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The Brute fighter archetype from Unearthed Arcana: Three Subclasses has the Brute Force feature, which adds a bonus die to damage dealt by weapons you are proficient in.

I want to know if abilities that work with weapon damage dice work with Brute Force's extra damage die, or not.

Below are some things that prompted this question:

• Would abilities like the half-orc's Savage Attack trait and the
  barbarian's Brutal Critical feature let you pick the bonus die
  instead?




• Would abilities like the Great Weapon Fighting fighting style* and
  the Savage Attacker feat let you re-roll the bonus die along with
  the original weapon dice?

The additional die counts as weapon damage

Unearthed Arcana: Three Subclasses, p. 2:

Brute Force

[...] Whenever you hit with a weapon that you’re proficient with and deal damage, the weapon's damage increases by an amount based on your level in this class, as shown on the Brute Bonus Damage table.
$$
begin{array}{c|c}
text{Fighter Level}&text{Damage Increase}\hline
3text{rd}&1text{d}4\hline
10text{th}&1text{d}6\hline
16text{th}&1text{d}8\hline
20text{th}&1text{d}10
end{array}
$$

The feature increases the damage of your weapon by a certain die which means this damage is considered one of the weapon's damage dice. This means the die granted by this feature can be used as (a) weapon damage die.

This means it can be used with all the features you mentioned:

• Half-Orc's Savage Attacks


• The Savage Attacker feat


• The Great Weapon Fighting Style


• Barbarian's Brutal Critical