Landslides of any type, and particularly soil slips, pose a great threat in mountainous and steep terrain environ- ments. One of the major triggering mechanisms for slope failures in shallow soils is the build-up of soil pore water pressure resulting in a decrease of effective stress. However, infiltration may have other effects both before and after slope failure. Especially, on steep slopes in shallow soils, soil slips can be triggered by a rapid drop in the apparent cohesion following a decrease in matric suction when a wetting front penetrates into the soil without generating positive pore pressures. These types of failures are very frequent in pre-alpine and alpine landscapes. The key factor for a realistic prediction of rainfall-induced landslides are the interdependence of shear strength and suction and the monitoring of suction changes during the cyclic wetting (due to infiltration) and drying (due to percolation and evaporation) processes. The non-unique relationship between suction and water content, expressed by the Soil Water Retention Curve, results in different values of suction and, therefore, of soil shear strength for the same water content, depending on whether the soil is being wetted (during storms) or dried (during inter-storm periods). We developed a physically based distributed in space and continuous in time model for the simulation of the hydrological triggering of shallow landslides at scales larger than a single slope. In this modeling effort particular weight is given to the modeling of hydrological processes in order to investigate the role of hydrologi- cal triggering mechanisms on soil changes leading to slip occurrences. Specifically, the 3D flow of water and the resulting water balance in the unsaturated and saturated zone is modeled using a Cellular Automata framework. The infinite slope analysis is coupled to the hydrological component of the model for the computation of slope stability. For the computation of the Factor of Safety a unified concept for effective stress under both saturated and unsaturated conditions has been used (Lu Ning and Godt Jonathan, WRR, 2010). A test case of a serious landslide event in Switzerland is investigated to assess the plausibility of the model and to verify its perfomance.

1. Hydrological Modelling of Slope Stability
Grigorios Anagnostopoulos
Paolo Burlando
Institute of Environmental Engineering, ETH Zurich
European Geosciences Union, Vienna, April 7 2011

2. Background
Computational framework
Test Case
Summary
Shallow landslide hazard
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.
Typical dimensions
Width ∼ tens of meters
Lenght ∼ hundreds of meters.
Depth ∼ 1-2 meters.
Landslides in Urseren Valey, Kanton Uri,
Switzerland
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3. Background
Computational framework
Test Case
Summary
Factors contributing to the phenomenon
Hydrological factors
Rainfall intensity and duration.
Antecedent soil moisture conditions.
Pore pressure change due to saturated and unsaturated flow of
water through soil pores.
Soil properties
Cohesion and friction angle (c,φ) of soil.
Root reinforcement provided by the vegetation.
Hydraulic conductivity and hysteretic behaviour of soil during
wetting and drying cycles.
Topography and macropores.
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4. Background
Computational framework
Test Case
Summary
State of the art of models
Deterministic models
Simplified low-dimensional models with various degrees of
simplification.
Numerical models solving the fully coupled three-dimensional
variably saturated flow and stress problem using conventional
numerical techniques (finite differences, finite elements).
Statistical models
Multivariate correlation between landslides and landscape attributes
and soil properties.
Analysis of duration and intensity of rainfalls triggering landslides.
Each one of them makes its own assumptions on various aspects
of the problem, thus limiting its range of applicability.
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5. Background
Computational framework
Test Case
Summary
Hydrological Component I
The Cellular Automata (CA) concept is used in order to model the
3D subsurface flow.
CA: General concepts
The domain is divided into discrete cells.
Each cell has its own state, which describes its physical condition.
The state of each cell evolves via simple rules based on neighbour
interactions.
These rules are implemented in the transition function which is
applied to all the cells of the domain.
Bottom-up approach in contrast with the discrete to continuum
to discrete paradox exhibited by the standard numerical methods.
CA concept is inherently parallel, as a collection of identical
transition functions simultaneously applied to all cells.
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6. Background
Computational framework
Test Case
Summary
Hydrological Component II
In the case of 3-D variably saturated flow
the mass balance equation plays the role of
the transition function:
(0,0,-1)
(-1,0,0)
Q5
Q1
(0,-1,0)
Q3
(0,1,0)
(0,0,0)
Q2
Q0
Q4
K αc
α∈I
hα − hc
lαc
Aαc +Sc = Vc σ(ψc )
∆h
∆t
(1,0,0)
(0,0,1)
σ(ψc ) =
Cc (ψc ), for ψc < 0
Ss ,
for ψc 0
Each cell of the lattice communicates with its neighbours only
through its faces.
Spatial heterogeneity is tackled because every cell has its own
constitutive hydraulic properties.
The boundary conditions can be of two types: constant head
(Diriclet) or constant flux (Neumann).
