Seismic Analysis with Newmark Method
1. Introduction
This tutorial will demonstrate how to model a multi-material slope with seismic loading in a multiple scenario model. We will demonstrate three different seismic analysis options including displacement analysis using the Newmark method.
The finished product of this tutorial can be found in the Tutorial 28 Seismic Analysis.slmd data file. All tutorial files installed with Slide2 can be accessed by selecting File > Recent Folders > Tutorials Folder from the Slide2 main menu
2. Model 1 - No Seismic Loading
From the Slide2 main menu, select File > Recent Folders > Tutorials Folder and read in the Tutorial 28 Seismic (initial).slmd file. This model is based on the non-homogeneous, three-layer slope found in Slide2 Verification Problem #4.
Notice the child scenario is named “No Seismic.” We will run this scenario first.
MATERIAL PROPERTIES
Let’s examine the material properties of the model. Select Define Material from the toolbar or the Properties menu.
Select Properties > Define Materials
Click through the first three materials and review the properties defined.
Select Cancel to close the Define Material Properties dialog when finished.
3. Compute
Before you analyze your model, save it as a file called Seismic Tutorial.slmd.
Select File > Save
Use the Save As dialog to save the file. You are now ready to run the analysis.
Select Analysis > Compute
4. Interpret
To view the results of the analysis:
Select Analysis > Interpret
This will start the Slide2 Interpret program. You should see the following critical slip surface with FS = 1.374.
5. Model 2 - Pseudostatic Seismic Loading
We will now duplicate the scenario, add a pseudostatic seismic load to the new model and re-run the analysis to determine its effect on the Safety Factor.
- Return to the Slide2 Model program.
- In the Document Viewer, right-click on No Seismic and select Duplicate Scenario.
- Right-click on this new scenario and select Rename.
- Enter Seismic = 0.15 as the scenario name.
- Click Save and Close.
PSEUDO-STATIC SEISMIC LOAD
In Slide2, pseudo-static seismic loads can be applied in the horizontal and vertical directions by specifying the corresponding Seismic load coefficient. The Seismic load coefficient is used to determine the seismic force applied to the slope. Ensure you have clicked on the Seismic = 0.15 scenario.
Select Loading > Seismic Load
In the dialog, enter a Horizontal Seismic load coefficient = 0.15. Notice that this value is positive in the direction of failure. Select OK when finished.
We are now finished creating this scenario and can proceed to run the analysis and interpret the results.
6. Compute
Select Analysis > Compute
Notice the scenario without results, Seismic = 0.15, is automatically selected to Compute. Select OK. The Slide2 Compute engine will proceed in running the analysis. When completed, you are ready to view the results in Interpret.
7. Interpret
To view the results of the analysis:
Select Analysis > Interpret
This will start the Slide2 Interpret program. For the Seismic = 0.15 scenario, you should see the following critical slip surface with FS = 0.992.
With the addition of horizontal seismic loading, the Global Minimum safety factor is now 0.992 compared to 1.374 before adding the seismic load. The seismic load has destabilized the slope. You may find it useful to tile the views, to view the results of both scenarios together. Minimize the master scenario to better compare.
Select Window > Tile Vertically
Above the Document Viewer pane, select Synchronize Views. Select the “Sync Zoom/Pan/View Mode” checkbox. Select Done.
Once activated, this feature allows you to apply the zoom and pan settings used in one scenario across all scenarios. Use the Zoom options as necessary to achieve the desired view of the slopes.
8. Model 3 - Critical Seismic Coefficient (kc) Analysis
In this tutorial, we have so far considered the effect of a pseudostatic seismic load on the minimum safety factor, by specifying a horizontal seismic load coefficient. In Slide2, we can also perform advanced seismic analysis to determine the critical seismic coefficient (kc) that results in a destabilized slope with FS = 1.
Return to the Slide2 Model program.
In the Document Viewer, right-click on No Seismic and select Duplicate Scenario. Rename the scenario Critical Acceleration.
PROJECT SETTINGS
For the Critical Acceleration scenario, we will change the Project Settings in order to determine the critical seismic coefficient. Ensure you have this scenario selected.
Select Analysis > Project Settings
Select the Seismic page from the list at the left of the dialog.
Select the “Advanced Seismic Analysis” checkbox. Notice that the “Compute Ky for all failure surfaces” option is selected. This option must be selected in order to compute ky for all failure surfaces. Select OK.
