As I was saying, I began to develop a slope stability model. What is a slope stability model, you may ask. Well, it’s pretty much what it sounds like. Some very clever people, starting many decades ago, began trying to solve a very complex issue of determining how safe a slope is, and whether or not it may fail. In a nutshell, you compare the sum of the resisting forces to the sum of the motivating forces. Divide the first by the second, and you get what we call the factor of safety. The difficulty is that there are more unknowns than equations, so some simplifying assumptions have to be made, and over the years, some very refined methods have been developed. So, that is a slope stability analysis.
A few of the things that are used as input values for a slope stability analysis include the cross-section of the slope (which I discussed in the previous blog), the strength characteristics of the various soil and rock types that make up the slope, the position of the water table (phreatic surface), and whether the water is flowing, external loads, like earthquakes, and whether any of the materials in the slope may loose strength (or stiffness) during shearing, or as the result of an earthquake.
So, I began to collect all of that information, and for what I could not establish, I used temporary parameters. For instance, the strength of the materials in the embankment that had failed. The main component of that embankment was clay. The value I needed is called a friction angle. A simple way to think of friction angle is to think of a block on an inclined plane. You raise the incline slowly, increasing the slope angle, and the angle where the block begins sliding is the friction angle between those two materials. There are sophisticated laboratory tests to establish the friction angle, but I didn’t have time for that. I needed to stabilize the embankment before it failed any further.
So, I set up the slope stability model as best I could, including a very minor earthquake that seemed to contribute to the failure. I made a best estimate of the position of the groundwater table. Then, I varied the friction angle of the clay until the model indicated that a failure could occur, that is, it would have a safety factor of one. That is how a back-analysis is completed, at least in this case. Next, to stabilize the slope, the owner would have to build a buttress onto the dam. This was the primary purpose for establishing the slope stability analysis.
I added a rock-fill buttress to the model, and varied the height and width of the buttress until an acceptable level of safety was obtained. I worked with the owner to have this buttress constructed.
The buttress was constructed as-designed, and the dam remains stable to this day. The owner expressed their extreme gratitude for preserving their facility, and it gave me a deep sense of accomplishment for having done so.
In next week’s follow up to this blog, I’ll make it clear that not every emergency can come out this well, but I’m very proud that this one did.