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Existing wall footing depth

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There is absolutely no way to figure out what depth is required from the provided information. What parameter are you even using to calculate this? Bearing depth is effectively independent of the applied load and is typically governed by geotechnical considerations
 
OK sounds like your boss may not be the best teacher here.
Let's start from the top.

There is overall so little information in this calculation that there is little we can actually review for you. All we can do is confirm that 1000/1500 = 0.67ft = 8"
Otherwise, all we can offer are general thoughts for you to consider and check yourself
I will outline some below so hopefully they can get you across the line

Firstly, is the load you've shown the new TOTAL or load or just the additional load?
You need to make sure you're accounting for the TOTAL load as you don't want to overstress the soil

Secondly, the q = 1500PSF value, is that factored at all (have you applied a strength reduction factor or some kind of factor of safety)
Where did you get that value from? Did you assume it, or was it a value provided by a geotech or from your own site investigations?

Thirdly, I would normally expect two loads and two capacities - a serviceability check, and an ultimate check.
In my country we would check the ultimate load (a larger demand) against a FOS of 2 (a strength reduction factor of 0.5)
We then also check the serviceability load against a FOS of 3 and design to the worst case

Fourthly, your load is PLF (I assume this is pounds per lineal foot?) and your capacity is PSF (pounds per square foot?)
So when you divide 1000PLF by 1500PSF you end up with 0.67 feet WIDTH not depth i.e., the 8" you've calculated is the minimum required width of footing
In my opinion the conclusion of 15" assumed therefore OK is a big concern - your role as the engineer in this case is to verify that the structure can handle the load, not just to assume a number larger than your calculated requirement
Is there an original detail or site investigation that underpins this 15" assumption? If so, don't say 'assumed', state the basis for that decision.

Finally, the devil is in the detail with these kinds of jobs. Adding another story to a foundation isn't just as simple as checking the bearing area. Is the extension over the whole house, or just part of it? New settlement will always occur with the added load even if your numbers say it's OK, so you want to consider whether there are any displacement-sensitive elements that could be a concern with a few millimetres of settlement.
How about loading nature - is it really a line load, or are there large point loads to consider? Is there reinforcement in the foundation that can help distribute any concentrated loads? What is the likelihood of fill or soft material that could lead to differential settlement (particularly if your loading is uneven)?

Best of luck with the checks


 
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