Barrier lakes are secondary disasters with associated landslides and debris flow that can cause serious damage to the downstream populations and areas. Existing studies are lacking in comprehensive descriptions of the rescue process, where the main channel streamflow varies and topographic erosion develops, as well as engineering disposal performs. This paper aimed to theoretically investigate the formation and emergency responses to barrier lakes using on-the-spot investigation and calculus theory. The results showed that the formation of a barrier lake led to a sudden variation in the flow-change rate (normal to infinite). However, after implementing emergency measures, this rate returned to normal. The whole rescue process could be regarded as the accumulation of disposal effects. Volume changes in the main streams were expressed by a differential equation of the lake surface area and water level variations. In addition, a corresponding theoretical description of flow discharges was also given when engineering measures such as the excavation of diversion channels and engineering blasting were adopted. Specifically, the theoretical expressions of flow discharge were given respectively in the developing stage and breach stable stage after the excavation of diversion channels. The flow discharge through certain sections was also described theoretically when engineering blasting was chosen to widen and deepen the cross-section of the diversion channels. Overall, this paper mathematicizes and theorizes the existing emergency measures, which helps to better understand their implementation principles and application requirements.

中文翻译：

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堰塞湖形成及应急响应实施后水动力过程的理论描述

堰塞湖是伴随滑坡和泥石流的次生灾害，会对下游人口和地区造成严重破坏。现有研究缺乏对主要河道水流变化和地形侵蚀发展以及工程处置进行的救援过程的全面描述。本文旨在利用实地调查和微积分理论从理论上研究堰塞湖的形成和应急响应。结果表明，堰塞湖的形成导致流量变化率的突然变化（正常到无限）。但是，在采取紧急措施后，这一比率又恢复了正常。整个救援过程可视为处置效果的累积。主要河流的体积变化用湖表面积和水位变化的微分方程表示。此外，还对采用开挖导流槽、工程爆破等工程措施时的流量进行了相应的理论描述。具体地，分别给出了导流渠道开挖后发育阶段和溃口稳定阶段的流量理论表达式。选择工程爆破拓宽和加深导流渠道断面时，也从理论上描述了流经某些断面的流量。总体而言，本文对现有的应急措施进行了数学化和理论化处理，有助于更好地理解其实施原理和应用要求。