1. Understanding
hydrological processes
to improve the
landslide model
prediction
Cristiano Lanni
University of Trento
Jeff McDonnell, OSU
Riccardo Rigon, UoT

2. Outline 1
HS11.7
1. Mapping shallow landslide using hydrological model:
the state of the art
2. The role of bedrock surface on subsurface
water-flow dynamics:
the PANOLA TRENCH HILLSLOPE
3. Is DWI able to follow surface topography ?
4. Looking to improve the performance of the
simpler hydrological models
© Oregon State Trento
University of University

3. 2
HS11.7
SIMPLE HYDROLOGICAL MODELS COMPLEX HYDROLOGICAL MODELS
1D – i.e. TRIGRS (Baum et al.,2002)
a) C o n s i d e r s t h e s t e a d y - s t a t e ∂ψ ∂θ ∂   ∂ψ 
= K (ψ ) −1
hydrological condition ∂t ∂ψ ∂z   ∂z 
b) Does not take into account the
3D – i.e. GEOtop (Rigon et al.,2006),
shear-strength in unsaturated soil
HYDRUS-3D
€ ∂ψ ∂θ ∂   ∂ψ ∂x 3 
= K x (ψ ) + 
∂t ∂ψ ∂x i  i  ∂x i ∂x i 
€
INFINITE SLOPE STABILITY MODEL
(accounting for unsaturated zone)
© Oregon State Trento
University of University

4. The role of bedrock shape:
Panola Trench Hillsope 3
HS11.7
Bedrock  High soil-depth variability
Ground
Flow direction
Bedrock
© Oregon State Trento
University of University depression

5. 4
HS11.7
Geometry 
α = 13° α = 20° α = 30°
PANOLA13 PANOLA20 PANOLA30
Soil (sandy-silt)  Ksat = 10-4 m/s
Bedrock  Ksat = 10-7 m/s
Triggering Factor  Intensity = 6.5 mm/h
Duration = 9 hours
© Oregon State Trento
University of University

6. 5
HS11.7
Panola13
t=6h
sat=3%
t=7h
sat=18%
t=9h
sat=43%  Saturated area at the soil-
bedrock interface
increases very rapidly
© Oregon State Trento
University of University
t=14h

7. 6
HS11.7
time
t=1h t=4h t=12h
.. ….…
Downslope Drainage efficiency
α = 13°
.. ….…
α = 20°
.. ….…
α = 30°
© Oregon State Trento
University of University

8. before proceeding further….
HS11.7
Lanni et al. 2010 (submitted to WRR)
1D
 No role played by
hillslope gradient
3D
 Significantly affected
by hillslope gradient
© Oregon State Trento
University of University

9. Moving to hillslope stability….
HS11.7
FACTOR OF SAFETY
MECHANICAL PROPERTIES Panola30
c’ = 0 kPa
φ’ = 30°
(FS=1)
(1<FS<1.05)
© Oregon State Trento
University of University
t=10h

10. +5.0% +12.0% 9
HS11.7
+1.4% +11.0%
t=0h t=6h t=7h
t=8h
+6.2%
+14.2%
+11.2%
+26.2%
t=9h
 Bedrock depression determines the threshold effect
© Oregon State Trento
University of University t=10h

11. 10
HS11.7
Hjerdt et al., 2004 WRR
€
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University of University

12. 11
HS11.7
 Maximum pore pressure
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University of University

13. 12
HS11.7
© Oregon State Trento
University of University

14. 12
HS11.7
N
1
N ∑( ( ) )(
ψ i − ψ ⋅ DWI ( i) − DWI )
cor(ψ ,DWI ) = i=1
var(ψ )⋅ var(DWI )
€
 INVERSE correlation  DIRECT
cor(ψ (t = 3h),Z) = −0.9
between SOIL-THICK correlation
and PRESSURE HEAD in between DWI
€ the I stage of rain- and PRESSURE
infiltration HEAD in the II
stage of rain-
cor(ψ (t = 11h),DWI ) = +0.83 infiltration
© Oregon State Trento
University of University
€

15. 13
HS11.7
 Unsaturated soil (vertical recharge)
p p
h t +1 = h t + Δt
i, j i, j θ sat − θ
ht ht+1
 Saturated soil (vertical recharge +
€
lateral flow +
DWI effect)
ΔV = qin – qout + p*[A
W(t) = k * qout(t)
ΔVi,j = qin – qout + p*[A(i,j)+1-Ai,j]
Basin Δt
γ ⋅ A 0.5
i, j
ki, j =
K
sat⋅ DWI β −t / ki, j
 αi, j ( t) = 1− e t ≤ Tp
  

p p
h t +1 = h t +  + Ai, j⋅ α (t) − A Δt
i, j i, j  θ sat − θ ai, j⋅ φ 

i, j ( )
i, j +1 ⋅ α (i, j ) (t)
+1 
 T /k  −t / k
αi, j ( t) =  e p i, j − 1 e i, j t > T
p
 €  
€ €
© Oregon State Trento
University of University
€

