Retrogressive failure of a static granular layer on an inclined plane
Retrogressive failure of a static granular layer on an inclined plane
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斜面上静态颗粒层的回归破坏
DOI：
10.1017/jfm.2019.215
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发表时间：
2019
影响因子：
3.7
通讯作者：
John Gray
中科院分区：
文献类型：
--
作者：
Aaron Russell;Christopher Johnson;A. Edwards;S. Viroulet;Francisco Melo Da Rocha;John Gray
当足够陡的斜坡上的一层静态颗粒受到扰动时，可能会形成向上传播的侵蚀波或后退破坏，将最初的静态材料与流动颗粒的下坡区域分开。本文表明，一个相对简单的深度平均雪崩模型与摩擦滞后是足以捕捉一个平面的倒退失败，是独立的横坡坐标。滞后建模与非单调有效的基础摩擦法，具有静态，中间（速度降低）和动态（速度增加）制度。实验和随时间变化的数值模拟都表明，在该系统中，稳定行进的后退波迅速形成，因此，采用行波方法导出了一维深度平均的精确解。波的速度由厚度的常微分方程中的临界点决定。临界点位于中间摩擦状态，摩擦力正好平衡重力的下坡分量。因此，在这种情况下，后退波是摩擦定律的函数形式的一个敏感的试验，在这种情况下，定常均匀流是不稳定的，因此不能直接用来确定摩擦定律。回归波存在的初始层深度和倾斜度的上限和下限被发现，并示出与实验确定的相图是很好的协议。对于Edwards等人提出的摩擦定律（J. Fluid.机甲师，第823卷，2017年，pp. 278-315，J.流体。机甲师，2019年，（提交））的波速的大小是稍微低于预测，但对于给定的初始层厚度，精确的解决方案准确地预测了更高的倾角在波速的增加。该模型还捕捉有限的波速在实验中观察到的倒退失败的开始。
When a layer of static grains on a sufficiently steep slope is disturbed, an upslope-propagating erosion wave, or retrogressive failure, may form that separates the initially static material from a downslope region of flowing grains. This paper shows that a relatively simple depth-averaged avalanche model with frictional hysteresis is sufficient to capture a planar retrogressive failure that is independent of the cross-slope coordinate. The hysteresis is modelled with a non-monotonic effective basal friction law that has static, intermediate (velocity decreasing) and dynamic (velocity increasing) regimes. Both experiments and time-dependent numerical simulations show that steadily travelling retrogressive waves rapidly form in this system and a travelling wave ansatz is therefore used to derive a one-dimensional depth-averaged exact solution. The speed of the wave is determined by a critical point in the ordinary differential equation for the thickness. The critical point lies in the intermediate frictional regime, at the point where the friction exactly balances the downslope component of gravity. The retrogressive wave is therefore a sensitive test of the functional form of the friction law in this regime, where steady uniform flows are unstable and so cannot be used to determine the friction law directly. Upper and lower bounds for the existence of retrogressive waves in terms of the initial layer depth and the slope inclination are found and shown to be in good agreement with the experimentally determined phase diagram. For the friction law proposed by Edwards et al. (J. Fluid. Mech., vol. 823, 2017, pp. 278–315, J. Fluid. Mech., 2019, (submitted)) the magnitude of the wave speed is slightly under-predicted, but, for a given initial layer thickness, the exact solution accurately predicts an increase in the wave speed with higher inclinations. The model also captures the finite wave speed at the onset of retrogressive failure observed in experiments.
颗粒自由表面流中的摩擦滞后和颗粒沉积
影响因子：
3.7
作者：
Edwards A
通讯作者：
Edwards A
侵蚀斜坡上的雪崩形成堤坝、槽沟和高架河道
影响因子：
3.7
作者：
Edwards A
通讯作者：
Edwards A