Analysis of stick-slip and earthquake mechanism

A mathematical model of a sliding system that contains a frictional surface embedded in an elastic specimen and machine is proposed to analyze the frictional behavior observed in laboratory and field. It is shown that stick-slip occurs if the slope of the velocity-stress relation on the sliding surface exceeds a critical value at a certain point between static and kinetic frictions. This condition, coupled with Amontons' law and other subsidiary relations, predicts the effects of normal stress, gouge thickness, temperature, and loading rate etc. on the stick-slip instability, consistent with known experimental evidence. The elastic-wave radiation associated with stick-slip is governed by Brune's source time function, in which rise time and effective stress are proportional to fault dimension and stress drop, respectively.     

摩擦生热对断层演化过程的影响:Ruina-和Chester-Higgs-模型的对比分析

利用速率-状态摩擦定律(Rate-and State-Dependent Friction Law:简称RSF定律),结合McKenzie-Brune摩擦生热模型,本文分别从Ruina提出的RSF定律和Chester-Higgs提出的RSF定律出发,通过一维弹簧-滑块模型,采用四阶变步长的Dormand-Prince算法,对断层演化过程进行了数值模拟,探讨了摩擦生热对断层演化进程的影响.模拟结果显示,与Ruina-模型相比,Chester-Higgs-模型在断层高速滑动时存有更大的摩擦强度,表明摩擦生热对断层具有一定的强化作用,且同临界滑移距离的取值相关.而且,Chester-Higgs-模型在失稳时的断层面温度远远低于Ruina-模型,表明摩擦生热在断层演化过程中能抑制断层面温度的剧烈升高,且正应力和临界滑移距离越大,两种模型的温差越为明显,而断层的刚度和尺度则对温度的影响很小.模拟两种模型周期演化过程的结果表明,在相同的初始条件下,Chester-Higgs-模型给出的断层失稳周期明显比Ruina-模型更短,说明摩擦生热对断层自身演化最显著的影响是较大地缩短了地震重复发生周期.当断层进入周期性演化后,Chester-Higgs-模型给出的摩擦强度大于Ruina-模型,且对第一次非周期性失稳的摩擦强度和剩余应力的继承性更好.另外,由ChesterHiggs-模型给出的静态应力降远小于Ruina-模型给出的结果,所对应的单个事件的滑移量也小于Ruina-模型.     

应力途径与岩石的摩擦滑动

用双剪法对济南辉长岩和点苍山大理岩进行了摩擦滑动实验.实验中的应力变化方式有两种.A 型实验:先使断层面上的正应力增加到一定值,然后保持正应力不变,并增加剪应力使断层发生粘滑;B 型实验:先使断层面上的正应力增加到一定的值,保持正应力不变,并增加剪应力到断层发生粘滑前的某一应力状态,再保持剪应力不变,减小正应力直到粘滑发生.实验表明,B 型实验中岩石的摩擦强度高于 A 型实验.A 型实验中粘滑发生前有声发射率增加的前兆,B 型实验中粘滑发生前看不到声发射率的明显增加.由实验得到一个启示,即闭锁断层的开锁可能采取两种形式:一种是冲开闭锁,即以剪应力的增加使断层发生错动;另一种是解开闭锁,即以正应力的减小使断层发生错动.断层的粘滑采取哪种形式,由断层带的应力变化途径决定.      

剪切载荷扰动对断层摩擦影响的实验研究

利用双轴伺服控制加载装置,采用3块花岗闪长岩标本组成的含有2个滑动面的直剪结构,开展了摩擦滑动实验。实验中通过在剪切方向上叠加正弦波状的位移扰动,研究了剪应力扰动对断层粘滑失稳的影响。研究表明,在恒定的正应力和位移速率下,标本表现出较为规则的粘滑;当在剪切方向叠加位移扰动后,随扰动振幅的增加,粘滑发生时间与扰动的相关性增大,粘滑的应力降和时间间隔的分布趋于离散,其中扰动能产生明显影响的临界振幅大致为0.05MPa;粘滑应力降和时间间隔随扰动振幅增大而逐渐离散的现象在较高正应力下更为明显,而相同扰动振幅下粘滑失稳发生时间与扰动的相关性也随正应力增加而增大;扰动周期对摩擦性状的影响不明显。研究结果意味着,地震引起的同震剪应力的变化不仅会引起邻近断层上地震发生时间的变化,也可能引起地震强度的变化     

