Deep interface depression or "pit formation", as a result of solute accumulation, due to double-diffusive convection in the directional solidification of succinonitrile (SCN) containing ethanol in an ampoule is investigated by a fully nonlinear numerical simulation. The calculated results are consistent with previous observations (Schaefer and Coriell, Metal. Trans. 15A (1984) 2109), and the instability margin falls between the convective and morphological boundaries at a low growth rate. For a high growth rate, the global interface depression becomes deep due to significant release of the heat of fusion; in this case, the critical concentration can be lower than the convective value. Near the instability margin, the pit forms at the center of the interface and is soon followed by constitutional supercooling. Also, the pit shape is affected significantly by the convective solute transport and thus the how structures. Such pit formation, results from the nonlinear coupling of double-diffusive convection and the interface deformation, and although differs from the traditional mechanisms, it could be an important route to interface breakdown.