Analysis Tools
Plans, Profiles and Cross-Sections
The first thing a geotechnical engineer should do when confronted with side-hill retaining walls is to review the available drawings. The plan view will show you where the wall line is with respect to existing slopes, roads, drainage structures and hopefully it will have existing ground contours as well to get a sense of the terrain. Wall profile sheets will give you the exposed wall height. The roadway or other civil designers might have assumed an embedment depth, but this will have to be determined from your analysis and may significantly increase your total wall height (exposed wall height plus embedment).
Cross-sections are crucially important to determine exactly how steep the existing slope is and to look at what types of temporary excavations and shoring might be required for various wall systems and whether there is room to construct them. For roadway projects, engineers usually cut cross-sections at spacings of 100-ft or more. For variable slope conditions, you may need to have cross-sections cut more frequently, like every 25-ft or even every 10-ft. I’m sure there are ways of using 3D CAD drawings or DTMs to visualize this information as well, but 2D cross-sections are still what I see as most common in practice.
Slope Templates
Measuring the slope magnitude or slope angle of the existing slope is an important step in the analysis. You can simply use a protractor on the cross-sections or measure inside your CADD drawings if you have them. But for roadway projects, slopes are usually expressed in terms of horizontal to vertical ratios. For example, a 45 degree slope would be 1H:1V, and a 30 degree slope would be about 1.7H:1V. I try to measure these slopes on every cross-section if possible. For long walls or large projects with many walls, this can take forever. So on a side-hill retaining wall project a number of years ago, I had created slope templates in a drafting program and copied them onto overhead transparencies. I’ve since lost the original MicroStation drawing I used, but I have a scanned copy that you can download below that should work as well. Just be careful that your printer or copier can use transparencies or you’ll jam it up by melting the transparency (speaking from experience)! You might be better off taking it to a photocopy place.
Figure 13: Example of slope template for measuring slope rates (H:V) of existing slopes on 1:1 cross-sections
Download the Slope Template PDF file that you can copy onto overhead transparencies and use to measure slope ratios. There is one template for right-facing slopes and one for left facing. When using the template, make sure the cross-section you are using it for is not distorted with respect to horizontal and vertical axis, i.e. 10-ft in the horizontal direction of the plot are as long as 10-ft in the vertical direction.
To use the templates, lay them on the cross sections and make sure the horizontal lines on the template are parallel to the horizontal lines on the cross-sections. Slide the template left or right until you find the line that best matches your slope and read off the slope ratio. Easy!
Composite Chart
Another tool I came up with for analyzing these types of walls grew out of the need to marry information gleaned from the various plans, profiles and cross-sections discussed above. It was an attempt to visualize this info quickly and effectively for an entire wall, and for lack of a better term, I call it a composite chart. You can download a sample version below and follow along as I explain what these charts are and what they are useful for.
Download a sample composite chart spreadsheet (XLS spreadsheet).
Station or length along the wall is plotted on the X-Axis. The primary Y-Axis is used for height values, and the secondary Y-Axis is used for slope ratios (I typically plot slope ratio, H:V, but you could plot slope angle if you wanted). There is one series for wall height or more correctly, the exposed wall height (Primary Y axis), and one series for slope in front of the wall (Secondary Y-Axis).
This works fine for an infinite slope type of situation, but real life isn’t so simple. In many cases, I’ve found that an existing slope can be approximated by a bi-linear slope. The “height” of the upper slope is also a useful property to look at so you can tell how close you are to being an infinite slope. Figure 14 below shows the simple bi-linear slope model.
Figure 14: Bilinear slope model
An example composite chart is shown in Figure 14 below. It may be a little confusing to look at, but if you stare at it for a while, you can probably start to make sense out of it. The great thing about these charts is that it summarizes pages and pages of cross-sections onto one sheet (after some labor intensive, mind-numbing work). And it can be invaluable when determining what cross-section(s) or generalized cross-section(s) to use for slope stability analysis. Frequently you will need to analyze more than one cross-section for your global stability analyses, so these charts can help you figure out which ones are the critical ones. In this example, the difference between the height of the upper slope (green line) and the exposed wall height (red line) gives you the height of steep slope below your retaining wall before the slope flattens out somewhat, a very useful parameter to have!
Figure 15: Example composite chart
Slope Stability Software
Finally, slope stability software is the most important tool when it comes to analyzing side-hill retaining walls. We’ve discussed this at length in previous sections, so I don’t think I need to say anything more.
