Dam analysis example

Dam analy­sis can be for­mu­lat­ed in LS-DY­NA ac­cord­ing to two-step ap­proach out­lined ear­li­er us­ing the IN­TER­FACE_­SSI and LOAD_­SEIS­MIC_­SSI cards im­ple­ment­ed for soil-struc­ture in­ter­ac­tion.

Two pre­lim­i­nary analy­ses are re­quired — a sta­t­ic analy­sis, and the aux­il­iary analy­sis to cap­ture the ef­fect of up­stream ground mo­tion.

Sta­t­ic analy­sis

In sta­t­ic analy­sis, the foun­da­tion rock and wa­ter are con­strained on the out­er bound­ary, and they are cho­sen to be suf­fi­cient­ly large to mod­el the sta­t­ic stress dis­tri­b­u­tion. This is not as oner­ous a con­straint as in dy­nam­ic analy­sis, where the out­ward prop­a­gat­ing waves would have re­flect­ed back from a fixed out­er bound­ary. On­ly the dam and the wa­ter are sub­ject­ed to grav­i­ty load­ing, the rea­son­ing be­ing that the cur­rent state of the foun­da­tion is al­ready its de­formed shape due to aeons of grav­i­ty act­ing up­on it. The fol­low­ing fig­ures show the mod­el and the “soil-struc­ture” in­ter­face, spec­i­fied us­ing IN­TER­FACE_­SSI_­STA­T­IC to record the sta­t­ic re­ac­tions. In a man­ner sim­i­lar to soil-struc­ture in­ter­ac­tion analy­sis — where the near­by non-lin­ear part of the soil was tak­en as part of the gen­er­al­ized struc­ture — here the near-field wa­ter, which may be­have non-lin­ear­ly, is tak­en to be part of the struc­ture, and the far-field wa­ter and the foun­da­tion rock are to­geth­er tak­en to be the “soil” so­main. Of course, any near­by non-lin­ear por­tion of the foun­da­tion rock may al­so be tak­en to be part of the struc­ture as nec­es­sary.

Aux­il­iary analy­sis

Aux­il­iary analy­sis in­volves on­ly the far-field wa­ter and the foun­da­tion rock, with the wa­ter do­main act­ing as the struc­ture, and the un­bound­ed wa­ter and foun­da­tion rock trun­cat­ed us­ing PML. The earth­quake ex­ci­ta­tion is ap­plied us­ing LOAD_­SEIS­MIC_­SSI on a seg­ment set at the wa­ter-foun­da­tion in­ter­face away from the PML bound­ary, and the mo­tions at the fu­ture “soil-struc­ture” in­ter­face are record­ed us­ing IN­TER­FACE_­SSI_­AUX for use in the sub­se­quent tran­sient analy­sis.

Tran­sient analy­sis

In the tran­sient analy­sis of the en­tire dam-wa­ter-rock sys­tem, the di­rect earth­quake ex­ci­ta­tion at the base of the dam is ap­plied us­ing LOAD_­SEIS­MIC_­SSI on a seg­ment set, and the ef­fect of the up­stream ground mo­tion, com­put­ed in the aux­il­iary analy­sis at the “soil-struc­ture” in­ter­face, is in­cor­po­rat­ed us­ing IN­TER­FACE_­SSI, which al­so reads in the sta­t­ic re­ac­tions com­put­ed in the sta­t­ic analy­sis.

The cor­re­spond­ing ex­am­ple in­put files for these analy­ses are dam-sta­t­ic.k, dam-aux­il­iary.k and dam-tran­sient.k, us­ing the ground mo­tion files el­cen­tro-x.ath, el­cen­tro-y.ath, el­cen­tro-z.ath. Please al­so see the README file.

NOTE: Please ig­nore er­ror mes­sages from LS-Pre­post flag­ging the IN­TER­FACE_­SSI cards as in­valid.