fill it with compacted fill dirt until you loose headroom.  Finish the work with open-graded aggregate.  Grout from the top when done with filling to obtain intimate support.

There may be other ways and I haven't had my coffee, but that's what comes to mind.

f-d

¡papá gordo ain't no madre flaca!

how is the car park fill supported now? is it a retaining wall? if so, will your excavation on the east side of the wall make this existing wall unstable?

If you need to support this existing car park fill / wall while you are overexcavating, then you may be better off demolishing the bridge anyway

It is not clear to me why you wish to dig first.  Filling with concrete means you have lots of money for this job.  Thus look at other ways, maybe cheaper also.

In that case, there are many different options.  I'd explore them before doing what you have planned.

One would be to drill through the deck and then use compaction grouting of the existing fill to compact it somewhat.  That would also provide support to the nearby park fill.  Chemical grouting is another way to solidify that old fill.  This treatment also could wait until all is filled, depending on details.

Getting new fill into the under-deck area then can be by may means.  One would be by belt conveyor, such as that used to pile aggregate into piles.

Another way is to use sand and large "conveyor" pipes and compressed air to blow it in there.

Final work would be compaction grouting of what you have placed, with pipes through the deck or pushed in horizontally.

If you still wish to fill with concrete, before you do that, install compaction grout pipes into the existing fill so you can pump in there later.  I've even used ordinary downspout  pipes for roof drains for this purpose.  After concrete has set, go to it to compact that fill under the concrete with injected grout via those pipes.  A concrete pump with a sand - cement mix works also.  You don't need high pressure for your job.

I am sure others here have some ideas.

Thanks for your replies.
The car park fill is not supported now and there is no retaining wall. The fill has a slope of about 45` which goes under the bridge.
The reason we want to dig first is that the fill material is very poor and is mostly rubbish. So we want to dig it first, compact it, and then fill it up to avoid future settlements.
But now I should go through the options oldestguy suggested. In the meantime, I would appreciate other new solutions.

Do you have to maintain traffic while doing this? If you could detour traffic and remove the bridge, wouldn't it be much easer? You could also eliminate the bumps at the ends of the bridge.

     Maybe the tyranny of Murphy is the penalty for hubris.  - http://xkcd.com/319/
 

Yes, we have to maintain the traffic (actually this has been the client's preferred option so far).

If you go with the compaction grouting routine at some stage, I would bet any good grouting contractor will tell you his work will "solidify" that rubbish.  After all, if that rubbish is holding the park area now, it will in the future and the grouting will be suitable for eventual bridge support also.

I've seen them do some amazing things, (and some unexpected things, like filling sewers or tilting in basement walls).

Now let's say not everything is done perfectly and eventually the bridge settles or sags in the middle.  It probably will not cause an accident, but it likely can be raised with slab jacking methods, should that ever happen.

Get the grouting guy there early for his practical ideas before going further.  Be sure to have them furnish references of past good jobs.  Not just anybody can do what you will need there.

Stay away from sand if possible . If there is  any slope it will wash out. You could use any size of aggregate to fill the voids or several different size aggregates then grout. If small aggregate is used you will need grout tubes installed and you will pump from the bottom up. If large aggregate is used and the voids are large enough.  You may be able just to drop grout from the top It is possible to get the same strengths as regular concrete using this method.

Intrusion Prepakt /marineconcrete.com
 

Pay good attention to Prepakt1.  That is his Business.  Been around for a long time.