Coulomb's passive pressure equation may be flawed

[yahoo123]

http://en.wikipedia.org/wiki/Lateral_earth_pressure

When I use the following values, the Kp coefficient a whopping 46!!!
pheta = 5
beta = 20
phi = 30
delta = 15

When using some other combinations, the Kp value can reach in excess of 100! Is the Coulomb's passive pressure equation flawed?

 

[BigH]

Roughly the first case you describe, the kp value should be about 6 to 6.5 (see Bowles, see Fang). Fang, for logrithmic surface, for phi = 30, the kp value ranges from 3 to slightly above 6. Did you happen to use excel where the angles have to be put in as radians instead of degrees?

 

[yahoo123]

How did you get 6 to 6.5? I did it in both excel and confirmed it by hand a few times and the same answer. I converted the degrees to radians when I did it in excel.

I also tried the Coulomb's equation in a different written differently (Civil Engineering Reference Manual 10th Edition by Lindeberg) and I still got the same answer.

 

[BigH]

First off, the equation given in the wikipedia is not the normal one that I have seen for Coulomb. See Bowles 6th edition, equation 11-6 (page 596)for example. I normally wouldn't "calculate" the value - I'd go to a table. For the value of 6 to 6.5, I went to Fang, Figure 6.9 at 30 deg to get a typical value of 6 for level backfill (log-spiral). As the wikipedia doesn't well define the terms (a sketch showing the terms would help) I used phi30, delta 16, Slope behind increasing at 5deg - you get 6.6. So 6 to 6.5 seems to be in the right ballpark. Do a check on other sources for the formula as well - most use a sin^2(alpha - phi). In Bowles table, the minimum value of kp is 1.914 (phi = 26deg, delta = 0, slope behind wall decreasing at 10deg, vertical wall) to an extreme of 87 (phi = 42deg, delta = 22deg; vertical wall and slope increasing at 15deg.

 

[LCruiser]

More proof Wikipedia is a failed experiment??

 

[DRC1]

Typically the angle of the back of the wall is measured from horiz. not vert. As Big H said, the equations don't look familiar. (there are a couple variations of the equations out there, but they all look fairly similiar and yield similar results) For the numbers you gave with a positive 20 deg backfill, 85 deg backslope to the wall, phi =30 and wall frition = 15deg, I got Kp = 11.4, using log sprial charts I got Kp = 11.9
Bottom line is you get what you pay for and wikipdia is worth its price.

 

[PEinc]

I used the equation out of Pile Buck's Steel Sheet Piling Design Manual. I used Phi = 30 degrees; wall friction = 15 degrees; slope behind wall = 20 degrees; slope below wall = 5 degrees. Kp = 6.310

 

[yahoo123]

I also used the Civil Engineering Reference Manual, which is written differently than the one on Wikipedia, but got the same result of 46.

Very strange.

 

[PEinc]

When I gave my previous answer, I assumed that the slope in front of the wall was an upward +5 degree slope. The original post just said 5 degrees. If the slope is a downward slope (-5 degrees), my Kp reduces to 3.961.

In Bowles' 1968 book, his table give Kp = 4.976 for phi = 30, beta = +20, delta = 15, a flat ground surface in front of the wall base, and a vertical wall. Therefore, if the ground slopes downward at 5 degrees, his Kp should be less than 4.976. Bowles' table does not list Kp for the downward slope.