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D = $alphaM * M + $betaK * Kcurrent +$betaKinit * Kinit + $betaKcomm * KlastCommit

rayleigh $alphaM $betaK $betaKinit $betaKcomm

$alphaM factor applied to elements or nodes mass matrix
$betaK factor applied to elements current stiffness matrix.
$betaKinit factor applied to elements initial stiffness matrix.
$betaKcomm factor applied to elements committed stiffness matrix.

please clarify the difference between ( $betaK $betaKinit $betaKcomm), what is the stiffness matrix used in each case.

does $betaK mean that the stiffness matrix generated from the last nonlinear gravity analysis is used and remain constant during the dynamic analysis?
does $betaKinit mean that the stiffness matrix generated from the initial linear case (undeformed case) ?
does $betaKcomm mean that the stiffness matrix generated from the nonlinear case and at every step in the dynamic analysis it will change to a new one (not constant in the dynamic analysis)?



In the examples on the site, I found that most soil problems use ($alphaM $betaK), while in structure uses ($alphaM $betaKinit ) or ( $betaKcomm ) only. is there a reason for that?

I have another question regarding the use of Region Command with Rayleigh damping (can I used both mass and stiffness coefficient for element and its nodes or do i need to do each one separately )

I am modeling a single bridge pier supported in pile cap considering soil-structure interaction as shown in the file.

-The piles are modeled as elastic force beam element. While the pier is modeled as nonlinear force beam element.
-The pile and pile cap are fully bonded to soil with EqualDOF in X and Y directions.
-The bridge weight and mass are applied to node 9515 at top of pier element.
-The earthquake loads are applied as an equivalent force equal to (Lysmer-Kuhlemeyer constant *
velocity) at node 117270.
-I have used "sp Constraint" to constrain base of the structure (nodes 1, 11726 and 117270 in X-direction during gravity analysis), then removed this constraint in earthquake analysis.

***I need your help on the following items:
-Are the steps used in modeling and analysis correct or not. and how can I improve it?
-The earthquake results show displacement osculation around an inclined line (not Zero). Also, the
velocity at node (1) is shifted from the original input velocity. output results are plotted in the
attached excel file.
-Do I need to add additional damping to the model to count for structure and soil dampings (radiational
damping) or is it inherited in soil material plastic behavior?
-How can I define an interface element between pile and soil, pile cap and soil?

Model and attached files (http://www.mediafire.com/file/hhnd92a9nzp901b/Model.zip)