断层自发破裂传播的数值模拟:速率状态摩擦定律本构参数的影响

地震往往受控于滑动面的摩擦性质,这种摩擦性质可以由速率状态摩擦定律较好地描述.速率状态摩擦定律中的本构参数a和b与动态摩擦系数相关,从而影响着同震位移与剪切应力的时空演化.本文在前人工作的基础上,采用三维边界积分方程法模拟速率状态摩擦定律控制下均匀全空间中平面断层的自发破裂传播过程,并详细讨论了a和b对滑动速率、剪切应力和破裂传播速度的影响.数值结果表明a和b的不同取值将导致不同的破裂行为,b－a的值越大,断层越不稳定,这种不稳定性有利于裂纹的产生与扩展.但滑动速率的时空分布不只依赖b－a,而且还与a和b的具体取值有关,断层面上滑动速率峰值与剪切破裂强度均随着a的减小而增大,随着b的增大而增大.相关结果有助于加深对断层自发破裂传播的认识.     

几种模拟断层泥摩擦滑动速度依赖性转换的实验研究

基于速率-状态摩擦定律,速度弱化是断层失稳的必要条件,速度弱化向速度强化的转换控制着断层从不稳定滑动向稳定滑动的转换.因此,断层摩擦滑动的速度依赖性转换是涉及断层带上地震活动特征、地震成核深度等的重要问题.     

模拟断层泥摩擦滑动速度依赖性转换的实验研究

基于岩石摩擦的速率-状态摩擦定律,速度弱化是断层失稳的必要条件,速度弱化向速度强化的转换控制着断层从不稳定滑动向稳定滑动的转换.因此,断层摩擦滑动的速度依赖性转换涉及断层带上地震活动特征、地震成核深度以及慢地震机制等重要问题.     

速率-状态依赖摩擦定律引入连续-非连续方法的检验及断层倾角的影响

断层黏滑是一种摩擦失稳,能够诱发地震、矿震等诸多地质灾害.目前,断层黏滑(包括断层亚失稳)研究,主要集中在实验方面和基于连续方法或非连续方法的数值模拟方面.为了弥补连续方法和非连续方法各自的不足,一些兼具二者优势的连续-非连续方法应运而生.为了检验引入速率-状态依赖摩擦定律的自主开发的拉格朗日元与离散元耦合连续-非连续方法的正确性并探究断层倾角对断层黏滑的影响,首先,模拟了滑块-底板模型的滑动-保持-滑动实验;然后,模拟了双轴压缩岩样的断层倾角的影响,重点考察了断层黏滑过程中亚失稳阶段摩擦系数的演化规律.研究发现,随着断层倾角的增大,岩样上表面平均差应力的绝对值-时步数目曲线的锯齿形由规则向不规则变化;初次黏滑发生时的时步数目、平均应力降、平均黏滑周期和平均峰值应力均减小.当断层处于黏滑前阶段时,断层面各处的摩擦系数和剪应力相差较小.当断层进入亚失稳阶段后,断层面上摩擦系数的平均值下降速度加快,这可作为断层进入亚失稳阶段的特征之一.引入速率-状态依赖摩擦定律后的拉格朗日元与离散元耦合连续-非连续方法的断层黏滑结果能与现有结果（例如,断层黏滑实验结果）基本吻合,但更加丰富,这在一定程度上...     

热水条件下角闪石断层泥的摩擦滑动性质——与斜长石断层泥的对比

基于速率与状态依赖性摩擦本构关系理论框架,在热水条件下研究了角闪石断层泥的摩擦滑动性质并与闪长岩的另一种主要矿物斜长石的摩擦滑动性质进行了对比.摩擦实验是在三轴实验系统上完成,有效正应力200 MPa,孔隙压力30 MPa,并将加载速率在1.22 μm/s和 0.122 μm/s之间实施了切换.结果表明角闪石的摩擦系数均值为0.70±0.01,随着温度增加没有系统性的变化,整体低于斜长石的摩擦系数(0.75±0.01);计算与实验表明,角闪石和斜长石的摩擦系数的体积分数加权平均值与闪长岩的摩擦系数基本一致;角闪石在实验温度范围内(100～614 ℃)显示速率强化(a-b>0),与斜长石在整个温度范围内的速率弱化(a-b<0)正好相反;角闪石的速率依赖性在整个实验温度范围内无系统性的变化.     

