Method-of-slices - CEG 4012 Lecture #23 Method of Slices...

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CEG 4012 Lecture #23 Method of Slices
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Slope Stability by the Method of Slices • Allows for variability of c- slope soils (not homogenous) • Also allows for seepage and external forces • Slope is divided into a series of vertical slices which intersect a trial circular failure surface • The bottom of each slice is straight line and contains only one type of soil:
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Slope Stability by the Method of Slices Draw free body diagram of a typical slice i and show the forces acting unit thickness: where: U i = Water pressure force T i = Shear force N i = Normal effective force E i = Normal forces on side S i = Shear force on sides W i = Weight of slice i = Inclination of slice failure plane x i = Width of slice L i = Length of slice failure plane In general: Too many unknowns must make simplifying assumptions . ....
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Geometry for method of slices for each slice must find weight, W i and base angle, i : – can draw slope with slices to scale and measure with scale and protractor – or can use trigonometry: first define the circle center, the circle radius R, the width x i of each, and the horizontal distance, x i , from the circle center to the slice center the volume of the slice is x i h i where h i = height of the slice at its center and h i = R cos α i y i where y i = distance to circle center above slice surface the weight of the slice, W i =  x i h i since
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Slice Geometry Example toe circle, i = 45 ° , center above toe, 5' slices, = 120 pcf, R = 40', H = 30', Y =40' for slice 3: x 3 = y 3 = 12.5', x 3 = 5' (40' - 12.5') = 27.5' α 3 = h 3 = R cos α 3 y 3 = W 3 = γ∆ x 3 h 3 = 40’ cos 18.21 ° 27.5’ = 10.5’ Y z 3
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External Forces in Method of Slices method of slices very flexible: – weight of slice may include both saturated and moist soil – slices may include more than one type of soil – weight of slice should include any water above slice (i.e. calculate total slice weight, the water pressure will be subtracted from N i ) – add vertical external forces to slice weight – add horizontal external forces x moment arm to resisting or driving moment, as appropriate
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Fellenius Method (1927) (also known as the Swedish Method) First method of slices developed and presented in the literature. Simplicity of the method: possible to compute factors of safety using hand calculations.
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This note was uploaded on 12/14/2011 for the course CEG 4012 taught by Professor Staff during the Fall '08 term at University of Florida.

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Method-of-slices - CEG 4012 Lecture #23 Method of Slices...

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