WSP
Question
Asked 18th Oct, 2014
How is the natural frequency of soil calculated?
How can we find the first and second natural frequency of soil model with L=50 m and depth of 20 m ?
The model has dynamic load with infinite element in borders.
What do f1 and f2 depend on in soil?
I need f1 & f2 to calculate alpha & beta coefficient Rayleigh damping
Most recent answer
1. For estimating the fundamental period (1/fn) of potential sliding blocks, please check Bray 2007 paper. (Tn= 2.6H/Vs or 4H/Vs, depends on the shape of sliding mass)
2. You can also use DEEPSOIL or RS2 software. RS2 has a quick tool to calculate the natural frequency quickly after you define the geometry and materials.
3. check Kramer 1996
Popular answers (1)
IRANDAMP
frequency of the nth mode of a soil column can be estimated as
fn=Vs.(2n-1)/4/H
in which n is the mode number, Vs is the average shear wave speed, and H is depth of the soil column.
If you need these frequencies to calculate damping matrix of the soil column, use n=1 and n=4 or 5, that is use f1 and f4 rather than f1 and f2 (2nd mode). This formulation is very very rough and has been proposed by Kramer in 1996. Note that this damping belongs to the inherent damping of the linear soil. Damping of the soil due to its nonlinear hysteretic behavior should be obtained based on its degradation curves (shear modulus and damping vs. shear strain). This latter technique is used in a classical equivalent linear analysis. You can also do a nonlinear analysis in time domain through either total stress or effective stress techniques. All of these analyses can be easily done through DEEPSOIL software which is free to download.
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All Answers (13)
Sahand University of Technology
you can use KRAMER 's book( the geotechnical earthquake engineering). Also, there is a program named SHAKE that you can model the soil profile with boundaries and then calculate the natural frequencies.
1 Recommendation
IRANDAMP
frequency of the nth mode of a soil column can be estimated as
fn=Vs.(2n-1)/4/H
in which n is the mode number, Vs is the average shear wave speed, and H is depth of the soil column.
If you need these frequencies to calculate damping matrix of the soil column, use n=1 and n=4 or 5, that is use f1 and f4 rather than f1 and f2 (2nd mode). This formulation is very very rough and has been proposed by Kramer in 1996. Note that this damping belongs to the inherent damping of the linear soil. Damping of the soil due to its nonlinear hysteretic behavior should be obtained based on its degradation curves (shear modulus and damping vs. shear strain). This latter technique is used in a classical equivalent linear analysis. You can also do a nonlinear analysis in time domain through either total stress or effective stress techniques. All of these analyses can be easily done through DEEPSOIL software which is free to download.
7 Recommendations
Institute of Disaster Prevention
In response to your question, I give you two suggestions, I hope to help you
(1) to soil, different from the structure, "the natural frequency of soil" is an unstrict appellation, we often call it "dominant frequency of site", because the dynamic characteristics and parameters of soil are dependent on strain level.
(2) if you need to get first and second natural frequency for caculating the Rayleigh damping coefficient in FEM analysis, you could establish the FEM model with Dynamic Artificial Boundary, then calculate the F1 and F2 according to the idea of FEM in structure analysis. The F1 and F2 is usually the dominant frequency of site in the elastic region(small strain level ,such as 10-6). In noninear analysis of soil model, all change.
3 Recommendations
Comenius University Bratislava
Fn = ((2*n - 1)*Vs)/(4*H)
Fn - is the natural frequency of the corresponding mode
n - is the mode number
Vs - is the average shear wave velocity
H - is the depth of the soil column
Vs = H/(sum (Hi/Vsi))
Hi - is the thickness of the each i - layer over bedrock
Vsi - is the shear wave velocity corresponding of the i - layer of the Hi thickness over bedrock
sum - is the sum of the fractions (Hi/Vsi)
In the relationship of the Mr..Seyed Amin Mousavi above, there is a mistake
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Électricité de France (EDF)
Hello
In addition to the above answers, may I suggest also a rather complete (but not the only one, of course) book: https://www.researchgate.net/profile/A_Pecker/publications?pubType=book&ev=brs_pubs_book
Good luck!
2 Recommendations
Imam Khomeini International University
Hi All. Thanks a lot.
in FEM analysis for example with Abaqus . i have to chose boundary in vertical border and bottom . which boundary element i have to select , finite or infinite , for frequency analysis.
Sharif University of Technology
Hi
I have the same problem. did you find a way? can you share it with me?
Homi Bhabha National Institute
For first frequency, quarter wave length methods is simple to use for uniform deposits. For layered medium, it is a bit tricky, as each layer acts as a filter. Analogy is MDOF system. If one can estimate equivalent Vs for the deposit, quarter wave length method may give approximate solution, with some errors. If the layers are differing in engineering properties, say, Vs, and density, significantly, this method may not be suitable. In such cases, reverse engineering, in terms of simple one dimensional wave propagation technique can be used, say, with DeepSoil or similar codes.
Recall the equation for resonance frequency of a single layer of thickness H and shear-wave velocity Vs, as, f = Vs/(4*H).
This is a quarter-wavelength condition, as it states that resonance will occur for a period for which the wavelength (VS/f) is 4 times the layer thickness. For higher modes, one can use, a factor of (2*n - 1), as explained by others, in the previous answers.
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Groupe STEBAT, Albertville, France
The quarter wave length methods could be applied for uniform deposits
Dalhousie University
Seyed Amin Mousavi Is this equation could be used to find the mass and stiffness damping parameters in Rayleigh damping?
For example, in Plaxis, I need to determine the target frequencies to calculate the mass and stiffness damping parameters. In the Plaxis manual it is written that the the first target frequency is first natural frequency of the soil deposit and the second target frequency is the predominant frequency of the input motion over the natural frequency of the soil. So if my input motion is a sinusoidal harmonic motion with a frequency of 100 Hz, so the predominant frequency is 100 Hz?
Thank you.
Yildiz Technical University
Hi,
I have a similar challenge in Plaxis. I prepared two models one is 5m sand on bedrock and 3 m clay on sand. The second model is 25 m sand on bedrock and 3 m clay on it to see the liquefaction effect. Vs sand = 150 m/s and I use the fn = Vs / 4H method. The dynamic motion is sinusoidal wave, "acc 3g and freq 3Hz ".
For 25 m thickness, f1 is smaller than f2 and I can have sinusoidal waves at the center of the sand. But for sand 5 m thickness, f1 > f2 (7,5-1) and the waves are not sunisodial anymore. This method seems does not working for thin layers. What should I do for thin layers?
Kind Regards,
Zeynep
1. For estimating the fundamental period (1/fn) of potential sliding blocks, please check Bray 2007 paper. (Tn= 2.6H/Vs or 4H/Vs, depends on the shape of sliding mass)
2. You can also use DEEPSOIL or RS2 software. RS2 has a quick tool to calculate the natural frequency quickly after you define the geometry and materials.
3. check Kramer 1996
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