剪切破裂与粘滑——浅源强震发震机制的研究

周口店花岗闪长岩的高温高压三轴实验和理论分析表明,剪切破裂和摩擦滑移具有类似的孕育过程和发生机制。剪切破裂贯通强度就是一种摩擦强度。剪切破裂和摩擦滑移各自都有渐进式和突发式之分。突发式摩擦滑移是已有断层的粘滑滑移。突发式剪切破裂则是完整岩石的初始粘滑滑移。考虑到地壳温度随深度增加,完整岩石剪裂强震要求较高的围压,因此,多数浅源强震的发震方式很可能是已有断层的粘滑     

正应力扰动对断层滑动失稳影响的实验研究

利用双轴伺服控制加载装置,采用三块花岗闪长岩标本组成的含有两个滑动面的直剪结构,开展了摩擦滑动实验.实验中通过在垂直滑动面的载荷上叠加正弦波状和方波状的扰动,研究了正应力扰动对断层黏滑失稳的影响.研究表明,在恒定的正应力和位移速率下,标本表现为规则的黏滑,叠加正应力扰动后,随扰动振幅的增加黏滑发生时间与扰动的相关性增大,黏滑应力降和时间间隔的分布趋于离散.黏滑应力降和时间间隔的平均值随平均正应力的增加呈线性增长,扰动叠加后黏滑应力降的离散度随平均正应力的增加而增大;黏滑应力降和时间间隔主要受应力变化幅度的影响,而与应力变化的速率关系不大.剪应力和正应力扰动都会对断层黏滑失稳产生影响,而正应力扰动的影响更明显.这两种扰动对断层黏滑失稳影响的机制存在差异,剪应力扰动只是改变断层滑动的推动力,而正应力扰动则改变了断层面上凹凸体的接触状态.     

地壳深部稳定性——震源体破裂机制和摩擦滑动机制的综合研究

本文通过地壳应力测量结果和地震资料的综合分析,对深部应力状态与断层运动的关系作了讨论:进而应用库仑准则,推导了三维应力作用下完整岩体和已有的任意空间方向断层面的失稳条件及其滑动方式的解析表达式.通过建立描述岩体和已有断层稳定性的两个函数————破裂函数 Fm 和摩擦函数 Ff,给出了应用破裂机制和摩擦滑动机制综合分析地壳稳定性和失稳性态的方法:根据这种分析方法并结合华北平原区的水压致裂应力测量资料,以及孔隙压力、大地热流等观测结果,定量研究了本区地壳的稳定问题,计算并图示了地壳内破裂函数沿深度的分布,以及各种走向和倾向断层面上的摩擦函数和剪应力分布;计算中以 Byerlee 定律作为断层运动的约束条件,并考虑了地壳密度纵向非均匀性导致的垂直应力沿深度的非线性增长以及深部超静水压力的异常孔隙压力作用.结果表明,华北平原区地壳失稳性态主要表现为已有断层的滑动;伴有高剪应力降的断层运动的深度范围在8至2.0多公里之间:陡断层稳定性低于缓断层,其运动方式以走滑为主;本区 NNE-NE 走向的陡断层是一组易震断层,其震时错动为右旋走滑;孔隙压力的增长对地壳稳定性有显著的影响;华北平原区深部高异常孔隙压力是地震活动的一种重要背景.      

