When you talk about “broken armies” from this war, I assume you are referring to the armies that absorbed horrible numbers of casualties. Because they suffered from so many men being killed and wounded, they became “broken,” losing their morale and their ability to fight effectively. If this is what you are talking about, the broken armies had an impact on the military conduct of the war and on the warring societies after the war was over.
The broken armies of WWI had a military impact on the war after they broke. Because the armies broke, they were no longer able to fight effectively. Sometimes, as with the French army in 1917, they mutinied, refusing to engage in any further offensive actions. When this happened, it made it even harder to achieve any sort of military victory than it already had been. This contributed to the stalemate that reined in this war.
The broken armies of WWI also impacted their societies after the war was over. The incredible carnage from the war traumatized the countries. In Russia, we can say that the broken armies helped to bring about the Russian Revolution and the withdrawal of that country from the war. After the war, the countries that had fought were generally very unwilling to think of the possibility of another war because they remembered the horrors that had led to the broken armies. This helped cause the UK and France, for example, to engage in a policy of appeasement later on when Hitler started to threaten Europe.
In these ways, the “broken armies” of WWI had an impact on the war and on societies and politics after the war.
The term "broken armies" is used to describe the armies in trenches, a defensive tactic employed very successfully by Germany and by France and Britain to a lesser extent. The groups of soldiers living in the trenches were called broken armies, because the units were divided into trenches that ran zig-zag, had horrible living conditions and, worst of all, lived in constant fear of death. The trenches had no latrines or waste disposal; soldiers suffered from trench foot and lice and did not get to shower more than once a month.
Trench-based warfare led to a stalemate on the western front, since neither side could move forward without suffering heavy casualties. The no-man's land was a kill zone and soldiers moving around could be easily picked off by machine fire. Any attempt to attack the trenches would lead to heavy death-tolls. (Of course, the use of tanks and poisonous gases provided some degree of success).
This stalemate combined with heavy casualties and horrible living conditions broke the morale of soldiers. The broken armies often had mutinies and soldiers suffered from physical and mental ailments, which made any chance of success very low. Newer weapons like tanks and poisonous gases were used. This type of warfare meant that frontal massive attacks were useless and specialized units with newer weapons had more chances of success. The broken armies had unhappy soldiers, millions of whom died and turned World War I into a war of attrition. This unhappy situation not only cost so many lives, but also vast resources of the country whose citizens were not happy with either (cost and casualty). This may also have been a cause for the swifter conclusion of the war.