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.     

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.     

Frictional heat generation and seismic radiation in a foam rubber model of earthquakes

Results from a study of stick-slip particle motion at the interface between two stressed foam rubber blocks indicate that normal vibrations and interface separation are an important part of the stick-slip process in foam rubber. The dimension of the dynamic slip pulse is small compared to the dimension of the model (approximately 10 cm vs. 200 cm) consistent with the abrupt-locking slip pulse model ofBrune (1970, 1976), andHeaton (1990). A comparison of frictional heat generation between stable-sliding and stick-slip foam rubber models indicates a linear relation between the temperature increase on the fault surface (for a given distance of slip) and the driving shear force for the stable-sliding model, while for the stick-slip model there is essentially no variation in frictional heat generation with an increase in shear stress. We performed experiments to investigate the ratio of normal motion to shear motion at different levels of normal stress in the stick-slip foam rubber model. Preliminary result indicate that the normal component of the particle motion increases more rapidly with increasing normal stress than the shear component. The phenomenon of interface separation and normal vibrations may thus explain some of the most frustrating problems in earthquake mechanics, e.g., the heat flow paradox, the long-term weakness of major active faults, and anomalousP-wave radiation.     

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.     

Creep,stable sliding,and premonitory slip

Summary The current status of laboratory investigations into creep, stable sliding and premonitory slip is reviewed and some new material is presented. It is postulated that pre-cut rocks and those with simulated gouge layers undergo a transition with increasing confining pressure from (1) stable sliding to stick-slip, to (2) sliding along the pre-cut with deformation of the country rock, to (3) homogeneous flow of the specimen without slip along the pre-cut. Stick-slip behavior is not always present. Decreasing displacement rates are found to enhance stick-slip. Mixtures of gouge are found to be significant in controlling the behavior of sliding with 10–20 percent of anhydrite mixed with quartz or clays mixed with anhydrite shifting the sliding mode from stable stick-slip or stick-slip to stable sliding, respectively. Premonitory slip may be one of the most significant short term precursors of earthquakes. Although widely recognized in the laboratory, little systematic work has been completed. Variations in pore pressure, resistivity and seismic velocities have been investigated. Clearly much work needs to be done into these topics before a clear understanding is achieved.     

Stick-slip and strain waves in the physics of earthquake rupture: experiments and models

The study of stick-slip is directly connected with the formulation of the consistent concept of seismicity migration and explanation of the nature of strain waves observed at the contacts of blocks and plates. We propose a phenomenological model to describe the initiation of stick-slip at the rough contact of blocks of rocks. The model contains the leading factors of stick-slip process (friction, roughness of contact surfaces, and asperity). The model reproduces the universal profile of slip velocity and displacement, velocity of dynamic rupture observed in experiments. The stick-slip motion at a rough surface of a fault is shown to be a nonlinear process and can be described by the generalized sine-Gordon equation. The results of calculations and a comparison with experimental data testify to the existence of waves of a new type — solitary waves of sliding. The analogies are found between the strain waves generated due to stick-slip at the contact of the blocks of rocks, strain waves in the crustal faults, and those within the lithosphere.     

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     

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.     

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.     

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     

Period Doubling Bifurcation of Stress Drop for Stick-slip and Its Physical Implication

It is revealed in frictional experiments on medium-scale samples that period doubling bifurcation of stress drop for stick-slip occurs due to macroscopic heterogeneity of the sliding surface under conditions for typical stick-slip.The observed data show that the period doubling bifurcation of stress drop results from the alternate occurrence of strain release along the whole fault and along part of fault.This implies that complicated nonlinear behavior corresponds to clear physical implication in some cases.     

黏滑实验的震级评估和应力降分析

本文通过三种结构模型的黏滑地震模拟实验,利用高频速度连续观测系统获得了地震失稳过程的速度特征,讨论了最大位移量的选取方法,估算了实验室黏滑型地震的矩震级,探讨了黏滑类型、应力降大小与震级的关系.结果表明,黏滑型地震的应力降过程可能包含一次到多次高频振荡,对应若干次黏滑子事件.高频振荡的摆动幅度很大,包含有多种频率成分,峰值速度0.003~0.008 m·s^-1.初步估计黏滑型地震的震级范围为-4.4~-3级,断层构造面的差异对各种黏滑模型的地震震级分布有明显影响.总体来看应力降与地震震级没有明显相关性,决定地震震级的主要因素应当是震源尺度.     

Effects of mining-induced seismic events on a deep underground mine

The performance of an underground excavation at the Lucky Friday Mine that was subjected to repetitive episodes of mining-induced seismic activities is assessed. Field measurements indicate that an underground excavation may respond to mining-induced seismicity with step changes in displacement of the rock mass around the excavation or step changes in excavation closures. However, step changes in displacement or closure were also observed without the presence of mine seismic events. This behavior may be explained using the concept of stick-slip on joints or bedding planes within the rock mass. The stick-slip mechanism is believed to be controlled by the state of stresses at a joint or bedding plane. Through this mechanism, joint displacement is accumulated in a progressive fashion leading to a weakening of rock mass around an excavation. As a result, the excavation becomes less stable and therefore is more susceptible to seismic impacts. The concept of using peak particle velocity to assess damage threshold for underground excavations may not be conservative when considering the effect of rock mass fatigue.     

