The director of transportation may designate and establish controlled-access highways as new and additional facilities or may designate and establish an existing public highway as included within a controlled-access facility. The director may provide for the elimination of intersections at grade of controlled-access facilities with existing public highways by grade separation or service road, or by closing off the highways at the right-of-way boundary line of the controlled-access facility; and after the establishment of any controlled-access facility, no highway which is not part of the facility shall intersect the same at grade. No public highway shall be opened into or connected with any such controlled-access facility without the consent and previous approval of the director. The consent and approval shall be given only if the public interest is served thereby.