Cathy, I think you have a running bamboo. You have my sympathy. I suggest you take a sample to the Chicago Botanical Garden for an accurate ID and advice. I googled it and found all kinds of crazy suggestions. I would also take sample of your soil. I think you will have to do a combination of industrial herbicide and black plastic. Good Luck, Nancy.
Identifying And Dealing With Invasive Bamboo Like Plant
Question From: ILLINOIS
Q: There is a very invasive plant in my yard that needs to be eliminated. It grows 6-9 ft tall, has hollow tubular stalks that look somewhat like bamboo, and giant green leaves that remind me of an indoor tropical plant. I live 25 miles North of downtown Chicago. Professional landscapers have tried to dig it out, and say the roots are more than 6 ft. deep. They also tried to kill it with heavy doses of industrial strength Round Up- nothing kills this beast! Someone told me it is called "Dock" but I can't find any information on it when I try to research this word. Do you know what it is, and how I could get rid of it? It is marching ever closer every year to a tree I love, and consuming more and more of my yard. Would it work to cut it all down to ground level, cover the area with black landscape fabric, and then heavy mulch to deprive it of light? Thank you!