泥流型和礫石型土石流有限元素分析初步探討

Abstract

本研究嘗試運用流體動力學之二相流分析以模擬土石流之運移與堆積行為。數值模擬係以COMSOL Multiphysics（以下簡稱COMSOL）有限元素模擬軟體為工具，將土石流視為黏性流體，以等位函數(Level Set) 法分辨空氣與土石流之自由介面，以便探討土石流運移的特性。COMSOL可同時輸入多重物理量，其中計算流體力學(CFD)模組可以同時模擬二相流之流體行為。土石流模擬所考慮之控制方程式包括連續方程式與動量方程式(Navior-Stokes方程式)，土石流的流變模式為非牛頓流，可包含降伏剪應力、黏滯力、顆粒碰撞產生的離散剪應力及土石流流床的粗糙度所產生的紊流力等項。 回顧檢討前人對土石流流變模式和參數的研究，可知土石流流變性質會隨顆粒粒徑分布、礦物性質、土石流的泥砂體積濃度等物理量的不同而有所差異，應合理考慮土石流的流變模式以及其流變性質。本研究整理文獻收集的土石流流變模式參數範圍，以供為隨後模擬的依據。 本研究繼而以COMSOL為分析平台，建立土石流運移的模型，允許兼而考量適合描述泥流型與礫石型土石流的複合流變模式。針對泥流型土石流的流變模式，採用等效賓漢流變行為的黏滯係數，令原本用於模擬牛頓流體的Navior-Stokes方程式可以模擬賓漢流體的流變行為。針對礫石型土石流的流變模式，考慮顆粒碰撞阻力/紊流力與剪應變率平方正相關，將顆粒碰撞阻力/紊流力以體積力（Volume force）加入原本用於模擬牛頓流體之Navior-Stokes方程式。流變模式中降伏剪應力為常數、黏滯力與流速流度梯度成正比，顆粒碰撞阻力/紊流力與流速流度梯度平方成正比。當忽略最後一項，此複合流變模式即簡化至賓漢流變模式。 本研究檢討上述之模擬方法是否可合理地模擬土石流啟動後之運移與推積行為，並探討不同因子、流變模式成分、與模式參數值如何影響土石流啟動後之運移與推積行為。本研究中所使用等位函數法(Level set Method)旨在區別土石流和空氣來做介面，但卻會發生土石流質量不守恆之問題，網格大小和二相流介面厚度可影響質量不守恆之程度。

This study aims to investigate the behavior of migration and deposition for debris flow using two-phase flow analysis of fluid dynamics. This work made use of “COMSOL Multiphysics” (herein referred to as "COMSOL") as the numerical simulation tool to simulate fluid behavior of two-phase flow. The rheological models of debris flow are assumed to be Non-Newtonian fluid, including yield shear stress, viscous stress, dispersive shear stress from particles collision, and turbulent stress from bed roughness, and so on. Reviewing rheological models and parameters for debris flows from previous studies, debris flow rheological properties vary with the particle size distribution, mineral properties, debris flow’s sediment concentration, and other physical quantities. It should be reasonable to consider the debris flow rheological model and its corresponding rheological properties together. This study deliberately validates the ranges of parameters which are collected in order, and view them as basis for simulation. This study regards COMSOL as an analysis platform to build debris flow migration model and to design debris flow rheological model as well. With the rheological model for mudflow, this study uses effective viscosity from the effective Bingham rheological behavior so that the Navior-Stokes equation originally simulating Newtonian fluid is able to simulate rheological behavior of Bingham fluid. For rheological model of stony debris flow, considering that particles collision force and turbulent force are square proportional to shear rate, this study adds particles collision force and turbulent force as volume forces to the Navior-Stokes equation originally simulating Newtonian fluid. Assuming that the yield shear stress is constant, viscous flow is proportional to the velocity flow gradient; the shear stress due to particle collision is proportional to the square of flow rate of gradient. When the shear stress is neglected, this rheological model is reduced to the Bingham model. This study evaluates whether the behavior of the migration and deposition of debris flow is reasonably simulated. The major role of the Level Set method is to distinguish the interface between debris flow and air. However, the problem of poor mass conservation for debris flow appears. It appears the mesh size and the interface thickness of two phase flow have an influence on the quantity of poor mass conservation.