You would use a tiling grass texture under the grass, you would then blend that texture with the dirt texture at the boundary between the two. You would also create a more irregular boundary between the dirt and the 3D grass. Don't just end the 3D grass abruptly. Add some tufts of grass randomly to break up the line. The blending between the 2D grass and dirt would also be a bit irregular.
I'm having a hard time finding a specific tutorial for your problem. But you want something like vertex blending or height blending. Unreal and Source both have terrain painting/blending tools. In a 3D package like Maya there's probably a texture paint tool somewhere. I'm not sure about Blender.
Decrease the density and the saturation towards the edge. Look at some reference images. There are usually more dead/dry grass next to paths as people and other things walks/goes on them. Maybe you can use some noise texture to modulate these properties on the edge.
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