Response:

“Abu Turab” means “Father of soil”. This title is amongst the most famous titles of Imam “Ali” [AS] and is considered one their most elegant one.

Sheikh “Ala’ al-Din Saktavari” in “mhadhrah ala 'waa 'l  ” book, p 113: “Ali bin abi Talib” {May god be pleased of him} is the first person who was named to this title, messenger of Allah [PBUH] gave him this title when he saw that he’s sleeping on the ground and his side is dusty, he told him out of kindness:

O “Abu Turab”! Wake up.

Allameh “Amini” says in “Al-Ghadir” book, vol. 6, p 337: it was amongst his most beautiful titles and from then one, it turned into a “Kiramat” {miraculous power} for him; because soil would tell him the news of the past and future until the day of resurrection. Understand it which is blunt secret.

“Abayah bin Rub’i” says: I said to “Abdullah bin Abbas”: when did messenger of Allah [PBUH] call “Ali bin abi Talib” [AS] “Abu Turab”? He answered: since “Ali” [AS] is the owner of the earth and god’s proof for its people after Prophet Muhammad [PBUH] and earth’s survival and composure depend on him, and I heard of messenger of Allah [PBUH] who said: on the day of resurrection, when infidel sees the reward and benevolence prepared for Shias of “Ali bin abi Talib” by god almighty, he’ll say: I wish I was one of the Shias of “Ali bin abi Talib” {Abu Turab}. And this is the meaning of this verse that infidel says: I wish I was soil.

 “Al-Sheikh al-Saduq” – ‘ilal al-Sharayi’ -vol. 1, p 156

Allameh “Helli” says about this sentence:

It might that uttering this verse in here is because of mentioning to another reason for naming him “Abu Turab”, because his Shias were called “Turab” {soil} due to their excessive humbleness and surrendering to his orders; as it’s written in holy verse: “And because he’s their leader, owner and ruler, he’s called “Abu Turab”.

Allameh Majlisi – Bihar al-Anvar – vol. 35 – p 51

Different narratives were quoted about when Prophet Muhammad [PBUH] gave this title to commander of the faithful Ali [AS]. Some of them say: “It was given to “Ali bin abi Talib” on “Jamadi al-Awwal” or “Jamadi al-Thani”, the second year of immigration in the battle of “Al-Ashirah”. It’s written in some other narratives that this title was given to him on the day that Prophet Muhammad [PBUH] made brotherhood covenant amongst all Muslims and selected “Ali bin abi Talib” for himself.

Of course, these narratives aren’t in contradictory at all; because Prophet Muhammad [PBUH] might have repeated it numerous times.

Good luck.