Syngenetic ice wedges form in polar regions in places where new sediment is periodically added to the ground surface (Layers A, B, C). Cracks that fill with ice and eventually sediment descend through the new layer into the older ice wedge below (Mackay, 1990). Repeat sedimentation, cracking, and sediment infilling produces sheeted ice wedges that appear to "grow" upward with the aggrading surface. The figure above shows syngenetic growth at 4 time steps.
At Time 1, the width of the ice wedge is W. Call this the original wedge.
At Time 2, Layer A is deposited, burying the former ground surface, and Crack X forms. Crack X descends through Layer A and a certain distance into the original wedge, expanding it by an amount that is some fraction of X. Let's call this distance f(X).
At Time 3, Layer B is deposited and Crack Y forms. Crack Y expands Wedge X by f(Y) and the original wedge by the amount f'(Y). The total amount of widening in the original wedge = W + f(X) + f'(Y).
At Time 4, Layer C is deposited and Crack Z forms, expanding the wedge Y by f(Z), wedge X by f'(Z), and the original wedge by f''(Z). The final width of the original wedge = W + f(X) + f'(Y) + f''(Z).
The volume of water increases when it freezes, the phase change from liquid to solid. Ground cracks form due to winter-summer temperature cycling (freeze-thaw action) effects on pore water in soils. In areas where no sedimentation occurs, wedges simply grow wider year after year (epigenetic ice wedges). In areas were the ground surface is aggrading, ground ice wedges rise with the surface.