断层滑动速率变化对滑动稳定性的影响

在与主压应力方向斜交的断层上,正应力与剪应力之间存在线性相关关系,以此为基础导出了小扰动条件下决定稳定性的临界刚度与滑动速率的关系。由于这一关系具有临界刚度随滑动速率增加而减小的特点,因此速率增加可能导致周期性粘滑向稳定滑动转化,而速率减小可能使本来稳定的滑动转化为周期性粘滑过程。在这种斜交断层中,速率增加虽然可能抑制周期性粘滑,但是稳滑时超过一定限度的速率增加会导致一次性不稳定滑动。三轴摩擦实验提供了关于粘滑与稳滑可相互转化的支持证据     

Simulation of Frictional Strength and Steady Relaxation Using the Rate and State Dependent Friction Model

In this paper, frictional strength of hard solids, such as rock–rock sliding surfaces, is studied as a function of waiting time and shearing velocity. A one dimensional spring–mass sliding system is numerically simulated under the quasistatic condition using the rate and state dependent friction model. It is established that frictional strength varies linearly with the logarithm of waiting time (also known as time of stationary contact or relaxation time, etc.) as well as logarithm of shearing velocity. Analytical expression developed for frictional strength is found to be valid only in the case of high stiffness of the connecting spring. In the steady relaxation simulation, a steadily sliding mass is suddenly brought to zero velocity and relaxation of the interfacial stress and corresponding velocity at the sliding interface is studied as a function of relaxation time in the velocity strengthening regime of friction. A mathematical relation is derived between state variable and waiting time using the concept of steady relaxation. The relaxation model is also compared with the experimental data from the literature. Finally, the present study enables one to unify the slide–hold–slide friction experiments.     

Time-dependent friction and the mechanics of stick-slip

Time-dependent increase of static friction is characteristic of rock friction undera variety of experimental circumstances. Data presented here show an analogous velocity-dependent effect. A theor of friction is proposed that establishes a common basis for static and sliding friction. Creep at points of contact causes increases in friction that are proportional to the logarithm of the time that the population of points of contact exist. For static friction that time is the time of stationary contact. For sliding friction the time of contact is determined by the critical displacement required to change the population of contacts and the slip velocity. An analysis of a one-dimensional spring and slider system shows that experimental observations establishing the transition from stable sliding to stick-slip to be a function of normal stress, stiffness and surface finish are a consequence of time-dependent friction.     

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.     

两种摩擦本构关系的对比研究

目前有两种最常用的岩石摩擦本构关系,其主要区别在于是否与静接触时间有关。对这两种本构关系的基本性质进行了对比研究,得出如下结论：（１）在匀速滑动的稳态附近,两种本构关系趋向一致;（２）在正应力恒定条件下,两种本构关系的主要差异在于克服摩擦力所需能量的大小。与静接触时间相关的本构关系在粘滑中需消耗较大的能量来克服摩擦阻力,在粘滑的减速段,这种本构关系可达到的最低速率比另一种本构关系低１０个数量级;（３）在正应力变化条件下,与静接触时间相关的本构关系基本继承了正应力恒定条件下的行为特征,而另一种本构关系在剪应力－速度相平面上却出现了一个长尾巴,使最低滑动速率降到比正应力恒定时的值低１０多个数量级     

Direct observation of frictional contacts: New insights for state-dependent properties

Rocks and many other materials display a rather complicated, but characteristic, dependence of friction on sliding history. These effects are well-described by empirical rate- and state-dependent constitutive formulations which have been utilized for analysis of fault slip and earthquake processes. We present a procedure for direct quantitative microscopic observation of frictional contacts during slip. The observations reveal that frictional state dependence represents an increase of contact area with contact age. Transient changes of sliding resistance correlate with changes in contact area and arise from shifts of contact population age. Displacement-dependent replacement of contact populations is shown to cause the diagnostic evolution of friction over a characteristic sliding distance that occurs whenever slip begins or sliding conditions change.     

