There was some kind of construction going on.

这不是口语。这是现在分词 going on 作定语。我们常说：

There were some people waiting over there.

这种there be 结构，如果转换的话，去掉 There，把 be 动词放在主语后，成为进行时态，意思不变：

Some kind of construction was going on.

Some people were waiting over there.

即便没有这个定语，许多 there be 结构，也可以去掉 there，把be 动词放在主语后，构成主系表结构。例如：

There is a picture on the wall.=

A picture is on the wall.

网友是不是觉得，这种变化很有趣啊。

    这是 there be 句型，不是口语里的语序。some kind of construction 是主语， going on 是后置定语， 全句不能改为：There was going on some kind of construction.

    There was some kind of construction going on.（划线部分是现在分词短语作定语，修饰construction） = There was some kind of construction which was going on. (划线部分是定语从句，修饰construction)