rutyoudaoicibaDictYouDict[rut 词源字典]
rut: The rut of deer [15] and the rut of a wheel [16] are not related. The latter in fact is historically the same word as route. Both go back ultimately to Vulgar Latin *rupta, which was a noun use of the past participle of Latin rumpere ‘break’ (source also of English rout and rupture). The etymological notion underlying it is therefore of a path that has been ‘broken’ by constant use, a ‘beaten track’.

It passed into Old French as rute or rote, and it was this that gave English rut, which originally denoted the ‘track’ made by a wheel. The later French form route is the source of English route [16]. Routine [17] comes from a French derivative of route. Rut ‘oestrus’ comes via Old French rut from Latin rugītus, a derivative of rugīre ‘roar’.
=> rout, rupture[rut etymology, rut origin, 英语词源]
rut (n.1)youdaoicibaDictYouDict
"narrow track worn or cut in the ground," 1570s, probably from Middle English route (see route (n.)); though OED finds this "improbable." Metaphoric meaning "narrow, monotonous routine; habitual mode of behavior" first attested 1839.
rut (n.2)youdaoicibaDictYouDict
"annually recurring sexual excitement in animals; animal mating season" (originally of deer), early 15c., from Old French rut, ruit, from Late Latin rutigum (nominative rugitus) "a bellowing," from past participle of Latin rugire "to bellow," from PIE imitative root *reu-. The verb is recorded from early 15c. Related: Rutting.