Two-dimensional mathematical model of debris flow

WANG Chun-xiang; BAI Shi-wei; ESAKI Tetsuro; MITANI Yasuhiro

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Two-dimensional mathematical model of debris flow

更新时间：2026-06-25

- Two-dimensional mathematical model of debris flow
- Vol. 28, Issue 6, (2007)
- 作者机构：
  
  1. 日本九州大学环境系统科学研究中心,福冈,日本,812-8581
  2. 中国科学院武汉岩土力学研究所,武汉,430071
- 作者简介：
- 基金信息：
- DOI：
  CLC： TU443
- Online First：13 September 2013，
  
  Published：2007
- 稿件说明：
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WANG Chun-xiang, BAI Shi-wei, ESAKI Tetsuro, et al. Two-dimensional mathematical model of debris flow[J]. 2007, 28(6).
DOI：

WANG Chun-xiang, BAI Shi-wei, ESAKI Tetsuro, et al. Two-dimensional mathematical model of debris flow[J]. 2007, 28(6). DOI：

摘要

泥石流是在重力作用下，由砂粒石块和水等组成的固液混合物，是一种发生于山区的复杂的地质灾害现象。泥石流主要是由暴雨诱发引起的，它沿着复杂的三维地形高速流动，具有流体流动的特性。为了模拟泥石流的运动规律，预测降雨诱发的泥石流的到达距离和泛滥范围，减少和避免泥石流引起的灾害，把泥石和雨水组成的固液混合物假定为遵循均匀、连续、不可压缩的、非定常的牛顿流体运动规律。基于质量守恒方程和Naiver-stokes方程，采用深度积分方法，推导出了一个模拟泥石流运动的二维数学模型。所有方程式可用有限差分法来求解。结合GIS，该模型可用于预测泥石流的流动距离和泛滥范围，以及泛滥范围内的危险房屋和路段，也可以用于泥石流灾害的风险性分析。

Abstract

Debris flow is the gravity flow of water

clay

granular and rock mixtures and often triggered by torrential rains in mountainous areas. It is a catastrophic disaster that consists of grain-fluid mixtures and moves rapidly across three-dimensional terrain. Most debris flows move downslope as fluids. To predict the runout distance and extent of the hazard area of rainfall-induced debris flows

we proposed a depth-averaged two-dimensional mathematical model

in which the debris and water mixture is assumed to be uniform continuous

incompressible

unsteady Newtonian turbulence fluid. Based on mass balance equation and Navier-Stokes equations

the mathematical model is derived using the method of depth-integrated equations. The finite difference method is necessary to solve the all equations. Based on GIS

the two-dimensional mathematical model of debris flow can be used to estimate the flow range

the potentially dangerous homes and roads for hazard and risk analysis.

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Related Institution

Department of Civil Engineering, Shaoxing University

School of Energy Engineering, Xi’an University of Science and Technology

Department of mathematics, Xi’an University of Arts and Science

Key laboratory of Mountain Hazard and Surface Process, Chinese Academy of Sciences

Chengdu Research Institute of Environment and Disaster in Mountationous Regions Chinese Academy of Sciences

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