An introductory presentation of my PhD research covering rainfall-induced landslides, subsurface hydrology, unsaturated soil mechanics, Ground Penetration Radars and some experimental data from a field campaign that I conducted.

1. Hydrological Modeling of Shallow Landslides
Internal Seminar, 12 October 2009
Anagnostopoulos Grigoris

2. 1.Introduction

3. 1.Introduction



Landslides triggered by rainfall occur in most
mountainous landscapes.
Most of them occur suddenly and travel long distances
at high speeds.
They can pose great threats to life and property.
Figure 1: Landslides in Urseren Valey
1.Introduction
2.PhD plan
3.Theoretical Background
Figure 2: Rutschung Hellbüchel, Lutzenberg, AR – Sept. 1st, 2002
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

4. 1.Introduction
Typical dimensions:



Main triggering mechanisms:






Rainfall intensity and duration.
Antecedent soil moisture conditions.
Pore pressure change due to saturated and unsaturated flow of
water through soil pores.
Cohesion and friction (c,φ) angle of soil.
Hydraulic conductivity and hysteretic behaviour of soil during
wetting and drying cycles.
Topography and macropores.
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans
Hydrological

Width ~ tens of meters.
Length ~ hundreds of meters.
Depth ~ 1-2 meters.
Soil Properties


5. 2.PhD Plan

6. 2.PhD Plan




Development of a physically based model for the
prediction of the location and timing of shallow
landslides.
Produce results in various scales varying from the
hillslope to the catchment scale.
Take into account as many as possible factors that
contribute to the phenomenon (unsaturated conditions,
hysteresis, macropores etc).
Verification of the produced model with experimental
data from a landslide-prone location.
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

7. 3.Theoretical Background

8. 3.Theoretical Background
Water flow through soil:
 The depth of the swallow landslides is 1-2 meters.
 The failure surface may be located in the vadoze zone
where unsaturated flow conditions exist.
 The hillslope subsurface flow that considers also the
unsaturated zone is described by the fully three
dimensional Richard`s equation:

 ( )
   K s K r ( )(  z )
t
dS w

  Sw Ss   s
, Sw 
d
s
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

9. 3.Theoretical Background
Limitations of the Richard`s equation:
 RE model is highly non-linear due to pressure head
dependencies in the storage and conductivity terms.
 It is solved numerically using Finite differences or Finite
element techniques.
 For large-scale problems the conventional numerical
methods are complex and time-consuming.
 RE cannot describe accurately some flows like gravitydriven fingers, which occur in an initially dry medium
infiltrated at small supply rates.
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

10. 3.Theoretical Background
Soil-Water Characteristic Curve Models (SWCC):
 Van Genuchten (1980) model is commonly adopted for
engineering applications:
  r
Se 
 (1   n )  m ,  0
s  r
Se  1,  0
1
m  1
n

The parameters are computed directly from special lab
tests or indirectly from the grain size distribution.
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

11. 3.Theoretical Background
Hysteretic phenomenon:
 Hysteresis is observed during consequent wetting and
drying cycles.

Models:


Conceptual, based mainly on the dependent domain theory
(Mualem, 1974).
Empirical, most of them based on VG model for the prediction
of main drying-wetting curves (Kool & Parker, 1983 – Huang et
al, 2005).
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

12. 3.Theoretical Background

Saturated soil mechanics:



One stress variable (σ-uw) controls the saturated soil behaviour
(Terzaghi, 1936).
Pore pressure is isotropic and invariant in direction (“neutral
stress”).
Unsaturated soil mechanics:


Two stress variables (σ-ua), (ua-uw) must be used for
unsaturated soils (Fredlung & Morgenstern, 1977).
Pore pressure (no longer “neutral”) disintegrates in:
1. Air pressure acting on dry or hydrated grain surfaces.
2. Water pressure acting on the wetted portion of grain
surfaces in menisci (ink-bottle effect).
3. Surface tension along the air-water interfaces.
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

