MAXIMUM Time Step Calculation

[FaizanAhmadNadeem]

Hi STKO Team,

In the supporting excel file of 8th webinar, where 30Hz ricket wavelet was used as an excitation, the formulae used to determine maximum time step is { element size/sqrt(bed rock's shear wave velocity) }. But I didn't find any source, where I can logically see that how this formulae is correct.

Can you please guide me, how that formulae is derived?

Thank you, in Advance!

[STKO Team]

It's called Courant-Friedrichs-Lewy (CFL) stability criterion.
However there is a mistake in the excel file. It should be mesh_size/shear_wave_velocity.

[FaizanAhmadNadeem]

Thank you for the response,

but why mesh_size/shear_wave_velocity?

why we are not using maximum wave velocity in the model, which is of course P-wave velocity, not shear wave's velocity?

CFL says, we should select a time interval in which, vibration information travels a distance less than the mesh size, and fastest moving information in FE model is P-wave! so, why we don't use P-wave? please correct me if i am wrong!

[STKO Team]

If you want to be sure, in the general case, yes, you should consider the P-Wave velocity as it's faster.
If I remember correctly, in that example, I was introducing only acceleration in X, which generates transverse motion (S-Waves). Of course, in the general case, P-Waves can also be generated as a result of complex interaction within the soil (different soil materials, interaction between waves, super-structure, etc..).
But that example was very simple, so to speed up calculation we only considered S-Waves.

Once again, it depends on the problem. Otherwise, if you want to be sure to pick a correct time step, use the fastest wave (P-Wave)

[FaizanAhmadNadeem]

Thank you so much for the clarification!

Can I have a suggestion from you?

Actually i am modelling soil vibrations induced by moving underground train. so, in my case, P-waves should be considered or it's not so much unrealistic to use maximum shear wave velocity instead of P-wave, to save computational cost?

what do you suggest?

[STKO Team]

Yes in your case, or in general for other generic source, I would use P-waves. At least you are sure not to make any mistake.

[FaizanAhmadNadeem]

Yes definitely.

Thank you so much for all the clarifications!

[STKO Team]

You're welcome