## Horizontal subgrade modulus for seismic pile analysis

## Horizontal subgrade modulus for seismic pile analysis

(OP)

I am used to calculating the modulus of horizontal subgrade reaction for piles which is asked to me by my structural engineering mates. I use different formulae and correlations already discussed in other threads about this subject. However, I cannot find design rules to establish that modulus to be used in a seismic modal analysis of a certain piled structure (with SAP2000, e.g). They have mentioned that they usually multiply by 3 the static modulus, but they cannot give me a reference to support such practice.

Reading some papers and books, in NCHRP 461 chapter 2, it can be seen that p-y curves for seismic loading are higher than for static loading, and so would be a Kh value (I understand that p-y method is more precise than a linear elastic Kh analysis, but modal analysis of a structure is linear). A simplified expression for dynamic p-y curve is given, but it is difficult to apply.

Increase in the subgrade response during dynamic loading seems to be related to certain viscous resistance, so it is understandable to use a higher Kh.

I know that dynamic soil-pile interaction modelling is a complex matter, but could anyone give me references to support a certain factoring of Kh for seismic analyses? why 3 times the static modulus instead of 2 o 5 times?

Thanks!

Reading some papers and books, in NCHRP 461 chapter 2, it can be seen that p-y curves for seismic loading are higher than for static loading, and so would be a Kh value (I understand that p-y method is more precise than a linear elastic Kh analysis, but modal analysis of a structure is linear). A simplified expression for dynamic p-y curve is given, but it is difficult to apply.

Increase in the subgrade response during dynamic loading seems to be related to certain viscous resistance, so it is understandable to use a higher Kh.

I know that dynamic soil-pile interaction modelling is a complex matter, but could anyone give me references to support a certain factoring of Kh for seismic analyses? why 3 times the static modulus instead of 2 o 5 times?

Thanks!

## RE: Horizontal subgrade modulus for seismic pile analysis

Also, your analysis need not be elastic in nature. See the program NERA, for example.

## RE: Horizontal subgrade modulus for seismic pile analysis

Bowles gives the simplest rule, just apply a coefficient ranging from 0.5 to 0.9, this implying seismic degradation of the reaction modulus.

As LRJ implies, a rigorous procedure would be to appply a degradation scheme to G or E which, to my knowledge, is only possible by seismic site response procedures.

Some regulations do provide a value of dynamic degradation of soil stiffness in function of PGA, which is a widely approximate method.

Also, some secant reasoned values of the first tract in the P-y dynamic curves might be applied.

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## RE: Horizontal subgrade modulus for seismic pile analysis

Alternatively, there's an article by Oztoprak and Bolton that presents stiffness degradation curves estimated from a database of test results in sands. The curves are of the form

G/G0 = 1 / [1 + ((gamma - gamma_e)/gamma_r)^a]and the article reference is the following:

Oztoprak, S. & Bolton, M. D. (2013). "Stiffness of sands through a laboratory test database." Géotechnique 63, No. 1, 54–70.

## RE: Horizontal subgrade modulus for seismic pile analysis

http://itd.idaho.gov/manuals/Manual%20Production/M...

This page shows some reductions of kh due to cyclic loading (earthquake loading), but note that this is based on Brom's method which calculate ultimate pile capacities. The same manual shows a FOS of 2.5 to get allowable capacities. Perhaps you can use a lower FOS for seismic conditions, which can be an analogy to what your structural engineers are thinking (increase of kh for seismic loading). But I was thinking that rather to use an increased kh, a lower kh due to soil degradation should be used instead. So I am confused now. I am interesting on this topic, since I will have a project in a medium/high seismic zone with pile foundations, so I will keep checking on this....

## RE: Horizontal subgrade modulus for seismic pile analysis

Oztoprak, S. & Bolton, 2013: do we have all the input values needed to use that chart? We usually don't know dynamic strain (needed at all depths along the pile shaft) unless we apply a seismic site response model.

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## RE: Horizontal subgrade modulus for seismic pile analysis

## RE: Horizontal subgrade modulus for seismic pile analysis

## RE: Horizontal subgrade modulus for seismic pile analysis

The modulus will degrade depending on the level of shear strain in the soil. It is not a constant value.

## RE: Horizontal subgrade modulus for seismic pile analysis

## RE: Horizontal subgrade modulus for seismic pile analysis

Simplest of all would be to half the static value, this is a procedure used in shallow foundations sometimes, which is coherent with the lower bound of the Bowles interval for the degradation coefficient: 0.5 to 0.9

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## RE: Horizontal subgrade modulus for seismic pile analysis

## RE: Horizontal subgrade modulus for seismic pile analysis

- Earthquake loading is cyclic, so degradation is expected, but

- Earthquake loading is dynamic, so a more rigid and viscous response is expected. These two issues are mentioned in NCHRP 461, and I understand that in the "Simplified Dynamic p-y Expresión" both have been considered, because depending on earthquake frequency in relation to soil type, the resulting multiplier may by higher or lower than 1.

- If we correlate the subgrade to soil moduli E or G, G/G0 curves are function of the shear strain. Considering kinematic interaction, the pile is a buried element and perhaps the above mentioned site response analyses apply(similar to those used in seismic tunnel or culvert design). But considering inertial interaction with the structure, which I was referring to, lateral deflections of piles induce high shear strains around them and G should be low, similarly to a static case. Therefore the more rigid response is due to rate effects (the dynamic nature of loading), rather than to a higher soil modulus. If the rate is low (wave loading) degradation is higher than rate effects and the response should be less rigid than in the static case; if the rate is high, dynamic effects might be higher than degradation effects and the response would be more rigid than in the static case.

Food for thought and investigation but in the end, for everyday structural analysis of simple buildings, my structural design colleagues ask me for a dynamic Kh for the modal analysis (which is an elastic analysis), and the furthest I've reached is that they run their models with various dynamic Kh multipliers as a sensitivity analysis.

## RE: Horizontal subgrade modulus for seismic pile analysis

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## RE: Horizontal subgrade modulus for seismic pile analysis

Geocito, as far as I know the above discussions are relevant to the inertial effects. The kinematic effects, that is, those caused by the 'push' of the seismic wave across the pile shaft, are usually ignored, but for the more sophisticated analyses and the very soft soil layers.

As to the <1 or >1 dynamic coefficient underlined by different literature, yes, they may be arguably due to the dominance of different overlapping behaviours, it is well known that dynamic stresses sometimes elicit a stiffer soil behaviour.

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## RE: Horizontal subgrade modulus for seismic pile analysis

## RE: Horizontal subgrade modulus for seismic pile analysis

The following illustration, from Vardanega and Bolton, 2013, shows a recent revision of the classic dynamic degradation curves for clay and silt by Vucetic & Dobry. As we see, for minuscule strains (or less minuscule strains but large PIs) there is no appreciable degradation. We need soil type which is usually known, we need PI which si usually known or can be reasonably estimated and we need last but not least the shear strain which is usually unknown and cannot be estimated with enough accuracy. This is the stumbling block. No shear strain, no G/Gmax. Shear strain is also a fucntion of depth, so it varies along the pile shaft. I would very much like to know if there are accepted methods to estimate the shear strain without a complete analysis of seismic site response.

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