The impact of damaged sidewalls at the joints between tubes on dam structures subjected to horizontal seepage is investigated. First, an experimental scheme is designed to test the mode and critical gradient of seepage failure of the soil in the damaged tubes. The effects of various overburden pressures (0, 5, 10, 20, and 30 kPa), hole radii(0.5, 1.0, 1.5, and 2 cm) and soil specimen properties were studied. The test phenomena and the changes in the pore water pressure were used to determine the seepage failure modes and the critical gradients under different conditions. Combined with the modified Terzaghi soil arching theory, a mathematical model was developed for the critical gradient for soil seepage failure. The model fitting curve was in good agreement with the laboratory test results. The critical gradient is independent of the overburden pressure and weakly dependent on the internal friction angle of the soil. The critical gradient increases with the cohesion. For fixed characteristic soil parameters, the critical gradient decreases at a gradually decreasing rate as the radius of the damaged hole increases.