基于速度-状态摩擦本构定律的三维DDA方法

原有三维非连续变形分析(DDA)方法采用常摩擦系数的Mohr-Coulomb定律作为切向破坏准则,然而当描述更大尺度构造块体的运动与变形时,常摩擦系数不再适用.速度-状态摩擦本构定律能够定量描述地震周期各阶段断层面剪应力变化,解释发震断层行为.本文将速度-状态摩擦定律与三维DDA方法相结合,首先推导了计算摩擦系数的实用公式,随后通过滑动-保持-滑动实验与速度步进实验算例对改进的三维DDA方法进行了验证.结果表明,应用速度-状态摩擦本构定律的三维DDA方法能够比较准确地模拟静摩擦的时间依赖性与动摩擦的速度依赖性,解决了将三维DDA方法在地学中应用的基本问题.     

Micromechanics of the velocity and normal stress dependence of rock friction

Among the second-order effects on friction the most important are those of variable normal stress and of slip velocity. Velocity weakening, which is usually considered the source of the stick-slip instability in rock friction, has been observed in velocity stepping experiments with Westerly granite. The friction change, , was –0.01 to –0.008 for a tenfold velocity increase. Using normal closure measurements, we observed dilation upon each increase in sliding rate. We also observed, for the first time, time-dependent closure between surfaces during static loading. The dilation that occurred during the velocity stepping experiment was found to be that expected from the static time-dependent closure phenomenon. This change in closure was used to predict friction change with an elastic contact model. The calculated friction change which results from a change in contact area and asperity interlocking, is in good agreement with the observed velocity dependence of steady-state friction. Variable normal stress during sliding has two effects, first in creating new partial slip contacts and locking some existing fully sliding contacts and second in increasing interlocking, for instance when normal load is suddenly increased. As a result, a transient change in friction occurs upon a sudden change in normal load.     

Effect of varying normal stress on stability and dynamic motion of a spring-slider system with rate- and state-dependent friction

Incorporating rate and state friction laws, stability of linearly stable (i.e., with stiffness greater than the critical value) spring-slider systems subjected to triggering perturbations was analyzed under variable normal stress condition, and comparison was made between our results and that of fixed normal stress cases revealed in previous studies. For systems associated with the slip law, the critical magnitude of rate steps for triggering unstable slips are found to have a similar pattern to the fixed normal stress case, and the critical velocity steps scale with a/(b - a) when k = k_cr for both cases. The rate-step boundaries for the variable normal stress cases are revealed to be lower than the fixed normal stress case by 7 %–16 % for a relatively large α = 0.56 with (b - a)/a ranging from 0.25 to 1, indicating easier triggering under the variable normal stress condition with rate steps. The difference between fixed and variable normal stress cases decreases when the α value is smaller. In the same slip-law-type systems, critical displacements to trigger instability are revealed to be little affected by the variable normal stress condition. When k ≥ k_cr(V_*), a spring-slider system with the slowness law is much more stable than with the slip law, suggesting that the slowness law fits experimental data better when a single state variable is adopted. In stick-slip motions, the variable normal stress case has larger stress drops than the constant normal stress case. The variable normal stress has little effect on the range of slip velocity in systems associated with the slowness law, whereas systems associated with the slip law have a slowest slip velocity immensely smaller than the fixed normal stress case, by ~10 orders of magnitude.     

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 the Transition to Steady Sliding in a 2D Granular Medium and a Fixed Particle Lattice

We report an experimental study of the stick–slip to steady sliding behavior of a solid object pulled, via a spring, across 2D granular substrates of photoelastic disks that are either fixed in a solid lattice (granular solid) or unconstrained, forming a granular bed. We observe a progression of friction regimes with increasing sliding speed, including single-slip, double-slip, and mixed stick–slip regimes, steady sliding, and inertial oscillations. For the case of the granular bed, we report a detailed analysis of frictional behavior for the low speed stick–slip regime, including spring and elastic energy dependencies during the stick and slip portions of the motion. For the case of the granular solid, we explore friction in the presence and absence of externally applied vibrations, and compare it with sliding on a granular bed, which is intrinsically disordered. We observe that external vibration reduces transition values for both the single-slip to double-slip transition and the stick–slip to steady sliding transition. Moreover, we observe that the effect of packing disorder on granular friction seems similar to the effect of vibration-induced disorder, a result that, to our knowledge, has not been reported previously in the experimental literature.     

