Make it round
The big problem he faces is not how much gunpowder he needs, but that the "cannon" will be ripped to pieces and the "barrel" will probably cave in after he fires the shot.
Compounding this problem is the fact that he is not firing a projectile out of the "barrel" but something that allows the combustion gasses to pass around it. Unlike a projectile that acts as a near perfect seal and trapping the gasses — the only exception being the rifling that allows some gasses to pass around it — the zombies take up no more than 50% of the cross section of the corridor. This means he needs a much bigger charge to eject the "projectile(s)".
The Tsar Cannon gives an idea how thick the walls of the barrel needs to be in order to stand up to the pressure.
Unless he reinforces the "barrel", the rock will most likely probably crack and collapse, trapping him in his hidey-place forever.
But things are not all doom and gloom... there are some upsides.
He does not need to worry about making more than one shot. If there is some damage — just not catastrophic such — then this is all right.
He is not firing a ball of iron at super-sonic speeds... he is firing flesh and bones at a few hundred miles per hour.
There are ways he can make this work.
Make it a round corridor instead. Making it round evens out the pressure and you do not get stress focus points at the corners, because there will be no corners.
Make the "lining" of the barrel layered and overlapping, with shock absorbing material between the rock and the lining. He needs something that is tough and hard, but that can crumble, to put between the lining and the rock.
I would suggest: tin cans. They can be pre-crumbled so that they are, say, 25-50% metal and 75-50% air. The sheet metal will press into the cans and the cans will absorb the energy and extend the time of the impulse which proportionally lessens the force on the rock, increasing the likelihood that the rock will not crack and collapse.
Make the explosion last longer. What he needs is not one big bang with tremendous pressure, because as Mythbusters concluded: high over-pressure (i.e. static pressure) does not equate to a big propulsive force, and especially not so when air can go around the projectile. What he needs is high dynamic pressure... i.e. a huge "wind" that keeps going until the barrel has been blown clear.
So what he needs his gunpowder to be divided up into several charges that explode sequentially in very rapid succession. This draws out the blast, creates a much better dynamic pressure (i.e. "wind") while keeping the static pressure down. This has actually been employed in real life, by Nazi-Germany during WWII, in the V-3 weapon.
So... how much powder?
When it then comes down to how much gunpowder he needs... well: this is anyone's guess, because the sum of human experience when it comes to black-powder powered 60-inch zombie cannons is — understandably — quite limited.
I would suggest that you hand-wave it by saying he made a couple of experiments.
One was laughably under-powered... not enough to make his chicken carcass-filled mannequins do anything other than fall over each other in a grotesque parody of Barbie dolls copulating.
The second attempt was a wee bit overpowered and unfortunately left him with a collapsed cave and some very angry visits from the local authorities after the shock-wave cracked windows, triggered burglar alarms, and scared Mr. Swanson's cows into stampeding through the nearby town... plus it left a huge swath of land down the mountain to stink of rotting chicken for a week before the scavengers had eaten all the chunks. This also gave him the idea to make it a sequential charge instead of one Big Bada-Boom
The last experiment however seemed to be quite all right, and it also gave him the idea to use shock-absorbers to help improve the survivability of the "barrel".
The actual numbers do not need to be specified, because that does not really add anything to the story. Think "Chekhov's Gun" here: do not go into details about elements that do not really add any value.
You asked for science. Well here it is: postulate that he experimented — i.e. used a comedic version of the scientific method — and then "eventually, he got it right".
...or he could just use a rocket engine
An alternate solution would be for your hero to not use a cannon but a rocket engine. A solid fuel rocket booster built into the deep end of the tunnel would provide a spectacular effect. The tunnel will not only be "blown" clear but also absolutely sterilized. Also solid rocket fuel is (usually) a lot safer than black powder. Your hero can even use black powder as rocket fuel. Black powder was actually used in rockets before it was used in guns.
There are a couple of problems with this. The main difficulty would be in obtaining the solid rocket fuel. And also that the tunnel will be glowing hot and probably dripping with molten rock and/or rocket fuel residue.... and also be filled with smoke from the still smoldering rocket engine.