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Multi-Stage Rapid Drawdown

1. Introduction

When the water level at a dam drops, the stabilizing force due to the weight of the water is removed. If the dam material has a low permeability and the water level drops quickly, then excess pore pressures will be slow to dissipate. This causes reduced stability in the slope. This tutorial describes how to use Slide3 to model rapid drawdown and examine the effect on dam stability and factor of safety.

Select File > Recent > Tutorials and read in the file Multi-Stage Rapid Drawdown – starting file from the installation folder.

This is the same model created in the tutorial file 04 - Stability of Dam. It already has a water table defined (full reservoir upstream) and material properties.

We will turn on the Rapid Drawdown analysis option, define the Rapid Drawdown undrained strength parameters, and re-run the analysis.

2. Project Settings

Select: Project Settings > Groundwater, turn on the Advanced checkbox and select Rapid Drawdown Method = Dunczan , Wright, Wong 3 Stage (1990). Select OK .

Project Settings Dialog - Groundwater Tab

Then Rapid Drawdown Change dialog will appear as following. Select OK.

Rapid Drawdown Change Dialog'

The significance of the different drawdown methods is discussed in the following sections.

3. Undrained Material Properties

For Rapid Drawdown analysis we must define undrained material properties of the relevant materials.

Materials Cube Icon Select: Materials > Define Materials

  • Select the Inner Core material and select the Rapid Drawdown tab.
  • Select the Undrained Behaviour checkbox and select Shear Strength Envelope Type = Total Stress R Envelope – Linear.
  • Enter CR = 3 kPa and PhiR = 23 degrees.

Material Properties Dialog

  • Select the Outer Core material and select the Rapid Drawdown tab.
  • Select the Undrained Behaviour checkbox and select Shear Strength Envelope Type = Total Stress R Envelope – Linear.
  • Enter CR = 3 kPa and PhiR = 23 degrees.

Material Properties Dialog

Click OK to save and close the Define Material Properties dialog.

The total stress R envelope is a way of representing the undrained strength of the material. It is also possible to specify a Kc = 1 envelope. For details about the meaning of these different envelopes, and their relationship to each other, see the information below.

About Strength Envelopes:

For undrained material, the shear strength can be determined from isotropic consolidated undrained (IC-U) laboratory tests. The total stress R envelope can be constructed as shown below.

Total Stress R Envelope Diagram

Where Effective Stress During Isotropic Consolidationis the effective stress during (isotropic) consolidation and Principal Stress Difference at Failure is the principal stress difference at failure. From the same laboratory test data, it is possible to construct a Kc = 1 envelope instead as shown below:

Normal And Shear Stress Figure

These two different envelopes are related through the following equations:

Envelope Equatiosn

Where Undrained Friction Angle is the undrained friction angle.

Army Corps Method

To perform the limit equilibrium analysis, the Army Corps method requires the R envelope. If the Kc = 1 envelope is entered instead, then it is converted using the above equations. The R envelope is then combined with the effective stress envelope to avoid relying on elevated shear strengths that result from negative pore pressures. The composite envelope is shown below.

Composite Envelope Figure

Other methods

The Lowe and Karafiath (1960) and the Duncan Wright and Wong (1990) methods require the Kc = 1 envelope. If the R envelope is entered instead, then it is converted using the above equations. Kc = 1 refers to an isotropically consolidated state. To get the envelope for an anisotropically consolidated material (where Kc ≠ 1) the drained failure envelope is plotted on the same graph. The drained envelope is assumed to represent the undrained shear strength of the soil at maximum allowable Kc (i.e. the value of Kc that results in failure during consolidation). The envelope to be used in the analysis is then interpolated between the two, using the value of Kc for each column in the limit equilibrium analysis of the slope prior to drawdown.

Normal and Shear Stress Figure

Slip Surfaces

We will use the default Slip Surface options (Ellipsoid, Cuckoo Search, Surface Altering optimization) so you do not need to specify these settings.

4. Results

Results Tab

Calculator Icon Save the file and Compute.

Select: Analysis > Compute

Select the Results workflow tab to view the results. Select Show Contours Contoured Model Icon from the toolbar.

You should see the following results. The critical slip surface from the GLE method gives a safety factor = 1.04.

Turn on the Show Contours option to display data contours on the slip surface.

Slip Surface Contours Model View

Notice that the critical slip surface is on the upstream (reservoir) side of the dam. In the Slide3 Rapid Drawdown analysis, when only one water table has been defined, it is assumed that full drawdown has occurred. All ponded water hydrostatic force on the upstream side of the dam is removed, thereby removing the stabilizing force of the water reservoir on the slope.

Comparison with Full Reservoir

If you compare the drawdown result with the Tutorial 04 result (full reservoir), note that in Tutorial 04 - Stability of Dam the critical slip surface is located on the downstream side of the dam, with a higher safety factor. In comparison, this tutorial with rapid drawdown locates the critical surface on the upstream side of the dam, with a lower safety factor.

5. Additional Exercises

Try other Rapid Drawdown methods, re-run the analysis and compare results. Select Project Settings > Groundwater > Advanced > Rapid Drawdown Method to change the method.

Lowe-Karafiath Method

The Lowe and Karafiath method is essentially the same as the Duncan, Wright and Wong method. The difference is that the Duncan, Wright and Wong method performs a third stage of calculation in which it checks if the effective stress after drawdown produces a drained strength that is less than the undrained strength. If any columns are found for which this is the case, then the drained strength is substituted and the analysis is rerun.

Army Corps Method

As described above, the Army Corps method uses a different failure envelope than the other methods. However we do not need to change the material properties since Slide3 automatically performs any required conversions. If you re-run the analysis with the Army Corps rapid drawdown method, you should see a significantly lower safety factor than the other methods. This agrees with the general belief that the Army Corps method gives results that are too conservative.

Partial drawdown

In this tutorial, we carried out the analysis assuming full reservoir drawdown. In Slide3 it is possible to define a second water table as a Drawdown Water Table. Select Groundwater > Add Water Surface and specify Water Type = Drawdown Surface. If a drawdown water table is defined, then the drawdown analysis will only lower the reservoir to the level of the Drawdown Water Table, rather than full drawdown. Add a Drawdown Water Table below the level of the main water table, re-run the analysis and compare results.

6. References

Corps of Engineers, 1970. Engineering and Design – Stability of Earth and Rock Fill Dams, Engineering Manual, EM 1110-2-1902. Department of the U.S. Army, Corps of Engineers, Office of the Chief of Engineers.

Duncan, J.M., Wright, S.G. and Wong, K.A., 1990. Slope Stability during Rapid Drawdown, Proceedings of H. Bolton Seed Memorial Symposium. Vol. 2.

Lowe, J and Karafiath, L., 1960. Stability of Earth Dams Upon Drawdown, Proceedings of 1st PanAm Conference on Soil Mechanic and Foundation Engineering. Mexico City, Vol 2.

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