Uniform surcharge offset from tank wall 1

[waytsh]

I am looking for an equation for the lateral pressure from a uniform surcharge located several feet back from the wall of a buried tank. Everything I have considers a uniform surcharge set directly against the structure. If anyone can help me out or point me to a good reference which addresses this situation I would greatly appreciate it. Thanks in advance.

 

[tincan]

From Dirt 101

h =(p/3)[arctan(x2y1/zRx2)-(x2y1z)/(x2^2+z^2)Rx2
arctan(x1y1/zRx1)+ (x1y1z)/(x1^2+z^2)Rz1

h = horizontal unit pressure at point on wall
p = surcharge unit loading
x1 = distance from wall to face of surcharge
x2 = distance from wall to back of surcharge
x12-x1 = width of surcharce normal to wall
y1 = lenght of surcharge
z = depth of point on wall
Rx1 = (x1^2+y1^2+z^2)^0.5
Rx2 = (x2^2+y1^2+z^2)^0.5

which is why we usually say screw it, take 1/3 the surcharge and apply it to the wall.

Best, Tincan

 

[waytsh]

Thanks for the reply. That is pretty cumbersome. Does the 1/3 of the surcharge assume that it is directly against the retaining wall? I have found something similar from the Army Corps of Engineers. I am curious to see how the results from the two equations compare.

I guess it wouldn't hurt to give a little background on my situation and what I am trying to accomplish. I have a rectangular concrete tank which was originally designed to be buried with the top of the tank at grade. Because of required piping elevations and gravity feed requirements the tank will need to be 5' lower than originally planned. In order to maintain the current configuration of the tank I was planning to locate a retaining wall around a portion of the perimeter to reduce the effect of the additional overburden. My dilema is finding out how far from the edge of the tank it needs to be to keep my tank walls at a resonable thickness. Just in case you were curious.

Thanks again for taking the time to type out the formula. I do appreciate it.

~ Waytsh

P.S. Do you have a good foundations reference that you would recommend?

 

[tincan]

The assumed 1/3rd is the horizontal pressure at the face of the tank. It's a direct take off of the old angle of repose for a 1 on 1 1/2 back slope. Am out of pocket. will chect book titles later.

Best, Tincan

 

[connect2]

Can't go wrong with Boussinesq, it's conservative and thats good given that your trying to define a linear elastic half space ???, and found in all the texts and modelling literature. Can get crazier and more mathmatical if you want? Agree with Tincan. Anyways the cost of forming and placing a 10" or 12" wall ain't much different concrete material costs and reinforcing aside. More important in a liquid tank is jointing both thermal loads and shrinkgage. In any case way cheaper to provide additional reinforcing in the tank wall than building a secondary wall to handle the increased backfill height. There's no such thing as 'Reasonable'.

 

[waytsh]

Thanks for the input connect2. The tank is actually precast and only a small portion is against the embankment. The way our forms are set up and with the configuration of the tank it would actually be very difficult to change wall thickness. It is much easier for us to pour a small retaining wall for the affected segemnt. Assuming of course that I can make an accurate anaylsis of the condition and determine how far back it would need to be.

 

[tincan]

?Have you checked the box capacity for the additional depth?
Also, we normally figure that anything outside a 1:1 slope has little or no effect. From the bottom of the tank go up on a 1:1 for the placement of the retaining wall. Sketch this out and see how it plays.
Tincan

 

[connect2]

yes your precast, post tensioned tank?, is then no doubt designed only for tension or outward 'hoop' stresses of the contained product so your problem is then one of determining the effect of an asymetrical compression load from the outside, right? which you feel it would be simplier to design a seperate structure to deal with this load, might be right in which case you have a relatively straight forward retaining wall problem which if you have a rigid wall, no translation, no rotation, Ko, shouldn't transmit load to your tank wall, however most tanks precast or not have ability to support a degree asymetrical compression loads, but then i'm not familiar with the design or the loads your involved in.