We are talking here about at least two characteristics of soil: its tilth, and its productivity. For productivity you need nutrients. and minerals are nearly always depleted. Tilth refers to the structure of the soil. And most soils need organic matter to improve the soil structure--especially clay soils that can develop a rock-like hardness without a good organic composition. I would never put any organic matter in the trash to be hauled away unless it was contaminated. If you have no immediate use for it, you can store it behind some bushes. By spring it will be compost, and you will be glad you had the foresight not to dispose of it. You may need to add nutrients such as rock powder as well.