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- 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!

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