Rupture and particle velocity during frictional sliding

Summary Laboratory measurements of rupture and particle velocity are in surprisingly good agreement with seismic values, providing further evidence that stick-slip friction is a suitable mechanism for shallow earthquakes. A simple theory is developed to explain the linear relationship observed between average particle velocity and stress drop for stick-slip events. Both stick-slip ruptures and cracks in brittle material commonly propagate at velocities roughly comparable to theS wave velocity of the material. Rupture normally begins relatively slowly and accelerates to a steady velocity in a few centimeters. Observations suggest that stick-slip ruptures can propagate atS wave speeds or occasionally greater and that cracks in pre-stressed glass can also propagate faster than theS waves. Fracture and thus rupture velocity of intact rock specimens is greatly influenced by the inhomogeneous structure of rock. Fracture may be modeled by coalescence of many cracks rather than growth of a single crack.Lamont-Doherty Geological Observatory Contribution No. 2627.     

Seismic velocity changes during fracture and frictional sliding

Fracture and frictional sliding are considered as phenomena involving brittle failure. Brittle failure is preceded by the formation of small (subcritical) cracks. In non-water-saturated rock, the distribution, shape and size of these suberitical cracks determine the change in the physical properties prior to failure. A model is proposed which suggests that the spatial and temporal distribution, shape and size of subcritical cracks within a stressed rock depend upon the rate of deformation and the volatile content.As a rock is stressed beyond about 50 percent of its ultimate failure stress, dilatancy is initiated. With increasing stress a broad zone of cracks develops within the dilatant region. The seismic velocities through this zone decrease markedly and the cracks grow more numerous., changing in size and shape. Before brittle failure of the rock occurs, the subcritical cracks interact, leading to a concentration of the zone. During the stage when the zone narrows, the seismic velocities in crease in the surrounding volume due to local rotation of stresses and consequent closure of some cracks. In most laboratory experiments the stage during which the velocity increases and the now intense deformation zone becomes narrow is very short and difficult to observe experimentally. At very low strain rates and with volatiles present, the crack growth and subsequent interaction lead to the narrowing of the intense deformation zone and therefore to an observable increase in velocity.The above is based upon an interpretation of a number of experiments. Using optical holography we have observed the development and subsequent intensification of a deformation zone. Ultrasonic velocity measurements showed a distinct anomaly (decrease followed by an increase) before failure. The anomaly was only detectable at our lowest experimental strain rates (3×10^–8/sec).     

Electrical resistivity changes in rocks during frictional sliding and fracture

Significant changes of electrical resistivity of saturated rocks and water pressure along sliding surface occurred during stick-slips in our direct shear experiment. Two types of changes of electrical resistivity occurred. In the first, resistivity decreased with increasing shear stress, reached minimum together with a sudden release of shear stress and returned to a higher value immediately afterwards. In the second, resistivity again decreased with increasing stress but, in contrast to the first type of changes, it decreased further upon the sudden drop of shear stress. The magnitude and the direction of the changes of water pressure on the sliding surface during stick-slip were not uniform, indicating local variations of surface deformation.     

Volume changes during fracture and frictional sliding: A review

Summary Volume changes in geologic materials have been measured with strain gauges, cantilever displacement gauges, or through observation of either pore or total volume. When porosity is less than 0.05, compaction is small or absent; apart from elastic strains in the minerals, dilatancy predominates, beginning at 50 to 75 percent of the fracture stress difference. When initial porosity exceeds about 0.05, compaction and dilatancy may overlap. The onset of dilatancy has not been identified, but most of the dilatancy occurs within about 10 percent of the fracture stress difference. In low porosity rocks, dilatancy increases initial porosity by a factor of 2 or more; in porous rocks or granular aggregates the increase is only 20 to 50 percent. However, the actual pore volume increase is larger in rocks of high initial porosity. Hence, earthquake precursors which depend on the magnitude of dilatancy should be more pronounced in porous rocks or in fault gouge. In contrast, precursors which are based on fractional changes in some porosity-related property may be more pronounced in rocks of low initial porosity. Future work is particularly needed on constitutive relations suitable for major classes of rocks, on the effects of stress cycling in porous rocks, on the effects of high temperature and pore fluids on dilatancy and compaction, and on the degree of localization of strain prior to fracture.     