岩石高速摩擦实验与地震物理过程

简述了最近20年来国内外岩石高速摩擦实验研究领域的进展和动态:岩石高速摩擦实验技术的发展实现了对高滑动速率、大位移的地震过程的实验模拟;其结果揭示了岩石和断层泥在地震滑动速率下的力学性状,深化了对断层滑动弱化机制、临界滑动距离、以及地震发生过程的认识和理解;实验在假玄武玻璃成因方面取得了重要进展,并提出了断层发生地震滑动可能留下的其它地质证据,可望为研究断层滑动性状与地震物理过程提供新的思路和信息.岩石高速摩擦实验今后的发展方向主要包括:发展具有加温系统和孔隙压系统的岩石高速摩擦实验装置,研究水热作用下岩石和断层泥的高速摩擦性状;室内实验和地震资料分析相结合研究断层滑动和地震机制;室内实验和野外地质调查相结合探索断层发生地震错动的地质证据等等.     

水热条件下富层状硅酸盐矿物糜棱岩的摩擦特性实验研究

为探索断层岩石摩擦特性对于断层力学性质的影响,我们采集了龙门山汶茂断裂韧性剪切带中的富含层状硅酸盐矿物的糜棱岩样品进行了水热条件下摩擦滑动实验研究.实验在三轴压机之上完成,实验温度为100~600℃,有效正压力100MPa,孔隙水压分别为30MPa和130MPa.为获得摩擦滑动的稳定性参数(a-b),剪切滑移速率在1.22μm·s-1,0.244μm·s-1和0.0488μm·s-1之间切换.实验发现在200~500℃的温度范围内,摩擦系数随着温度的增加而显著增大(约0.56~0.72).在200~300℃范围内,随温度的升高糜棱岩的摩擦滑动表现出由稳定的速度强化向不稳定速度弱化转变的趋势.在有效正压力不变的情况下,孔隙水压的增大会促进糜棱岩的摩擦滑动在500~600℃温度范围内由不稳定的速度弱化向稳定的速度强化的转变.实验给出的断层在原地深度处的脆性和塑性变形机制的转变,有助于理解断层深部的地震成核机制以及成核的温压条件.     

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.     

An example of slip instability resulting from displacement-varying strength

A rock cylinder, containing a clay-filled sawcut making an angle of 30° to the sample axis, was deformed at constant confining and pore pressures and constant remote shortening rate. The sawcut surfaces contained a series of regularly spaced ridges and grooves oriented perpendicular to the direction of shear. The interaction of these grooved surfaces resulted in a sliding strength which varied periodically with displacement. By varying the effective machine stiffness through the use of an electronic feedback circuit, a range of stable and unstable slip behavior was achieved. In this way, we examined fault slip behavior which was dominated by displacement-dependent strength.     

