Tutorial 38 Coupled Drawdown Analysis

Coupled Drawdown Analysis 38-1

RS2 v. 9.0 Tutorial Manual

Coupled Drawdown Analysis with Slope Stability

In this tutorial, RS2 is used to simulate slope drawdown to determine its effect on slope stability, specifically the change in slope factor of safety. Furthermore, this problem considers different drawdown rates for fully drained, drained, and undrained conditions.

The completed models can be found in the Tutorial 38 Coupled Drawdown Analysis folder. All tutorial files installed with RS2 9.0 can be accessed by selecting File > Recent Folders > Tutorials Folder from the RS2 main menu.

Topics covered

Drawdown

Shear strength reduction

Staged groundwater analysis

Transient groundwater

Coupled Analysis

Fully drained, drained, and undrained loading conditions

Definition of Drainage Conditions

The drainage conditions used in RS2 are defined as follows:

Drained – Fluid can move into and out of the model, total volume (voids and soil skeleton) can change. Drainage is a function of time. Excess pore pressures can exist. Transient pore pressure state.



Undrained – Fluid cannot move into or out of the model. Zero volume change. Excess pore pressure is a function of applied loads.

Fully drained – Zero excess pore pressure. Drained analysis at infinite time. Steady-state result.

In this tutorial, a fully drained example and undrained example are analyzed. A drained example is also analyzed, with the different drawdown rates of R=0.1m/day, 0.25m/day, 0.5m/day, 0.75m/day, and 1m/day. For the overall analysis of the problem, the drawdown ratios used were L/H = 0.2, 0.4, 0.6, 0.8, and 1.0 (where L is the external water level drop from the initial water level, and H is the slope height or initial water level).

Model

Start the RS2 9.0 Model program. Import the geometry for the model. From the File menu, under Import, select Import DXF. In the DXF Options dialog, make sure External Boundary is checked and click Import. Navigate to the Tutorial 38 folder in the Examples > Tutorials folder, and open the file Tutorial 38 Drawdown Analysis.dxf. The imported external boundary should look like the following model:

Note the model has a slope height, H, of 7m and a slope ratio of 3:1.

Project Settings

Open the Project Settings dialog from the Analysis menu and select the Groundwater tab. Set the Method = Transient FEA and Initial Pore Pressures = Steady State FEA.

Select the General tab. Select Solid-Fluid Interaction: Coupled (Biot) to simulate the different drainage conditions to accurately determine slope stability. The stability of a slope is dependent on the internal and external forces applied, including pore pressure and surface water. A change in the water level causes seepage induced pore pressures and stress induced excess pore pressure to develop, which dissipates over time resulting in consolidation, and thus potentially decreasing slope stability.



Make sure the Units option is set to Metric, stress as kPa, the time units to Days and the permeability units to centimeters/second.

Next, select the Strength Reduction tab. Check Determine Strength Reduction Factor, and then check Coupled Formulation, as shown below.

Click on the Advanced setting, and select User-Defined Convergence Parameters and change the convergence type to Absolute Force & Energy, as shown in the figure below.



Fully Drained

For the fully drained example, select the Stages tab and change the number of stages to 2. Change the staging information to the following:

Close the dialog by clicking OK.

Boundaries

Using the imported DXF geometry file, the external boundaries have already been established.

We need to add a vertex representing the drawdown level on the slope. Select Edit under Boundaries, and select Add Vertices. Input the coordinate points 10.2, -1.4 and hit Enter. The slope should look like the model below.



Materials

Next we will move to the Materials and Staging tab to assign materials and properties to our model. From the Properties menu select Define Materials. Change the unit weight, Poisson's ratio, Young's Modulus, Tensile strength, Friction angle, and Cohesion to the following shown in the figures below. In order to conduct a slope stability analysis, ensure that the material type is Plastic and Apply SSR is checked.



These properties will remain the same for all three drainage examples.

Hydraulic

Next we will define the hydraulic properties. From the Properties menu select Define Hydraulic. For each material, change the model to "Constant". Change the hydraulic conductivity (Ks) to 1e-6 cm/s.

