AASHTO traffic surcharge on MSE Wall 2

[TehMightyEngineer]

Per AASHTO LRFD Bridge Design Spec. 5th ed. (2010) article 3.11.6.4 the live load surcharge can be ignored if it is applied on the backfill greater than 1/2 the wall height behind the back face of the wall. Makes sense.

Now, for a traditional wall this is easy and obvious. However, for a MSE wall what is the back face actually defined as? I think it should be the back of the reinforced earth area but my boss and P.E. thinks it should be the back face of the block wall in front of the reinforced earth. This makes sense to me but I'm not sure if it's the intent of the code. What is the opinion here?

Maine EIT, Civil/Structural. Going to take the 1st part of the 16-hour SE test in April, wish me luck!

 

[Doctormo]

"I was wondering if the live load surcharge gets reduced or terminated at a depth (such as the 8' limit for live load and live load surcharge on buried structures such as culverts). Do you know of any prevision for this?"

There is no MSE wall provision for varying a standard uniform live load with depth since the load is considered an infinite condition in all directions and would not dissipate with depth as a strip or line load would. This situation does not happen in reality but the load model is very simplified (like the 2' of soil surcharge) and is just q x Ka for active earth pressure.

The culvert situation is different based on the size of the pipe/structure, depth of cover, etc. Soil arching action may occur that dissipates load with depth so the model for a buried pipe or structure code can have a special provision that accounts for these conditions. The reverse is true if a pipe/structure only has minimal cover and a wheel load can be right on top of the pipe/structure where the uniform surcharge and load reductions would not be appropriate from a structural sense.

 

[TehMightyEngineer]

Makes sense, thanks for all your help.

Maine EIT, Civil/Structural. Going to take the 1st part of the 16-hour SE test in April, wish me luck!

 

[fattdad]

just recall if you are using horizontal stress equations from Boussinesq within your spreadsheet, the computed values must be doubled. When you use the Boussinesq equations you calculate a change in horizontal stress at a given depth and radial distance from the applied vertical load, but the assumption is there is more soil beyond the study point. In retaining wall calculations we typically calculate the change in horizontal stress at the face of a retaining wall where there is no soil on the opposing side. To offset this difference, the calculate load is doubled. This is not arbitrary!

Now if you are calculating the load acting on the back plane of the reinforced zone (what I'd do), the issue may be moot. Not sure if it'd be consistent with Boussinesq, but at least there is the 0.7H (or whatever the grid length turns out to be) that separates you from the point of no soil.

Not to confuse that is. . .

f-d

¡papá gordo ain’t no madre flaca!

 

[Doctormo]

f-d,

You are taking this thread past the point of simple uniform live load surcharges on MSE walls and entering the controversial area of when and where to apply and double Bousinesseq lateral loadings. The text book and design guide formulas would have the 2X built into them if it was as simple as "always double the load" and the simple formulas do not address an anisotropic reinforced mass (all classical earth pressure theories have this limitation). It is actually more a function of the type of retaining wall system, type of backfill material, relative density, and so on that seems to increase the stress on the wall from the formula values.

The AASHTO MSE wall sections actually have methods of distributing strip loads and footing loads that do not use Boussinesq formula and are based on simple Ka (and Ko conditions for inextensible reinforcement) and vertical/lateral stress distributions. I can't say that I agree with some of these methods but they are part of the AASHTO code for MSE walls referenced in this thread.

Not so sure TehMightyPirate asked for this discussion.

 

[TehMightyEngineer]

Well, my question has been answered to a degree I'm satisfied with. I'm always willing to learn and had never heard of Bousinesseq lateral loadings until now. By all means, educate me!

From what I can tell I think Doc is correct in that the AASHTO code does not use Bousinesseq loadings when you consider strip loads or other vertical loads above the MSE wall. It definitely doesn't when you consider live load surcharge from vehicles.

Maine EIT, Civil/Structural. Going to take the 1st part of the 16-hour SE test in April, wish me luck!

