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R. M
agri
tte
- L
a gra
nd
e m
area
, 19
51
Riccardo Rigon e Cristiano Lanni
Using complex models and conceptualizations for modeling shallow landslides hydrology
Monday, October 10, 11
“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
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
3
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 ?
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
4
Richards
First, I would say, it means that it would be better to call it, for
instance: Richards-Mualem-vanGenuchten equation, since it is:
Se = [1 + (��⇥)m)]�n
Se :=�w � �r
⇥s � �r
C(⇥)⇤⇥
⇤t= ⇥ ·
�K(�w) �⇥ (z + ⇥)
⇥
K(�w) = Ks
⇧Se
⇤�1� (1� Se)1/m
⇥m⌅2
C(⇥) :=⇤�w()⇤⇥
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
4
Richards
First, I would say, it means that it would be better to call it, for
instance: Richards-Mualem-vanGenuchten equation, since it is:
Se = [1 + (��⇥)m)]�n
Se :=�w � �r
⇥s � �r
C(⇥)⇤⇥
⇤t= ⇥ ·
�K(�w) �⇥ (z + ⇥)
⇥
K(�w) = Ks
⇧Se
⇤�1� (1� Se)1/m
⇥m⌅2
Water balance
C(⇥) :=⇤�w()⇤⇥
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
4
Richards
First, I would say, it means that it would be better to call it, for
instance: Richards-Mualem-vanGenuchten equation, since it is:
Se = [1 + (��⇥)m)]�n
Se :=�w � �r
⇥s � �r
C(⇥)⇤⇥
⇤t= ⇥ ·
�K(�w) �⇥ (z + ⇥)
⇥
K(�w) = Ks
⇧Se
⇤�1� (1� Se)1/m
⇥m⌅2
Water balance
ParametricMualem
C(⇥) :=⇤�w()⇤⇥
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
4
Richards
First, I would say, it means that it would be better to call it, for
instance: Richards-Mualem-vanGenuchten equation, since it is:
Se = [1 + (��⇥)m)]�n
Se :=�w � �r
⇥s � �r
C(⇥)⇤⇥
⇤t= ⇥ ·
�K(�w) �⇥ (z + ⇥)
⇥
K(�w) = Ks
⇧Se
⇤�1� (1� Se)1/m
⇥m⌅2
Water balance
ParametricMualem
Parametricvan Genuchten
C(⇥) :=⇤�w()⇤⇥
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
5
Does exist a free available and reliable solver of Richards equation ?
12. Surface Fluxes 12.2. Values of reference
Surface description z 0(cm) ReferenceMud flats, ice 0.001 Sutton (1953)Smooth tarmac 0.002 Bradley (1968)Large water surfaces 0.01 - 0.06 Numerous referencesGrass (lawn up to 1 cm) 0.1 Sutton (1953)Grass (artificial, 7.5 cm high) 1.0 Chamberlain (1966)Grass (thick up to 10 cm high) 2.3 Sutton (1953)Grass (thin up to 50 cm) 5 Sutton (1953)Trees (10-15 m high) 40-70 Fichtl and McVehil (1970)Large city 165 Yamamoto and Shimanuki (1964)
Table 12.9: Example of roughness parameters for various surfaces (Evaporation into the Atmosphere, Wilfried Brutsaert, 1984)
����������
���
� �������
������������
���������� ����������������
� ��������� ����������
! �!�����!� �������
��"�����������
�!����������
���#$�%��"�� &��������%��"��
� ��'��� ��!���!�
�(�%�����"��
��! �� ��� ��'
��! � ��
! �!�����!� �������
� ���� ��� ��'
Figure 12.1: Water fluxes
page 54 of 92
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
6
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
6
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
6
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
6
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
7
X - 52 LANNI ET AL.: HYDROLOGICAL ASPECTS IN THE TRIGGERING OF SHALLOW LANDSLIDES
Figure 2: Experimental set-up. (a) The infinite hillslope schematization. (b) The initial suction head profile.
