Artificial barriers are widely used to prevent leakages. However, due to construction errors during the wall installation, passages with small dimensions may occasionally penetrate through the barrier, undermining its tightness. A three-dimensional discretized algorithm (TDA) is proposed for quantitatively estimating the transient-state discharge rate through defective cutoff walls. By discretizing the wall into a three-dimensional refined mesh grid, the algorithm enables an examination of penetrating passages, an evaluation of defect dimensions, and an estimation of discharge rate through the penetrating passages. A rigorous realization-by-realization comparison between the TDA and the finite element method (FEM) was made, and it was found that the TDA results show strong correlations with the FEM results, but at a remarkably lower (1/10 3-1/10 4) computational cost. The TDA generally gives a discharge rate that is 0.1-1.0 times greater than its FEM counterpart, as the lengthened seepage distance due to random corrugations in the penetrating untreated zone cannot be replicated by the TDA.