Lateral Earth Pressure

[KeithGray]

I am a bridge designer and have always designed long heeled retaining walls with either at-rest or Rankine Active lateral earth pressure theory. I have always learned that Coulomb lateral earth pressure was for short heeled walls and that the vertical soil pressure could not be used in the overturning calcs when Coulomb was used.

I'm now being told that Coulomb can be used in place of Rankine for almost all walls, including long heeled retaining walls. The theory now is that a wedge of soil develops over the heel that doesn't move and that creates a batter that the lateral pressure acts against. You get friction between the soil and soil that helps your overturning calculations. I think it's limited to 2/3 of the soil friction angle.

I'm also being told that you can take the full weight of the soil above the footing into account when calculating the resistance to overturning.

Coulomb theroy almost always gives me shorter heels so it seems like I would never use Rankine again in my calculations.

Have any of you heard that you can use Coulomb for long heeled retaining walls?
Can you explain when you would still use Rankine?
Can you explain why the engineering community has used Rankine for so long when Coulomb was developed earlier and would have given us more economical walls?

 

[SlideRuleEra]

See Chapter 4 of the "California Trenching & Shoring Manual" for an understandable comparison of the Rankine and Coulomb methods. Here is a link

http://www.dot.ca.gov/hq/esc/construction/Manuals/TrenchingandShoring/ch4_earth.pdf

http://www.SlideRuleEra.net

 

[UcfSE]

The equations used to derive Rankine pressure assume no friction exists between the soil and the wall. Coulomb takes this friction into account. Depending on the actual friction between the soil and the wall, neglecting it may or may not hurt. Rankine theory is simpler to use and the equations are less messy but are also less accurate since, obviously, friction exists in the real world. Often the loss of accuracy isn't enough to really make a difference given the relatively large safety factors used in retaining wall design. There are some other differences in addition.

Before calculators, having much simpler equations makes a huge difference in what engineers prefer to use as long as the results are acceptable.

 

[KeithGray]

Thanks for the replies. I'd like to clarify one point in the question that doesn't seem to be addressed in any references. If there is a wedge of soil above the heel that doesn't move and the Coulomb Pressure acts on that wedge, does the friction force that develops between the soil and soil take into account some of the weight of the soil above the heel. I think that accounting for the weight of the soil wedge that doesn't move would be fine but the soil above and beyond that I think comes into play with the friction component. I think that is why my text book states that for short heeled walls using Coulomb theory, you cannot take the weight of the soil above the short heel into account in your overturning calculations.

Does that make any sense?

 

[DRC1]

Active pressure is the minimum pressure a soil mass generates against a wall. It is devloped as the soil wedge moves down relative to the wall, usually achived through a slight rotation of the wall. Rankine was developed in the late 1700's. It assumes that the lateral force on a wall is the resultant of the active force diagram and is horizontal. It also assumes the failure wedge of the soil to be defined as a straight line. Late (in the late 1800's) Coulomb recognized that friction develops along the wall as the soil wedge moves. This friction angle is on the order of 1/3 to2/3 of the soil friction angle. For level backfill, Rankine and Coulomb values are similar. Coulomb also assumed the failure wedge was defined by a straight line. Log spiral thoery has been developed which treats the failure surface as a complex curved surface and yields more accurate values. Which value you use is a matter of experince in your soil type.
You can use the weight of the soil block above the wall footing. I would not use the value of the soil wall fiction to reduce overturning. It is only used to determing Coulomb coefficents.
You ask if you can use the full weight of the soil over the heel. Yes however if part of the backfill is below the water table, then use the bouyant unit weight.
To answer your last question,the wedge of soil needs to move. I do not know why the soil above the heel would not be counted in the calculations, regardless of the heel length. However on a final note, in order to use active pressures, your structure must be able to tolerate rotation. For a 20 ft high bridge abutment, the anticipated movement would be on the order of 1/4 to 1/2 inch lateral movement. Thus for structures for which lateral movements are not desirable, Ko (at rest) coefficents should be used.

