The basic way to "archive" projects would be to use the rt-click/"Export" command from Site Admin when clicking on a project in the list. this generates a "QCP" file (actually a ZIP) containing what is needed to re-create the project database and repository. Even with the newer ALM 12.6 and 15, QCP generation still has some limits with extremely large projects (>>20Gb).
It will deactivate the source project during the QCP creation and can be sped up a bit by using Site Admin running on the ALM Server (if possible), since it does not have to go so "far" over the network.
As a matter of fact, the latest ALM 15.5 includes an "archive" utility in the Site Admin menu (across the top). this is related to the ALM Robot tool, but can do in effect a "bulk" archive of selected projects. It actually just automates the rt-click/export process and results in various QCP files for the selected projects. Be careful as with "robot" and any other automation tools doing migration or backup like this, it may get "stuck or fail on a given project and leave you to spend much more time to figure out that it failed on a certain project and why.
A fall-back "archive" process is what we like to call "raw" -- de-activate your project, take a project DB backup as well as ZIPping up the corresponding project repository folder. Keep these together (maybe add the DB backup to the ZIP) and name appropriately to indicate what ALM version and project name. LATER, you can do the reverse if needed and can restore the project as you would when migrating a project.