Fiqh-us-Sunnah Volume 1, Purification and Prayer, Fiqh 1.063A.

This is proven by the Qur’an, sunnah and ijma’ (consensus). The Qur’an says, “And if you are ill, or on a journey, or one of you comes from relieving himself, or you have touched women, and you do not find water, then go to high clean soil and rub your face and hands (therewith). Lo, Allah is Benign, Forgiving” (an-Nisa’: 43). From the sunnah we have the hadith related by Abu Umamah in which the Prophet, upon whom be peace, said, “All of the earth has been made for me and my nation a pure place of prayer. Whenever a person from my nation wants to pray, he has something with which to purify himself, that is, the earth.” (Related by Ahmad.) Finally, there is a consensus that tayammum forms a legitimate part of the shari’ah, as it replaces ablution or ghusl under specific circumstances.