Static AND dynamic modulus degradation

[Mccoy]

Dear colleauges,
this issue has being gnawing at the background of my mind for a while now, and it's about time to submit it to your valuable attention.
We know that elastic and shear moduli decrease their value with an increase in strain deformation. Tangent moduli, Eo and Go, may be 10 times the value of secant moduli at large deformations. The adjustment tangent-to-secant may be done in various ways, some of such are called 'degradation schemes', as per the articles by Fahey et al. 1994, advertised by Paul Mayne 1999 and herein attached (chapter 3). It is based upon the determination of the mobilized shear strenght under the foundations and the application of a suitable hyperbolic law. References are contained in the attached Pdf.
Dynamic degradation takes place during earthquakes and in presence of intense vibratory motions. the degradation procedure is usually based on degradation curves, different for each material, where the deformation value is estimated or calculated with numerical methods of local seismic response. There are also tables though, like in the Eurocode 8, where the degradation is in function of the ground acceleration (with an uncertainty band which can be used to adjust for the soil type).
Now, I regularly apply these schemes. One thing makes me wander though. We have for instance a building foundation which mobilizes one third of the available shear strenght. According to Mayne this is the same thing as saying that the actual load is one third the soil bearing capacity. We'll degrade the modul accordingly. Using Fahey et al. procedure, with this degree of strain the modulus becomes 40% of its original value at zero deformation.
Now comes the earthquake though, since we've built in a higly seismic area. Now we have a seismic deformation field (with an alternate sign) which overlaps the static deformation field.
A typical value in my area in medium dense soil is 0.36.
Here I'm lost, since I found no literature which explains how the twine shall compose, a simple summation? about 0.8 in my case? It may be unlikely since the resulting settlement in many cases would be excessive but it doesn't in real life. Alternatively, it may be that the building practice actually mobilizes less soil capacity than what we think.
What are your thoughts on the combination of static and dynamic degradation? Are you aware of any references in the literature?

 

[Mccoy]

Sorry but I posted before I saw one value which needs clarification. It is obvious, but I prefer to be as clear as possible. 0.36+0.4 degradation is equal to about 0.8 degradation, which means that total(E/Eo or G/Go) = 1-0.8 = 0.2, that is the modulus would degrade to 20% of its original value if the hypothesized law of summation holds.

 

[moe333]

Mccoy; Interesting question. I have really only dealt with shear modulus reduction when performing seismic site response with software like SHAKE that uses reduction curves as a function of shear strain for different materials/plasticity/confining stresses/OCR/etc. SHAKE is generally for free field and level ground conditions and does not consider external shear stresses from.

I have never thought about modulus reduction as a result of a static load like a foundation. If modulus was reduced as the result of a static load you should be able to measure it with SPT/CPT before and after the static load was applied...I have never seen any studies on this.

I know there has been some relatively recent work by Jon Bray (UC Berkeley) and others in evaluating how the presence of static building loads affects liquefaction potential. I'm not sure if the building loads affect CSR, CRR, or both. But these studies may provide some insight to your question.

 

[Mccoy]

moe333, I too sometimes use those numerical analyses but the software I know best is STRATA.
A good reference on modulus static degradation is Atkinson 2000, which I'm attaching here. But I also realized that in the Foundation Engineering Handbook, 1991, the settlements chapter by Holz, displays some plots of the Elastic modulus varying in function of mobilized shear.

Thanks for the tips on Jon Bray's work, I'll search that, I'm also going back to the Towatha textbook on earthquake geotechnical engineering which I remember had some brief reference on static+shear strenght, that's in the context of liquefaction so not generally applicable but even a specific case is better than nothing.
I'll be back here to further the discussion, my aim is to reach some technically reasonable conclusions to include in my reports.

 

[Mccoy]

So far I didn't find much but the gist is something counterintuitive, that is, relatively large static shear prevents a large strain to develop in cyclic conditions. In particular, the cyclic strenght of sand is increased by the presence of a static shear. Qualitatively, it would seem there is some sort of locking effect triggered by static shear which prevents further strain due to cyclic shear (Vaid & Finn, 1979).
FHWA (circular 3, 1997) proposed a k_a coefficient (function of the horizontal shear below foundations or embankments) to use in liquefaction potential assessment, this multiplying factor has the effect to increase the liquefaction resistance. The only relevant paper from Jon Bray I found reports an improved degradation curve in clays in the post-construction condition (pile foundations) hence being coherent with the above facts.

Now, all this may be a little confusing since apparently, in the presence of a foundation there would be no more reason to consider cyclic degradation. It all depends on the respective values of cyclic and static shear though, since small deformations are actually facilitated by static shear (the opposite occurs for large deformations). To apply such concepts to my purposes, that is the determination of operational shear modulus to find an optimum modulus of subgrade reaction, requires some quantification of the horizontal static shear stress. Also, I found no clear procedures or schemes like the one advised by Paul Mayne. All in all, I'll go on ruminating on the subject, in the meanwhile in the routine reports I'm going to proceed like before, only now I'll specify that summation of static and dynamic degradation is not advisable since it could result according to the literature in an unduly overconservativeness.