Rigid unreinforced pavement with Westergaard equations

[Okiryu]

Hi, first time posting here, but long time reader...

I am writing from Japan and am trying to calculate the thickness of an unreinforced concrete pavement that will receive large mobile crane loads. Based on the crane specs, the maximum load at the front axle was calculated to be approx 100 kips. I am using Westergaard equation to verify stresses in the concrete under this load conditions. I was told that the original Westergaard equations have been modified several times and would like to ask if anybody has a good reference where to find the most updated Westergaard equations or if there is a different approach to calculate rigid pavement thickness for large crane loads.

BTW, I have calculated a 12 inches thick pavement. Modulus is 100 pci, concrete flex strength is 650 psi. I am assuming 10000 passes during a 20 years design life. Do you think that 12 inches pavement under the above conditions is a reasonable thickness for this pavement?

Thanks all in advance for your help.

 

[Denial]

This might not directly answer your question, but I have developed a pair of spreadsheets that calculate the bending moments in "rigid" slabs supported on a continuous elastic foundation:[ ] one for the interior case, and one for the edge case.[ ] At the very least these might help you confirm (or otherwise) an answer obtained by another method.

The spreadsheets are downloadable from my web site

http://rmniall.com

 

[Ron]

Okiryu....your computed thickness is reasonable. You can check it by elastic layer analysis as referenced in Principles of Pavement Design by Yoder and Witczak, or Pavement Analysis and Design by Yang H. Huang. Both also show manual methods of application of Westergaard's equations (later versions).

For elastic layer analysis, if the tensile stress at the bottom of the concrete layer is less than 50% of the flex strength, then the repetitions are unlimited.

 

[Okiryu]

Denial, Ron, thank you for your replies. My reviewer was telling me that 12" is too thick for this pavement under the above explained conditions and asked to double check my calcs. I already started to check Denial website and also purchased the Yang H.Huang book.

One more question, do you normally consider also stresses in pavement due to temperature changes? I think that it will depend on where are you located and climate conditions. Right now, I am considering only the stresses for vehicle loads and then increasing 30 percent to cover stresses due to the temperature changes. I am located in a tropical island at the south of Japan and I was not sure about the temperature differences between day and night, so I just decided to increase 30% the stresses exerted by vehicle loads. I think that might be only approx.5 celsius degrees difference here between day and night.
I will try to calculate it, but just wanted to ask if this is normally checked.
Also, besides Westergaard's equations, are there any other methods to calculate stresses in concrete pavements under vehicle loads?

Thanks again for your assistance.

 

[dik]

Is the loading 'channelised' or at random?

Dik

 

[Okiryu]

Dik, with "channelised" do you mean that in most of the times the load will be applied at predetermined locations? Means that will be a specific location where the loads will be applied?

If that is what "channelized" loading means, I think that since the load will be exerted by a mobile rough terrain crane that can operate without any restrictions at the proposed area, the loading will be at random.

 

[Ron]

Temperature is usually not a big issue in this type of pavement, assuming it is not long and narrow. Tropical conditions usually do not have significant temperature variation as you might find in colder climates.

As for alternate methods, I suggest again...elastic layer analysis. There are several multilayer elastic layer programs available or you can do it manually. It is a good method, particularly for "ground truthing" the more conventional methods.

As for the parameters to input for elastic layer analysis, I would use the following:

Modulus of Elasticity of Concrete - 3000ksi-3500ksi
Poisson's Ratio - 0.15

Use similar parameters for the subbase. You can compute correlation properties using the AASHTO Pavement Design Manual. This manual will also give other methods for analysis.

Good luck.