Artillery bombardment slowly makes the terrain muddy (which compounds the effects of Rain Storms) and give it a ruined look. The aspect of the ground can give you an idea of how much bombardment it has received (light brown, dark brown, grey, dark grey).
Artillery bombardment can create craters of various sizes. They can be used as a great cover position by infantry. They are indestructible but can be filled using a Shovel: equip the shovel, switch to upgrade mode (
F), then press
E on the crater and select the "Fill In" option and start shoveling the blueprint.
Artillery bombardment can ruin and even destroy trees and bushes.
Structures built on terrain that's been bombarded become more vulnerable to damage. The effect depends on how bombarded the terrain is, which is visually represented by the look and color of the ground (light brown, dark brown, grey, dark grey). The increased vulnerability varies among damage types. In the worst cases, the structure may receive 2 or 2.5 times the normal damage amount.