I need to patch some concrete outside and I want to be able to match the
color (basically 'dirty looking') and make it look old & weathered.

Can I just add a little 'dirt' (i.e. soil) to the mix to make it look
darker and dirtier or will this create problems such as encouraging
organic growth or weakening the concrete (I would only add a little
bit).

Any better ways to weather concrete?

Note: it's only a small patch so I was hoping for something simple and
cheap...