9. Compute
Select Analysis > Compute
The new scenario, Critical Acceleration, is automatically selected to Compute. Select OK.
The Slide2 Compute engine will proceed in running the analysis. When completed, you are ready to view the results in Interpret.
10. Interpret
To view the results of the analysis:
Select Analysis > Interpret
You should see the following critical slip surface with the critical seismic coefficient displayed (ky = 0.146).
Now select the All Surfaces option to view all circles generated by the analysis:
Select Data > All Surfaces
Let’s use the Filter Surfaces option, to display only surfaces with a critical seismic coefficient (Ky) below 0.15, the value we specified in the previous scenario Seismic = 0.15.
Select Data > Filter Surfaces
In the Filter Surfaces dialog, select the “Surfaces with a Ky below” option, enter a value of 0.15, and select Done.
As you can see, there are a number of unstable surfaces for this model, wherein a seismic coefficient less than 0.15 would result in a destabilized slope. This makes sense, since the Global Minimum factor of safety for the Seismic = 0.15 scenario, is 0.992 (i.e. just below one).
11. Model 4 - Newmark Displacement Analysis
We will now perform a Newmark displacement analysis to determine the critical Newmark displacement that results from seismic loading.
Return to the Modeler. In the Document Viewer, right-click on the Critical Acceleration scenario and select Duplicate Scenario. Rename it Newmark Displacement.
PROJECT SETTINGS
We will now change the Project Settings for the new scenario in order to determine the Newmark displacements.
Select Analysis > Project Settings
Select the Seismic page from the list at the left of the dialog.
Notice that the “Advanced Seismic Analysis” checkbox is selected, as it was in the Critical Acceleration scenario. This option must be selected in order to compute Newmark displacements. The Newmark analysis in Slide2 is based on the program SLAMMER, developed by the U.S. Geological Survey. The permission to use the SLAMMER code by Dr. Jibson and Dr. Rathje in Slide2 is gratefully acknowledged.
Select Newmark Analysis Options and Define Seismic Record.
Notice that in Slide2 there are a number of ways the seismic record can be entered. Time and acceleration data points can be manually entered into each cell or copied in from a table. Alternatively, the seismic record can be imported from a Slammer or Slide2 (.ssr) file, or chosen from a list of Example Records containing historical data from a selection of earthquakes.
For this tutorial, we will use data from the Example Record of Mammoth Lakes-1 1980, CVK090 with a peak ground acceleration (PGA) of 0.416 g. Select Example Record and set Earthquake = Mammoth Lakes-1 1980 and Record Name = CVK-090.
Notice that a summary of the Earthquake Properties, which includes the PGA and PGV of the selected record, is displayed.
Select OK to close the Example Seismic Records dialog.
Notice that once the time and acceleration data points have been entered, the acceleration vs. time plot is generated in the Define Seismic Record dialog.
Select OK to close the Define Seismic Record dialog when finished reviewing the seismic record data.
In the Newmark Analysis dialog, notice the Newmark Analysis Type option. In Slide2, we are able to define the Newmark Analysis Type as either Rigid, Coupled, or Decoupled. We can also run all three at once. Also, notice that the displacement can be computed by examining the Positive Accelerations, Negative Accelerations, Mean Accelerations, or the Maximum positive/negative accelerations of the seismic record. We can also run all these displacement options at once.
For this tutorial, we will set Newmark Analysis Type = Rigid and Displacement computed using = Maximum positive/negative acceleration.
Select OK to close the Newmark Analysis dialog.
Select OK in the Project Settings dialog.
12.Compute
Select Analysis > Compute
The Slide2 Compute engine will proceed in running the analysis. When completed, you are ready to view the results in Interpret.
13. Interpret
To view the results of the analysis:
Select Analysis > Interpret
You should see the following critical slip surface with the critical Newmark displacement displayed = 4.380 cm.
Select Window > Tile Vertically
This allows us to view all the different scenarios at once.
This concludes the seismic analysis tutorial.
References
Jobson, R.W., Rathje, E.M., Jibson, M.W., and Lee, Y.W., 2013, SLAMMER – Seismic LandSlide2 Movement Modeled using Eatherquake Records (ver.1.1, November 2014): U.S. Geological Survey Techniques and Methods, book 12, chap. B1, unpaged