Browsing a logs it appears:
Soul Fragments are gathered rather like Motes of Anger from [Tiny Abomination in a Jar]. Autoattack can generate and special attacks can generate. Some attacks appear to have multiple proc chances (early in the log I see an auto-attack + Plague strike generating 3 Soul Fragments all with the same timestamp, disease (re-)application could proc).
Thus many chances to build Soul Fragments = extremely fast ramp-up time.
When the 10th Fragment is earned, Chaos Bane immediately procs doing damage and providing a 10 second buff of 270 Str. For the duration of this buff, no new Soul Fragments are earned (ICD). However, within 0.046 seconds of Chaos Bane fading a new Fragment is earned.
Up-time of 270 Str buff is 10 seconds divided by (10 seconds + time to build stack). Modk built a stack from 0 to 10 in 6.5 seconds. When in constant combat looks like he averaged about 6.5 to 9-ish seconds per stack. So up-time for a DK would be expected to be 50% plus. I would expect a Ret to be similar (many Ret attacks give multi-proc chances), Warriors (to my understanding) have the least multi-proc chance attacks, but I'd still estimate close to 50% up-time.
Damage proc appears modified by some buffs (***** of Elements/Ebon Plague? Others?). 3118 hit to single trash target is outside its listed range. Smaller hits to many mobs in range (Severed Essence + Valk trash example taken) varied by nearly 20%, showing some are debuffed, others are not (otherwise should vary by 1-3 damage based on division and system rounding). Partial resist occurs. No crits seen.
TLDR: Modeling it as 270 Str with 50% up-time and a damage proc every ~20 seconds is a good rough approximation. Accurate modeling of the value of the damage proc requires more knowledge of what buffs/debuffs modfiy it.