 

[fattdad]

for the following conditions:

Q = a given point load
z = a given depth
r = a given horizontal distance, and
R = a given hypotenuse

The change in horizontal loading is given by,

Delta H = (3Q/2*pi)(z*r^2/R^5)

Please realize that the horizontal distance value "r" can be at any radial point surrounding Q (i.e., our
inclination is to consider only those points on a wall closest to the point load, but the equation is for any point).

Here's the line load equation:

Ql = a given line load (force/length)
Z = a given depth
X = a given horizontal distance perpendicular to the line load
R - a given hypotenuse

Delta H = (2Ql/pi)*(z*x^2/R^4)

When applying these formula in a spreadsheet to solve horizontal loads acting on a wall, the answers are doubled.

These are the Boussinesq equations (well two of them at least).

Hope this helps. . . Sorry if I confused.

f-d

¡papá gordo ain’t no madre flaca!

 

[Doctormo]

TehMightyPirate

Pictures will be a bit more helpful. You can find some of the Bousinesseq information in AASHTO LRFD 2012 also. Starts in Section 3.11.6 - Surcharge loads; ES and LS (pp 3-123 in my edition) and is followed by the MSE wall methods. There is also the trial wedge method which will give you different answers yet and is equally valid in its own way.

You will have to look at the various geotechnical text books such as Bowles to get background information on lateral pressure distribution as different methods are appropriate for different situations. Earth reinforced structures violate the basic assumptions of Coulomb, Rankine, and Bousinesseq so the internal analysis with surcharges is a bit of a mystery still.

 

[PEinc]

fattdad, you wrote, "if you are using horizontal stress equations from Boussinesq within your spreadsheet, the computed values must be doubled." Bowles' 1968 Foundation Analysis and Design, Page 299, Eq. 6-26, does talk about doubling lateral pressure to more closely match measured pressures for a Boussinesq LINE load. However, there is no doubling indicated for point loading or strip loading. I have not seen this doubling suggestion written in any other books nor have I ever seen any owner agency (e.g. railroad or DOT) require this doubling. In addition, I discussed this with a very prominent and well published geotechnical engineering professor/researcher/author who also has never heard of this doubling. Can you please cite a reference for doubling the already very conservative Boussinesq lateral surcharge pressure?

http://www.PeirceEngineering.com

 

[fattdad]

I just have my notes from J. M. Duncan. I was taught in grad school that any "free-field" elastic solution (i.e., Boussinesq horizontal stress equations - line load, point load, etc.) need to be doubled. This from correlations by Spangler in the 1930s. I also have a note that Racine made the correlation. I just don't know who Racine is and I don't think I mean to write Rankine and got my ink pen confused.

Sorry I can't be more precise. I can look further into this however.

f-d

¡papá gordo ain’t no madre flaca!

 

[RFreund]

I think there may be some confusion here (possibly by me).
Boussinesq doesn't really have a 'line or strip load' equation. He only has an elastic solution for a point load. You can discretize an area and sum the results of the individual point loads. However this will not match the results of the "Terzaghi modified" line load equation.
So I have heard of using the Boussinesq (elastic) equation for a point load and discretizing an area (Bowles does this in his fourth addition) adjusting poisson's ratio and applying a factor of saftey.
I have also 'heard' of using the "Terzahi modified" equations and applying a FS for rigid walls however I agree with PEinc that I do not see it frequently in texts.
One text that has a FS of 2 when using modified line and strip loads but not for point loads is Principles of Geotechnical Engineering" 2nd Edition by Braja M. Das. He also gives the resultant force from integration siting Jarquio (1981). I should note that he incorrectly uses H opposed to pi in the denominator of the strip load equation. Also he does not have this section in his more current editions.
Gotta love the topic of lateral earth pressures, even as a structural.


