Abstract: This work compares the slowness friction law with the Ruina Dieterich friction law under both constant normal stress and variable normal stress conditions Dynamic motion with the slowness friction law in a single degree of freedom system is analyzed numerically and compared with the other By examining the property of the equations,it can be seen that the two constitutive laws converge to each other during motions around a certain steady state This is also implied by the consent in linear stability analyses for both cases as shown in previous studies Under constant normal stress condition,the two constitutive laws differs in many aspects:(a) Stress displacement curve in stick slip with the slowness friction law is different from the Ruina Dieterich friction law in that the stress change during acceleration and deceleration are strongly not symmetric;(b) In the deceleration phase,the slowness law has a roughly constant stress segment in which the logarithm of state and logarithm of velocity are linearly coupled,and most portion of the state value recovers during this segment;(c) With slowness friction law,dynamic stress drop scales with both b a and stiffness; (d) The minimum velocity in the deceleration phase with the slowness law is less than the Ruina Dieterich law by 10 orders of magnitude Under variable normal stress condition,the phase plane plot with the slowness law is similar to the constant normal stress case except the non appearance of constant state line whereas that of Ruina Dieterich law has a long tail in the deceleration phase in which little hysteresis occurs

Key words: Frictional property, Numerical simulation, Stick slip

摘要： 目前有两种最常用的岩石摩擦本构关系,其主要区别在于是否与静接触时间有关。对这两种本构关系的基本性质进行了对比研究,得出如下结论:(1)在匀速滑动的稳态附近,两种本构关系趋向一致;(2)在正应力恒定条件下,两种本构关系的主要差异在于克服摩擦力所需能量的大小。与静接触时间相关的本构关系在粘滑中需消耗较大的能量来克服摩擦阻力,在粘滑的减速段,这种本构关系可达到的最低速率比另一种本构关系低10个数量级;(3)在正应力变化条件下,与静接触时间相关的本构关系基本继承了正应力恒定条件下的行为特征,而另一种本构关系在剪应力-速度相平面上却出现了一个长尾巴,使最低滑动速率降到比正应力恒定时的值低10多个数量级。

关键词: 摩擦特性, 数值模拟, 粘滑