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(OP)
Hello,

I'm wondering how to correctly take into account earthquake load defined by spectrum when the structure is supported by piles? I know that scaling of spectrum heavily depend from the subsoil characteristics. So, what if our structure lies on piles...which subsoil coefficient take into account, for rock or soft soil? There is a huge difference?
If I summarize: how to deal with friction/end bearing piles and their influence on scaling spectrum?

Replies continue below

### RE: Spectrum load and piles?

I would bet there's almost no difference due to the inclusion of the piles. Earthquakes and the huge halfspace of soil most surely overpowers anything we put in and on it.

So I would take into account the soft soil, normally.

For liquefactable soils would be other case, somewhat like marine structures.

If you know the
shearwave velocity at the hard substrate
thickness of the soft layer
main frequency of the top strong motion cycles
damping in the soft layer

you may accrue an impact factor, i.e., how bigger the effect will be at the surface than at the bedrock, just as the whip effect on equipment at roofs on the shake of the building.

But then, we have mainly earthquake data for the surface. Through the relationship of the forcing frequency at the surface and the natural frequency of the building (a stable property) you may accrue another impact factor on surface accelarations to be applied to the building, i.e., for closer frequencies in building and forcing you will be having bigger earthquake response. Grossly said you need that impact factor times the ground acceleration producing overall base shear.

But as you see, is the one of the soft soil, since the value for input is at surface and already aountinf for the nature of the subsoil in modern codes.

### RE: Spectrum load and piles?

To clarify even more what I think...

The shearwave at the bedrock would move the soft soil layers and these will move the buildings. So normal scale buildings even in piles would move on the shakings of the soft soil below, and the effect of the nature of the soft soils present is already in the codes to state what they think is a proper base shear for such buildings.

You may, however have tall imposing buildings really deeply seated in the bedrock. For these and starting from the codes we should think in inverse way, we have a base shear but at the surface and we could make use of some determination of how much the forces imparted at the bedrock are magnified byh the shaking at the surface. Then we would have, by dividing by such magnification factor, what is the shaking at the bedrock where our tall building lies.

So we could determine forces from this setup with the problem of how the soft soil affects by hammering the vibration of the building, something that maybe can be made through solid elements in FEM of the soil properties, or any evaluation standing Monobe-Okabe like or otherwise. Not entirely different of the piles moving on a liquefied slurry, some liquid, always forces on the walls and foundations.

### RE: Spectrum load and piles?

(OP)
Thank you ishvaaag for this very valuable post! Can you recommend me some further reading?

BTW: You also mentioned whip effect on equipment at the roof of which I'm wondering too. I know that exist a huge influence on everything attached on the roof, but how to take it into account. The only way I can think of is to read accelerations from the top of the building (from dynamic analysis) and load the equipment with those accelerations. But, what if I don't possess the results (accelerations) from dynamic analysis? Is there the way to overcome such analysis and estimate impact factor by hand?

### RE: Spectrum load and piles?

The proper way I think is to include if in simplified way the equipment and its structural link to the building

If you need to forfeit the entire building design, UBC 94 section 1632 was dedicated to nonbuilding structures but makes an interesting exception for rigid equipment of natural period less than 0.06 secs, for which a V=0.5·Z·I·W is directly given.

I propose you may also use the following procedure, that engages the evaluation of two simple impact factors, one for the soil-building pair, and another for the building-equipment pair.

Q=40 for reinforced concrete structure
Q=45 for presstressed concrete structure
Q=60 for bolted steel structure
Q=100 for welded structure

r1=fN_earthquake / fN_building

The natural frequency of the earthquake can be read from the strong motion record; there uses to be 3 or 4 strong motion responses up to 5 Hz, so maybe 3 Hz can be typical when unknown.

The natural frequency of the building  can be read from lookup tables for the different types of buildings; the spanish seismic code NCSR-02 renamed NCSE-02 has a set of formulas to establish a useful guess of such natural period (inverse of natural frequency).

Impact_factor1=1/(sqrt(1+r1^4-r1^2·(2-(1/Q^2))))
not to be taken less than 1

Now the exact same process is repeated for the impact factor between building and the equipment atop superstructure.

r2=fN_building / fN_equipment_superstructure

The natural frequency of the building  can be read as above. You may need to calculate or guess the natural frequency of the equipment, but you gain that you need not to model an entire building for a roof job just out of this thing.

Q normally now that of bolted or welded.

Impact_factor2=1/(sqrt(1+r2^4-r2^2·(2-(1/Q^2))))
not to be taken less than 1

Now if bga is the basic ground acceleration at pavement level, considering the following horizontal force at the center of gravity of the equipment must be a reasonable guess of a seismic force there:

F=W·bga·Impact_factor1·Impact_factor2

where W is the tributary weight of the equipment at its c.o.g. (you may subdivide the forces if complex in shape, or better subdivide equipment by support structures).

This is based on Bolton's statement of the calculation of an impact factor:

Structural Dynamics in Practice
A guide for Professional Engineers
Arthur Bolton
McGraw Hill 1994,

not an earthquake seismic design text.

On the other subject, still to add that...

precisely what the codes are doing when giving some consideration to the subsoil is to mimick through their method the amplification of accelerations that happens through the soft soil layers, so for normal buildings I have scarce doubt that the proper surface value is what needs to be used. To proceed otherwise I would think we would need to have a building rigidly tied to the bedrock, and likely quite deep, for when superficial no code has cared to express correction to the proposed value (other than to take the proper type of soil).

But if you were in such situation of deep bedrock and building rigidly founded there the soil itself would become in its vibration load for the building, and you would have first to have the acceleration at the bedrock derived from that at the surface (which can be made just by an impact formula similar to that used above). Then it would appear the problem of how to realistically (even if in simplified ways) model the earthquake hammering on the basement walls, for it can heavily affect the structural behaviour. An inmediate approximation is to model some solid of soil around the basement hole in elastic terms, that if scandalously incorrect, we use to practice everytime we calculate halfspace pressures etc. A nice problem waiting for people to add knowledge.

### RE: Spectrum load and piles?

That's how I see it:

Shallow foundations: you consider the acceleration at the base of the foundations.

Deep piled foundations: you consider the acceleration at the top of the piles, since the bending and shear imposed by the structure's mass governs. Even if pile is rock-socketed, the non-amplified signal at the base does not govern.

Also other forces act upone the pile's shaft, shear for strong rigidity contrasts in soil layers, bending moments from horizontal accelerations, i suppose socketed piles can be viewed as constrained at the head and at the base. Some detailed modelling is necessary.

The deep basement issue which Ishwaag describes is an interesting case which codes usually do not describe, especially so how to consider the horizontal forces acting upon the basement walls.

If the basement lays upon the bedrock, clearly there is no seismic amplification at its base .

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