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7. Background
Computational framework
Test Case
Summary
Hydrological Component III
Soil Water Retention Curves
We used a modified Van Genuchten (VG) (Ippisch et al, 2006),
which corrects the unrealistic conductivity values predicted by the
classical VG model:
Se =
1
Sc [1
1
+ (α|h|)n ]−m , for h < he
, for h he
Hysteresis model
Different curves followed during the
drying and wetting processes.
It is crucial for the continuous
simulation of soil water content during
storm and inter-storm periods.
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8. Background
Computational framework
Test Case
Summary
Geotechnical Component
Despite their limitations, infinite slope analysis and the factor of
safety concept are used due to their simplicity.
Infinite Slope analysis limitations
Long, continuous slopes where the sliding surface is parallel to the
surface.
The thickness of the unstable material is small compared to the
height of the slope.
The end effects on the sliding block are neglected.
A factor of safety equation for both unsaturated and saturated
conditions is used, which uses the concept of effective stress (Lu
Ning and Godt Jonathan, WRR, 2010).
FOS =
tanφ
2c
uα − uw
+
+ Se
(tanβ + cotβ)tanφ
tanβ γz sin2β
γz
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9. Background
Computational framework
Test Case
Summary
Napf catchment: Overview
Location: Kanton Bern, Switzerland.
Area: 2, 5 km2 (48 % forested).
Altitude: 900 m − 1360 m.
Triggering event: A 3-hour precipitation event at 15-16 July 2002
caused many soil slips.
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10. Background
Computational framework
Test Case
Summary
Input data
Surface topography: A 3x3 m Digital Elevation Model is used.
Slope: It is calculated from the DEM using the ArcGIS routine.
Soil Depth: An exponential model, which relates the soil depth to
1
the slope is used: d = 3.0 · e (− 40 ·slope) .
Soil Parameters:
The soil map of switzerland (Bodeneignungskarte) was used for the
identification of the soil classes.
Representative values from the literature are used for the soil
properties of each soil class.
Land use: The land use map of Switzerland was used, which has a
100x100 m resolution.
Precipitation: We used the historical record of the Napf station,
which is located 5 km at the north of the catchment.
Initial conditions: We ran the model for a 6-month period prior to
the event in order to create more realistic soil moisture conditions.
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12. Background
Computational framework
Test Case
Summary
Model Validation
The performance of the model tested against:
The inventory of occurred landslides during the rainfall event of
15-16 July 2002.
The results of a frequently used model (TRIGRS ver 2.0).
TRIGRS
The catchment is modelled as a two dimensional array of non
interacting columns.
The water flow is considered vertical in each soil column.
Each column consists of two zones: an unsaturated zone which is in
top of the saturated zone. The two zones interact with each other
through the rise of the water table.
Infinite slope analysis is used for the computation of slope stability.
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13. Background
Computational framework
Test Case
Summary
Results I: Temporal evolution
Evolution of factor of safety during the 3-hour triggering event.
1.05
1
0.95
0.9
0.85
0.8
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14. Background
Computational framework
Test Case
Summary
Results I: Temporal evolution
Evolution of factor of safety during the 3-hour triggering event.
1.05
1
0.95
0.9
0.85
0.8
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15. Background
Computational framework
Test Case
Summary
Results I: Temporal evolution
Evolution of factor of safety during the 3-hour triggering event.
1.05
1
0.95
0.9
0.85
0.8
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16. Background
Computational framework
Test Case
Summary
Results I: Temporal evolution
Evolution of factor of safety during the 3-hour triggering event.
1.05
1
0.95
0.9
0.85
0.8
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17. Background
Computational framework
Test Case
Summary
Results II: Destabilised areas
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18. Background
Computational framework
Test Case
Summary
Results III: Quantitative data
True Positive Rate (%)
False Positive Rate (%)
Accuracy (%)
Precision (%)
Sliding Area (%)
Cell3D FOS
40.2
6.3
92.4
14.7
6.5
TRIGRS
23.5
11.2
82.5
4.5
13
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19. Background
Computational framework
Test Case
Summary
Summary, conclusions and future work
1
A reduced complexity model based on Cellular Automata is used for
the simulation of rainfall-induced landslides.
2
Emphasis is given on the detailed simulation of the water flow and
the resulting pore water pressures.
3
A simple model for slope stability based on infinite slope analysis is
coupled to the hydrological component.
4
The proposed model had a relatively good performance despite the
lack of detailed hydrological and soil data.
5
An elasto-plastic model will be incorporated in order to describe
better the soil behaviour due to stress and suction changes.
6
A parallel version in OpenMP and CUDA will be implemented in
order to simulate bigger catchments.
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20. Thanks for your attention!