This property will also remain the same for all three drainage examples.

Mesh

Next we move to the Mesh tab. Here we may specify the mesh type and discretization density for our model. For this tutorial, we will use a 6-noded finite element mesh type.

From the Mesh menu select Mesh Setup.

This dialog allows you to customize parameters of your mesh. We want to use a uniform, 6-noded element mesh. We must change the Mesh type to Uniform, the Element type to 6 Noded Triangles and the Default Number of nodes to 1000 as shown:



Click the Discretize button and then the Mesh button. Click OK to close the dialog. The mesh will look like this:

Groundwater

Since there are no liners or additional reinforcement in our model, we will skip the Support tab and move on to the Groundwater tab. We will now model the drawdown along the slope between the two stages.

From the Groundwater menu select Set Boundary Conditions.

The Add Groundwater Boundary Condition dialog appears. Follow the steps below to create the water table drawdown:

1. Ensure you are on Stage 1 tab. From the BC Type drop down menu, select Total Head (H).

2. Enter a Total Head Value (m) of 0 meters.

3. You are now in selection mode. Ensure that Apply at this stage only is checked. We want to apply the Total Head boundary condition to all boundaries, so select over the entire model.



When your selection looks similar to the model above, click “Apply” from the Add Boundary Conditions dialog and then close the dialog.

4. Now move onto the next stage and select the Stage 2 tab. From the From the BC Type drop down menu, select Total Head (H) and enter a Total Head Value (m) of -1.4 meters.

5. Select the right vertical boundary, the adjacent horizontal boundary, and the slope segment as shown in the model below:

Click "Apply" and then close the dialog.

The two stages of your model should have groundwater conditions shown in the following models

Stage 1:



Stage 2:

Notice the change in water level from an elevation of 0m to -1.4m, corresponding to L = -1.4m, with regards to the drawdown ratio (L/H) of 0.2.

Restraints

By default, all segments of the external boundary are fixed. Since the top of this model represents a free surface we need to free the top surface. Go to the Displacements menu and select Free. Click on the four sections that make up the top external boundary and hit Enter. You will see that the fixed boundary conditions have disappeared from the top external boundaries, shown in the figure below

We need to re-establish the fixed boundary condition on the top corners. Select Restrain X,Y from the Displacements menu, select the left and right vertical boundaries and hit Enter. Your model should now look like this:



Loading

Due to drawdown, we will need to apply a ponded water load to the slope.

Click on the tab for Stage 2. From the Loading menu, select Distributed Loads and then select Add Ponded Water Load. Ensure the orientation is Normal to boundary then check Stage Load.

Select Stage Total Head and the dialog should appear.

Enter the Total Head values for the two stages according to the dialog shown below and then click OK to close the dialog.

Click OK to close the Add Ponded Water Load dialog. You will now be prompted to select a boundary on which to apply the load. Select the horizontal and slope sections on the top of the boundary as shown below:



Hit Enter and your model should now have a load that looks like this:

Next, select the Stage 1 tab. Repeat the previous steps until you reach the Stage Total Head dialog. Uncheck "Apply" for Stage 2 to account for the change in load with drawdown. The dialog should now look like this:

Click OK to close the Add Ponded Water Load dialog. Select the top slope section on the boundary as shown below:



Hit Enter and your model should now have a load that looks like this:

Field Stress

Because the top of the model represents the true ground surface, we want to use a gravity field stress. Go to the Loading menu and select Field Stress.

For Field Stress Type select Gravity and click the check box for Use actual ground surface. Leave the values as the default values given.

Click OK to close the dialog.

You have completed the definition of the fully drained model. Save the model specifying it as the Fully Drained Example using the Save option in the File menu.



To create the models for the other drawdown ratios, simply change the vertex location to the corresponding depth as well as the groundwater boundary conditions and loading, outlined in the table below:

Drawdown Ratio (L/H)

Drawdown Depth (m)

0.2 -1.4 0.4 -2.8 0.6 -4.2 0.8 -5.6 1.0 -7

Additionally, to determine the slope factor of safety for initial condition (L/H = 0), simply take any of the drainage models and delete the second stage to conduct shear strength reduction for the initial stage.