Figure 3: The soil-pixel hillslope numeration system (the case of parallel shape is shown here). Moving from 0 to 900 (the total number of
soil-pixels), corresponds to moving from the crest to the toe of the hillslope
Table 1: Physical, hydrological and geotechnical parameters used to characterize the silty-sand soil
Parameter group Parameter name Symbol Unit ValuePhysical Bulk density ⇥b (g/cm3) 2.0
% sand - - 60% silt - - 40
Hydrological Saturated hydraulic conductivity Ksat (m/s) 10�4
Saturated water content �sat (cm3/cm�3) 0.39Residual water content �r (cm3/cm�3) 0.155
water retention curve parameter n [�] 1.881water retention curve parameter � (cm�1) 0.0688
Geotechnical Effective angle of shearing resistance ⇤0 � 38Effective cohesion c0 kN/m2 0
D R A F T September 24, 2010, 9:13am D R A F T
The OpenBook hillslope
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
8
Conditions of simulation
Homogeneous soil
Gentle slope Steep slope
Wet Initial Conditions
Dry Initial Conditions
Intense Rainfall
Low Rainfall
Moderate Rainfall
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
9
Initial Conditions
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
10
X - 54 LANNI ET AL.: HYDROLOGICAL ASPECTS IN THE TRIGGERING OF SHALLOW LANDSLIDES
(a) DRY-Low (b) DRY-Med
(c) DRY-High (d) WET-Low
(e) WET-Med (f) WET-High
Figure 5: Values of pressure head developed at the soil-bedrock interface at each point of the subcritical parallel hillslope. The slope of
the pressure head lines represents the mean lateral gradient of pressure
D R A F T September 24, 2010, 9:13am D R A F T
Simulations result
Lanni and Rigon
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
11
Is the flow ever steady state ? X - 54 LANNI ET AL.: HYDROLOGICAL ASPECTS IN THE TRIGGERING OF SHALLOW LANDSLIDES
(a) DRY-Low (b) DRY-Med
(c) DRY-High (d) WET-Low
(e) WET-Med (f) WET-High
Figure 5: Values of pressure head developed at the soil-bedrock interface at each point of the subcritical parallel hillslope. The slope of
the pressure head lines represents the mean lateral gradient of pressure
D R A F T September 24, 2010, 9:13am D R A F T
Lanni and Rigon
Richards 3D for a hillslope
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
12
X - 54 LANNI ET AL.: HYDROLOGICAL ASPECTS IN THE TRIGGERING OF SHALLOW LANDSLIDES
(a) DRY-Low (b) DRY-Med
(c) DRY-High (d) WET-Low
(e) WET-Med (f) WET-High
Figure 5: Values of pressure head developed at the soil-bedrock interface at each point of the subcritical parallel hillslope. The slope of
the pressure head lines represents the mean lateral gradient of pressure
D R A F T September 24, 2010, 9:13am D R A F T
Simulations result
Lanni and Rigon
Richards 3D for a hillslope
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
13
X - 54 LANNI ET AL.: HYDROLOGICAL ASPECTS IN THE TRIGGERING OF SHALLOW LANDSLIDES
(a) DRY-Low (b) DRY-Med
(c) DRY-High (d) WET-Low
(e) WET-Med (f) WET-High
Figure 5: Values of pressure head developed at the soil-bedrock interface at each point of the subcritical parallel hillslope. The slope of
the pressure head lines represents the mean lateral gradient of pressure
D R A F T September 24, 2010, 9:13am D R A F T
Simulations result
Lanni and Rigon
Richards 3D for a hillslope
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
14
LANNI ET AL.: HYDROLOGICAL ASPECTS IN THE TRIGGERING OF SHALLOW LANDSLIDES X - 55
(a) (b)
Figure 6: Temporal evolution of the vertical profile of hydraulic conductivity (a) and hydraulic conductivity at the soil-bedrock interface
(b) of a soil-pixel located in the mid-slope zone. Results are shown for the case representing DRY antecedent soil moisture conditions, Low
rainfall intensity and parallel hillslope shape of the subcritical (gentle) case
D R A F T September 24, 2010, 9:13am D R A F T
Three order of magnitude faster !
