Hello,
First of all I would like to appreciate your thought of pursuing a PhD, but I really doubt if you could find a suitable institute other than IIT's or NIT's for your PhD.
Alternatively, I have heard about a new Institute, RICSSBE (Royal Institution of Chartered Surveyors), with its affiliation to the Amity University,they have set up a Campus in Noida, which offers PhD in construction related fields.
You may want to check their website for more information :-
hope that is helpful