高温高压条件下辉长岩的摩擦强度及其速率依赖性

在干燥条件下对辉长岩的摩擦本构参数进行了实验研究。结果表明 :1 )辉长岩模拟断层泥的摩擦速度依赖性参数 (a -b)基本为正或者接近于没有速度依赖性 ,表明在干燥条件下不具备不稳定滑动的成核条件 ,对下地壳地震成核的可能性有参考意义 ;2 )摩擦强度在干燥条件下与Byerlee定律高度一致 ,表明在下地壳的高温环境下Byerlee定律仍可给出适当的强度估计 ,至少在干燥条件下如此 ;3)Byerlee定律给出的剪应力强度与正应力的关系中有一个截距 ,但是本研究中关于模拟断层泥的结果却没有明显的截距 ,表明断层物质的有无在摩擦强度的表现上存在重要差异     

弹性回跳模型:从经典走向未来

弹性回跳模型包含3个基本要点:1)地震来自于断层的运动;2)断层运动导致其两侧的岩石发生不均匀的弹性变形,积累巨大的能量,地震中部分弹性能得以释放;3)在断层带的各个点上积累能量的过程是缓慢而不均匀的。Brace(1966)提出弹性回跳的物理机制应当用摩擦滑动过程中出现的不平稳滑动(jerky sliding motion或stick-slip)来解释。Byerlee定律以量化形式表达了地壳摩擦规律,但是没有给出变差的范围。用弹簧滑块模型比拟粘滑,摩擦单元被抽象为刚性滑块,变形被归结于实验加载机的机械框架。后人在此基础上发展了所谓的速度依赖性模型。实验结果表明,速度扰动所带来的摩擦系数变化远远小于材料本身摩擦系数波动,其影响几乎可以忽略不计。而刚性摩擦滑块的假定与实验观测不符,本质上违反了弹性回跳模型所描述的地震现场考察结果。回到经典就是回归对地震现场问题的研究,这是正确的未来之路。     

基性岩摩擦本构参数与下地壳地震成核的可能性

摩擦滑动的力学行为能够很好地由速率和状态依赖性摩擦本构关系来描述。文中对地壳岩石滑动稳定性的控制因素进行了综述:1)微小扰动对摩擦滑动的影响分析(线性分析)表明,摩擦滑动中不稳定产生的重要条件是速率依赖性参数a-b<0,在这种条件下,地震滑动可以在断层上成核;2)下地壳的水含量测定表明,可能存在“干”、“湿”两种情况,而已有岩石流变实验结果表明稳定大陆内部下地壳在干燥条件下为脆性变形行为;3)近年来发现一部分强震发生在基性的下地壳,使辉长岩高温高压摩擦实验受到重视。干燥条件下辉长岩的摩擦实验研究表明,在420~615℃的温度范围内,速度弱化可能是典型的滑动行为。综合考虑较冷大陆内部下地壳可能出现的“干燥”条件以及在此条件下不大可能发生塑性流动等相关因素,这一结果可能就是在一些地区下地壳发生地震的原因     

白云母对岩盐断层带摩擦速度依赖性影响的实验研究

为更好地理解层状硅酸盐对断层强度、滑动速度依赖性及地震活动特征的影响,利用双轴摩擦实验对含白云母岩盐断层带在干燥及含水条件下摩擦的速度依赖性进行了实验研究,并观测了摩擦滑动过程中的声发射,分析了断层带的微观结构.实验结果表明,干燥条件下含白云母岩盐断层带在0.1 ～ 100μm/s的速度范围内表现为黏滑和速度弱化,增大σ2会使断层带从速度弱化向速度强化转化,速度依赖性转换出现在0.1 μm/s,其中断层滑动表现为稳滑或应力释放时间较长的黏滑事件;含水条件下含白云母岩盐断层带在0.05 ～0.01μm/s的速度范围内表现为速度强化,0.1 ～10μm/s的速度范围内表现为速度弱化,50～100μm/s的速度范围内又转换为速度强化行为.含白云母岩盐断层带在干燥条件下一次黏滑伴随一个或一丛声发射事件,而在含水条件下与稳滑相对应,滑动过程中并未记录到声发射事件.显微结构观察表明,速度弱化域的主要变形机制是岩盐颗粒的脆性破裂和局部化的滑动;干燥条件下,速度强化域的主要变形机制是岩盐颗粒的均匀破裂;含水条件下2个速度强化域对应不同的微观机制,高速域的速度强化受控于岩盐颗粒在白云母相互连结形成的网状结构上的滑动及其均匀碎裂作用,而低速域的速度强化还受岩盐的压溶作用控制.通过与岩盐断层带摩擦实验结果对比可知,白云母的存在对于燥岩盐断层带摩擦滑动方式和速度依赖性没有显著影响,而在含水条件下白云母的存在使得岩盐断层带滑动趋于稳定.实验结果为分析含层状硅酸盐断层的强度和稳定性提供了依据.此外,在速度依赖性转换域上观察到的应力缓慢释放的现象进一步证实了在岩盐断层带摩擦滑动过程中观察到的现象,这对慢地震机制研究具有参考意义.     

