As shown in the attached file, there is a difference between these methods. Could anyone explain why?
The equation in prof. Kramer's textbook is rigorously defined for perfectly horizontal, infinite layer of thickness H, with perfectly linear elastic homogenious material with shear wave velocity Vs. Is this the actual case in the FLAC manual? Because at prima vista the title "Block under gravity" sounds a bit different.
As seen in line 3 of the FLAC code, the model of material is selected as elastic (m=model e=elastic), The Block means a horizontal and homogeneous soil mass of 3 meters thickness and the soil is subjected to gravity. So I think the situation is similar to the Prof.Kramer's book.
Dear Dr. Zekri
the difference is due to the different conditions that you are considering.
The example of FLAC, in fact, refers to the application of the weight force and the solution is about the elastic oscillation of the element volume, while the theoretical solution: f = Vs/4H, is the first fundamental frequency of the elastic response under simple shear condition.
I hope that I have been useful to you,
Regards.
Dear Dr Zekri,
As Dr Tropeano noted the FLAC example is for the vertical degree of freedom and Vs/4H is for horizontal.
I modelled an infinite layer with SAP2000, and got the same horizontal vibration frequency 14.43 Hz (like the analytical). For vertical degree of freedom I've got 31.19 Hz, which is Vp/4H (the analytical sollution), so it looked alright. Then I noticed the text of the figure: gravity suddenly applied to a square grid. So: if you model a square 3x3 meters with the given material properties, plane strain setup and restrain the translation at the bottom edge you'll get close to 25 Hz. With SAP2000 I've got 26 Hz which in my opinion is reasonable.
Best regards,
I really appreciate for these clear answers. Specially thanks to Dr. Andreev for examination the problem with SAP.
Sincerely
Dear all,
I wonder what methods I can use for evaluating natural frequency of slopes using FLAC2D.
Kind regards
Hi Pooria
Just analyse your model WITHOUT damping (This is called "free- vibration analysis). Then find the time (period) of a complete cycle of displacement. You need the displacement time history of a representative point (normally at the top of the model). The natural frequency is the reverse of the period. For more details, take a look at Flac2d's manual, dynamic analysis, example 1.5, P. 1.54.
Regards
Dear Ms. Zekri
I appreciate your help
The free-field boundary conditions are applied to my main model. should I apply these boundaries while assessing natural frequency?
Regards
Applying free-field condition means adding values to the damping matrix of lateral elements (at the left and right side of the model). In this way the incident wave will be absorbed (= damped), So I think for natural frequency we should't apply FF.
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