与唐山地震有关的深部岩石力学特性的数值模拟

根据构造地震的发生机制,本文提出了一个数学模型。该模型不仅能模拟岩石摩擦试验的粘滑特性,而且在该模型基础上建立起来的数值模拟方法能对构造地震的发生作出定性和定量的分析,并经过对唐山地震序列的数值模拟,可得到对震源深部岩石的力学性质的一些认识。     

岩石粘滑的自锁模型及数值模拟

本文根据岩石摩擦的自锁模型,通过数值模拟讨论了围压和围压介质刚度对粘滑及其应力降的影响。结果表明:围压的增大有利于发生粘滑;粘滑应力降随围压的增大而增大;天然地震应力降低于室内粘滑应力降是由围压介质刚度引起的。     

Discrete Element Modeling of Stick-Slip Instability and Induced Microseismicity

Using Particle Flow Code, a discrete element model is presented in this paper that allows direct modeling of stick-slip behavior in pre-existing weak planes such as joints, beddings, and faults. The model is used to simulate a biaxial sliding experiment from literature on a saw-cut specimen of Sierra granite with a single fault. The fault is represented by the smooth-joint contact model. Also, an algorithm is developed to record the stick-slip induced microseismic events along the fault. Once the results compared well with laboratory data, a parametric study was conducted to investigate the evolution of the model’s behavior due to varying factors such as resolution of the model, particle elasticity, fault coefficient of friction, fault stiffness, and normal stress. The results show a decrease in shear strength of the fault in the models with smaller particles, smaller coefficient of friction of the fault, harder fault surroundings, softer faults, and smaller normal stress on the fault. Also, a higher rate of displacement was observed for conditions resulting in smaller shear strength. An increase in b-values was observed by increasing the resolution or decreasing the normal stress on the fault, while b-values were not sensitive to changes in elasticity of the fault or its surrounding region. A larger number of recorded events were observed for the models with finer particles, smaller coefficient of friction of the fault, harder fault surroundings, harder fault, and smaller normal stress on the fault. The results suggest that it is possible for the two ends of a fault to be still while there are patches along the fault undergoing stick-slips. Such local stick-slips seem to provide a softer surrounding for their neighbor patches facilitating their subsequent stick-slips.     

岩石的双剪摩擦及震源时间函数的实验研究

本文介绍了岩石的双剪摩擦滑动实验。在实验宁测量了不同正应力条件下的粘滑应力降和位移值,求出了静、动摩擦系数;用瞬态波形存储器记录了粘滑过程中位移随时间的变化曲线,得出了震源时间函数,它的形状与布隆提出的震源时间函数极为相似,两者皆以指数形式下降,它的数值与野外实测结果大致相近。为验证实验数据的准确性,本文还对粘滑的理想模型进行了分析和计界。理论、实验和野外观测的结果大体一致。     

正断层黏滑错动作用下隧道抗错断技术模型试验研究

为提高穿越黏滑断层隧道的结构安全性和稳定性,开展了正断层黏滑错动作用下隧道抗错断措施作用效果室内模型试验。通过分析结构纵向应变、接触压力及安全系数,对未采取措施、结构加强、结构加强并施设减错层、结构加强并施设减错缝、结构加强并施设减错层和减错缝5种工况进行了对比分析。研究结果表明:采用减错措施（减错层/缝或减错层+减错缝）后,沿隧道纵向结构纵向应变、接触压力增加倍数由剧烈变化变为较均匀变化;仅采用结构加强措施抵抗正断层黏滑错动对隧道结构的影响,效果有限;通过采用减错措施消减正断层黏滑错动对隧道结构的影响,效果明显,结构安全系数最小值增加8倍以上;通过采用结构加强并施设减错层和减错缝措施抵抗和消减正断层黏滑错动对隧道结构的影响,效果显著,结构安全系数最小值增加25.45倍。研究成果可为高烈度艰险山区黏滑正断层隧道的抗错断设防设计提供参考。     

Effect of fault jogs on frictional behavior: An experimental study

Studying the effect of geometrically irregular bodies on the mechanical behavior of fault activity is of significance in understanding the seismic activity along a fault zone. By using rock mechanics ex- periment with medium-scale samples, we have studied the effect of fault jogs, the most common irregularity along fault zones, on frictional behavior. The research indicates that extensional fault jog can be easily fractured because of its low strength and the fractured jog has no obvious resistance to fault sliding, and the micro-fractures occurring in the jog are indicative of stick-slip along the faults. The fault zone containing extensional jogs is characterized by velocity weakening and can be described by rate and state friction law. Compressional fault jog makes fault sliding more difficult because of its high fracturing strength, but the micro-fractures occurring in the tensile areas around fault ends at higher stress level can provide necessary condition for occurrence of stick-slip along the faults before the jog is fractured and thus act as precursors of fault instability. Compression jog can be taken as a stable indicator of fault segmentation until the jog is completely fractured and two faults are linked.     

黏滑断层隧道刚柔并济抗减错技术研究

为提高强震区黏滑断层隧道的结构安全性和稳定性,以都汶高速友谊隧道F1黏滑断层段为研究背景,对黏滑断层隧道采用刚柔并济抗减错技术进行研究.研究结果表明:采用结构加强措施抵抗断层黏滑错动影响,结构位移抗减错效果不显著,结构内力的平均抗减错效果在23％～33％之间;施设减错层有利于消减断层黏滑错动对隧道结构的影响,其拱顶沉降...