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Retaining wall Design (Quick Question): Coulombs Theory 5

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kellez

kellez

Civil/Environmental
Nov 5, 2011
276
Hi everyone, I am having a debate with another engineer and i want your thoughts.

I am using Coulombs Theory to calculate the Total Active Pressure, Pa acting on the retaining wall shown in the picture.

1st step:
calculate the coulombs active pressure coefficient, Ka which is 0.556

2nd step:
calculate the Total Active Pressure, Pa:
Pa = 0.5KaγH[sup]2[/sup]

Ka is the coulombs active pressure coefficient = 0.556
γ is the unit weight of retained soil = 20kN/m[sup]3[/sup]
H is the height of the retained soil

My question is, what shall i use for height of the retained soil, H in the equation above? H1 or H2 (see picture)


SAVE_20200129_135342_cxxplm.jpg
 
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Hi everyone, I am having a debate with another engineer and i want your thoughts.

I am using Coulombs Theory to calculate the Total Active Pressure, Pa acting on the retaining wall shown in the picture.

1st step:
calculate the coulombs active pressure coefficient, Ka which is 0.556

2nd step:
calculate the Total Active Pressure, Pa:
Pa = 0.5KaγH[sup]2[/sup]

Ka is the coulombs active pressure coefficient = 0.556
γ is the unit weight of retained soil = 20kN/m[sup]3[/sup]
H is the height of the retained soil

My question is, what shall i use for height of the retained soil, H in the equation above? H1 or H2 (see picture)
For Rankine, I am sure you need to use H1, but i am not sure if this changes in Coulombs theory.

Thank you everyone for your time.



SAVE_20200129_135342_cxxplm.jpg
 
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In practice, I calculate earth pressure against the surfaces exposed to soil, so H1 H2 is the wall height. However, in addition to soil below the top of the wall, you have a sloping surcharge load to be included in the earth pressure calculation.
 
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retired13 said:
In practice, I calculate earth pressure against the surfaces exposed to soil, so H1 is the wall height.
Click to expand...

did you actually mean H2 instead of H1?
 
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Yes, H2. I'll correct my comment above. Thanks for the catch.
 
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H2 is the wall height. The slopes are included in the equations.
 
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Agree that H2 is the dimension to use in the relation as Ka includes the effect of the backslope angle.

It's trickier when the backslope is broken. In those cases, I'll do a Culmann analysis, including surcharges. Note that in your example, H1 does help with the weight of the stabilizing soil over the heel of the CIP wall.
 
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ok, so everyone agrees that when you use Coulombs Active Earth pressure coefficient then the effect of the slope is already taken into account therefore we use H2 (height of wall) when calculating the Total Active Pressure and not the height of the sloped soil.

I will make you a tricky question now then....

Please have a look at the two pictures below, its the same wall however in the second one, i highlighted the retained soil above the heel just to show what would happen if the highlighted section was also concrete? (it is said that the retained soil above the heel inside the virtual plane is assumed to be part of the wall)

According to everyones comments above, in the 1st case (picture below) everyone would use the height of the wall H to calculate the total active earth pressure Pa
Screen_Shot_2020-01-31_at_8.01.10_AM_gro8xb.png



However in the 2nd picture everyone would use the height of the sloped soil Hh
Screen_Shot_2020-01-31_at_8.01.10_AM_copy_yxws3b.png


Therefore the result is that you will have the same Coulombs Active Earth Pressure Coefficients but use a different height
therefore you will get higher Total active earth pressure Pa for the 2nd case?
 
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I believe the Rankine's theory is not recommend for retaining wall with slopping back fill, for which Coulomb's theory should be used.
 
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I believe the Rankine's theory is not recommend for retaining wall with slopping back fill, for which Coulomb's theory should be used.
Click to expand...

??

The post above doesn't mention Rankine.

I agree with his point. For structural design of the wall use the height to the top of the wall, but for global stability and sliding the height should be to the fill level above the back of the heel.

Doug Jenkins
Interactive Design Services
 
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I agree with your assessment. This is my usual practice in case of sloped grade.
For stability, I consider height H1 for active pressure calculation. Because the largest wedge of soil which is trying to slide or overturn the wall away is applying pressure at face bc. All smaller wedges are supported by retaining wall.
For design of wall, height of soil at wall face is used to calculate the pressure on wall.

I think the difference in pressure coefficients from Coulomb and Rankine is, one method consider friction between wall-soil interface and other does not. And both method have provisions for sloped back fill.

Euphoria is when you learn something new.
 
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IDS,

The failure block shown is from Rankine theory, which valid only on a smooth vertical surface without friction. Coulomb's theory considers all, thus is preferred.
 
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Both are Rankine, evident by angle of the resultant force and the vertical plane.
 
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Shazbot. My original response edited. I can only say that it's been awhile since I considered stability of a semigravity wall... MSE wall is similar...
 
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Agree with using the h1 height for the concrete wall design, and h2 for global stability/overturning effects.

Look up the concept/term called 'virtual back of the wall', basically this states for stability you imagine the forces acting on a virtual plane at the back of the soil that's over the footing (basically identical to your "2nd picture" above).
 
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If you are using Rankine method, then it is correct to use H1. But you used Coulomb's equation to derive Ka, then you shall stick to that method. Since the use of Rankine method is prevalent in the North America, it is difficult to find any practical design case to demonstrate the correctness of using H1, or H2 for coulomb's earth pressure calculation, however, the linked material might provide clue to the answer (pay attention to all parameters defined there and references). Link
 
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Retired13 said:
IDS,
The failure block shown is from Rankine theory, which valid only on a smooth vertical surface without friction. Coulomb's theory considers all, thus is preferred
Click to expand...

OK, I agree with that.

For a cantilever retaining wall shouldn't we take the Alpha angle (back of wall angle to the horizontal) as the line from the back of the heel to the top of the wall?

If I do for the wall in the first post I get a horizontal Ka value of 0.69, rather than the 0.56 quoted in the text.

Doug Jenkins
Interactive Design Services
 
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IDS,

The graph below may help you to compare these two theories/methods. You need to estimate the friction angle of the soil and wall friction in order to calculate Ka using Coulomb theory though. (I suggest to try ∅ = 25°, and δ = 0.5*∅ - 0.75*∅)

c1_ogmpup.png
 
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retired13 - I wasn't comparing the two. The original example says it was using the Coulomb Ka, but the value seems to be much too low.

Doug Jenkins
Interactive Design Services
 
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