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。      

Nonuniform friction as a physical basis for earthquake mechanics

A review of simple models and observations suggests that the main first-order features of active faulting-mechanical instability, the frequency-magnitude relations, seismic and aseismie slip, seismic radiation, incoherency and rupture stoppage — may be explained by a single characteristic of crustal faults: the spatial variation of the effective frictional stress, which resists slippage on faults. Faultoffset data suggest that rupture propagation ceases in regions of high resistance which act, as barriers. In these regions slippage is associated with negative stress drop. The spacing and the amplitudeA() of the barriers, as inferred from the frequency-magnitude and moment relation for earthquakes, obeys a simple statistical relationA()^p. On the scale of particle motion, this variability of frictional stress provides a mechanical instability which may be associated with the concept of dynamic friction. Invariably, the rapid particle motion in the model is always preceded by accelerated creep. The particle acceleration is highly irregular, giving rise to an almost random acceleration record on the fault. The particle displacement is relatively smooth, giving rise to simple displacement time function in the far field. Rupture propagation time is approximately proportional to the gradient of frictional stress along the fault. Consequently sharp changes of this stress may cause multiple events and other long period irregularities in the fault motion.The power density spectrum associated with the frictional stress implies that stress may be related to a Poisson distribution of lengths. The autocorrelation of such type of distribution yields a correlation lengthk _L ^–1 , similar perhaps toHaskell's (1964) andAki's (1967) correlation lengths inferred from spectral analysis of seismic waves. The partial incoherency of faulting implies that preseismic deformation may be significantly incoherent, consequently the prediction of small moderate earthquakes may be subject to inherent uncertainties. We conclude that frictional stress heterogeneities may be necessary and sufficient to explain active faulting associated with small and moderate earthquakes.     

THE GEOLOGICAL AND ROCK MECHANICAL DISTINCTION EVIDENCE BETWEEN STICK-SLIP AND CREEP IN HOST ROCK SEGMENTS OF FAULT

Paleo-seismic and fault activity are hard to distinguish in host rock areas compared with soft sedimentary segments of fault. However, fault frictional experiments could obtain the conditions of stable and unstable slide, as well as the microstructures of fault gouge, which offer some identification marks between stick-slip and creep of fault. We summarized geological and rock mechanical distinction evidence between stick-slip and creep in host rock segments of fault, and analyzed the physical mechanisms which controlled the behavior of stick-slip and creep. The chemical composition of fault gouge is most important to control stick-slip and creep. Gouge composed by weak minerals, such as clay mineral, has velocity weakening behavior, which causes stable slide of fault. Gouge with rock-forming minerals, such as calcite, quartz, feldspar, pyroxene, has stick-slip behavior under condition of focal depth. To the gouge with same chemical composition, the deformation mechanism controls the frictional slip. It is essential condition to stick slip for brittle fracture companied by dilatation, but creep is controlled by compaction and cataclasis as well as ductile shear with foliation and small fold. However, under fluid conditions, pressure solution which healed the fractures and caused strength recovery of fault, is the original reason of unstable slide, and also resulted in locking of fault with high pore pressure in core of fault zone. Contrast with that, rock-forming minerals altered to phyllosilicates in the gouges by fluid flow through degenerative reaction and hydrolysis reaction, which produced low friction fault and transformations to creep. The creep process progressively developed several wide shear zones including of R, Y, T, P shear plane that comprise gouge zones embedded into wide damage zones, which caused small earthquake distributed along wide fault zones with focal mechanism covered by normal fault, strike-slip fault and reverse fault. However, the stick-slip produced mirror-like slide surfaces with very narrow gouges along R shear plane and Y shear plane, which caused small earthquake distributed along narrow fault zones with single kind of focal mechanism.     

Bounding of near-fault ground motion based on radiated seismic energy with a consideration of fault frictional mechanisms

The energy radiated as seismic waves strongly depends on the fault rupture process associated with rupture speed and dynamic frictional mechanisms involved in the fault slip motion.Following McGarr and Fletcher approach,we derived a physics-based relationship of the weighted average fault slip velocity vs apparent stress,rupture speed and static stress drop based on a dynamic circular fault model.The resultant function can be approximately used to bound near-fault ground motion and seismic energy associated with near-fault coseismic deformation.Fault frictional overshoot and undershoot mechanisms governed by a simple slip-weakening constitutive relation are included in our consideration by using dynamic rupture models named as M-and D-models and proposed by Madariaga(1976) and Boatwright.We applied the above function to the 2008 great Wenchuan earthquake and the 1999 Jiji(Chi-Chi) earthquake to infer the near-fault ground motion called slip weighted average particle velocity and obtained that such model-dependent prediction of weighted average ground velocities is consistent to the results derived from the near-fault strong motion observations.Moreover,we compared our results with the results by McGarr and Fletcher approach,and we found that the values of the weighted average particle velocities we obtained for these two earthquakes are generally smaller and closer to the values by direct integration of strong motion recordings of the near-fault particle velocity waveform data.In other words,if this result comes to be true,it would be a straightforward way used to constrain the near-fault ground motion or to estimate source parameters such as rupture speed,static and dynamic stress drops.     

