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.     

Coulomb constitutive laws for friction: Contrasts in frictional behavior for distributed and localized shear

We describe slip-rate dependent friction laws based on the Coulomb failure criteria. Frictional rate dependence is attributed to a rate dependence of cohesionc and friction angle . We show that differences in the stress states developed during sliding result in different Coulomb friction laws for distributed shear within a thick gouge layer versus localized shear within a narrow shear band or between bare rock surfaces. For shear within gouge, shear strength is given by =c cos + _n sin, whereas for shear between bare rock surfaces the shear strength is =c cos + _n tan, where and _n are shear and normal stress, respectively. In the context of rate-dependent Coulomb friction laws, these differences mean that for a given material and rate dependence of the Coulomb parameters, pervasive shear may exhibit velocity strengthening frictional behavior while localized shear exhibits velocity weakening behavior. We derive from experimental data the slip-rate dependence and evolution ofc and for distributed and localized shear. The data show a positive rate dependence for distributed shear and a negative rate dependence for localized shear, indicating that the rate dependence ofc and are not the same for distributed and localized shear, even after accounting for differences in stress state. Our analysis is consistent with the well-known association of instability with shear localization in simulated fault gouge and the observation that bare rock surfaces exhibit predominantly velocity weakening frictional behavior whereas simulated fault gouge exhibits velocity strengthening followed by a transition to velocity weakening with increasing displacement. Natural faults also exhibit displacement dependent frictional behavior and thus the results may prove useful in understanding the seismic evolution of faulting.     

Mineralogy and physical nature of clay gouge

Fault gouges have been observed in the surface outcrops, in shallow excavations, and in deep (300 meters below the surface) tunnels and mines in fault zones. The 2-microns fractions in these fault gouges may compose a few percent to more than fifty percent of the total mass in the outcrops, and the mineralogy of the 2-microns fractions consists of a variety of clays (the common ones are montmorillonite, illite, kaolinite, chlorite, vermiculite and mixed-layer clays) and some quartz, feldspars, etc.Although we cannot yet conclude directly from the studies of gouges that similar gouges exist at depths where many large shallow earthquakes are generated, there is a strong possibility that they do, based on (1) available equilibrium data on various clays — for example, kaolinite has been found to exist at 4 kb and 375°C (±15°C) (Thompson, 1970) and montmorillonite + kaolite has been found to exist at 450°C and 4 kb (Velde, 1969); (2) the compatibility of laboratory velocity data in gouge (Wang et al., 1977) with those in a model for central California (Healy andPeake, 1975); (3) the capability of clays to undergo sudden earthquake-like displacements (Summers andByerlee, 1977); (4) the petrology of intrafault cataclastic rocks in old fault zones (Kasza, 1977); and (5) the compatibility of gouge mineralogy with the mineralogy of hydrothermal clay deposits.If clay gouges are indeed significant components of the fault zone at depth, then the mechanical properties of clays under confining pressures up to 4 kb are important in the behavior of faults. Very few experiments have been performed under such high pressures. But from the physical makeup of clays, we can infer that (1) the range of possible behavior includes stable sliding with vermiculite and montmorillonite (asByerlee andSummers, 1977, have proven) to stick-slip-like behavior with kaolinite, chlorite, etc.; (2) the absence or presence of water will greatly affect the strengths of gouges — it is possible that water may reduce the strength of gouge to a fairly small value.     

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.     

Gravity anomaly and density structure of the San Andreas fault zone

A densely spaced gravity survey across the San andreas fault zone was conducted near Bear Valley, about 180 km south of San Francisco, along a cross-section where a detailed seismic reflection profile was previously made byMcEvilly (1981). WithFeng andMcEvilly's velocity structure (1983) of the fault zone at this cross-section as a constraint, the density structure of the fault zone is obtained through inversion of the gravity data by a method used byParker (1973) andOldenburg (1974). Although the resulting density picture cannot be unique, it is better constrained and contains more detailed information about the structure of the fault than was previously possible. The most striking feature of the resulting density structure is a deeply seated tongue of low-density material within the fault zone, probably representing a wedge of fault gouge between the two moving plates, which projects from the surface to the base of the seismogenic zone. From reasonable assumptions concerning the density of the solid grains and the state of saturation of the fault zone the average porosity of this low-density fault gouge is estimated as about 12%. Stress-induced cracks are not expected to create so much porosity under the pressures in the deep fault zone. Large-scaled removal of fault-zone material by hydrothermal alteration, dissolution, and subsequent fluid transport may have occurred to produce this pronounced density deficiency. In addition, a broad, funnel-shaped belt of low density appears about the upper part of the fault zone, which probably represents a belt of extensively shattered wall rocks.     

