In all of these sentences, the dependent clause is modifying the entire sentence, not a single word.  I have called them relative clauses that modify the  entire independent clause, but I suppose that one could call them something else.

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From:   Michael Kischner[SMTP:[log in to unmask]]
Reply To:       Assembly for the Teaching of English Grammar
Sent:   Saturday, August 28, 1999 5:58 PM
To:     [log in to unmask]
Subject:        Re: Difference between "as" and "which"

To reply to my own message -- does the fact that most of the "as" clauses
in the original example can be moved to a position before the main clause
signify that they are something other than relative clauses -- more
adverbial in nature?  Not that this would have any necessary effect on
whether they sound natural or unnatural with a "not."

On Sat, 28 Aug 1999, Michael Kischner wrote:

> I think you're on to something Rebecca.  Good sleuthing!  I note, too,
> that the "as" clauses can all be placed before the main clause -- except
> for1b, which sounds even more unnatural in that position than it does
> following the main clause.
>
> On Fri, 27 Aug 1999, rebecca s. wheeler wrote:
>
> > Hi folks,
> >
> > Regarding the example 1b which sounds bad...,
> > >
> > > > 1-a. You carried the luggage yourself, which was not necessary.
> > > > 1-b. You carried the luggage yourself, as was not necessary.
> > > > 2-a. He is a foreigner, which is evident from his accent.
> > > > 2-b. He is a foreigner, as is evident from his accent.
> > > > 3-a. Her feet were bare, which was the custom in those days.
> > > > 3-b. Her feet were bare, as was the custom in those days.
> > > > 4-a. She has married again, which was natural.
> > > > 4-b. She has married again, as was natural.
> > > > 5-a. Tom was not at home, which is often the case with him.
> > > > 5-b. Tom was not at home, as is often the case with him.
> >
> >
> >
> > I note a difference between example 1, and the others which may be relevant.
> >
> > Note that the first which/as clauses have "not" inside them. None of
> > the others do. Indeed, if we take out the "not", 1b becomes just fine:
> >
> > 1b: You carried the luggage yourself, as was necessary.
> >
> > I THINK that's fine.
> >
> > So, something is going on with the "not" element. Question is what.
> >
> > Notice,
> >
> > 2a. He is a foreigner, which is not evident from his accent.
> > 2b. He is a foreigner, as is not evident from his accent.
> >
> > While 2a may sound a nudge odd, 2b is flat out bad, I think. What I
> > SUSPECT is happening is that "as" functions to join clauses which are
> > alike in meaning in some significant way. That is, like "and", "as"
> > signals commonality or affirmation. But when you bring in a "not", it
> > seems that there is a clash with "as".
> >
> > Notice,
> > 2c. He is happy, as we can all see.
> > 2d. He is happy, as we can not all see.
> >
> > The contrast of final clause with first clause becomes fine if we put
> > an explicit contrast word in.
> >
> > 2e. He is a foreigner, although it's not evident from his accent.
> >
> > There's surely more to the story, as seen in 2f. Here, there is no
> > explicit connecting word (e.g. which, although, as), and the "not" is
> > perfectly good.
> >
> > 2f. He is a foreigner, a fact not evident from his accent.
> >
> > So, I think that the problem has arisen in the original sentence 1b
> > because "as" signals a "continuation" in some sense of the meaning of
> > the first clause, but then the "not" signals a clash.
> >
> > so, whatch'all think?
> >
> > cheers!
> >
> > rebecca
> >
> >
> >
> >
> >
> >
> >
> > ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> >
> > Rebecca S. Wheeler, Ph.D.
> > Assistant Professor of English
> > Department of English                   phone:  (757) 594-8891
> > 50 Shoe Lane                            fax:    (757) 594-8870
> > Christopher Newport University          email:  [log in to unmask]
> > Newport News, VA 23606-2998
> >
> > ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> >
>