On a model of frictional sliding

A model of frictional sliding with anN-shaped curve for the sliding velocity dependence of the coefficient of friction is considered. This type of friction law is shown to be related to dynamic i.e., velocity dependent ageing of asperity junctions. Mechanisms of ageing for ductile (Bowden-Tabor) and brittle (Byerlee) materials, though different in nature, lead to qualitatively similarN-shaped velocity dependencies of the coefficient of friction. Estimates for the velocities limiting the range of negative velocity sensitivity of the coefficient of friction are obtained for the ductile case and—albeit with a lesser degree of reliability—for the brittle one. It is shown by linear stability analysis that discontinuous sliding (stick-slip) is associated with thedescending portion of theN-shaped curve. An instability criterion is obtained. An expression for the period of the attendant relaxation oscillations of the sliding velocity is given in terms of the calculated velocity dependence of the coefficient of friction. It is suggested that the micromechanically motivated friction law proposed should be used in models of earthquakes due to discontinuous frictional sliding on a crustal fault.     

Acoustic emission processes occurring during high-pressure sand compaction

Granular materials submitted to uniaxial compression undergo pore space reduction due to mechanisms such as particle rearrangement and grain crushing. These changes in the internal structure of the material release energy in the form of elastic waves that can be detected by sensors sensitive to acoustic emission. In this study, Acoustic emission monitoring with a wavelet-based signal processing technique is used to identify the various mechanisms occurring during high-pressure sand compaction. Particle movement, grain failure, friction between grains and the surface of the compression cell and intergranular friction are studied. Acoustic emission data recorded during these simplified tests are used to characterize each phenomenon. Wavelet transform analyses allow the identification of useful features, making possible frequency discrimination among sliding, rolling, friction and grain fragmentation processes. For instance, we observe that at low stress, grain flow is characterized by the lowest centroid and peak frequencies, while at greater stresses, intergranular friction and grain fragmentation have the higher values. In the tests performed, the stress–strain evolution and final condition of the tested sand are broadly consistent, irrespective of the condition employed: continuous, stepwise or even variable loading rate or temperature. However, Acoustic emission data manifest much more complex behaviour (including thermal, load-rate dependency and delayed fragmentation phenomena) than that suggested by stress–strain relationships. At low stress levels, grain flow (sliding/rolling) is a relevant strain-accommodation mechanism, but so is crushing due to the effect of concentrated forces at the grain contact level. At high stresses, when crushing is generalized, intergranular friction is also a relevant phenomenon due to the increase in the coordination number produced by previous fragmentation.     

Aspects of asperity-surface interaction and surface damage of rocks during experimental frictional sliding

Summary Mechanisms for the dissipation of energy during the frictional sliding of rocks includes brittle fracture, plastic deformation, frictional heating, and elastic distortion. The first three energy sinks are manifested by surface damage during frictional sliding. Normal load, temperature, and the velocity of the sliding surfaces as well as surface roughness and hardness all influence the nature of surface damage which includes the generation of structures such as wear grooves, gouge, and welded particles.Lamont-Doherty Geological Observatory Contribution No. 2620.     

Constitutive behavior and stability of frictional sliding of granite

An understanding of the frictional sliding on faults that can lead to earthquakes requires a knowledge of both constitutive behavior of the sliding surfaces and its mechanical interaction with the loading system. We have determined the constitutive parameters for frictional sliding of initially bare surfaces of Westerly granite, using a recently developed high pressure rotary shear apparatus that allows long distances of sliding and therefore a greater assurance of attaining steady state behavior. From experiments conducted at room temperature and normal stresses of 27–84 MPa several important results have been found. (1) A gouge layer 100 to 200 m thick was developed from the initially bare rock surfaces after 18 to 70 mm of sliding. (2) The steady state frictional resistance, attained after about 10 mm of sliding, is proportional to the negative of the logarithm of the sliding velocity. (3) Abrup changes in the velocity of sliding result in initial changes in the frictional resistance, which have the same sign as the velocity change, and are followed by a gradual decay to a new steady state value over a characteristic distance of sliding. This velocity weakening behavior is essentially identical with that found by several previous workers on the same material at lower normal stress. (4) Our results are well described by a two state variable constitutive law. The values of the constitutive parameters are quite similar to those found previously at low normal stress, but the characteristic distance is about an order of magnitude smaller than that found at 10 MPa normal stress with thicker layers of coarser gouge. (5) We have approximated our results with a one state variable constitutive law and compared the results with the predictions of existing nonlinear stability analysis; in addition, we have extended the stability analysis to systems possessing two state variables. With such formulations good agreement is found between the experimentally observed and theoretically predicted transitions between stable and unstable sliding. These results allow a better understanding of the instabilities that lead to earthquakes.     