Comprehensive study on stability of deep crust and unstable behavior of earthquake source by both failure mechanism and frictional sliding mechanism

In this paper the relation between fault movement and stress state in deep crust is discussed, based on synthetic analysis of the crustal stresses measured over the world and the concerned data of focal mechanism. Using Coulomb criterion for shear failure and frictional slip, analytical expressions for estimating stabilities of intact rock and existing fault in the crust and for identifying the type of faulting (normal, strike-slip or thrust fault) are derived. By defining the Failure FunctionF _m and the Fraction FunctionF _f, which may describe steadiness of crustal rock and existing fault, respectively, a synthetic model is set up to consider both fracturing mechanism and the sliding mechanism. By this model, a method to study stability and unstable behavior of crustal rock and fault at different depths is given. According to the above model, quantitative study on the crustal stability in the North China plain is made in terms of the measured data of hydraulic fracturing stress, pore-fluid pressure, terrestrical heat flow in this region. The functionsF _m andF _f and the shear stresses on faults with different strike angle and dip angle at various depths in this region are calculated. In the calculation the constraint condition of fault movement obeys Byerlee’s Law, and the depth-dependent nonlinear change in the vertical stress due to inhomogeneity of crustal density and the high anomalous pore-fluid pressure in deep crust of this region are considered. The conclusions are: the unstable behavior of the crust in the North China plain is not failure of crustal rock but slip on existing fault; the depth range where stick-slip of fault may happen is about from 8 to 20 km or more; stability of steep fault is lower than that of gentle sloping fault; the shear stresses in the range where may occur stick-slip are nearly horizontal; the steep faults trending from NNE to NE in this region are liable to produce strong earthquakes, whose co-seismic faultings are, for the most part, right lateral slip; the change in pore-fluid pressure in depth remarkably affects the stability of the crust and the increase in pore-fluid pressure, therefore, would be an important factor exciting strong earthquake in this region. The above theoretical inferences are consistent with the data measured in this region. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologia Sinica,13, 450–461, 1991. This work is supported by Chinese Joint Seismological Science Foundation.     

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.     

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.     

Development of shear localization in simulated quartz gouge: Effect of cumulative slip and gouge particle size

Frictional sliding experiments were conducted on two types of simulated quartz gouge (with median particle diameters 5 m and 25 m, respectively) at confining pressures ranging from 50 MPa to 190 MPa in a conventional triaxial configuration. To investigate the operative micromechanical processes, deformation texture developed in the gouge layer was studied in samples which had accumulated different amounts of frictional slip and undergone different stability modes of sliding. The spatial patterning of shear localization was characterized by a quantitative measurement of the shear band density and orientation. Shear localization in the ultrafine quartz gouge initiated very early before the onset of frictional sliding. Various modes of shear localization were evident, but within the gouge zoneR ₁-shears were predominant. The density of shear localization increased with cumulative slip, whereas the angle subtended at the rock-gouge interface decreased. Destabilization of the sliding behavior in the ultrafine quartz gouge corresponded to the extension ofR ₁-shears and formation of boundaryY-shear segments, whereas stabilization with cumulative slip was related to the coalescence ofY-shear segments to form a throughgoing boundary shear. In the coarse quartz gouge, the sliding behavior was relatively stable, probably because shear localization was inhibited by distributed comminution. Two different models were formulated to analyze the stress field within the gouge zone, with fundamentally different predictions on the orientations of the principal stresses. If the rock-gouge interface is assumed to be bonded without any displacement discontinuity, then the maximum principal stress in the gouge zone is predicted to subtend an angle greater than 45° at the interface. If no assumption on displacement or strain continuity is made and if the gouge has yielded as a Coulomb material, then the maximum principal stress in the gouge zone is predicted to subtend an angle less than 45°. If the apparent friction coefficient increases with overall slip (i.e., slip-hardening), then the Riedel shear angle progressively decreases with increasing shear strain within the gouge layer, possibly attaining a zero value which corresponds to a boundaryY-shear. Our quantitative data on shear localization orientation are in reasonable agreement with this second model, which implies the coefficient of internal friction to be about 0.75 for the ultrafine quartz gouge and 0.8 for the coarse gouge. The wide range of orientations for Riedel shear localization observed in natural faults suggests that the orientations of principal stresses vary as much as in an experimental gouge zone.     

