Horizontal force on a retaining wall from a vertical point load 2

[Trevski]

Hello there, first time post from a very new civil engineer:

I'm designing a mass concrete wall which will act as a headwall to a culvert. Farm machinery is expected to pass over the culvert within 0.5-1m. The wall is only 1.2m high.

I was thinking I should design the wall assuming the vehicle wheels will act as a point load, a distance from the wall and this is transferred to a horizontal load.

I’ve seen a few formula that tell me the horizontal stress, which I can see varies with depth but I guess I need the total force. Is there a formula for this? Should I be designing as a point load or is a strip load more appropriate.

Any help much appreciated.

 

[miecz]

Lateral force due to live load is often simplified by treating the live load as a uniform overburden pressure. The traditional traffic overburden pressure is 250 psf, but, the latest AASHTO code makes this pressure a function of the wall height. The overburden pressure increases with decreasing wall height, so your short wall would have a higher overburden. This overburden then gets factored by the active pressure coefficient to get a uniform lateral pressure to the wall. You can use more precise means to arrive at lateral forces, but if your work will be reviewed by your DOT, you should get agreement on the method first.

The headwall should also be designed for a lateral force from an accident.

 

[palmahouse]

You are on the right track. Modeling the loads as point loads is a reasonable approach. There is the St. Vincents Principal that states that in elastic theory, the way you model the load distribution on the ground has less effect on the calculated distributed loads as you get furher from the load, and the magnitude has greater effect(or something like that). At any rate, it shouldn't matter much provided you use the correct magnitude.

You can use a computer program called STRESS or charts in NAVFAC DM7.02 to calculated the horizontal stresses in your elastic medium (the wall backfill) at the back of your wall. You typically get a stress profile distributed in a "teardrop" shape. Combine the magnitudes of each load, draw a diagram showing the distribution of the total horizontal load, integrate it to figure out the total load, and simplify the distribution to facilitate design (sometimes an inverted triangle makes sense).

What you should think about, however, is the stresses you calculate from STRESS or the charts assume that your wall is fixed. If it is free to deflect, the actual surcharge loads will be less. Sometimes I justify using 3/5 of the calculated horizontal stresses, which is near the ratio of the active/at-rest earth coefficients. Of course, you can use the full load and know you are conservative.

 

[ruready]

Miecz,
Which AASHTO code and what section, thanks

 

[msquared48]

In general, considering the extra overbutrden load mentined above, I only apply it below the level of a 45 degree line extending to the wall face from the load. The farther the load is from the wall, and the deeper the footing under the load, the less the overturning and shear effects on the retaining wall.

Mike McCann
MMC Engineering

 

[fattdad]

When using Bousinesq equations to calculate horizontal stress from a point load or an areal load acting on a retaining wall, the calculated delta H must be multiplied by 2. Bousinesq forumla are based on an infinate elastic medium and when you place a retaining wall, you are dealing with an elastic half-space. Because of that the countering force is not present and must be accounted for by doubling the calculated force.

This according to my earth pressure professor, J. Mike Duncan.

f-d

¡papá gordo ain’t no madre flaca!

 

[BigH]

fattdad - understand that your 2x is typically presumed correct although I remember seeing some recently argue this is not really the case . . . something that might be better served in research than yet another attempt to determine the bearing capacity factors . . .

 

[fattdad]

BigH: I just make the point to counter the earlier perspective pertaining to at-rest v. active earth pressures and the potential wall movement as justification to REDUCE the calculated load. I'm not sure I'd reduce any calculated horizontal load from a Bousinesq formula when there is an equally compelling reason to double it! The actual answer, however, is something that is likely an enigma - I mean even the Bousinesq equations are based on soil assumptions and mother nature is never that kind.

f-d

¡papá gordo ain’t no madre flaca!

 

[palmahouse]

fattad and BigH,

I think that you need to increase the calculated stesses using Bousinesq in consideration of the elastic 1/2-space effect. I also read something as BigH did, and have the paper in my files somewhere, indicating that 2X may be unrealistic, and this was based on data from a rigid wall, fixed from rotation, with strain gauge instrumentation - seemed credible to me.

The point is, I believe you should increase the horizontal stresses you calculated using Bousinesq. I increased the load in my previous analyses(but forgot to mention that in my previous post).

Better yet, why bother with Bousinesq? You can us the semi-empierical chart solutions in NAVFAC that are specifically applicable to wall surcharges (which do consider the effect of the elastic 1/2-space effect - I have verified in the past). However, at that point, you should consider reducing the horizontal stresses associate with wall deflections (as I mentioned in my previous post). In fact, NAVFAC, although oversimplified, has some discussion on this topic (in the retaining wall section - 7.02). I encourage us all to review this.

In the end, I bet Duncan has the most insight on this, but that he would agree (with the discussion in NAVFAC) that you need to reduce the calculated horizontal stresses depending on your judgement regarding the effects of slight wall deflections on the stresses - assuming such deflections are tolerable.

 

[fattdad]

Active v. at-rest provide for stress reductions owing to wall movement. After all it has nothing to do with the wall movement, it has to do with strain along the failure surface mobilizing the interface friction in the first place. I would not use interface friction reduction as justification to reduce the forces calculated from Bousinesq elastic formula. To me it's not germane. Then again. . .

I really haven't looked at the NAVFAC charts on this matter, but likely should.

f-d

¡papá gordo ain’t no madre flaca!

 

[miecz]

ruready

Article 3.11.6.4 of the AASHTO LRFD Specification, 3rd Edition.