13. 3.Theoretical Background
Unsaturated shear strenght:
 It is described in terms of the independent stress state
variables:
 f  c  (u - uw ) tan  b  (  u ) tan 


φb is highly non linear function of
matric suction and can vary from a
value close to φ (saturated
conditions) to as low as 0o (near
dryiness).
It can be expressed as:
tan  b 
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
  r
tan 
s  r
5.Cellular Automata
6.Field Campaign
7.Future plans

14. 3.Theoretical Background
Infinite slope analysis (Factor of Safety concept):
 Appropriate for long continuous slopes where the
thickness is small compared to the height.
 The end effects can be neglected.
 Each vertical block of soil above the failure plane have
the same forces acting on it.
FoS 

1.Introduction
2.PhD plan
3.Theoretical Background
tan 
2c


tan   H ss sin 2 
(ua  uw )
n m
(1   (ua  uw ) )  H ss
4.State of the art
5.Cellular Automata
(tan   cot  ) tan 
6.Field Campaign
7.Future plans

15. 3.Theoretical Background
Constitutive models for unsaturated soils:
 Elasto-plastic models for unsaturated soils are based
on the Cam Clay model.
 Barcelona Basic Model (Alonso et al, 1990) is the
basis of many unsaturated elasto-plastic models:
 The yield surface is three dimensional in the p-q-s
space and the elastic domain increases as the
suction increases.
 A volumetric stress-strain relationship (influenced
by sunction) is considered.
 An hysteresis model is incorporated.
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

16. 4.State of the Art

17. 4.State of the art
SHALSTAB (Montgomery and Dietrich, 1994)
 The model couples digital terrain data with a steadystate water flow model and a slope stability model.
 Assumptions
Rainfall influences water flow only by modulating steady
water table heights.
 Water flow is exclusively parallel to the slope.
 Slope stability is computed using an infinite slope analysis.
Limitations:
 Neglects slope-normal redistribution of pore-water
pressures associated with transient infiltration of rain.


1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

18. 4.State of the art
dSLAM (Wu and Sidle, 1995)

It is a distributed physically based model combining a slope
stability model with a 1-D kinematic wave model for the water
flow accounting for vegetation and root strength.

Assumptions
Rainfall influences water flow only by modulating quasisteady water table heights.
 Water flow is exclusively parallel to the slope.
 Slope stability is computed using an infinite slope analysis.
Limitations:
 Neglects the water flow in the unsaturated zone of soil,
which is crucial for triggering landslides.


1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

19. 4.State of the art
TRIGRS (Baum, Savage and Godt, 2002)
 It computes transient pore-pressure changes and
attendant changes in the factor of safety based on the
Iverson`s (2000) linearised solution of Richard`s
equation.
 Linearised Richard`s equation:
C ( )  

  1

  2  [ K L (   sin  )] 
Co t
x
x


 

 

 2  ( K L  )   [ K z (   cos  )]
y
y
z
z
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

20. 4.State of the art
TRIGRS (Baum, Savage and Godt, 2002)



If ε<< 1 ( ε= H/Α1/2, where H is the soil depth and A is the
catchment area that influences ψ) the terms multiplied by ε
can be neglected.
If we assume Kz=Ksat and C=Co the equation becomes a 1-D
linear diffusion equation which can be solved analytically:

 2
 Do cos 2  2
Limitations:
t
t
 The model assumes flow in saturated or nearly saturated
homogenous, isotropic soil.
 Pore water pressure is only function of depth and time.
 The results are very sensitive to initial conditions.
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

21. 4.State of the art
D`Odorico et al framework, 2005



An existing body of modeling approaches is put together in
order to calculate the return period of landslide-triggering
precipitation.
The relative importance of long-term (slope parallel) flow with
respect to short-term (vertical) infiltration combined with the
characteristics of the hyetograph are explored.
Several features of previous models are coupled:



A model of subsurface lateral (steady, long-term) flow
(Montgomery and Dietrich, 1994).
A model of transient (short-term) rainfall infiltration (Iverson 2000).
Intensity-duration-frequency relations of extreme precipitation are
used to determine the return period of landslides.
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

