Whenever the city council shall have caused any of the things enumerated in Section 19-2 to be done after due resolution and notice to the owner, and upon failure of the owner to do and perform the things aforesaid, then the council shall have power to assess the whole cost of such work, including the cost of the publication of the notice, against the property upon which such work was done and against the owner of the property; provided, that no assessment shall be made against any property, or its own, or personal liability declared unless such property shall be specially benefited by the work so done upon the same to the extent of such assessment; provided further, that the city council may by one resolution require the several things to be done as enumerated in Section 19-2, or any one of such things, on any number of pieces of property. In such case the specific thing to be done on each and every separate piece of property shall be clearly stated in the resolution, and notice shall be given to each owner in the manner provided for in Section 19-3. (Code 1941, Art. 86-50)