Rankine Passive Condition (Coduto vs Bowles)
Rankine Passive Condition (Coduto vs Bowles)
(OP)
I am trying to compare how Coduto and Bowles calculate the Passive Pressure using Rankine. I am doing this for my personal knowledge - I tend to learn something when I have a difficult time figuering something out. I have spent some time and I can't get Coduto's and Bowles answers to agree.
I would really appreciate if someone can help me out in determing if I am doing something wrong with my interpretations.
I would really appreciate if someone can help me out in determing if I am doing something wrong with my interpretations.





RE: Rankine Passive Condition (Coduto vs Bowles)
If you can't find that, go back to early writings of Terzaghi or perhaps Taylor.
Most modern writers are using earlier work of others when they write books these days, especially when it comes to something like Rankine.
RE: Rankine Passive Condition (Coduto vs Bowles)
Conduto does it somewhat differently in that he doesn't "change" kp to the horizontal by hiding cos(beta) into the fancy equation - he forces you to use kp and then multiply by cos(beta) (see equation 23.11 - note he has kp*cos(beta) but Bowles just has kp' (where the ' is the combo effect).
In another "way" Conduto x cos(beta) should equal Bowles. From your post, 3.654 x cos(beta) =(?) 3.598.
cos(beta) = 0.9848 xo 3.654 x .9848 = 3.598. I'd say they are equal. The "cos(beta)" term really doesn't become that important until beta approaches 25deg when the cos(beta) = 0.9.
Anyway - that's my take on it. You just forgot to multiply Conduto's term by cos(beta).
RE: Rankine Passive Condition (Coduto vs Bowles)
1. Coduto Eq. 23.13 in his book is not multiplied by cos(beta)
2. Coduto Eq. 23.11 (Normal force between soil and wall) is multiplied by cos(beta).
3. If I multiply Codutos Kp by cos(beta) as you shown in your calculation to obtain Kp=3.598, wouldn't that mean I would be multiplying by cos(beta) twice. Once in the Kp calculation and another one in the Pp/b.
Thanks For Your Help.
RE: Rankine Passive Condition (Coduto vs Bowles)
RE: Rankine Passive Condition (Coduto vs Bowles)
Coduto:
Kp [Eq. 23.13] = 3.654
Pp/b [Eq. 23.11] = 27.204 (normal force between soil and wall)
Bowles:
Kp [Eq. 11-8a] = 3.598
Pp [Eq. 11-9] = 27.200 (Force at a wall angle Beta)
Pph [Bowles, page 603] = 26.78
1. Using Coduto's formulas to find Pp I get 27.204. And using Bowles formulas to get Pp I get 27.200. Both numbers agree.
2. However, Coduto is calling his Pp/b the normal force between soil and wall). His Figuere 23.9 shows Pp/b basically horizontal.
3. From his Figures Bowels is calling his Pp Force at wall angle of beta, then he goes ahead and calculates the horizontal component by multiplying Pp by cos beta.
I guess that is my greatest confusion that Coduto and Bowles Pp numbers agree based on the formulas they are using (Coduto using cos beta in his Pp formulas and Bowles using cos beta in his Kp formula). BUT Coduto is calling his Pp normal force between soil and wall and Bowles is calling his Pp Force at a wall angle of beta.
Would really appreciate if you can help me out in clarifying this. I have attached Coduto's figure 23.9.
RE: Rankine Passive Condition (Coduto vs Bowles)
RE: Rankine Passive Condition (Coduto vs Bowles)
1. In my example for Bowles Force to agree with Coduto's Pp Horizontal Forcce, cos(beta) is only used ONCE, in the Ka term.
2. But in Bowles Example on page 604, to find the horizontal force component, he is using the cos(beta) TWICE, once in the Ka term and then in the Pa,h term.
RE: Rankine Passive Condition (Coduto vs Bowles)
RE: Rankine Passive Condition (Coduto vs Bowles)
RE: Rankine Passive Condition (Coduto vs Bowles)
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RE: Rankine Passive Condition (Coduto vs Bowles)