Every ordinance providing for an improvement to be paid for in whole or in part by special assessments passed subsequent to the adoption of this Charter, shall contain an estimate by the City Engineer of the life of the proposed improvement. Any assessment thereafter made for replacing such improvement within such period of estimated life shall be limited to a sum not in excess of thirty-three and one-third percent (33-1/3%) of the cost of such replacement. Assessments for replacements at or after the expiration of such estimated period of life shall be subject to no limitation except as provided for assessments for original improvements.