If the property owner fails, neglects or refuses to remove old sidewalks, repair old sidewalks or construct new sidewalks as required by council order, then the city may proceed to remove, repair or construct the same at any time within a period of one year from the date on which the property owner was ordered to have completed such work; and the cost and expense of such work, or such amount or proportion thereof as the council deems just, shall be assessed against the property as provided in this chapter. (Prior code § 9-1-9)