Willow Tree Roots
Roots need leafy branches to grow. So, the roots will not continue to expand without leaves to feed them. Keep suckers mowed down or chemically treated and roots will not expand. However, dead roots will remain in the soil for many years.
Grinding the stump will greatly reduce re-sprouting, known as suckers, but willow can continue to send sprouts up from large roots left behind in the soil. Keep these sprouts mowed down and eventually the old roots will lose their stored energy and stop sprouting. This could take several seasons.
You can chemically treat the freshly cut stump with herbicide, such as glyphosate, in fall or in spring to help kill the roots. The cut must be fresh, and please always read and follow all label precautions. Glyphosate kills all plants on which it is sprayed or applied. The roots gradually take up the herbicide and die.
Here is a reference for you on the topic of tree stumps, should you need it.
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