The key for understanding
Lanni and Rigon
Richards 3D for a hillslope
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
15
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
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
C(⇥)⇥�⇥t = ⇥
⇥z
⇤Kz
�⇥�)⇥z � cos�
⇥⌅+ ⇥
⇥y
⇤Ky
⇥�⇥y
⌅+ ⇥
⇥x
⇤Kx
�⇥�)⇥x � sin�
⇥⌅
⇥ ⇥ (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
The Richards equation on a plane hillslope
Iver
son
, 20
00
; C
ord
ano a
nd
Rig
on
, 2008
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
C(⇥)⇥�⇥t = ⇥
⇥z
⇤Kz
�⇥�)⇥z � cos�
⇥⌅+ ⇥
⇥y
⇤Ky
⇥�⇥y
⌅+ ⇥
⇥x
⇤Kx
�⇥�)⇥x � sin�
⇥⌅
⇥ ⇥ (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
The Richards equation on a plane hillslope
Iver
son
, 20
00
; C
ord
ano a
nd
Rig
on
, 2008
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
C(⇥)⇥�⇥t = ⇥
⇥z
⇤Kz
�⇥�)⇥z � cos�
⇥⌅+ ⇥
⇥y
⇤Ky
⇥�⇥y
⌅+ ⇥
⇥x
⇤Kx
�⇥�)⇥x � sin�
⇥⌅
⇥ ⇥ (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
The Richards equation on a plane hillslope
Iver
son
, 20
00
; C
ord
ano a
nd
Rig
on
, 2008
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
17
The Vertical Richards Equation
Iver
son
, 20
00
; C
ord
ano a
nd
Rig
on
, 2008
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
C(⇥)⇤⇥
⇤t=
⇤
⇤z
⇤Kz
�⇤⇥
⇤z� cos �
⇥⌅+ Sr
Vertical infiltration: acts in a
relatively fast time scale because
it propagates a signal over a
thickness of only a few metres
17
The Vertical Richards Equation
Iver
son
, 20
00
; C
ord
ano a
nd
Rig
on
, 2008
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
C(⇥)⇤⇥
⇤t=
⇤
⇤z
⇤Kz
�⇤⇥
⇤z� cos �
⇥⌅+ Sr
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
The Vertical Richards Equation
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
Sr =⇤
⇤y
⇤Ky
⇤⇥
⇤y
⌅+
⇤
⇤x
⇤Kx
�⇤⇥
⇤x� sin �
⇥⌅
19
The Lateral Richards Equation
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
Sr =⇤
⇤y
⇤Ky
⇤⇥
⇤y
⌅+
⇤
⇤x
⇤Kx
�⇤⇥
⇤x� sin �
⇥⌅
Properly treated, this is reduced to
groundwater lateral flow, specifically to the
Boussinesq equation, which, in turn, have
been integrated from SHALSTAB equations
19
The Lateral Richards Equation
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
20
The Decomposition of the Richards equation
In vertical infiltration plus lateral flow is possible under the assumption
that:
Time scale of infiltration
soil depth
constant diffusivity
time scale of lateral flow
hillslope length
reference conductivity
reference hydraulic capacity
Iver
son
, 20
00
; C
ord
ano a
nd
Rig
on
, 2008
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
21
When simulating is understanding
•But Is the condition:
verified ?
cou
rtes
y of
E. C
ord
ano
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
22
When simulating is understanding
The scale factor strongly varies with time
On the basis of the only MvG scheme, it is very difficult to say at
saturation. However
cou
rtes
y of
E. C
ord
ano
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
23
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
cou
rtes
y of
E. C
ord
ano
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
24
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
cou
rtes
y of
E. C
ord
ano
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
25
So
What happens is that, at the beginning the conditions for considering
just the vertical flow are satisfied
cou
rtes
y of
E. C
ord
ano
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
26
So
What happens is that, at the end the conditions for considering just the
vertical flow are NOT satisfied. Because D0b >> D0 top
cou
rtes
y of
E. C
ord
ano
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
27
Therefore when a perched water table form
Instead
And lateral flow dominates (is as fast ) than infiltration
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
K(Se) = KsSve
�f(Se)f(1)
⇥2
f(Se) =� Se
0
1�(x)
dx
Where v is an exponent expressing the connectivity between pores, evaluated by Mualem
for various soil types.
