The verb face is used in many different senses, with varied types of argument (subject, object) and (arguably including) oblique objects.
'Face' can mean [all blockquotes Merriam-Webster unless otherwise attributed]
- (2b) [transitive verb]: cover the front or surface of
where it often, perhaps usually, takes a with-phrase showing what is used
- faced the building with marble
It is probably best to consider this as a [V] + [DO] + [PP] construction, though it could be argued that the PP is a mandatory element. But examples can be found without a PP:
- Built by local legendary stonemason Monte Nystrom (who also built the
fireplaces at nearby Custer State Park resorts) in 1929, this
structure is truly a masterpiece as Nystrom faced the building using
55 tons of petrified wood. [LandWatch]
- A common example of inappropriate installation methods is the use of a mineral insulant with mast climbers to face the building top to
bottom [pbc today]
However, intuitively, a similar construction with the sense of 'face' used here
- (1) [transitive verb]: confront ...
- faced him with evidence of treachery
- We are faced with/by a [massive] problem.
sounds to be more cohesive (heading for the grammatical counterpart of collocation, colligation, a fixed phrase). A with-string such as 'with evidence of treachery' alters 'The prosecuting council faced the defendant' beyond all recognition.
- A massive problem faces the museum continuously.
may sound clunky, but it is not ungrammatical, so it would be natural to see 'We are faced by a massive problem' merely as a typical passive transform. But this can't be argued for the variant (they are synonymous sentences, perhaps with minor differences in nuances) using 'with'.
Indeed, the Farlex Dictionary of Idioms gives a separate entry for the string 'faced with':
faced with (something):
- Forced to handle, deal with, or confront something.
- My meditation practice definitely helps me whenever I'm faced with a stressful situation at work.
- Faced with mounting pressure from activists, the government finally agreed to reverse its controversial policy....
[+ a subsense]
And it may be more sensible to see 'faced with' and 'faced by' as lexemes, as with 'up against', which Oxford Languages labels a 'phrase' (ie a fixed phrase). Of course, there is the sense of passive as suggested, more so with examples such as
The last two examples show what I consider is a difference in contexts where the with- and the by- phrases are more natural. 'Faced by' seems the better choice when an invading army is the enemy (indeed, the more literal meaning of 'faced by' may be intended ... it doubtless informs the choice). But for non-sentient causes of problems, difficulties, 'faced with' seems more natural. Of course, there will be examples where both seem equally appropriate.