I need to find the theoretical depth of embedment, D, using the free earth suppo

Question

I need to find the theoretical depth of embedment, D, using the free earth support method.
The givens are a surcharge qu= 350psf
L1=10.8 ft
L2 = 21.6 ft
the layers are sand with density = 108 lb/ft^3
next layer of sand with sat density 125 lb/ft^3
last layer is clay with c=850 lb/ft^2

I have figured out the following,
Ka=0.27
Kp=3.69
O'1=314.92 lb/ft^2
O'2=680 lb/ft^2
qu*ka=94.5 lb/ft^2
Sum of the pressures = 15507.8
sum of moments around E = 144710.7
z = 9.3 ft

This is where I am having trouble. I don't know how to figure out O'6 with having a surcharge in the problem. The formula I have is O'6=4c-(density*L1 + density' *L2). I feel like I am getting the wrong answer because my value is 881.4. Using this I get a theoretical depth = 9.75, I think the answer is somewhere around 12 ft. Can anyone tell me what I am doing wrong? Thanks.

Explanation / Answer

Hi I have done the solution for this in my notebook. But the solution is too big , I cannot type it here.. So please rate me Lifesaver and I'll share the answer with you through email or cramster inbox. I don't do this generally, but I have no other option here because there's very less time remaining... you need not worry as I have the solution ready

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