In those limited parts of cemetery sections where upright headstones have already been permitted and installed prior to the passage of the ordinance codified in the chapter, other upright stones shall be located at the head of each grave space or plot and such installation shall be at the expense of the lot owner. A six-inch border, three inches in thickness, composed of concrete, shall be poured at the base of each stone, and the top of this border shall be flush with the cemetery grade level as established by the city.