Dam break problems occur in a variety of applications. In the present paper we are especially concerned with the mining industry, where a dam break can be a catastrophic event with significant harm to the environment. In this case, the materials involved have a yield stress property, i.e., they flow only when a threshold is overcome by the stress that acts on the material. The plastic number, which measures the importance of the yield stress in the overall characteristic stress, is the main dimensionless number analyzed, and carbopol solutions are the kind of material employed. Since slip is common in motions of yield stress materials, the influence of this phenomenon is investigated by a comparison between the flow over a smooth and a rough surface. An image processing that captures the evolution of the shape of the interface as well as particle image velocimetry measurements were employed as tools to understand the role played by the plastic number in the problem. A number of cases presented a triangular depression that originated from a difference between the flow below the initial yield surface position and a rigid body motion above the initial surface position.