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Exercise 4 Deterministic landslide hazard assessment

Exercise 4 Deterministic landslide hazard assessment. Cees van Westen. Associated Institute of the. Objective. In this exercise, a simple slope stability model (the infinite slope model ) is used to calculate safety factor maps for different conditions.

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Exercise 4 Deterministic landslide hazard assessment

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  1. Exercise 4Deterministic landslide hazard assessment Cees van Westen Associated Institute of the ISL 2004

  2. Objective • In this exercise, a simple slope stability model (the infinite slope model) is used to calculate safety factor maps for different conditions. • The effect of groundwater depth and seismic acceleration is evaluated using input maps of these factors for different return periods of rainfall (related to the groundwater level) and earthquakes (related to the seismic acceleration). • In ILWIS, the model is represented by a user-defined function. Different scenarios are calculated by changing the variables of this function. The model is applied on a data set of the city of Manizales, in central Colombia. ISL 2004

  3. Shear strength / stress Shear stress = W sin  / A Shear strength (Mohr-Coulomb criterion) s = c +  tan   = normal stress = W cos  / A c = cohesion (KPa)  = angle of internal friction (degrees)  and c are geotechnical properties, which are measured in the laboratory using triaxial tests or shearbox tests. ISL 2004

  4. Safety Factor The degree of slope hazard can be expressed by the Safety Factor (F) which is the ratio of the forces that make a slope fail and those that prevent a slope from failing. • F < 1 unstable slope conditions, • F = 1 slope is at the point of failure, • F > 1 stable slope conditions. ISL 2004

  5. Weight of the block: Shear component of weight: Normal component of weight: Infinite slope Infinite slope: • Conditions at crest and toe of the slope may be ignored. • Resulting forces from left and right are equal g = unit weight of soil (N/m3). ISL 2004

  6. Shear stress: Normal stress: Shear component of weight: Safety factor: Normal component of weight: Infinite slope Stress = Force / area ISL 2004

  7. Height watertable above failure surface Weight of the water: Normal component of water weight: Pore pressure on JK: Factor of safety including pore pressure: Infinite slope & water pressure ISL 2004

  8. Visualization of the input data Soil depth map Values ranges from 0.2 to 57 m Slope map ISL 2004

  9. Slope information • ILWIS Mapcalc functions work with radials and not with degrees e.g. 360 degrees = 2 *  radials = 2 * 3.14 = 6.3832 • With some Mapcalc calculations in which you will use the inbuilt ILWIS functions DEGRAD( ), SIN( ), COS( ), and SQ( ), first some maps are prepared that will be frequently used in this application: • map SI, sine of slope • map CO, cosine of slope • map CO2, squared cosine of slope ISL 2004

  10. Preparation of data ILWIS works with slope in Radians Slrad:=degrad(Slope_map) Co2=sq(Co) Co:=cos(Slrad) Si:=sin(Slrad) ISL 2004

  11. Input data known: M: Zw/Z = Depth to groundwater / Depth to failure surface c' = effective cohesion (Pa= N/m2) = 11000 Pa w = unit weight of water (N/m3) = 10000 N/m3 z = depth of failure surface below the surface (m) = map Soildepth  = slope surface inclination () = map Slope_map ’ = effective angle of shearing resistance () = 32  tan(') = tangent of the effective angle of shearing resistance = 32°, thus tan(') =0.625 ISL 2004

  12. User-defined function • The Safety Factor formula as presented above will be transformed into a user-defined function FS. This function already contains the known parameters (maps Soildepth, SI, CO, CO2 and the known constants) but it also contains the variables Gamma and m. • The function can then be easily applied for various heights of the watertable (zw), by filling out the variables Gamma and m. This will result in a number of Safety Factor maps for specific watertable heights. • Function FS reads: (Cohesion + (Gamma-M * Gammaw)* Z*Co2* Tanphi) / (Gamma*Z*Si*Co) ISL 2004

  13. Function fs ISL 2004

  14. Function fs ISL 2004

  15. Factor of Safety when Dry Percentage of Area Unstable: 1.26 Critical: 1.92 Stable: 95.38 ISL 2004

  16. Factor of Safety when Saturated Percentage of Area Unstable: 15.80 Critical: 26.81 Stable: 57.39 ISL 2004

  17. Percentage Area Comparison Percentage Area under different classes when Dry Unstable: 1.26 Critical: 1.92 Stable: 95.38 Percentage Area under different classes when Saturated Unstable: 15.80 Critical: 26.81 Stable: 57.39 ISL 2004

  18. Infinite slope and earthquake C’ = effective cohesion (Pa) z = depth of failure surface below terrain surface γ = unit weight of soil (Nm-3) β = terrain suface inclination (degrees) ρ = bulk density (kgm-3) Ah = peak horizontal acceleration in rock (ms-2) N = amplification of seismic acceleration in soil γw = unit weight of water (Nm-3) M = groundwater/soil thickness ration zw/z Zw = height of the water table above failure surface (m) φ’ = effective angle of shearing resistance (degrees) ISL 2004

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