A way to go, free and totally Ubuntu-based:
- Create disk image using Clonezilla. It supports creating Live CD/USB to create a clean copy. Works quicker than creating a tarball/zip-archive particularly bcs it operates on a lower level.
- To access the image, restore it from the compressed files using steps from here and mount it using mount tool.
P.S. Clonezilla produces a compressed image, so in order to browse it you have to uncompress and restore. The suggesed approach could be convenient both for storing a backup with respect to disk space and browsing the image while unpacking it only upon necessity.
If one needs to access the image frequently (not my case, I just need a backup), there is an option to keep raw uncompressed ready-to-mount image only.
P.P.S It seems that Clonezilla tool has an option for creating an uncompressed raw image right away.