The City shall have control of all sidewalks in the public streets and alleys of the City and may construct, repair and replace such sidewalks as a public improvement and may provide for the payment of the cost thereof by special assessment or it may require the abutting owners to so do. If the latter procedure shall be followed, and any abutting owner shall fail to construct such sidewalk after being required to do so by resolution of the Council and upon such notice as the Council shall provide, then the City may construct such sidewalk and collect the costs thereof from the abutting property owner, or may make a special assessment in the same manner as herein provided for the making of special assessments where any expense has been incurred by the City upon or in respect to any particular lot or parcel of land.