Each map has an overall "Disarm Difficulty Level". Most of chests require your Disarm Value (Disarm skill * rank modifier + boost bonus) to be equal or higher than the Disarm Difficulty Level. Certain special chests can have a different Disarm Difficulty Level than the overall one. But this is always an exception. For example, the Titan Stronghold in Avlee has Disarm Difficulty Level 32 but the chest with the Perfect Bow has a lover level.If your Disarm Value is equal or higher than the Disarm Difficulty Level then you always suceed in opening the chest. If it isn't sufficient then you always fail and the chest explodes. Therefore, if you fail on your first chest in the area then you (most likely) fail while opening any chest here. You aren't enough good fo this area right now.
When the chest explodes, the course of events depends on your having Perception or not. The ones without the Perception skill are simply hit by a (higher level) spell. The (average) damage taken depends on their magic resistances. The ones with the Perception skill use their LUC + Perception * rank modifier for determining the course of events. They can even avoid being hit at all.
In my experience, the biggest difference consists in having or not having the Perception skill. Your chances are considerably better with the skill, therefore, buy Perception to everybody in your party even if you aren't planning to train a particular character in Perception. As a bonus, the Perception skill also protects you from being diseased when you explore trash heaps. Having the skill suffices.