The tree roots were starving our plants. We dug the dirt out of that bed (it was a very difficult thing to do due to roots) we mixed and poured cement into the bottom and let it cure. The cement pavers that are used for sides have cracks in between for water to drain. This should keep better moisture in this bed and the roots out. The cracks in between the side walls should keep this bed drained. If there is a problem with drainage we will use a masonry bit and drill holes around the bottom.
If you are starting off with vegetable gardening in your backyard, consider your trees. I have read that it is not good for the tree to cut out these roots but when they took over our only area to grow vegetables we had to take a risk to save our little sunny spots.