The Council may provide in whole or in part the cost of replacing any improvement existing in the street at the time of the adoption of this Charter, by levying special assessments as hereinbefore provided; but any assessment for such replacement in less than twenty (20) years from the date of a prior assessment for the improvement to be replaced 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.