Hysteretic models for sliding bearings with varying frictional force

The friction pendulum system is a sliding seismic isolator with self‐centering capabilities. Under severe earthquakes, the movement may be excessive enough to cause the pendulum to hit the side rim of the isolator, which is provided to restrain the sliding. The biaxial behavior of a single friction pendulum, in which the slider contacts the restrainer, is developed using a smooth hysteretic model with nonlinear kinematic hardening. This model is extended to simulate the biaxial response of double and triple friction pendulums with multiple sliding surfaces. The model of a triple friction pendulum is based on the interaction between four sliding interfaces, which in turn is dependent upon the force and displacement conditions prevailing at these interfaces. Each of these surfaces are modeled as nonlinear biaxial springs suitable for a single friction pendulum, using the yield surface, based on the principles of the classical theory of plasticity, and amended for varying frictional yield force, due to variation in vertical load and/or velocity‐dependent friction coefficient. The participation of the nonlinear springs is governed by stick‐slip conditions, dictated by equilibrium and kinematics. The model can simulate the overall force‐deformation behavior, track the displacements in individual sliding surfaces, and account for the ultimate condition when the sliders are in contact with their restrainers. The results of this model are verified by comparison to theoretical calculations and to experiments. The model has been implemented in programs IDARC2D and 3D‐BASIS, and the analytical results are compared with shake table experimental results. Copyright © 2013 John Wiley & Sons, Ltd.     

The effect of normal stress on the real area of contact during frictional sliding in rocks

The real area of contact during frictional sliding has been determined as a function of changing normal stress in triaxial experiments through the use of thermodyes. Utilizing the technique, described by Teufel and Logan in 1978, with saw-cut surfaces inclined 35° to the load axis, determinations were made for monolithologic sliding of Tennessee sandstone and Indiana limestone and dilithologic sliding of the same rocks. Confining pressures to 200 MPa were investigated at a constant shortening rate of 10^–2 mm/sec and at room temperature. Direct measurements were made of single-asperity areas and the asperity density. The product of these measurements gives the percent area of real contact across the sliding surface. Single-asperity area and density are found to remain relatively constant during the displacement. Single-asperity areas are in the ranges of 0.4 to 6×10^–2 mm² for sandstone, 0.8 to 2×10^–2 mm² for limestone, and 0.2 to 24×10^–2 mm² for sandstone sliding against limestone. These values are smaller than the grain size of either rock. The values increase with increasing normal stress for both monolithologic and dilithologic sliding. In sandstone the asperity density increases from about 0.8 to 2.75 contacts per square millimeter in a logarithmic fashion. Monolithologic limestone has values of about 0.9 contacts per square millimeter and does not show significant change with increasing normal stress. The percent area of real contact increases in all cases, with average maximum values of 16% of the apparent area at a normal stress of 374 MPa in sandstone, 18% at 25 MPa in limestone, and 22% at 123 MPa in the dilithologic specimens. The normal stress recalculated for the real area of contact approaches the unconfined compressive strength for sandstone and limestone.     

Effects of temperature and sliding rate on frictional strength of granite

Layers of artificial granite gouge have been deformed on saw-cut granite surfaces inclined 30° to the sample axes. Samples were deformed at a constant confining pressure of 250 MPa and temperatures of 22 to 845°C. The velocity dependence of the steady-state coefficient of friction (^ss) was determined by comparing sliding strengths at different sliding rates. The results of these measurements are consistent with those reported bySolberg andByerlee (1984) at room temperature andStesky (1975) between 300 and 400°C. Stesky found that the slip-rate dependence of (^ss) increased above 400°C. In the present study, however, the velocity dependence of (^ss) was nearly independent of temperature.     

First passage of a sliding rigid structure on a frictional foundation

The first passage problem for a sliding rigid block on a frictional foundation, subjected to Gaussian white noise through the foundation, is studied. A well-posed boundary value problem is formulated from Markov process theory and solved for the ordinary moments of time to first passage by the finite element method. A range of parameters is studied representing a simple seismic base isolation system. Results of Monte Carlo simulation are given for comparison.     

