粘性泥石流一维运动数学模型

粘性泥石流是指自然界中最典型的一种泥石流。作者依据野外原型观测和室内实验，证实该类流体具有带流核的层流特征并可用宾汉（Ｂｉｎｇｈａｍ）模型来表达。在此基础上推导其阻力和平均流速计算方法。我们认为，粘性泥石流作为不可压缩连续介质流体，符合质量、动量守恒律，因此可采用纳维－斯托克斯方程组来表达。考虑到它为拟线性双曲型偏微分方程组和阻力参数等特点，应用Ｌａｘ－Ｆｒｉｅｄｒｉｃｈｓ差分格式，选用云南东川蒋家沟的原型观测资料作为边、初值条件，编制计算机程序及数据库，而获得粘性泥石流水深、流速等要素的时空变化规律。该模型可以直接用于泥石流工程防治和量化的预测和警报

ONE DIMENSION MODEL OF MOVEMENT OF DEBRIS FLOW

The research on the mathematical model of movement of debris flow includes basic behaviours of fluid(rheological properties,flow pattern,and flow regimes etc),basic kinematic equations and its numerical solving method.The object of our research program is visco plastic debris flow.Five set data obtained from prototype observation and flume experiments at Jiangjia Ravine,China,Toutle River,USA,University of California,Davis,and Swizeland,etc,are used to analysis fluid characteristics.Based on the phenomena and analysis we think that the visco plastic debris flow posseses laminar behaviour with rigid plug.In our research,the fluid is simplified into single phase fluid,i.e. the collision between grains and their exchange of momentum will be neglected.Therefore,we affirm that visco plastic debris flow can be expressed by Bingham Model.According to the constitutive relation of Bingham,the fluid resistance and the theoretical calculation equation of mean velocity are obtained.The equation and its simplified method are good calibratied by the data from prototype observation at Jiangjia Ravine and flume experiment at University of California,Davis.Three ways of calculating rheological parameters were introduced in this report.We find that the data from SHL 1 rheometer,at Jiangjia Ravine can be used for viscous plastic debris flow in our model.It is emphasized that viscous debris flow is a continuous and unpressure fluid,it can be expressed by Eqs of Navier Stoeks which is a non linear bicurve partial differential equations. Lax Friedrichs form of difference method is chosen for solving the equations.Some softwares were developed in our research which including pre treatment,calculation and post treatment.The softwares data are from prototype or experiment in flume for mathematical model.As calculating samples,two groups of prototype data from Jiangjia Ravine,in 1991 and 1994 were used in model.We know some laws from these results,for example,the velocity behind the front of wave is larger than the surges,the shape of front of wave can maintain a longer distance (over half of total distance usually) and etc.These laws are accord with our observation in the field.