The Minimized Power Geometric model: An analytical mixing model for calculating polyphase rock viscosities consistent with experimental data
The Minimized Power Geometric model: An analytical mixing model for calculating polyphase rock viscosities consistent with experimental data
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DOI：
10.1002/2013jb010453
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发表时间：
2014-04-01
影响因子：
3.9
通讯作者：
Grasemann, B.
中科院分区：
文献类型：
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作者：
Huet, B.;Yamato, P.;Grasemann, B.
在这里，我们介绍最小化幂几何 (MPG) 模型，该模型可预测延性流动过程中变形的任何多相岩石的粘度。构成相的体积分数和幂律参数是唯一需要的模型输入。该模型基于变形过程中岩石中消耗的机械功率的最小化。与基于最小化的现有混合模型相比，我们使用拉格朗日乘数方法以及应变率和应力几何平均的约束。这使我们能够确定多相岩石粘度、其幂律参数以及各相之间应变率和应力的分配的解析表达式。幂律整体行为是我们模型的结果，而不是假设。将模型结果与 15 个已发表的两相聚集体实验数据集进行比较表明，即使存在较大的粘度差异，MPG 模型也能准确再现实验粘度和蠕变参数。具体而言，实验粘度与 MPG 预测粘度之间的比率平均值为 1.6。与实验值的偏差可能是由于模型忽略的微观结构过程（应变局部化和同时代的其他变形机制）造成的。不基于几何平均的现有模型与实验数据的拟合较差。只要牢记混合模型的局限性，MPG 模型就可以在构造地质学和数值模拟中提供巨大的应用潜力。
Here we introduce the Minimized Power Geometric (MPG) model which predicts the viscosity of any polyphase rocks deformed during ductile flow. The volumetric fractions and power law parameters of the constituting phases are the only model inputs required. The model is based on a minimization of the mechanical power dissipated in the rock during deformation. In contrast to existing mixing models based on minimization, we use the Lagrange multipliers method and constraints of strain rate and stress geometric averaging. This allows us to determine analytical expressions for the polyphase rock viscosity, its power law parameters, and the partitioning of strain rate and stress between the phases. The power law bulk behavior is a consequence of our model and not an assumption. Comparison of model results with 15 published experimental data sets on two-phase aggregates shows that the MPG model reproduces accurately both experimental viscosities and creep parameters, even where large viscosity contrasts are present. In detail, the ratio between experimental and MPG-predicted viscosities averages 1.6. Deviations from the experimental values are likely to be due to microstructural processes (strain localization and coeval other deformation mechanisms) that are neglected by the model. Existing models that are not based on geometric averaging show a poorer fit with the experimental data. As long as the limitations of the mixing models are kept in mind, the MPG model offers great potential for applications in structural geology and numerical modeling.