Effect of displacement rate on the real area of contact and temperatures generated during frictional sliding of Tennessee sandstone

Summary The real area of contact has been determined, and measurements of the maximum and average surface temperatures generated during frictional sliding along precut surfaces in Tennessee sand-stone have been made, through the use of thermodyes. Triaxial tests have been made at 50 MPa confining pressure and constant displacement rates of 10^–2 to 10^–6 cm/sec, and displacements up to 0.4 om. At 0.2 cm of stable sliding, the maximum temperature decreases with decreasing nominal displacement rate from between 1150° to 1175°C at 10^–2 cm/sec to between 75° to 115°C at 10^–3 cm/sec. The average temperature of the surface is between 75 and 115°C at 10^–2 cm/sec, but shows no rise from room temperature at 10^–3 cm/sec. At 0.4 cm displacement, and in the stick-slip mode, as the nominal displacement rate decreases from 10^–3 to 10^–6 cm/sec, the maximum temperature decreases from between 1120° to 1150°C to between 1040° to 1065°C. The average surface temperature is 115° to 135°C at displacement rates from 2.6×10^–3 to 10^–4 cm/sec.With a decrease in the displacement rate from 10^–2 to 10^–6 cm/sec, the real area of contact increases from about 5 to 14 percent of the apparent area; the avergge area of asperity contact increases from 2.5 to 7.5×10^–4 cm². Although fracture is the dominate mechanism during stick-up thermal softening and creep may also contribute to the unstable sliding process.     

热水条件下花岗质糜棱岩的摩擦滑动实验研究

为了探讨大陆地壳断层深部的力学性质,我们选择了采自红河断裂带的糜棱岩作为实验样品,进行热水条件下的高温高压摩擦滑动实验.实验在一个以气体为介质的高温高压三轴实验系统中进行.实验条件是：有效正应力为200 MPa;孔隙水压为30 MPa（在400 ℃到600 ℃之间为超临界水条件）;温度为100 ℃到600 ℃;轴向加载的速率范围从0.04 μm/s到0.2 μm/s再到1 μm/s.实验结果表明：（1）当温度小于300 ℃时,糜棱岩的摩擦强度随着温度的上升而增大;当温度大于300 ℃时,糜棱岩的摩擦强度随着温度的上升而减小.这种趋势和以往花岗岩的摩擦滑动数据基本一致;（2）糜棱岩在200 ℃和400 ℃时表现为速度弱化,其余温度下为速度强化;（3）糜棱岩与已有花岗岩的摩擦滑动数据并不完全一致;（4）花岗质糜棱岩速度弱化向速度强化转变的温度在430 ℃附近,以此我们可以推测：在变形机制为摩擦滑动的深部条件下,地震成核的深度范围可以比以往的估计更深.     

考虑支座摩擦滑移及结构碰撞的非规则人字形桥梁地震响应分析

针对非规则人字形桥梁在地震作用下灾变严重的问题,以一座非规则人字形桥梁为研究对象,建立其空间分析模型,研究综合考虑支座摩擦滑移、结构碰撞对非规则人字形桥梁地震响应的影响。结果表明:邻梁间的碰撞作用可使得桥梁墩顶位移及内力相比不考虑时有所减小,但同时也使梁体产生了较大的加速度脉冲效应;当考虑支座摩擦滑移和结构碰撞时,固定墩墩顶位移和邻梁相对位移峰值有一定程度增大,然而对梁体加速度脉冲效应结果影响并无统一规律;纵向地震波作用下,非规则人字形桥梁不仅存在顺桥向的碰撞,横桥向的碰撞响应也不容忽视。非规则人字形桥梁进行抗震设计计算时应选取符合实际情况的计算模型,考虑支座摩擦滑移及结构间的碰撞。     

Dilatancy and fracture induced velocity changes in rock and their relation to frictional sliding

Summary Laboratory room temperature triaxial friction tests on sawcut granite and serpentinite specimens suggest that stick-slip at high confining pressures is preceded by dilatancy in the intact rock adjacent to the shear surface. By using a fast-reacting servo-loading system in combination with a high resolution digital computer recording system it is possible to obtain a more realistic picture of the stick-slip mechanisms and the stress drop associated with unstable slip. Fracturing in granite under biaxial loading leads to a significant anisotropy in dilation andP-wave velocity of the rock. Velocity decreases remarkably in the directions of minor principal stresses with no indication for velocity recovery before macroscopic shear fracture development.The results suggest that dilatancy and velocity anomalies may precede crustal earthquakes under certain tectonic conditions.

