Energetics of a two-phase model of lithospheric damage, shear localization and plate-boundary formation
Energetics of a two-phase model of lithospheric damage, shear localization and plate-boundary formation
复制标题
岩石圈损伤、剪切局部化和板块边界形成的两相模型的能量学
DOI：
--
复制
发表时间：
2003
期刊：
影响因子：
--
通讯作者：
Y. Ricard
中科院分区：
文献类型：
--
作者：
D. Bercovici;Y. Ricard
Bercovici et al. （2001a， J. Geophys.）提出的压实和损伤两相理论。Res.,106, 8887‐8906)采用了界面表面能、压力和粘性变形之间的非平衡关系，从而提供了一个损伤（空洞产生和微裂纹）模型，以及弱化、破坏和剪切局部化的连续描述。在这里，我们研究了模型的进一步变化，考虑了(1)当在混合物上平均时，界面表面能如何在相之间分配；(2)变形功划分的可变性如何极大地促进了局部化；(3)损伤和局部化在热量输出和大块能量交换中的表现。分子键和活化能的微物理考虑表明，相之间表面能的明显分配随相的粘度而变化。当这种划分在两相理论中使用时，它捕获了McKenzie （1984， J. Petrol）的熔融压实理论。， 25, 713‐765)，以及在同伴论文中提出的空洞损伤理论（Ricard & Bercovici，提交）。基于这种理论的一维剪切局部化计算仍然显示出至少三种可能的损伤和局部化机制：在低应力下是弱局部化，具有扩散缓慢演变的剪切带；在高应力下，存在强局部化和窄的快速生长带；在更高的剪切应力下，系统可能遭受广泛分布的损伤而不局部化。然而，局部化的强度受到变形功分配随膨胀率的变异性的强烈控制，由参数γ表示。对于γ γ - 1，允许极端局部化，具有孔隙度（弱区）的尖锐剖面，几乎不连续的分离速度和有效的奇异膨胀率。最后，检查了一维系统的体热输出，以辨别有多少变形功被有效地存储为表面能。在高应力、分布损伤的情况下，随着界面表面能量的增加，热输出减少。然而，在弱或强局部化情况下，系统总是释放表面能，而不管是否存在损伤，因此实际上释放的热量略多于通过外部做功输入的能量。此外，损伤水平的增加（以最大功分配f *表示）使局部化系统释放表面能更快，因为损伤增强了相分离和孔隙场的聚焦，从而产生更快的净界面表面积损失。然而，当在相似的发展阶段（例如，局部化的峰值孔隙率）比较不同程度损伤的情况时，很明显，增加的损伤会导致较小的相对热释放，并延缓净界面表面能的损失。该损伤和剪切局部化模型的能量学和能量分配用于估算地幔对流形成板块边界和生成板块的能量损失。
SUMMARY The two-phase theory for compaction and damage proposed by Bercovici et al. (2001a, J. Geophys. Res.,106, 8887‐8906) employs a nonequilibrium relation between interfacial surface energy, pressure and viscous deformation, thereby providing a model for damage (void generation and microcracking) and a continuum description of weakening, failure and shear localization. Here we examine further variations of the model which consider (1) how interfacial surface energy, when averaged over the mixture, appears to be partitioned between phases; (2) how variability in deformational-work partitioning greatly facilitates localization; and (3) how damage and localization are manifested in heat output and bulk energy exchange. Microphysical considerations of molecular bonding and activation energy suggest that the apparent partitioning of surface energy between phases goes as the viscosity of the phases. When such partitioning is used in the two-phase theory, it captures the melt-compaction theory of McKenzie (1984, J. Petrol., 25, 713‐765) exactly, as well as the void-damage theory proposed in a companion paper (Ricard & Bercovici, submitted). Calculations of 1-D shear localization with this variation of the theory still show at least three possible regimes of damage and localization: at low stress is weak localization with diffuse slowly evolving shear bands; at higher stress strong localization with narrow rapidly growing bands exists; and at yet higher shear stress it is possible for the system to undergo broadly distributed damage and no localization. However, the intensity of localization is strongly controlled by the variability of the deformational-work partitioning with dilation rate, represented by the parameter γ .F orγ � 1, extreme localization is allowed, with sharp profiles in porosity (weak zones), nearly discontinuous separation velocities and effectively singular dilation rates. Finally, the bulk heat output is examined for the 1-D system to discern how much deformational work is effectively stored as surface energy. In the high-stress, distributed-damage cases, heat output is reduced as more interfacial surface energy is created. Yet, in either the weak or strong localizing cases, the system always releases surface energy, regardless of the presence of damage or not, and thus slightly more heat is in fact released than energy is input through external work. Moreover, increased levels of damage (represented by the maximum work-partitioning f ∗ ) make the localizing system release surface energy faster as damage enhances phase separation and focusing of the porosity field, thus yielding more rapid loss of net interfacial surface area. However, when cases with different levels of damage are compared at similar stages of development (say, the peak porosity of the localization) it is apparent that increased damage causes smaller relative heat release and retards loss of net interfacial surface energy. The energetics and energy partitioning of this damage and shear-localization model are applied to estimating the energy costs of forming plate boundaries and generating plates from mantle convection.