Slope with Ponded Water

Transcription

1 1 Introduction Slope with Ponded Water The purpose of this illustrative example is to show how the stability of a partially submerged slope can be modeled with SLOPE/W. Features of this simulation include: Entry and Exit slip surface Partial submerged slope Pore-water pressures modeled with a piezometric line How to alter the unit weight of water of the ponded water layer Hand calculation of some slice forces 2 Configuration and setup Figure 1 shows the geometry of the partial submerged slope. The water layer is 3 m high, and a piezometric line is used to specify the pore water pressure condition of the slope. Figure 1 Geometry of the partial submerged slope 3 Changes to how water is modeled in SLOPE/W Version 7.1 In Version 7.1, the historic option to define water as a no-strength material has been removed from SLOPE/W. Any file created in an earlier version that modeled water as a no-strength material will automatically be updated the first time you open the file in Version 7.1 to use the new approach. If the weight of the water was modeled in earlier files using a pressure boundary, you will see a warning message when you open the file in Version 7.1 suggesting that the pressure line may be redundant and need to be removed. This error message will only occur if the pressure line was drawn to correspond within a specified tolerance of the piezometric line. If the pressure line was drawn at a different elevation SLOPE/W Example File: Slope with ponded water.doc (pdf) (gsz) Page 1 of 7

2 for some reason, the warning message will not appear. Please note that pressure lines are now referred to as surcharge loads in Version 7.1, which is more accurate. The new approach that has been implemented in Version 7.1 computes the stabilizing weight of the water acting on the ground surface by looking at the positive pore-water pressures that exist along the ground surface. This approach will work for piezometric lines, pressure heads defined using a spatial function or finite element computed heads. The presence of positive pore-water pressures on the ground surface line will be visually represented by a shaded area showing the extent of the ponded water and with arrows indicating the direction that the water force will be acting on the free body. Water forces will act normal to the ground surface line. Pore-water pressures at the base of each slice will be computed differently depending on the method used. For piezometric lines, the vertical distance from the base of the slice up to the relevant piezometric line multiplied by the unit weight of water as defined under SET: Units and Scale, will determine the porewater pressures that exist at the base. For pressure heads developed using a pressure head spatial function, the pore-water pressures will be determined using a numerical process called Kriging. For finite element generated pore-water pressures, the location of the base of the slice, relative to the nearest finite element nodes, will be determined and the pore-water pressures will be interpolated from the finite element computed results. For the example being described in this article, a piezometric line has been created and assigned to both the foundation and embankment materials. Accordingly, the stabilizing weight of the water will be applied in the analysis and is represented with a shaded zone and arrows. 3.1 Case 1 Water layer modeled with a piezometric line In this case, the ponded water is modeled with a piezometric line. Note that the piezometric line is drawn across the anticipated surface of the ponded water where pressure equals zero (P = 0). The area between the ground surface line and the piezometric line has been shaded to indicate the extent of positive porewater pressures and arrows have also been painted along the ground surface to indicate the direction that the water force is acting. The global unit weight of water under SET: Units and Scale has been defined as kn/m 3 as shown in Figure 2. This is the value that will be used together with the vertical height of the piezometric line to compute the correct pore-water pressure at the base of each slice. This is also the unit weight that will be used to compute the water force acting on the ground surface. If you want to use a different value, you can change the global value and then do a quick hand-calculation to confirm to yourself that the unit weight being used is what you have input. SLOPE/W Example File: Slope with ponded water.doc (pdf) (gsz) Page 2 of 7

3 Figure 2: Set Units and Scale dialogue box where you can define the global unit weight of water Figure 3 shows the critical slip surface and the factor of safety of the partially submerged slope. The factor of safety is Figure 3 Critical slip surface and factor of safety of the partial submerged slope when modeled with a piezometric line. Figure 4 shows the free body diagram and the force polygon of slice #4, which is located half way down the submerged portion of the slope. Note the line load acting on the top of the slice which represents the resultant water force (F) contributed from the water layer. SLOPE/W Example File: Slope with ponded water.doc (pdf) (gsz) Page 3 of 7

4 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

5 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 m and a slope angle (α) of 45- degrees, the vertical and horizontal water forces would be: Fv = (9.807 x 1.5) x m x 1 m = kn FH = (9.807 x 1.5) x [ m x tan(45)] = 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 ) = ( ) = 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 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 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

6 Figure 6 A surcharge load used to modify the global weight of water for the water force acting on the submerged slope The critical slip surface and the factor of safety of the partially submerged slope is shown in Figure 7. The factor of safety is The small increase in factor of safety is due to the slight heavier ponded water which gives additional resisting force against the slide mass. Figure 7 Critical slip surface and factor of safety with the water weight modified using a surcharge load SLOPE/W Example File: Slope with ponded water.doc (pdf) (gsz) Page 6 of 7

7 The free body diagram and the force polygon of slice #4 is shown in Figure 8. Note that the load of kn acting on the top of the slice has increased slightly from the computed value shown in Figure 4, due to the slightly more dense water acting on the submerged slope. Figure 8 Free body diagram and force polygon of slice #4 SLOPE/W Example File: Slope with ponded water.doc (pdf) (gsz) Page 7 of 7