Fortress of Apocalypse

A 2011 manga about young criminals and zombies.

Yoshiaki Maeda, 16 years old, was convicted of murder. He says he is innocent, but no authority or the others young criminals in the detention centre he was put in believe in him. That soon will not matter any more anyway, because a zombie infection begins to spread through the world outside the prison. Ironically, the place that most people want to escape from is now the place they want to remain in...

Written by Yuu Kuraishi. Art by Kazu Inabe. Published on Kodansha's Monthly Shounen Rival.

Tropes used in Fortress of Apocalypse include:

Big Good: Though none of the young criminals are exactly "good", and Hitotsukabuto was probably the one with biggest potential to be bad once his sentence was over because his father is an Yakuza, he serves as this once the initial panic ends by simply trying to assure the safety of all the other inmates.
Chainsaw Good: Some are used to cut zombies heads...or to simply cut through the zombies.
Combat Pragmatist: Yoshioka generally always tries to catch his opponents when their guards is down. Hitotsukabuto sees that as a signal of weakness.
Crapsack World: After the zombie apocalypse? Definitely.
Good Is Not Nice: Specially when almost everybody good is a convicted criminal.
Knife Nut: Yoshioka uses knives as weapons, less to hand-to-hand and more like darts. Of course, his opponents are mostly undead corpses, and don't would be wise to face them in close range, so that's justified.
Off with His Head: The first time a chainsaw is used, by Yoshioka, he uses it to cut a zombie's head off.
Police Are Useless: The main characters go to a JSDF base to seek weapons and discover that almost everyone was killed or zombified.
Sole Survivor: The main characters find one(and scared) soldier on the JSDF base...and he dies not too long after, victim of some kind of human-zombie-dog.
Super Strength: Some zombies are so strong they can bend iron with their mandibles.
The Needs of the Many: As the situation becomes clear, many characters adopt this point of view, even to the point of using living humans as bait for the undead. That's why Hitotsukabuto almost kills the protagonists until they convince him they can be useful by bringing weapons from outside: taking an important resource as a car on a whim made him see them as a danger to the greater group.
The Smart Guy: Yamanoi is shown to be academically smart and quickly adapts to the situation, to a scary level.
Our Zombies Are Different: They are fast, they do spread through bite, they cannibalize themselves, but they also can join each other in some kind of organism(?) with some weird human-looking "thing" that serves as their "brain".