Why do the Shi’ah prostrate on Turbah (dried Mud)?

Prostration on Turbah is the Sunnah of the Prophet Mohammad (SAWA) and it is verified in Sunni documents too:

Abu-Sa'eed said that he had seen the Prophet doing his prostration (Sajdah) on mud, so much so that he could see the stains of mud on his forehead.

(Sunni Document: Saheeh Bukhari, Part 1, p. 104)

The Prophet used to rest his forehead on the earth (Turbah) while prostrating.

(Sunni Document: Saheeh Bukhari, Part 1, p. 97)

The Prophet declared that the best place for prostration was the earth or a thing that grows from the earth.

(Sunni document: Kanz al-Ummaal, Part 4, p. 113)

The Allah-chosen Infallible Imams of the Shi'ah and the Shi’ah obey the Prophet whom God has commanded humankind to obey. (Qur'an, Surah Nesa’(4), Verse 59; …)

Imam Ali (SBUH) has said:

... The Ta’wil (original Allah-intended meaning) of the first prostration (in each rak'ah of every Salah) is that you enter in your heart- when you are prostrating on earth-: O’ Allah! You have created me from earth; and when raising your head, enter in your heart: O' Allah! From earth, You have brought me out.

In the second prostration, enter in your heart: O' Allah! You shall return me to earth; and when raising your head, enter in your heart: O' Allah! From earth, You shall raise me again ... .

(Mostadrak al-Wasaa'el al-Shi'ah; …)

From the (earth) did We create you, and into it shall We return you, and from it shall We bring you out once again.

(Qur'an, Surah TaaHaa(20), Verse 55)