On the Mathematical Analysis of an Elastic-gravitational Layered Earth Model for Magmatic Intrusion: The Stationary Case

In the early eighties Rundle (1980, 1981a,b, 1982) developed the techniques needed for calculations of displacements and gravity changes due to internal sources of strain in layered linear elastic-gravitational media. The approximation of the solution for the half space was obtained by using the propagator matrix technique. The Earth model considered is elastic-gravitational, composed of several homogeneous layers overlying a bottom half space. Two dislocation sources can be considered, representing magma intrusions and faults. In recent decades theoretical and computational extensions of that model have been developed by Rundle and co-workers (e.g., Fernández and Rundle, 1994a,b; Fernández et al., 1997, 2005a; Tiampo et al., 2004; Charco et al., 2006, 2007a,b). The source can be located at any depth in the media. In this work we prove that the perturbed equations representing the elastic-gravitational deformation problem, with the natural boundary and transmission conditions, leads to a well-posed problem even for varied domains and general data. We present constructive proof of the existence and we show the uniqueness and the continuous dependence with respect to the data of weak solutions of the coupled elastic-gravitational field equations.     

岩盐断层带摩擦滑动的速度依赖性转换及其地震学意义

为了深入理解断层带摩擦滑动速度依赖性转换及其机制,利用双轴摩擦实验对干燥及含水条件下岩盐断层带摩擦的速度依赖性进行了实验研究,并观测了摩擦滑动过程中的声发射,分析了断层带的微观结构.实验结果表明,干燥岩盐断层带在0.1~100 μm/s的速度范围内表现为速度弱化,增大σ₂会使断层带向速度强化转变;含水条件下岩盐断层带在1~100 μm/s的速度范围内表现为速度弱化,而在0.1~0.01 μm/s的速度范围内表现为速度强化,速度依赖性转换出现在0.1~1 μm/s,其中断层表现为振荡或应力释放时间较长的黏滑事件;岩盐断层带在干燥条件下表现出很强的声发射活动,每个黏滑均对应一丛声发射事件,而在含水条件下一次黏滑只对应一个声发射事件.显微观察表明,局部化的脆性破裂是速度弱化域的主要变形机制,分布式的碎裂流动是干燥岩盐断层带在速度强化域的变形机制,颗粒边界迁移以及压溶作用的塑性变形是含水条件下岩盐断层带在速度强化域的主要变形机制,而脆性破裂和塑性变形共同控制着速度依赖性转换域断层带的变形.水的存在促进岩盐发生塑性变形,进而导致断层带从速度弱化向速度强化转换.上述结果有助于理解断层带上地震活动的特征和慢地震的机制.     

Laboratory measurement of compaction-induced permeability change in porous rocks: Implications for the generation and maintenance of pore pressure excess in the crust

Permeability exerts significant control over the development of pore pressure excess in the crust, and it is a physical quantity sensitively dependent on the pore structure and stress state. In many applications, the relation between permeability and effective mean stress is assumed to be exponential and that between permeability and porosity is assumed to be a power law, so that the pressure sensitivity of permeability is characterized by the coefficient and the porosity sensitivity by the exponent . In this study, we investigate experimentally the dependence of permeability on pressure and porosity in five sandstones with porosities ranging from 14% to 35% and we review published experimental data on intact rocks, unconsolidated materials and rock fractures. The laboratory data show that the pressure and porosity sensitivities differ significantly for different compaction mechanisms, but for a given compaction mechanism, the data can often be approximated by the empirical relations. The permeabilities of tight rocks and rock joints show relatively high pressure sensitivity and low porosity sensitivity. A wide range of values for and have been observed in relation to the mechanical compaction of porous rocks, sand and fault gouge, whereas the porosity sensitivity for chemical compaction processes is often observed to be given by 3. We show that since the ratio / corresponds to the pore compressibility, the different dependences of permeability on porosity and pressure are related to the pore structure and its compressibility. Guided by the laboratory data, we conduct numerical simulations on the development of pore pressure in crustal tectonic settings according to the models ofWalder andNur (1984) andRice (1992). Laboratory data suggest that the pressure sensitivity of fault gouge is relatively low, and to maintain pore pressure at close to the lithostatic value in the Rice model, a relatively high influx of fluid from below the seismogenic layer is necessary. The fluid may be injected as vertically propagating pressure pulses into the seismogenic system, andRice's (1992) critical condition for the existence of solitary wave is shown to be equivalent to >1, which is satisfied by most geologic materials in the laboratory. Laboratory data suggest that the porosity sensitivity is relatively high when the permeability is reduced by a coupled mechanical and chemical compaction process. This implies that in a crustal layer, pore pressure may be generated more efficiently than cases studied byWalder andNur (1984) who assumed a relatively low porosity sensitivity of =2.     