Drained

To model the drained example all steps remain the same as that of the fully drained example, except for the change in time and the change in drainage condition.

The following outlines the drainage conditions and time for each drawdown ratio depending on the drawdown rate.

R = 0.1m/day:

Name Time (days) Drained? Initial Conditions 0 Drained

L/H = 0.2 14 Drained L/H = 0.4 28 Drained L/H = 0.6 42 Drained L/H = 0.8 56 Drained L/H = 1.0 70 Drained

R = 0.25m/day:


L/H = 0.2 5.6 Drained L/H = 0.4 11.2 Drained L/H = 0.6 16.8 Drained L/H = 0.8 22.4 Drained L/H = 1.0 28 Drained



R = 0.5m/day:



R = 0.75m/day:


L/H = 0.2 1.867 Drained L/H = 0.4 3.733 Drained L/H = 0.6 5.6 Drained L/H = 0.8 7.467 Drained L/H = 1.0 9.333 Drained

R = 1.0m/day:



Undrained

For the undrained example, select the Stages tab and change the number of stages to 2. Change the staging information to the following:



Close the dialog by clicking OK.

All other steps, including Materials, Mesh, Loading, and Restraints, follow those outlined for the Fully Drained example, except the groundwater boundary conditions.

Groundwater

From the Groundwater menu select Set Boundary Conditions.

To simulate undrained conditions, groundwater boundaries are only applied to the first stage, outline below:

1. Ensure you are on Stage 1 tab. From the BC Type drop down menu, select Total Head (H).

2. Enter a Total Head Value (m) of 0 meters.

3. You are now in selection mode. Ensure that Apply at this stage only is checked. We want to apply the Total Head boundary condition to all boundaries, so select over the entire model.



When your selection looks similar to the model above, click “Apply” from the Add Boundary Conditions dialog and then close the dialog. Your model for both stages should now look like this

Stage 1:

Stage 2:

Compute

Run the models using the Compute option in the Analysis menu. The analysis should take several minutes to run.



Interpret

Once the model has finished computing (Compute dialog closes), select the Interpret option in the Analysis menu to view the results.

The Interpret program starts and reads the results of the analysis. Displayed should be the Maximum Shear Strain.

Maximum Shear Strain

The Fully Drained Maximum Shear Strain contours and Critical SRF values for the different drawdown ratios are shown in the figures below:

L/H = 0.2:

L/H = 0.4:



L/H = 0.6:

L/H = 0.8:

L/H = 1.0:

The Drained Maximum Shear Strain contours and Critical SRF values for the different drawdown ratios are shown in the figures below:



L/H = 0.2:

L/H = 0.4:

L/H = 0.6:

L/H = 0.8:



L/H = 1.0:

Additionally, the Undrained Maximum Shear Strain contours and Critical SRF values for the different drawdown ratios are shown in the figures below:

L/H = 0.2:

L/H = 0.4:



L/H = 0.6:

L/H = 0.8:

L/H = 1.0:



Strength Reduction Factor

To analyze the change in Strength Reduction Factor due to drawdown, the following graph was developed based on model results for the three different drainage cases.

As can be seen, the factor of safety values for the Fully Drained model are higher than the other two drainage conditions due to the slow drawdown. The undrained model has the lowest factor of safety values as this boundary condition simulates rapid drawdown causing a decrease in slope stability, as outlined at the beginning of this tutorial.



Finally, it can be seen the factor of safety values for the Drained models for the different drawdown rates are all within the envelope of the two extreme drainage conditions, Fully Drained and Undrained. The factor of safety values decrease, closer to that of the Undrained example, as the drawdown rate increases, concluding that the more rapid the drawdown rate along a slope, the less stable the slope becomes.

This concludes the Drawdown Analysis Tutorial.

Tutorial 38 Coupled Drawdown Analysis

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