Soil preparation is the key for getting most and the best from your container blackberry plants.
Blackberries grow best in well-drained sandy or a bit loamy soils, where pH is between 4.5 and 7.5, so we can say, they thrive in a slightly acidic soil.
In soils with pH above 8.0 you will experience iron chlorosis and you will need to add iron chelates.
A good home made compost or other organic matter is always welcome to improve soil aeration and drainage. You can also add perlite or sand for better aeration and water-holding capacity.
If you are mixing home compost into the soil, make sure its well decomposed and free of weeds, because you don't want weeds to compete with your blackberry plants.
Raw organic materials can also be added into your container soil, such as manure, woodchips, sawdust, but make sure they are well decomposed, especially take caution not to mix sawdust or woodchips into your blackberry potting soil, since they are tying up nitrogen for their decomposition.
You can add fresh manure, preferably chicken manure in small quantities, but avoid putting it near or in contact with the roots, since fresh manure can burn the gentle blackberry roots.
If you dont have home compost and other ingredients at your hand, buy a bag of good quality soil for berries, or some quality organic soil for peppers and tomatoes, and by the means of organic, its worth to spend a bit more on a quality container blackberry soil, since you will eat them in the end!