The old man stood there,a pipe in his mouth 为什么是独立主格结构

a pipe in his mouth 是独立主格结构，意思和with a pipe in his mouth一样。
其中in his mouth用来说明逻辑主语a pipe的位置。
独立主格结构的两个要素：一是结构中有自己的逻辑主语；二是逻辑主语与句子的主语不一致。

the old man 和 a pipe两个主语不一致，因此产生独立。
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a pipe in his mouth =with a pie in his mouthwith +名词+介词短语的结构with可以省略The old man stood there这里不缺成分,主语是old man,a pie in his mouth做伴随状态,主语是pie,前后两部分的主语不一致,所以是...

a pipe in his mouth 是独立主格结构，作伴随状语，修饰stood
独立主格结构是由名词+非谓语动词构成
The old man stood there，a pipe in his mouth =The old man stood there and a pipe was in his mouth