Obtaining the correct velocity input in quiet boundaries

The velocity input motion for quiet boundaries is converted to a stress as 2 * rho * Cs (for horizontal velocity). However, when measuring the actual velocity at the base of a model it often differs from the intended velocity. It is not clear that this difference can be accounted for by simply multiplying the stress by some constant, as at times the model is under-representing the input, while at others, it is overshooting. How should one evaluate de adequacy of this boundary condition for the given model? What determines how much the intended input and the actual motion differ by?

It’s logic in my opinion. For this configuration, the measured velocity at the base is the supposition of the input motion and the downward motion reflected back from the ground surface.

When I compare the input signal to what is actually obtained using sigma = 2 rho Cs, it appears to be producing consistently higher amplitudes not related to reflecting waves back from the surface, as one does not see a cyclic pattern across time in this comparison. So, the recommendation is simply to use the formula and not consider the different signal that is produced? Here, the peak is 55% higher than the input at the quiet boundary.

For a compliant base simulation, a quiet boundary is specified along the base of the FLAC3D mesh. See the section on quiet boundaries. Note that if a history of acceleration is recorded at a gridpoint on the quiet base, it will not necessarily match the input history. The input stress-time history specifies the upward-propagating wave motion into the FLAC3D model, but the actual motion at the base will be the superposition of the upward motion and the downward motion reflected back from the FLAC3D model.

Jumping here late, I have also been puzzled with this mismatch. I’m aware the comparison should be done at the surface of the model as suggested as Mejia and Dawson (2006), however, by fact I know in opensees they can have a perfect match at the base between input and measured waves, something that in FLAC3D seems to struggle. Have you tried using an elastic linear model only in the first row of your model and see the comparison?

When using quiet boundary for dynamic analysis in FLAC3D, the input at the base is the upward motion (or, half of the outcrop motion), while the recording at the base is the within motion.

In sum, make sure the input at base is half of the outcrop motion with quiet boundary, not the within motion, during deconvolution.

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