EIT

http://www.HowToEngineer.com

 

[PEinc]

One more note, railroads (especially Conrail) have required Boussinesq strip surcharge load analyses for many years on many projects. Conrail does not require the load to be doubled. However, Conrail also requires a Cooper E80 rail load which itself is very heavy. Knowing how conservative Conrail is, I would think that Conrail would not hesitate to require a doubled surcharge load if they had the chance or saw a reference recommending such. I have used Boussinesq many, many times without doubling the answer. I have also used many times Boussinesq lateral pressures which were reduced for flexible and semi-flexible retaining walls (sheeting walls). I've never been accused of being too conservative (except by project foremen who are always smarter than the engineers) and I have a pretty good track record in wall design. I have to think that doubling Boussinesq is not necessary. But, it's your design. Do as you think necessary.

http://www.PeirceEngineering.com

 

[fattdad]

This discusion is really beside the OP. For delta sigma V, the correction for "non-free-field" conditions is not warranted. It's the Boussinesq (or other similar elastic equations) for horizontal loading where Duncan told me (us) to apply the 2-fold correction. He did not use the term safety factor. Any such safety factor would be the onus of the structural engineer (i.e., just like we don't apply a safety factor to Rankine earth pressures, that is).

f-d

sorry to the OP if I got this thread off-topic. Sometimes I just need somebody to talk geek with, sigh. . .

¡papá gordo ain’t no madre flaca!

 

[FixedEarth]

The attached excerpt from AREMA requires that the 2.0 factor be used on the numerator. Note that it is for a strip load.
I use the 2.0 when a strip load is within 1.5H of a retaining wall, even if it is a private job. Eventually, it is your level of understanding and comfort level. See attached.

 

[PEinc]

The 2 in the above referenced AREMA Boussinesq strip load formula is the normal constant in the equation. It is not a doubled constant. I assume that if you believed in doubling the pressure, you would change to 2 to a 4.

http://www.PeirceEngineering.com

 

[RFreund]

I knew there was some confusion!

I thought that you were referring to the 2 in the equation as doubled. Azizi "Engineering in Geotechnics" says that the strip load value is doubled to account for rigid wall effects and displays the equation as FixedEarth shows in his attachment. So this would lead me to believe that the 2 in the numerator is doubling what the equation would normally result in. I believe Poulos and Davis also give the equation w/out the 2 in the numerator.

Also see here:

http://www.ejge.com/iGEM/Articles/FactorOf2/FactorOf2.htm

Another tangent (and also one of my favorite threads) the last post by miecz mentions a book published in Poland and I always wanted to know that reference and if anyone else thought his equation was an acceptable solution.

http://www.eng-tips.com/viewthread.cfm?qid=150849

EIT

http://www.HowToEngineer.com

 

[PEinc]

The equation with the 2 already in it is the equation I see and use. I assumed that fattdad was saying to double that equation (2 x 2). I guess we all need to know what specific equation we are talking about. There would be less confusion.

http://www.PeirceEngineering.com

 

[FixedEarth]

We are not researchers. All we can do is pick Rankine, Spangler, Tschebotrioff, Boussineq, or whoever and be happy with our choice. It is obvious even with the 2 in the numerator that the lateral stresses are conservative. If it wasn't conservative, a lot of design build shoring engineers would be in distress- see PEinc comments.

Look at it this way. If strip load surcharge is 0.51H away, Bousinnesq theory misses the shored height so it does not apply (1:2 H:V distribution). If that surcharge is 0.61H away, it misses Rankine's pailure plane so it does not apply. But with the 2 in the numerator, the lateral stresses are felt by the wall until you are greater than 1.5H away.

Same issue with sheetpile design. The Swedish method gives very liberal values yet in Sweden they have worked for 100 years. So I guess we agree to each have a preferred method for surcharges and be o.k. with other research findings.

 

[PEinc]

Well said. Amen?

http://www.PeirceEngineering.com

 

[FixedEarth]

.

 

[RFreund]

Amen.


Now where is this Swedish research?

EIT

http://www.HowToEngineer.com