到底‘dàodǐ’ (at last, in the end, finally; after all, in the final analysis): When used with a verb, it signals that the event named by the verb happens or succeeds finally after undergoing a process.
Zhǎo le jǐ gè yuèdàodǐ zhǎodào le yī fèn bǐjiào lǐxìng de gōngzuò.
(After looking for a job for months, he found a relatively ideal one finally.)
Xià le yī gè xīngqī de yǔjīntiān zǎoshang tiān dàodǐ qíng le.
(After raining a week successively, it became clear this morning finally.)
The adverb ‘dàodǐ’ may occur in a question, it focuses on the speaker’s insistence on finding an answer:
Duì nàjiàn shì nǐ dàodǐ yǒu shénme kànfǎ.
(What are you driving at? What do you think of the matter after all?)
Zhè gè zì dàodǐ shì shénme yìsi.
(What does this character mean exactly?)
‘dàodǐ’ may express the meaning of ‘bìjìng’ (after all; when all is said and done), implying ‘self-evident’ reason:
Rénjiā dàodǐ shì dàxué jiàoshòu, wèntí jiěshì de hěn tòuchè.
(He is a college professor after all, so he explained the issue clearly.)
Míngpái dàodǐ shì míngpái, zhìliàng jiùshì hǎo.
(It is a famous brand after all, the quality is really good.)
 Loar, J. K. (2011). Chinese syntactic grammar: functional and conceptual principles. New York: Peter Lang.