Hydrological Modelling of Slope Stability

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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.

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Hydrological Modelling of Slope Stability

  1. 1. Hydrological Modelling of Slope Stability Grigorios Anagnostopoulos Paolo Burlando Institute of Environmental Engineering, ETH Zurich European Geosciences Union, Vienna, April 7 2011
  2. 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 Hydrological Modelling of Slope Stability 2 / 17
  3. 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. Hydrological Modelling of Slope Stability 3 / 17
  4. 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. Hydrological Modelling of Slope Stability 4 / 17
  5. 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. Hydrological Modelling of Slope Stability 5 / 17
  6. 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). Hydrological Modelling of Slope Stability 6 / 17
  7. 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. Hydrological Modelling of Slope Stability 7 / 17
  8. 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 Hydrological Modelling of Slope Stability 8 / 17
  9. 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. Hydrological Modelling of Slope Stability 9 / 17
  10. 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. Hydrological Modelling of Slope Stability 10 / 17
  11. 11. 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. Hydrological Modelling of Slope Stability 12 / 17
  12. 12. 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 Hydrological Modelling of Slope Stability 13 / 17
  13. 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 Hydrological Modelling of Slope Stability 13 / 17
  14. 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 Hydrological Modelling of Slope Stability 13 / 17
  15. 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 Hydrological Modelling of Slope Stability 13 / 17
  16. 16. Background Computational framework Test Case Summary Results II: Destabilised areas Hydrological Modelling of Slope Stability 14 / 17
  17. 17. 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 Hydrological Modelling of Slope Stability 15 / 17
  18. 18. 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. Hydrological Modelling of Slope Stability 16 / 17
  19. 19. Thanks for your attention!

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