土石流の構成則に基づいた粒子法モデルの構築と堆積過程への適用

摘要

The shallow water equations are generally used for numerical simulation of debris flows. In this method, the distributions of the flow velocity u and sediment concentration c are vertically averaged. Therefore, the calculation may be inaccurate when the upper and lower layers have different flow directions, as with countergradient flows. We propose a numerical simulation method for calculating the vertical distributions of u and c in debris flows. Our method is based on the moving particle semi-implicit (MPS) method, which was originally used for incompressible viscous fluid flows with free surfaces. Some modifications are necessary to adapt the method for debris flows. We introduce the constitutive equations of Egashira et al. to the MPS method. In Egashira's equations, debris flows are treated as a continuum. Thus, the proportion of gravel in a debris flow is expressed using the variable c. Similarly, each particle has an associated c value in our modified MPS method. In Egashira's sediment concentration equations, the equilibrium vertical distribution of c is obtained by integrating the rate of change of c in the vertical direction from the riverbed. In our method, c values spread among nearby particles, in order to reduce the difference between the equilibrium rate of change c and the actual rate of change of c. Numerical simulations of debris flow are performed. In the equilibrium condition, there is good agreement with the vertical distributions of u and c and those derived from the constitutive equations. In the condition where the riverbed gradient becomes less steep, there is good agreement with experimental results with a very short relaxation time, including those involving the formation of a convex upward deposition shape in the initial deposition process. Results for the initial deposition process are not produced with existing simulation methods that are based on the assumption of local equilibrium of average sediment concentration. However, simulations with a very short relaxation time show that local equilibrium is established as well as in existing methods. This indicates that the assumption of local equilibrium of sediment concentration is correct, and that because it evaluates the local equilibrium of each particle, our model can yield good results.%本研究ではMPS法の枠組み内において，土石流を一流体として扱い，土石流を濃度の情報を持つ粒子の集合体として扱うモデルを構築した。抵抗則•濃度則には江頭らの構成則を用いた。濃度則においては，濃度分布式によって算出される平衡濃度勾配に向かって状態が遷移するように，周辺粒子と濃度を交換するモデルとした。本研究で構築した手法は，堆積層における流速分布に今後の検討が必要な部分もあるが，構成則に基づく平衡状態の分布形や堆積形状を概ね再現可能であることを確認した。その上で，勾配急減点における堆積過程への適用性を検証した。検証には高濱らの実験結果を用いた。