16. 14
HS11.7
 Unsaturated soil  Saturated soil
  
p  
h t +1 = h t +
p p
i, j θ sat − θ Δt h t +1 = h t +  + Ai, j⋅ α (t) − A Δt
i, j i, j i, j  θ sat − θ ai, j⋅ φ 

i, j ( )
i, j +1 ⋅ α (i, j ) (t)
+1 
 
€
 Irregular shape
€
© Oregon State Trento
University of University

17. 14
HS11.7
 Unsaturated soil  Saturated soil
  
p  
h t +1 = h t +
p p
i, j θ sat − θ Δt h t +1 = h t +  + Ai, j⋅ α (t) − A Δt
i, j i, j i, j  θ sat − θ ai, j⋅ φ 

i, j ( )
i, j +1 ⋅ α (i, j ) (t)
+1 
 
€
SHALSTAB
€ NEW SIMPLE MODEL
© Oregon State Trento
University of University

18. TAKE HOME MESSAGGES 15
HS11.7
1.a First, vertical rain-infiltration induces the
infiltration-front propagation
1.b Then, lateral-flow could “turn on” because of the built-up
pore-water pressures at the soil-bedrock interface
1.c Finally, bedrock shape (i.e., spatial soil thickness
variability) could affect the flow dynamics, inducing a fast
decrease of FS
2. Putting DWI concept in modelling approach and removing
S-S assumption it seems possible to improve the prediction
performance of the simpler hydrological models
3. Please, take care in the use of SHALSTAB:
The hydrological ratio p/T represents a calibration
parameter rather than real physical properties
…but Montgomery and Dietrich also wrote this in their original paper
© Oregon State Trento
University of University

19. Thank you
for your attention!
cristiano.lanni@gmail.com

20. HS11.7
EXTRA SLIDES
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University of University

21. Threshold for initiation of
3
HS11.7
Subsurface water-flow
 The precipitation threshold for initiation of Subsurface Stormflow
seems related to the micro-topography in the bedrock
 Saturated patched recorded at the soil-bedrock interface are
usually a balance between upslope accumulated water and
downslope drainage efficiency
© Oregon State Trento
University of University by Jeff McDonnell and his research team

22. 6
HS11.7
 Max pressure head at the SOIL-BEDROCK INTERFACE
Unsat
Sat
α = 13° α = 20° α = 30°
© Oregon State Trento
University of University
Downslope Drainage efficiency

23. 7
HS11.7
Panola13
t=6h
sat=3%
t=7h
sat=18%
t=9h
sat=43%  …..and than the average value of
positive pore-water pressure
continues to grow
© Oregon State Trento
University of University
t=14h

24. 7
HS11.7
time
 1D & 3D mechanism
t=1h t=4h t=12h
1. Vertical flow
2. Lateral flow & bedrock obstructions
panola13
.. ….…
panola20
.. ….…
N
2
var(ψ ) =
1
N ∑( ψ ( i) − ψ )
panola30
i=1
.. ….…
€
© Oregon State Trento
University of University

25. 12
HS11.7
Rain 1: Rain 2:
Intensity = 6.5 mm/h Intensity = 12 mm/h
Duration = 9 hours Duration = 5 hours
Rain = 58.5 mm Rain = 60 mm
t=10h t=5h
FS<1  12.6% FS<1  48.9%
© Oregon State Trento
University of University

26. 12
HS11.7
SHALSTAB
Maximum pore pressure
p= 5% I
h p A
=
Z T b sin β
© Oregon State University
University of
Trento

27. 14
HS11.7
SHALSTAB model
 Water-mass balance in steady state condition
Qsup + Qsub = I ⋅ A
h
ν ⋅ A+K b Z cos β sin β =I⋅A
€ sat Z
h p A
€ =
Z T b sin β
T = hydraulic trasmisivity
Z = soil-thick
€  γ h  tanφ ' h = water-table thick in steady-state condition
FS = 1− w  € β = local slope
 γ Z  tan β € A = Upslope contributing area
€ q = effective rainfall
© Oregon State Trento
University of University
€
€

28. 15
HS11.7
€
SHALSTAB COMPLEX HYDROLOGICAL MODEL
p= 5% I
 The limitation of water-table grows everywhere
steady-state condition
 “A” determines the Unable to account for
water-table thick distribution “topography obstructions”
© Oregon State Trento
University of University

29. 17
HS11.7
 Unsaturated soil  Saturated soil
  
p  
h t +1 = h t +
p p
i, j θ sat − θ Δt h t +1 = h t +  + Ai, j⋅ α (t) − A Δt
i, j i, j i, j  θ sat − θ ai, j⋅ φ 

i, j ( )
i, j +1 ⋅ α (i, j ) (t)
+1 
 
€
 Planar shape €
© Oregon State Trento
University of University