To stop a wedge.

[ValentinianVictrix]

Vegetius (III.19) mentions a formation called the forfex (forceps, or pincers) apparently an open V designed to envelop an attack by wedge:

"There is also a method of resisting the wedge when formed by the enemy. The wedge is a disposition of a body of infantry widening gradually towards the base and terminating in a point towards the front. It pierces the enemy's line by a multitude of darts directed to one particular place. The soldiers call it the swine's head. To oppose this disposition, they make use af another called the pincers, resembling the letter V, composed of a body of men in close order. It receives the wedge, inclosing it on both sides, and thereby prevents it from penetrating the line."

But we should not imagine Roman infantry of any era passively awaiting the arrival of the enemy. Late Roman troops in particular had a formidable array of missiles, and any attacking force would have to wade through a barrage of arrows, catapult projectiles, sling bullets, javelins and plumbatae before reaching the Roman front line. Such a bombardment would very likely either break up the attack or stall it completely, making the attackers vulnerable to a Roman counter-charge.

You would think that such a bombardment would have that effect Nathan, but its clear in Ammianus and other works that this was rarely the case. There are several battle accounts where casualty figures were given, its stressed that most casualties were caused when one army broke and the victorious one then slew the routers in the pursuit. And of course whilst the Romans did indeed put up a tremendous missile barrage at battles such as Argentoratum, that did not prevent the Allemanni from breaking through the Roman front line and crash into the second where they were finally beaten off.
Both the Late Romans and their barbarian counter-parts used wedge formations called either the 'Hogs Head', the 'Cuneus' or the 'Saw tooth', these are described in action by Ammianus and others.