Answer: In my experience, perennials would need a much deeper soil than that for a number of reasons. First, the top few inches of soil can dry out very quickly and without a deeper layer to hold more moisture, this would cause stress on the plants. Second, the roots of these long lived plants tend to reach much deeper, sometimes over a foot deep. In general, the larger the plant the larger the root system will be. Also, in order for them to survive the cold winter weather, their roots need to be down deep where they are better insulated from both cold and from the freeze thaw cycle. Finally, I would be concerned about the lack of drainage during extremely wet weather since excess moisture can not soak down into the asphalt the way it would into the soil.
I would suggest a minimum depth of 18 inches for best results with most perennials. If you want to grow annuals which are a little less demanding in terms of root space, you would still probably want a minimum of six to eight inches.
In essence what you are doing is building a container, so you might also want to make some holes in the asphalt to allow rain water to soak into it much the way drainage holes in a pot would work.
I have seen garden areas created on top of asphalt by first breaking it up and turning it topsy turvy to partially expose the soil below, then building upward by adding top soil and organic matter to create a giant raised bed. This can enable you to grow not only flowers but possibly also shrubs.
No matter which approach you use, keep in mind that the raised beds and planter boxes all require careful attention to watering since they drain and dry out faster than a garden area in the ground would. They will also need special care with fertilizing and regular additions of organic matter and/or fresh soil to keep the fertility levels and soil structure suitable for healthy plants.
Best of luck with your project!
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