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Zusammenfassung Triaxiale Scherversuche an polierten Scherflächen in Granit- und Serpentinitproben (Normaltemperatur) lassen schließen, daß instabile Gleitvorgänge auf den Scherflächen bei sehr hohen Manteldrücken mit vorhergehenden Auflockerungen (Dialatanz) des intakten Gesteins in der Umgebung der Scherfläche verbunden sind. Durch die Verwendung eines reaktions-schnellen Servobelastungssystems in Verbindung mit einem hoch-auflösenden digitalen Aufzeichnungssystem konnte erstmals ein Einblick in den tatsächlichen Ablauf des instabilen Gleitprozesses gewonnen werden. Der Bruch in Granit bei biaxialer Belastung führt zu einer signifikanten Anisotropie der Auflockerung des Gesteinsgefüges und damit der Geschwindigkeit seismischer Wellen. Die Geschwindigkeit derP-Wellen nimmt in Richtung der beiden kleineren Hauptspannungen mit fortschreitender Deformation kontinuferlich ohne Anzeichen eines Geschwindigkeitsanstiegs vor der Entwicklung des makroskopischen Scherbruchs ab.Die Ergebnisse lassen den Schluß zu, daß Dilatanz und damit verbundene Geschwindigkeitsanomalien Erdbeben in der Kruste bei bestimmten tektonischen Bedingungen vorangehen können.

     

Acoustic emission phenomena due to plasticity of rocks

Acoustic emission patterns arising at the stage of plastic deformation (creep and relaxation) of plastic and brittle rocks are discussed. It is suggested that these patterns are related to the spatial localization of plastic deformation and strain hardening of rocks under loads exceeding the yield strength.     

岩盐断层带黏滑及稳滑过程中声发射活动特征的初步分析

本文利用双轴摩擦实验对含水条件下岩盐断层带摩擦滑动性状进行了实验研究, 观测和分析了摩擦滑动过程中的声发射活动, 并利用扫描电镜分析了断层带的微观变形结构.结果表明, 含水岩盐断层带在伴随黏滑的速度弱化域和伴随稳定滑动的速度强化域, 摩擦过程中均产生了大量声发射事件; 黏滑过程与稳滑过程中的小声发射事件存在共同之处, 即两者均表现为能级低; 但黏滑过程中的小声发射事件的优势频率既有低频(10 kHz左右)和中频(100 kHz左右), 也有高频(370 kHz左右), 而在稳定滑动过程中, 小声发射事件的优势频率仅有低频和中频, 缺少高频事件.这种差异与两者变形主导机制的不同密切相关.在断层黏滑循环中, 接近摩擦峰值时声发射发生率明显增加, 但高频事件减少、中频和低频事件增加; 进入亚失稳阶段后, 声发射只有低频和中频信号, 几乎不再出现高频信号.这种差异与断层带变形方式的变化密切相关.

     

The effects of sliding velocity on the frictional and physical properties of heated fault gouge

The frictional properties of a crushed granite gouge and of gouges rich in montmorillonite, illite, and serpentine minerals have been investigated at temperatures as high as 600°C, confining pressures as high as 2.5 kbar, a pore pressure of 30 bar, and sliding velocities of 4.8 and 4.8×10^–2 m/sec. The gouges showed nearly identical strength behaviors at the two sliding velocities; all four gouges, however, showed a greater tendency to stick-slip movement and somewhat higher stress drops in the experiments at 4.8×10^–2 m/sec. Varying the sliding velocity also had an effect on the mineral assemblages and deformation textures developed in the heated gouges. The principal mineralogical difference was that at 400°C and 1 kbar confining pressure a serpentine breakdown reaction occurred in the experiments at 4.8×10^–2 m/sec but not in those at 4.8 m/sec. The textures developed in the gouge layers were in part functions of the gouge type and the temperature, but changes in the sliding velocity affected, among other features, the degree of mineral deformation and the orientation of some fractures.     

摩擦-碟簧三维复合隔震支座的性能试验研究

对适用于大跨结构的摩擦-碟簧三维复合隔震支座进行了振动台试验研究,该支座在水平向和竖向分别采用摩擦滑移装置和碟型弹簧隔震。在水平向,试验重点测试了简谐激励和地震动激励下支座的滞回性能,考察了竖向荷载变化及地震动强度对隔震性能的影响,以期为建立水平隔震理论模型提供依据;在竖向,对碟型弹簧的等效阻尼比和等效刚度进行了测试,研究了竖向预压荷载和动力荷载对竖向滞回性能的影响。结果表明,复合隔震支座在水平向和竖向均具有较好的滞回性能,竖向等效阻尼比在0.10～0.15间,且随着预压荷载的增加而增大。