Face-up Normal Monsters on the field are unaffected by your opponent's Spell Cards. This card is destroyed during your second Standby Phase after activation.
Rulings
Individual Card FAQs
If you skip your second Standby Phase with "Solomon's Lawbook", etc., then "Dust Barrier" remains on the field and its effect continues to apply.
If "Imperial Order" is active during the 2nd Standby Phase after activation, "Dust Barrier" is still destroyed.
Spell|
Continuous