蒙脱石的脱水作用对断层摩擦本构行为的影响

利用高温双轴摩擦装置，研究了含蒙脱石的断层带在不同温度下摩擦滑动的速度依赖性，以期了解脱水作用对摩擦行为的影响。结果表明，断层带摩擦强度随温度而升高，而速度依赖性较为复杂，以１．４ｕ／ｓ为界，室温和１００℃时，低滑动速率下表现为微弱的速度弱化，高滑动速率下则表现为速度强化；２００℃时均为速度强化；３００℃时高滑动速率下仍为速度强化，但低滑动速率下转变为速度弱化；４００℃以上，均为明显的速度弱化。摩擦行为的变化与脱水过程及相应的断层物质变形方式的变化密切相关     

Slow-moving deformation pulses along tectonic faults

A model of slow-moving disturbances of deformation is proposed to interpret the observed propagations of earthquake foci and nonseismic creep. The analysis is based on the assumption that thin fault gouge participates in the viscous slip. Nonuniform deformation diffusses at the rate of ν = μw/2η for the gouge of viscosity η and thickness w that is enclosed by the elastic rocks of rigidity μ. A crack-like solution propagates uniformly, involving the discontinuity that bounds the faulted area by an unfractured part, or by another gouge with different viscosity. The unit of the propagation velocity of such cracks is also given by the above-defined ν. Comparing the expression of ν with the various field observations, most of which yield the propagation speeds of 10–10⁴ km/year, the effective viscosity of the gouge is estimated as 10¹¹–10¹⁴ poises. The nonseismic fault creep in central California is analysed, and a little higher value of acting stress is obtained than the result of Nason and Weertman (1973).     

The frictional behavior of lizardite and antigorite serpentinites: Experiments,constitutive models,and implications for natural faults

Laboratory studies of the frictional behavior of rocks can provide important information about the strength and sliding stability of natural faults. We have conducted friction experiments on antigorite and lizardite serpentinites, rocks common to both continental and oceanic crustal faults. We conducted both velocity-step tests and timed-hold tests on bare surfaces and gouge layers of serpentinite at room temperature. We find that the coefficient of friction of lizardite serpentinite is quite low (0.15–0.35) and could explain the apparent low stresses observed on crustal transform faults, while that of antigorite serpentinite is comparable to other crustal rocks (0.50–0.85). The frictional behavior of both types of serpentinite is well described by a two-mechanism model combining state-variable-dominated behavior at high slip velocities and flow-dominated behavior at low velocities. The two-mechanism model is supported by data from velocity-step tests and timed-hold tests. The low velocity behavior of serpentinite is strongly rate strengthening and should result in stable fault creep on natural faults containing either antigorite or lizardite serpentinite.     

Travel-time residuals and three-dimensional velocity structure of Italy

Jeffreys-Bullen P and PKP travel-time residuals observed at more than 50 seismic stations distributed along Italy and surrounding areas in the time interval 1962–1979, indicate the complex velocity pattern of this region. Strong lateral velocity inhomogeneities and low velocity zones are required to explain the observed pattern of residuals. In particular, late arrivals of about 1 sec are observed in the Apenninic mountain range, requiring both greater crustal thickness and low velocity layers, coherent with seismic refraction data and surface wave dispersion measurements. The seismic stations located in the Western and Eastern Alps indicate the presence of high velocities. In the Western Alps the strong azimuthal variation of residuals and the high values of early arrivals have a close relationship to the Ivrea body, an intrusive crustal complex characterized by a velocity as high as 7–7.2 km/sec.A travel-time inversion performed with theAki et al. (1977) block model, confirms the peculiar characteristics and the sharp variations in the lithosphere of the whole Italian region, with values of velocity perturbations between many adjacent blocks, ranging in size from 50 to 100 km, and independent from the earth parametrization chosen, reaching values up to 10% in the lithospheric part and 5% in the asthenosphere. 3-D inversion requires also high velocity along the Tyrrhenian coastal margin, equivalent to an uprise of major crustal and lithospheric discontinuities along this part of the Italian peninsula. Moreover low velocity material must be present in the northern part of the Adriatic foreland, in the lithosphere-asthenosphere system, closely related to the stress and seismicity pattern, and the lateral bending of the lithosphere in the same region.     

Wave propagation in two layered medium under initial stresses

Summary In this paper, the frequency equation for phase velocity of waves propagated in a laminated medium consisting of two eleastic layers of finite thickness under initial stresses, has been obtained. It has been shown that when wave length becomes very small compared to the thickness of each layer, the wave approaches two Rayleigh waves at the two outer surfaces with the possibility of Stoneley waves at the interface. The propagation ofSH-waves in the composite medium under initial stresses has also been discussed. A particular case has been taken to find the velocity of Love wave in the homogeneous half space under initial compressive stresses.Biot's incremental deformation theory has been used.     