不同摩擦本构关系对断层自发破裂动力学过程的影响

地震是断层的摩擦失稳过程.摩擦本构关系对断层的破裂成核、破裂传播、破裂速度、能量释放、破裂终止等起着至关重要的控制作用.为了比较不同摩擦关系在断层自发破裂动力学过程中的影响,文中引入目前应用最为广泛的4种典型摩擦本构关系,它们分别是：滑移弱化摩擦关系,速率弱化摩擦关系,以及速率-状态相依摩擦关系中的老化定律和滑动定律.研究中利用有限单元方法对上述4种摩擦关系控制的断层自发破裂过程分别进行模拟计算,模拟结果显示：当模型参数相同时,不同摩擦关系模拟的破裂行为总体上具有一致性,都可以产生亚剪切破裂或超剪切破裂,并且破裂传播速度的大小与摩擦本构关系的类型无关.此外,它们之间还存在着较大的差异：（1）速率弱化摩擦关系可以模拟脉冲型破裂;而其他3个摩擦关系只能模拟裂纹性破裂.（2）不同摩擦关系模拟的超剪切破裂转换长度不同,速率-状态相关摩擦关系的老化定律相比其他摩擦关系需要更大的转换长度才能实现亚剪切破裂转变为超剪切破裂;而速率弱化的摩擦关系的超剪切转换长度可以为0,即不需要转换距离就直接产生超剪切破裂.（3）速率弱化摩擦关系模拟的破裂速度自成核后很快就达到稳定值;而其他类型摩擦关系模拟的破裂传播则要经历由缓慢破裂到逐渐加速直至达到稳定破裂的过程.值得特别指出的是,本文所使用的4种摩擦关系都不能完整地反映实际大地震破裂过程的摩擦属性,需要进一步深入研究.     

Simulation of the Influence of Rate- and State-dependent Friction on the Macroscopic Behavior of Complex Fault Zones with the Lattice Solid Model

-- In order to understand the earthquake nucleation process, we need to understand the effective frictional behavior of faults with complex geometry and fault gouge zones. One important aspect of this is the interaction between the friction law governing the behavior of the fault on the microscopic level and the resulting macroscopic behavior of the fault zone. Numerical simulations offer a possibility to investigate the behavior of faults on many different scales and thus provide a means to gain insight into fault zone dynamics on scales which are not accessible to laboratory experiments. Numerical experiments have been performed to investigate the influence of the geometric configuration of faults with a rate- and state-dependent friction at the particle contacts on the effective frictional behavior of these faults. The numerical experiments are designed to be similar to laboratory experiments by Dieterich and Kilgore (1994) in which a slide-hold-slide cycle was performed between two blocks of material and the resulting peak friction was plotted vs. holding time. Simulations with a flat fault without a fault gouge have been performed to verify the implementation. These have shown close agreement with comparable laboratory experiments. The simulations performed with a fault containing fault gouge have demonstrated a strong dependence of the critical slip distance D_c on the roughness of the fault surfaces and are in qualitative agreement with laboratory experiments.     

自维持断层蠕滑过程和余震发生率的衰减特征—以汶川MW7.9地震序列为例

基于Dieterich地震活动性理论,本文推导出计算余震发生率和余震累积次数的一般表达式,其中主震后发震断层内部的剪切应力随时间的演化过程遵从Jeffreys-Lomnitz蠕变模型,且与修正Omori定律直接相关。修正Omori定律中的p值与震后断层的短时应力加卸载过程正相关。采用Rubin和Ampuero 给出的震后断层自维持蠕滑模型本文得出计算余震发生率的近似表达式,并对2008年汶川地震序列进行拟合。结果表明,p值的大小直接对应了速率-状态摩擦定律中摩擦参量b/a,而修正Omori定律中的c值则与速率-状态摩擦定律中的临界滑移D_c相关。对于汶川余震序列而言,拟合结果显示b/a约为1.13,D_c约为2—3 cm。Rubin-Ampuero震后自维持蠕滑描述了震后孕震层内部短暂的速率变化特征,是孕震断层演化过程不可缺少的环节。      