Aft
er M
ual
em, 1
97
6
IS THIS TRUE ?
28
We need to go back to the basics
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
K = Ks Kr
Having defined the relative hydraulic conductivity:
⇥ =1�
�S�1/m
e � 1⇥1/n
And expressed the suction in terms of van Genuchten’s expression::
The integral can be calculated:
Aft
er M
ual
em, 1
97
6
29
IS THIS TRUE ?
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
there results:
K(Se) = KsSve
⇤1�
�1� S1/m
e
⇥m⌅2
(m = 1� 1/n)
or, by expressing everything as a function of the suction potential:
K(⇥) =Ks
�1� (�⇥)mn [1 + (�⇥)n]�m
⇥2
[1 + (�⇥)n]mv (m = 1� 1/n)
30
PARAMETRIC FORMS OF THE HYDRAULIC CONDUCTIVITY
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
31
THEREFORE
•The results are strictly related to the validity of the MvG theory and
parameterization
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
32
Another issue
Extending Richards to treat the transition saturated to unsaturated zone.
Is it :
At saturation: what does change in time ?
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
33
Another issue
Extending Richards to treat the transition saturated to unsaturated zone. Which means:
cou
rtes
y of
M. B
erti
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
34
If you do not have this extension you cannot deal properly with from
unsaturated volumes to saturated ones.
Or
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).
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
35
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)
cou
rtes
y of
M. B
erti
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
36
Stability onstage
The good old infinite slope
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
37
Infinite Slope with unsaturated conditionsThe equation
e.g. Lu and Godt, 2008
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
38
It is enough to say that a point is unstable to state that a landslide
occurs ?
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
39
LANNI ET AL.: HYDROLOGICAL ASPECTS IN THE TRIGGERING OF SHALLOW LANDSLIDES X - 59
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 SHAPE TF5% TF10% TF15% TF30% TF50%
DR
Y
Low
Divergent 41h � � � �Parallel 41h � � � �
Convergent 41h 60h � � �
Med
Divergent 14-15h 15-16h 17-18h � �Parallel 14-15h 15-16h 16-17h 18h �
Convergent 14-15h 14-15h 14-15h 15h �H
igh Divergent 7-8h 8-9h 9-10h 10-11h 12h
Parallel 7-8h 8h 8-9h 8-9h 8-9h
Convergent 7-8h 7-8h 7-8h 7-8h 8-9h
WE
T
Low
Divergent 3-4h � � � �Parallel 3-4h � � � �
Convergent 3-4h 4-5h � � �
Med
Divergent 2-3h 3-4h 4-5h � �Parallel 2-3h 3h 3-4h 4-5h �
Convergent 2-3h 2-3h 2-3h 2-3h �
Hig
h Divergent 1-2h 1-2h 1-2h 3h 5h
Parallel 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 - - - 5 h - 0h not achieved
D R A F T September 24, 2010, 9:13am D R A F T
Lan
ni
and
Rig
on
, 20
11
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
40
Total volume of waterin hillslope
T o t a l v o l u m e o f r a i n f a l l w a t e r i n hillslope
Total volume of water in hillslope before the event remained inside the hillslope
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
41
X - 60 LANNI ET AL.: HYDROLOGICAL ASPECTS IN THE TRIGGERING OF SHALLOW LANDSLIDES
Table 4: A matrix of the rain volumes RFi and total water volume VFi (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.
