The key is adding organic matter. One of the best amendments you can buy is mushroom manure.Yeah my soil is heavy clay. Got a new roto tiller last year, will add more compost and fresh top soil. The clay when it gets warm and dry compacts like concrete then the rain just runs away. Was thinking of even adding some sand.
You also need to add soil microbes to enhance the growth of good fungi that aid in root development
Adding BioChars is also important as it serves as an active site for microbial growth
Another good sources of organic matter is chicken feed believe it or not Of course you can add leaves in the fall or gras clippings and fill them in well (as long as your not putting insecticides and weed killers on the lawn )
Overall thought the key is organic matter, soil microbes and BioChar.