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Two-dimensional mathematical modelling of debris flows with practical applications

机译：泥石流的二维数学建模及其实际应用

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The paper deals with mathematical modelling of landslide - debris flow. One-dimensional models can be used in upper parts of the affected regions where debris flow is in a steep narrow canyon, while at relatively flat downstream areas near villages two-dimensional models are neccessary. Two mathematical models are described into more detail: one-dimensional model DEBRIF1D and two-dimensional model PCFLOW2D, both developed at the Faculty of Civil and Geodetic Engineering of the University of Ljubljana. Basic continuity and momentum conservation equations were accomplished with the non-Newtonian Bingham plastic fluid model proposed by O'Brien and Mien. As a case study, numerical simulations of the landslide - debris flow, which occurred in November 2000 and destroyed a part of the village Log pod Mangartom, Slovenia, was performed. Hydrographs of the debris flow discharge at the upstream end of the affected village were determined by the model DEBRIF1D and then used as the upstream boundary condition for the simulations by two two-dimensional models: PCFLOW2D and a commercial model FLO-2D. The three models were calibrated by field measurements and then used efficiently to determine the necessary measures for the future protection of the village. A special feature of the DEBRIF1D model enables direct computation of the initial hydrograph. Validity of the quadratic equation expressing resistance was roughly confirmed by field measurements even for changing flow regimes.
机译：本文涉及滑坡-泥石流的数学建模。一维模型可以用于受影响区域的上部，在这些区域中，泥石流位于陡峭的狭窄峡谷中，而在村庄附近相对平坦的下游区域，则需要二维模型。更详细地描述了两个数学模型：一维模型DEBRIF1D和二维模型PCFLOW2D，这两个模型都是由卢布尔雅那大学土木工程学院开发的。基本的连续性和动量守恒方程是由O'Brien和Mien提出的非牛顿Bingham可塑性流体模型完成的。作为案例研究，对滑坡-泥石流进行了数值模拟，该滑坡发生于2000年11月，摧毁了斯洛文尼亚Log Pod Mangartom村庄的一部分。由DEBRIF1D模型确定了受影响村庄上游端的泥石流排放水文图，然后通过两个二维模型（PCFLOW2D和商业模型FLO-2D）将其用作模拟的上游边界条件。通过实地测量对这三个模型进行了校准，然后有效地使用它们来确定对村庄的未来保护所必需的措施。 DEBRIF1D模型的一个特殊功能可以直接计算初始水位图。即使对于变化的流态，通过现场测量也大致证实了表示阻力的二次方程的有效性。

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