Heyy Anne,
Where are you located..?
If in Europe, as discussed earlier, you can try for RICS, they offer management careers in streams related to Civil and Construction.
If in India, RICS has set up a campus in Noida with affiliation to Amity University.
They also offer a PhD in these streams.
You can check their website for more details

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