RAIN SHAPEF5% F10% F15% F30% F50%
DRY WET DRY WET DRY WET DRY WET DRY WET
RF
i(m
3)
Low
Divergent � � � � � � � �Parallel � � � � � � � �
Convergent � � � � � �
Med
Divergent � � � �Parallel � �
Convergent � �H
igh Divergent
Parallel
Convergent
VF
i(m
3)
Low
Divergent � � � � � � � �Parallel � � � � � � � �
Convergent � � � � � �
Med
Divergent � � � �Parallel � �
Convergent � �
Hig
h Divergent
Parallel
Convergent
�15m3 - - 125m3 - - 230m3 - - 350m3 - - > 520m3 not achieved
Table 5: A matrix of the times needed to achieve specific percentages of destabilized hillslope area for a continuous rainfall simulation for
a 5-day period. The case of steep hillslopes
A.C. RAIN SHAPE FT( 5%) FT(10%) FT(15%) FT(30%) FT(50%)
DRYLow Parallel 32h 35.5h 38h 39h �High Parallel 7h 7h 7h 7h 7h
WETLow Parallel 0.25h 0.25h 0.25h 0.25h 0.25h
High Parallel 0.25h 0.25h 0.25h 0.25h 0.25h
�60h - - - - - - - - - - - > 0h not achieved
D R A F T September 24, 2010, 9:13am D R A F T
Lan
ni
and
Rig
on
, 20
11
Monday, October 10, 11
IWL 2 Napoli, 28-30 Settembre 2011
Rigon & Lanni
42
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%)
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Ground surfaceBedrock surface
Soil-depth variability
Bedrock depression
Panola and the soil depth question
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α = 13° α = 20° α = 30°
Soil (sandy-silt) Ksat = 10-4 m/s
Bedrock Ksat = 10-7 m/s
Rain Intensity = 6.5 mm/h Duration = 9 hours
Slope
Soil properties
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45
Q (m
3 /h)
t=9h
t=18h
t=22h
Hillslope water dischargeo 2 peaks α = 13°
t=6h t=9ht=7h t=14h
Lan
ni
et a
l., 2
01
1
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46
time
t=6h
t=9h
t=7h
Saturated area at the soil-bedrock interface increases very rapidly…..
α = 13°
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1D
3D
No role played by hillslope gradient
1° STEP:
Vertical rain-infiltration
2° STEP: Lateral-flow
Infiltration-front propagation
Downslope drainagelimited by bedrock topography
Same as in the ideal planar case
Lan
ni
et a
l., 2
01
1
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48Downslope Drainage efficiency
Pressure growing
α = 13° α = 20° α = 30°
Lan
ni
et a
l., 2
01
1
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time
t=6h
t=9h
t=7h
α = 13°
…..and then the average value of positive pore-water pressure continues to grow
Pressure growing
Lanni et al., 2011
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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.
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51
(FS=1)
(1<FS<1.05)
t=10h
α = 30°
c’ = 0 kPaφ’ = 30°
If you tilt you slide
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52
In complex topographyof 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
•However, there is an interplay between slope and bumpiness of the bedrock
which is not trivial at all.
•The mechanism where infiltration comes first and lateral flow later continues
to be valid
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53
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)
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54
Another case and its complexity: Duron
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55
Duron stratigraphyFa
rab
egoli
et
al.,
20
11
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56
Duron soil depthFa
rab
egoli
et
al.,
20
11
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57
Duron geomorphologyFa
rab
egoli
et
al.,
20
11
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58
Duron soil coverFa
rab
egoli
et
al.,
20
11
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59
Duron land useFa
rab
egoli
et
al.,
20
11
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60
And a tentative association of those maps withhydrological characters
Wit
h D
all’A
mic
o ,F
arab
egoli
et
al.,
20
11
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61
Forecasting of temperaturein a point
In time
Wit
h D
all’A
mic
o ,F
arab
egoli
et
al.,
20
11
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62
Soil water content at different depthin a point
Wit
h D
all’A
mic
o ,F
arab
egoli
et
al.,
20
11
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63
Pro
bab
ilit
y of
lan
dsl
idin
gSi
mon
i et
al, 2
00
8
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64
Duron
Pro
bab
ilit
y of
lan
dsl
idin
gSi
mon
i et
al, 2
00
8
Monday, October 10, 11
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65
Duron
Pro
bab
ilit
y of
lan
dsl
idin
gSi
mon
i et
al, 2
00
8
Monday, October 10, 11
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66
Duron
Pro
bab
ilit
y of
lan
dsl
idin
gSi
mon
i et
al, 2
00
8
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67
Duron
Pro
bab
ilit
y of
lan
dsl
idin
gSi
mon
i et
al, 2
00
8
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68
And the snow again !
Duron
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69
Duron
Temperature of snow !
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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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71
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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Thank you for your attention.
G.U
lric
i -
20
00
?
72
Monday, October 10, 11
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