Halliday & Matthiessen (2014: 486-7):
If the dependent clause is non-finite, the circumstantial relationship is made explicit by the structural conjunction or conjunctive preposition. The conjunctions are a subset of those occurring in finite clauses, and their meaning is essentially the same. The prepositions tend to be somewhat less specific, e.g. in turning the corner, on thinking it over, with you being away, without John knowing; and the meaning of the clause introduced by a preposition may vary according to the sense of the primary clause:
||| Without having been there || I can’t say what happened. |||
(cause: reason ‘because I wasn’t there’)
||| Without having been there || I know all that happened. |||
(condition: concessive ‘although I wasn’t there’)
||| Without having been there || I rather like the place. |||
(indeterminate)
Nevertheless, it is usually possible to assign these clauses to the categories of time, manner and cause, and to match the prepositions up in a general way with the conjunctions.