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入水滑坡体所产生涌浪的波峰高度及传播时间是此类灾害预警和风险评估最为关注的特性参数。本文通过对滑坡体和水波相互作用的耦合数学模型进行数值求解,研究了以上2个特性参数与滑坡体形状及运动过程的关系。数学模型中假设滑坡体兴波区域内水波横向能量扩散可忽略,在立面二维的简化下应用非线性浅水方程描述水波过程;假设滑坡体底部流体法向流速为零,应用简化的Novier-Stokes方程描述底部流动;在滑坡体的运动方程中考虑了惯性力、水波波动压力、底部流体对滑坡体的阻力和浮托力以及滑坡体和滑动面间的摩擦力等。数值结果表明:滑坡体水平速度越大,涌浪传播越快;当滑坡体水平速度接近波速时,滑坡体具体形状对波峰高度有显著影响;当滑坡体水平速度大于波速时,波峰高度随滑坡体速度的增大而减小。因此,以往数学模型中对滑坡体具体形状的忽视,或者设定过大的滑坡体速度,都有可能导致波峰高度的低估,不利于防灾减灾。
The crest height and propagation time of the waves generated by the water slide body are the most important characteristic parameters of such disaster warning and risk assessment. In this paper, by numerical coupling of coupled mathematical model of landslide body and water wave interaction, the relationship between above two characteristic parameters and the shape and movement of landslide body is studied. In the mathematical model, it is assumed that the lateral wave energy diffusion in the landslide wave region is negligible. The nonlinear shallow water equation is used to describe the water wave process under the simplified two-dimensional facade. Assuming that the normal flow velocity at the bottom of the landslide body is zero, a simplified Novier- Stokes equation is used to describe the bottom flow. In the equation of motion of landslide body, the inertial force, fluctuating pressure of water wave, the resistance and floating force of the bottom fluid to the landslide body and the friction between landslide body and sliding surface are considered. The numerical results show that the greater the horizontal velocity of the landslide, the faster the wave propagation. When the horizontal velocity of the landslide approaches the wave velocity, the specific shape of the landslide has a significant effect on the height of the wave. When the horizontal velocity of the landslide is greater than the wave velocity, Body velocity increases and decreases. Therefore, neglecting the specific shape of landslide body or setting excessive landslide body velocity in the previous mathematical models may lead to underestimation of peak height, which is not conducive to disaster prevention and mitigation.