FRICTIONAL PROPERTIES OF A NATURAL FAULT GOUGE FROM DRILLED CORES IN THE LONGMENSHAN FAULT ZONE CUTTING GRANITIC ROCK

In this paper, we report friction experiments performed on natural fault gouge samples embedded in granitic rock from drilled core by a project entitled "the Longmenshan Fault Shallow Drilling(LMFD)". Compared with other natural fault gouge, this yellow-greenish gouge(YGG)is dominantly chlorite-rich. The maximum content of chlorite reaches 47%in the YGG. To understand the frictional properties of the YGG sample, experiments were performed at constant confining pressure of 130MPa, with constant pore pressure of 50MPa and at different temperatures from 25℃ to 150℃. The experiments aim to address the frictional behavior of the YGG under shallow, upper crustal pressure, and temperature conditions. Compared with previous studies of natural gouge, our results show that the YGG is stronger and shows a steady state friction coefficient of 0.47~0.51. Comparison with previous studies of natural gouge with similar content of clay minerals indicates a sequence of strengths of different clay minerals:chlorite > illite > smectite. At temperatures up to 150℃ hence depths up to~8km in the Longmenshan region, the YGG shows stable velocity-strengthening behavior at shallow crustal conditions. Combined with the fact of strong direct velocity effect, i.e., (a-b)/a>0.5, faults cutting the present clastic lithology up to~8km depth in the Longmenshan fault zone(LFZ)are likely to offer stable sliding resistance, damping co-seismic rupture propagating from below at not-too-high slip rates. However, as the fault gouge generally has low permeability, co-seismic weakening through thermal pressurization may occur at high slip rates(>0.05m/s), leading to additional hazards.     

Study of fault slip modes

We present the data of the laboratory experiments on studying the regularities of gradual transition from the stick-slip behavior to aseismic creeping on the interblock boundary. The experiments show that small variations in the material composition in the principal slip zones of the faults may cause a significant change in the fraction of seismic energy radiated during the dynamic unloading of the adjacent segment of the rock mass. The experiments simulate interblock sliding regimes with the values of the scaled kinetic energy differing by a few orders of magnitude and relatively small distinctions in the strength of the contacts and in the amplitude of the released shear stresses. The results of the experiments show that the slip mode and the fraction of the deformation energy that goes into the seismic radiation are determined by the ratio of two parameters—the stiffness of the fault and the stiffness of the enclosing rock mass. An important implication of the study for solving the engineering tasks is that for bringing a stressed segment of a fault or a crack into a slip mode with low-intensity radiation of seismic energy, the anthropogenic impact should be aimed at diminishing the stiffness of the fault zone rather than at releasing the excessive stresses.     

Frictional Properties of a Low-Angle Normal Fault Under In Situ Conditions: Thermally-Activated Velocity Weakening

The Zuccale fault is a regional, low-angle, normal fault, exposed on the Isle of Elba in central Italy that accommodated a total shear displacement of 6–8 km. The fault zone structure and fault rocks formed at <8 km crustal depth. The present-day fault structure is the final product of several deformation processes superposed during the fault history. In this study, we report results from a series of rotary shear experiments performed on 1-mm thick powdered gouges made from several fault rock types obtained from the Zuccale fault. The tests were done under conditions ranging from room temperature to in situ conditions (i.e., at temperatures up to 300 °C, applied normal stresses up to 150 MPa, and fluid-saturated.) The ratio of fluid pressure to normal stress was held constant at either λ = 0.4 or λ = 0.8 to simulate an overpressurized fault. The samples were sheared at a constant sliding velocity of 10 μm/s for at least 5 mm, after which a velocity-stepping sequence from 1 to 300 μm/s was started to determine the velocity dependence of friction. This can be represented by the rate-and-state parameter (a–b), which was determined by an inversion of the data to the rate-and-state equations. Friction of the various fault rocks varies between 0.3 and 0.8, similar to values obtained in previous studies, and decreases with increasing phyllosilicate content. Friction decreases mildly with temperature, whereas normal stress and fluid pressure do not affect friction values systematically. All samples exhibited velocity strengthening, conditionally stable behavior under room temperature conditions and (a–b) increased with increasing sliding velocity. In contrast, velocity weakening, accompanied by stick–slips, was observed for the strongest samples at 300 °C and sliding velocities below 10 μm/s. An increase in fluid pressure under these conditions led to a further reduction in (a–b) for all samples, so that they exhibited unstable, stick–slip behavior at low sliding velocity. The results suggest that phyllosilicate-bearing fault rocks can deform by stable, aseismic creep at low, resolved shear stress and low shear rate conditions. An increase in fluid pressure or loading of stronger portions could lead to a runaway instability. The runaway instability might be limited in size because of (1) the fault heterogeneity, (2) the observed strengthening at higher sliding velocities, and (3) a co-seismic drop in pore-fluid pressure.