He spent a lot of time at work, at the expense of his marriage.

at 在这里表示"处于某种状态或关系"。 the 是定冠词，特指后面的expense。 expense 来自动词 expend（花费、消耗），名词形式指"花费、代价"。 of 表示所属关系，连接expense和marriage。 at the expense of 是固定搭配，意思是"以...为代价"，表示获得某事物的同时牺牲了另一事物。