FLAC3D の動的解析における境界条件です。
まずは「その2」の Local nonviscous damping を利用する方法↓。
A Local Damping Scheme For Nonreflecting Boundary Conditions In Surface Wave Modeling
https://www.earthdoc.org/content/papers/10.3997/2214-4609-pdb.190.sur03
次いで、Document の説明から2種。丁寧に説明されています。
Dynamic Modeling Considerations — FLAC3D 7.0 documentation (itascacg.com)
動的解析の Quiet Boundaries（吸収境界）
In dynamic problems, however, such boundary conditions cause the reflection of outward propagating waves back into the model, and do not allow the necessary energy radiation. The use of a larger model can minimize the problem, since material damping will absorb most of the energy in the waves reflected from distant boundaries. However, this solution leads to a large computational burden. The alternative is to use quiet (or absorbing) boundaries. Several formulations have been proposed. The viscous boundary developed by Lysmer and Kuhlemeyer (1969) is used in FLAC3D. It is based on the use of independent dashpots in the normal and shear directions at the model boundaries. The method is almost completely effective at absorbing body waves approaching the boundary at angles of incidence greater than 30°. For lower angles of incidence, or for surface waves, there is still energy absorption, but it is not perfect. However, the scheme has the advantage that it operates in the time domain. Its effectiveness has been demonstrated in both finite-element and finite-difference models (Kunar et al. 1977). A variation of the technique proposed by White et al. (1977) is also widely used.
Dynamic analysis starts from some in-situ condition. If a fixed boundary is used while generating the static stress state, this boundary condition can be replaced by quiet boundaries; the boundary gridpoints will be freed, and the boundary reaction forces will be automatically calculated and maintained throughout the dynamic loading phase. However, changes in static loading during the dynamic phase should be avoided. For example, if a tunnel is excavated after quiet boundaries have been specified on the bottom boundary, the whole model will start to move upward. This is because the total gravity force no longer balances the total reaction force at the bottom that was calculated when the boundary was changed to a quiet one.
Free-Field Boundaries
The boundary conditions at the sides of the model must account for the free-field motion that would exist in the absence of the structure.
In order to apply the free-field boundary in FLAC3D, the model must be oriented such that the base is horizontal and its normal is in the direction of the z-axis, and the sides are vertical and their normals are in the direction of either the x- or y-axis. If the direction of propagation of the incident seismic waves is not vertical, then the coordinate axes can be rotated such that the z-axis coincides with the direction of propagation. In this case, gravity will act at an angle to the -axis, and a horizontal free surface will be inclined with respect to the model boundaries.
Vp,Vsの計算方法は SPH でも同様の計算をしていました。そうすると、初期定常の計算時から動的なポアソン比、剛性等を入力する必要があるのでしょう。静的な値で初期定常を行っていると、動的な値へ切り替えた際に定常状態が崩れます。
また、放射状の波を扱う際は、吸収境界が良さそうですね。張替えのサンプルはコチラ↓
; Set Initial Conditions
model gravity 10
; Set Boundary Conditions - Roller boundaries
zone face apply velocity-normal 0 range group 'West2' or 'East2'
zone face apply velocity-normal 0 range group 'Bottom'
; Static equilibrium
model dynamic active off
model solve convergence 1
; dynamic
zone face apply-remove range group 'Bottom' ; Remove velocity boundary
zone face apply quiet range group 'Bottom' ; Add quiet boundary
zone dynamic free-field on ; Free field boundaries
; Solve to time 0.015
model dynamic active on
model solve time-total 0.015
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