This is a difficult question to answer - because there are many ways you could do it. And there are pros and cons to each method. I'll just give an overview:
As an overall design, you need to keep track of: the original texture, the "darkness" applied, and the "transparency" applied. One thing I can say almost for sure is you want to "accumulate" the results of the explosions somewhere - what you don't want to be doing is maintaining a list of all explosions that have ever happened.
So you have surfaces for texture, darkness and transparency. You could probably merge darkness and transparency into a single surface with a single channel that stores "normal", "dark" (or a level of darkness) and "transparent".
Because you probably don't want the dark rings to get progressively darker where they intersect, when you apply an explosion to your darkness layer with the max function (Math.Max in C#).
To produce your final texture you could just write from the darkness/transparency texture to your original texture or a copy of it (you only need to update the area that each explosion touches).
Or you could use a pixel shader to combine them - the details of which are beyond the scope of this question. (Also a pixel shader won't work on XNA 4.0 on Windows Phone 7.)