LANDSLIDES AND SURFACE FUNCTIONS

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LANDSLIDES AND SURFACE FUNCTIONS

• FE423 - January 27, 2000

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OUTLINE

• Slope, Aspect, Curvature
• Sensitivity Analysis
• Monte Carlo

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Slope, Aspect, Curvature
Z Ax2y2 Bx2y Cxy2 Dx2 Ey2 Fxy Gx
Hy I Z(0,0) I Z(0,1) E H I Z(0,-1) E
- H I dZ/dx 2Axy2 2Bxy Cy2 2Dx Fy
G d2Z/dx2 2Ay2 2By 2D

• Slope is first partial.
• Curvature is second.
• Test question?

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Sensitivity Analysis

• qo is the surcharging weight of the vegetation
• ? is the angle of the slope
• ? is the friction angle of the soil
• C is the soil cohesion
• Cr is the root reinforcement
• h is the soil thickness
• z is the saturated thickness
• gw is the unit weight of water
• gs is the unit weight of saturated soil

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Sensitivity Analysis

• How important is each term of an equation?
• Do we have to know them exactly?
• How important is their variability?

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Sensitivity Analysis

• Fma
• Increasing m by 10 increases F by 10
• Same with a.
• F is equally sensitive to m and a.

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Sensitivity Analysis

• FS strength/stress
• Increasing strength by 10 increases FS by10.
• Increasing stress by 10 decreases FS by10.

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Sensitivity Analysis

• FS(cohesionfriction)/weight
• If cohesion is zero then 10?10.
• If cohesionfriction then 10 increase in one
  only results in 5 increase in the other.

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Sensitivity Analysis

• qo is the surcharging weight of the vegetation
• ? is the angle of the slope
• ? is the friction angle of the soil
• C is the soil cohesion
• Cr is the root reinforcement
• h is the soil thickness
• z is the saturated thickness
• gw is the unit weight of water
• gs is the unit weight of saturated soil

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Monte Carlo

• How do you handle uncertainty in parameters?
• Choose a value for each parameter
• Calculate FS
• Repeat