We applied saturated and unsaturated theory to establish a three dimensional finite element model (FEM), based on a proposed concrete faced sand-gravel dam, aiming to simulate the seepage field of the dam and its foundation under the condition of slab joint local failure. The different length, width, and position of the slab joint local failure were combined in the simulation condition. Overall, the results showed that a single local failure of slab joint had large influence on the local seepage field around the slab joint failure and little influence on the entire seepage field. Additionally, the saturated field is enlarged by the increase of length and width of the slab joint failure and the decrease of the position, besides the seepage field is affected mostly by the position and minimally by the width. The results also revealed that the great increase of the saturated surface was caused by the slab joint full-length failure under the action of superhigh-head. Thus, these factors should be taken into consideration during the design in order to avoid large-scale failure of slab joint.