Application for permission to do any street work in or upon any unaccepted public street in the City and County of San Francisco by private contract must be made in writing to the Director of Public Works, which application shall contain a comprehensive description of the work to be done. Said Director shall thereupon investigate such application, and if after investigation the Director determines that the public interest or convenience requires the doing of the proposed work and that the same is expedient and will not be productive of detriment to the public safety or convenience, he is hereby authorized to grant permission for the doing of the same as applied for or as modified by the direction of the City Engineer, subject to the conditions and provisions in this Article hereinafter prescribed and provided.