Most of the roots will be in the top one to two feet of soil and will extend out to around three times the diameter of the canopy. Roots will not enter sealed pipes unless there is a break in the pipe. This used to be more of a problem back in the days when sewer pipes often leaked a little. Since your picture didn't come through (guess you tried since this post is in the gallery), I can't tell what it might have had to do with the text of your post.

I have a lot of willows, and they're entwining. Just had a huge thunderstorm, almost tornado, blast through here yesterday, so everything's tangled. What a mess. What I'm finding is that one must monitor the branches carefully because if they cross or touch they will rub each other and make wounds which hurt the trees and invite insects and fungus. I like the look of mixed foliage but it's more work. I use a binoculars and tall pruners. Had to cram lots of trees in here to suck up a swamp water problem. Willows like sunshine and will get leggy competing with each other. Had I had enough land would have planted them far apart to be specimen trees to shine in their individual glory. Look into the Prairie Cascade, imho the most beautiful of all willows, very fast growing and strong and hardy with bright golden branches in winter and large glossy dark green leaves in summer.

Salix purpurea 'Pendula'.

I think you mean invasive :-) And neither is really considered an invasive species although both will have aggressively water seeking root systems. Plant far away from any septic system or underground sewer or water pipes.