利用远震P波波形反演渤海地震的震源参数

本文研究用理论地震图反演地震震源参数的方法,利用16个WWSSN台记录的渤海地震（1969年7月18日,M=7.4）远震P波波形,用我们的反演方法重新测定了该地震的震源参数。文中以剪切位错源的理论地震图与实际观测记录波形的相关程度为判据,测得该地震的震源参数为:地震矩3.9×10²⁷达因·厘米;震源破裂持续时间6秒;位错面两个可能的选择解是:（1）θ_s=207°,δ=87°NW,λ=-159°,右旋;（2）θ_s=298.6°,δ=69°NE,λ=-3.6°,左旋。其中θ_S、δ、λ分别是震源位错面的方位角、倾角和错滑角;震源深度为25公里。数值运算的结果还表明,本文提供的测定震源参数的方法实际效能良好。 文中还与用P波初动符号方法测定的震源参数结果进行了对比分析。     

A numerical study of comparison of two one-state-variable,rate- and state-dependent friction evolution laws

The two one-state-variable, rate- and state-dependent friction laws, i.e., the slip and slowness laws, are compared on the basis of dynamical behavior of a one-degree-of-freedom spring-slider model through numerical simulations. Results show that two (normalized) model parameters, i.e., Δ (the normalized characteristic slip distance) and β?α (the difference in two normalized parameters of friction laws), control the solutions. From given values of Δ, β, and α, for the slowness laws, the solution exists and the unique non-zero fixed point is stable when Δ>(β?α), yet not when Δ < (β?α). For the slip law, the solution exists for large ranges of model parameters and the number and stability of the non-zero fixed points change from one case to another. Results suggest that the slip law is more appropriate for controlling earthquake dynamics than the slowness law.     

Finite Element Analysis of a Sandwich Friction Experiment Model of Rocks

-- Sandwich friction experiments are one of the most widely used standard methods for measuring the frictional behavior between rocks. A finite element code for modeling the nonlinear friction contact between elastoplastic bodies has been developed and extended to analyze the sandwich friction experiment model with a rate- and state-dependent friction law. The influences of prescribed slip velocity and variation of movement direction and state on the friction coefficient, the relative slip velocity, the normal contact force, the frictional force, the critical frictional force and the transition of stick-slip state between the deformable rocks are thoroughly investigated, respectively. The calculated results demonstrate the usefulness of this code for simulating the friction behavior between rocks.     

Stability analyses and numerical simulations of the single degree of freedom spring-slider system obeying the revised rate- and state-dependent friction law

The linear and nonlinear stabilities of the single degree of freedom spring-slider system which accords to the revised rate- and state-dependent friction law (RSF) (Nagata et al. J Geophys Res 117 (B2):B2314, 2012) are analyzed. The revised ageing law obtained by Nagata et al. (J Geophys Res 117 (B2):B2314, 2012) incorporates the effects of changes in shear stress. Numerical simulations on the cyclic stick–slip motions of the system are developed and compared with the results of the systems according to the original ageing law or the slip law. From the insight of the stability analyses and numerical simulations, it is found that the revised ageing law integrates the “healing effect” feature of the original ageing law and the dynamic slip features of the slip law. In the stick–slip cycles, the velocity decreases with non-constant states during the dynamic overshoot for the revised ageing law, which is different from both the original ageing law and the slip law. Although the revised ageing law concluded from the low velocity friction experiments cannot account for the earthquake-like high velocity friction experiments, it can be used in earthquake nucleation with low velocity. The stability analyses and the results of numerical simulations are helpful to understanding the implications of the revised ageing law.     

The micromechanics of friction in a granular layer

A grain bridge model is used to provide a physical interpretation of the rate- and state-dependent friction parameters for the simple shear of a granular layer. This model differs from the simpler asperity model in that it recognizes the difference between the fracture of a grain and the fracture of an adhesion between grains, and it explicitly accounts for dilation in the granular layer. The model provides an explanation for the observed differences in the friction of granular layers deformed between rough surfaces and those deformed between smooth surfaces and for the evolution of the friction parameters with displacement. The observed evolution from velocity strengthening to velocity weakening with displacement is interpreted as being due to the change in the micromechanics of strain accommodation from grain crushing to slip between adjacent grains; this change is associated with the observed evolution of a fractal grain structure.