All sums collected on account of such assessment shall be placed in the city treasury to the credit of a special fund, which shall be designated by the name of the proceeding. The special fund shall be used only for paying the costs and expenses of the improvement described in the resolution ordering the work, including the cost of all posting and publication provided for in this part and any other incidental expenses connected with the proceeding. The city council may at any time advance to such special fund out of any available funds in the city treasury, sums in excess of the amount to be paid by the city toward the cost of such improvement and may reimburse the city for such advances by repaying the amount thereof out of any money that thereafter comes into such special fund.