Answer: As you have seen, gravel is a great seedbed, it also does not help feed the soil and nourish the peonies. The plastic is not recommended in a perennial garden situation as it prevents air and rain from reaching the soil. Here are some alternatives to consider.
Crabgrass is an annual grass, so it grows from seed each year. One way to prevent it is by using a preemergent such as corn gluten meal. This needs to be spread over the soil before the seeds begin to germinate, so the rule of thumb is to apply when the forsythia bushes bloom in your neighborhood. You may need to reapply several times during the season to maintain control, and do not rake or disturb the soil as it will disturb the barrier formed by the pre-emergent.
Another option would be to mulch the area; mulch should be raked and fluffed periodically to prevent inblown seeds from germinating. The mulch has an added benefit of breaking down over time and helping to enrich the soil. It should be applied about three inches thick.
You can also use newspaper, dampened and spread about ten sheets thick, under the mulch. This excludes light and smothers underlying weeds and seeds and prevents them from growing. The mulch will hide it, eventually both will rot down naturally.
I hope this gives you some ideas.
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