Calculating Primary and Differential Settlement of a Covered Steel Tank

[jessikat_93]

1. A covered steel tank (unit weight=80kN/m^3) 15m in diameter x 10m high and with 20mm wall thickness is filled with liquid (unit weight=9 kN/m^3) up to a height of 9.9m. The tank sits on a concrete (unit weight=25kN/m^3) foundation. 15m in diameter x 0.6m thick. The foundation rests on the surface of 5m thick soft, normally consolidated clay above a thick layer of gravel. The geotechnical data of the clay are Cc=0.6, Cr=0.08, Cv=10m^2/year, w=48%. Groundwater level is 0.5m below the surface. Assume the foundation is flexible.
a. Calculate the primary consolidation settlement at the centre of the tank.
b. Calculate the differential consolidation settlement between the centre and the edge of
the tank.
c. Calculate the time for 50% consolidation to occur.
d. The tank was loaded to half its capacity and kept there for 2 years. Calculate the
settlement. The tank was then drained: calculate the rebound.

Homework Equations

a)
Ppc=H0/(1+e0)*Cc log(sigma(fin)/sigma(z0))
sigma(fin)=sigma(z0)+Delta*sigma(z)
sigma(z0)=(Ysat-Yw)z
Delta*sigma(z)=(3Q)/(2 pi z^2 [1+(r/z)^2]^(5/2))

b)
Ppc=H0*mv*Delta sigma
differential settlement= PpcB-PpcA

c)
Cu=(0.197*Hdr^2)/t50
t50=(0.197*Hdr^2)/Cu

d)
I'm very unsure about this part of the question but I think it is similar to part A just with a different weight?

The Attempt at a Solution

I have so far found all the equations I think I need, however there are too many unknowns for me to complete the entire question so I was hoping that someone would be able to shed some light on the situation and help me with finding all the unknowns.

 

[Valkarie]

a)Ppc=H0/(1+e0)*Cc log(sigma(fin)/sigma(z0))H0=9.9me0=?Cc=0.6sigma(fin)=?sigma(z0)=(Ysat-Yw)zYsat=?Yw=0.5mz=?Delta*sigma(z)=(3Q)/(2 pi z^2 [1+(r/z)^2]^(5/2))Q=?r=7.5mb)Ppc=H0*mv*Delta sigmaH0=9.9mmv=?Delta sigma=?differential settlement= PpcB-PpcAc)Cu=(0.197*Hdr^2)/t50Hdr=9.9mt50=(0.197*Hdr^2)/CuCu=?d)Ppc=H0/(1+e0)*Cc log(sigma(fin)/sigma(z0))H0=?e0=?Cc=0.6sigma(fin)=?sigma(z0)=(Ysat-Yw)zYsat=?Yw=0.5mz=?Delta*sigma(z)=(3Q)/(2 pi z^2 [1+(r/z)^2]^(5/2))Q=?r=7.5m