Granular Controls on Periodicity of Stick-Slip Events: Kinematics and Force-Chains in an Experimental Fault

It is a long-standing question whether granular fault material such as gouge plays a major role in controlling fault dynamics such as seismicity and slip-periodicity. In both natural and experimental faults, granular materials resist shear and accommodate strain via interparticle friction, fracture toughness, fluid pressure, dilation, and interparticle rearrangements. Here, we isolate the effects of particle rearrangements on granular deformation through laboratory experiments. Within a sheared photoelastic granular aggregate at constant volume, we simultaneously visualize both particle-scale kinematics and interparticle forces, the latter taking the form of force-chains. We observe stick-slip deformation and associated force drops during an overall strengthening of the shear zone. This strengthening regime provides insight into granular rheology and conditions of stick-slip periodicity, and may be qualitatively analogous to slip that accompanies longer term interseismic strengthening of natural faults. Of particular note is the observation that increasing the packing density increases the stiffness of the granular aggregate and decreases the damping (increases time-scales) during slip events. At relatively loose packing density, the slip displacements during the events follow an approximately power-law distribution, as opposed to an exponential distribution at higher packing density. The system exhibits switching between quasi-periodic and aperiodic slip behavior at all packing densities. Higher packing densities favor quasi-periodic behavior, with a longer time interval between aperiodic events than between quasi-periodic events. This difference in the time-scale of aperiodic stick-slip deformation is reflected in both the kinematics of interparticle slip and the force-chain dynamics: all major force-chain reorganizations are associated with aperiodic events. Our experiments conceptually link observations of natural fault dynamics with current models for granular stick-slip dynamics. We find that the stick-slip dynamics are consistent with a driven harmonic oscillator model with damping provided by an effective viscosity, and that shear-transformation-zone, jamming, and crackling noise theories provide insight into the effective stiffness and patterns of shear localization during deformation.     

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.     

岩石摩擦滑动的声发射b值

用双剪法进行岩石摩擦实验并测定了声发射b值。实验表明,粘滑发生前b值稳定并稍有增加,多次粘滑过程中b值基本不变,随着正应力的增加b值增加。     

Dynamic Rupture in a 3-D Particle-based Simulation of a Rough Planar Fault

An appreciation of the physical mechanisms which cause observed seismicity complexity is fundamental to the understanding of the temporal behaviour of faults and single slip events. Numerical simulation of fault slip can provide insights into fault processes by allowing exploration of parameter spaces which influence microscopic and macroscopic physics of processes which may lead towards an answer to those questions. Particle-based models such as the Lattice Solid Model have been used previously for the simulation of stick-slip dynamics of faults, although mainly in two dimensions. Recent increases in the power of computers and the ability to use the power of parallel computer systems have made it possible to extend particle-based fault simulations to three dimensions. In this paper a particle-based numerical model of a rough planar fault embedded between two elastic blocks in three dimensions is presented. A very simple friction law without any rate dependency and no spatial heterogeneity in the intrinsic coefficient of friction is used in the model. To simulate earthquake dynamics the model is sheared in a direction parallel to the fault plane with a constant velocity at the driving edges. Spontaneous slip occurs on the fault when the shear stress is large enough to overcome the frictional forces on the fault. Slip events with a wide range of event sizes are observed. Investigation of the temporal evolution and spatial distribution of slip during each event shows a high degree of variability between the events. In some of the larger events highly complex slip patterns are observed.