope
⇤ ⇥⌅ ⇤ ⌅ ⇤ ⇥⌅
⇥ ) ⇥ )
C(⇥) ⇥ = ⇥
Kz cos + ⇥
Ky ⇥ + ⇥
Kx sin
Iverson, 2000; Cordano and Rigon, 2008
⇥t ⇥z ⇥z ⇥y ⇥y ⇥x ⇥x
⇥ ⇥ (z d cos )(q/Kz ) + ⇥s
Bearing in mind the previous positions, the Richards equation, at hillslope
scale, can be separated into two components. One, boxed in red, relative
to vertical infiltration. The other, boxed in green, relative to lateral flows.
16
Rigon & Lanni
Monday, October 10, 11
23. IWL 2 Napoli, 28-30 Settembre 2011
The Richards equation on a plane hillslope
⇤ ⇥⌅ ⇤ ⌅ ⇤ ⇥⌅
⇥ ) ⇥ )
C(⇥) ⇥ = ⇥
Kz cos + ⇥
Ky ⇥ + ⇥
Kx sin
Iverson, 2000; Cordano and Rigon, 2008
⇥t ⇥z ⇥z ⇥y ⇥y ⇥x ⇥x
⇥ ⇥ (z d cos )(q/Kz ) + ⇥s
Bearing in mind the previous positions, the Richards equation, at hillslope
scale, can be separated into two components. One, boxed in red, relative
to vertical infiltration. The other, boxed in green, relative to lateral flows.
16
Rigon & Lanni
Monday, October 10, 11
24. IWL 2 Napoli, 28-30 Settembre 2011
The Richards equation on a plane hillslope
⇤ ⇥⌅ ⇤ ⌅ ⇤ ⇥⌅
⇥ ) ⇥ )
C(⇥) ⇥ = ⇥
Kz cos + ⇥
Ky ⇥ + ⇥
Kx sin
Iverson, 2000; Cordano and Rigon, 2008
⇥t ⇥z ⇥z ⇥y ⇥y ⇥x ⇥x
⇥ ⇥ (z d cos )(q/Kz ) + ⇥s
Bearing in mind the previous positions, the Richards equation, at hillslope
scale, can be separated into two components. One, boxed in red, relative
to vertical infiltration. The other, boxed in green, relative to lateral flows.
16
Rigon & Lanni
Monday, October 10, 11
25. IWL 2 Napoli, 28-30 Settembre 2011
The Vertical Richards Equation
Iverson, 2000; Cordano and Rigon, 2008
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Rigon & Lanni
Monday, October 10, 11
26. IWL 2 Napoli, 28-30 Settembre 2011
The Vertical Richards Equation
Iverson, 2000; Cordano and Rigon, 2008
⇤ ⇥⌅
⇤⇥ ⇤ ⇤⇥
C(⇥) = Kz cos + Sr
⇤t ⇤z ⇤z
Vertical infiltration: acts in a
relatively fast time scale because
it propagates a signal over a
thickness of only a few metres
17
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Monday, October 10, 11
27. IWL 2 Napoli, 28-30 Settembre 2011
The Vertical Richards Equation
⇤ ⇥⌅
⇤⇥ ⇤ ⇤⇥
C(⇥) = Kz cos + Sr
⇤t ⇤z ⇤z
In literature related to the determination of slope stability this equation
assumes a very important role because fieldwork, as well as theory, teaches
that the most intense variations in pressure are caused by vertical infiltrations.
This subject has been studied by, among others, Iverson, 2000, and D’Odorico
et al., 2003, who linearised the equations.
18
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Monday, October 10, 11
28. IWL 2 Napoli, 28-30 Settembre 2011
The Lateral Richards Equation
⇤ ⌅ ⇤ ⇥⌅
⇤ ⇤⇥ ⇤ ⇤⇥
Sr = Ky + Kx sin
⇤y ⇤y ⇤x ⇤x
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Monday, October 10, 11
29. IWL 2 Napoli, 28-30 Settembre 2011
The Lateral Richards Equation
⇤ ⌅ ⇤ ⇥⌅
⇤ ⇤⇥ ⇤ ⇤⇥
Sr = Ky + Kx sin
⇤y ⇤y ⇤x ⇤x
Properly treated, this is reduced to
groundwater lateral flow, specifically to the
Boussinesq equation, which, in turn, have
been integrated from SHALSTAB equations
19
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Monday, October 10, 11
30. IWL 2 Napoli, 28-30 Settembre 2011
The Decomposition of the Richards equation
Iverson, 2000; Cordano and Rigon, 2008
In vertical infiltration plus lateral flow is possible under the assumption
that:
soil depth hillslope length
time scale of lateral flow
constant diffusivity
reference conductivity
Time scale of infiltration
reference hydraulic capacity
20
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Monday, October 10, 11
31. IWL 2 Napoli, 28-30 Settembre 2011
When simulating is understanding
•But Is the condition:
verified ?
