If the work is abandoned by the city before work is actually started or before any materials, supplies or equipment have been furnished or used, the incidental expenses incurred previous to such abandonment, unless provision has otherwise been made therefor, shall be paid out of the city treasury, but such expense for which the city is liable and which shall have been paid by it may be charged as incidental expenses against the district benefited in any new proceeding had or taken for any work which includes substantially the same work as that which was included in the abandoned proceedings.