how to eradicate?
Wasco County Oregon
Common purslane is edible so while you are contemplating a control method you could reduce the population by adding it to salads. But seriously, the primary method of management for common purslane is prevention. Watch for its inclusion in nursery pots to avoid importing to your garden. Purslane is a prolific seeder; once it has become established it is difficult to control.
The publication linked below gives more information about the plant as well as cultural, biological, and chemical control methods. Make sure you have correctly identified the plant before you make a decision and if you choose to use chemicals be sure to read and follow all of the label directions.