基于HBP本构模型的泥石流动力过程SPH数值模拟

本构模型是描述泥石流流变特性的关键，也是决定其动力过程数值模拟准确性的核心问题之一。泥石流流体属多相混合物，现有的研究已证实其存在剪切增稠或剪切变稀的现象，传统基于Bingham及Cross线性本构关系的数值模型难以准确描述泥石流流变特性。文中探讨了Bingham模型在低剪应变率下的数值发散问题，在光滑粒子流体动力学（SPH）方法框架上建立了整合Herschel-Bulkley-Papanastasiou(HBP）本构关系的稀性泥石流动力过程三维数值模型。相比传统基于浅水波假设的二维数值模型，所述方法从三维尺度建立SPH形式下的泥石流浆体纳维?斯托克斯方程并进行数值求解，可获取泥石流速度场时空分布及堆积形态，同时采用HBP本构关系描述泥石流流变特性，能在确保数值收敛的前提下反映泥石流流体在塑性屈服过渡段及大变形状态下应力?应变的非线性变化。为验证提出方法的合理性，结合小型模型槽实验观测进行了对比，结果表明数值模拟与实测结果基本吻合。

Smoothed particle hydrodynamic numerical simulation of debris flow process based on Herschel-Bulkley-Papanastasiou constitutive model

A rational constitutive model is critical for numerical simulation of rheological behavior of debris-flow. It is also one of the key issues that determine the accuracy of numerical simulation of its dynamic process. The numerical models based on Bingham and Cross constitutive models has been observed failing to simulate the shearing thickening and thinning phenomenon of the rheological behavior of debris-flow that belongs to multi-phase mixture of fluid and debris. We discuss the numerical divergence problem of using the Bingham model with low shear strain rate. To simulate the dynamic flow process of diluted debris-flow, the 3D numerical model is set up, applying an alternative solution of the Herschel-Bulkley-Papanastasiou(HBP) constitutive model with the smoothed particle hydrodynamic(SPH) method. Comparing to the traditional two-dimensional numerical model based on the hypothesis of shallow water wave, the proposed method in this paper solves Navier-Stokes equations describing the debris-flow with the SPH in three-dimension, thus the velocity field and deposition pattern of debris flow can be simulated. The proposed method incorporates the HBP constitutive model, ensuring the numerical convergence, can perform well to reveal the non-linear variation of stress-strain relationship of debris flow at transition phase of plastic yield and large shear rate. The proposed method is verified by a flume experiment. It indicates that the simulation results match well with the experimental measurements.