Answer: Most plants do best with about an inch of rainfall a week during the warm part of the growing season. (Tip: A coffee can makes a good sprinkler gauge.) You have to consider temperature as plant needs vary significantly from spring to the scorching days of summer in your north Texas garden.
Your clay holds a lot of moisture and you need to be careful not to overwater. Try giving plants a good soaking once a week if it doesn't rain a half inch or more. Mulching helps reduce the loss of water from evaporation, and as mulch decays, it will improve soil drainage and texture, so keep heaping on the mulch! Ultimately, you just have to watch the plants, feel the soil (gooey clay vs. hard and dry) and learn to water properly for your garden. Adding organic matter like you have done is a great idea! I suggest having the Agricultural Extension Office (ph# 817/599-6591) test your soil - they may suggest the addition of certain mineral amendments, which can make a world of difference in the soil texture.
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