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Scattering Analysis Framework

A scat­ter­ing analy­sis frame­work, de­vel­oped by Bielak and co-work­ers as part of the ef­fec­tive seis­mic in­put method, is adopt­ed as the ap­proach for soil-struc­ture in­ter­ac­tion analy­sis in LS-DY­NA. This ap­proach con­sid­ers soil-struc­ture in­ter­ac­tion to be caused by the scat­ter­ing of the free-field ground mo­tion by the pres­ence of the struc­ture, and the ap­pro­pri­ate earth­quake forces and the use of an ab­sorb­ing bound­ary fol­low ra­tio­nal­ly from this view­point.

Con­sid­er the fol­low­ing two in­de­pen­dent states as part of a thought ex­per­i­ment: 

earthquake excites free-field

(a) soil is ex­cit­ed by an earth­quake in the ab­sence of the struc­ture, and

 

structure scatters free-field motion

 (b)  the struc­ture dis­turbs and scat­ters the in­com­ing earth­quake wave.

 Note that both these states can­not oc­cur in re­al­i­ty: it can be ei­ther one or the oth­er. 

If we take the dif­fer­ence of the foun­da­tion mo­tion in the two states, we are left with on­ly the scat­tered mo­tion, hav­ing elim­i­nat­ed both the earth­quake source and the in­com­ing wave. The scat­tered mo­tion — be­cause it is gen­er­at­ed sole­ly by the struc­ture — prop­a­gates en­tire­ly out­ward from the struc­ture.

structure causes scattered motion

Now the un­bound­ed do­main can be re­placed by a trun­cat­ed bound­ed do­main, but with­out on­ly sim­ple bound­ary con­di­tions, the out­er bound­ary will re­flect spu­ri­ous waves back to the struc­ture. This may be avoid­ed by us­ing an ab­sorb­ing bound­ary to re­duce the wave re­flec­tion and ap­pro­pri­ate­ly mod­el the un­bound­ed do­main be­yond.

absorbing boundary models the unbounded domain

We shall use per­fect­ly matched lay­ers as the ab­sorb­ing bound­ary, and the scat­tered-wave for­mu­la­tion will pro­vide the equiv­a­lent earth­quake forces, termed as the ef­fec­tive seis­mic in­put.