courtesy of E. Cordano
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Monday, October 10, 11
32. IWL 2 Napoli, 28-30 Settembre 2011
When simulating is understanding
On the basis of the only MvG scheme, it is very difficult to say at
saturation. However
courtesy of E. Cordano
The scale factor strongly varies with time 22
Rigon & Lanni
Monday, October 10, 11
33. IWL 2 Napoli, 28-30 Settembre 2011
When simulating is understanding
At the beginning, at the bedrock we are we are on the red line, at the
surface on the blue line
courtesy of E. Cordano
23
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Monday, October 10, 11
34. IWL 2 Napoli, 28-30 Settembre 2011
When simulating is understanding
At the end, at the bedrock we are we are on the red line, at the surface
on the blue line
courtesy of E. Cordano
24
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Monday, October 10, 11
35. IWL 2 Napoli, 28-30 Settembre 2011
So
What happens is that, at the beginning the conditions for considering
just the vertical flow are satisfied
courtesy of E. Cordano
25
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Monday, October 10, 11
36. IWL 2 Napoli, 28-30 Settembre 2011
So
What happens is that, at the end the conditions for considering just the
vertical flow are NOT satisfied. Because D0b >> D0 top
courtesy of E. Cordano
26
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Monday, October 10, 11
37. IWL 2 Napoli, 28-30 Settembre 2011
Therefore when a perched water table form
Instead
And lateral flow dominates (is as fast ) than infiltration
27
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Monday, October 10, 11
38. IWL 2 Napoli, 28-30 Settembre 2011
IS THIS TRUE ?
We need to go back to the basics
⇥2
f (Se )
K(Se ) = v
K s Se
After Mualem, 1976
f (1)
Where v is an exponent expressing the
connectivity between pores, evaluated by Mualem
for various soil types.
Se
1
f (Se ) = dx
0 (x)
28
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Monday, October 10, 11
39. IWL 2 Napoli, 28-30 Settembre 2011
IS THIS TRUE ?
Having defined the relative hydraulic conductivity:
After Mualem, 1976
K = Ks Kr
And expressed the suction in terms of van Genuchten’s expression::
1 ⇥1/n
⇥= Se 1/m
1
The integral can be calculated:
29
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Monday, October 10, 11
40. IWL 2 Napoli, 28-30 Settembre 2011
PARAMETRIC FORMS OF THE
HYDRAULIC CONDUCTIVITY
there results:
⇤ ⇥m ⌅2
K(Se ) = v
K s Se 1 1 1/m
Se (m = 1 1/n)
or, by expressing everything as a function of the suction
potential:
⇥2
mn n m
Ks 1 ( ⇥) [1 + ( ⇥) ]
K(⇥) = n mv (m = 1 1/n)
[1 + ( ⇥) ]
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Monday, October 10, 11
41. IWL 2 Napoli, 28-30 Settembre 2011
THEREFORE
•The results are strictly related to the validity of the MvG theory and
parameterization
31
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Monday, October 10, 11
42. IWL 2 Napoli, 28-30 Settembre 2011
Another issue
Extending Richards to treat the transition saturated to unsaturated zone.
Is it :
At saturation: what does change in time ?
32
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Monday, October 10, 11
43. IWL 2 Napoli, 28-30 Settembre 2011
Another issue
Extending Richards to treat the transition saturated to unsaturated zone.
Which means:
courtesy of M. Berti
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Monday, October 10, 11
44. IWL 2 Napoli, 28-30 Settembre 2011
Or
If you do not have this extension you cannot deal properly with from
unsaturated volumes to saturated ones.
where we just saw most of the phenomena of
interest happens
Obviously it can be done much better. Only in very special cases the specific
storage can be expressed in the way we showed (e.g. Green and Wang, 1990).
34
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Monday, October 10, 11
45. IWL 2 Napoli, 28-30 Settembre 2011
In any case
the question relies also in the reliability of the SWRC close to saturation
(e.g. Vogel et al., 2000, Schaap and vanGenuchten, 2005; Romano, 2010)
courtesy of M. Berti
35
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Monday, October 10, 11
46. IWL 2 Napoli, 28-30 Settembre 2011
Stability onstage
The good old infinite slope 36
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Monday, October 10, 11
47. IWL 2 Napoli, 28-30 Settembre 2011
Infinite Slope with unsaturated conditions
The equation
e.g. Lu and Godt, 2008
37
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Monday, October 10, 11
48. IWL 2 Napoli, 28-30 Settembre 2011
It is enough to say that a point is
unstable to state that a landslide
occurs ?
