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# 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!

### RE: Horizontal subgrade modulus for seismic pile analysis

Having a stiffer response for cyclic loading seems reasonable to me, e.g. due to rate effects. However, the factor of 3 is almost certainly arbitrary and would likely be based on experience.

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

### RE: Horizontal subgrade modulus for seismic pile analysis

As far as I know literature on the dynamic Kh is apparently contradictory, since many different values are obtained, ranging from less than unity to up to 5 times unity.
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.

### RE: Horizontal subgrade modulus for seismic pile analysis

If you have access to a more or less accurate value of the small strain shear modulus G0 either by direct measurement of by correlation from in-situ tests, you could estimate the stiffness degradation in cyclic conditions using the average reduction factors G/G0 in table 4.1 of Eurocode 8-5, depending on the ground acceleration.

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

As a reference, look at page 9-87 of the FHWA manual for driven piles:

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

### RE: Horizontal subgrade modulus for seismic pile analysis

Avscorreia, the problem with the EC8 method is, apart from the fact that it is a crude approximation, we don't know the PGA at all depths, along the pile shaft.

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.

### RE: Horizontal subgrade modulus for seismic pile analysis

Mccoy, I agree with you. EC8's method is crude and the Oztoprak's curves need too many parameters that can't be determined easily. But when only a couple of SPTs are available how accurate can we be either way? For me, these are only ballpark estimates but are OK for regular structures.

### RE: Horizontal subgrade modulus for seismic pile analysis

Just want to double check, but based on the above replies, do you agree to it is correct to consider a lower modulus (degraded modulus) for seismic analysis?

### RE: Horizontal subgrade modulus for seismic pile analysis

#### Quote (Okiryu)

Just want to double check, but based on the above replies, do you agree to it is correct to consider a lower modulus (degraded modulus) for seismic 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

Yes, agree that it will depend on the magnitude of strains and it is not linear.

### RE: Horizontal subgrade modulus for seismic pile analysis

Okyriu, the EC8 tables would be a rough reference to degrade G or Vs. There are some relationships in the NIST GCR 12-917-21, 2012 , Soil-Structure Interaction for Building Structures publication, freely available. If my memory is not being treacherous.
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

### RE: Horizontal subgrade modulus for seismic pile analysis

Hi McCoy, I was looking at the Japanese Code for Buildings and it is recommended that the modulus be reduced by (y^-0.5), which "y" is the pile deflection. This reduction applies for deflections greater than 10mm. So as it was mentioned above, the reduction in soil modulus will depend on the magnitude of strains. However, I noted that even large changes in the soil modulus (for example, large reductions) do not significantly affect the lateral resistance of piles...

### RE: Horizontal subgrade modulus for seismic pile analysis

(OP)
- 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

@ okyriu: I did not know the japanese guidelines. If they suggest to apply the reduction only for deflections >10mm then it is implied that, by that standard, up to one centimeter the stress-strain relationship is considered to be linear. That is the same to say that in that strain range the deformation behaviour belongs to the initial domain of the degradation curve where degradation is negligible. We are located in the linear, initial tract of the p-y curves construct. These things though are undoubtedly better discussed with an accompanying illustration, I'm trying to attach one in a successive post.

### RE: Horizontal subgrade modulus for seismic pile analysis

#### Quote (Geocito)

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.

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.

### RE: Horizontal subgrade modulus for seismic pile analysis

Hi McCoy, actually the Japanese guidelines shows an increase of modulus for deflections lesser than 10mm. The degradation for deflections greater than 10mm is not linear as you mentioned. But again, what I noticed is that the horizontal modulus does not significantly affect the lateral resistance of piles. It will be nice if you can post the illustration you refer to. Thanks...

### RE: Horizontal subgrade modulus for seismic pile analysis

Okiryu, it's interesting that the modulus increases according to the Japanese standards, a phenomenon which is reported in some Japanese literature but not for all soils and conditions. Yes, in well designed piles, with abundant steel, resistance is not so dependent upon Kh, which after all does not need to be calculated with great precision, usually.
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.

www.mccoy.it

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