sanity check on spring constant for dynamic analysis of mat

[ARS97]

I've designed a 14' x 14' x 3' mat foundation to support a jaw crusher & steel support frame, but now I'd like to check the natural frequency in comparison to the operating frequency of the machine (3.8 Hz). I will be using a finite-element model in Staadpro that utilizes spring supports at each node of the foundation.

My main question is whether or not my calculated values for the spring constant are reasonable.

Right, wrong, or otherwise, I cannot convince the customer or my employer (a design/build construction company) to pursue geotechnical services to establish better soil parameters. So, for the sake of furthering the conversation, let's assume the following:

soil poisson ratio = 0.35
void ratio = 0.4

I've been using ACI 351.3R-04 as my main reference. For this application, I was assuming a uniform soil condition and using the Richart-Whitman model as shown in section 4.2.1.1. Since this is a square foundation, the impedance can be found from equations (4-13e) thru (4-13g).

The dynamic shear modulus has been calculated as 1,206,105 psf (per equation 3-34), assuming a probable confined pressure of 300 psf.

Vertical impedance, kv = 54,553 k/ft
Horizontal impedance, ku = 43,311 k/ft

These spring values above just seem high to me. Are they within reason?

*NOTE - I will post this in the structural section as well......thanks

 

[fattdad]

No clue, but I worked for 13 years with structural engineers who designed industrial floor slabs and routinely gave them values of 125 to 300 pci for subgrade modulus (range for compacted soils). They'd sometimes add a bit more for the dense-graded subbase materials as ACI allows that.

f-d

¡papá gordo ain’t no madre flaca!

 

[ARS97]

Yeah, but I'm pretty sure that the subgrade modulus, which is typically used for static conditions, isn't used for a dynamic analysis of a machine foundation. I'm seeing something called a dynamic shear modulus being required. I'm not sure of the correlation between the two though, if there is one. I used the subgrade modulus for the structural design, but that's it.

 

[fattdad]

many, many years ago, I took a graduate-level geotechnical engineering course in earthquake engineering. If memory serves me right (fair warning), dynamic shear modulus was likened to low-strain shear modulus. The low-strain shear modulus taken as 10 percent of the shear modulus at failure.

DON'T DO ANY ENGINEERING BASED ON THIS REFLECTION!!!

Just a thought. . .

f-d

¡papá gordo ain’t no madre flaca!

 

[Mccoy]

fattdad is correct, the dynamic shear modulus is pertinent to low-shear levels and the operational shear modulus sometimes must be degraded. The strain field imposed upon the soil by the vibrating machinery may be low, actually the seminal paper by Gazetas 1991 clearly says in those cases we should used a low strain G-modulus (although I believe that's not always true).
Also, dynamic subgrade modulus very often is only a little lower than the static modulus, unless specific conditions occur, like great width of foundation and, most important of all, resonance frequency of the soil layer equal to the machinery frequency.
The shear strain value of 58 MPa is not out of whack, although you give no clues as to the soil type existing below the foundation.
The frequency of your machine is within the medium-range frequency for soils, if you have a rigid layer within 10-30 meters of depth you may have resonance and consequent drop in subgrade modulus, but I'm speaking very broadly since we do not know the soil profile nor the velocity profile of the shear waves.