We analyse through numerical simulations, experiments, and scaling laws the dam-break problem for viscoplastic materials. Numerically, both two and three-dimensional (2D and 3D) scenarios are considered thanks to a proposed adaptive stabilized finite element framework able to compute efficiently free surface flows of highly viscoplastic materials. We choose to focus on the Bingham model. Momentum and mass equations are solved by using the Variational MultiScale method coupled with a regularization technique and anisotropic mesh adaptation. A convective self-reinitialization Level-Set method is used to describe the interface evolution. The obtained 2D multiphase results on viscoplastic column collapses show good agreement with literature. Additionally, new 3D simulations for both cylindrical and prismatic columns are explored through energy budget and new scaling laws based on which the collapse process is divided into three regimes: (1) viscous; (2) visco-plastic (mixed); and (3) plastic. These regimes are stressed for a wide range of initial column aspect ratio (1–20) and Bingham number (0.003–0.3). Lastly, the simulations are compared to experiments either taken from existing literature or performed using tailings, mineral suspensions, Carbopol, Mayonnaise, and Ketchup for cylindrical and conical columns.

我们通过数值模拟，实验和比例定律分析粘塑性材料的溃坝问题。在数值上，考虑到二维和二维（2D和3D）方案，这要归功于提出的自适应稳定有限元框架，该框架能够有效地计算高粘塑性材料的自由表面流。我们选择关注宾厄姆模型。动量和质量方程是通过使用变分多尺度方法结合正则化技术和各向异性网格自适应来求解的。对流自重初始化Level-Set方法用于描述接口演化。在粘塑性柱塌陷中获得的二维多相结果与文献显示了很好的一致性。另外，通过能量预算和新的比例定律，探索了圆柱柱和棱柱柱的新3D模拟，基于这些定律，塌陷过程分为三个状态：（1）粘性；（2）粘塑性的（混合的）；（3）塑料。这些方案在初始柱长宽比（1–20）和宾厄姆数（0.003–0.3）的广泛范围内受到强调。最后，将模拟与从现有文献中获得的实验进行比较，或者将实验与尾矿，矿物悬浮液，Carbopol，蛋黄酱和番茄酱用于圆柱和圆锥形色谱柱进行比较。