Elastic Methods for Strip Load

[RFreund]

In Foundation Analysis and Design, Bowles 4th Edition, he recommends discretizing a strip load into a finite number of point loads, then finding the pressures via Boussinesq's equation for a point load acting on a semi infinite elastic mass. Then adding the pressures caused by the point loads to find the pressure on a retaining wall due to the strip load.

I have compared this method to (what I thought was) the integrated form of the Boussinesq formula for point load acting on an elastic 'mass'. The results do not match. You may say this is due to the incorrect Poisson's ratio being used (plane strain vs triaxial) however I have checked this as well and even for a corrected Poisson's ratio the difference is large.

See attached.

This has been a real thorn in my side for a long time. Can any one shed some light on this?

Thanks in advance!!

EIT

http://www.HowToEngineer.com

 

[BigHarvey]

There is a Boussinesq solution for strip loads.

 

[RFreund]

Right, my question is why does the Boussinesq solution for a strip load not even come close to matching the results found by using Boussinesq solution for a 'strip' of point loads?

EIT

http://www.HowToEngineer.com

 

[BigHarvey]

I tried a 10 m long strip load with 1 ton/lm and placed a point at 1 m perpendicular to one end and 10 m depth. With the strip solution I get a stress of 0.0275 tons/m2.
Now if i use 10 point loads of 1 ton and calculate the stress at the same location Iget 0.0247 tons/m2, ie 90% of the previous value. Is that what you call "not even close" ?

 

[RFreund]

I will try to duplicate your calculation as I would call that 'very close'. I actually hope that I am in error. See attached to make sure we are comparing apples to apples. And did you have to use metric? I don't know what those units are!!

EIT
www.HowToEngineer.com

 

[BigHarvey]

I'm french, hence the metric units. I use a chart by RE Fadum for the strip load solution ( see attachment )but the equation is not given on the chart.

 

[RFreund]

I joke about the units. I realize we (US) are the only ones that use this crazy system of units.
As for the chart - Interesting, I will look into this and see how it compares.

Do you use y = 1.0 for infinite strip load?

EIT

http://www.HowToEngineer.com

 

[BigHarvey]

I used y=10m and 10 x l ton loads spaced 1m ( first one being at y=0 ). These charts were distributed during late Jorj Osterbergs's soil mechanichs classes ( 1980/1981 ) at NU. I believe they must be from the 40's.

 

[BigHarvey]

I forgot 1 ppoint load in my discretization : the result is 0.0294 tons/m2 instead of 0.0247. The difference with the strip solution is 7% in this case.