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.     

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.     

Finite Element Analysis of Fault Bend Influence on Stick-Slip Instability along an Intra-Plate Fault

— Earthquakes have been recognized as resulting from stick-slip frictional instabilities along the faults between deformable rocks. A three-dimensional finite-element code for modeling the nonlinear frictional contact behaviors between deformable bodies with the node-to-point contact element strategy has been developed and applied here to investigate the fault geometry influence on the nucleation and development process of the stick-slip instability along an intra-plate fault through a typical fault bend model, which has a pre-cut fault that is artificially bent by an angle of 5.6° at the fault center. The numerical results demonstrate that the geometry of the fault significantly affects nucleation, termination and restart of the stick-slip instability along the intra-plate fault, and all these instability phenomena can be well simulated using the current finite-element algorithm.     

Some properties of unstable slip on rough surfaces

In this paper we report results obtained from various friction experiments under direct and oblique shear loading conditions. We used four rock types of varying brittleness (quartzite, anhydrite, limestone, pyrophyllite) with different surface roughness. The observations concentrate on the time span several milliseconds before dynamic failure occurs. During this period a premonitory, unstable phase of slip (slip 2) occurs. This differs importantly from a premonitory, stable process (slip 1) with durations of hundreds of seconds. On smooth surfaces slip 2 is usually observed with ductile rocks and less reliably with brittle rocks. Slip 2 is mostly accompanied by acoustic emissions, which increase in rate of occurrence and in magnitude until the stick-slip event. Foreshocks are observed during approximately 50% of the slip 2 events on rough surfaces. Foreshocks far exceed the acoustic noise level, which is also prevalent before stick-slip events on rough surfaces. In the direct shear experiment, where two faults are being loaded simultaneously, in about 20% of the cases precursory slip 2 was observed on the opposite side on which the final stick-slip event occurred.     

Sedimentary Basins and the Blockage of Lg Wave Propagation in the Continents

v--vThe phenomenon of "Lg blockage," where Lg is strongly attenuated by crustal heterogeneities, poses a serious problem to CTBT monitoring because Lg is an important seismic phase for discrimination. This paper examines blockage in three continental regions where the Lg blockages may be caused by large, enclosed sedimentary basins along the propagation path. The Barents Sea Basin blocks Lg propagation across the Barents Sea from the Russian nuclear test sites at Novaya Zemlya to Scandinavian stations. Also, "early Lg" waves are observed in Sn codas on NORSAR, NORESS, and ARCESS recordings of Novaya Zemlya explosions where direct Lg is blocked. Early Lg waves may have resulted from Sn-to-Lg mode conversion at the contact between the Barents Basin and the Kola Peninsula. The Northern and Southern Caspian Sea Basins also block Lg waves from PNEs and earthquakes, perhaps due to thick, low-velocity, low-Q sediments replacing the granitic layer rocks in the crust. Lg blockage has also been observed in the Western Mediterranean/Levantine Basin due to low-Q sediments and crustal thinning. A "basin capture" model is proposed to explain Lg blockage in sedimentary basins. In this model, shear waves that reverberate in the crust and constitute the Lg wave train are captured, delayed, and attenuated by thick, low-velocity sediments that replace the "granitic" layer rocks of the upper crust along part of the propagation path. Sn waves, which propagate below the basin, would not be blocked and in fact, the blocked Lg waves may be diverted downward into Sn waves by the low velocity sediments in the basin.     

循环荷载下饱和岩石的滞后和衰减

通过对饱和砂岩和大理岩的循环荷载实验,分析了饱和岩石在循环荷载下的应力-应变滞后回线、瞬时杨氏模量、泊松比的“X”形变化曲线,以及杨氏模量随应变振幅的增加而减少等滞后现象,并分析了施加外力的应变振幅对衰减的影响,认为岩石在循环荷载作用下的衰减与应变振幅成正比,提出的衰减b值反映了岩石在循环荷载作用下衰减的程度. 岩石的衰减和滞后存在密切的关系,通过饱和岩石的宏观行为,探讨了饱和岩石在循环荷载下的滞后和衰减现象的微观机理,认为孔隙流体流动在岩石的滞后和衰减中起着重要作用,岩石内部的颗粒接触粘合和黏滑摩擦可能是孔隙岩石在循环荷载作用下产生滞后和衰减的原因.     

Microfracture processes in the breakdown zone during dynamic shear rupture inferred from laboratory observation of near-fault high-frequency strong motion

High-frequency velocities are measured during stick-slip motion in the immediate vicinity of a fault in a granite sample to reveal the microscopic process taking place in the breakdown zone defined in the slip-weakening model. It is found that 1) the onset time of the observed strong motion approximately coincides with the local rupture onset time, 2) the observed near-fault high-frequency strong-motion duration is approximately proportional to the local breakdown time, and 3) the power spectra of strong motions exhibit significant amplitudes at frequencies above the value off _max, wheref _max is a cut-off frequency relevant to rupturing the breakdown zone. These observations suggest that the high-frequency motion would be due to the incoherent brittle microfracture whose characteristic scale is much shorter than the breakdown zone size. We present a stochastic fault model to synthesize the near-fault high-frequency velocity waveforms. In the model, a number of small circular subfaults are distributed randomly on the fault and the rupture onset time of an individual subfault is assumed to be random. The main features of the observed velocity waveforms are well explained by this numerical modeling. It is concluded that approximately half of the total energy of high-frequency elastic waves observed at a point is radiated from the propagating breakdown zone. We emphasize the importance of the observation of near-fault high-frequency strong motions for large shallow earthquakes.     

