Offset Surcharge - Bousinessq History of Modifications

[RFreund]

Can someone clarify the history of exspirements or modifications to Bousinessq equation for offset surcharge?

I have been researching this topic the last week pretty extensively and will have some questions based on the actual calcs that I will post in a different thread.

I'm curious as to why the same equation is used with credit given to different people. I'm curious of each persons contribution.

Point Load modification: Terzaghi (most commen), Spangler and Midlin.

Line Load modifications: same as above.

Strip Load: Credit seems to be given to Tang. However it does not appear that this calculation is modified. The equation is given in Poulos and Davis and there is no comments that it is modified but some say it is modified by Tang. Are there any modifications to the strip load equation (except for the factor of 2 debate)? If it is not modified I should be able to discritize a strip load into a number of point loads and obtain the same answer however this does not seem to be the case. I will post more on this later in a different thread currently I'm interested in the history.

Are there any texts that explain/discuss the text results and the modifications?

Thanks in advance!

EIT

 

[yakpol]

Bousinessq developed formula only for a point load. Modifications you mentioned are either simplification for one particular value of poisson ratio or integration of original formula (e.g. line or strip loads).

 

[FixedEarth]

Let us say you have vertical strip load and no excavations. The lateral stress due to this strip load will be per Boussinesq equation. Now you make an excavation, build a wall and you are obstructing the lateral stress load path with a wall, the lateral stress increases to about 2 times the Boussinesq equation value.

Some researchers say this is because there is a mirror image, others say the new wall can not take shear stress, yet some say measured experimental values are just 2 time the theory. You pick the explanation you like, just plug the 2.0 in the numerator!

For references, try Tschebottariof, R.F. Scott, Jumikis and Cernica.

 

[RFreund]

I have created a spreadsheet as Bowels recommended in his 4th edition (or maybe it was his 5th edition) where you only use Bousinessq's equation so that you may use any value of posions ratio and also multiply by whatever factor you deem necessary. You can adopt the equation for line strip and area by breaking the uniform load into discretized point loads.
I thought that only the point and line load formulas where modified by Terzaghi and that the strip load was just an integration but no modification. Is that correct or is the strip load equation modified as well?

The equation I refer to is
Pstrip = k* Q/pi * (beta-sin(beta)*cos(2alpha))
where k=1 for very flexible wall. k=2 for rigid wall

I ask because when I compare it to my spreadsheet I get different solutions. Also what is the modification?

EIT

 

[paganel]

Check the file attached,it will explain.