Obviously, quiet is the wrong word for a war, but there had to have been times in the war where nothing of significance happened. Four years is a long time for a war, and everyone needs breaks, even a bunch of militaristic Europeans.
In 1914 and 15 there were frequent informal truces between enlisted men. The most famous of these was the Christmas Truce of 1914. These were not approved of by the various high commands, nor by certain forces that had taken serious losses already, and as the fighting became more bitter, they stopped happening.
http://simonjoneshistorian.com/2015/01/06/understanding-the-1914-christmas-truce/