Boussinesq Surcharge Formulas

[cancmm]

In using conventional Boussinesq surcharge formulas, I'm finding that the formulas are erroneous in that there is no upper limit to the applicability. In other words, I could place a strip load surcharge half a mile away from a 50' high wall and still see appreciable lateral loads being imposed onto the wall. How do others handle this situation in applying a reasonable upper limit?

Thanks!

 

[fattdad]

I just can't believe the load would be "appreciable." The angles would be pretty acute, eh? Please post the equations you are using along with the magnitude, distance and width of the load. That way it'll be easier to appreciate your concern.

we had a string of threads on horizontal loads on retaining walls owing to surface loads. No doubt there are a range of potential problems (i.e., do you multiply the loads by 2).

f-d

¡papá gordo ain’t no madre flaca!

 

[cancmm]

fattdad,

Angles are definitely acute but they do have an impact nonetheless. And yes, I am using the notorious factor of 2 in the equation posted below.

Sigma = (2*q/PI)(Beta - Sin(Beta)Cos(2*Alpha))

The half mile was a bit of an exaggeration but it does highlight the scenario. Here's a set of parameters for discussion:

1000 PSF surcharge, 1000 foot wide strip, set back = 500 feet, wall height = 50 feet

Intuitively I would expect there to be a negligible effect on the wall at this distance but my results indicate it is about 15% of a full uniform load. Now if I increase the setback to 1000 feet, it's still about 6%.

I recall some theory that surcharge loads beyond the active plane are generally disregarded. Perhaps this applies?

 

[BigH]

Forget for the moment the wall. Determine the horizontal stress at a point from the line load at 50 ft depth. See Poulos and Davis (page 37). For a strip load 500 ft from the wall of 1000 ft wide, x/b equals 2. For a point 50 ft deep, z/b = 0.1 (50/500). On the table, the nearest point is z/b = 0.25 for an influence factor of 0.0987. With z/b = 0 implies influence factor is 0, then at 50 ft depth (the deepest part of the wall), the influence factor is 0.04. With the line load of 1000 psf, 0.04x1000 = 40 psf. This isn't even equivalent to a foot of water acting at the base of the wall - of course, it is triangular application . . . so am not sure how you are getting such a high "load" on the wall from such far away surcharge. . . even if you are "doubling" as some suggest. I wouldn't even consider it . . . Surcharges can be taken into account using the graphical Culmann method - but you will see you are too far away

 

[PEinc]

It is not uncommon to ignore surcharge loads that are located behind the theoretical failure plane. Some design specifications require the surcharges to be as much as the height of the wall behind the wall before they can be ignored. Yes, Boussinesq will give surcharge pressures even though the surcharge is far from the wall, but, as pointed out, the magnitude of the lateral pressure decreases quickly.

http://www.PeirceEngineering.com

 

[RFreund]

Such a great subject and seemingly so many different good answers for it.

As for an upper limit - you can use the failure plane/angle by Coulomb or by trial wedge (Culmann). A 1:1 failure angle is frequently used and is usually conservative. Terzaghi gives some insight as well but I need to dig this up again. There are a couple good discussions on here about this topic as well.

Side note:
I have a problem with the strip load equation typically used (also referenced above by Poulos and Davis) in that it does not produce similar results as if you were to discretize the strip load and sum the pressures from a series of point loads from the 'original' point load Boussinesq equation (as Suggested by Bowles in his 4th Edition) . I have a post on my blog about this that I can like to later.

EIT

http://www.HowToEngineer.com