If the work consists of improvements on or additions to sewers or water mains already installed or paving already laid, and all bids for such work were rejected and the work done by the municipality, and if, in the opinion of the engineer acting for the municipality, the work can be done in separate sections or work units, it shall not be necessary that all of the work be completed before the special assessments are made. The governing body, by resolution adopted at any time before or after the work has been commenced, may specify what part of the improvements shall constitute a separate section or work unit, and upon completion of the work in one or more of such separate sections or work units, the special assessments may be made in the same manner and with the same force and effect as if all of the work in the entire improvement district had been completed. Failure for any reason to complete the work in any remaining separate section or work unit included within such improvement district shall not affect the validity of the special assessments made or the special assessment warrants issued for the work completed.