Why do the Shia Prostrate on Turbah (Clay Tablet)?
At first, it should be said that the Shia prostrate on stone and soil – in other words, the turbah (dried clay), and prostrating ‘on’ something does not mean prostrating ‘to’ that thing. That means they prostrate on Turbah to worship God, not the Turbah!
According to the Islamic tradition, at the time of the Prophet, Muslims would prostrate on the mosque floor which was then covered with soil and grit, and under intense heat, they would take a handful of soil and keep it in their hands until it cooled down and they could easily prostrate on it.
Jabir Ibn Abdullah al-Ansari says, “I was performing the Dhuhr (midday) prayer along with the Prophet and I took a handful of soil to cool it down so I could prostrate on it (1). One of the companions avoided placing his forehead on the ground, but the Prophet told him to let his forehead touch the ground.” (2)
The Prophet saw a man prostrating on a part of his turban. He signaled him to push the turban back and pointed at his forehead (which meant that he should prostrate on his [bare] forehead). (3)
There are other Sunni narratives which state that the Prophet used to prostrate on mat and khumra (clay used for pottery). (4)
There is a famous hadith (saying) of the Prophet which has also been mentioned in Sahih al-Bukhari: “The (pure) earth has been made for me as a place of prostration and an agent of purification.” (5)
Prohibition of Prostration on Cloth and the Like Even Under Difficult Circumstances
Khabbab ibn al-Aratt says: “We complained to the Prophet that the intense heat rising from the sand burns our foreheads and hands, but the prophet didn’t accept our complaint.” (6)
Ibn al-Athir, in explaining this narrative, writes that: “It means that the Prophet did not allow them to prostrate on a part of their clothes.” (7)
Another narrative by Jabir Ibn Abdullah al-Ansari goes: “As we were performing the midday prayer along with the Prophet, we would take a handful of soil and grit and pour it from one hand to the other to cool it down so we could prostrate on it.” (8)
Further to explaining this narrative, Al-Bayhaqi says: “If it was allowed to prostrate on the clothes one was wearing, it would have been easier than cooling sand down in one’s hands.” (9)
These two narratives along with several others indicate that it is not permissible to prostrate on cloth even under difficult circumstances.
 Musnad Ahmad Hanbal, vol. 2, pg. 327, hadith by Jabir; Sunan al-Bayhaqi, vol. 1, pg. 439
2) Kanz al-Ummal, vol. 7, pg. 465, hadith no. 19810
3) Sunan al-Bayhaqi, vol. 2, pg. 105
4) Musnad Ahmad Hanbal, vol. 6, pg. 179, 309, 331, 377; vol. 2, pg. 192, 198
5) Sahih al-Bukhari, vol. 1, pg. 91; Sunan al-Bayhaqi, vol. 2, pg. 433
6) Al-Bayhaqi, Al-Sunan al-Kubra, vol. 2, pg. 104
7) Ibn al-Athir, Al-Nahayah, vol. 2, pg. 497
8) Musnad Ahmad Hanbal, vol. 3, pg. 337
9) Al-Bayhaqi, Al-Sunan al-Kubra, vol. 2, pg. 105