The G8 can't be dissolved as it isn't an organisation. It has no constitution and no founding treaties. It doesn't even have a headquarters.
Back in '75 the leaders of six industrialised countries had a meeting on economic cooperation, they held several more meetings, later inviting Canda, and later Russia, becoming the G7 and G8. But the G8 is fundamentally unlike the UN or EU or ASEAN. It is not a federation, rather it is the name given to a series of multilateral meetings. If a country wanted to leave the G8, it would just not turn up. If the G8 wanted to include another country they would just invite them.
The G20 meetings are formed on the model of the G8: Leaders of nations meeting to discuss matters of common concern. There is no constitution, rules or charter.
If the G8 countries find it useful meet as a group of 8 (or 7 now that Russia is not routinely invited) then it will continue. Both G8 and G20 will continue in some form as long as the various governments find them useful. I would not be surprised if there are other meetings held with various numbers of participants, which then get titled "G15" or "G22" for example, such meetings have been held in the past (G15 was a group of developing nations, G22 was the precursor to the G20)
I don't know what you are referring to about G8 failed to solve a crisis, but G20 succeeded.