The stability and behavior of a frictional system with a two state variable constitutive law
The stability and behavior of a frictional system with a two state variable constitutive law
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具有二态变量本构律的摩擦系统的稳定性和行为
DOI：
10.1007/bf00877210
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发表时间：
1986
影响因子：
2
通讯作者：
T. Tullis
中科院分区：
文献类型：
--
作者：
M. Blanpied;T. Tullis
在自然断层和实验室岩石摩擦样品上滑动的性质取决于沿滑动面的材料与加载表面的弹性变形材料之间的相互作用。对于给定的弹簧刚度，涉及单个摩擦块和弹簧的类似系统显示稳定或不稳定的滑动，这取决于摩擦本构律的细节。gu等人（1984）在分析弹簧和块体模型的行为和稳定性时，使用了描述实验室岩石摩擦的状态变量本构定律，强调本构定律只有一个状态变量。由于通常需要两个状态变量来充分描述实验室岩石摩擦阻力，因此我们对具有这种摩擦本构律的系统的行为进行了数值研究。这类系统的性能和稳定性取决于五个本构参数和弹簧刚度的值，但最重要的单个量是弹簧刚度与临界刚度的比值。这种系统的行为可以用三维相空间图有效地表示出来。如果稳态摩擦与滑移速度呈负相关，那么对于弹簧刚度几乎等于或大于临界刚度，稳定面将相空间中保持稳定的点与将变得不稳定的点分开。相空间的二维投影虽然不能完整地描述系统行为，但在许多情况下是有用的，并且类似于用于单状态变量系统的简单相平面图。在我们的分析预测和实验室对稳定性的观察之间发现了很好的一致性。这种基于二维行为预测的预测，可以简单地在实验期间实时进行，以便与实际行为进行比较。一般来说，如果稳态摩擦显示出对滑移速度的正依赖，则系统将仅表现出稳定滑动，但如果两个状态变量以相反的符号演变，则可能出现一个有趣的例外，即更快速发展的状态变量单独作用将产生负速度依赖。在这种情况下，滑动最终总是会减慢并稳定下来，但在这种情况发生之前，速度可能会变得非常高，以至于在实验室的实际目的中，这种行为被称为粘滑，而在断层上，这种行为被称为地震。
The nature of sliding on natural faults and laboratory rock friction samples depends on the interaction between the material along the slip surface and the elastically distorted material that loads the surface. Similar systems involving a single friction block and a spring show stable or unstable sliding for a given spring stiffness, depending on the details of the friction constitutive law. State variable constitutive laws describing laboratory rock friction have been used previously byGu et al. (1984) in an analysis of the behavior and stability of spring and block models, with an emphasis on constitutive laws having only one state variable.Since two state variables are often necessary to describe adequately laboratory rock frictional resistance, we have conducted a numerical study of the behavior of systems with this type of friction constitutive law. The behavior and stability of such systems depends on the values of the five constitutive parameters and the spring stiffness, but the most important single quantity is the ratio of the spring stiffness to a critical stiffness. The behavior of such systems can be usefully represented in a three dimensional phase space plot. If the steady state friction shows a negative dependence on slip velocity, then for spring stiffnesses nearly equal to or greater than the critical stiffness a stability surface separates points in phase space that remain stable from those that will become unstable. Two dimensional projections from phase space, while not complete descriptions of system behavior, are useful in many situations and are similar to the simpler phase plane plots used for one state variable systems. Good agreement is found between the predictions of our analysis and laboratory observations of stability. Such predictions, based upon two dimensional projections of behavior, can be done simply enough to be made in real time during experiments for comparison with actual behavior.Generally, if the steady state friction shows a positive dependence on slip velocity, the system will exhibit only stable sliding, but an interesting exception to this can occur if the two state variables evolve with opposite signs in such a way that the more rapidly evolving one acting alone would produce a negative velocity dependence. In such situations the sliding always eventually slows down and becomes stable, but it is possible for the velocities to become so high before this happens that for practical purposes in the laboratory the behavior would be called stick slip, and on a fault it would be called an earthquake.