Passive earth pressure using theory of plasticity

[WBell]

I am trying to create a Mathcad worksheet to calculate the active and passive pressure coefficients using the method described in Bowles, Foundation Analysis and Design, 5th Ed. Specifically, there are 4 equations (pp. 609-611) given for the "passive log-sandwich mechanism" (see attached).

Although I have been able to solve the equation for the passive pressure coefficient, K_p for a smooth wall, the values are orders of magnitude greater than the published values in the text. I have carefully checked the inputs and the equation and have not gotten a satisfactory solution.

Any comments regarding the method or solutions for the equations are appreciated.

 

[PEinc]

Did you check to see if there is a publisher's list of errata for the edition of Bowles that you are using? Maybe there is a typo in the equations.
EDIT: I just checked Bowles' smooth wall equations in the 4th edition, Page 490, and they look the same as those you attached. The equations have an awful lot of plus or minus terms. Could one or more of those be your problem?

http://www.PeirceEngineering.com

 

[HTURKAK]

I would have two commnents


1-Pls look to the following para.

(In solving Eqs. (11-10) through (11-13), it is necessary to solve for the maximum value of Kp or Ka. The maximizing of these equations depends on the two variables ρ and φ. This requires a search routine in computer program B-23. The values of the two dependent variables are initialized to approximately
ρ = 0.5(α + β)
φ = 0.2(α + β)
With these initial values, the search routine is used to revise the values until convergence is
obtained. In most cases values from which Kp is computed are found after not more than 20 iterations...

So, ρ and φ shall be selected with iteration..

2- the plus or minus shall be selected for Ka : upper sign regardless of plus or minus Kp= lower sign regardless of plus or minus..



I hope my respond help you..








Not to know is bad;
not to wish to know is worse.

NIGERIAN PROVERB

 

[dik]

I'm not a geotekkie, but the statement seems a tad silly...

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

 

[Milliontown]

I'm not a geotekkie, but the statement seems a tad silly...

It makes sense to me, but I am more than a tad silly.

Say you have a footing for a bridge located at the toe of an embankment, the passive pressure acting on that footing would be conservative if it was overestimated; you would design for that larger loading on the footing.

If you need the passive resistance say in a cantilever wall or for sliding stability, overestimating the passive pressure would be unconservative. It all depends on what you the passive pressure is acting against.

 

[dik]

If it consistently overestimates the strength, then it is very likely conservative, else there is another mechanism at play.

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik