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.     

采用不同摩擦定律动态模拟断层阶跃

众所周知,断层阶跃在某些情况下可使破裂贯通,而在另外的一些情况下则可能使破裂终止。然而,不同摩擦定律公式对跨越破裂的影响尚未得到广泛的探讨。本研究采用二维动态有限元方法探讨张性和压性两种环境下不同摩擦参数如何影响破裂跨越阶跃的能力。我们比较了线性滑动弱化摩擦和三种速率—状态依从摩擦:衰变定律、滑动定律、强速率弱化滑动定律。我们发现,对于相同有效滑动弱化距离的摩擦参数,该摩擦定律的函数形式可对最大跨越距离有显著影响。将摩擦定律调整为具有等效破裂能量时,我们发现这种摩擦定律的函数形式对跨越破裂的影响次之。最后,我们发现采用特定参数时,一旦破裂在次断层段重新起始,跨越阶跃系统的破裂延迟可导致先前未曾见到的超剪切转换模式,即使初始应力场阻碍这种转换也如此。对复杂几何形态如断层阶跃采用多种摩擦定律进行研究可有助于更好地认识和理解破裂性质对模型及统计分析中采用的摩擦定律类型的依赖性。     

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。      

论非均匀断层滑动弱化速率的标定

尝试用二维断层模型来描述断层在不稳定开始时滑动弱化速率的定标律。断层由一系列受滑动摩擦力作用变弱的片区组成，这些片区被牢固的障碍体所分隔。第一组断层包含不同尺度总滑动长度相同的片区的平均分布，而第二组断层由各种分形康托尔集合组成。破裂的整体活动性质由指数增长率λ来描述。对无限均匀的断层，系数λ由摩擦定律的弱化速率控制。在非均匀断层系中我们估算每一个断层的弱化速率，因为一个断层系的指数增长率λ与均匀断层是一致的。利用这种均匀断层的破裂过程，我们根据不同尺度均匀性断层和给定的系数λ来计算弱片区上的弱化速率。对于大尺度的破裂，弱化速率与尺度无关，长片区的开始过程类似于无限断层的破裂情况。本文考虑的是小尺度和所有不同几何形状的破裂，弱化速率记为α=β0^*／a，其中a为破裂尺度或者单个断层长度的一半，β0^*≈1．158。本文计算了滑动弱化距离Dc的值，在此基础上讨论了计算结果的物理含义，并给出了这个参数与尺度相关的可能解释。     

岩石高速摩擦实验的进展

文中简述了地震动力学国家重点实验室近年来在岩石高速摩擦实验方面的进展。为了深化断层与地震力学研究,实验室建设了一套旋转剪切低速-高速摩擦实验装置,可开展滑动速率介于板块运动速率(cm/a量级)至地震滑动速率(m/s量级)的岩石摩擦实验,其中高速摩擦性能填补了实验室的技术空白。以此为依托,围绕汶川地震断层带力学性质研究,开展了一系列高速摩擦实验。结果表明,龙门山断裂带断层泥的高速摩擦性质具有一致性,其高速滑动下显著的滑动弱化必定在汶川地震中极大地促进了破裂的扩展;断层弱化的主导机制是与摩擦生热相关的过程,包括凹凸体急速加热弱化和热压作用;断层泥在经历高速滑动弱化之后摩擦系数可在5~10s内恢复0.4,断层强度的快速恢复是同震主破裂带余震减少的原因之一。基于对实验装置现状和现有成果的分析,展望了近期实验室岩石高速摩擦的发展方向。     

穿过具有平滑边界凹凸体的无震位错的传播

介绍了沿着有非均匀摩擦力的断层的索米格连纳位错传播的二维模式。断层滑动是由随时间缓慢增加的均匀的外界剪切应力驱动的,位错在断层平面上的最小摩擦区成核,此区域被周围较高摩擦区(凹凸体)所限制。所研究的情况是具有平滑边界且有恒定摩擦梯度特征的凹凸体。对于接近弱带摩擦的外界剪切应力值来说,由于出现凹凸体,位错的传播被缓慢降下来,只是当它越过边界时,位错前缘才以逐渐增加的速度前移。模式表明:在给定的外界剪切应力值的条件下,滑动幅度在有限的和恒定的摩擦梯度情况下比在具有陡峭边界的凹凸体情况下要大些。与传播速度不一样,滑动速率在位错过程中永远是增加的。该模式指出在什么程度上,位错受断层上摩擦分布的影响。要理解断层上摩擦不稳定性的机制,需要详细地了解滑动速率和滑动历程。     

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.     

地震滑动加速和减速过程中的摩擦作用

在地震滑动过程中,断层动态摩擦是地壳内控制地震破裂的决定性因素。天然地震的脆性裂纹理论[1-3]使得以下观点被普遍接受:在地震断层快速滑动的过程中,断层摩擦力减弱,即所谓的滑动弱化[1]。高速断层泥实验[4-5],以及最近关于热增压[6-7]和摩擦熔化[8]的试验都支持该理论。但是,这些研究均仅针对固定的断层滑动速率。在本文中,我们的实验展示了不同滑动速率下断层物质的摩擦行为——这一模型的设置更接近天然地震的特征。实验结果表明,在断层滑动加速和减速的过程中,断层摩擦经历了增长、弱化和再增长。这种摩擦变化可能可以由低滑动速率下和更现实的滑动速率之下的速率-状态摩擦行为[9-10]来解释,但包含了不同的物理机制和不同的规模。最初的摩擦增强可能会阻碍小破裂向大地震的发展。断层滑动减速过程中的摩擦增强可能导致地震破裂呈脉冲状[11-14],并使得静态应力下降到与动态应力变化相比较低的水平[15]。     

断层阶区对滑动行为影响的实验研究

研究断层带几何非规则体对断层活动的力学影响,对于理解断层带上的地震活动具有重要的理论和实际意义．通过中尺度标本岩石力学实验,研究了走滑断层带最常见的一种非规则体．断层阶区对滑动行为的影响．研究表明,拉张断层阶区由于强度较低而很容易发生破裂,破裂后的阶区对断层的滑动无明显阻碍作用,但阶区的微破裂对断层滑动失稳具有指示作用;含拉张阶区的断层带具有速度弱化特征,可用速率一状态摩擦定律表述．挤压阶区由于破坏强度很高,使得断层滑动较为困难,但随着应力水平的增加,阶区外断层端部拉张区的微破裂为断层在阶区未破裂之前发生粘滑失稳提供了变位条件,并因此可作为断层失稳的前兆;挤压阶区可作为断层分段的稳定标志,直到阶区完全破裂使两条断层完全连通．     

基于Chester-Higgs模型探讨摩擦生热对断层演化进程的影响

速率和状态相依赖的摩擦定律是本文采用的重要定律。结合Chester-Higgs摩擦模型和McKenzie-Brune摩擦生热模型,在一维弹簧-滑块-断层近似模型下,利用四阶变步长的Dormand-Prince算法,研究探讨了断层摩擦生热对断层演化的影响。结果表明:与忽略温度影响的情形相比,摩擦生热造成的温度上升可导致断层滑移时刻的略微提前,并伴随着摩擦系数和状态变量的下降,同时也使得断层的滑移量和应力降略有减小,而滑移速率有所增大;另外,在考虑温度影响时,有效正应力和临界滑移距离也会影响断层的演化过程,断层上的有效正应力越大,断层失稳时刻越提前,温度上升越明显;断层的临界滑移距离越大,断层失稳时刻则越迟,温度上升越显著,但当临界滑移距离超过5 cm时,具有不同临界滑移距离的断层,失稳时的温度则基本保持一致。      

Dynamic faulting under rate-dependent friction

We discuss the effects of rate-dependent friction on the propagation of seismic rupture on active faults. Several physicists using Burridge and Knopoff's box and spring model of faulting have proposed that fault complexity may arise from the spontaneous development of a self-similar stress distribution on the fault plane. If this model proves to be correct, it has important consequences for the origin of the complexity of seismic sources. In order to test these ideas on a more realistic earthquake model, we developed a new boundary integral equation method for studying rupture propagation along an antiplane fault in the presence of nonlinear rate-dependent friction. We study rupture dynamics of models with single and twin asperities. In our models, asperities are places on the fault with a higher value of prestress. Othewise all fault parameters are homogeneous. We show that for models with such asperities, a slip velocity weakening friction leads to the propagation of supersonic healing phases and to the spontaneous arrest of fracture if the prestress outside the asperities is low enough. For models with asperities, we can also observe narrow slip velocity pulses, qualitatively similar to the so-called Heaton pulses observed in some earthquake accelerograms. We also observe a complex distribution of stress after the rupture that depends on details of the initial distribution of asperities and on the details of the friction law.     

Constitutive relations for fault slip and earthquake instabilities

Constitutive relations for fault slip are described and adopted as a basis for analyzing slip motion and its instability in the form of earthquakes on crustal faults. The constitutive relations discussed include simple rate-independent slip-weakening models, in which shear strength degrades with ongoing slip to a residual frictional strength, and also more realistic but as yet less extensively applied slip-rate and surface-state-dependent relations. For the latter the state of the surface is characterized by one or more variables that evolve with ongoing slip, seeking values consistent with the current slip rate. Models of crustal faults range from simple, single-degree-of-freedom spring-slider systems to more complex continuous systems that incorporate nonuniform slip and locked patches on faults of depth-dependent constitutive properties within elastic lithospheric plates that may be coupled to a viscoelastic asthenosphere. Most progress for the rate and state-dependent constitutive relations is at present limited to single-degree-of-freedom systems. Results for stable and unstable slip with the various constitutive models are summarized. Instability conditions are compared for spatially uniform versus nonuniform slip, including the elastic — brittle crack limit of the nonuniform mode. Inferences of constitutive and fracture parameters are discussed, based on earthquake data for large ruptures that begin with slip at depth, concentrating stress on locked regions within a brittle upper crust. Results of nonlinear stability theory, including regimes of complex sustained stress and slip rate oscillations, are outlined for rate and state-dependent constitutive relations, and the manner in which these allow phenomena like time-dependent failure, restrengthening in nearly stationary contact, and weakening in rapidly accelerated slip, is discussed.     

Earthquake Recurrence in Simulated Fault Systems

We employ a computationally efficient fault system earthquake simulator, RSQSim, to explore effects of earthquake nucleation and fault system geometry on earthquake occurrence. The simulations incorporate rate- and state-dependent friction, high-resolution representations of fault systems, and quasi-dynamic rupture propagation. Faults are represented as continuous planar surfaces, surfaces with a random fractal roughness, and discontinuous fractally segmented faults. Simulated earthquake catalogs have up to 10⁶ earthquakes that span a magnitude range from ～M4.5 to M8. The seismicity has strong temporal and spatial clustering in the form of foreshocks and aftershocks and occasional large-earthquake pairs. Fault system geometry plays the primary role in establishing the characteristics of stress evolution that control earthquake recurrence statistics. Empirical density distributions of earthquake recurrence times at a specific point on a fault depend strongly on magnitude and take a variety of complex forms that change with position within the fault system. Because fault system geometry is an observable that greatly impacts recurrence statistics, we propose using fault system earthquake simulators to define the empirical probability density distributions for use in regional assessments of earthquake probabilities.     

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.     

Experimental study on nucleation process of stick-slip instability on homogeneous and non-homogeneous faults

The nucleation process of stick-slip instability was analyzed based on the experimental measurements of strain and fault slip on homogeneous and non-homogeneous faults. The results show that the nucleation process of stick-slip on the homogeneous fault is of weak slip-weakening behavior under constant loading point velocity. The existence of a short “weak segment” on the fault makes slip-weakening phenomenon in nucleation process more obvious, while the existence of a long “weak segment” on the fault makes the nucleation process changed. The nucleation is characterized by accelerating slip in a local region and rapid increase of shear stress along the fault in this case, which is more coincident with the rate and state friction law. During the period when fault is locked, increasing of shear stress causes lateral elastic dilation near the fault, and the rebound of the dilation at the time of instability causes an instantaneous increase of normal stress in the fault plane, which is an important factor making fault be rapidly locked and its strength recovered.     

Influence of regional background stress fields on the spontaneous rupture of the major faults around Xiluodu dam,China

Simulations of the spontaneous rupture of potential earthquakes in the vicinity of reservoir dams can provide accurate parameters for seismic resilience assessment, which is essential for improving the seismic performance of reservoir dams. In simulations of potential spontaneous ruptures, fault geometry, regional stress fields, constitutive parameters of the fault friction law, and many other factors control the slip rate, morphology, and dislocation of the rupture, thereby affecting the simulated ground motion parameters. The focus of this study was to elucidate the effects of the background stress field on the nucleation and propagation of spontaneous ruptures based on the factors influencing potential M > 7 earthquake events on the Leibo Middle Fault (LBMF) and the Mabian-Yanjing Fault (MB-YJF) in the Xiluodu dam (XLD) region. Our simulation results show that the magnitude of the regional background stress field plays a decisive role in whether a destructive earthquake exceeding the critical magnitude will occur. We found that the direction and magnitude of the regional stress significantly affect the range of rupture propagation on the fault plane, and fault geometry affects the spatial distribution of the rupture range. Under the same regional stress field magnitude and orientation, a more destructive, high-magnitude earthquake is more likely to occur on the LBMF than on the MB-YJF.     

Experimental study on nucleation process of stick-slip instability on homogeneous and non-homogeneous faults

The nucleation process of stick-slip instability was analyzed based on the experimental measurements of strain and fault slip on homogeneous and non-homogeneous faults. The results show that the nucleation process of stick-slip on the homogeneous fault is of weak slip-weakening behavior under constant loading point velocity. The existence of a short "weak segment" on the fault makes slip-weakening phenomenon in nucleation process more obvious, while the existence of a long "weak segment" on the fault makes the nucleation process changed. The nucleation is characterized by accelerating slip in a local region and rapid increase of shear stress along the fault in this case, which is more coincident with the rate and state friction law. During the period when fault is locked, increasing of shear stress causes lateral elastic dilation near the fault, and the rebound of the dilation at the time of instability causes an instantaneous increase of normal stress in the fault plane, which is an important factor making fault be rapidly locked and its strength recovered.