We use a nonlocal viscoelastic damage model to investigate the conditions that enable water-free surface crevasse propagation in grounded marine-terminating glaciers. Our simulations, on idealized rectangular ice slabs in contact with the ocean, show that crevasses propagate faster in thicker ice slabs. We find that: (1) the fraction of ice slab thickness penetrated by surface crevasses decreases with increasing seawater depth near the terminus; (2) a no-slip (fixed) basal boundary condition retards crevasse growth; and (3) crevasses form closer to the terminus when the seawater depth is larger or when the glacier base is fixed to the bedrock, which could lead to calving of smaller icebergs. However, water-free surface crevasses can penetrate (nearly) the entire ice thickness only in thicker ice slabs terminating in shallow seawater depths. This leads us to the conclusion that surface crevasses alone are not responsible for calving events in marine-terminating and thin glaciers.