38
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Monday, October 10, 11
49. IWL 2 Napoli, 28-30 Settembre 2011
Table 3: A matrix of the times needed to achieve specific percentages of destabilized hillslope area for a continuous rainfall simulation for
a 5-day period.
A.C. RAIN SHAP E TF 5% TF 10% TF 15% TF 30% TF 50%
Divergent 41h
Low
P arallel 41h
Convergent 41h 60h
DRY Divergent 14-15h 15-16h 17-18h
M ed
P arallel 14-15h 15-16h 16-17h 18h
Convergent 14-15h 14-15h 14-15h 15h
High Divergent 7-8h 8-9h 9-10h 10-11h 12h
P arallel 7-8h 8h 8-9h 8-9h 8-9h
Convergent 7-8h 7-8h 7-8h 7-8h 8-9h
Divergent 3-4h
Low
Lanni and Rigon, 2011
P arallel 3-4h
Convergent 3-4h 4-5h
Divergent 2-3h 3-4h 4-5h
W ET
M ed
P arallel 2-3h 3h 3-4h 4-5h
Convergent 2-3h 2-3h 2-3h 2-3h
Divergent 1-2h 1-2h 1-2h 3h 5h
High
P arallel 1-2h 1-2h 1-2h 2-3h 2-3h
Convergent 1-2h 1-2h 1-2h 1-2h 1-2h
60h - - 20 h - - - 10 h - - - 5h - 0h not achieved
39
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Monday, October 10, 11
50. IWL 2 Napoli, 28-30 Settembre 2011
Total volume of water
in hillslope before the
event remained inside
the hillslope
Total volume of water Total volume of
in hillslope rainfall water in
hillslope
40
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Monday, October 10, 11
51. IWL 2 Napoli, 28-30 Settembre 2011
Table 4: A matrix of the rain volumes RF i and total water volume VF i (Rain volume + Pre-rain soil-water volume) needed to achieve
specific percentages of hillslope area for a continuous rainfall simulation for a 5-day period.
F 5% F 10% F 15% F 30% F 50%
RAIN SHAPE
DRY WET DRY WET DRY WET DRY WET DRY WET
Divergent
Low
P arallel
RF i (m3 ) Convergent
Divergent
M ed P arallel
Convergent
Divergent
High
P arallel
Convergent
Lanni and Rigon, 2011
Divergent
Low
P arallel
Convergent
VF i (m3 )
Divergent
M ed
P arallel
Convergent
Divergent
High
P arallel
Convergent
41
15m3 - - 125m3 - - 230m3 - - 350m3 - - > 520m3 not achieved
Rigon & Lanni
Monday, October 10, 11
52. IWL 2 Napoli, 28-30 Settembre 2011
So simple, too simple ?
• (The evident and little informative statement) We found that
wet volumes causes faster obtaining of instability
•However, the it seems that in simple settings the total volume
of water required to destabilized a certain percentage of area is
not very much variable (variation is included in 10%)
42
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Monday, October 10, 11
53. IWL 2 Napoli, 28-30 Settembre 2011
Panola and the soil depth question
Soil-depth variability
Ground surface
Bedrock surface
Bedrock depression
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Monday, October 10, 11
55. IWL 2 Napoli, 28-30 Settembre 2011
Hillslope water discharge
o 2 peaks
α = 13°
t=9h
t=6h t=7h t=9h t=14h
t=22h
Q (m3/h)
t=18h
Lanni et al., 2011
45
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Monday, October 10, 11
56. IWL 2 Napoli, 28-30 Settembre 2011
α = 13°
tim
e
t=6h
t=7h
t=9h
Saturated area at the soil-bedrock interface increases very
rapidly…..
46
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Monday, October 10, 11
57. IWL 2 Napoli, 28-30 Settembre 2011
Same as in the ideal planar case
1° STEP:
1D
Vertical rain-infiltration
Infiltration-front propagation
No role played by hillslope
gradient
2° STEP:
3D Lateral-flow
Lanni et al., 2011
Downslope drainage
limited by bedrock topography 47
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59. IWL 2 Napoli, 28-30 Settembre 2011
Pressure growing
α = 13°
tim
e
t=6h
t=7h
Lanni et al., 2011
t=9h
…..and then the average value of positive pore-water pressure
continues to grow
49
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Monday, October 10, 11
60. IWL 2 Napoli, 28-30 Settembre 2011
At the time of the simulations
We were not looking at this but, please observe that, increasing slope
decreases instability but drainage is more efficient.
