UPDATE 2014-01-14: The attached .zip file now contains a Mathcad Prime 3.0 worksheet (.mcdx) and—for those of you who are still using earlier verisions of Mathcad—an Adobe Acrobat printout (.pdf) of the worksheet so can see how it is put together.
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About twenty-five years ago, I designed a small nuisance water/storm drainage lift station for a small, isolated watershed in petroleum tank farm. The lift station was so small that it contained only one submersible pump inside a standard 48-inch-diameter manhole. For the manhole, which was only about 10 feet deep, I specified the standard sewer/storm drainage manhole in the Public Works Standards of the City of [shall be nameless to protect the guilty] . Unfortunately, because this was a private project, the design had to go through the City's Development Department for approval, not Public Works, and therein lies the genesis of this worksheet.
The Development Department refused to approve my design without structural calculations for the manhole. Never mind that the City already had thousands of these manholes in streets and other high traffic areas, as well is in dirt areas, while mine was in a location where post-construction traffic was highly unlikely. Never mind that some of the City's manholes were more than 30 feet deep. Never mind that there are millions of similar manholes dotting the free world, virtually all of which were installed without the requirement to perform structural calculations. However, this was not the first time this City's Development Department had required the ridiculous and it would not be the last time.
Rather than provide structural calculations for the manhole in question, I decided instead to calculate the theoretical maximum depth of a standard manhole based on the equivalent fluid theory for soil pressure. My point was to show how ridicuous their request was without being too overt about rubbing their noses in it. Yep, that's right, I was going to deliberately yank the tail of the approving agency, but I was confident (and correct) that they wouldn't figure out my modus operandi. My inspiration for doing the calculations this way was an older engineer I had worked with a few years before. He had casually mentioned to me one day that he had calculated the maximum depth of a manhole when he was a young engineer and had come up with nearly 1/4 mile.
So, the purpose of this worksheet is to calculate a ridiculous structural situation that is partly based on flawed assumptions. Namely, how deep can you construct a manhole before it fails? As with many of my worksheets, the math is pretty simple, but Mathcad is how I choose to do it and document it. Enjoy.
