is generally how we say it in English, though the operation does consist in "wedging", "filling the gap", etc.

In certain bridge-buildiing methods, for instance, you will build spans outwards from the piers, which means that the two halves meet mid-span. To give the bridge structural integrity, the two halves are jacked apart, and concrete is cast in the gap. When the jacks are released, the two half-spans want to "bounce back" to their original position, thereby tightly sandwiching the new concrete "wedge" and the whole structure is thereby prevented from flapping about.

Folding up a paper serviette, raising the leg of a rocky table and wedging the serviette underneath it is nothing short of "clavage"!!!