Earthshaker

They say some people are born to move mountains, but those who are truly great don't bother to stop there.  Through years of training, Earthshakers have honed their body to peak performance, such that they have become like a mountain;  immovable, unshakeable, unstoppable.  At their strongest, a single blow can shatter the earth or anything else that stands in their way.   

Strength of Mountains

Starting when you choose this path at 3rd level, you dig into the earth and leave cracks where you step, and your rage is infused with the raw power earth.  When you hit a creature with a melee attack, you may attempt to Shove or Grapple them as a bonus action.   At the 5th, 10th, 15th, and 20th levels in this class, the distance you can shove a creature increases by 5 feet.

While raging, your size catagory is considered gargantuan for how much you can lift, drag, carry, and push and you can't be forcibly moved or knocked Prone against your will by normal means, such as being shoved or after falling from a great height.

Empowered Resistance

At 6th level, you've hone your resistances to near perfection.  Reduce all damage you take that you are resistant to by an amount equal to half your barbarian level.  This reduction takes place after the damage is halved.

Unshakeable

At 10th level, your rage makes you immovable even to powerful magical forces, and you can stride through the earth with ease. You have a climbing speed equal to your movement speed on stone surfaces, and can walk vertically and upside down while leaving your hands free, as you dig your feet into the stone like pitons, and you no longer take fall damage.

While raging, you cannot be Frightened, teleported, have your movement speed reduced, or be displaced against your will by any means, and any critical hit aginast you is considered a normal hit.  When you fall unconcious or die while touching stone, you may choose not to end your rage, you do not have to fall prone, and if you die, you can have your corpse become petrified into stone that is immune to bludgeoning, piercing, and slashing from nonmagical weapons.

Gigaton

At 14th level, you hone the raw forces of earthquakes into a single powerful blow.  As an action, make a melee attack.  On a hit, the target takes 10d12 magical bludgeoning damage.  Regardless of whether the attack hits, the creature makes a strength or dexterity saving throw against your attack roll, attempting to dodge or resist the force behind blow.  On a fail, the target is knocked back a distance equal to up to 5 times your strength score.  Objects and structures take double damage from this attack.   You may choose not to deal damage if you are only trying to throw or push something and not directly damage it.

Instead of attacking a creature, you may strike the earth, causing an Earthquake centered on yourself (Save DC = 8 + Proficency + Strength Mod).  When cast this way, the spell does not require your concentration.

Once you use this feature, you can't use it again until you finish a long rest.