When, in the judgment of Council, the public necessity may require it, any sidewalk pavement may be condemned because of its unsafe condition, or because it is not laid out of suitable materials or in the manner and according to the specifications provided therefor; and the owner of the abutting property may be required to relay the same, after notice of the order of Council, in the same manner as provided by Section 913.08; and upon the refusal or failure of such property owner to do so, the Mayor may cause the same to be done and the cost thereof assessed against such property owner in the manner provided by Section 913.09, and such assessment shall become a lien against such property in the manner provided by Section 913.09.