 

[BigH]

DRC1 - agree with your nice post - but . . . if I remember correctly, it was Coulomb in about 1775 (I remember this from "Civil War" days (if you are British!) and it was Rankine in about 1860 or so. (I just did a check in Taylor's book and he confirms Rankine was 1860s - but Coulomb was in 1773). I always wondered why we consider Rankine since it is a 'special case' of Coulomb (friction at wall set as zero) - but go figure -

I would like to know the reference to the short heel comment as given by Keith Gray in his last sentence - 6 March posting.

 

[KeithGray]

BigH, The reference I have is Principles of Foundation Engineering, Fourth Edition by Braja M. Das. It's on page 391 and it shows a gravity wall with a short heel. When it shows it being analysed with Rankine, it shows the weight of soil above the heel contributing. When it shows Coulomb it does not and then in the text it states that "If Coulomb's active pressure theory is used, the only forces to be considered are Pa(Coulomb) and the weight of the wall, Wc."

DRC1, you said that you wouldn't use the soil wall friction to reduce overturning? Does that mean that you wouldn't incline the resulting active force by the delta angle? That's really the core of my question. I think that vertical component, which factors in friction and thus some normal force, cannot be used in combination with the full weight of soil above the heel. I think it's double counting that contribution.

Thanks again for your thoughts.

 

[Panars]

I have the 2nd edition of Das, and I think I found the reference on page 291. It appears to me that Das is not including the weight of the soil wedge above the heel because the Coulomb active pressure is applied to the face of the gravity retaining wall, not the wedge of soil. So, the wedge of soil above the heel is not part of the free body in a free body diagram.

Whether or not to include the weight of the soil wedge above the heel is decided primarily based on the geometry of the wall. I would say that if you were using Coulomb's method to analyze a wall with a long heel and the active pressure was applied to the soil wedge above the heel, then you would include the weight of the soil wedge in the overturning calcs.

 

[shockstressed]

Horror
I would think you run a risk of losing the wall by a slip plane, rather than friction assisting the retention
Mike Stagg

 

[KeithGray]

Panars,

What I've been told about Coulomb and long heeled walls is that there is a wedge of soil that doesn't move, that sits on the heel. It is triangular shaped, and mimics a back batter on the stem. My understanding is that the Coulomb active force is applied to that triangular wedge. Therefore my thought was to use the weight of the triangular wedge in the overturning but not the rest of the soil that would make the full rectangle that you would count if you were using Rankine, where the active pressure acted on the vertical face at the back of the heel. That seems in line with what is shown in Das. Would you agree with that?

 

[Panars]

KeithGray-
I agree and would include the weight of the triangular wedge of soil that doesn't move.

As an additional note, AASHTO LRFD code goes into this in some detail on page 3-65. Both the 17th edition and the LRFD 3rd edition show Coulomb active earth pressure being applied to a vertical surface at the base of the heel on a semi-gravity cantilever wall.

 

[DRC1]

Typically there is a vertical projection from the edge of the heel and it is assumed this rectangle of soil moves with the wall. an inclined failure plane results from the edge of the heel and risesat about a 60 deg. angle, but this is not the plane to which the pressure is applied. It is applied to the vertical face.
To answer your earlier question, the columb coeeficent is the lateral(horizontal) earth pressure coefficent which considers the effect of wall friction. It is a different computation than Rankine. I do not include the friction force in the wall stability computations. I assume the resulant lateral force is horizontal. Although for active and passive coefficents, I generally use log spiral, and I generally use Ko (at rest) for permenant aplications (except sheeting).

 

[KeithGray]

Thank you all for your help giving me perspective on this issue.

 

[NoWittyHandle]

My understanding is that the Rankine Method is used for flexible retaining walls and that the Coulomb Method is used for gravity walls. My understanding is also that the amount of wall friction due to active pressure is small. Wall friction does have a dramatic effect on passive pressure.