How can we eliminate foxtails in yard? Weed-whacked them and tried sweeping. Don't want dangerous chemicals.

Our dog keeps getting these horrid things in her nose. They grow in our yard by themselves. We do not have a lawn there, so it's not like we water the area. My husband doesn't want to use Round-Up or some other dangerous chemical. I'm at the end of my rope. He weed-whacked the whole yard the other day and I swept up what I could with a broom and dustpan. The problem is that they're now on the ground rather than growing on stalks. I can't keep the dog inside 24/7 and all dogs sniff the ground.