Particle size distribution of cataclastic fault materials from Southern California: A 3-D study

The particle size distributions of fault gouge from the San Andreas, the San Gabriel, and the Lopez Canyon faults in Southern California were measured using sieving and Coulter-Counter techniques over a range of particle sizes from 2 m to 16 mm. The distributions were found to be power law (fractal) for the smaller fragments and log-normal by mass for sizes near and above the peak size. The apparent fractal dimensionD of the smaller particles in gouge samples from the San Andreas fault, the San Gabriel fault and the Lopez Canyon gouge were 2.4–3.6, 2.6–2.9 and 2.4–3.0, respectively. The averageD for the Lopez Canyon gouge was 2.7±0.2, which is in agreement with earlier studies of this gouge using planar 2-D sections. The fractal dimension of the finer fragments from all three faults is observed to be correlated with the peak fragment size, with finer gouges tending to have a largerD. A computer automaton is used to show that this observation may be explained as resulting from a fragmentation process which has a grinding limit at which particle reduction stops.     

白云母对岩盐断层带摩擦速度依赖性影响的实验研究

为更好地理解层状硅酸盐对断层强度、滑动速度依赖性及地震活动特征的影响,利用双轴摩擦实验对含白云母岩盐断层带在干燥及含水条件下摩擦的速度依赖性进行了实验研究,并观测了摩擦滑动过程中的声发射,分析了断层带的微观结构.实验结果表明,干燥条件下含白云母岩盐断层带在0.1 ～ 100μm/s的速度范围内表现为黏滑和速度弱化,增大σ2会使断层带从速度弱化向速度强化转化,速度依赖性转换出现在0.1 μm/s,其中断层滑动表现为稳滑或应力释放时间较长的黏滑事件;含水条件下含白云母岩盐断层带在0.05 ～0.01μm/s的速度范围内表现为速度强化,0.1 ～10μm/s的速度范围内表现为速度弱化,50～100μm/s的速度范围内又转换为速度强化行为.含白云母岩盐断层带在干燥条件下一次黏滑伴随一个或一丛声发射事件,而在含水条件下与稳滑相对应,滑动过程中并未记录到声发射事件.显微结构观察表明,速度弱化域的主要变形机制是岩盐颗粒的脆性破裂和局部化的滑动;干燥条件下,速度强化域的主要变形机制是岩盐颗粒的均匀破裂;含水条件下2个速度强化域对应不同的微观机制,高速域的速度强化受控于岩盐颗粒在白云母相互连结形成的网状结构上的滑动及其均匀碎裂作用,而低速域的速度强化还受岩盐的压溶作用控制.通过与岩盐断层带摩擦实验结果对比可知,白云母的存在对于燥岩盐断层带摩擦滑动方式和速度依赖性没有显著影响,而在含水条件下白云母的存在使得岩盐断层带滑动趋于稳定.实验结果为分析含层状硅酸盐断层的强度和稳定性提供了依据.此外,在速度依赖性转换域上观察到的应力缓慢释放的现象进一步证实了在岩盐断层带摩擦滑动过程中观察到的现象,这对慢地震机制研究具有参考意义.     

Source parameters of some presumed Semipalatinsk underground nuclear explosions

Summary Short-period vertical-componentP-wave spectra of seven presumed Semipalatinsk underground nuclear explosions, recorded by the Swedish seismic station network, are investigated. The events considered have closely spaced foci and cover the magnitude range fromm _b=5.5 tom _b=6.6. Spectra of six of these explosions show pronounced minima, varying from about 1.5 to 1.8 cps, which could be explained as principle minima due toP-pP interference. Supposing a nearsurfaceP-wave velocity at the test area of 4 km/sec, the shot depths are estimated to vary roughly from 750 to 1350 m. In order to obtain an estimate of the yield, the observed spectra are compared withHaskell's theoretical source spectra. For four events, relative yield estimates fit well the predicted values for explosions fired in a granitic medium. The behaviour of the remaining three explosions is discussed in detail.     

Microstructural features of fault gouges from Tianjing-shan-Xiangshan fault zone and their geological implications

Detailed observation of the microstructural features of 11 fault gouge and 3 fault breccia samples collected from Tianjingshan-Xiangshan fault zone has revealed that fault gouge can be classified into 3 types: flow banded granular gouge, foliated gouge and massive gouge. The determination of the shape preferred orientation (SPO) of survivor grains in fault gouges indicates that the foliated gouge displays a profound SPO inclined to the shear zone boundary, similar to theP-foliation; flow banded granular gouge displays a SPO parallel to the shear zone boundary, while massive fault gouge and fault breccia display a random SPO. All these fault gouges fall in different fields of shear rate ternary diagram.