As a minimum you can model a cylinder of soil with a diameter equal to 6-10 times of the total  layers' depth. Generally, in soil-structure interaction analyses, all soil layers down to the bed rock (in theory) is modelled. Perhaps you should also add the underlain layer. You fix all degrees of freedom at the bottom should be fixed (mimicking the bedrock high stiffness).  At the side soil boundary, nodes displacement and rotation were allowed only in vertical Z direction. If your software has infinite element, it is better to use them to represent the surrounding soil.

For a single layer on rigid bedrock, the first period is 4H/Vs, the second period is 4H/3Vs, the third is 5H/Vs. You don't need ABAQUS to calculate them. Good luck.

Dear Sirous Yasseri,

Thank you so much for your response. Well, I examine what you said, however the elements of my model distorted with hourglass error. As a result, I tried to refine the mesh but the elements again distorted. I thought when I fixed horizontal motion of lateral boundaries this constraint did not allow to system to had free vibration.

Do you have any suggestion?

You re sincerely

Ali Abolhasanpoor

Dear Stoyan Andreev,

Thank you so much for your response. Well to be quite honest, I have pile-soil-pile system which I want to calculate the natural frequencies to substitute in Rayleigh damping equation to evaluate Alpha & Beta coefficients. So, I want to examine a simple example to understand do I consider proper boundary conditions and dimensions for my geometry and compare the results of Abaqus program with theory.

Would you please guide me what boundary conditions I should choose at base and lateral boundaries of my geometry and which transverse and longitudinal lengths are suitable?

Best regards.

Hi,

You can use infinite element around the lateral boundaries.

You can try one of these to address hourglassing: 

The problem may be due to reduced integration method. The reduced integration is method is used to prevent "locking", in particular "shear locking", in some finite elements which prevents the solution from correctly converging. This is basically an error introduced to cover another. The best way to prevent the "hourglass" effect is through using higher order finite element formulations.

Dear Ali,

A soil deposit of 0.9m height with the first natural frequency of 25.68 Hz seems to be a false problem. First: can a layer of 90cm considered as a soil profile? Which civil structure vibrates with 25.68Hz? The frequency of 25.68 is out of consideration in soil dynamics, the cut off frequency generally used is 25Hz, to have the min wavelength 3.6980m (tdimension of elements are between 1/5 and 1/8 wavelenght). Good luck

Can you clarify why do you need modelling damping? Also, are you interested in only vertical soil modes? Regarding your boundary conditions on the 'sides' of the model, be careful if they are reflective or dissipative, as implied above.

If you are doing a soil structure analysis of a building, are you aware of Whitman approach to modelling soil impedances for the soil structure interaction - there are equations in e.g. ASCE 4-98 which could be used (depending on your soil conditions, layering etc.).