Irreversible thermodynamic and viscoelastic model for power-law relaxation and attenuation of rocks
Irreversible thermodynamic and viscoelastic model for power-law relaxation and attenuation of rocks
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DOI：
10.1016/j.tecto.2006.03.049
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发表时间：
2006-12
期刊：
影响因子：
2.9
通讯作者：
Y. Kawada;H. Nagahama;Hiroaki S. Hara
中科院分区：
文献类型：
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作者：
Y. Kawada;H. Nagahama;Hiroaki S. Hara
本文从不可逆热力学出发，导出了岩石粘弹性本构关系。该模型引入了两个具体的参数，一个是内部状态变量，它是一个关于微观结构的变量，如晶体中的缺陷或微裂纹，另一个是通过归一化各种温度行为得到的温度降低时间。大量的内部状态变量有各自的弛豫时间，并显示各自的时间演化，而一组时间演化产生的时间幂律行为的岩石。内部状态的时间演化被视为广义麦克斯韦模型的元素的动力学，应力-应变关系由响应函数表示，遵循时间幂律的线性系统理论。这种关系被逆公式化以从输出数据调查源场。该模型使我们能够解释岩石瞬态和稳态行为的基于实验的本构定律（例如，二辉橄榄岩）遵循时间幂律并且对于多晶体的衰减行为（例如，橄榄石）由品质因数和频率之间的关系表示。这两个法律显示幂律的变形时间或频率取决于在多晶体或岩石的分形结构，和实验的高温行为可以外推到长变形时间或高频率的行为。
A constitutive law for viscoelastic behaviour of rocks is derived from irreversible thermodynamics. To this model, two specific parameters are introduced; one is an internal state variable which is a variable concerning the microstructures such as defects in crystals or microcracks, and the other is a temperature reduced time obtained by normalizing the various temperature behaviours. A large number of internal state variables have the respective relaxation times and show the respective time evolutions, while a set of the time evolutions generates temporal power-law behaviour of rocks. The time evolutions of internal states are regarded as dynamics of elements of the generalized Maxwell model, and the stress–strain relation is represented by a response function following a temporal power-law in terms of linear system theory. This relation is inversely formulated to investigate the source field from output data. This model enables us to explain experimentally-based constitutive laws for transient and steady-state behaviour of rocks (e.g., lherzolite) following a temporal power-law and for attenuation behaviour of polycrystals (e.g., olivine) represented by a relation between the quality factor and frequency. Both laws show power-laws on deformation time or frequency depending on the fractal structure in polycrystals or rocks, and the experimental high-temperature behaviours can be extrapolated to long deformation time or high frequency behaviour.