22. 4.State of the art
GeoTOP-FS (Simoni et al, 2007)


It is a distributed, hydrological-geotechnical model which
simulates the probability of shallow landslides and debris flow.
Characteristics:





It is based on GEO-top distributed hydrological model which
models latent and sensible heat fluxes and surface runoff.
Soil suction and moisture are computed by numerically integrating
Richard`s equation in a 3-D scheme.
The relation between the suction ψ and volumetric water content θ
is given through the van Genuchten (1980) model.
Soil failure mechanisms are described through an infinite slope
model.
Accounts for additional root cohesion, tree weight and surface
runoff to the calculation of FS.
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

23. 4.State of the art
Statistical framework for predicting landslides.

Approaches:



Most statistical models rely on either multivariate correlation between
mapped landslides and landscape attributes or general associations
with soil properties (Carrara et al, 1995; Chung et al, 1995).
Other models analyze the intensity and duration of rainfalls triggering
landslides. They built the critical rainfall threshold curves
(Wieczorek,1987; Wieczorek et al, 2000; Crosta and Frattini, 2003).
Limitations:



Lack of process-based analysis.
Unable to assess the stability of a particular slope with respect to
certain storm characteristics.
Unable to assess the return period of the landslide-triggering
precipitation.
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

24. 5.Cellular Automata

25. 5.Cellular Automata
Basic definitions






CA are dynamical systems discrete both in space and time.
In space, a finite state automata is distributed over the nodes
of regular lattice.
Each automaton can be in one of any finite number of states.
Each automaton is connected to every other automaton at
pre-determined distance.
In time, each automaton updates its state synchronously with
all other automata.
This update is done according to fixed mapping function (local
transition function) from the present states of the automata to
their future states.
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

26. 5.Cellular Automata
Macroscopic Cellular Automata for Unsaturated flow



All existing numerical methods for solving field equations have a
differential formulation as their starting point.
To obtain a discrete formulation of the fundamental equation is
not necessary to go down to the differential form and then go up
to the discrete (as most of numerical algorithms do).
CA can be used for the simulation of 3-D unsaturated water flow
by considering the macroscopic equation of mass balance
between the cells of the lattice:
ha  hc
hc
  Kc ( l ) Aa  VcCc t  Sc

a
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

27. 5.Cellular Automata
Macroscopic Cellular Automata for Unsaturated flow





The states of the cell must account for all the characteristics
relevant to the evolution of the system.
The discrete mass balance equation plays the role of the local
transition function used to update the states of the cells.
CA can be used for the simulation of 3-D unsaturated water flow by
considering the macroscopic equation of mass balance between
the cells of the lattice.
At the beginning the cells are in arbitrary
states representing the initial conditions
of the system.
The CA evolves by changing the states
of all cells according to the transition
function.
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

28. 5.Cellular Automata
Why Cellular Automata?






It`s how nature works: simple local rules produce a very complex
global behavior.
Simulation of large-scale problems using fully coupled system
equations shows computational limitations.
Both the dimension of the grid and the time step should be small
in order to achieve convergence.
CA allow to increase the spatial and temporal domain of
simulations with acceptable computational requirements.
CA are inherently parallel, as a collection of identical transition
functions simultaneously applied to all cells.
Thus, the simulation can be accelerated tremendously by
running it simultaneously in many processors.
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

29. 5.Cellular Automata
Sample problem for testing a CA algorithm

A simple case, for which analytical solutions of Richard` s
equation exist (Tracy, 2006), is selected for testing the accuracy
of a CA algorithm.

