Finding the missing pieces. #engineering #tunnel #mathematics #concrete #civilengineering #geology

The tunnel system under my house carries stress from the footings above and the government wants to know how much. I provided the following, but it was rejected for brevity and poor references. How did I end up in this situation? Well, we need to go back to a vacation I took earlier in the summer to the deep hills of West Virginia. While I was walking in the forest, I was pondering the problem of soil dynamics and how to calculate stress propagation from a load far above. I know it's slow, but how do I prove it? While driving home, I saw this building. Interesting, civil and structural engineering. I stopped in and he gave a few minutes to help out and he found a document buried deep in his attic of engineering marvels. Exactly what I needed. I snapped a picture and went home and unfortunately I did not note the source. I searched for it all over Google and could only find it on engineering study materials. Well, anyway, I had the perfect solution. Well, that didn't work out so well. I got called out. I need to do a better job now. So, I asked CHAT GPT. The new O1 model is incredible and it designed a really sophisticated solution using the Boussinesq equation. Solved the stress increase as 62 PSF. Beautiful, but this will not be accepted as a source either. A civil engineer follower suggested I review the Navy Facilities Engineering Command Design Manual 7.02, which covers foundations and earth structures. After a few hours of review, I could not find specific equations that I could use. I found another manual. 7.01, which covers soil mechanics. On page 167, we finally have the source of the chart that I used. Not only that, but there is an equation. As a special treat for the 15% of you that are still here on the video, let's solve this together and get nerdy. Here we have the equation as provided. We know that P is 1700 PSF and that we have a right angle. Use the Pythagorean theorem to solve the two hypotenuses. Now we need angle Y and get it using trig. Sine Y equals opposite over hypotenuse. Getting Y alone requires getting the arc sine of 0.39. Getting out my old college calculator to do an inverse sine. Y equals 23 degrees. Do the same for A and we get 5 degrees. Let's note them and start filling out the equation. A plus 2Y equals 51. Get the sine and cosine out of the way. Total in the bracket is 3.16 and we get 1711 PSF. That is 100% a mistake. Let's ask ChatGPT again. For this time, let it know how we are trying to solve it. Okay, it looks like the right approach, although there are some differences in how the angles are defined. Oh, it's using radians. That makes sense. Back to my work, I am using 5 degrees when I should be using 0.09 radians. Now we get 0.146 which solves to 79 PSF. Now we are in line with where we should be and are using an established method with source. So I am going to tack on a safety factor to get to the 102 PSF which I already had. I love a science girl.