Trench warfare. Warfare fought between men in trenches. No, I think trench warfare is about as good as it gets. Would the word "attrition" work for you? - attrition: constant wearing down to weaken or destroy (often in the phrase war of attrition)

The Battle, or better said the Siege of Petersburg was mainly a trench warfare and a war of attrition.

WWI was fought to gain ground, thus the trenches; designed to hold taken ground. The high losses of troops caused attrition. Vietnam was NOT fought to gain ground, and is thusly termed a war of attrition.

Trench warfare is a form of warfare in which combatants occupy fighting lines, consisting largely of trenches, in which troops are largely immune to the enemy's small arms fire and are substantially sheltered from artillery. It has become a byword for attrition warfare, for stalemate in conflict, with a slow wearing down of opposing forces