k
  ( k h ) 
t
z
k  k s k r , k r  e ah , h  e ah  e ahr
2h  a
h
h
a ( s   r )
c
,c 
z
t
ks
1
x
y
ln[e ahr  (1  e ahr ) sin
cos
], h( x, y , z , 0)  hr
a
a
b
1
x
 y a ( L z)
ahr
ahr
h  ln{e  (1  e ) sin
cos
e2
a
a
b

sinh  z 2 
[

( 1) k k sin(k z )e   t ]}

sinh  L Lc k 1

h ( x, y , L, t ) 
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

30. 5.Cellular Automata
Sample problem for testing a CA algorithm
Pressure height h (m)
Pressure height h (m)
0
-2
-4
-6
-8
0
-10
-2
-4
-6
Pressure height h (m)
-8
-10
0
3
-8
-10
-8
-10
2
3
-6
1
2
3
4
5
6
(x=5, y=5), t=30s
7
CA
4
5
6
(x=5, y=5), t=60s
7
Analytical
8
depth (m)
1
2
-4
0
depth (m)
0
1
depth (m)
0
-2
CA
Analytical
4
5
6
8
CA
Analytical
(x=5, y=5), t=120s
7
8
9
9
9
10
10
10
Pressure height h (m)
Pressure height h (m)
0
-2
-4
-6
-8
0
-10
-2
-4
-6
Pressure height h (m)
-8
0
-10
2
3
3
3
4
5
6
7
(x=5, y=5), t=240s
CA
Analytical
8
depth (m)
2
-6
1
2
-4
0
1
depth (m)
0
1
depth (m)
0
-2
4
5
6
7
(x=5, y=5), t=480s
8
4
5
6
CA
7
Analytical
8
9
9
10
CA
Analytical
9
10
(x=5, y=5), t=960s
10
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

31. 6.Field Campaign

32. 6.Field Campaign
Urseren Valley, Kanton Uri, 21/7-31/7/2009.
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

33. 6.Field Campaign
Persons involved:
 Grigoris Anagnostopoulos
 Markus Konz
 Marco Sperl
 Stefan Carpentier
 David Finger
 Kathi Edmaier
 Florian Köck
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

34. 6.Field Campaign
Disturbed
samples

Simulation of shallow landslides requires detailed
knowledge of soil parameters and their spatial
variability.
Parameters to be determined:
 Subsurface topography (Ground Penetration Radar).
 Grain size distribution.
 Atterberg limits.
 Soil Water Characteristic Curves (SWCC).
 Dry bulk density and porosity.
 Cohesion (c) and friction angle (φ).
 Saturated hydraulic conductivity (Ks).
Undisturbed
samples and
in situ tests

1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

35. 6.Field Campaign
In situ shear box test
700
600
Shear force (N)
500
400
300
Shearbox 1
Shearbox 2
Shearbox 3
Shearbox 4
Shearbox 5
200
100
0
0
10
20
30
40
50
Horizontal diplacement (mm)
18
Vertical diplacement (mm)
16
14
12
10
8
6
Shearbox 1
Shearbox 2
Shearbox 3
Shearbox 4
Shearbox 5
4
2
0
0
5
10
15
20
25
30
35
40
45
50
Horizontal diplacement (mm)
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

36. 6.Field Campaign
Inverse Auger Test
100.00
Relative frequence (%)
90.00
80.00
70.00
60.00
50.00
40.00
30.00
20.00
10.00
0.00
1.00E-06
1.00E-05
1.00E-04
Hydraulic Conductivity (m/s)
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

37. 6.Field Campaign
Classification tests
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

38. 6.Field Campaign
Ground Penetration Radar (GPR)

High resolution GPR measurements (100,250
MHz) revealed deformations of a clay layer
around the cutting edge of a landslide.
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

39. 7.Future Plans

40. 7.Future plans





The CA algorithm, combined with a FS concept for the
slope stability, will be implemented for a real case study
for which data before and after the event exist.
Compare its results to other popular models (TRIGRS)
and TOPKAPI.
If the results are satisfactory the algorithm will be
programmed in parallel environment for greater
efficiency in larger scales.
Establish regionalization methods for soil parameters.
Incorporate subsurface topography anomalies
(macropores, deformation of soil layers etc) which can
lead to local failures.
1.Introduction
2.PhD plan
3.Theoretical Background
4.State of the art
5.Cellular Automata
6.Field Campaign
7.Future plans

41. Thank you for your attention!