It's quite easy to do Rob, but forget the grass growing in the joints. That only happens on disused airfields, or areas which don't get much attention. On a passenger apron at a civil airport, the concrete would be as clean and tidy as possible. Things haven't changed much, so just have a look at a parking lot (for tarmac) or any concrete-paved area, airport if possible, and you'll see what it looks like. The main differences would be the sand and spar mix used, which would affect the colour.
But don't just draw or paint the joints onto the base - it'll look just like what it is - either cut individual 'slabs' from card, or use a single piece of card, glued onto the base board, and score it to represent the joints, then paint and add various tones. It should look something like this, on the 1/72nd scale 'Dak' I did for a friend's father. In this instance, the colour of the rather clean concrete was based on the actual airport as it was in the 1960s - other places may have more of a sand or brown-coloured apron.