What are the various Horde mode fortifications in Gears of War 3 and how do they work?

Solution 1:

Fortifications

Barrier

These are used to slow or damage enemies, and can be a handy way to block off paths into your defended area. Upgrades give them additional longevity and damage-dealing abilities.

Decoy

These are used to draw enemy fire. Upgrades give decoys more health, and the final upgrade gives them explosives that detonate upon their death.

Sentry

The sentry is an automated turret that does low damage. When fully upgraded, they can stun an enemy with their fire.

Turret

A turret is a player-controlled fixed weapon capable of heavy damage. Upgrades give them increased range, damage abilities, and heavier armor for the protection of the user.

Silverback

This is a heavy mech piloted by a player.

General Upgrade Information

Upgrades can only be performed between rounds, and require that you have both the necessary amount of cash and the appropriate level. Be aware that some levels do not give you actual upgrades, but instead affect your ability to repair your fortifications.

Upgrades are not shared between players. In your example, only you can use the barriers, but I believe all players can repair them.

Upgrades are persistent between rounds, and only disappear when destroyed.

For more information, such as precise costs of fortification upgrades, see the source link: Gears of War 3 Fortifications