Slope with ponded water.pdf - GEO-SLOPE International Ltd.

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GEO-SLOPE International Ltd, Calgary, Alberta, Canada www.geo-slope.com Figure 4 Free body diagram and force polygon of slice #1 The resultant water force (F) contains both the vertical and horizontal water force components, which are computed as being the water pressure acting over the vertical or horizontal area of the slice (assuming a unit depth). Figure 5 Schematic submerged slice showing the parameters used in the water force calculation Referring to the single schematic slice shown in Figure 5, the resultant force (F) can be spot-checked by calculating the horizontal and vertical weight components as shown below: SLOPE/W Example File: Slope with ponded water.doc (pdf) (gsz) Page 4 of 7
GEO-SLOPE International Ltd, Calgary, Alberta, Canada www.geo-slope.com The vertical and horizontal forces acting on a submerged slice can be computed as: where: FV = (γ x Hw) x bV x unit depth FH = (γ x Hw) x bH x unit depth γ = unit weight of water Hw = height of the water at the top, centre of the slice bv = width of the slice as given in the slice force information bH = bv* tan(α) For slice #4, with a water depth of 1.5m, a slice width (bV) of 0.43787 m and a slope angle (α) of 45- degrees, the vertical and horizontal water forces would be: Fv = (9.807 x 1.5) x 0.43787 m x 1 m = 6.441 kN FH = (9.807 x 1.5) x [0.43787 m x tan(45)] = 6.441 kN* * which is the same as the vertical component since the slope is at 45 – degrees. The resultant force is therefore computed as: F 2 = √(FH 2 + FV 2 ) = √(6.441 2 + 6.441 2 ) = 9.1 kN The small difference between the computed F value and the line load acting on the top of the slice is due to numerical round-off in the hand-calculations. 3.2 Case 2 – Water weight modified with a surcharge load By default, the weight of the water and the pore-water pressures at the base of the slice will both be computed using the global weight of water. However, there may be a time where you want to use one unit weight to compute the pore-water pressure at the base of the slice and a different unit weight to compute the water force acting on the submerged slices. To do this, you would define the unit weight of water for the pore-water pressure computation using SET: Units and Scale, as shown in Figure 2. The global value would also be used to compute the weight of the slice, but you could modify this value by defining a surcharge load with either a positive or negative unit weight to add or subtract load as desired. In the second analysis in this detailed example, the global unit weight of water has been left at the default value of 9.807 kN/m 3 , and a surcharge load with a positive unit weight of 0.1 kN/m 3 . In defining this value, the water force will essentially be computed as if the unit weight of water was defined as 9.907 kN/m 3 . Figure 6 shows the surcharge load defined overtop of the shaded area representing ponded water between the piezometric and the ground surface lines. SLOPE/W Example File: Slope with ponded water.doc (pdf) (gsz) Page 5 of 7
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Slope with ponded water.pdf - GEO-SLOPE International Ltd.

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