The secretary of transportation shall make partial payment to a contractor performing any road or bridge work under contract with it, as the work may progress, said partial payment not to be less than ninety percent (90%) of the contract price of the material delivered and work done and accepted. The secretary shall provide by regulation, to be made a part of all specifications, for the withholding of not more than ten percent (10%) of the full contract price of any such work until the work is satisfactorily completed and approved by the secretary and the provisions of the contract and bond therefor have been fully satisfied.