Therefore there should be a specific slope angle which is, given the
condition of the simulation the more unstable.
50
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61. IWL 2 Napoli, 28-30 Settembre 2011
If you tilt you slide
α = 30°
(FS=1)
(1<FS<1.05)
c’ = 0 kPa
φ’ = 30°
t=10h
51
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Monday, October 10, 11
62. IWL 2 Napoli, 28-30 Settembre 2011
In complex topography
of the bedrock
•Topography commands the patterns of instability and convergence of
fluxes can increase instability (so obvious again!)
•The temporal dynamics of instabilities is also affected due to the
filling and spilling effect, and different parts of the hillslope can
become unstable at different times
•The mechanism where infiltration comes first and lateral flow later continues
to be valid
•However, there is an interplay between slope and bumpiness of the bedrock
which is not trivial at all.
52
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Monday, October 10, 11
63. IWL 2 Napoli, 28-30 Settembre 2011
Lessons Learned
• Simple stability analysis can be successful. Probably not for the right
reasons
• Simple settings give simple results (the total weight of water commands
the creation of large instabilities)
•This is due in the model to the compound of the vanGenuchten and
Mualem theory (which could not be real)
•Soil depths counts
•On small scales instabilities could be controlled by constraints of local
topography
•Boundary conditions matter (trivial kinematic approaches could not work)
53
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64. IWL 2 Napoli, 28-30 Settembre 2011
Another case and its complexity: Duron
54
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65. IWL 2 Napoli, 28-30 Settembre 2011
Farabegoli et al., 2011
Duron stratigraphy
55
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66. IWL 2 Napoli, 28-30 Settembre 2011
Farabegoli et al., 2011 Duron soil depth
56
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67. IWL 2 Napoli, 28-30 Settembre 2011
Farabegoli et al., 2011
Duron geomorphology
57
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68. IWL 2 Napoli, 28-30 Settembre 2011
Farabegoli et al., 2011
Duron soil cover
58
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69. IWL 2 Napoli, 28-30 Settembre 2011
Duron land use
Farabegoli et al., 2011
59
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70. IWL 2 Napoli, 28-30 Settembre 2011
And a tentative association of those maps with
hydrological characters
With Dall’Amico ,Farabegoli et al., 2011
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71. IWL 2 Napoli, 28-30 Settembre 2011
Forecasting of temperature
in a point
With Dall’Amico ,Farabegoli et al., 2011
In time
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72. IWL 2 Napoli, 28-30 Settembre 2011
Soil water content at different depth
in a point
With Dall’Amico ,Farabegoli et al., 2011
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73. IWL 2 Napoli, 28-30 Settembre 2011
Probability of landsliding
Simoni et al, 2008
63
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74. Duron
IWL 2 Napoli, 28-30 Settembre 2011
Probability of landsliding
Simoni et al, 2008
64
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75. Duron
IWL 2 Napoli, 28-30 Settembre 2011
Probability of landsliding
Simoni et al, 2008
65
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Monday, October 10, 11
76. Duron
IWL 2 Napoli, 28-30 Settembre 2011
Probability of landsliding
Simoni et al, 2008
66
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Monday, October 10, 11
77. Duron
IWL 2 Napoli, 28-30 Settembre 2011
Probability of landsliding
Simoni et al, 2008
67
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Monday, October 10, 11
78. Duron
IWL 2 Napoli, 28-30 Settembre 2011
And the snow again !
68
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79. Duron
IWL 2 Napoli, 28-30 Settembre 2011
Temperature of snow !
69
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80. IWL 2 Napoli, 28-30 Settembre 2011
Lessons Learned
• Cows count ;-)
•Landslide forecasting is complex for dynamical reasons
•But also because it is a local phenomena where a lot of “accidents” (i.e.
land-use-landcover) modify the local hydrology and the “cohesion of soils”
•There is a missing link between all of those characteristics and
hydrological, and geotechnical parameters
•Cohesion exists but its estimation is kind of elusive when we are talking
about turfs and root strength
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81. IWL 2 Napoli, 28-30 Settembre 2011
Credits
We are indebted to Emanuele Cordano for the participation to some early
stage of this research, and providing at late request, some plots of
hydraulic diffusivity.
We thank Enzo Farabegoli, Giuseppe Onorevoli and Martina Morandi for
allowing to use the maps of Duron catchment which resulted after three
years of detailed surveys.
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82. IWL 2 Napoli, 28-30 Settembre 2011
Thank you for your attention.
G.Ulrici - 2000 ?
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