in-situ tests applied to subgrade modulus for mat

[geodr]

I have a question about a topic some of you may be tired of – subgrade modulus – but it does have some interesting features, and I hope someone may have some insight. We are providing recommendations to a structural engineer for modulus of subgrade reaction values beneath a 2.5-ft thick mat foundation measuring approximately 100 ft x 200 ft in plan, for them to use in their SAFE analysis. The mat is bearing on highly weathered and fractured rock – sandstone and shale – which becomes more competent with depth. The SE wants values of subgrade modulus for both static and seismic loading.

Another contractor did some in-situ tests on spread footings at the site to establish load-deflection relationships for the weathered rock. These tests were made using the Rapid Pile Load Tester (see

http://www.americanpiledriving.com/rplt_00.html)

which drops a 25 ton mass on the footing (or pile) from increasing heights (increasing loads), which induces increased deflections, and a nonlinear load-deflection curve can be constructed from the observed data. The mass has heavy duty springs attached to the bottom, which has the result of delivering the load over 0.2 to 0.4 seconds, which we accept to be analogous to seismic loading rates. Footings measuring 2-, 4-, and 6-foot square were tested, all embedded approximately 2 feet below grade. So we have good nonlinear subgrade modulus curves for small footings, but need to extend them to the full sized mat.

And that is my question - does anyone have a recommended method for scaling the results of these tests to the full sized mat ? Also, is it appropriate to use a uniform subgrade modulus over the entire mat, or use some variation ? I know Terzaghi suggests k = k1/b for strip footings (k1 being subgrade modulus from plate load test on a 1x1 plate, and b being footing dimension), NAVFAC DM 7.2 presents equations for cohesive and granular soils that based on this geometry reduce to k = 0.83 k1/b (cohesive) and k = 0.26 k1/b (granular), and Bowles presents a Vesic relationship where k is proportional to b^1/3, as well as his own method that is also a function of b. Scaling the footing test results to the mat using Vesic, I get k = 0.12 k6 and using Bowles I get k = 0.3 k6, where kmat = modulus for full sized mat and k6 = (tangent) modulus from the test on the 6x6 footing.

I searched this archive and found a few threads that address this topic, probably the best was from BigRed Geo back in July that Focht3 referred to as the McClelland “unit area” approach. I have employed this iterative approach before for a mat on sand over stiff clay, but in this case I may have a hard time quantifying settlement on weathered rock. And there is the problem of what value to start with. Based on some of your earlier posts, there are some misgivings in this group about Bowles recommendations. So I’m wondering if there are any other suggestions out there.

Thanks,
Geodr

 

[Focht3]

[blue]geodr[/blue]:


What a wonderful post! Someone actually did a thorough search on the question before posting! If you weren't the one posting the question, I'd give you a star!

You clearly have a good idea of my general thoughts on this topic, so I won't reiterate them here. Given the circumstances you have provided, I would be inclined to use Vesic's approach as a first cut. I would then temper my recommendations using the RPLT results. That's where things get sticky -

In the interest of full disclosure, I haven't designed a mat that large on rock. Most of mine would be better categorized as large spread footings, so the issue of the "unit load area" didn't come up. My gut says that you won't have a total settlement problem, but differential movements could be a problem if the weathered zone varies much.

Now to the RPLT results. I would consider using the results to come up with curves of Young's modulus E versus strain to address the issue of nonlinearity of the material. Do this for each test area width, and see if a size effect appears. I doubt it will - due to the natural variability of the rock and the small variation in test area size. But it's worth a try.

Then run the mat analysis using your first cut k-value from Vesic's method. Review the results, and modify as your judgment (and the RPLT data) guides you.

Let us know what happens -



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