June 7th, 2018, 12:48 PM  #1 
Newbie Joined: Jun 2018 From: Oregon Posts: 2 Thanks: 1  Complex volume calculation.
Sorry for the massive amount of text, but I've never seen anything quite like this before in 12 years of construction. I work as a residential contractor, and currently have a project building an addition on a house for a hot tub. The homeowner insisted on doing the concrete pad himself, citing prior experience in commercial concrete finishing. Now after seeing the pad in place for the first time, what we feared would happen has indeed happened, but to an almost unimaginable degree... The homeowner now has a 10x18 foot pad of 4" thick concrete poured against the north wall of his house. It was very obviously not level, even from 40 feet away at the street. Did I mention that this is for a hot tub? HERE IS THE MATH PROBLEM The highest point of the pad is at the north edge, about 5'6" from the east edge. The NE corner is 3/8" low. The SE corner is 5 1/2" low. The NW corner is 1 3/4" inches low. The SW corner is 6 1/4" low. Assuming that we are to fill the area to a depth of one inch above the current high point, exactly how many cubic yards of concrete would be needed to fill this are. For the sake of simplicity, let's assume that all slopes from the high point to the low point are straight lines. How the heck does one even calculate this without dividing the thing into one foot wide wedges along the entire length of the pad? I never took any calculus in college, but I'm thinking that even the first couple calculus classes would not have covered this type of problem. In retrospect, we should have insisted that he let me excavate and set the forms, as this would have cost him less than $500. I'm betting that even the minimum amount of concrete, excluding labor, to build this thing up to level will now exceed that amount. We went to his house numerous times to discuss the desired size of the room and lay out the footprint of the pad along the adjoining exterior wall. We staked out a rectangular 10x18 footprint with equal length diagonals. The ground sloped up away from the house, so we marked a line on the house to indicate the point level with the ground level at ten feet from the house. This should have given him an indication of the depth he needed to excavate the outer long edge of the footprint. When he was half finished excavating the area for the pad, we told him that he would need to bring the edge away from the house down at least six more inches to get a 1/4" per foot slope away from the house. He seemed to understand, and assured us it would be no problem. We are now regretting not stopping by one more time after working another job, to actually see what he did before the concrete was poured. Sadly, sometimes people want to try to save a little money, and you can't tell them any different. This guy should have listened to the professionals. Thanks for reading. I already roughly figured 1.65 yards to fill it in, but will just call it two, to cover the steps now need build to give access the elevated pad... 
June 7th, 2018, 03:05 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,835 Thanks: 2162 
Is the current surface of the concrete curved? Do you want the final concrete surface to have a gentle slope? If so, how will you achieve that slope, and will the lowest part of it be a point or an edge of the pad?

June 7th, 2018, 05:11 PM  #3 
Newbie Joined: Jun 2018 From: Oregon Posts: 2 Thanks: 1 
The current surface is probably curved. It was neither level nor true For the purpose of my question, I would just assume every to be true between points of reference; such that a straight line can connect any two points across the shorter dimension. The minutia of measuring the relative height of every relevant point is prohibitively intensive. The way I posed the question assumes that one can project a straight line from the highest point, to each corner, and that the surfaces between these lines can just be assumed to be relatively flat. This is seriously the most messed up new concrete have ever seen; being only ten feet from the edge along the existing structure to the outer edge, with a difference of over six inches in heightthough this six inch difference is over a diagonal of about 16 feet from SW corner to an area along the north edge about 5 feet from NE corner. I just overestimated for practical purposes using a wedge volume calculation. So it's not like this is actually useful somehow. Even If I knew the correct approach to calculate this, a quick approximation and some overage is the the only practical solution in the field. I came to the forum simply out of curiosity over what kind of math would be used to accurately calculate the volume needed to bring the rest of the surface up to a perfectly level rectangular plane. Figured it is probably much healthier to examine the curious nature of this surface, than to start throwing tools, pulling out my hair and walk away from the job cursing. 
June 7th, 2018, 11:44 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,835 Thanks: 2162 
That answers my first question. Can you answer the remaining questions?


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calculation, complex, volume 
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