Cohesive zone length of metagabbro at supershear rupture velocity

We investigated the shear strain field ahead of a supershear rupture. The strain array data along the sliding fault surfaces were obtained during the large-scale biaxial friction experiments at the National Research Institute for Earth Science and Disaster Resilience. These friction experiments were done using a pair of meter-scale metagabbro rock specimens whose simulated fault area was 1.5 m?×?0.1 m. A 2.6-MPa normal stress was applied with loading velocity of 0.1 mm/s. Near-fault strain was measured by 32 two-component semiconductor strain gauges installed at an interval of 50 mm and 10 mm off the fault and recorded at an interval of 1 MHz. Many stick-slip events were observed in the experiments. We chose ten unilateral rupture events that propagated with supershear rupture velocity without preceding foreshocks. Focusing on the rupture front, stress concentration was observed and sharp stress drop occurred immediately inside the ruptured area. The temporal variation of strain array data is converted to the spatial variation of strain assuming a constant rupture velocity. We picked up the peak strain and zero-crossing strain locations to measure the cohesive zone length. By compiling the stick-slip event data, the cohesive zone length is about 50 mm although it scattered among the events. We could not see any systematic variation at the location but some dependence on the rupture velocity. The cohesive zone length decreases as the rupture velocity increases, especially larger than \( \sqrt{2} \) times the shear wave velocity. This feature is consistent with the theoretical prediction.     

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.     

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.     

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.     

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.     

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.     

The phase velocities of Rayleigh waves and the lateral variation of lithospheric structure in Tibetan Plateau

According to a Sino-U. S. joint project, eleven broadband digital PASSCAL seismometers had been deployed inside the Tibetan Plateau, of which 7 stations were on the profile from Lhasa to Golmud and other 4 stations situated at Maxin, Yushu, Xigatze and Linzhi. Dispersions and phase velocities of the Rayleigh surface waves (10s–120s) were obtained on five paths distributed in the different blocks of Tibetan Plateau. Inversions of the S-wave velocity structures in Songpan-Ganzi block, Qiang-Tang block, Lhasa block and the faulted rift zone were obtained from the dispersion data. The results show that significant lateral variation of the S-wave velocity structures among the different blocks exists. The path from Wenquan to Xigatze (abbreviated as Wndo-Xiga) passes through the rift-zone of Yadong-Anduo. The phase velocities of Rayleigh waves from 10s to 100s on this path are significantly higher than that on other paths. The calculated mean crustal velocity on this path is 3.8 km/s, much greater than that on other paths, where mean crustal velocities of 3.4–3.5 km/s are usually observed. Low velocity zones with different thicknesses and velocities are observed in the middle-lower crust for different paths. Songpan-Ganzi block, located in the northern part of Tibetan Plateau is characterized by a thinner crust of 65 km thick and a prominent low velocity zone in the upper mantle. The low velocity zone with a velocity of 4.2 km/s is located at a depth form 115 km to 175 km. While in other blocks, no low velocity zone in the upper mantle is observed. The value of Sn in Songpan-Ganzi is calculated to be 4.5 km/s, while those in Qiang-Tang and Lhasa blocks are about 4.6 km/s. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, Supp., 566–573, 1992.     

Dynamical analysis of volcanic explosion

Visible phenomena accompanied by volcanic explosions at Sakurajima Volcano in Kyushu, Japan, were recorded by means of a TV camera and still cameras to make clear the process of explosive eruption of a Vulcanian type by image analysis and to enable a discussion of the process of explosive eruption. The most interesting phenomenon observed by the TV camera was visible shock waves passing through the atmosphere above the crater. The instant disappearance of thin clouds and the condensation of dense clouds were induced by the passage of shock waves. Explosion-quakes, which occurred at a depth of 1–2 km beneath the active crater, clearly preceded the explosion at the crater bottom. The atmospheric shock waves were generated in the crater 1.1–1.5 seconds later than the occurrence of the explosion-quake and propagated with the velocity of Mach 1.3–1.5 in a height range from 300 m to 600 m above the crater. Eruption clouds expanded subspherically for several seconds after the ejection and then the eruption column developed upwards at a certain velocity. The maximum ejection velocity of volcanic blocks, which was obtained from the analysis of photo-trajectories, was 112–157 m/sec. The internal pressure which ejected the volcanic blocks was estimated to be 138–271 bars in the case of the explosive eruptions analyzed. The results of analysis suggest that a high-pressure gas chamber was formed just beneath the crater bottom before the explosive eruption and that pressure waves caused by the explosion-quake acted as the trigger for the explosive eruption.