多矿物岩石流变性的有限元计算

Finite element computation of rheology for multi-mineral rocks. Acta Petrologica

本文利用有限元计算方法从单矿物的流变关系式来确定其组合而成的岩石整体的流变规律。建立了三维不可压缩流体的粘弹性有限元模型,计算模型的骨架矿物橄榄石为立方体,填充矿物尖晶石分别取为立方体、单一球体和多个球体,模拟双矿物在三轴压缩实验条件下的蠕变变形过程。首先,本文验证了使用有限元方法数值模拟双矿物在三轴压缩实验下的蠕变变形的可行性。其次,计算研究了当填充矿物为弱矿物时几何外形对整体流变强度的影响,结果表明,填充矿物的几何外形为立方体时比球体时对整体的流变强度有更大的影响。当填充矿物体积不同时,随着填充矿物体积的增加,填充矿物对整体流变强度的影响也不断加大。最后利用三维模型得到的双矿物整体的流变强度结果,归纳出了填充矿物尖晶石占体积5％,10％,15％,20％时和骨架矿物橄榄石构成的双矿物岩石的蠕变关系式。与Tullis利用平面应变模型归纳出的双矿物经验流变关系式比较,发现Tullis的经验流变公式存在较大的误差,而本文得到的双矿物蠕变公式与理论结果更好地符合本文结果为研究地幔多矿物岩石流变规律提供了新的途径。

The finite element method was used to calculate the flow law of poly-mineralic rock from the end-member flow laws. In this work we established an incompressible three-dimensional finite element visco-elastic model. The geometry of poly-phase aggregates is taken to be a cube and the inclusion a small cube, a round ball or several round balls, respectively. The creep process of the model under tri-axial compression was simulated. First of all, we verified the applicability of simulating the creep process of poly-mineralic rock under the tri-axial compression using the finite element method. Then, through the finite element calculation, we find that the cubic inclusion has more influence on the calculated result than the spherical inclusion does when the inclusion is weak. It is observed that comparing to fixed volume of aggregates, the larger the inclusion volume is, the stronger influence the inclusion has on the flow laws of polymineralic rock. At the end, we deduced the spinel and olivine (with 5%, 10%, 15%, 20% volume percentage spinel, respectively) two phase aggregate flow law by finite element calculation. The flow laws deduced in this work matches the theoretical result better than Tullis's empirical equation. Therefore, the result of our work provided a new method to study the flow laws of polymineralic rock in mantle.