Effectively it's a cannon. Look up the rules for cannons.
Or just give the poor bozo on the other side a Reflex save or die.
Here's how I'd do it.
5d6 fire and 2d6 bludgeon from the anvil and 1d4 piercing from the caltrops.
There'd be no attack roll. It's effectively a line. Reflex save is as per the best spell used in it... bead (SL1, CL1) or stone shape (SL3, CL5) ... so DC 14 negates.
Now for houseruling, I'd make it DC 14 negates if the target has a 5' square to step out of the line of fire, and DC 14 for half otherwise (such as in a 5' wide hallway).
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This may seem weak, but consider an E6 world where 90% of the people who you'd aim this at would have to dodge or die. 7d6+1d4 damage is an average of 27 damage, which would destroy almost any level 1-2 NPC.
It might not even propel the anvil at all. There is a reason that cannon balls are round and sized to be a near-perfect match to the diameter of the cannon's bore. Just build a crude stone bombard and drop an anvil in, and all the explosion will just blast out around that anvil, leaving it right where it is, or maybe, pushing it a little bit up the barrel where it flops embarrasingly on the ground.
The caltrops might leave the makeshift cannon's barrel, but not at the speeds you want, for the same reason. Compare to shotgun shells, where the pellets completely seal off the barrel AND have a plug to hold them in place for a bit (mere nanoseconds, but it really does matter) before they are forced out of the barrel.
In order to fire a heavy projectile, match the shape of it to the shape of the barrel so that there is no way for the explosion to escape around it (this way the blast MUST push the projectile in front of the expanding gasses).
As for the damage of it, this is pretty far afield of the actual rules, so the damage can be whatever your GM wants. Me, I might use the catapult rules for it.
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... wait, what?
You have access to so much black power that you use KEGS of it as breaching charges? Oookay...
Still, what you're built is called a "Petard". Rules wise, I'd say 6d6 (5d6 for charge, +1d6 for rock [calling a rock a "shaped charge" is a bit of a stretch]), reflex for half (like any explosion). DC determined by your appropriate trap making skill.
DM Blake is absolutely correct. For the cannon to even work at all, the projectile has to be a near-perfect fit of the barrel, otherwise the expanding gases will just blow around the object and barely push it. Ask the mythbusters who have experience with these things.
Also, this is why early guns used wadding to push the ball out of the barrel since the lead balls themselves were not uniform enough to seal the barrel. This is also why shotguns use wadding to this day.
Besides that, such an arrangement would likely push the "cannon" back farther than the anvil went forward. Assuming the cannon didn't become a fragmentary grenade itself.
Exploding a keg of black powder would generate an unbelievable amount of choking, acrid, blinding smoke.
If someone tried this on one of my games, the end result would likely be an anvil on someone's toe, a choking cloud of noxious gas, some fort saves and a few scorchmarks on the door.
Oh, and peals of laughter from the other side.